/ 

.. 

NASA-CR~177855 19860014155 

A Reproduced COpy 

ReprodUced for NASA 

by the 

Center for AerOSpace Information 

------

LIBRARY COpy 

:: :\j 2:1 1992 

SEARCH CEfITEfl LAUGLrr:~RY UASA 

HAMPTOU, VIRGINII\ 
3 117601355 6213 NA A CR-,?1 CSC/TM-85/6119 

NAVIGt\TION STUD'V FOR LOW-ALTITUDE 

I::ARTH S~ATELLITES 

(NAS A-CR-1778 55) N AV IGA'J~ICN STU DY .r'OR 

LOW-ALTITUDE EAR1B SA1ELLITES (Computer 

Sciences Corp.) 171 p HC A08/MF A01 

N86-23626 

CSCL 22A Unclas 

G3/18 09118 

Prepared for 

NATIONAll AERONAUTICS ,AND SPACE ADMINISTRATION 

IGoddard Space flight Center 

Greenbelt, Maryland 

CONTRACT NAS 5-27888 

Task Assignment 44500 

DECEMBER 1985 

esc 

CO:MPU'TEll E;CIErIJCES CORPORATION ... 
'.::3C/'1 ~- 85/6119 

NAVIGA1ION S~ULY FOR LOW-AL'1I'1UDE EA~'lH SATELLI'lES 

Frepared by: 

f'. R. Pastor' 

b. T. Fang 

C. P. Yee 

Prepared for 

GODDARD SPACE FLIGHT CENTER 

Ey 

COMPUTER SCIENCES CORPORATION 

Under 

Contract ~AS 5-27688 

Task Assignment 445UO 

Approved by: 

'Date {%4 L ~ 11#//8, C. Berry ~ Date 

FunctIonal Area anager 

Mf:~# 12/Z,~~S--

Date 

ProJect Manager 
This Page Intentionally Left Blank 
ABSTRACT 

This document descr1bes several nav1gat1on studies for lowalt1tude Earth satell1tes. The use of Global Pos1t1on1ng 

System Navigation Package data for Landsat-5 orb1t deterw1-

nat10n 1S evaluated. In addit1on, a nav1gation analys1s for 

the proposed Track1ng and Data Acqu1sition System 1S presented. Th1S analys1s, based on slmulat10ns emploY1ng oneway Doppler data, is used to determine the agreewent between 

the Research and Development Goddard 1ra]ectory Determ1-

nation System and the Sequential Error Analys1s Program results. Properties of several geopotent1al error models are 

stud1ed as they apply to orb1t nav1gat1on error anlaysis, 

and an exploratory study of orb1t smoother process n01se 1S 

presented. 

P"nEC£DING PAGE a.ANK HOT F1LMm 

lli 

DIlL 
This Page Intentionally Left Blank 
~ABLE OF CO~TEN~S 

Sectlon 1 - Introductlon • • • • • • • • • • • • • •• 1-1 

Section 2 - Landsat-S Orblt Determlnatlon USlng GPSPAC 

2.1 

2.2 

2.3 

2.4 

2.S 

2.6 

2.7 

Data ..... I. • • • • •••••••• 2-1 

OverVlew of Study Data. • • •••••••••• 

Analysis of Landsat-S GPSPAC Data Orblts. . .• 

Orblt Solutlons USlng Data From Slngle GPS 

Satellltes •••••••••••••• . . Assessment of Landsat-S Orblts Computed From 

GSTDN Data. • • • • •••••••....•• 

2.4.1 Comparlson of Large Overlap Dlfferences 

2- 2 

2- 3 

2-7 

2-14 

2.4.2 

to Landsat-4 GSTDN Solutions • • • • • • 2-14 

Analysls of Landsat-S Larger-ThanExpected Overlap Ephemeris 

2.4.3 

Differences. • • • • • • • • • • • • •• 2-17 

Landsat-S Solutlons Involvlng Fewer 

Tracking Statlons. • • • • • • • • • 2-19 

2.4.4 Analysis of Landsat-4 GSTDN Solutlons 

Wlth Reduced Number of Tracklng Stations •••••••• . . . . 

Analysls of Posslble Mlsmatches Between GLI and 

R&D GTDS. • • • • • • • • ••• '" 

Conclusions ••••••• ••• • • • • 

References. 

2-21 

2-27 

2-34 

2-15 

Sectlon 3 - Low-A1tltude Sate111te Navlgatlon Using 

3.1 

Slmulated TDAS One-Way Doppler Data. 3-1 

Slmu1atlon ScenarlO • 

3.1.1 

3.1.2 

3.1.3 

TDAS Conflguratlon • 

User Satelllte •••• 

Tracklng Data ••• 

. . . . 3-1 

3-1 

3- 3 

3- 3 

3.2 Orblt Determlnatlon Scenarlo. . ••.. '. 3-4 

3.3 Slmulatlon/Orblt Determlnatlon Error Results. • •• 3-6 

0112 

3.3.1 

3.3.2 

3.3.3 

3.3.4 

3.3.S 

Geopotentlal Error • . • . • • • • • 

Clock Acceleratlon Error • • . • • 

TDAS Ephemerls Error ••...••• 

Error Results Wlth Less Frequently 

Sampled Data • • • • • • . • . 

Comparison Between FLBT and FLST 

Tracking Modes • • • • . . • • • • 

v 

· . . 

· . . 

· . . 

· . . 

3- 6 

3-11 

3-12 

3-16 

3-20 

~.lamGi~AlLY BLAilK 
TABLE OF CONTENTS (Cont'd) 

Sectlon 3 (Cont'd) 

3.4 

3.5 

Concluslons • 

References. • · . . . 

Sectl0n 4 - Lumped Geopotentlal Model for GEM-9 •• 

4.1 

4.2 

4.3 

4.4 

4.5 

4.6 

The Lumped Error Model ••••••••••..•.• 

Global Dlstribution of Gravity Error for Dlfferent Geopotential Error Models ••••••••• 

Navigatlon and Orbit Predictl0n Errors Introduced by Geopotential Uncertainty • • • • • • • . 

Comparlson with Landsat-5 Orblt Determlnation 

Results • • • • • • • • • • • • • • • • . . . Concluslons • • • • • • • • • • • • • • • • • • 

References. • · . . . Sectlon 5 - Orbit Smoother Process Noise Study 

Section 6 - Concluslons •• · . . . AppendlX A - Valldatl0n and Verlficatlon of the SEA 

Smoother/TDAS Capablllty 

Append1x B - Utllities for Geopotential Error Model 

Studies 

Vl 

0112 

3-20 

3-22 

4-1 

4- 3 

4- 8 

4-32 

4-33 

4-35 

4-38 

5-1 

6-1 
LIST OF ILLUSTRATIONS 

FIgure 

2-1 PartIal ObservatIon ReSIdual Report for GPSPAC 

Data OrbIt SolutIon (Run G4B) • • • • • • .• 2-n 

2-2 RepresentatIve ObservatIon ResIdual Plots 

for GPSPAC Data SolutIons EmploYIng ComposIte and SIngle GPS SatellIte ObservatIon Sets • • • • • • • • • • • • . • • • • . 2-13 

2-3 Landsat-5 GSTDN Orbit Solution Overlap 

EphemerIs Comparison. • • • • . • • • • • • • 2-18 

2-4 Plot of Ground Tracking Passes and OrbIt 

Solution Arcs Involving April 1984 

Landsat-5 GSTDN Data. • • • . • • • • • . •• 2-20 

2-5 Plot of Ground TrackIng Passes and Orbit 

Solution Arcs InvolvIng October 1982 

Landsat-4 GSTDN Data. • • • • • • • • • • •• 2-25 

2-6 EphemerIs Comparison Between GPS OrbIt 

(RUN G4A) SolutIons With and Without Reference Frame Mismatch CorrectIon. • • • • • 2-29 

3-1 TDAS Configuration. • • • • • • • • • • • • • • 3-2 

3-2 Geopotentlal (GEM-9/GEM-l DIfference Model) 

Error Projections In the User Orbit Plane 

as DetermIned From R&D GTDS FLBT Simulat ion. . . . . . . . . . . . . . . . . . . . . 3-3 User Clock AcceleratIon Error ProJections In 

the User Orbit Plane as Determined From R&D 

3-8 

GTDS FLBT SImulation. • • • • • . • • • • •• 3-13 

3-4 TDAS EphemerIS Error Projections in the User 

Orbit Plane as DetermIned From R&D GTDS 

FLBT SimulatIon ••••••••••••••• 3-17 

4-1 Global DIstrIbutIon of Gravitational Acceleration Uncertainties at an AltItude of 

200 KIlmeters, Computed From the Lumped GeopotentIal Error Model Using GEM-9 Standard 

DevIatIons. • • • • • • . • • . • . • • . •. 4-6 

4-2 GEM-9/MDl One-Half Difference Model, 

200-KIlometer AltItude • . . • • . • • . 4-10 

4-3 GEM-9/MDl One-Half DIfference Model, 

400-KIlometer AltItude . • • • • . • • • •• 4-11 

4-4 GEM-9/MDl One-Half DIfference Model, 

600-KIlometer AltItude • . . . . • • • • • . 4-12 

4-5 GEM-9/SAO One-Half DIfference Model, 

200-Kilometer AltItude • • • . • • • 4-13 

4-6 GEM-9/SAO One-Half DIfference Model, 

400-KIlometer AltItude • . . • . • • • • •. 4-14 

Vll 

0112 
Flgure 

4-7 

4-8 

4-9 

4-10 

4-11 

4-12 

4-13 

4-14 

4-15 

4-16 

4-17 

4-18 

4-19 

4-20 

4-21 

4-22 

4-23 

Table 

LIST OF ILLUSTRATIONS (Cont'd) 

GEM-9/SAO One-Half Difference Model, 

600-Kilometer Altitude . • • • • • . • • . . 

GEM-9/GEM-5 Difference Model, 200-Kllometer 

Altitude ................. . 

GEM-9/GEM-5 Dlfference Model, 400-Kllometer 

Altitude ................. . 

GEM-9/GEM-5 Difference Model, 600-Kilometer 

Altitude ................. . 

GEM-5/MDl One-Half Difference Model, 

200-Kilometer Altitude ••••••••••• 

GEM-5/MDl One-Half Dlfference Model, 

400-Kllometer Altltude ••••••••••. 

GEM-5/MDl One-Half Dlfference Model, 

600-Kilometer Altitude • • • • . . . . . GEM-9 Standard Deviatlon Model, 

400-Kilometer Altitude ••••••••••• 

GEM-9 Standard Deviation Model, 

600-Kilometer Altitude ••••••••••• 

GEM-9 Formal Uncertainties with Random 

Slgns, 200-Kilometer Altitude •••••••• 

GEM-9 Formal Uncertainties with Random 

Slgns, 400-Kllometer Altitude •••••••. 

GEM-9 Formal Uncertainties With Random 

Signs, 600-Kilometer Altitude •••••••• 

GEM-9 Formal Uncertalnties Wlth Random 

Phase, 200-K~lometer Alt~tude .••....• 

GEM-9 Formal Uncertainties With Random 

Phase, 400-Kilometer Altitude •••••••. 

GEM-9 Formal Uncertalnties with Random 

Phase, 600-Kilometer Altitude •••••.•• 

GEM-9 Uncorrelated Standard Deviatlon Model, 

200-Kilometer Altitude ••••••.•.•. 

Gravity Map at a 200-Kllometer Altitude for 

the Nonaxisymmetric Portion of GEM-9 •••. 

LIST OF TABLES 

4-1'3 

4-16 

4-17 

4-18 

4-19 

4-20 

4-21 

4-22 

4-23 

4-24 

4-25 

4-26 

4-27 

4-28 

4-29 

4-30 

4-31 

2-1 Landsat-5 GPSP~C Data Orblt Solutlon 

Characteristlcs and Comparlsons Wlth GSTDN 

Solutions • • • • • . • • . • . • • . . • •. 2-5 

Vlll 

0112 
LIST OF TABLES (Cont'd) 

Table 

2-2 Landsat-~ GPSPAC Data Range-Rate and Evenly 

Welghted Orblt Solutlon Characteristics 

and Comparisons With GSTDN Solutlons. • • 2-8 

2-3 Characterlstics of GPSPAC Data Solutlons 

USlng Observations From Slngle GPS Satellites. . . . . . . . . . . . . . . . . . . . 2-10 

2-4 Intercomparisons of GPSPAC Data Solutions 

USlng Single and Composite GPS Observation 

Sets. . . . . . . . . . . . . . . . . . . .. 2-11 

2-5 1984 GSTDN Data Orblt Solution Character2-6 

2-7 

2-8 

2-9 

3-1 

3-2 

4-1 

5-1 

5-2 

0112 

istics •••••••••••.••••• 

1985 GSTDN Data Orbit Solution CharacteristlCS. . . . . . . . . . . . . . . . .. 

Additional Landsat-5 GSTDN Data Orblt Solution Characterlstics ••••.•••••• 

Summary of Landsat-4 GSTDN Solutions With Reduced Number of Tracklng Statlons • • • • • • 

Reference Rotated GPSPAC Data Orbit Solutlon 

Characteristics and Comparisons with Nonrotated Solutions • • • • • • • • • • • • • • 

Tracking Schedules for 600-KilometerAltitude, 28-Degree-Inclination User 

Satellite • • • • • • • • • • •• ••• • 

Navigation Error Comparison Between R&D GTDS 

Simulatlon and Previous SEA Error Analysis 

Result 5 • • • • • • • • • • • • • • • • • • • 

Navigation Errors Resulting From Geopotential Uncertainties ••••••••••.••• 

Orbit Smoother Performance for the TDAS 

Navigation Scenario ••••••••• 

Landsat-5 Orblt Smoother Error Caused by 

One-Half GEM-9/SAO Differences ••• 

lX 

. . 

. . . 

2-15 

2-16 

2-22 

2-23 

2-32 

3-5 

3-21 

4-34 

5- 2 

5- 3 
SECTION 1 - IN'l'RODUCTION 

~his document describes several studies performed for the 

National Aeronautics and Space Administration/Goddard Space 

Flight Center (NASA/GSFC) relating to low-altitude Earth 

satellite navigation analysis. The first two studies analyzed the accuracy of satellite orbit determinat10n using 

advanced nav1gation systems: the Global Positioning System 

(GPS), currently under development, and the Tracking and 

Data Acquis1tion System (~DAS), under study as a successor 

to the Track1ng and Data Relay Satel11te System (TDRSS). 

The latter two studies analyzed lumped geopotential modeling 

and orb1t smoother process noise, two major components 

associated with orbit determination error analysis. 

The GPS nav1gat10n study analyzed the orbit determination 

capabilities of the Landsat-S (70S-kilometer (km) altitude, 

98-degree (deg) inclination) satellite. Landsat-S uses 

navigation messages from GPS satellites that are extracted 

by an onboard Global Positioning System Navigation Package 

(GPSPAC). This study extended the effort of a previous 

analysisl that considered Landsat-4 GPSPAC data. The results of the Landsat-S study and its comparison with the 

Landsat-4 study are presented 1n Sect10n 2. 

The TDAS navigation study, presented in Section 3, analyzed 

the performance of a GOO-km, 28-deg inclination satellite 

using simulated TDAS one-way Doppler data. The study used a 

lB. T. Fang and E. Seifert, "An Evaluation of Global Posit10ning System Data for Landsat-4 Orbit Determination," 

paper delivered at AIAA 23rd Aerospace Science Meeting, 

January 1985; also Computer SC1ences Corporation, 

CSC/TM-84/G077, Track1n and Data Acquisition S stem 

Global Pos1tioning System (TDAS GPS) Nav1gat1on Analys1s, 

September 1984. 

1-1 

0112 
number of TDAS enhancements that have been made to the Research and Development Goddard Trajectory Determ1nat10n 

System (R&D GTDS). It served as a ver1f1cation of a prev10us 

study that considered the same satellite scenar10 but used 

the TDAS enhanced Sequential Error Analysis (SEA) program. 

The analysis of lumped geopotent1al modeling, presented in 

Sect10n 4, studied several error models. All models use 

spher1cal-harmonic representations but with different sets 

of coefficients representing the errors. Global grav1ty 

error waps and orbit propagation errors corresponding to 

d1fferent error models are presented. 

The orbit_smoother process noise study investigated the new 

smoother capacity to the SEA program. Limited investigations using this capacity have been performed to further 

explore orbit smoothers and also to validate the fading memory process noise option of the SEA smoother capability. 

~he results of this study are presented in Section 5. 

Append1X A descr1bes the validation of the SEA program 

smoother/TDAS capability used in the orbit smoother process 

noise study. Appendix B describes ut1l1t1es used 1n conjunction with the lumped geopotent1al error wodel study. 

1-2 

0112 
SECTION 2 - LANDSAT-5 ORBIT DETERMINATION USING GPSPAC DATA 

This section discusses the accuraC1es of GPSPAC data for 

computing Landsat-5 orbits. The GPSPAC data were extracted 

from telemetry and processed by a large, sophisticated, 

batch orbit determination program (R&D GTDS) to produce 

16-hour arc orbit solutions. The accuracies of the GPSPAC 

data and the orbit solutions were inferred from the follow1ng: 

• Observation residuals 

• Overlap ephemeris comparisons 

• Comparisons w1th independent solutions derived from 

ground tracking data 

As with the Landsat-4 GPSPAC data, it was found that pseudorange data appear inferior to delta pseudorange (Doppler) 

data. Efforts were made to determine whether pseudorange 

data are corrupted by several possible preprocessing sources 

of errors or whether data from individual GPS satellites may 

be defective. The latter effort involved computing 

Landsat-5 orbits from data from a single GPS satellite and 

was also a subject of interest by itself. 

Section 2.1 presents an overview of the data studied and the 

orbit determination scenarios used. Section 2.2 describes 

Landsat-5 orbit solutions computed from GPSPAC data; Section 2.3, solutions based on data originating from single 

GPS satellites; and Section 2.4, solutions obta1ned from 

grouna tracking data and inquiries into their accuracy 

degradation in comparison with Landsat-4 solutions. Section 2.5 investigates several possible sources of preprocess1ng errors and Section 2.6 summarizes the conclusions of 

the study. 

2-1 

0112 
2.1 OVERVIEW OF STUDY DATA 

The Landsat-4 spacecraft (70S-km altitude, 98-deg inclInation orbIt), launched in July 1982, carried an experiwental 

NAVSTAR (Reference 2-1) GPSPAC and was the first satellite 

to use the GPS. The GPSPAC has a receiver/processor assembly that receives and decodes GPS tracking measurements 

and estimates the Landsat-4 position and velocity by using 

an onboard Kalman filter. The tracking measurements providea by GPSPAC are called pseudoranges and delta-pseudo 

ranges. ~he former are decoded from pseudorandom noise 

ranging code and represent measured signal transIt times 

from the GPS satellites to Landsat-4. The latter are computed from Doppler shifts of carrier signals, integrated 

over a nominal interval of 0.6 second. The term "pseudo" IS 

used because these measurements were derived from the Landsat 

clock, WhICh was not synchronized with the GPS clocks. The 

quoted precisions of these data are 1.5 meters (m) for the 

pseudorange and 2 centimeters (cm) for the delta pseudorange. 

Landsat-S, launched in July 1984, is a replacement for the 

disabled.Landsat-4 spacecraft. It has similar mission objectives and orbit characteristics. It also carrIes a 

GPSPAC with minor software modifications to avoid some known 

anomalies (Reference 2-2) that occurred In the Landsat-4 

GPSPAC. 

During the previous task assignment (42100), an investigation of the Landsat-4 GPSPAC data quality (Reference 2-3) 

was undertaken. The present study extended that effort to 

Landsat-S GPSPAC data. As in the Landsat-4 study, the R&D 

GTDS batch orbit determinatIon differential correction (DC) 

program was used to process both the GPSPAC telemetry to the 

ground and Ground Spaceflight Tracking and Data Network 

2-2 

0112 
(GSTDN) data. R&D GTDS allows extensive force modeling that 

is unava11able in the onboard GPSPAC Kalman filter. 

The data in this study were obtalned over four separate time 

periods: 1n April and August of 1984, and in May and July of 

1985. The base11ne force model and the orbit determination 

scenario used for the GSTDN and GPSPAC data solutions are as 

follows: 

GPSPAC data solutions 

21-by-21 Goddard Earth Model 

(GEM)-9 geopotential model 

Jacchia-Roberts atmospheric 

denslty model 

Cowell integrator 

16-hour data arc length 

Solve for orbital elements, 

drag parameter, clock bias, 

clock drift 

Select every 10th pair of 

observations 

Use observation standard deviations = 1000 m (pseudorange) and 0.8 cm (delta 

pseudorange) 

GSTDN data solutions 

2l-by-21 GEM-9 geopotential 

model 

Jacchia-Roberts atmospheric 

density model 

Cowell integrator 

30-hour data arc length 

Solve for orbital elements, 

drag parameter 

Select all observations 

Use range-rate observations 

only for orbit solution 

2.2 ANALYSIS OF LANDSAT-5 GPSPAC DATA ORBITS 

Elght 16-hour data arcs using the NAVSTAR system's GPS data, 

as received by Landsat-5 GPSPAC, were processed wlth the R&D 

GTDS DC program and the same base11ne force model employed 

in analyzing the Landsat-4 GPSPAC orbits. (These orbits 

will henceforth be referred to as the baseline set of GPSPAC 

data orbits.) As will be d1scussed in Section 2.4, the 

Landsat-S GSTDN solutions displayed ephemeris overlap differences consistently larger than those observed for 

Landsat-4. In comparison, the Landsat-4 GSTDN solutlons 

d1splayed enough accuracy to be used as definitive solut10ns. Because of this degradation, the Landsat-S GSTDN 

2-3 

0112 
orblts could not be used as deflnitive solutions for comparlson with corresponding GPSPAC solutions. Therefore, the 

present Landsat-5 analysis used the comparison among overlapping GPSPAC data orbit ephemerides and observation residuals to provide an idea of the GPSPAC accuracies. 

The maximum ephemeris position differences for the four 

Landsat-5 GPSPAC data overlap periods vary from 64 to 19 m, 

compared to maxima with an average )f 2! m, and a standard 

devlation of 14 m for six Landsat-4 GPSPAC overlap periods. 

As shown in Table 2-1, the 1984 GPSPAC overlap comparisons 

of 61 and 64 m are larger than the 1985 GPSPAC overlap comparisons of 19 and 32 m. (It is interesting to note that 

studied GPSPAC data solutions in 1985 involve six GPS satellites whereas those in 1984 involve five; nonetheless, reference to GPSPAC data solutions by the year of observation 

is for convenience only.) The improvement in the overlap 

comparisons f?r the 1985 GPSPAC data solutions, but no 

improvement in the corresponding 1985 GSTDN data (which is 

summarized in Section 2.4), appears to rule out the possibility that some unexplained dynamic errors common to GSTDN 

and GPSPAC data solutions are responsible for poor 1984 

GPSPAC comparisons. 

An examinatlon of data residuals of the Landsat-5 GPSPAC 

orbit solutions shows that large pseudorange measurement 

cesiduals exist and vary substantlally from GPS satellite to 

GPS satellite. These characteristics are in agreement with 

those observed in the Landsat-4 GPSPAC data solutions. Figure 2-1, which is a partial listing of a typical Landsat-5 

GPSPAC observation residual report illustrating the large 

pseudorange residuals, displays no correlation between 

pseudorange residuals and delta-pseudorange measurements. 

This rules out systematic time tag errors as possible 

sources for the systematic GPSPAC range errors observed. 

2-4 

0112 
N 

I 

U1 

Table 2-1. 

ARC START ARC RUN TIME LENGTH ID (ddte houri IhouI.I 

G4A 840413 16 

2h 

G4B 840413 16 

14 h 

G8A 840807 16 

3h 

G8B 840807 16 

15 h 

G5A 850524 16 

19 h 

G5B 850525 16 

7 h 

G7A 850726 16 

o h 

G7B 850726 16 

12 h 

/ 

Landsat-5 GPSPAC Data Orbit Solution Characteristics and Comparisons 

With GSTDN Solutions 

RESIDUAL MAXIMUM POSITION DIFFERENCES SOLVE FOR PARAMETERS STATISTICS OVER 4 HOUR OVERLAP OF ADJACENT MAXIMUM POSITION DIFFERENCES 

NO OF STANDARD ARCS Imetersl FROM GSTDN ORBITS Imetersl 

OBSERVA DEVIATIONS REMARKS TIONS . DELTA B B RANGE RANGE RADIAL C ALONG Ql RSS RADIAL C ALONG RSS 1I0- 3 secl 1I0- 8 secl Imetersl Icml TRACK TRACK secl 

1297 1592 -3127 -3262 100 I 239 134 306 45 I 543 

569 144 610 613 

1192 2900 -4772 -3257 7150 227 106 352 703 771 ONLY EVERY 10TH 

PAIR OF OBSERVATION 

DATA PROCESSED 

1103 2125 1036 -2283 84 25 225 140 169 49 I 504 

166 76 638 639 

1110 3 OIl -0197 -2278 8302 238 243 789 680 683 

1190 4913 -2228 -06494 7644 221 135 119 522 533 

494 767 179 194 

1146 -6119 -2508 -06467 6633 219 189 312 772 773 

1142 2493 -06720 - 03611 8439 218 - - - -

50B 194 295 321 

1000 -2259 -08280 -03571 5393 218 - - - -

NOTES SATELLITE AND TIME PERIOD LANDSAT 5 APRIL 1984 - JULY 1985 

DATA GPS RANGE AND DELTA RANGE WITH RANGE WEIGHTED LIGHTLY 

FORCE MODEL BASELINE 

. SOLVE FOR PARAMETERS DRAG SCALE FACTOR Ql = ACD/CD• CLOCK BIAS B AND DRIFT B AT EPOCH 

C LAND RSS ARE THE ACROSS TRACK ALONG TRACK AND ROOT SUM SQUARED COMPARE DIFFERENCES RESPECTIVELY 

. 

~ 

~ ~ 

o 

~ 
N 

I 

0"1 

TIME OF OB~ GPS NO YYMMDD HHMM ~~ ~~SS 

840414 0335 31 3291 

840414 0335 31 3291 

840414 0336 50 6492 

840414 0336 50 6492 

840414 0337 56 6295 

840414 0337 56 6295 

840414 0339 II 4100 

8404 4 0339 II 4100 

8404 4 0340 45 4795 

B404 4 0340 45 4795 

8404 4 0342 32 4520 

8404 4 0342 32 4520 

8404 4 0344 02 3532 

8404 4 0344 02 3532 

8404 4 0345 24 4544 

8404 4 0345 24 4544 

8404 4 0347 27 2582 

8404 4 0347 27 2582 

8404 4 0348 47 4369 

8404 4 0348 47 4369 

8404 4 0350 08 2155 

8404 4 0350 09 2155 

8404 4 0351 27 7209 

8404 4 0351 27 7209 8~04 4 0352 53 9826 

840414 0352 53 9826 

8404 4 0354 27 2715 

8404 4 0354 27 2715 

8404 4 0355 33 2106 

8404 4 0355 33 2106 

8404 4 0356 51 0495 

8404 4 0356 51 0495 

8404 4 0357 58 3687 

8404 4 0357 58 3687 

8404 4 0359 04 3080 

8404 4 0359 04 3080 

8404 4 0400 10 2473 

8404 4 0400 10 2473 

8404 4 040 I 16 2066 

8404 4 040 I 16 2066 

8404 4 0402 35 4460 

8404 4 0402 35 4460 

8404 4 0403 41 4255 

-8404 4 0403 41 4255 

8404 4 0404 47 3651 

8404 4 0404 47 3651 

8404 4 0405 53 J248 

8404 4 0405 53 3248 

8404 4 0407 12 6445 

840414 0407 12 6445 

840414 0408 18 6243 

840414 0408 18 6243 

840414 0409 24 5443 

840414 0409 24 5443 

840414 0410 30 4643 

840414 0410 )0 4643 

840414041144 4827 

840414 0411 414827 

840414 0413 50 2200 

840414 0413 50 2200 

B40414 041~ 41 0254 

3 

3 

3 

3 

3 

3 

3 

3 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

4 

EDIT 

... 

08SERVIITIOIJS M~D COMPUTED OBS 

GTDS DC PROGRIIM 

GTDS 08SERVATIDN RESIDUIIL REPORT 

08S 

TYPE 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

[JELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DELR 

RGPS 

DElR 

RGPS 

END OF ITERATION NUM8ER 5 o O-C RIITIO 

20555 9966 o 1936 

20608 7939 

o 6073 

20694 0352 o 9446 

20834 7875 I 3144 

23799 3095 

4 3860 

21428 8755 

2 2053 

21784 7896 

2 5404 

22150 9298 

2 8066 

23359 5568 

-3 0905 

22950 2739 

-3 0316 

22547 0940 

-2 9541 

24098 2891 

3 4928 

24604 2494 

3 5391 

21344 9189 

- 2 5820 

21067 8473 

- 2 4572 

20759 3714 

-2 2944 

20510 3762 

-2 1406 

20283 8295 - I 9789 

20075 6410 - I 8066 

19886 8684 - I 6245 

19687 3051 -I 3939 

19544 8821 

- I 1933 

19424 9645 

-0 9862 

19328 0879 

-0 7735 

19242 9191 

-0 5122 

19198 5680 

-0 2921 

19178 5132 

-0 0710 

19182 7473 o 1498 

24689 3524 

-3 8457 

23878 5729 

-3 8836 

19525 7211 

57 7255 o 4729 

56 0749 o 5600 

56 7501 

-0 8825 

54 9823 

2 2863 

47 8019 - I 3533 

53 5017 

-4 5615 

50 3040 

-2 4399 

48 9816 - I 5124 

83 6347 

3 0651 

85 5167 

-0 6679 

85 9179 

4 6284 

50 5839 

3 1373 6 I 4064 I 8366 

98 8276 

5 2484 

105 3006 I 9778 

107 9952 o 0562 

lOB 7452 

4 0504 I I I 2355 

-0 1794 

113 8694 I 8112 I 12 9890 - I 4928 

114 0285 

1 7330 

114 2552 o 3029 

119 1568 I 3532 

1139587 

-0 7324 

114 6570 I 3105 

114 0210 o 6002 

1148783 

-17220 

115 0050 

-3 2074 

135 7784 I 5200 

137 8933 o 7933 

109 6832 

UNITS FOR INFORMIITION 

RESIDUIILS 

TO SIGMA 

o 0577 o 5911 o 0661 o 7000 o 0568 I 1031 o 0550 

2 8579 o 0478 I 6916 o 0535 

5 7018 o 0503 

3 0499 o 0490 

1 8906 o OB36 

3 B314 o 0855 o 8349 o 0859 

5 7855 o 0506 

3 9216 o 0514 

2 2958 o 0988 6 5605 o 1053 2 H22 

o 1080 o 0703 o 1087 

5 0629 o 1112 o 1243 o 1139 

2 2640 o 1130 I 8660 o 1140 

2 1662 o 1143 o 3787 o 1192 I 6915 o 1140 o 9154 o 1147 I 6381 o 1140 o 7603 o 1149 

2 1525 o 1150 

4 0092 o 1358 I 9000 o 1379 o 9917 o 1097 

c 

20555 9389 o 1936 

20608 7379 

o 6073 

20693 9784 o 9447 

20834 7325 

1 3144 

23799 2617 

4 3860 

2142B 8220 

2 2053 

21784 7393 

2 5404 

22150 BB08 

2 8066 

23359 4731 

-3 0906 

22950 1884 

-3 0315 

22547 0081 

-2 9542 

24098 2386 

3 4928 

24604 1980 

3 5390 

21344 8200 

-2 5B20 21067 74'1J -2 ':572 

20759 2634 

-2 2944 

20510 2674 

-2 1407 

20283 7183 

-1 9789 

20075 5272 -I 8066 

198B6 7554 -I 6245 

196B7 1911 

-1 3939 

19544 7679 

- I 1933 

19424 B453 

-0 9862 

19327 9740 

-0 7735 

19242 8044 

-0 5122 

19198 4540 

-0 2921 

19178 3984 

-0 0709 

19182 6323 o 1499 

24689 2167 

-3 B457 

23878 4350 

-3 8836 

195256115 

ELV TO 

GPS 

26 47 

26 47 

25 89 

25 88 24 99 

24 98 

23 54 

23 53 - 1 3 I 

- I 34 17 76 

17 74 

14 48 

14 45 I 1 21 11 IB 2 07 2 10 5 46 

5 48 8 86 

8 89 -4 98 - 5 0 I 

-8 99 -9 02 ,~ 65 

.9 68 

22 32 

22 34 

25 39 

25 41 

27 97 

27 99 

30 39 

30 41 

32 70 32 72 

34 88 

34 90 

37 26 

37 28 

39 03 

39 05 

40 57 

40 58 

41 84 

41 85 

42 99 

43 00 43 61 

43 61 

43 89 

43 89 

43 84 

43 84 

43 84 

43 84 o 37 o 40 

39 35 

EOII FLIIG 

T A 

o 0 

o 0 o 0 o 0 o 0 

o 0 

o 0 o 0 

o 0 o 0 o 0 o 0 o 0 o 0 o 0 o 0 o 0 

o 0 o 0 o 0 o 0 o 0 o 0 o 0 

o 0 o 0 o 0 ? 0 o 0 o 0 o 0 o 0 o 0 

o 0 o 0 o 0 o 0 

o 0 o 0 o 0 o 0 o 0 

o 0 o 0 o 0 o 0 o 0 o 0 o 0 

o 0 o 0 o 0 

o 0 o 0 o 0 o 0 o 0 o 0 

o 0 o 0 o 0 

OBS 

NO 

1099 

1 00 

I 0 I 

I 02 I 03 I 04 I 05 I 06 I 07 I 08 1 09 1 10 I 11 

1 12 I 13 I 14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

132 

133 

134 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

154 

155 

156 

157 

158 

159 

:co 

~:::a 

·~I '2~ 

~~ 

:ltJ 

RANGE~ IIRF IN KM RIINGES liRE IN METERS =COMPUTEfO-C) (NOT IN NORMIIL MIITRIK' 

RIITES liNn RIINGE DIFFERENCES 

ANGLES liRE IN DEGREES DIR COSINES SCIILED BY 1000 

OTIC liRE ." MICROSECONDS 

liRE IN KM/SEC RIITES liND RIINGE DIFfRN liRE IN 

ANGLES liRE IN SECONDS OF ARC DIR COSINES SCIILED BY 1000 

OTIC liRE IN MICROSECONDS 

CM/SEC" =EDIT BY ELEVATION liNGLE =EDIT BY 3 SIGMII CRITERIII ····=EDIT FROM SCOPE $ =EDIT BY ATMOSPIlERIC INTERFERENCE 

Figure 2-1. Partial Observation Residual Report for GPSPAC Data Orbit 

Solution (Run G4B) 
. ~ 

t \ 

. ' 

Stud1es (discussed more fully in Section 2.5) that examine 

the effects of correcting assumed GPSPAC time tag errors 

give results that support this conclusion about no time tag 

errors. GPSPAC data observation residuals will be discussed 

further in Section 2.3. 

In keep1ng with the methods employed in the Landsat-4 GPSPAC 

analysis, the baseline GPSPAC data orbit determ1nat10n 

scenario was repeated with two d1fferent a priori observation weight specifications. When the weights were set to 

10 m for pseudorange observat10ns and 1000 cm for deltapseudorange observat10ns (effect1vely producing a range-only 

solution), the orbit compar1son with the independent GSTDN 

data orb1t produced larger differences than those seen in 

the baseline delta-range-only solutions in Table 2-1. When 

the weights were set to 1.S m and 0.2 cm, respectively (in 

accordance with quoted data precision), the orbit solutions 

resulted in larger overlap differences than the baseline 

delta-range-only solutions but were typically smaller than 

the corresponding range-only solution. These trends in the 

var10usly weighted Landsat-S GPSPAC solutions are in agreement with the trends observed in the Landsat-4 data. 

1able 2-2 summarizes the Landsat-S results. 

2.3 ORBIT SOLUTIONS USING DATA FROM SINGLE GPS SATELLITES 

As discussed in Section 2.2, the observed large pseudorange 

residuals present in the GPSPAC data solutions do not appear 

to be specific to any single GPS satellite. Nevertheless, 

there was 1nterest in whether intercomparisons of GPSPAC 

solutions, each using data from only a single GPS NAVSTAR 

satellite, would divulge erratic data assoc1ated with a GPS 

or would provide insight 1nto the cause of the observed large 

pseudorange res1duals. It was uncerta1n whether single GPS 

relay solut10ns would even converge because of the lack of 

2-7 

0112 
IV 

I 

co 

Table 2-2. Landsat-5 GPSPA~ Data Range-Rate and Evenly Weighted Orbit Solution 

Characteristics and Comparisons With GSTDN Solutions 

SOLVE FOR PARAMETERS ARC START ARC NO OF RUN TIME LENGTH OBSERVA 10 Idate, hourI Ihoursl TIONS 

Ql B 

110-3 seer 

R4A 840413 16 1295 -0209 -3128 

2h 

R4B 840413 16 1191 1316 -4772 

14 h 

R8A 840807 16 1102 19757 1036 

3h 

RBB 840807 16 1109 1556 -0197 

15 h 

P4A 840413 16 1278 -0867 -3128 

2h 

P4B 840413 16 1183 0969 -4772 

14 h 

P8A 840807 16 865 6756 1035 

3 h 

PBB 840807 16 1103 36 79 -0197 

15 h 

NOTES SATELLITE AND TIME PERIOD LANDSAT 5 APRIL-AUGUST 1984 

FORCE MODEL BASELINE 

. 

B 

110-8 seel seer 

-3261 

-3256 

-2283 

-2278 

-3261 

-3256 

-2283 

-2277 

RESIDUAL MAXIMUM POSITION DIFFERENCES STATISTICS, OVER 4 HOUR OVERLAP OF ADJACENT STANDARD ARCS Imetersl DEVIATIONS 

DELTA RANGE RANGE RADIAL C ALONG RSS Imetersl leml TRACK 

4185 266 

72 18 48 51 

5035 2110 

6452 323 

45 23 171 172 

6852 312 

36 79 2112 

29 14 36 39 

4801 262 

5526 308 

48 24 177 178 

6393 313 

SOLVE FOR PARAMETERS DRAG SCALE FACTOR Ql = 4CD/CD CLOCK BIAS B AND DRIFT B AT EPOCH 

C LAND RSS ARE THE ACROSS TRACK ALONG TRACK AND ROOT SUM SQUARED COMPARE DIFFERENCES RESPECTIVELY 

MAXIMUM POSITION DIFFERENCES 

FROM GSTDN ORBITS Imetersl 

REMARKS 

RADIAL C ALONG RSS TRACK 

25 25 70 73 

RANGE SOLUTION 

30 13 112 113 

43 15 133 134 

ONLY EVERY 10TH 

PAIR OF OBSERVATION 

DATA PROCESSED 

31 16 99 101 

24 28 64 68 

26 18 101 103 

EVENLY WEIGHTED 

SOLUTION 

49 33 186 191 

ONLY EVERY 10TH 

PAIR OF OBSERVATION 

32 21 122 125 DATA PROCESSED 

~ ~ 

~ 

o 
suff~c~ent geowetry. First, all observations, except for 

those qssociated with the requested GPS satellite, were 

ed~ted from the GPSPAC data. Next, the result~ng single GPS 

satellite data were input into an unmodified R&D GTDS run to 

process GPSPAC data. These single relay orbit solutions--

except as otherwise specified--used the same dynamics, 

modeling, etc., employed in the correspo~ding composite relay solutions. 

Contrary to geometrical considerations, the single GPS 

satellite solut~ons displayed robustness in their ability to 

recover the clock parameters and to converge us~ng very 

short observation arcs. The single GPS solutions can converge in as little as two Landsat orbital periods provided 

that the observation timespan's placement is chosen so as to 

minimize GPS-Landsat nonvisibility periods. Also, the 

single GPS satellite solutions, even those of short duration, can recover the clock parameters (clock bias and 

drift) when no a priori information is provided. Table 2-3 

summarizes the characteristics of several s~ngle GPS satell~te GPSPAC data solutions. 

Recovery of the clock parameters to a high degree of agreement, together with the single relay solution's ab~lity to 

converge even w~th no a priori clock information, ~ndicates 

that the clocks in the GPSPAC data are highly observable. 

This high clock observability provides the ability to resolve small variations in the clock parameters. This clock 

variab~lity is evident, in Table 2-3, between range and 

delta-range solutions over the same observation timespan. 

The clock parameters can be expressed in terres of their resulting corrections to pseudorange measurements to yield an 

effective range offset. Using this technique, the var~ability of the observed clock for the ensemble of single GPS 

satell~te solutions over the same observation timespan is 

presented in Table 2-4. 

2-9 

0112 
N 

I 

I-' 

o 

Table 2-3. Characteristics of GPSPAC Data Solutions Using Observations From Single 

GPS Satellites 

RESIDUAL 

STATISTICS, 

OBSERVATIONS STANDARD 

RUNa FROM GPS ARC NO OF DEVIATIONS 

10 SATELLITE LENGTH OBSERVA-

(hours) TIONS 

NO DELTA 

RANGE RANGE (meters) (em) 

G42A 2 3 577 235 201 

G42B 2 3 577 235 201 

G43A 3 25 430 4186 201 

G43B 3 25 423 153 202 

G43C 3 3 592 1291 280 

G43D 3 3 592 2434 209 

G43E 3 3 585 212 211 

G43F 3 3 585 212 2 11 

NOTES SATELLITE AND TIME PERIOD LANDSAT-5, APRIL 1984 

DATA ALL AVAILABLE PAIRS OF OBSERVATIONS PROCESSED 

FORCE MODEL BASELINE 

SOLVE-FOR PARAMETERS 

. B B 

1/1 (10- 3 sec) (10- 8 seel 

sec) 

-0290 ;- 3 1277 -32631 

-0290 -31277 -32631 

0001 - 3 1276 -32640 

-0145 -3 1280 -32606 

0007 -3 1269 -32668 

-0003 -3 1279 -32615 

0557 -3 1276 -32631 

0557 -3 1276 -32631 

SOLVE-FOR PARAMETERS DRAG SCALE FACTOR 1/1 = ACD/CD, CLOCK BIAS B, AND DRIFT B AT EPOCH 

aAll SOLUTION ARC TIMES START ON 840413, 2 HOURS 

COMMENTS ON RUNb 

COMBINED SOLUTION 

COMBINED SOLUTION, ZERO A PRIORI 

CLOCK PARAMETERS 

DELTA-RANGE SOLUTION 

COMBINED SOLUTION 

RANGE SOLUTION 

DELTA-RANGE SOLUTION 

COMBINED SOLUTION 

COMBINED SOLUTION, ZERO A PRIORI 

CLOCK PARAMETERS 

bALL SOLUTIONS INVOLVE PAIRS OF GPS RANGE AND DELTA-RANGE OBSERVATIONS IN COMBINED SOLUTIONS, BOTH DATA TYPES HAVE COMPARABLE 

WEIGHTINGS IN DELTA-RANGE SOLUTIONS, RANGE IS WEIGHTED LIGHTLY, IN RANGE SOLUTIONS, DELTA-RANGE IS WEIGHTED LIGHTLY 

01121131-1185 
tv 

I 

I-' 

I-' 

/ 

Table 2-4. Intercomparisons of GPSPAC Data Solutions Using Single and Composite 

GPS Observation Sets 

RESIDUAL 

STATISTICS, SOLVE-FOR PARAMETERS STANDARD OBSERVATIONS 

RUNa FROM GPS NO OF DEVIATIONS 

ID SATELLITE OBSERVANO TIONSb DELTA 

RANGE RANGE 111 (meters) (cm) 

G4A ALL GPSs-COMPOSITE 1297 100 1 239 1 591 

G41 1 2650 670 220 • -3280 

G42 2 2446 1526 220 0487 

G43 3 2581 1853 227 1 621 

G44 4 3000 180 4 249 9872 

G45 5 2080 554 229 -0331 

NOTES SATELLITE AND TIME PERIOD LANDSAT-5, APRIL 1984 

DATA GPS RANGE AND DELTA-RANGE, WITH RANGE WEIGHTED LIGHTLY 

FORCE MODEL BASELINE 

. B B 

(10- 3 sec) (10- 8 sect 

sec) 

-312752 -326234 

-312855 -325963 

-3 12708 -326375 

-3 12681 -326434 

-3 12924 -325785 

-312828 -326020 

SOLVE-FOR PARAMETERS DRAG SCALE FACTOR 111 = ACD/CD, CLOCK BIAS B, AND DRIFT B AT EPOCH 

aALL SOLUTIONS HAVE DATA ARC LENGTHS OF 16 HOURS STARTING ON 840413,2 HOURS 

RANGE EQUIVALENT 

CLOCK DIFFERENCE 

FROM COMPOSITEc 

(meters) 

-

76 

-10 I 

-38 I 

I 

130 

45 

bFOR COMPOSITE SOLUTION, ONLY EVERY 10TH PAIR OF OBSERVATION DATA IS PROCESSED, FOR SINGLE GPS SATELLITE SOLUTIONS, 

ALL PAIRS OF OBSERVATION DATA ARE PROCESSED 

cTHIS VALUE IS THE DIFFERENCE BETWEEN THE RANGE EQUIVALENT CLOCK ERROR FOR RUN 10 G4A AND THE RANGE EQUIVALENT 

CLOCK ERROR FOR THE GPS SATELLITE SOLUTION CORRESPONDING TO THE TABLE ENTRY THE RANGE EQUIVALENT OF CLOCK ERROR 

IS CALCULATED AS dR = (B + BAt) C, WHERE At IS CHOSEN AS HALF THE SOLUTION ARC LENGTH, OR 8 HOURS, AND C IS THE SPEED 

OF LIGHT 

01121131'1185 
PossIbly related to the observed clock varIations are characteristic gross structure signatures of the pseudorange resIdual in the GPSPAC SolutIon plots. The typical pseudorange 

residual plots can be fit fairly well with a linear, nonzero 

slope function. This is most pronounced in single.GPS 

satellite solutions but is also present in composIte GPS 

solutions. Representative pseudorange residual plots for 

both single GPS satellite and composite GPS solutions are 

shown in FIgure 2-2. One possible interpretation of the 

nonzero slope structure in the pseudorange resIduals is that 

an inconsistency occurs in the observed clock drift rate 

between the pseudorange and delta-pseudorange GPSPAC data 

measurements. 

In the search for information pertaining to the anomalous 

large pseudorange residuals, the inconsistency between 

pseudorange and aelta-pseudorange measurements was rediscovered. This was previously discussed In connection with 

comparisons of GPSPAC data delta-range solutions to range 

solutions. In those instances, the inconsistency was most 

notable in the Landsat-4 analysis, when the delta-range 

solutions gave better comparison with GSTDN solutions than 

the corresponding range or evenly weighted solutions. In 

its present manifestation, the inconsistency can be interpreted as a mismatch between the observed clock parameters 

for delta pseudor~nge and pseudorange data. Alternately, 

the inconsistencies could be attributed to uncorrected 

signal propagation errors or difficulties with electronics. 

Finally, intercomparisons between single GPS satellite solutIons and between single satellite and composite SolutIons 

did not reveal any highly erratIc sIngle GPS satellite. All 

single satellIte solutions agree within a maximum of ~ 80 m, 

and typically less than ~ 40 m. when observations corresponding to that GPS satellite for WhICh single GPS satellite SolutIon intercomparisons show the largest devIatIons 

2-12 

0112 
IV 

I 

I-' 

w 

tal ~~~----------------------------------------------------------------------------------------------------------------------------------~'41 

-:1_ ....... 

en .. ""::'-I.'~ 

-" .. .a ::-.. ~ -- --;- .a.-- _ ...... ..... - .. _00c..- e 00' ... - - - II .. "r:r'"' ... ..r" , 

-..::.. ..... ~.:::--

.._ .. .J:... _.I ...... _ 

~w~ 

L---------~----------------------------------------------------------------------l~ ~ II 0 I- ~ 

~ 

r'- t ...... 

-- -

! 

loOi ~ 3 ,. ,. '8 

HOURSA~~~'ZHOU~S 

te) ,3000 II _JI _ ___ II 

" " II II ---, 

.. 

E 

II 

-3000 

,110 

~ 

.-- .. .,------

~ - .'-0- r,---J ~ -~ II" II ., & i i a i i /I. 'Ii iii II i i Ii I I iI. i ., • i I '110 200 zoo zoo 340 ., 4ZO 440 4110 8ZO 540 IlOO IZO ... 100 1110 IlOO Il1O 

MlNUnSAFT£RIM04'30HOURS 

Figure 2-2. Representative Observation Residual Plots for GPSPAC Data Solutions 

Employing Composite and Single GPS Satellite Observation Sets 

(a) 

(b) 

(c) 

Range residuals for a solution that em9foys observations from all available GPS 

NAVSTAR satellites - a com~osite solution (Run G7B). 

Composite solution's corresponding delta-range residuals. Delta-range residual 

plots for single GPS satellite solutions display similar signature and residuals. 

Range residuals for a GPSPAC data solution using observations from a single GPS 

satellite (Run G-43). 
were edited from a composite solution, the large pseudorange 

res1duals are still seen. 

2.4 ASSESSMENT OF LANDSAT-5 ORBITS COMPUTED FROM GSTDN DATA 

2.4.1 COMPARISON OF LARGE OVERLAP DIFFERENCES 10 LANDSAT-4 

GSTDN SOLUTIONS 

GSTDN data for this task were processed in 30-hour overlapp1ng arcs, w1th overlap periods of 6 hours each. The difference between two adjacent orbital solutions in the 

overlap period serves as a measure of the GSTDN datadetermined orbital accuracy. In this study, Landsat-5 GSTDN 

data from two different calendar years were processed. 

Overlapping arcs, sets of two runsftach, were processed for 

April and August 1984 and for May 1985. The first two sets 

correspond to available GPSPAC data sets. The May 1985 

GSTDN data were chosen, based on optimal GSTDN and GPSPAC 

data availability, from 13 timespans in 1985. 

The maximum ephemeris position differences for the three 

overlapping periods were 106, 59, and 110 m. The rootmean-square (rms) ephemeris position differences for the two 

overlap per10ds were 64, 33, and 83 m. These d1tferences 

are considerably greater than those in the Landsat-4 study. 

For Landsat-4, the maximum ephemeris position differences of 

seven overlap comparison per10ds averaged 29 m, with a 

standard deviation of 13 m. The rms ephemeris posit10n differences for the Landsat-4 overlap periods averaged 18 m, 

with a standard deviation of 7 m. Tables 2-5 and 2-6 summarize the results of Landsat-5 GSTDN characterist1cs. 

Although th1s study processed only a lim1ted number of GSTDN 

tracking intervals, independent results indicate that 1984 

and 1985 Landsat-5 solutions give consistently larger overlap differences when compared to the prev10us Landsat-4 

2-14 

0112 
N 

I 

I-' 

Ul 

Table 2-5. 1984 GSTDN Data Orbit Solution Characteristics 

COMPUTED 

ARC START ARC NO OF NO OF DRAG SCALE RUN TIME LENGTH TRACKING OBSERVA- FACTOR 10 (date, hour) (hours) STATIONS TIONS Ql = ACD/CD INVOLVED 

GOA 840413 30 3 507 -1472 

Oh 

GOB 840414 30 5 702 -0919 

Oh 

GDM 840807 30 3 399 -8833 

Oh . 

GDN 840808 30 4 444 -7493 

Oh 

S4A 840413 30 3 507 -1965 

Oh 

S4B 840414 30 5 702 -0674 

Oh 

S8A 840807 30 3 399 -3858 

Oh 

S8B 840808 30 4 444 -4348 

o h 

GMA 840413 30 3 507 -1549 

Oh 

GMB 840414 30 5 702 -1092 

Oh 

GMC 840413 30 3 507 -1 136 

Oh 

GMD 840414 30 5 703 -0959 

Oh 

NOTES SATELLITE AND TIME PERIOD LANDSAT·5. APRIL-AUGUST 1984 

DATA GSTDN RANGE·RATE DATA 

RSS, ROOT·SUM·SQUARED 

RESIDUAL MAXIMUM POSITION DIFFERENCES 

STATISTICS, OVER 6·HOUR OVERLAP OF ADJACENT 

RANGE· RATE ARCS (meters) 

STANDARD 

DEVIATIONS CROSS- ALONG· RSS 

(em/sec) RADIAL TRACK TRACK TOTAL 

3048 

106 138 1057 1058 

4114 

3478 

81 87 584 592 

2956 

3035 

102 138 101 1 1013 

4100 

3454 

77 81 698 703 

2960 

3238 

107 136 101 2 101 7 

3860 

. 

2775 

95 98 839 842 

2822 

--

REMARKS 

BASELINE MODEL JACCHIA 

ROBERTS ATMOSPHERIC 

DENSITY MODEL, A PRIORI 

DRAG COEFFICIENT CD = 20, A DRAG SCALE FAC· 

TOR SOLVED FOR, 21 x 21 

GEM 9 GEOPOTENTIAL 

MODEL 

HARRIS·PRIESTER F100 

ATMOSPHERIC DENSITY 

MODEL, A PRIORI DRAG 

COEFFICIENT CD = 2 0, A 

DRAG SCALE FACTOR 

SOLVED FOR, 21 x 21 GEM 

9 GEOPOTENTIAL MODEL 

BASELINE ATMOSPHERE 

MODEL, WITH 36 x 36 GEM 

lOB GEOPOTENTIAL MODEL 

BASELINE MODEL WITH 36 

x 36 GEM lOB GEOPOTENTIAL MODEL, MARSH STA· 

TION COORDINATES 

I 

It> 

? 

~ 

~ 

(; 
N 

I 

I-' 

0"1 

Table 2-6. 1985 GSTDN Data Orbit solution Characteristics 

ARC START ARC NO OF NO OF COMPUTED 

RUN TIME LENGTH TRACKING OBSERVA- DRAG SCALE 

10 STATIONS FACTOR (date, houri (hoursl INVOLVED TIONS Q1 = ~CD/CD 

GS1 850524 30 3 239 -11 07 

6 h 

GS2 850525 30 5 270 440 

6h 

GSA 850524 30 4 400 -897 

6 h 

GSB 850525 30 6 387 573 

6h 

.- - ---------------

NOTES SATELLITE AND TIME PERIOD LANDSAT-5, MAY 1985 

DATA GSTDN RANGE-RATE DATA 

RSS IS ROOT-SUM-SQUARED 

RESIDUAL MAXIMUM POSITION DIFFERENCES STATISTICS, OVER 6-HOUR OVERLAP OF STANDARD ADJACENT ARCS (metersl DEVIATIONS REMARKS 

RANGE DELTA CROSS- ALONG- RSS 

(metersl RANGE RADIAL TRACK TRACK TOTAL (eml 

- 1319 BASELINE MODEL 

11 1 264 1073 1102 

- 1 396 RANGE-RATE DATA ONLY I 

1047 5361 NO OBSERVATION PROCESS162 197 690 69 1 ING PERFORMED, BOTH 

RANGE AND RANGE-RATE 

4322 5775 DATA INCLUDED 

-------

01121131')185 
GSTON solutions. Tracking statistics do indicate an increas1ng amount of TORS-East tracking data available for 

Landsat-5 in 1985. Overlap differences of TORS-only solut10ns, assoc1ated with the single-TORS S-band certificat10n 

results, report 82, 71, 35, and 74 m (Reference 2-4). In 

addition, private conversations with investigators 

(Yur1 Nakai, Computer Sciences Corporation) who are analyzing 1985 Landsat-5 orbit solution overlap differences uS1ng 

combinations of GSTON, ~DRS5, and B1lateration Ranging 

Transponder System (BRTS) data indicate ephemeris overlap 

differences consistently larger than the average 29 m observed for Landsat-4. 

2.4.2 ANALYSIS OF LANDSAT-5 LARGER-THAN-EXPECTED OVERLAP 

EPHEMERIS DIFFERENCES 

It was originally thought that these larger-than-expected 

overlap ephemeris differences could be attributed to inadequacies in atmospher~c density modeling. Modeling error was 

suspected because the overlap comparison plot of the alongtrack difference, as shown in Figure 2-3, displays sinusoidally increasing differences that are generally typical 

of force modeling m1smatch between the orbit solut10ns involved. No significant improvement was seen, however, when 

a different atmospheric model (Harris-Priester) was used. 

In an attempt to reduce these ephemeris differences, the 

April 1984 GSTDN data arcs were again processed using the 

standard orbit determination scenariO, but with two variations. First, orbits were obtained by using the 36-by-36 

GEM-lOB geopotential model. Second, a second set of orbits 

was obtained by uSing the Marsh tracking station position 

coordinates in addition to the GEM-lOB model. As was also 

true in the Landsat-4 study, using these improved models did 

not result in substantial improvement in orbit determination 

performance. The results of the 1984 GSTDN orbit determination runs are summarized in Table 2-5. 

2-17 

0112 
GIDS COMPARE PROGnAM 

, •••• POSITION DIFFERENCE SATELLITE LS-5 8402101 

I --------- --------- --------- --------- --------- --------- --------- --------- -------- --------- I 

110 00 

08 00 

A 

L 

0 

II 

G 66 00 

T 

R 

A 

C II 00 

I< 

0 

I 

f 22 00 

f 

E 

R 

E 

N IJ 0 0 

I c 

I-' E 

OJ S 

I -22 00 

N 

M 

E 

T -44 00 

E 

R 

S 

• 

-66 00 

• 

-S8 00 

• 

- I 10 00 

I --------- --------- --------- --------- --------- I o 0 0 15 50 2 25 3 00 3 16 4 60 5 25 G 00 6 15 1 50 

TIME FROM VVMMOO UIIMMSS IN URS 

840414 0 

Figure 2-3. Landsat-5 GSTDN Orbit Solution Overlap Eph~merls Comparison 
Although the previous Landsat-4 experience with unified 

S-band (USB) tracking data revealed systematic errors in the 

range observat10ns, the May 1985 GSTDN data arcs were reprocessed using both range and range-rate observat10ns. 

This was done to determine if range errors were caused by 

redundant observat10n correction preprocess1ng in R&D GTDS. 

When the preprocessing was deleted, the resulting orbit 

solutions still displayed large range and range-rate res1dual statist1cs. Probably because of the greater observability affordea by the range observations, the maX1mum posit10n 

difference was decreased from 110 to 69 m--still large in 

compar1son with the Landsat-4 accuracies. The results of 

the 1985 GSTDN orb1t determination runs are summarized in 

Table 2-6. 

2.4.3 LANuSAT-5 SOLUTIONS INVOLVING FEWER TRACKING STATIONS 

In comparison to previous Landsat-4 GSTDN data, the 

Landsat-5 solutions involved fewer ground tracking stations. In the typical Landsat-4 GSTDN 30-hour arc solutions, between 6 and 10 ground stations were involved in 

tracking. For the six baseline Landsat-5 GSTDN solutions in 

Tables 2-5 and 2-6, between three and five tracking stations 

were involved. 

Irregularity of the Lanasat-5 tracking passes may also contribute to the larger-than-expected overlap ephemeris d1fferences. Figure 2-4 displays a plot of the ground tracking 

passes for Landsat-5 GSTDN data, beg1nning on April 13, 

1984. This plot shows the 30-hour intervals for baseline 

run IDs GDA and GDB and their corresponding overlap interval 

extend1ng from 0 hours to 6 hours on Apr11 14 (840414). 

Because it was suspected that the sparse tracking over the 

GuA-GDB 6-hour overlap contr1buted to its poor ephemer1s 

overlap comparison (from Table 2-5, a maximum pos1tion difference rss of 106 m), alternate 30-hour arcs were chosen. 

2-19 

0112 
N 

I 

N 

C 

l ABBBe BAB 

j4-- DATA ARC FOR RUN 10 GOA 

• 

AI: 

.. I I YJ 

: AB; AB B e 0 A B B B E B ~ L. ! DATA ARC FOR RUN 10 GOB 

A B B B~ 

lOA 0 DATA ARC FOR RUN 10 GO: : 0 A 0 C C 0 A • AO AO 0 C 0, C • F 0 0 I 

~ ~ 0 0 O! 'DATA ARC FOR RUN 10 GOD 

~ A B B B e BA B AB AB B e 0 

DATA ARC FOR RUN 10 GDE , .1 , I 

'e 0 1 ABBB E BA Bee 0 AFBBI 

~ ! DATA ARC FOR RUN 10 GDF • 

840413 

Oh 

6h 12 h 18 h 840414 

Oh 

6h 12 h 18 h 

HOURS AFT~R APRIL 13. 1984 

840415 

Oh 

6h 12 h 

A B B B C BA B AB ABB C 0 ABBBE BABCC 0 

LEGEND 

A - GDS8 

B - ULA3 

C - MAD3 

0- AG03 

E - GWM3 

F - GDS3 

NOTES CAPITAL LETTERS INDICATE THE CORRESPONDENCE BETWEEN TRACKING 

PASSES (WITH A TYPICAL DURATION OF 10 MINUTES) AND THE TRACKING 

STATION FROM WHICH THE MEASUREMENT SIGNAL ORIGINATED 

THE TRACKING PASSES ABOVE THE TIME AXIS CONTRIBUTE TO THE ORBIT SOLUTION OVER THE DATA ARC 

THE TRACKING PASSES BELOW THE TIME AXIS ARE PRESENT IN THE 

GSTDN DATA BASE 

18 h 840416 

Oh 

A F B B 

~ ~ 

o 

f'igure 2-4. Plot ot Ground Tracklng Passes and Orblt Solution Arcs Involving 

April 1984 Landsat-5 GSTDN Data 
These alternate arcs, labeled GDC and GDD, begin at 840413 

18 hours and 840414 18 hours, respectively, and have a 

6-hour overlap beginning at 840414 18 hours. As seen from 

the plot in Figure 2-4, this alternate overlap time includes 

more uniform tracking. This is reflected in the GDC-GDD 

overlap ephemeris comparison RSS of 44 m (from Table 2-7), 

which is a significant improvement over the GDA-GDB overlap 

(although it is still inferior to the Landsat-4 GS~DN overlap maxima, which have an RSS average of 28.8 m). Part of 

this improvement may also result because the alternate GDC 

and GOD arcs involve more tracking stations, four and six, 

respect1vely, compared to three and five for GOA and GOB. 

A second set of GSTDN data orbit solut1ons were performed, 

using 39-hour arcs. These two arcs, labeled GDE and GDF, 

also have a 6-hour overlap, beginning at 840414 9 hours. 

The maximum position difference rss of this overlap 1S 72 m 

(Table 2-7). Although the number of tracking stations involved remafned the same as in the GDC-GDD solutions, the 

larger orbit arcs resulted in a poorer overlap comparison. 

This suggests that the relatively sroall number of stations 

involved in Landsat-S GSTON data cannot be compensated for 

by extending orbit solutions over arcs of greater duration, 

thereby increasing the number of observations and possibly 

the number of tracking stations. Instead, the GOE-GOF overlap, when compared to GDC-GDD errors, indicates that the 

force modeling errors begin to increase at a greater rate 

than the observational benefits. 

2.4.4 ANALYSIS OF LANOSAT-4 GSTON SOLUTIONS WITH REDUCED 

NUMBER OF TRACKING STATIONS 

To determine 1f poor Landsat-S GSTON solutions result from 

the small number of tracking stations involved, Landsat-4 

GSTDN solutions with a reduced number of tracking stations 

were generated. The results of these solutions are summarized in Table 2-8. The f1rst entry 1n the table, the 

2-21 

0112 
N 

I 

N 

N 

Table 2-7. Additional Landsat-5 GSTDN Data Orbit Solution Characteristics 

COMPUTED 

ARC START ARC NO OF NO OF DRAG SCALE RUN TIME LENGTH TRACKING OBSERVA- FACTOR 10 (date, hour) (hours) STATIONS TIONS '11 = I1CD/CD INVOLVED 

GDC 840413 30 4 703 2045 

18 h 

GOD 840414 30 6 723 0065 

18 h 

GDE 840413 39 4 767 -0424 

Oh 

GDF 840414 39 6 829 -0390 

9 h ---- -- ~-- - ----

NOTES SATELLITE AND TIME PERIOD LANDSAT-5, APRIL 1984 

DATA GSTDN RANGE-RATE DATA 

RSS IS ROOT SUM SQUARED 

SEE FIGURE 2-4 FOR TRACKING PASSES AND ORBIT SOLUTION ARCS 

RESIDUAL MAXIMUM POSITION DIFFERENCES 

STATISTICS, OVER 6-HOUR OVERLAP OF ADJACENT 

RANGE-RATE ARCS (meters) REMARKS STANDARD 

DEVIATIONS CROSS- ALONG- RSS 

(em/sec) RADIAL TRACK TRACK TOTAL 

384 BASELINE MODEL 

84 104 442 443 

354 

444 

145 135 714 716 

431 

~ 

~ ~ 

o 
N 

I 

N 

W 

Table 2-8. Summary of Landsat-4 GSTDN Solutions With Peduced Number of Tracking Stations 

COMPUTED 

ARC START NO OF NO OF NO OF DRAG SCALE RUN TIME TRACKING TRACKING OBSERVA- FACTOR ID STATIONS PASSES (date, hour) ACCEPTED ACCEPTED TIONS 111 = IICD/CD 

GL4 821001 10 16 145 -0236 

Oh 

GL5 821002 6 16 116 -0294 

Oh 

GL41 821001 3 4 207 -on9 

Oh 

GL51 821002 4 9 468 -0347 

Oh 

GL42 821001 4 9 453 -0251 

o h 

GL43 821001 4 6 304 -0286 

o h 

GL52 821002 2 7 367 -0349 

o h 

GL44 821001 6 11 661 -0268 

Oh 

NOTES SATELLITE AND TIME PERIOD LANDSAT-4, OCTOBER 1982 

DATA GSTDN RANGE-RATE DATA 

RSS IS ROOT SUM SQUARED 

ALL SOLUTIONS HAVE DATA ARC LENGTHS OF 30 HOURS 

SEE FIGURE 2-5 FOR TRACKING PASSES AND ORBIT SOLUTION ARCS 

RESIDUAL MAXIMUM POSITION DIFFERENCES 

STATISTICS, OVER 6-HOUR OVERLAP OF ADJACENT 

RANGE-RATE ARCS (meters) REMARKS STANDARD 

DEVIATIONS CROSS- ALONG- RSS 

(em/sec) RADIAL TRACK TRACK TOTAL 

262 LANDSAT-4 BASELINE 

24 152 62 155 SOLUTION (PRESENTED 

FOR COMPARISON) 

345 

317 LANDSAT-4 SOLUTIONS 

103 231 1552 1554 WITH REDUCED NO OF 

TRACKING STATIONS 

294 

65 82 256 257 

289 

299 

11 7 137 305 333 

287 

70 54 287 287 

260 

--- - ~ 

~ 

~ ~ 

o 
overlap comparison between the nonreduced Landsat-4 arcs GL4 

and GL5, is presented as the standard for comparison. The 

rema1ning entries in the table present comparative ephemeris 

overlap differences for orbits generated over the same timespans as GL4 and GL5 but using different reduced sets of 

tracking stations. 

The Landsat-4 GL4-GL5 set was chosen because 1t displays the 

smallest ephemeris overlap difference of all the Landsat-4 

GSTDN comparisons. It was reasoned that the GL4-GL5 set 

would therefore produce the greatest range of sensitivity to 

reduced tracking station scenarios. In addition, because of 

the large number of stations involved, 1t was hoped,that 

appropriate subsets of the GL4-GL5 tracking stations could 

be found to approximately reproduce the tracking geometries 

available in the Landsat-5 GSTDN solut10ns. Unfortunately, 

the latter purpose was frustrated by the absence of valid 

Landsat-4 observations corresponding to tracking stations in 

the Landsat-5 station set and the geometrical complications 

introauced in choosing substitution stations. 

The reduced station results in Table 2-8 do produce poorer 

overlap compar1sons. Specifically, as seen in set GL41-GL51 

in comparison to set GL42-GL51, overlap comparisons aeteriorate rapidly after some cutoff number of tracking station. As shown in the table, below this cutoff number the 

number of tracking passes involved begins to play an increasing importance in the overlap differences. As shown in 

Figure 2-5, which d1splays the tracking schedules for those 

runs summarized in Table 2-8, the number and duration of 

nontracking 1ntervals also appears to affect the ephemer1s 

differences. 

Because of these complications 1ntroduced by station geometry, the number of tracking passes, and the amount and 

2-24 

0112 
N 

I 

N 

U1 

I G G FA, H C I C IJD 0 FE F B I ... DATA ARC FOR RUN 10 GL4 I • 

I G F F ICC 0 GE E F F G EG F I ... ! DATA ARC FOR RUN 10 GL5 ~ 

I A C C B: I I 14 DATA ARC FOR RUN 10 GL41 I • 

I F FI C C 0 F F F I 

14 ! DATA ARC FOR RUN 10 GL51 t1 

I F A C C F FB I F FI /4 DATA ARC FOR RUN 10 GL42 I • 

I F FI C C 0 F F F I j4 : DATA ARC FOR RUN 10 GL51 • 

C 0 F F 

I A C C DO B I 

14 DATA ARC FOR RUN 10 GL43 ~ 

I F FI C C F F F I ... I DATA ARC FOR RUN 10 GL52 • 

I F A CICIDD F FB I " 

... DATA ARC FOR RUN 10 GL44 I • 

I F FI C C F F F~ ... I DATA ARC FOR RUN 10 GL52----:----~ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 

821001 6 h 12 h 18 h 821002 6 h 12 h 18 h 821003 6 h 

Oh Oh Oh 

HOURS AFTER OCTOBER 1. 1982 

G G FB AB BH C IC IJ 0 JD FE BF B B B G F B FB B C C 0 GE E F BF B BI B G EG F B 

LEGEND 

A - GDSS 

B - ULA3 

C - MAD3 

0- AG03 

E - MIL3 

F - GDS3 

G - BLTA 

H - MADS 

I - ORR3 

J - BDA3 

NOTES CAPITAL LETTERS INDICATE THE CORESPONDENCE BETWEEN TRACKING 

PASSES (WITH A TYPICAL DURATION OF 10 MINUTES I AND THE TRACKING STATION FROM WHICH THE MEASUREMENT SIGNAL ORIGINATED 

THE TRACKING PASSES ABOVE THE TIME AXIS CONTRIBUTE TO THE ORBIT SOLUTION OVER THE DATA ARC 

THE TRACKING f>ASSES BELOW THE TIME AXIS ARE PRESENT IN THE 

GSTDN DATA BASE 

Figure 2-5. Plot of Ground Tracking Passes and Orbit Solution Arcs Involving 

October 1982 Landsat-4 GSTDN Data 
durat10n of nontracking intervals, the reduced station results were inconclusive in determ1ning the extent to wh1ch 

poor Landsat-5 GSTDN orbit solutions result solely from the 

small number of tracking stations. One very interest1ng 

statistic is that, for the Landsat-4 GSTDN tracking intervals (Figure 2-5), an average of 88 percent of the available 

stations and only 50 percent of the available tracking 

passes were accepted and thus contributed to the solution. l In contrast, for the Landsat-5 GSTDN tracking intervals (Figure 2-4), all the available stat10ns and all the 

available tracking passes were accepted and thus contr1bute 

to the solution. This may indicate that the Landsat-5 solutions, because of the lower density of data, incorporated 

observations that would otherwise be edited out. 

The present results and the prev10us Landsat-4 exper1ences 

lead to the conclusion that more stations, although each 

contains random errors and possibly even systematic errors, 

result not only in better observation geometry but-also in a 

larger number of observations. A large amount of data 18 

needed because many observations w1ll be ed1ted out because 

of validity, elevation, or 30 editing. After this editing, if a sufficient amount of data remains, the remaining 

error sources can be averaged out in the orbit determination 

process to produce small ephemeris overlap differences. In 

short, more stations provide more measurements, more observability, and better statistics in dealing with existing observation error sources. 

IAva1lable refers to observations--associated with a particular tracking pass or station--that are both present 1n 

the input data ~nd not deleted by user observation accept/ 

reject criteria; accepted data must meet the previous available cr1teria and must also not be edited out of the orbit 

solution due to either validity editing, elevation edit1ng, 

or 30 ed1ting. 

2-26 

0112 
2.5 ANALYSIS OF POSSIBLE ~ISMATCHES BETWEEN GLI AND R&D GTDS 

This section presents the results of an analysis to determine 1f possible 1nconsistencies or inaccuracies introduced 

in the R&D GTDS·orbit determination processing cause the , 

large pseudorange measurement residuals seen in both 

Landsat-4 and Landsat-5 GPSPAC data orbits (as descr1bed in 

Section 2.2). In the course of this analysis, the R&D GTDS 

code, which processes GPSPAC data, was investigated for correctness and consistency with the mathematical specifications of the GPSPAC/Landsat-D Interface System (GLI) 

(Reference 2-5). As noted in Section 2.1, the GPSPAC extracts GPS data from telemetry that is in turn preprocessed 

to transform it from Earth-fixed to inertial coordinates. 

In addition to other functions, GLI performs this preprocessing of the Landsat GPSPAC data for use in R&D GTDS. 

This investigation verified the correctness of the R&D GTDS 

code that processes the GPSPAC data. However, a coordinate. 

frame mismatch can occur when the coordinate reference frame 

of the R&D GTDS orbit integrator does not match the inertial 

frame of the GPSPAC data's internal state, which is included 

with the observations. For instance, 1n run ID G4A of 

Table 2-1, the Landsat-5 GPS orbit solution 1S integrated in 

a true-of-reference-date (TOR) coordinate frame (Reterence 2-6) referenced to April 13, 1984. However, the observations' GPS inertial position and velocities are expressed 

in a coordinate frame referenced to April 8, 1984, the" date 

EPOCH of the GPSPAC data observation file. Because the R&D 

GTDS does not check for reference frame inconsistency between the GPSPAC observations and the integration reference 

frame, it fails to take into account the Earth's precession 

and nutation effects (Reference 2-7) occurring in the 5 days 

between April 8 and April 13. 

2-27 

0112 
To correct this reference frame inconsistency, each GPS observatlon's posltion and veloclty (the Sand SDOT) vector 

(expressed in the GPSPAC EPDATE TOR frame) is rotated by a 

stand-alone routine to the reference date to be used by the 

R&D GTDS orbit integrat~r. For the G4A run, this rotation 

was from the April 8, 1984, to the April 13, 1984, TOR coordlnate frame. This rotated GPSPAC data were then proce~sed 

in an R&D GTDS DC run. The resultant Landsat-5 GPSPAC orblt 

solution still displays the same large pseudorange residuals 

previously observed. In fact, the converged orbit solution 

results in a state vector of the same magnitude as that generated in the nonrotated G4A run, except that lt was rotated 

through a small angle. This result was to be expected because the reference frame rotatl0n does not affect the 

individual GPSPAC pseudorange and delta-pseudorange measurements. Instead, it rotates the entire ~AVSTAR GPS multisatellite constellation through a fixed angle, which in this 

case corrects for the precession and nutation effects occurring between April 8 and April 13. 

~he comparison plot between the nonrotated G4A orblt and the 

G4A orbit with no reference frame inconsistency is shown in 

Flgure 2-6. The comparison displays a constant difference 

in the spacecraft along-track direction. Because Landsat 

has a 98-deg-inclination orbit, this offset is due primarily 

to nutation effects. The difference in the cross-track direction, due primarily to precession effects, displays a 

sinusoldally varying function of perlod roughly equal to 

Landsat's own 98-minute period. The zeros ln the difference 

function occur approximately over the poles while the extremes occur near the equatorial crossings. 

Table 2-9 summarizes the characteristics of comparlsons 

between nonrotated and reference rotated GPSPAC solutions 

for Landsat-4 and -5. The solutions were performed for 

Landsat-4 arcs to determine if reference rotation would 

2-28 

0112 
tv 

, 

tv 

~ 

1 50000 

G10S COMPARE PROGRAM 

••••• POS"'OO 0'"...... SA""". 'S-6 •••• ,.' I --------- --------- --------- --------- --------- ----- ________________________________________ I 

1 20000 

It o 90000 

A 

0 

I 

A 

l o 60000 

0 

I 

F 

F o 30000 

E 

It 

E 

N 

C o 00000 

E 

S 

I 

N 

-0 30000 

C 

E 

N 

T 

-0 60000 

J 

M 

E 

T 

E 

-0 90000 

It 

S 

-I 20000 

-I 50000 

I --------- --------- --------- --------- --------- ---- _________________________________________ I 

• D • DD • DD • DD • D. I. •• I •• D I. D. I. DD I •• D 'D DD 

TIME FReM VVMMDO HUMMSS IN HRS 

840413 20000 

Figure 2-6. 

Ephemeris Comparison BetWeen GPS Orblt (Run G4A) Solutions With and 

Wlthout Reference Frame Mlsmatch Correction (1 of J) 
I\.) 

I 

W 

0 

26 00000 

GTDS COMPARE PROGRAM ••••• POSITION DIFFERENCE I ---- _______________________________ _ 

--------- ------- SATELLITE LS-5 --------- 8402101 --------- r 

C 

20 00000 

R 

0 

S 

S 15 00000 

T 

R 

A 

C 

I( 

10 00000 

0 

I 

f 

F fJ 00000 

E 

R 

E 

N a a 

C 

E 

S 

I 

N 

-5 00000 

M 

E 

T 

E 

-10 00000 

R 

S 

-15 00000 

-20 00000 

-25 00000 

I --------- --------- --------- --------- --------- ---- _________________________________________ I 

' , 2 " , " e " • " " 00 ., 00 I. " I.e " I. " 20 00 

TIME FRau VVMAlDO HlIMMSS IN HRS 

840413 20000 

Flgure 2-6. 

Ephemeris Comparlson Between GPS Orbit (Run G4A) Solutions Wlth and 

Without Reference Frame Mismatch Correction (2 of 3) 
A 

L 

0 

N 

G 

T 

R 

A 

C 

I< 

D 

I 

F 

F 

E 

R 

E 

tv N 

I C 

W E 

S 

I-' 

I 

N 

M 

E 

T 

E 

R 

S 

GTDS COMPARE PROGRAM 

••••• POSITION DIFFERENCE SATELLITE LS-5 8402101 

I --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- I 12 50000 

10.00000 

7 50000 

5 00000 

2 50000 

-0 00000 

-2 50000 

-5 00000 

-7 50000 

-10 00000 

-12 50000 •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• t ••••••• 

--------- --------- --------- --------- --------- --------- --------- --------- --------- --------- I o 2 00 4 00 6 00 8 00 10 00 12 00 14 00 16 00 18 00 20 00 

Figure 2-6. 

TIME FROM VVIIIMOD 1IIIIIIM5S IN HRS 

840413 20000 

Ephemerls Comparison Between GPS Orbit (Run G4A) Solutions Wlth and 

Without Reference Frame Mismatch Correctl0n (3 of 3) 
I'J 

I 

w 

N 

Table 2-9. 

RUN ARC START ARC NO OF 

10 TIME LENGTH OBSERVA 

(dale houri Ihoursl TIONS 

Reference Rotated GPSPAC Data Orbit Solution Characteristics and 

Comparisons With Nonrotated Solutions 

RESIDUAL MAXIMUM POSITION DIFFERENCES STATISTICS, MAXIMUM POSITION DIFFERENCES SOLVE FOR PARAMETERS STANDARD OVER 4 HOUR OVERLAP OF ADJACENT FROM GSTDN ORBITS (melersl 

DEVIATIONS ARCS Imelersl 

. B B RANGE DELTA ALONG ALONG Q1 110-3 secl 110-8 secl Imelersl RANGE RADIAL C TRACK RSS RSS· RADIAL C TRACK RSS RSS' 

secl Icml 

REMARKS 

GP1R 820910 16 705 -0305 -0369 -0786 132 5 253 II 1 444 317 497 465 SATELLITE LANDSAT 4 

18 h 25 158 130 185 205 

GP2R 820911 16 682 -1 107 -0708 -07B5 2469 279 117 417 551 637 636 

6h 

GP4R 821001 16 738 -0230 -0571 -0704 3128 359 122 619 321 649 481 

19 h 102 344 473 540 538 

GP5R 821002 16 592 -0610 -0875 -0702 2942 343 63 552 372 654 633 

7h 

GP6R 821112 16 790 -0277 -1027 -0546 13120 240 100 593 339 626 415 

19 h 74 145 407 411 410 

GP7R 821113 16 795 -0693 -1264 -0545 1451 262 76 727 396 802 531 

7h 

G4AR 840413 16 1297 1594 -3127 -3262 1000 239 134 541 575 790 543 SATELLITE LANDSAT 5 

2h 

NOTES FORCE MODEL BASELINE ONLY EVERY 10TH PAIR OF OBSERVATION DATA IS PROCESSED 

. SOLVE FOR PARAMETERS DRAG SCALE FACTOR Ql = ACDICD CLOCK BIAS B AND DRIFT B AT EPOCH 

C LAND RSS ARE THE ACROSS TRACK ALONG TRACK AND ROOT SUM SOUARED COMPARE DIFFERENCES RESPECTIVELY 

aFOR COMPARISON PURPOSES RSS CORRESPONDING TO PREVIOUSLY REPORTED NON ROTATED GPSPAC DATA SOLUTIONS IFOR LANDSAT 4 FROM REFERENCE 2 31 ALL OTHER TABLE ENTRIES ARE FROM 

ROTATED SOLUTIONS 

I 

~ 

'" 

~ 

~ 

o 
improve the GPSPAC-GSTDN ephemeris overlap compares. In 

most cases, very little difference is seen. Contrary to 

what was expected, ln four instances, the reference frame 

rotation gives larger GPSPAC-GSTDN differences; although 

this may be caused by some geometric effect, these results 

are not fully understood and should be studied further. In 

any case, the rotation of the reference frame does not appear to cause, or affect, the large pseudo range residuals 

seen in any of the GPSPAC delta-range solutions. 

A possible processing mismatch occurs if the GLI and R&D 

GTDS programs use dlfferent Greenwich hour angle {GHA} constants. To account for error on the order of 100 m, the GHA 

correction is estimated to be a rotation of roughly the same 

order of magnitude as that used to correct the coordinate 

reference frame inconsistency, that is, approximately 2 x 

-4 10 deg. As was expected, the correction of posslble GHA 

errors resulted in comparison plots analogous to the reference frame rotation correction. 

This study also considered other conceivable errors that can 

produce range error signatures on the order of 100 m and 

appear GPSPAC range-dependent, but are delta-range insensitive--in short, the range error signatures match the trend 

of the pseudorange residual errors seen in both the 

Landsat-4 and -5 GPSPAC solutions. Two possible error 

sources, which under certain scenarios meet this error signature and can be corrected for in the R&D GTDS processing, 

are time tag errors associated with a measurement or with 

the transformation from Earth-fixed to inertial coordinates. when these postulated errors were fixed, in isolatlon or in combination, the characteristic pseudorange 

residual errors ln the R&D GTDS orbit solutions were increased or were only mildly affected, but they were still 

present. 

2-33 

0112 
2.6 CONCLUSIONS 

The maJor conclusions concerning the accuracies of GPSPAC 

data for computing Landsat-5 orbits can be summarized as 

follows: 

1. Landsat-5 orbit determination using GPSPAC data 

Landsat-5 orbit solutions computed from GPSPAC deltapseudorange (Doppler) data are good. Maximum differences 

between GPSPAC and GSTDN solution are generally under 70 m. 

~aximum differences between partially overlapping GPSPAC 

solutions are even smaller. There is a good possibility 

that the GPSPAC solutions are superior to the GSTDN solutions in accuracy. 

2. For orbit determination instead of real-time navigation, simultaneous data from four GPS satellites are not 

necessary. The results indicate that approximately 3 hours 

of data from a single GPS satellite are sufficient to resolve the Landsat-5 orbit and clock. A study of a randomly 

selected sample shows that the Landsat-5 orbit solutions 

based on individual GPS satellites agree to within 80 m, and 

typically less than 40 m. 

3. As with the case of Landsat-4 GPSPAC data, there 

exist some inconsistencies between the Landsat-5 GPSPAC 

pseudorange and delta-pseudorange data. Landsat-5 solutions 

derived from pseudorange data generally differ from the 

GSTDN solutions by maximas over 100 m. Furthermore, large, 

GPS-independent, range observation residuals of over 100 m 

are seen in delta-pseudorange Landsat-5 GPSPAC data solutions. Based on these, it may be concluded that the pseudoranges have systematic errors on the order of 100 m in 

addition to the expected clock errors. The cause of these 

systematic errors has not been determined, although bad data 

2-34 

0112 
trom an individual GPS satellite and several easily committed preprocessing errors have been elim~nated as possible 

reasons. 

4. In connection with the GPSPAC study, the computation of Landsat-5 orbits from GSTDN data was undertaken. 

Unfortunately, there are not as many ground tracking stations for Landsat-5 as for Landsat-4, and the accuracy of 

the resulting Landsat-5 orbit solutions is not as good as 

that of the corresponding Landsat-4 solutions. Investigation shows that this degradation cannot be attributed solely 

to dynami~ modeling errors accentuated by the sparsity of 

tracking coverage. 

2.7 REFERENCES 

2-1. P. M. Jamiczek, editor, Global Positioning System 

Papers Published in Navigation. washington, DC: 

Institute of Navigat~on, 1980 

2-2. W. P. Birmingham, B. L. Miller, and W. L. Stein, "Experimental Results of Using the"GPS for Landsat-4 Onboard Navigation," paper presented at Institute of 

Navigation National Aerospace Meet~ng, March 1983 

2-3. B. T. Fang and E. Seifert, "An Evaluat~on of Global 

Positioning System Data for Landsat-4 Orbit Determ~nation," paper delivered at AIAA 23rd Aerospace Science 

Meeting, January 1985; also Computer Sciences Corporation, CSC/TM-84/6077, Tracking and Data ACquisition 

System/Global Positioning System (TDAS/GPS) Navigation 

Analysis, September 1984 

2-4. Computer Sciences Corporation, CSC/TM-85/6731, Flight 

Dynamics Division (FDD) Single-TDRS S-Band Navigation 

Cert~f~cation Results for Early Tracking and Data Relay Satellite System (TDRSS) Users, Part II - Cert~ficat~on Results, J. O. Cappellar~, Jr., P. Y. Kay, and ~. H. Nikonchuk, September 1985 

2-5. Nat~onal Aeronaut~cs and Space Administration, 

STL-82-001, GPSPAC/Landsat-D Interface (GLI) System 

Description, J. B. Dunham, H. M. Silsk~, and 

W. T. Wallace, April 1982 

2-35 

0112 
2-6. Computer SC1ences Corporation, CSCjTM-80j6028, Primary 

Coordinate Systems and Coordinate System Transformations in GTDS, R. L. Smith and M. J. Lucas, June 1980 

2-7. Goddard Space Flight Center, X-582-76-77, Mathematical 

Theory of the Goddard Trajectory Determ1nation System, 

J. O. Cappellari, Jr., C. E. Velez, and A. J. Fuchs 

(editors), April 1976 

2-36 

0112 
SECTION 3 - LOW-ALTITUDE SATELLITE NAVIGATION USING 

SItvlULATED TDAS ONE-\'V'AY DOPPLER DATA 

This study investigated the extent of agreement between 

orbit determination results using simulated TDAS one-way 

Doppler da~a and linear error analysis results from a previous study. The simulation and orbit determination results 

were obtained using the R&D GTDS TDAS enhancements described 

in Reference 3-1. These simulation/orbit determ1nat1on results were compared, for an analogous satellite navigation 

scenario, with error analysis results presented in Reference 3-2 and produced using the TDAS-enhanced SEA program. 

The scenario used to generate the R&D GTDS simulated data is 

presented in Section 3.1, and the corresponding orbit determ1nation scenario, in Section 3.2. From the previous SEA 

error analys1s results, the dominant orbit error sources for 

the satellite considered in this study were geopotential 

uncerta1nty, clock acceleration, and TDAS ephemeris errors. 

The contributions from these error sources, found using the 

R&D GTDS simulation/orbit determination results, and their 

comparison w1th the error analysis results are discussed in 

Section 3.3. Conclusions are presented in Section 3.4. 

3.1 SIMULATION SCENARIO 

3.1.1 TDAS CONFIGURATION 

The present study considered a TDAS configuration identical 

to that used in the SEA error analysis study in Reference 3-2. The conf1guration consists of three geosynchronous satellites located at longitude 73 deg, 188 deg, 

and 318 deg east. These satellites are located relative to 

the continental United States as shown in Figure 3-1. Relay 

track1ng of the user satellite occurs through either of the 

two fronts ide TDAS relays. In addition, tracking signals 

from the ground may be relayed through the 73-deg backside 

3-1 

0112 
2 

TDAS (FRONTSIDE) 

318°E LONGITUD~ 

,...,...., ..-""'" / ....... '- / 

,... 

1 ,.....- / 

,.....- I --~~ / 

USER / 

/ 

/ 

/ 

/ 

/ 

TDAS (BACKSIDE) 

73°E. LONGITUDE 

I 

/ 

/ 

/ 

/ 

I 

/ 

/ 

/ 

/ 

Figure 3-1. TDAS Configurat1on 

3-2 

/ 

/ 

/ 

/ 

/ 
TDAS vla one of the frontside TDAS, when the target is not 

observable to the fronts ide TDASs. 

3.1.2 USER SATELLITE 

One user satellite at a 28.8-deg inclination and 600-km altltude was considered. The satelllte is considered to have 

2 

an area-to-mass ratio of 0.0027 meters per kilogram 

(m2/kg). This spacecraft orbit scenari~ is similar to 

that planned for the Space Telescope mission. A nominal 

drag coefficient of CD = 2.0 is assumed. 

3.1.3 TRACKING DATA 

The R&D GTDS one-way TDAS tracking data simulate tracking 

signals originating from the ground and relayed through the 

TDAS satellites to be received and decoded for range and 

Doppler information by the user satellite. In this simulation, range-rate Doppler data are modeled as the range difference between two consecutive integrated ranges, spaced 

10 seconds (sec) apart. To reproduce the errors present In 

the previous error analysis study, the data simulated are 

corrupted by various systematic and random errors. The 

baseline truth model used in simulating the one-way TDAS 

data is as follows: 

Description 

Geopotential 

Solar flux/atmospheric 

density 

Random measurement error 

Range 

Range-rate equivalent of 

Doppler nOlse 

Measurement biases 

Range 

Range-rate equlvalent of 

Doppler blas 

User clock error .. 

B 

0112 

Model 

2l-by-2l GEM-9 

Harris-Priester FlSO, CD = 2.0 

5 m 

5 millimeters (mm)/sec 

10 m 

1 mm/sec 

10-10 (sec/sec)/day 

3-3 
Descript~on 

TDAS ephemeris error He~ght 

Crosstrack 

Alongtrack 

25 m 

23 m 

40 m 

Model 

Two alternate tracking schedules, similar to those used in 

Reference 3-3, were considered: the broadcast or beacon 

mode, in which continuous tracking is available, and the 

scheduled mode, in which tracking is scheduled for 30 minutes (min) every orbit, cycled through the three TDAS satellites w~th a 20- to 25-min data gap in between. For 

convenience, these will be referred to as the forward-link 

beacon tracking (FLBT) and forward-link scheduled tracking 

(FLST) • 

During the tracking periods, observations were simulated at 

a rate of one pair of range and range-rate measurements 

every 20-sec (although, in the orbit solutions, the observation weights were adjusted to result in a range-rate solution). The user satellite is sometimes visible to two TDAS 

satellites simultaneously. To be consistent with the error 

analysis study, it was assumed that the user satell~te is 

tracked through one TDAS satellite and then switched to the 

next TDAS satellite when the first one leaves the user's 

field of view. In contrast with previous studies (References 3-1 and 3-4), no attempt was made to minimize tracking 

through the backside TDAS. The FLBT and FLST tracking 

schedules used are shown in Table 3-1; it is identical to 

that used in the error analysis study in Reference 3-2. 

3.2 ORBIT DETERMINATION SCENARIO 

An extended Kalman f~lter (EKF) orbit determination solution 

was used to reduce the simulated data discussed above. In 

th~s solution, the variables estimated were the position and 

velocity vectors, an effective atmospheric drag coefficient . (PI)' and the bias and drift of the onboard clock (B and B). 

3-4 

0112 
Table 3-1. Tracking Schedules for 600-Kilometer-Altltude, 

28-Degree-Inclinatlon User Satellite 

FORWARD-LINK BEACON TRACKING FORWARD-LINK SCHEDULED TRACKING 

TDAS1 TDAS2 TDAS3 TDAS1 TDAS2 TDAS3 

0-3 64-95 3-64 100-110 65-75 5-15 

95-132 166-200 132-166 205-215 170-180 135-145 

200-236 269-305 236-269 305-315 270-280 240-250 

305-340 372-408 340-372 410-420 375-385 340-350 

408-444 475-510 444-475 510-520 480-490 445-455 

510-547 580-612 547-580 615-625 580-590 550-560 

612-650 684-715 650-684 720-730 685-695 655-665 

715-753 788-819 753-788 820-830 790-800 755-765 

819-856 890-924 856-890 925-935 895-905 860-870 

924-960 993-1028 960-993 1030-1040 995-1005 960-970 

1028-1064 1096-1131 1064-1096 1135-1145 1100-1110 1065-1075 

1131-1168 1200-1234 1168-1200 1235-1245 1200-1210 1170-1180 

1234-1271 1304-1336 1271-1304 1340-1350 1305-1315 1275-1285 

1336-1375 1409-1439 1375-1409 1410-1420 1375-1385 

1439-1440 

3-5 
1he following state process noises were 1ntroduced: between 

measurements, the variances of the velocity components in-

-10 

crease at a rate of 10 square meters per second cubed 

2 2 (m /sec )/seci s1m1larly, the clock drift rate var1ance increases at a rate of 10- 6 nanoseconds (nsec) per sEcond 

cubed (nsec/sec)2/sec between measurements. The complete 

base11ne offset force model is summar1zed as follows: 

Descr1ption 

Geopotent1al 

Solar flux/atmospheric 

density 

User clock error 

B (clock bias) 

B (clock drift) 

A prior1 offset in user 

satellite state (from 

truth model state) 

Model 

2l-by-2l GEM-7 

Harris-Priester F200, CD = 2.2 

10- 2 sec 

10- 6 sec/sec 

300 m in x, y, Zi (pos1tions) 

30 cm/sec in x, y, Z (velocities) 

The baseline a prior1 statistics are as follows: 

Descript10n 

A pr10r1 state uncertainty 

User H, C, L 

Orb1t H, C, L 

User 

Clock 

Bias 

Dr1ft 

Drag parameter 

Gravitational constant, GM 

Process noise 

Veloc1ty variance growth rate 

Clock dr1ft rate variance 

Standard Deviat10n 

500 m 

1 m/sec 

1 msec 

200 nsec/sec 

1 

0.25 parts per m1llion (ppm) 

10-~0 (m2/sec2)~sec 

10- 0 (nsec/sec) /sec 

3.3 SIMULATION/ORBIT DETERMINATION ERROR RESULTS 

3.3.1 GEOPOTENTIAL ERROR 

To compare the s1mulation results of this study with the 

error analysis results of the previous study, a common geopotent1al error model was chosen. The common error model, 

which can be accommodated uS1ng R&D GTDS, 1S the o1fference 

3-6 

0112 
-It 

between the 8-by-8 GEM-l and the GEM-9 truncated to 15 by 

15. In R&D GTDS, the contribution from the GEr-1-9/GEM-l difference model was determined using the following method. 

F1rst, data were simulated using the baseline version of the 

truth model except that the geopotential model employed was 

the GEM-9 truncated to 15 by 15. These data were next reduced using two variations of the baseline force model. The 

first variation employed the same GEM-9 15-by-15 geopotential model used in s1mulating the data. In effect, this run 

1ncorporated no geopotential model mismatch. The second 

orbit determination run employed the 8-by-8 GEM-I, so that 

the run incorporated the GEM-9/GEM-l model mismatch. Finally, the reduced ephemeris files of the two orbit 

solutions were compared, with statistics generated on the 

user's state vector differences over time. To the extent 

that nonlinear effects can be ignored, the differences in 

the ephemeris comparisons should ar1se solely from the 

GEM-9/GEM-l model mismatch. 

Very close agreement was seen between the R&D GTDS simulation and the prev10us SEA error analysis results for geopotential errors arising from the GEM-9/GEM-l difference 

model. In the error analysis study, an FLBT maX1mum position error for the GEM-9/GEM-l difference was reported as 

38 mi in this study, 42 m was found uS1ng the simulat10n/ 

orb1t determination method discussed previously. As shown 

1n Figure 3-2, the geopotential errors display the character1st1c signature that the projections along the spacecraft 

h, C, and L directions are approx1mately the same, with the 

H projection being the smallest. In addition, the rss total 

geopotent1al error contribution is observed to be fairly 

constant in time. These observations are in agreement with 

the error signatures for the GEM-l/GEM-9 errors found from 

the SEA error analysis results. 

3-7 

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User Orbit Plane as Determined From R&D GTDS FLBT Slmulatlon (1 of 3) 

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User Orbit Plane as Determined From P&D GTDS FLBT Simulation (2 of 3) 

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1 
3.3.2 CLOCK ACCELERATION ERROR 

The clock acceleration error was determined uS1ng the fol10w1ng method. Data were first simulated using the base11ne 

truth model and reduced with the baseline force model; a 

converged user ephemeris file was then generated. Next, 

data were again simulated, using the same tracking schedule, 

but the baseline truth model was modified to exclude user 

clock acceleration offset. These simulated data were then 

reduced, using the same base11ne force model as before, and 

a converged ephemeris file was generated. As the f1nal step 

in determining the user clock accelerat10n error, the differences between these two user ephemeris f1les was calculated. 

Very good agreement was found for the errors due to clock 

acceleration between R&D s1mulation and the SEA error analysis results of the previous study. In this study, a maximum 

clock acceleration error for FLBT tracking was 26 m; in khe 

previous study, the maximum observed was 30 m. In the error 

analysis study, it was observed that the clock accelerat10n 

error contribution to the range-rate measurement error increases with elapsed time and is generally linear and in the 

spacecraft alongtrack direction. This study's simulation 

runs, Wh1Ch are range-rate solutions, are in agreement with 

those observat10ns. 

It should be noted that the present study's R&D solution 

used an EKF, whereas the prev10us study used a Kalman Filter 

(KF) ~l Even with this difference, the s1mulat10n and 

error analys1s results show agreement 1n the interaction 

IThe EKF, a variation to the KF, differs in that the solvefor state vector is corrected at each observation instead of 

wait1ng until the last observation. Descriptions of the EKF 

and KF in terms of the1r 1mplementation in R&D GTDS are provided in Reference 3-5. 

3-11 

0112 
between clock process noise and clock acceleration error 

observed. The R&D GTDS FLBT results are 26 m compared with 

SEA's 30 m for clock acceleration error. Figure 3-3 displays ephemeris comparison plots of the contribution of acceleration error resulting from the R&D GTDS FLBT ~ode. 

In addition, simulation and error analysis runs display consistent results if clock drift process noise is not used to 

compensate for clock errors in the filter. In SEA, when 

clock drift process noise is absent, clock acceleration 

causes an error reaching 200 m in an FLBT range-rate orbit 

solution after 24 hours. In R&D GTDS, simUlations under the 

same scenario give a similarly inflated clock acceleration 

error of 132 m. 

3.3.3 TDAS EPHEMERIS ERROR 

R&D GTDS and SEA use slightly different TDAS ephemeris error 

modeling initialization. As described in Reference 3-1, the 

satellite ephemeris error model present in SEA is used in 

R&D GTDS for TDAS satellites. A description of this ephemeris error model and its input is presented in Reference 3-5. In the R&D GTDS 1mplementation, to allow the 

greatest flex1bility possible, the input phase angles 8 

and ~ are specified separately for each TDAS relay. In 

contrast, in SEA, only a slngle seed--input 1nto a random 

number generator--is used to specify the phase input initialization for the up to 18 GPS satellites possible. The 

output of the SEA random number generator has been determined, but because these numbers are real and the input 

phases into R&D GTDS are integers, an error of up to 0.5 deg 

can occur. This input mismatch can result in small inconsistenc1es between R&D GTDS and SEA ephemeris error contribut1ons. In the case of small phase angles, this mismatch 

is enlarged because of the trigonometric functions involved. Nevertheless, close agreement 1S seen between the 

3-12 

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861101 30000 

EPHEM FILE ON UNIT 24. DATA RECORDS START AT 861101 0 

EPHEM FILE ON UNIT 81. DATA RECORDS START AT 861101 0 

USER'S NOTES 

Figure 3-3. User Clock Acceleration Error Projections in the User Orblt Plane as 

Determined From R&D GTDS FLBT Simulation (1 of 3) 

16 
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861101 30000 

EPHEM FILE ON UNIT 24, DATA RECORDS START AT B61101 0 

EPHEM FILE ON UNIT BI, DATA RECORDS START AT B61101 0 

USER'S NOTES 

Figure 3-3. User Clock Acceleration Error Projections in the User Orbit Plane as 

Determined From R&D GTDS FLBT Simulation (2 of 3) 

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861101 30000 

EPHEM FILE ON UNIT 24, DATA RECORDS START AT 861101 0 

EPHEM FILE ON UNIT 81, DATA RECORDS START AT 861101 0 

USER'S NOTES 

Figure 3-3. User Clock Acceleration Error Projections in the User Orbit Plane as 

Determined From R&D GTDS FLBT Simulation (3 of 3) 

18 
simulation and error analys1s results for the contr1but1on 

of TDAS ephemeris error. 

In R&D GTDS, the method of determin1ng the contr1bution to 

TDAS ephemeris error is similar to that used 1n determin1ng 

clock acceleration error. Specifically, instead of using 

the baseline truth model without clock acceleration, data 

are simulated without TDAS ephemeris error. The data are 

reduced using the baseline force model, and the converged 

ephemer1s is then compared with an ephemeris generated using 

the baseline truth and force models. 

From SEA, the contribution from TDAS ephemeris error is 

23 m; from R&D GTDS simulation results for the FLBT mode, 

this error is 19 m. The ephemeris error, as shown in Figure 3-4, has its largest contribution in the alongtrack direction where 1t increases rapidly at first but then appears 

to saturate or display very slow growth. Similar signatures 

are seen in the SEA error analysis results. 

3.3.4 ERROR RESULTS WITH LESS FREQUENTLY SAMPLED DATA 

Previous error analysis results show that systematic error 

is the dom1nant error source. Little performance degradation would therefore be expected if the tracking data are 

reduced by sampling. Error analysis results also indicate 

that there is very little d1fference in nav1gation performance if tracking data are sampled and processed at 3-min 

intervals instead of the 20-sec intervals used in the baseline scenar10. This observation is similarly verified in 

this study's simulation results. In varying the sample 

rate, the observation we1ghts must, however, be properly 

scaled to offset the increase in the navigation error covariance resulting from the rarefied tracking data. Alternately, as employed in the SEA error analys1s study, the 

change in sample rate may be compensated for through scaling 

the process n01se. 

3-16 

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861101 30000 

EPHEM FILE ON UNIT 24, DATA RECORDS START AT 861101 0 

EPHEM FILE ON UNIT 81, DATA RECORDS START AT 861101 0 

USER'S NOTES 

Figure 3-4. TDAS Ephemeris Error Projections in the User Orbit Plane as 

Determined From R&D GTDS FLBT Simulation (1 of 3) 

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B61101 30000 

EPHEM FILE ON UNIT 24, DATA RECORDS START AT B61101 0 

EPHEM FILE ON UNIT BI, DATA RECORDS START AT B61101 0 

USER'S NOTES 

Flgure 3-4. TDAS Ephemeris Error Projections in the User Orbit Plane as 

Determined From R&D GTDS FLBT Simulation (2 of 3) 

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861101 30000 

EPHEM FILE ON UNIT 24, DATA RECORDS START AT 861101 0 

EPHEM FILE ON UNIT 81, DATA RECORDS START AT 861101 0 

USER'S NOTES 

Figure 3-4. TDAS Ephemeris Error Projections in the User Orbit Plane as 

Determined From R&D GTDS FLBT Simulation (3 of 3) 

18 
3.3.5 COMPARISON BETWEEN FLBT AND FLST TRACKING MODES 

In agreement with the SEA error analysis results, this 

study's FLST simulation results displayed navigation performance infer10r to that in the FLBT mode. ~able 3-2 contrasts the error contributions in the two modes and their 

comparison with the results obtained from the SEA error 

analysis. The error analysis and simulation results display 

the same 1ncreasing trend in geopotential error contribution 

from FLBT to FLST mode. R&D and SEA results also show that 

clock acceleration error is reduced in the FLST mode. 

As discussed in the error analysis study, caution must be 

exercised in comparing FLST and FLBT results directly because the two modes have different amounts of tracking but 

nonetheless use the same baseline process noise. In addition, in comparing R&D GTDS simulation results with the previous SEA error analysis results, a certa1n amount of caution 

must be exercised because R&D GTDS employs an EKF whereas 

SEA uses a KF. The difference in processing between the two 

types of filters may cause some of the differences between 

the error analysis and simulation results, specifically the 

errors seen for TDAS ephemeris. 

3.4 CONCLUSIONS 

Surpr1sing agreement is seen between R&D GTDS simu1at10n results and SEA error analysis results for a 600-km altitude 

and 28-deg-inc1ination spacecraft for both the FLST and FLBT 

modes. The agreement is a conf1rmat1on of the error analysis results and provides confiaence in the methods used in 

the SEA error analysis program and the meaningfulness of its 

results. Because it directly parallels the actual orbit 

determination process, there is no direct substitution for 

the method of simulation and orbit determination used 1n 

this study. In comparison to SEA, simulation systems such 

as R&D GTDS are much larger and more env1ronmenta11y 

3-20 

0112 
Table 3-2. Navigation Error Comparison Between R&D GTDS 

Simulation and Previous SEA Error Analysis 

Results 

MAXIMUM POSITION ERROR (m) 

DURING 24 HOURS OF NAVIGATION 

FOR TWO TRACKING MODES 

ERROR SOURCE FLST FLBT 

SEAa R&D GTDS SEAa R&D GTDS 

20 180 20 20 180 

SEC SEC SEC SEC SEC 

GEOPOTENTIAL (GEM-9/GEM-l 

DIFFERENCE MODEL) 63 872 935 38 422 

CLOCK ACCELERATION 17 148 148 30 243 

TDAS EPHEMERIS 23 208 214 23 155 

aSEA RESULTS WERE REPORTED FOR ONLY THE 20-SEC OBSERVATION SAMPLING FREQUENCY 

bRUN WAS NOT PERFORMED 

3-21 

20 

SEC 

b 

256 

186 
dependent, and so they are inherently more difficult to use 

and are computationally more expensive. The consistency of 

th~s study's simulation results with previous error analysis 

would therefore suggest that, after suitable calibration 

between simulation and er~or analysis has been ensured, efficiency of effort may be obtained in performing the majority of the navigation analysis with an error analysis 

program such as SEA. 

3.5 REFERENCES 

3-1. Computer Sciences Corporation, CSC/TM-84/6077, Trackin and Data Ac uisition S stem/Global Positioning 

System (TDAS GPS) Navigat~on Analysis, E. Se~fert and 

P. R. Pastor, September 1984 

3-2. --, CSC/TM-84/6161, Satellite Orbit Determination 

USing Tracking and Data Acquisition System/Global Positioning System, P. R. Pastor, December 1984 

3-3. Stanford Telecommunications Inc., STI/E-TR-25066, 

Tracking and Data Acquisition System (TDAS) for the 

1990's, B. Elrod, A. Jacobsen, R. Cook, and R. Singh, 

May 1983 

3-4. Computer Sciences Corporation, CSC/TM-83/6138, Trackin and Data Rela Satellite S stem/Global Positionin 

System (TDRSS GPS) NaVigation Analysis, E. Seifert and 

M. Mallick, September 1 83 

3-5. --, CSC/SD-84/6057, Sequential Orbit-Determination 

Error Analysis Program (SEA) Programmer's Reference 

and User's Guide (Rev~sion 1) Volume 1, P. R. Pastor, 

December 1984 

3-22 

0112 
SECTION 4 - LUMPED GEOPOTENTIAL MODEL FOR GEM-9 

The follow1ng spherical harmonic representation of the geopotential is generally recognized as the most convenient for 

orbital analysis: 

v = ;M [1 + i; t~ -r (C 1m cos rnA 

where 

+ s ~m sin rnA) J 

( 4-1) 

GM = geocentric gravitational constant 

= mean equatorial radius of the Earth 

normalized associated Legendre funct10n of 

degree ~ and order m 

r, ~, A = distance to the center of the Earth, latitude, a~d longitude 

C~m' S~m = normalized spherical harmonic coefficients 

The quantity GM provides a scale for the whole field; a 

e 

provides a scale for the altitude dependence, r; and C~m and 

S~ characterize the geographic, or nonspherical, variat10ns. A geopotential model is defined by these parameters. Of necessity, the field is truncated at some finite 

degree and order. Over the years, NASA/GSFC has developed a 

series of progressively more accurate GEMS based on satellite tracking data, satellite-borne altimetry, and surface 

gravimetry. GEM-lOB (Reference 4-1), complete to degree and 

order 36 by 36, is currently the most accurate model. The 

Goddard Trajectory Determination System (Reference 4-2) , 

which is used for operational orbit determination at GSFC, 

has provisions for GEM-9 (Reference 4-3) further truncated 

to degree and order 21 by 21. 

4-1 

0112 
Even with accurate geopotential models such as GEM-9 and 

GEM-lOB, the uncertainty in these models remains a major 

error source for low-altitude Earth satellite orbit determination. Geopotential error arises because of truncatlon 

(omlsslon error) and because of errors in the spherical harmonic coefficients (commission error). Generally, with the 

derivation of a GEM, an error covariance matrix descr~bing 

the uncertainties and correlations of the spherical harmonlc 

coefficients is a standard byproduct. In prlnciple, it 

woule be straightforward to use this covariance matrix in 

linear error analysis to compute the effect of commission 

error on satellite orbit determination accuracy. However, 

the size-of the covariance matrlx makes this approach prohibitively expensive in computations. 

As a simpler alternative, a so-called lumped geopotential 

error model was suggested (Reference 4-4) and implemented in 

orblt determination error analysis programs. Briefly, this 

approach takes the weighted differences of the geopotential 

coefficients of two independent geopotential models and computes the orbit determination error resulting from the 

lumped effect of these differences. Subsequently, standard 

deviations, which are the scaled-up formal uncertainties of 

GEM spherical harmonic coefficients, were used in place of 

the coefficient differences. The theoretical objection to 

the us~ of standard devlations was first raised in Reference 4-5. Its practical inadequacy was brought out in ViVld 

graphical displays in Reference 4-6. 

Section 4.1 descrlbes the rationale of the lumped geopotentlal error model. Section 4.2 discusses the global eistrlbution of gravity error for different geopotentlal error 

models. Sectlon 4.3 discusses navigation and orbit prediction errors introduced by geopotentlal uncertalnty. Section 4.4 compares results obtained using TDRS data with 

4-2 

0112 
those from the lumped geopotential error model for GEM-9. 

Section 4.5 presents conclusions. 

4.1 THE LUMPED ERROR MODEL 

The derivat10n of each GEM 1S always accompanied by a careful error analysis to assess its accuracy. Reference 4-7 on 

GEM-7 and GEM-8 is an outstanding example of the conscientiousness and thoroughness associated with such assessments. Analyses of GEM-9 and GEM-10 accuracies are available 

in References 4-3 and 4-1, respectively. Reference 4-8 contains a discussion of gravity model improvement and its implications for operational orbit determination. 

As d1scussed before, each GEM is accompanied by an error covariance matrix associated with the geopotential coefficients. The covariance matr1x 1S computed based on assumed 

precisions of tracking and other data from which the geopotential is derived. Because not all error sources in 

tracking data and in spherical harmonic coefficient estimation methods can be accounted for, the computed error covariance is not a true indication of the accuracy of the 

spher1cal harmonic coefficients. Part of the objective of 

geopotential model accuracy analysis 1S to derive a calibration factor, which is used to scale up the standard deviations from the error covariances to more realistic levels. 

The cal1bration factor is typically around 3.3. 

One of the obvious methods of assessing a geopotential model 

is to compare it with other independently der1ved geopotential models. The lumped geopotential error model, first 

proposed by Martin and Roy (Reference 4-4), takes one-half 

the differences of two uncorrelated models of comparable 

accuracy as a measure of the accuracies of the individual 

models. The rationale can be explained as follows. Let 

c~ ) and (c~ ) be the geopotential coeff1-

m model A m model B 

cients of the two models. If the two models are uncorrelated 

4-3 

0112 
but of comparable accuracy, their average 1S closer to the 

truth, Le., 

. (4-2) 

and an est1mate of the individual errors can be obtained as 

(~Cim)model A = (C~m)model A - (C~m)truth (4-3) 

.. ~ [(C~m)mOdel A - (C~m)mOdel BJ 

Of course, an estimate using the sample mean based on only 

two samples, as in Equation (4-3), is not very reliable. 

The lumped model introduces additional samples or statistics 

by cons1dering not a single C~m but the whole set of C~m's 

and Sim's in the geopotential model. In other words, it is 

not say1ng that ~Cim as given in Equation (4-3) is a good 

ind1cator of the accuracy of individual coefficients, but 

that the aggregate effect of all ~C~m's on the computed 

orbit is a reasonable representation of the effect of the 

geopotential uncertainty on orbit determination. 

The key assumption of the lumped model is the requirement 

that the two models be uncorrelated. Th1S generally means 

that the models be derived by two different organizat1ons 

based on different data sets. It also implies that this 

lumped model does not adequately represent omission errors. 

The assumption that the two models are of equal accuracy is 

not essential, as the s1mple average in Equation (4-3) can 

be replaced by a weighted average. In the spirit of min1mum 

variance estimators, the weights can be chosen to be 1nversely proportional to the var1ances of the 1nd1vidual 

4-4 

0112 
, .. 

models. In practice, an educated guess or external calibration can be used to assign the weights. 

The lumped model has been used in many orbit determination 

error analysis studies, perhaps not so much because it is a 

good model but because nothing better is available. Part of 

the difficulty of this approach is the availability of 1ndependent models. In a study (Reference 4-9) of onboard orbit 

determination using GEM-9 truncated to various degrees, it 

was suggested that the lumped model be used to represent the 

uncertainty in the truncated GEM-9 as follows: GEM-9 standard dev1ations would be used to represent the uncertainties 

of those spherical harmonic coefficients retained in the 

truncated model, and truncation errors would be represented 

by the truncated high degree and order GEM-9 spherical harmonic coefficients themselves. There are two theoretical 

objections (Reference 4-5) to the use of standard deviations 

instead of coefficient differences in the lu~pe~ model: 

• The errors in the geopotential coefficients are 

likely to have both positive and negative signs, 

whereas the standard deviations are all positive. 

• The standard deviations do not contain information 

about correlations among the coefficients. 

It may be argued that, because the primary 1nterest 1S in 

orb1t determination errors, rather than in the errors in the 

geopotential coeff1cients, the use of the positive standard 

deviations may not be objectionable 1f the orbit error sensitivities to these coefficients are randomly distributed to 

serve to randomize their aggregate effect. Elrod, however, 

showed that this is not the case (Reference 4-6). Figure 4-1, reproduced from Reference 4-6, shows that the use 

of GEM-9 standard dev1ations results in a nonuniform global 

distribution of gravitational accelerat10n errors that is 

greater in the Northern Hemisphere with a singularity near 

4-5 

0112 
-, 

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ORIGINAL PAGE IS 

Of POOR QUALJTY 

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o deg longitude and 60 deg latitude. Such anomalous distribution is not supported by other evidence. Furthermore, 

Elrod showed that the anomaly does not occur if the rss result is obta1ned rather than the algebraic sum of the lumped 

error model. There is no question that the use of GEM-9 

standard deviations in the lumped error model is faulty. 

The effect of false singularity is perhaps not serious for 

error analysis of the batch orbit determinat10n method, but 

it can exaggerate local navigation errors in sequential 

navigation methods. 

Because the standard deviations do not convey information 

about correlations, an obvious alternative is to assume that 

all errors in the spherical harmonic coefficients of a geopotent1al are uncorrelated. The total error of the geopotential model can thus be obtained as the rss of the error 

contribution of individual coefficients. Although it is 

known that certain geopotential coefficients are highly correlated, this model is perhaps as reasonable as any, short 

of hav1ng to consider the actual correlations. The major 

drawback of this model is the excessive amount of computation required to compute separately the error contr1but1ons 

of 1ndividual error coefficients, versus the spirit of the 

lumped error model. At best, only the level of orb1t determination error resulting from geopotential uncertainty can 

be expected; therefore, the computationally expensive rss 

approach may not be justifiable, and simpler alternatives 

would be desirable. The following alternatives are proposed 

as candidates for study: 

• Random-S1gn Method--The lumped model will use the 

GEM-9 standard deviations, with positive and negative signs 

randomly assigned to them. 

4-7 

0112 
• Random-Phase Method--The terms involv1ng the spherical harmonic coefficients in the geopotential representation, Equation (4-1), may be written as 

Cn cos rnA + Sn sin rnA = ~C~ + S~ cos (rnA - ¢ ) Jfvm Jfvm Jfvm Jfvm m (4- 4) 

In this method, the amplitudes 

are computed from GEM-9 standard deviations, but the phase 

angles, ¢ , are selected from a uniform random distribut10n 

m 

between 0 and 2TI (for zonals, the phase is randomly chosen as 

o or TI, i.e., random sign). 

In addit10n to these models dependent on internal accuracy 

estimates, two geopotent1al models uncorrelated w1th GEM-9 

are used in conjunction with GEM-9 to form geopotent1al difference error models. One of these is the 1969 Smithsonian 

Astrophys1cal Observatory (SAO) Standard Earth (Reference 4-10), referred to as the SAO model below. The other 

will be referred to as the MDl model. One-half of the difference of this model and GE~-S has been considered representative of the accuracy of GEM-S (Reference 4-11). Both 

the SAO and MDl models are inferior to GEM-9 in accuracy. 

4.2 GLOBAL DISTRIBUTION OF GRAVITY ERROR FOR DIFFERENT GEOPOTENTIAL ERROR MODELS 

The gravitational acceleration as specif1ed by a geopotential model will have errors that vary w1th the geographical 

location (long1tude and latitude) and decrease with the altitude. A gravity error map such as that 111ustrated in 

F1gure 4-1 shows the magnitude (but not the direction) of 

4-8 

0112 
the gravitational acceleration error at a given altitude as 

a functlon of longitude and latitude, as predicted by a geopotentlal error model. Different error models give rise to 

different error characteristics. Of interest are orders of" 

magnitude a~d geographical fluctuations of the errors. Figures 4-2 through 4-22 are gravity error maps at 200-, 400-, 

and GOO-km altitudes for the following geop?tential error 

models: 

• GEM-9/MDI one-half difference model 

• GEM-9/SAO one-half difference model 

• GEM-9/GEt-1-5 dlfference model 

• GEM-5/MD-l one-half difference model 

• GEM-9 standard deviation model 

• GEM-9 random sign model 

• GEM-9 random-phase model 

• GEM-9 uncorrelated model 

The difference models, discussed in Section 4.1, are selfexplanatory. The GEM-9 standard devlation model uses positive GEM-9 standard deviations as spherical harmonic error 

coefficients. The gravity error map for this model at 

200-km altitude is shown in Figure 4-1, so only the maps at 

400- and GOO-km altltudes are shown here. The random-slgn 

and random-phase models are also explalned in Section 4.1. 

A number of variants of these models were also considered, 

but they did not show slgniflcant difference from those described here. The uncorrelated model is based on the rss of 

the contrlbutions of indivldual coefflcients; computing these 

errors is expensive, and the gravlty error maps were taken 

from Reference 4-G. To provide a reference for gauging the 

magnitudes of gravlty errors, Flgure 4-23 shows a map representing the gravltational acceleration (not the error) resulting from the nonaxisymmetrlc (i.e., the nonzonal) portion 

4-9 

0112 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL ACI'EL ERA TION {"'GALl <LA T> 

90 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 

85 2 2 :3 :3 4 5 5 5 6 6 6 5 5 4 4 :3 :3 :3 :3 :3 4 5 5 6 6 6 6 6 6 6 5 5 4 :3 :3 2 2 

80 :3 :3 4 5 6 7 7 6 6 5 5 5 4 4 :3 :3 2 2 2 :3 :3 4 4 4 5 5 5 5 5 4 :3 2 :3 :3 4 4 :3 

75 4 4 6 8 10 10 10 8 6 4 3 3 3 4 4 :3 2 2 :3 4 4 4 :3 ..J 4 5 6 5 5 :3 2 2 :3 4 4 4 4 

70 4 3 4 7 9 9 8 7 5 5 4 3 I 3 4 4 2 2 2 3 4 5 5 4 4 4 5 6 5 4 2 4 5 5 4 4 4 

65 4 4 5 9 10 7 :3 2 4 6 6 3 2 4 7 7 4 3 :3 :3 4 6 6 4 I I :3 6 8 6 :3 4 5 5 4 3 4 

60 5 6 6 7 8 5 4 :3 4 5 5 5 4 :3 6 6 6 5 5 6 6 6 5 4 2 2 4 7 9 8 6 5 4 2 :3 3 5 

55 5 5 5 2 5 2 4 5 2 5 5 6 4 2 4 :3 6 5 6 7 9 6 5 4 2 2 6 9 7 6 7 3 4 2 2 3 5 

50 4 5 2 2 5 4 4 4 2 5 4 6 6 4 4 3 6 3 5 7 7 4 5 I :3 3 6 10 5 3 6 3 4 4 2 3 4 

45 5 5 2 4 4 :3 :3 5 6 8 2 6 6 3 4 5 10 5 6 7 4 2 5 3 4 3 8 7 2 I 4 2 4 4 :3 3 5 

40 • [; :3 2 7 7 6 5 5 8 10 3 4 7 3 4 5 9 :3 5 6 3 2 5 3 4 4 6 4 5 6 4 4 8 7 7 2 5 

35 • 5 4 2 6 7 6 6 5 5 9 2 3 6 3 3 3 10 4 6 6 2 I 5 3 5 3 3 4 7 6 3 5 10 6 5 2 5 

30 • 6 6 2 7 6 3 5 7 10 14 4 3 6 3 6 7 12 5 5 6 4 I 6 5 5 3 5 9 6 6 3 8 9 4 6 3 6 

25 + 6 8 4 7 6 6 5 6 3 16 4 5 5 3 3 4 9 4 6 5 3 4 3 3 4 2 6 12 9 9 5 10 9 3 5 2 6 

20 • 8 10 6 7 5 6 5 6 4 14 7 5 2 4 5 8 10 4 7 6 4 5 5 5 5 2 9 17 II 13 7 14 II 4 5 4 8 

15 + 10 14 9 7 3 7 5 5 5 16 10 5 2 5 6 8 9 5 10 I 6 9 9 9 7 4 13 23 14 16 12 14 13 8 8 7 10 

10 + 12 15 11 7 5 8 6 7 7 14 10 6 2 4 4 6 6 10 10 3 2 12 14 13 9 5 15 24 18 17 16 14 16 9 12 8 12 

5 • 12 18 13 8 7 9 8 9 9 13 8 6 2 4 4 6 7 12 12 4 4 15 20 16 15 7 16 25 19 17 17 15 16 10 13 II 12 

0 + 11 20 14 9 6 10 10 8 10 13 6 6 4 4 5 7 8 12 11 3 6 20 24 20 18 13 18 26 20 15 14 16 15 13 10 12 11 

""" -5 + 10 16 12 8 6 10 10 8 10 10 7 4 4 3 3 6 7 12 10 4 7 19 23 2 I 18 15 18 23 18 11 8 12 14 10 8 12 10 

I - 10 8 14 11 7 5 9 9 8 9 9 7 3 3 I 2 4 6 10 10 5 10 20 22 22 10 16 18 2 I 15 9 4 10 13 7 7 9 8 ........ - 15 5 9 9 6 4 7 8 9 6 8 6 4 4 2 2 3 6 9 7 3 8 16 18 20 17 15 17 19 II 6 7 8 10 5 5 6 5 

0 -20 4 4 6 5 4 5 8 9 3 7 6 4 3 2 3 2 5 7 6 6 9 11 16 18 13 12 14 13 10 5 9 5 7 4 3 3 4 

-25 3 1 5 5 5 3 6 8 3 6 6 3 3 4 3 2 5 4 4 5 8 7 13 14 9 10 10 9 10 4 7 4 5 1 3 3 3 -30 3 4 4 4 5 :3 6 9 :3 6 5 I 3 4 2 2 4 2 2 2 6 4 8 11 5 8 7 6 6 2 6 4 5 3 2 3 :1 -35 2 3 2 3 6 4 4 6 2 4 4 1 3 4 3 3 4 ;Z 1 1 5 2 5 9 4 5 4 3 4 :3 4 3 3 2 3 4 2 -40 1 3 2 2 6 6 5 6 0 5 3 2 3 5 4 5 6 4 3 2 3 3 2 8 5 I :3 2 3 5 4 :3 2 3 :3 2 1 -45 + 2 I 1 3 6 5 4 5 4 5 2 2 :3 5 :3 2 4 :3 :3 :3 3 5 5 8 5 :3 5 4 :3 5 4 3 :3 :3 2 I 2 -50 2 1 2 4 7 7 6 5 5 6 2 2 :3 7 5 4 5 :3 1 :3 3 5 5 5 3 '1 5 7 5 :3 2 4 4 3 2 2 2 

-55 :3 2 :3 4 5 8 7 :3 4 5 3 :3 3 4 5 5 6 4 3 4 4 4 3 5 :3 1 4 7 5 3 3 " 5 :3 1 :3 :3 - 60 4 4 2 :3 " 5 4 2 4 3 1 3 3 4 5 4 5 2 3 5 6 6 " 5 4 2 3 5 5 2 2 4 " :3 1 :3 d 

65 4 4 2 :3 4 5 5 4 5 4 4 6 6 5 4 3 3 3 3 5 5 4 4 5 4 2 3 5 6 4 4 5 4 3 2 3 4 

-70 :3 4 5 OJ 4 4 " 4 5 5 6 7 7 5 4 3 3 4 4 4 3 :3 3 5 6 6 5 5 5 4 " 4 3 3 3 3 :3 

-75 4 4 4 " 4 3 " 4 5 5 5 5 5 5 4 3 3 3 3 3 :3 3 4 6 7 8 7 6 4 3 4 4 4 4 4 " 4 -80 3 3 :3 :3 :3 :3 :3 :3 3 3 3 :3 :3 2 2 2 2 2 2 2 2 2 :3 .. OJ 5 5 5 5 5 6 6 5 5 " 3 3 -85 2 2 2 1 I I 1 2 2 2 2 2 2 2 2 2 2 2 2 I 1 1 2 2 :3 3 4 " 5 5 5 5 5 " :3 3 2 -90 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 '1 3 3 3 3 1 :1 1 :1 3 3 2 2 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1 -1--1--1--1--1--1--1 - 1 I - -I- 1--1--1--1- -1--1--1--1 1 - - I - I - - I -

"lONG> 0 20 40 60 80 100 120 140 160 180 200 '20 '40 2!;O 280 300 320 340 160 

Figure 4-2. GEM-9/MDl One-Half Difference Model, 200-Kilometer Altitude 
UNCERTAINTV IN NONSPHERICAL GRAVITATIONAL ACCELFRATION IMGALI 

<LAT> 

90 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 

85 I I I 2 2 2 3 3 3 3 3 3 3 2 2 2 2 I 2 2 2 2 3 3 3 3 3 3 3 3 3 2 2 2 I I I 

80 2 2 2 3 .. .. .. .. 3 3 3 2 2 2 2 I I I 1 1 2 2 2 2 2 3 3 3 2 2 I I I 2 2 2 2 

75 2 2 3 .. 5 6 6 5 3 2 2 1 1 2 2 2 1 1 1 2 2 2 2 2 2 3 3 3 2 2 I 1 2 2 2 2 2 

70 2 2 3 .. 5 5 5 .. 3 3 3 2 1 2 2 2 1 I I 2 2 3 3 2 2 2 3 3 3 2 I 2 3 3 2 2 2 

65 2 2 3 5 5 .. 2 I 3 .. 3 2 I 3 .. 4 2 2 2 2 3 3 4 2 I I 2 4 5 4 2 2 3 3 2 2 2 

60 3 3 3 .. 5 3 2 2 2 3 3 3 2 2 3 3 3 3 3 3 .. 3 3 2 I I 2 4 5 4 4 3 2 I 2 2 3 

55 3 3 2 2 3 1 2 3 2 3 3 3 2 I 2 2 3 3 3 4 5 .. 3 2 I 2 3 5 4 3 4 2 2 1 1 2 3 

50 2 3 1 I 3 I 2 3 2 3 3 3 .. 2 2 2 3 2 3 4 .. 2 3 0 I 2 4 6 3 I 3 2 2 2 1 1 2 

45 3 3 2 2 2 1 2 3 .. .. 2 3 .. 2 2 3 5 3 3 .. 2 I 2 2 2 2 4 4 2 1 2 0 2 2 2 2 3 

40 3 2 I 4 4 3 3 3 4 6 2 2 .. 2 2 3 5 2 3 3 1 I 3 1 2 2 4 3 3 3 2 2 4 4 4 1 3 

35 2 2 I 3 .. 3 .. .. 3 5 2 2 3 2 2 2 5 2 3 3 1 I 3 2 3 2 2 3 4 3 2 3 6 3 3 I 2 

30 3 3 I .. 4 2 3 5 6 8 3 2 3 2 3 .. 7 3 2 3 2 0 3 3 3 2 3 5 3 3 2 4 5 2 3 I 3 

25 .. 3 4 3 .. 4 .. 4 4 5 9 3 3 3 2 2 2 5 2 3 3 2 2 I 2 2 I 4 7 5 5 3 6 5 2 2 1 3 

20 .. 6 .. .. 4 .. .. .. 2 8 4 3 I 2 3 .. 6 2 3 3 2 ~ 2 3 3 I 5 10 7 8 5 8 6 3 3 2 .. 15 6 9 6 5 3 .. 3 4 3 9 6 3 I 3 3 .. 5 3 5 I 3 5 5 5 .. 3 8 14 9 10 8 8 8 5 5 4 6 

10 • 7 10 7 5 .. 5 4 5 4 8 6 4 2 2 2 .. 3 6 5 2 1 7 8 8 5 3 10 15 12 11 10 8 10 6 7 5 7 

5 • 8 11 9 6 5 6 5 5 6 8 5 4 I 2 3 .. .. 7 7 3 2 9 12 10 9 5 11 16 13 11 10 9 9 7 8 6 8 

0 7 12 9 6 4 7 7 5 6 8 .. .. 2 2 3 4 5 7 7 2 .. 12 15 12 II 8 12 17 13 10 9 9 9 8 6 7 7 

"'" -5 7 10 8 6 .. 7 6 5 6 6 4 2 2 2 2 .. 5 7 6 2 5 12 14 13 II 10 12 15 12 8 5 7 8 6 5 7 7 

- 10 5 8 7 5 4 6 6 5 6 6 .. 2 2 I I 3 4 6 6 3 6 12 14 I .. 12 10 II 13 10 6 2 6 7 4 4 5 5 I - 15 3 6 6 .. 3 5 5 5 .. 5 3 2 2 1 2 2 4 6 5 2 5 10 12 12 10 10 1 I 12 7 5 .. 5 6 3 3 3 3 

I-' -20 2 2 .. 3 3 3 5 5 2 4 3 3 2 I 2 I 3 .. .. 3 5 7 10 10 8 8 9 8 6 4 5 3 4 2 2 2 2 

I-' -25 2 0 3 3 3 2 4 5 2 3 4 2 2 2 2 2 3 2 3 3 .. 4 8 8 6 6 6 5 6 3 4 2 3 I 2 2 2 

-30 2 2 2 3 3 2 .. 5 2 3 3 1 2 2 I I 2 2 I I 3 3 5 6 3 5 .. 3 3 I 3 2 3 2 I 2 2 

-35 I I I 2 3 2 3 3 1 2 2 1 I 2 2 2 2 I I 1 3 I 3 4 2 3 2 2 2 I 2 2 2 I I 2 I 

-40 I I 1 2 4 3 3 3 0 2 1 1 2 2 2 2 3 2 2 1 1 I I 4 3 I 1 1 2 2 2 1 I 1 1 I I 

45 I I I 2 3 3 2 2 2 2 I 1 2 3 2 1 2 2 I 2 I 2 3 5 3 2 3 2 2 3 2 2 I I 1 I I 

-50 1 0 1 2 4 3 3 3 3 3 2 2 2 3 2 2 2 1 0 2 2 3 3 3 2 I 3 4 3 2 1 2 2 2 1 1 I 

-55 2 1 2 2 3 4 4 2 3 3 2 2 1 2 2 3 3 2 1 2 3 2 2 3 2 1 2 4 3 2 2 2 3 2 I 2 2 

-60 2 2 I 2 2 2 2 I 2 2 1 2 2 2 3 2 3 1 1 3 4 3 3 3 2 1 2 3 3 I I 2 2 2 1 2 2 

-65 2 2 I 2 2 3 2 2 3 2 2 3 3 3 2 2 2 2 2 3 3 3 2 3 3 I I 3 3 3 2 3 2 2 2 2 2 

-70 2 2 3 3 2 2 2 3 3 3 3 4 4 3 2 2 2 2 2 2 2 1 2 3 3 3 3 3 3 2 2 2 2 2 2 2 2 

-75 2 2 2 2 2 2 2 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 :1 4 .. 4 3 2 .2 2 2 2 2 2 2 2 

-80 2 I I I 2 2 2 2 2 2 2 2 2 2 2 I I I I I 1 1 2 2 3 .J 3 3 3 3 3 3 3 3 2 2 2 

-85 .. I 1 I I 1 I 1 I 1 1 1 1 I 1 1 1 I 1 I 1 1 I I 1 2 2 2 2 3 3 3 3 2 2 2 2 1 

-90 1 I 1 1 1 I 1 I 1 1 1 1 I I I 1 I 1 I I 1 I 1 I I 1 1 I 1 I I I 1 I I I 1 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1- 1--1--1--1--1--1--1--1--1--1--1--1--1---

<lONG> 0 20 40 60 80 100 120 140 160 180 200 220 7,fO 260 280 300 320 340 360 

Flgure 4-3. GEM-9/MDl One-Half Difference Model, 400-Kilometer Altitude 
UNCERTAINTV IN NONSPHERICAL GRAVITATIONAL ACCELfRATION (MGALI <LAT> 

90 I 1 I 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 I I 1 1 1 1 

85 1 I I 1 1 1 1 1 2 2 2 2 1 1 1 I 1 1 1 1 1 1 I 2 2 2 2 2 2 1 1 1 1 1 I 1 1 

80 1 1 1 2 2 2 2 2 2 2 1 1 I 1 1 1 0 0 0 1 1 1 I 1 1 1 1 1 I 1 1 1 1 1 1 1 1 

75 1 1 2 3 3 3 3 3 2 1 1 1 1 1 1 1 1 0 1 1 1 1 1 I 1 2 2 2 I 1 1 1 1 1 1 1 1 

70 2 1 2 2 3 3 3 2 2 2 2 1 0 1 1 I 1 1 1 1 1 2 2 1 1 I 2 2 2 1 I I 2 2 I 1 2 

65 I 1 2 3 3 2 1 I I 2 2 1 I 2 2 2 1 I I I 2 2 2 2 I 0 I 2 3 2 I I 2 2 1 I I 

60 2 2 2 3 3 2 1 1 I 2 2 2 1 I 2 2 2 I 2 2 2 2 2 I I I I 3 3 3 2 2 I 1 1 I 2 

55 2 2 I I 2 I 1 2 I 2 2 2 1 0 1 I 2 2 2 3 3 2 2 I I I 2 3 2 2 2 2 1 I 1 1 2 

50 I I 1 I I 0 I 2 2 2 2 2 2 1 1 I 2 I 2 2 2 I 2 0 I I 2 3 2 I 2 I 1 I 0 I I 

45 1 2 1 1 1 1 1 2 2 2 1 2 2 1 I 2 3 2 2 2 I 0 1 1 I I 2 2 I I I 1 2 1 1 I I 

40 1 1 I 2 2 2 2 2 2 3 1 1 2 1 1 1 3 I 1 2 1 1 1 1 I I 2 2 2 2 I I 3 2 2 I 1 

35 1 I I 2 2 1 2 2 2 3 1 I 2 I I 1 3 1 2 2 I 0 1 I 2 I 1 2 2 2 I 2 3 2 2 I I 

30 I 2 1 2 2 1 2 3 3 5 2 1 2 1 1 2 4 I 1 2 1 0 2 2 2 I 2 3 2 I I 3 3 I 1 I 1 

25 1 2 2 2 2 2 3 3 3 5 2 2 2 1 1 1 3 I 1 2 I I I I I 0 2 4 3 3 2 3 3 I 1 I I 

20 2 4 3 3 3 3 2 3 1 5 3 2 1 2 2 2 3 2 2 1 1 I 1 2 2 I 3 6 4 5 3 5 4 2 I I 2 

15 3 5 4 3 2 3 2 2 2 5 4 2 1 2 2 3 3 2 3 0 2 3 3 3 3 2 5 9 6 6 5 5 5 3 3 2 3 

10 4 6 5 4 3 3 2 3 3 5 4 2 1 1 1 2 2 3 3 1 1 4 5 5 3 2 6 10 8 7 6 5 6 4 4 3 4 

5 5 7 6 4 3 4 3 4 4 5 3 3 1 1 2 2 2 4 4 2 2 6 8 6 6 4 7 10 9 7 6 5 6 4 5 4 5 

0 5 8 6 4 3 4 4 4 4 5 3 2 I I 2 3 3 4 4· I 2 7 9 8 7 6 8 II 9 7 5 6 5 5 4 5 5 

~ -5 4 6 5 4 3 4 4 3 • 4 3 1 1 1 2 3 3 5 4 2 3 7 9 8 7 6 8 10 8 5 3 4 5 4 3 5 4 

I - 10 3 5 5 3 3 4 4 3 4 3 3 1 1 1 1 2 3 4 4 2 4 7 9 9 8 6 7 9 7 4 I 3 4 3 3 3 3 

...... - 15 2 4 4 3 2 3 4 3 3 3 2 I 2 I I 2 4 3 I 3 6 7 8 7 6 7 8 5 4 3 3 J 2 2 2 2 

N -20 I 2 J 2 2 3 J J I 2 2 2 2 I I 2 J 2 2 J 4 6 6 5 5 6 5 4 J J 2 2 I I I I 

-25 1 0 2 2 2 2 3 3 1 2 2 1 1 1 1 1 2 2 2 2 3 5 5 4 4 4 3 3 2 3 1 1 0 1 I I 

-30 I I 2 2 2 I 2 J I 2 2 I I I 1 I I I I 2 2 3 J 2 3 2 2 2 I 2 I I I I I 

-35 I I I 1 2 1 2 , I 0 I 1 1 1 I I 1 1 1 I 2 I 2 I 1 I I I 1 I 1 I 1 

-40 0 I I 1 2 2 1 I u I 1 1 1 1 1 2 I 1 1 I I I 2 2 I 0 1 1 1 I 1 I I I 0 

-45 I I I I 2 I I I I I 0 1 I I 1 I I 1 1 I I 2 J 2 I I I I I I I I 0 I I 

-50 1 0 1 1 2 2 2 2 2 2 1 1 1 2 1 1 0 0 1 I 2 2 2 I I I 2 2 1 1 1 I 0 1 1 

-55 1 0 I I 1 2 2 I 2 2 1 1 I 1 I 2 1 1 1 2 I I 2 I 0 1 2 2 1 I I 2 0 I I 

-60 I I I I I 1 1 1 1 1 0 I 1 I 2 I I I 2 2 2 2 2 2 I I 2 2 I 0 I I I I 1 

-65 I I 1 1 1 1 1 I 2 I 2 2 2 1 1 I I 2 2 I 2 2 2 I I 2 2 I I 2 2 I 1 1 

-70 1 1 1 I 1 I 1 2 2 2 l 2 2 2 2 1 2 1 1 1 I I 2 2 2 2 2 2 1 I 1 I 1 2 I 

-75 I I I I 1 I 2 2 2 2 2 2 2 2 2 1 I 1 I 1 I I 2 2 2 2 2 I I I I I 2 2 I 

-80 I I I 1 I I 1 I I 1 1 I 1 1 1 I 1 1 1 1 I I I 2 2 2 2 2 2 2 2 2 I I I 

-85 1 0 0 0 0 0 0 I I I 1 1 I 1 I I I 1 0 0 0 I I I I I I I I I I I I I I 

-90 1 I I I I 1 I I I I 1 I I I I I I I I I I I I 1 1 I I I I I 1 I I I I 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1-- --1--1--1--1--1--1--1- -1--1--1--1--1--1--1--1--1-- --1--1--1---

"LONG> 0 20 40 60 80 100 120 140 160 180 200 220 '40 260 280 300 320 340 360 

Flgure 4-4. GEM-9/MDl One-Half Difference Model, 600-Kilometer Altltude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL ACCELERATION IMGAL) <LilT> 

90 + 4 4 4 .. 4 4 4 4 4 4 4 4 4 4 .. .. .. .. .. .. .. 4 .. 4 4 4 .. 4 .. .. 4 .. 4 4 4 4 4 

85 + 3 3 3 3 3 4 4 4 5 5 5 5 5 4 .. 4 3 3 3 3 3 4 .. 4 5 5 5 5 4 4 4 4 3 3 3 3 3 

80 + 2 I I I 2 3 3 4 .. 5 5 4 4 4 3 2 1 1 1 2 3 3 .. .. 4 5 5 5 5 4 4 3 2 2 2 2 2 

75 2 I I I 2 3 4 5 5 4 3 2 3 3 3 3 2 2 2 3 4 3 3 2 I 3 4 5 5 5 4 3 2 2 2 2 2 

70 3 2 2 2 3 .. 5 6 6 5 4 .. 4 5 5 .. 3 2 2 3 .. 4 3 3 3 4 5 6 6 6 5 5 4 4 3 3 3 

65 + 3 2 2 2 2 3 3 .. 4 6 9 9 8 6 5 4 .. 2 0 2 3 .. 4 5 5 5 5 6 6 5 5 6 6 6 4 3 3 

60 + 2 2 I 2 2 2 2 2 3 5 9 11 9 8 6 6 6 5 2 2 3 .. 5 6 6 5 5 5 4 4 4 7 8 7 5 3 2 

55 2 2 .. 5 3 2 2 2 3 3 6 8 7 8 8 7 7 6 .. 3 3 3 5 5 5 4 5 6 5 2 5 7 8 6 4 4 2 

50 4 3 6 8 3 3 4 4 .. 5 4 4 .. 6 8 7 6 5 .. .. 2 2 4 " 4 3 4 6 5 3 6 7 6 3 4 5 4 

45 7 4 5 8 5 4 6 7 8 10 5 3 2 3 7 7 5 4 5 .. 3 I 2 4 4 3 3 4 4 4 5 7 6 2 4 6 7 

40 8 4 3 6 6 4 6 9 10 13 7 3 3 2 6 5 .. 7 7 .. 2 2 1 2 3 3 3 2 3 4 2 5 5 2 2 6 8 

35 + 7 5 4 6 5 5 4 7 9 10 6 4 4 4 7 5 4 7 6 3 2 2 2 2 2 2 3 I 2 3 I 5 4 2 I 4 .. 7 

30 • 6 4 4 6 5 7 4 3 7 7 3 3 .. .. 7 6 3 7 .. 2 2 2 3 3 2 2 2 3 2 6 2 7 4 3 3 3 6 

~!i 25 + 5 2 4 6 3 5 3 2 5 6 4 3 3 2 .. 4 .. 5 2 3 3 2 3 3 I 2 2 4 4 6 2 7 5 5 6 3 5 

20 3 3 3 8 5 7 4 3 6 7 4 3 2 3 2 .. .. 4 3 2 .. 2 3 4 2 I I 3 5 5 3 4 5 6 7 3 3 

10 

15 

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3 

3 

5 

4 5 8 

4 8 3 

3 8 5 6 

7 5 5 7 

7 

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3 

5 

3 

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6 3 3 2 

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7 

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2 4 3 - 5 2 2 g§ 4 10 6 9 5 6 9 5 3 3 5 3 3 5 5 4 I I I 2 3 9 6 3 2 4 4 7 6 3 4 I 3 3 2 

0 2 2 2 10 6 7 4 5 9 5 4 3 3 2 5 6 5 4 2 2 3 2 5 8 7 4 3 5 5 8 7 3 4 3 3 2 2 ~ -5 5 3 3 7 4 8 5 6 7 5 5 3 3 2 5 5 .. 3 3 2 3 3 5 6 6 5 6 6 6 7 6 4 3 2 I 3 5 ::0..- I - 10 7 5 3 6 7 10 6 6 7 5 4 3 3 4 4 .. 2 3 5 4 2 I 3 4 4 5 8 6 7 7 5 4 2 3 3 4 7 

t-' - 15 5 4 4 6 8 8 5 5 6 5 3 4 4 4 4 5 3 4 6 4 3 0 4 4 3 4 9 5 7 6 3 3 3 5 5 5 5 

W -20 4 3 5 5 6 4 4 4 4 4 I 4 5 3 4 5 5 4 5 4 5 3 6 6 2 4 9 4 5 3 I 4 4 5 6 6 4 -g;g -25 4 2 4 5 4 3 2 3 2 4 3 4 6 3 2 3 5 4 3 5 9 7 8 7 I 3 5 3 3 2 I 3 4 .. 5 6 4 

-30 3 2 2 4 5 4 3 4 .. 5 3 2 6 2 I I 2 2 3 6 10 8 10 7 4 2 2 5 5 3 I 2 4 3 4 4 3 F!C) 

-35 2 I 2 5 7 5 5 6 6 4 4 3 7 3 2 2 I I .. 6 8 7 8 7 6 3 3 8 7 3 2 2 4 3 3 3 2 

-40 

-45 

-50 

+ 

+ 2 

I 

I 3 

2 

I 2 

2 

2 2 

3 

4 

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6 7 8 

7 6 7 7 

7 

5 

5 

6 

3 

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3 

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6 

7 

6 

6 

9 

7 

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-55 I 2 2 2 3 3 5 6 6 5 6 5 3 2 2 3 4 4 4 4 6 .. 2 3 4 4 4 4 4 2 4 5 5 3 3 2 I 

-60 2 2 2 2 I 2 5 6 7 6 6 6 5 3 I I 3 4 4 4 5 5 3 2 2 3 2 3 5 4 4 5 6 6 6 4 2 

-65 4 4 5 5 4 4 6 7 7 7 6 6 5 4 3 2 3 5 6 5 5 5 5 5 4 3 3 4 5 5 4 5 6 7 7 6 4 

70 6 7 8 8 7 6 6 6 6 5 4 4 4 4 5 4 4 5 5 5 5 6 7 7 6 6 7 7 8 7 6 6 6 7 7 6 6 

-75 7 7 7 7 7 6 5 4 .. 3 2 2 3 5 5 5 5 4 .. .. 5 6 6 6 7 7 8 9 9 8 7 7 7 8 8 7 7 

-80 + 7 6 6 5 4 4 4 4 4 .. .. .. .. .. 4 .. .. 4 4 4 4 .. .. 5 5 6 7 7 7 7 6 7 7, 7 7 7 7 

-85 5 4 4 .. .. 4 .. .. .. 4 .. 4 .. 3 3 3 3 2 2 2 2 2 2 2 2 3 3 3 3 4 .. .. 4 4 5 5 5 

-90 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I I I I I I I I I I I I I I I , 2 2 2 2 2 2 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1---

--LONG> 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 

Flgure 4-5. GEM-9/SAO One-Half Difference Model, 200-Kilorneter Altitude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL ACrfLERATION CMGALI ~lll T> 

90 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 

e!5 2 2 2 2 2 2 2 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 2 2 2 2 2 2 2 2 80 I I I I I 2 2 2 3 3 3 3 3 2 2 I I 0 I I 2 2 2 2 2 3 3 3 3 2 2 2 2 I I 1 I 

75 I I I I I 2 3 3 3 2 2 I 2 2 2 2 I I I 2 2 2 2 , , 2 3 3 3 3 3 2 2 2 2 I , 

70 2 2 , , 2 3 3 4 4 3 3 3 3 3 3 2 2 , , 2 2 2 2 2 2 2 3 4 4 4 4 3 3 3 2 2 2 

65 2 2 , I 2 2 2 3 3 4 5 6 5 4 3 3 2 2 I I 2 3 3 3 3 3 4 4 4 4 4 4 5 4 3 2 2 60 I , , , 2 I I I 2 3 6 7 6 5 4 4 4 3 2 I 2 3 3 .. 4 4 4 4 3 3 3 5 6 5 3 2 1 

'55 I , 2 3 2 I I 1 2 2 4 5 5 5 5 4 5 4 2 , I 2 3 4 4 3 3 4 3 2 3 5 6 4 3 3 I 

'50 3 2 3 5 2 I 2 2 3 3 2 3 3 4 5 5 4 3 3 2 I I 2 3 3 2 3 4 3 2 4 5 4 3 3 3 3 

45 4 2 3 5 3 2 4 4 5 6 3 2 , 2 4 4 3 3 3 3 2 I 2 2 2 2 2 3 3 2 3 4 4 I 3 4 4 

40 5 3 2 4 3 2 4 6 6 7 4 2 2 I 3 3 3 4 4 2 2 , , , 2 1 2 , 2 2 2 3 3 , 2 4 5 

35 5 3 3 4 3 3 3 5 5 6 4 2 3 2 4 3 2 5 4 2 2 I 2 2 2 , 2 I , 2 I 3 3 2 I 3 5 

30 4 3 3 4 3 4 2 3 5 4 2 2 2 2 4 3 2 4 3 I I 1 2 2 , , , 2 I 3 2 4 3 2 2 3 4 

25 3 2 3 3 2 3 2 2 4 3 2 2 2 2 3 3 3 3 , I 2 , 2 2 1 , , 2 3 4 2 4 3 4 4 2 3 

20 2 3 3 5 3 4 2 2 4 4 2 2 I 2 2 2 3 3 I 2 2 2 2 3 2 , , 2 3 3 2 2 3 4 5 2 2 , 5 2 4 3 5 , 4 3 3 4 5 2 2 2 3 2 2 2 3 3 I 3 2 2 4 3 , , , 2 3 2 2 4 3 3 3 2 

10 2 3 4 5 2 5 4 3 4 4 3 3 3 3 2 2 I 2 2 1 , 2 2 5 3 , 1 2 2 3 3 2 4 , 2 3 2 

5 , 2 3 6 4 5 4 4 6 3 2 2 3 2 2 3 3 2 0 1 I 2 2 6 4 2 2 3 3 4 4 2 3 I 2 2 I 

0 I , 2 6 4 4 3 3 5 3 2 2 2 2 3 3 3 3 I 1 2 2 4 6 5 3 2 4 4 5 5 3 3 2 , , I 

~ -5 3 2 , 4 3 5 3 4 4 3 3 2 2 , 3 3 2 2 2 2 2 2 3 .. 4 3 4 4 4 5 4 3 2 2 , 2 3 , 0 4 3 2 4 4 6 4 4 4 3 3 2 2 2 3 2 2 2 3 2 2 , 2 2 3 3 6 4 5 4 3 3 2 2 , 2 4 I - '5 4 3 3 3 5 5 4 3 4 3 2 2 3 2 2 3 2 2 4 2 2 0 2 2 2 3 6 4 5 4 2 2 2 3 3 3 4 I-' 20 3 2 3 3 4 3 3 2 2 2 I 2 3 2 2 3 3 3 3 3 4 2 4 4 , 2 5 3 4 2 , 3 3 4 4 4 3 ~ 25 3 2 3 3 3 2 2 2 , 3 2 2 4 2 I 2 3 2 2 4 6 5 6 5 , , 3 2 2 , I 2 3 3 3 4 3 

-30 2 , 2 3 3 3 2 3 ~ 3 2 2 3 I I I 1 I 2 4 6 5 7 5 2 , 1 3 3 2 1 I 2 2 3 3 2 

-35 , , I 3 4 4 3 4 4 3 2 2 4 2 I I I 1 3 4 5 5 6 5 4 2 2 5 4 2 I 2 3 3 3 2 I 

-40 I , I 3 4 4 4 4 3 , 3 4 5 3 2 I 2 2 3 3 4 3 4 4 4 3 3 5 4 I 3 2 2 3 3 I 1 

-45 , , 1 2 4 4 5 4 2 2 4 4 5 3 2 1 3 3 3 1 2 I 2 .. 4 4 4 3 3 2 3 2 2 3 3 I I 

-50 I 2 , I 3 4 5 4 3 3 5 4 3 , I 2 3 3 2 I 2 I 2 1 4 .. 4 3 3 2 3 2 , I 2 , I 55 , 1 , , 2 2 3 4 3 3 4 3 2 I 1 2 3 2 2 2 3 3 2 2 3 3 3 2 2 , 2 3 3 2 2 I , 

-60 I 2 2 2 1 I 3 4 4 4 4 4 3 2 I I 2 2 3 2 3 3 2 , 2 2 I I 2 2 3 3 4 4 3 2 I 

65 3 3 3 3 3 2 3 4 5 4 4 4 3 2 2 , , 3 3 3 3 3 3 3 3 2 2 2 3 3 3 3 4 4 5 4 3 

-70 4 4 5 5 5 4 4 4 4 3 2 2 2 3 3 2 2 3 3 3 3 4 4 4 4 .. 4 5 5 4 4 4 4 5 5 4 4 -75 4 4 5 5 4 4 3 3 2 2 I , 2 3 3 3 3 3 2 3 3 4 4 4 4 '5 5 6 6 5 5 4 5 5 5 5 4 

-80 4 4 3 3 3 3 3 3 3 3 2 2 2 3 3 3 3 3 2 2 3 3 3 1 3 4 4 4 4 4 4 4 4 4 4 4 4 

-85 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 , , 1 2 2 2 2 2 2 2 2 2 3 3 3 3 

90 I , I , , , , I I I , I I 1 I , , I I 1 0 0 0 0 0 0 0 0 , , , , , I 1 , 1 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1- 1 -1--1--1--1--1--1--1--1--1--1--1--1--1---

~lOI~G'> 0 20 40 60 80 100 120 • '40 '60 180 200 220 140 260 280 300 320 340 360 

Figure 4-6. GEM-9jSAO One-Half Difference Model, 400-Kilometer Altitude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL ACCELERATION IMGAL) <LAT> 

90 I I I I I I 1 1 1 1 1 I I I I 1 1 I I 1 1 1 1 1 1 I 1 1 1 1 1 1 I I 1 1 I 

85 1 1 1 I I 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 I 1 1 I 1 I 1 80 1 1 0 0 I 1 1 1 2 2 2 2 2 I 1 I I 0 0 1 1 1 1 I 1 2 2 2 2 2 1 1 I I 1 I I 

75 .. I 1 0 0 I I 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 I 2 2 2 2 2 2 1 1 1 1 I 

70 .. 1 1 I I I 2 2 2 2 2 2 2 2 2 2 2 1 1 1 I 2 2 1 I I 2 2 3 3 3 3 2 2 2 2 1 I 65 I 1 1 I I 1 2 2 2 3 3 4 3 3 2 2 2 I 1 1 1 2 2 2 2 2 :3 3 3 3 3 3 3 3 2 2 1 60 .. I 0 I I I I I 1 2 2 4 4 4 3 3 2 3 2 I I I 2 2 1 3 3 3 3 3 2 3 4 4 4 3 2 I 

55 I 0 I 2 I I I 1 1 1 2 3 3 3 4 3 3 3 2 I I I 2 3 2 2 3 3 3 2 2 3 4 3 3 2 I 

50 2 I 2 3 I I I I 2 2 I 2 2 3 4 3 3 2 2 1 I 1 2 2 2 2 2 3 2 I 2 3 3 2 2 2 2 

45 + 3 I 2 3 I I 2 3 3 4 2 I I I 3 3 2 3 2 2 I 0 I 2 2 I I 2 2 I 2 3 3 I 2 3 3 

40 3 2 I 2 2 I 2 4 4 5 3 2 I I 2 2 2 3 3 2 I 0 I I I I I 1 1 I 1 2 2 I I 3 3 

35 .. 3 2 2 3 2 2 2 3 4 4 2 2 2 2 3 2 1 3 3 1 I I I I I I I 0 I I 1 2 2 I I 2 3 

30 + 3 2 2 3 2 2 2 2 3 2 1 1 2 2 3 2 1 3 2 1 I I 2 I I I I I 1 2 I 3 2 2 2 2 3 

25 2 1 2 2 I I 1 2 2 2 I 1 1 I 2 2 2 2 1 1 I 1 1 2 I I I 1 2 2 I 3 2 3 3 2 2 

20 + I 2 2 3 2 2 2 2 3 3 I I I 1 I 2 2 2 1 I 2 I I 2 I I I 1 2 2 I 2 2 3 3 2 I 

15 I 2 2 3 I 2 2 2 3 3 2 I I 2 I 1 I 2 2 I 2 I I 2 2 I 0 I 2 2 I 1 3 2 3 2 I 

10 I 2 2 3 I 3 3 2 3 3 2 2 2 2 I 1 I I 1 I 1 I I 3 2 I I I I 2 2 2 2 I I 2 I 

5 .. I I 2 4 3 3 2 2 3 2 1 2 2 I I 2 2 2 I. 0 1 I 2 4 3 I I 2 2 3 3 2 2 I I I 1 

0 0 I I 4 3 3 2 2 3 2 I I 2 I 2 2 2 2 I I I I 3 4 3 2 2 3 3 3 3 2 2 I 1 I 0 

~ -5 2 I 1 3 2 3 2 2 3 2 2 1 2 I 2 2 I 2 I 1 I I 2 3 3 2 3 3 3 3 3 2 2 I 0 I 2 

I - 10 3 2 I 2 3 4 3 3 3 2 2 I 2 2 2 I I I 2 2 I I I I 2 2 4 3 3 3 3 2 2 I I 2 3 

I-' - 15 3 2 2 2 3 3 3 2 3 2 I I 2 2 1 2 I 2 3 2 I I 1 I I 2 4 3 3 3 2 2 2 2 2 2 3 

U1 -20 2 I 2 2 3 2 2 2 2 2 I I 2 I 2 2 2 2 2 2 2 2 3 2 I 1 4 2 2 2 I 2 2 2 3 3 2 

-25 2 I 2 2 2 2 I I 1 2 I 2 2 I I I 2 I I 2 4 3 4 3 I I 2 I 2 I I I 2 2 2 3 2 

-30 I I I 2 2 2 2 2 I 2 I I 2 I I I I 1 I 2 4 4 5 3 2 0 I 2 2 I I I 2 2 2 2 I 

-35 I 0 I 2 3 2 2 2 2 2 I I 3 I I 0 I 1 2 2 3 3 4 3 2 I I 3 3 I I I 2 2 2 I I 

-40 0 0 I 2 3 3 3 3 2 I 2 2 3 2 I I I 2 2 2 2 2 3 3 3 2 2 3 2 I 2 I 2 2 2 I 0 

45 0 I 0 I 3 3 3 2 I I 3 3 3 2 I I 2 2 2 I I I 2 3 3 2 3 2 2 I 2 2 I 2 2 I 0 

50 I I 0 I 2 2 3 3 2 2 3 3 2 I I I 2 2 I I I I I 2 3 '2 3 2 2 I 2 2 I I I I I 

55 0 I I I I I 2 :3 2 2 :3 2 2 1 I I 2 2 2 I 2 2 I 2 2 '2 2 I I I 2 2 2 2 I I 0 

-60 + I I I I I I 2 2 3 3 2 2 2 I I I I 1 2 2 2 2 I I I I I I 1 I 2 2 2 2 2 2 I 

-65 2 2 2 2 2 2 2 :3 3 3 2 2 2 2 I I 1 2 2 2 2 2 2 2 2 2 I 2 2 2 2 2 2 3 3 3 2 

-70 3 3 3 3 3 3 2 3 2 2 1 1 I 2 2 2 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 

-75 3 3 3 3 3 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 3 3 3 3 3 3 3 3 

-80 3 2 2 2 2 2 2 2 2 2 2 I I 2 2 2 2 2 2 2 2 '2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 

-85 2 2 I 1 I 1 1 1 I I 1 1 1 I I 1 I I I I I 1 I I I I I I I I I I I 2 2 2 2 

-90 I I I I I I I I I I I I I I I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I) 0 0 I I 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1---

<LnNG> 0 20 40 60 80 100 120 140 160 180 200 • 220 240 260 280 300 320 340 360 

Figure 4-7. GEM-9/SAO One-Half Difference Model, 600-Kllometer Altitude 
UNCERTAINTY IN NONSPHERICAl GRAVITATIONAL AcrFI ERI\TION IMGAl) 

<lI\T> 

90 I I I I I I I I I I I I I I I 2 2 2 2 2 2 2 I I I I I I I I I I I I I I I 

85 • I I I I I I I I 0 I I I 2 2 3 3 3 3 3 3 3 3 3 2 2 2 I I I I I I I 1 I I I 

80 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 2 2 

75 2 2 3 3 3 3 3 3 2 2 2 2 2 2 2 I 2 4 5 5 5 4 4 4 5 6 6 6 6 6 7 7 6 5 3 2 2 

70 3 4 4 3 4 3 3 3 3 2 2 2 2 3 4 4 5 6 6 7 7 8 8 7 I; 7 7 7 8 9 10 10 8 6 4 3 3 

65 5 6 5 3 3 4 4 5 6 5 5 4 4 4 5 6 8 9 10 10 10 13 13 10 7 8 9 8 7 9 10 9 7 6 4 4 5 

60 4 4 3 2 4 7 8 6 5 6 6 5 5 6 7 9 10 II 12 II II 15 16 10 5 ., 8 6 3 6 8 8 7 4 3 3 4 

55 5 4 2 4 10 12 II 6 3 8 8 6 6 8 10 13 12 II II 8 8 13 14 9 5 4 7 6 2 4 5 7 10 6 3 3 5 

50 6 5 2 7 16 19 II 7 4 8 8 6 8 12 14 16 II 8 9 6 4 9 8 B 6 4 6 8 8 7 4 6 12 9 8 4 6 

45 5 6 3 10 14 19 10 7 8 II 7 4 8 13 12 14 10 6 B 7 8 10 4 6 7 5 5 9 12 8 4 5 9 9 9 5 5 

40 I 5 5 9 9 II 7 6 7 13 6 3 5 10 6 7 8 6 8 6 9 II 6 7 9 6 4 7 II 7 4 3 5 4 6 3 I 

35 6 5 5 7 5 7 10 6 5 9 4 3 2 6 3 3 4 5 8 6 6 8 8 7 8 6 4 6 8 5 3 7 7 6 9 7 6 

30 7 4 7 8 4 7 II 10 7 7 2 3 4 5 5 3 3 9 7 4 4 4 7 r; 6 5 4 8 5 3 3 9 7 9 II 7 7 

25 5 4 7 7 4 6 7 8 6 6 3 3 5 4 5 5 2 10 6 6 2 2 4 4 3 4 5 10 8 5 2 6 4 6 9 3 5 

20 2 3 9 4 2 4 5 6 2 4 4 I 3 5 5 7 2 8 5 7 2 2 5 5 2 4 6 8 II 6 2 2 4 5 10 4 2 

15 3 5 9 4 1 ') 6 10 3 5 7 5 4 B 3 5 2 6 2 7 5 2 6 4 2 2 4 4 7 5 3 9 6 5 9 5 3 

10 3 4 5 4 0 I 8 10 4 6 9 6 7 6 3 4 2 5 3 5 4 3 4 5 5 I 4 4 4 5 5 II 6 4 6 4 3 

5 2 2 5 4 I 3 6 8 6 6 10 2 7 2 2 5 5 6 5 4 2 I 4 6 7 2 5 8 4 4 3 8 6 4 6 2 2 

0 I 3 7 5 3 5 4 7 7 4 8 3 5 4 2 6 5 6 5 3 3 3 7 (j I; 4 7 R 4 4 2 4 6 4 7 4 I ~ -5 5 5 6 6 5 4 5 7 4 2 6 4 3 4 3 5 3 6 6 2 I 4 10 4 5 4 6 4 3 3 3 3 5 6 6 6 5 

I - 10 7 4 3 5 6 2 6 6 4 3 5 4 3 2 3 7 3 6 6 3 3 4 7 6 '5 3 4 I 2 6 2 1 5 7 5 6 7 

f-' - 15 4 2 3 5 7 I 5 5 4 4 4 3 5 3 2 6 I 5 5 5 2 4 6 6 4 2 8 I 3 7 I 3 4 7 6 5 4 

0'\ -20 2 2 2 5 5 3 3 6 3 4 4 2 4 3 3 3 3 5 3 5 2 2 5 5 5 6 9 2 4 6 3 4 4 6 6 6 2 

-25 3 2 2 5 6 6 4 9 3 2 3 2 2 3 5 4 4 5 3 4 3 2 5 4 5 5 6 3 4 3 3 3 4 7 3 7 3 

-30 4 2 2 4 5 5 3 8 4 0 2 2 I 3 9 9 5 4 4 5 2 3 4 5 4 4 2 3 2 2 2 3 3 7 5 8 4 

-35 5 3 4 5 6 4 2 5 5 3 2 3 3 ~ 10 10 7 5 6 7 7 5 2 3 2 3 4 3 3 2 2 3 4 7 8 8 5 

-40 7 6 8 6 6 6 4 4 5 5 4 5 4 4 5 7 8 9 10 9 9 4 1 4 4 3 3 3 4 5 3 4 3 7 10 8 7 -45 10 8 7 5 5 7 6 5 t 3 6 7 3 4 3 5 6 8 10 9 7 2 3, 5 4 3 3 I 3 5 4 5 3 5 9 8 10 

-50 9 9 8 5 4 5 6 6 5 I 5 8 6 6 3 5 6 4 5 4 5 4 4 ., 3 3 2 2 3 2 3 5 4 2 4 5 9 

-55 5 9 10 5 3 5 3 5 5 2 3 5 6 7 4 4 5 2 3 4 7 7 4 ') 2 4 3 2 5 4 5 5 8 5 4 3 5 

-60 6 8 6 4 2 3 4 4 4 3 2 4 6 6 6 6 6 5 4 4 6 8 5 4 4 6 4 3 6 6 6 6 9 8 7 4 6 

-65 7 7 5 5 5 4 4 I 2 2 I 3 4 5 ,6 9 9 8 6 3 3 7 9 9 7 7 6 6 7 6 5 5 7 8 8 7 7 

-70 7 10 II II 10 7 5 3 2 2 2 4 5 6 7 8 9 8 7 5 6 8 10 10 9 9 9 10 9 8 7 6 7 7 6 6 7 

-75 8 10 II II 9 8 6 4 4 4 4 6 7 8 8 7 6 4 3 2 4 6 8 9 9 9 9 10 9 8 8 8 9 9 8 8 8 

-80 8 8 7 6 5 4 3 3 3 3 4 5 5 6 6 6 5 4 3 3 4 6 7 7 8 8 8 8 8 8 9 9 10 10 10 9 8 

-85 6 5 4 4 3 2 I I I I 2 2 3 3 3 4 4 4 5 5 5 6 6 Ii 6 1 7 7 7 7 7 7 7 7 7 6 6 

CJO 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 ,I 4 4 4 4 4 4 4 4 4 4 4 4 4 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1 1- 1--1--1--1--1 - 1 - - 1 - -I -1--1--1--: 

~LONG> 0 20 40 60 80 100 120 140 160 180 2(10 '}')n ~40 260 280 30(1 320 34(1 360 

Figure 4-8. GEM-9/GEM-5 Difference Model, 200-Kilometer Altltude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAl ACC'FlFRAITON IMGAll 

<LAT'> 

90 0 0 0 0 0 0 0 0 0 0 I I I I I I I I I I I I I I I I I I 0 0 0 0 0 0 0 0 0 

85 0 0 I I I I 0 0 0 0 0 I I I I I 2 2 2 2 2 2 2 I I I I I 0 0 0 0 I I I I 0 

80 I I I I I I I I I I I I I I I I 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I I I 

75 I I 2 2 2 2 2 2 I I I I I I I I 2 3 3 3 3 2 2 :) :) 4 4 4 4 4 4 4 4 :) 2 2 I 

70 2 3 2 2 2 2 2 2 2 2 2 I 2 2 3 3 3 .. 4 4 4 5 5 .. 4 5 5 5 5 6 7 6 6 4 3 2 2 

65 3 3 3 2 2 3 3 3 3 3 3 3 3 3 :1 4 5 6 7 6 6 B 8 6 5 5 6 5 5 6 7 6 5 4 3 3 3 

60 2 3 2 I 3 4 4 4 3 4 4 3 3 4 5 6 7 7 8 7 7 9 10 6 4 4 6 4 :) 4 5 5 5 :) 2 2 2 

55 3 2 I 2 6 7 6 4 2 4 5 .. .. 6 7 9 8 7 7 5 5 8 8 6 4 :) 5 4 2 2 3 .. 6 4 2 2 3 

50 3 3 I .. 9 II 7 .. 3 5 5 .. 5 7 9 10 7 5 5 .. 3 6 5 5 .. 3 4 6 5 4 2 3 7 5 4 2 3 

45 3 3 2 6 8 II 6 .. 5 6 .. 3 5 8 7 8 6 .. 5 4 5 6 2 4 5 4 .. 6 7 5 2 2 5 5 5 2 3 

40 I 3 3 5 5 7 .. .. .. 7 .. 2 3 6 .. 5 5 3 5 .. 6 7 3 I 6 4 3 5 7 5 3 I 3 2 3 2 I 

35 3 3 .. .. 3 .. 6 .. 2 5 2 2 I .. 2 2 3 3 5 .. 4 5 5 4 5 4 2 4 5 3 3 4 4 4 5 4 3 

30 .. 2 4 5 2 4 6 6 4 .. I 2 2 .. 3 2 2 5 .. 3 2 3 4 3 4 3 2 5 4 2 2 5 4 5 6 4 4 

25 3 2 4 4 2 3 .. 5 3 3 2 2 3 3 .. 3 2 6 4 3 I I 3 2 2 2 3 6 5 3 I 3 3 4 5 2 3 

20 I 2 5 3 I 2 3 4 2 2 2 I 2 3 3 .. 2 5 3 4 I I 3 2 I 2 3 5 6 3 I I 3 3 5 2 I 

15 2 3 5 3 I 2 .. 6 2 3 .. 3 3 .. 2 3 2 3 2 .. 3 1 3 2 1 1 2 3 5 3 2 5 4 3 5 3 2 

10 2 2 3 2 0 1 5 6 3 3 5 .. 4 3 2 3 I 3 2 3 3 2 2 3 3 I 3 3 3 3 3 7 4 3 3 2 2 

5 1 1 3 3 1 2 .. 5 .. 3 6 2 .. I 1 3 3 3 3 2 I 1 3 4 4 2 3 5 3 2 2 5 4 2 4 2 1 

0 1 I 4 3 I 3 3 5 .. 2 5 2 3 2 I 3 3 4 3 2 I 2 5 " 3 2 4 5 2 2 I 3 3 3 4 2 I 

~ -5 3 2 3 4 3 2 3 4 3 I 4 3 2 2 2 2 2 4 3 I I 3 6 :) 3 3 3 3 2 2 2 2 3 4 4 3 3 

I - 10 4 2 2 3 3 I 4 4 2 2 3 3 2 I 2 .. 2 .. 3 2 2 3 4 3 3 2 2 I 2 3 I I 3 4 3 4 4 - 15 2 I 2 3 .. 1 3 4 2 2 3 2 3 I I 4 1 3 3 3 I 2 3 :) :) 2 4 0 2 4 I 2 3 4 4 4 2 ...... -20 I I I 3 3 2 3 4 2 2 3 1 2 2 2 2 I 3 2 3 I 2 3 :) 3 :1 5 I 2 3 1 2 3 4 4 4 1 ....,J -25 2 1 I 3 3 3 3 5 2 1 2 1 I 2 3 3 2 3 2 3 I 1 :1 3 3 3 3 I 3 2 I 2 3 4 2 4 2 

-30 3 1 I 3 3 3 2 5 2 0 1 1 I 2 6 6 3 :3 3 3 2 I 2 3 3 3 I I 2 1 I 2 2 4 :1 5 3 

-35 • 4 2 2 3 3 3 2 3 3 2 I I 2 3 6 7 5 4 .. 5 4 3 I 2 2 2 3 2 2 2 1 2 2 5 5 5 4 

-40 • 5 .. 4 3 3 4 3 2 3 3 2 3 2 2 4 5 5 6 6 6 5 3 I 2 2 2 2 2 2 3 2 2 2 5 7 5 5 

-45 6 5 5 3 3 4 4 3 2 2 4 4 2 3 2 3 4 5 6 5 4 2 2 :1 3 2 1 I 2 3 2 3 2 4 6 5 6 

-50 6 6 5 3 2 3 3 3 3 1 3 .. 3 .. 2 3 .. 3 3 2 3 3 3 3 2 2 I 1 2 1 2 3 2 1 3 3 6 

-55 3 5 6 3 I 3 2 2 3 , 2 3 4 4 3 2 3 2 I 2 .. 4 3 I I 3 2 2 3 3 3 3 4 3 2 I 3 

-60 4 .. 4 2 I 2 2 2 2 2 I 2 .. .. 4 4 .. 3 2 I 3 5 3 3 3 4 3 2 4 3 4 4 5 5 4 3 4 -65 .. 4 3 3 3 2 2 1 2 I I 2 3 3 .. 5 6 5 4 2 2 4 5 5 5 5 4 4 4 4 4 4 4 5 5 5 4 

-70 5 6 7 7 6 5 3 2 2 2 2 3 3 4 5 5 5 5 .. 3 .. 5 6 6 6 6 6 6 6 5 .. .. 4 5 4 4 5 

-75 5 6 7 7 6 5 4 3 3 3 3 4 4 5 5 5 4 3 2 I 2 4 5 5 5 6 6 6 6 5 5 5 6 6 5 5 5 

-80 5 5 4 4 3 3 2 2 2 2 3 3 4 4 4 3 3 2 2 2 3 3 4 .. 5 5 5 5 5 5 5 6 6 6 6 5 5 

-85 3 3 3 2 I I 0 0 I I I 2 2 2 2 2 3 3 3 3 3 4 4 4 .. " 4 4 4 " " " 4 4 4 4 3 -90 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 '} " 1 3 3 :1 3 1 3 2 '} 2 2 '} 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1- 1--1--1--1--1--1--1--1--1--1--1--1---

"LONG'> 0 20 40 60 80 100 120 140 160 180 200 220 '}-10 ,}F;O 280 300 3'0 1.tO 36(1 

Figure 4-9. GEH-9/GEM-5 Different Model, 400-Kilometer Altitude 
UNCERTAINTV IN NONSPHERICAL GRAVITATIONAL AC"EIFRATION 'MGAL' <LAT~ 

90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

85 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 I I I I I I I I I I I I 0 0 0 0 0 0 0 0 0 0 

80 + 0 0 I I I I 1 I I I I 1 I I 1 I 1 I I 1 1 1 1 I 1 2 2 I I • I I 1 I I I I 0 

75 I I I 1 1 1 1 I 1 I I 1 1 I 1 1 1 2 2 2 2 I I 2 2 2 3 3 3 3 3 3 3 2 2 1 I 

70 2 2 2 1 2 I I 1 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 3 2 2 2 

65 2 2 2 I 2 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 5 5 4 3 3 .. .. 3 4 .. .. 3 3 2 2 2 

60 2 2 1 1 2 3 3 2 2 2 2 2 2 3 3 4 5 5 5 5 5 6 6 .. 3 3 4 3 2 3 4 3 3 2 1 2 2 

55 + 2 2 1 1 4 4 4 3 1 3 3 2 3 4 5 6 5 5 5 4 3 5 5 .. 3 2 3 3 1 I 2 3 4 2 1 1 2 

50 + 2 2 I 3 5 7 4 3 2 3 3 2 3 5 5 6 5 3 3 2 2 4 3 3 3 2 3 .. 3 2 I 7 4 3 2 I 2 

45 • 2 2 2 3 5 7 4 3 3 4 2 2 3 5 5 5 4 2 3 3 3 4 1 3 1 3 3 4 5 3 I I 3 3 3 I 2 

40 • I 2 2 3 3 4 3 3 2 4 2 I 2 4 3 3 3 2 3 3 4 4 2 3 4 3 2 4 5 3 2 I 2 I 2 I 1 

35 2 2 2 3 2 2 4 2 I 3 1 1 1 2 2 2 2 2 3 2 3 3 3 3 .. 3 2 3 4 2 2 2 2 2 3 2 2 

30 2 I 3 3 1 2 4 3 2 2 1 I 1 2 2 2 2 3 3 2 2 2 3 2 3 2 I 3 3 2 2 3 2 3 4 2 2 

25 + 2 1 2 2 1 I 3 3 2 2 I I 2 2 3 2 2 4 3 2 0 I 2 2 I 1 2 4 3 2 I 2 2 2 3 I 2 

20 • 1 I 3 2 1 1 2 3 1 I I I I 2 2 3 2 3 2 2 I 1 2 • I) I 2 3 4 2 I 1 2 2 3 I I 

15 I 2 3 2 I 1 3 4 1 1 2 2 2 2 2 2 I 2 2 2 2 1 2 1 1 I I 2 3 2 2 3 2 2 3 2 1 

10 + 1 2 2 2 0 1 3 3 2 2 3 2 3 2 1 2 1 2 2 2 2 1 2 2 2 I 2 2 2 2 2 4 2 2 2 2 1 

5 + 1 1 2 2 0 1 3 3 2 2 4 1 2 0 1 2 2 2 2 1 I 1 2 2 2 1 2 J 2 I 2, 4 2 1 2 I 1 

0 + 0 I 2 2 I 2 2 3 3 I 3 2 2 I 0 I 2 3 2 I I 2 3 3 2 2 2 3 2 I I 2 2 2 J I 0 

-5 • 2 1 2 2 2 I 2 3 2 I 3 2 I I 1 I 2 3 2 I 0 2 4 2 2 7 2 2 I I I 1 2 2 2 2 2 

~ - 10 2 I I 2 2 I 2 3 2 I 3 2 I I I 2 2 3 2 I 1 2 3 2 2 I I I I 2 I I 2 3 2 2 2 

- 15 2 I I 2 2 I 2 2 1 2 2 2 2 I I 2 I 2 2 2 I 2 2 2 2 I 2 0 I 3 I 1 2 2 3 3 2 I -20 I I 1 2 2 I 2 2 1 I 2 1 I I I I I 1 2 2 I I 2 2 2 2 3 0 2 2 I I 2 2 3 3 I 

r-' -25 I I 1 2 2 2 2 3 1 1 I I 1 I 2 2 1 2 1 2 1 1 2 2 2 2 2 I 2 I 0 I 2 3 2 3 I 

00 -30 2 1 I 2 2 2 1 3 2 0 0 0 1 2 4 4 2 2 2 2 1 I I 2 2 2 I I 1 I 1 I 2 3 2 3 2 

-35 2 I 2 2 2 2 I 2 2 I I I I 2 4 4 3 3 3 3 3 2 I 2 2 2 2 2 I 1 I I I 3 4 3 2 

-40 3 3 3 2 2 3 2 2 2 2 I 2 2 2 3 3 3 4 4 4 3 2 I 2 2 I I I 2 2 I I I 3 4 3 3 

-45 4 3 3 2 I 2 2 2 I I 2 2 I 2 2 2 3 3 4 3 2 I I 2 2 I I I I 2 I 2 I 2 4 3 4 

-50 4 4 3 2 I 2 2 2 I I 2 3 2 2 I I 2 2 2 2 2 2 2 2 I I I I I I I 2 I I 2 2 4 

-55 2 3 3 2 I I I 1 I 1 I 2 3 3 2 1 2 1 0 I 2 3 2 I I 2 2 I 2 2 2 2 2 2 2 I 2 

-60 + 2 3 2 I 0 I I I 1 1 I 2 2 3 2 3 3 2 I 0 2 3 2 2 2 2 2 2 2 2 3 3 3 3 3 2 2 

-65 + 3 3 2 2 2 2 I I I 1 I I 2 2 3 3 4 3 3 I 2 J 3 J 3 J 3 3 3 3 J J 3 3 3 3 3 

-70 + 3 4 4 4 4 3 2 I I I 1 2 2 3 3 3 3 3 3 2 2 3 .. .. 4 .. 4 4 4 3 3 3 3 3 3 3 3 

-75 3 4 4 4 4 3 3 2 2 2 2 3 3 3 3 3 2 2 I I 2 2 3 3 3 .. 4 4 4 4 3 3 4 4 3 3 3 

-80 + 3 3 J 2 2 2 2 2 2 2 2 2 2 3 2 2 2 I I I 2 2 2 3 3 J 3 3 3 3 3 3 4 .. .. 3 3 

-85 2 2 I 1 I I 0 0 0 1 I 1 I 1 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 2 3 3 3 3 2 2 2 

-90 I I I I I I I I I 1 I 1 1 I I I 1 I I I , 2 2 '} , 7 , 2 2 2 2 2 I I I I I 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1- I - -1--1--1--1--1--1--1--1--1--1--1--1---

<LONG> 0 20 40 60 80 100 120 140 160 180 200 ,}20 ,-to 21;0 280 300 320 340 360 

Figure 4-10. GEM-9/GEM-S Difference Model, 600-Kilometer Altitude 
UNCERTAINTY IN NONSPHERICAL GRAVITATION~L ACCELERIITION « "'GAll "-L II T"> 

90 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 

85 2 2 2 3 4 4 5 5 5 6 5 .5 5 4 4 3 3 3 3 3 3 4 4 5 5 5 6 6 6 5 5 4 4 3 3 2 2 

80 2 3 3 4 5 6 6 6 5 5 4 4 4 3 3 2 2 I I 2 2 2 2 J 3 4 4 5 5 4 4 3 3 3 3 3 2 75 3 3 4 6 8 9 8 7 5 3 2 2 3 4 4 3 2 I 2 3 3 2 I I I 2 3 4 4 4 4 3 2 2 3 3 3 

70 3 I 3 6 8 8 7 6 4 4 3 2 I 4 6 6 4 4 5 5 4 3 I I 2 3 4 5 5 5 4 3 3 3 3 3 3 

65 3 3 5 9 10 9 5 2 2 4 4 4 4 6 9 10 7 7 7 7 6 4 2 2 2 5 6 8 8 6 5 4 4 4 3 2 3 

60 4 6 6 8 10 8 5 2 I 2 4 7 7 6 8 8 7 7 6 6 6 5 3 3 2 4 6 8 9 8 8 6 3 2 2 2 4 55 3 6 5 3 10 8 3 2 I I 3 7 5 4 5 4 6 6 4 5 7 6 3 J 2 2 6 10 8 6 9 6 2 I 2 3 3 

50 6 7 3 4 12 9 4 3 3 2 2 6 5 4 5 5 5 2 2 4 6 5 I 4 5 3 6 13 9 3 6 4 3 3 2 5 6 

4G 7 7 3 3 8 6 4 4 6 3 I 7 6 4 3 6 8 3 3 4 6 6 5 6 7 2 7 10 8 4 5 I 5 7 6 6 7 

40 5 6 3 3 8 7 6 4 7 4 2 5 7 5 2 4 8 4 6 6 6 6 7 6 6 2 4 7 10 8 6 4 7 8 8 4 5 

35 7 6 3 5 9 4 6 2 7 6 2 3 6 4 4 3 10 6 10 8 4 3 4 2 3 3 4 7 I I 8 4 7 8 5 7 5 7 

30 8 7 4 6 7 5 9 2 9 I I 3 4 5 2 7 8 12 4 7 6 3 3 3 3 3 3 7 12 6 7 4 12 10 7 I I 5 8 

25 6 9 2 4 6 6 8 2 7 14 3 6 4 2 5 4 9 2 7 3 4 3 2 4 3 2 8 16 7 9 6 I I 10 5 9 I 6 

20 8 I I 3 5 4 4 5 4 4 12 5 5 0 3 4 5 10 3 8 4 3 5 5 6 4 2 9 17 13 14 8 15 12 5 10 3 8 

15 + I I 16 6 5 3 5 3 7 6 14 7 4 3 3 4 5 8 3 10 4 4 9 10 I I 7 4 12 22 17 18 13 17 13 9 I I 6 I I 

10 + 13 17 9 6 5 7 3 9 6 13 8 5 4 3 4 4 6 8 9 4 2 12 16 15 8 5 14 24 19 18 16 19 15 10 13 8 13 

5 + 13 18 II 7 6 8 7 8 7 13 5 6 2 3 4 3 7 10 10 5 3 16 22 19 I'J 6 16 28 19 18 16 17 16 I I 15 11 13 

oj:::. 0 I I 21 12 9 7 10 II 7 9 13 3 4 2 4 4 4 8 10 10 4 5 20 27 23 16 I I 17 30 20 16 14 16 15 14 II 14 II 

I -5 9 17 10 9 7 10 11 7 10 10 4 2 4 3 4 4 6 9 9 3 7 19 25 23 17 1'3 16 25 19 13 8 12 14 I I 7 15 9 

I-' - 10 9 13 I I 6 7 9 10 8 9 10 5 2 4 I 3 4 5 8 10 5 9 18 23 24 19 14 16 2 I 16 12 4 9 12 6 5 10 9 

..0 - 15 7 9 9 4 7 8 10 10 7 9 5 4 5 I 3 2 5 7 7 3 8 15 19 21 17 16 14 19 13 10 7 8 9 4 3 6 7 -20 5 4 6 4 6 6 9 10 5 8 6 4 5 2 4 I 4 4 5 3 8 I I 15 18 13 14 II 14 12 8 8 4 5 2 I 3 5. 

-25 3 2 5 4 5 5 8 II 5 7 6 3 3 3 4 3 3 2 4 3 7 7 II 14 9 10 10 8 12 6 7 3 5 2 2 2 3 

-30 3 4 5 3 5 2 8 12 4 6 4 2 3 2 5 5 3 I 3 3 6 5 7 10 4 8 7 5 7 2 6 3 7 5 4 2 3 

-35 4 3 2 4 7 4 5 8 4 5 4 2 3 5 8 8 6 I 3 5 6 3 5 8 3 4 3 2 3 2 3 3 5 4 4 3 4 

-40 3 4 2 5 9 8 7 8 3 7 3 4 4 5 6 8 9 4 4 3 2 I I 7 6 2 2 2 2 3 4 2 4 4 3 4 3 

-45 + 3 4 3 4 7 9 7 6 5 6 3 4 4 6 .. 5 6 4 5 3 2 4 .. 7 5 3 4 3 2 3 3 3 4 4 3 3 3 

-50 + 6 5 3 3 7 8 7 6 8 6 2 3 4 7 5 4 4 2 3 2 3 5 5 4 3 2 4 6 .. 2 3 5 .4 3 3 3 6 

-55 + 5 5 3 2 5 7 8 5 6 5 2 3 5 5 4 5 6 3 2 2 6 7 4 .. 3 I 4 7 3 2 3 5 4 2 3 3 5 

-60 4 4 ;) I 3 5 4 I 5 4 I 3 5 6 6 6 7 4 2 4 8 9 6 6 5 4 3 5 5 3 4 6 6 4 4 3 4 -65 3 3 I I 3 5 .. 4 6 5 .. 6 6 5 5 5 6 4 2 .. 6 8 8 9 7 5 .. 5 6 4 5 7 6 4 3 3 3 

-70 ;) 3 I I 2 4 5 5 6 5 5 6 5 .. 3 3 3 '3 3 3 5 6 8 9 8 8 8 7 .. I 3 5 4 2 I 3 3 

-75 4 3 2 2 2 3 .. 5 5 5 4 3 2 2 3 3 3 2 2 3 4 5 7 8 10 II 10 9 6 5 5 6 5 4 4 .. .. -80 4 3 2 2 2 2 3 3 3 3 2 • I I I 2 2 3 3 3 3 .. 5 6 7 7 8 8 8 8 8 8 8 8 7 6 5 .. -85 4 3 3 2 2 I 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 " 4 5 5 6 6 6 7 7 7 6 6 5 4 -90 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 "] 3 3 1 3 3 4 4 4 4 4 4 4 4 4 3 3 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1 - 1 - 1 - - 1 -1--1--1--1--1--1--1--1--1--1--1--1--1---

"-LONG> 0 20 40 60 80 100 120 140 160 180 200 220 110 260 280 300 320 340 360 

Figure 4-1l. GEM-S/MDl One-Half Difference Model, 200-Kilometer Altitude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL ACCElERATION (MGALI <LAT> 

90 + 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 

85 + I I I 2 2 2 3 3 3 3 3 3 3 2 2 2 2 I I 2 2 2 2 3 3 3 3 3 3 3 3 2 2 2 I I I 

80 + I 2 2 3 3 3 3 3 3 3 2 2 2 2 I I I I I I I I I I 2 2 2 2 2 2 2 2 2 2 2 2 I 

75 + 2 2 2 4 4 5 5 4 3 2 I I I 2 2 2 I I I 2 I I I I I I 2 2 2 3 2 2 I I 2 2 2 

70 + 2 I 2 4 5 5 4 3 2 2 2 I I 2 4 4 3 3 3 3 3 2 I 0 I 2 3 3 3 3 2 2 2 2 2 2 2 

65 + 2 2 3 5 6 5 3 I I 2 2 2 2 4 6 6 5 4 5 4 4 2 I I 2 3 4 5 5 4 3 3 2 2 I I 2 

60 + 2 3 3 5 6 5 3 I I I 2 4 4 4 5 5 4 4 4 4 4 3 2 2 I 2 4 5 5 4 5 4 2 I I I 2 

55 + 2 3 2 2 6 4 2 I I I 2 4 3 3 3 3 4 3 2 3 4 3 2 2 I I 4 6 5 3 5 4 2 I I I 2 

50 3 4 I 2 7 5 2 2 2 I 2 3 2 2 3 3 3 2 I 2 3 3 0 2 3 2 4 8 5 I 3 2 2 2 I 2 3 

45 + 4 4 2 I 5 4 2 2 4 2 I 4 3 2 2 3 4 2 I 2 4 3 3 4 4 2 4 6 5 3 3 I 3 4 3 3 4 

40 + 3 3 2 2 5 4 3 2 4 2 I 3 4 3 I 2 4 2 4 4 4 3 4 3 3 2 2 5 7 5 3 2 4 4 4 2 3 

35 4 3 2 3 5 2 4 2 4 3 I 2 3 3 3 2 6 4 5 4 3 2 2 I 2 2 2 5 7 4 3 4 5 2 4 3 4 30 + 4 3 2 3 4 3 5 2 5 6 2 2 3 2 4 5 7 3 4 3 2 2 I 2 2 I 4 7 3 3 3 6 5 3 5 2 4 

25 2 4 I 3 4 4 5 2 4 8 2 3 2 I 3 2 5 2 4 I 2 2 I 2 2 I 5 9 4 5 4 6 6 3 4 I 2 

20 + 4 6 2 3 3 3 3 3 2 7 3 3 I 2 2 2 5 2 4 2 2 3 3 3 3 2 5 10 8 9 5 8 7 3 5 2 4 

15 • 6 10 4 3 3 3 2 4 3 8 5 2 2 2 2 3 4 2 5 2 2 5 6 6 4 :) 8 13 II II 8 10 8 6 6 4 6 

10 + 8 II 6 4 3 5 3 5 4 8 5 3 2 2 2 2 3 5 5 2 I 7 10 9 5 3 9 15 13 II 10 12 9 6 8 5 8 

5 8 II 7 5 4 5 5 5 4 7 3 3 I 2 2 2 4 6 6 3 2 10 14 12 8 5 10 18 13 II 10 10 10 7 9 7 8 

0 7 13 8 6 5 6 7 5 6 7 2 3 I 2 3 3 5 6 6 2 3 12 17 14 10 7 II 19 14 10 9 10 9 8 7 8 7 

-5 + 6 10 7 6 5 7 7 5 6 6 2 I 2 2 3 3 4 5 6 2 4 II 15 14 10 9 II 16 12 9 5 7 8 7 5 9 6 ~ - 10 + 6 8 7 4 5 6 6 5 6 6 3 I 2 I 2 3 3 5 6 3 6 II 14 15 12 9 10 13 10 8 2 5 7 4 4 6 6 

I - 15 + 4 5 6 3 5 5 6 6 4 5 3 2 3 I 2 2 3 4 4 2 5 9 12 13 II 10 9 12 8 7 4 5 5 3 2 4 4 

tv -20 + 3 3 4 2 4 4 6 6 3 5 4 2 3 I 3 I 3 3 3 2 4 6 9 II 8 9 7 9 7 6 5 2 2 I I 2 3 

0 -25 I 0 3 3 3 3 5 6 3 4 4 2 2 2 3 2 2 2 2 2 4 4 7 8 6 6 6 5 7 4 4 I 2 2 I I I 

-30 I 2 3 2 2 I 5 7 3 3 3 I I I 3 3 2 I 2 2 3 3 4 5 3 5 5 3 4 I 3 2 4 3 3 I I 

-35 + 2 2 2 2 3 3 3 5 2 2 2 I 2 2 5 5 3 I 2 3 3 2 3 4 2 3 2 I I I 2 2 3 2 3 2 2 

-40 • 2 2 I 3 5 5 4 4 2 3 I 2 3 3 4 5 5 3 3 2 2 I I 4 3 I I I I I 2 I 2 2 2 2 2 

-45 • 2 2 2 2 4 5 4 3 3 3 I 2 3 3 3 3 4 3 3 2 I 2 3 4 3 2 2 2 I 2 I 2 ' 2 3 2 2 2 

-50 + 3 3 2 2 4 4 4 3 4 4 I 2 2 3 3 2 2 I 2 I 2 3 3 3 2 I 2 3 2 I I 3 3 2 2 2 3 

-55 + 3 3 2 I 3 4 4 3 4 3 2 2 3 3 2 3 3 2 I 2 4 4 2 2 2 I 2 3 2 I 2 3 2 I 2 2 3 

-60 2 2 2 I 2 3 2 I 3 2 I 2 3 4 3 4 4 2 I 3 5 5 4 4 3 2 2 2 3 2 3 4 3 2 2 2 2 

-65 + 2 2 I I 2 3 2 2 3 3 2 3 3 3 3 3 3 2 I 2 4 4 5 5 5 3 2 3 3 2 3 4 4 2 2 2 2 

-70 2 2 I I 2 2 3 3 3 3 3 3 3 2 2 2 2 2 2 2 3 4 5 5 5 5 5 4 2 I 2 3 3 I 0 2 2 

-75 2 2 2 I I 2 2 3 3 3 2 2 I I 2 2 2 I I 2 2 3 4 5 6 6 6 5 4 3 3 3 3 3 2 2 2 

-80 2 2 I I I I I 2 2 2 I I I I I I 2 2 2 2 2 3 3 4 4 5 5 4 4 4 5 5 5 4 4 3 2 

-85 2 2 I I I I I I I I I I I 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 3 3 3 2 

-90 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 '2 2 2 2 2 2 '2 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1 -1--1--1 -1--1--1--1--1--1--1--1--1--1--1--1--1---

<'LONG> 0 20 40 60 80 100 120 140 160 180 200 220 2<10 260 280 300 320 340 360 

Figure 4-12. GEM-5/MDl One-Half Difference Model, 400-Kilometer Altitude 
UNCERTAINTV IN NONSPHERICAL GRAVITATIONAL ACCELERATION IMGALI 

<LAT> 

90 I I I I I I 1 1 1 1 1 1 1 I I 1 I I 1 1 I 1 I I 1 I I I I 1 1 1 1 I 1 1 I 

85 1 0 1 I 1 I I 1 2 2 2 2 1 1 t t t t t t t I t t I 2 2 2 2 t t t t t t t t 80 I I I I 2 2 2 2 2 t I t I I I I 0 0 0 0 0 0 1 I I I I 1 t 1 1 1 1 I I 1 I 

75 I 1 1 2 3 3 3 2 2 t I 0 0 I 1 I I I I I I I 0 0 0 I I t I 2 I I I t I I I 

70 I I I 2 3 3 2 2 I t t t I I 2 2 2 2 2 2 2 I 0 0 I I 2 2 2 2 I I I I I I I 

65 I I 2 J 4 3 2 I t I I I 2 2 3 3 3 3 3 3 2 1 I I I 2 2 3 3 2 2 2 I 1 I 1 1 60 I 2 2 J 3 3 2 I t t I 2 2 2 3 3 3 3 2 2 2 2 I I I I 2 3 3 3 3 2 I I 0 t I 

55 ~ I 2 I I 3 3 t I I 0 I 2 2 2 2 2 2 2 I 2 2 2 I I I I 2 4 3 2 3 2 I I 0 I I 

50 2 2 I I 4 3 I I I t I 2 I I 2 2 2 I 0 I 2 2 0 2 2 I 3 5 3 0 2 2 2 I I I 2 

45 2 2 I I 3 3 t I 2 t t 2 2 2 I 2 3 I I I 2 2 I 2 3 "1 2 4 4 2 2 I 2 2 2 t 2 

40 2 2 I I 3 2 2 t 2 t t 2 2 2 I I 3 I 2 2 3 2 2 2 2 I I 3 4 3 2 t 3 2 2 t 2 

35 2 I I 2 3 I 2 2 2 2 I t 2 2 2 2 4 2 3 3 2 I I I I I I 3 4 3 2 3 3 I 2 2 2 

30 2 I I 2 2 2 3 2 3 4 I I 2 I 3 3 4 2 2 2 I I I I I I 2 5 2 2 2 4 3 2 3 t 2 

25 I 2 I 2 2 2 3 2 2 4 2 2 I I 2 2 3 I 2 I I I I I I 0 3 6 3 3 3 3 4 2 2 0 I 

20 2 4 2 2 2 2 2 2 I 4 2 2 I I I I 3 I 2 I I I 2 "1 2 I 3 6 6 6 4 5 5 2 3 I 2 

15 4 6 3 2 2 2 I 3 2 5 3 t I I I I 2 I 3 I t 3 4 4 3 2 5 8 8 7 6 6 5 4 4 2 4 

10 5 7 4 J 3 3 2 3 2 5 3 2 I I I I 2 3 3 I I 4 6 6 3 2 6 10 8 7 7 7 6 4 5 3 5 

5 5 7 5 J 3 3 3 3 3 4 2 2 I I 2 2 2 4 4 2 I 6 9 7 5 3 7 12 9 7 6 6 6 4 6 5 5 

0 5 8 5 4 3 4 5 3 3 4 I 2 0 t 2 2 3 3 4 I 2 8 II 9 6 '5 8 13 9 7 5 6 6 5 5 5 5 

~ -5 4 6 4 4 3 4 5 3 4 3 I I I I 2 2 3 3 4 t 3 7 10 9 7 6 7 II 8 6 3 4 5 4 3 5 4 

I - 10 4 5 4 J 3 4 4 3 3 3 2 I I I I 2 2 3 4 2 4 • 7 9 9 7 6 7 9 7 5 2 3 4 3 3 4 4 

N - 15 ~ 3 4 4 2 3 4 4 4 3 3 2 2 2 I I I 2 3 3 I 3 6 7 8 7 6 6 8 5 5 3 3 3 2 2 2 3 Oel I-' -20 2 2 2 2 2 3 4 4 2 3 2 2 2 I 2 I 2 2 2 I 2 4 6 6 5 'l 5 5 4 4 3 I I I 0 I 2 

25 I 0 2 2 2 2 4 4 2 2 2 t I I 2 I I I 2 I 2 3 4 5 4 4 4 4 4 3 3 I I I I I I "';(1j -. -30 I I 2 I I I 3 4 2 2 2 I I 2 2 I I I I 2 2 3 3 2 3 3 2 2 I 2 I 2 2 2 I I 

8~ -35 I I I 2 2 2 3 I I I I I I 3 3 2 I I 2 2 I I 2 I "1 I I I 0 I I 2 2 2 I I 

-40 I I 2 3 3 2 2 I 2 t I 2 2 3 3 3 2 2 I I I I 2 2 I I I 0 I I I t 2 2 2 I 

-45 2 I I 2 3 2 2 2 2 I t 2 2 2 2 2 2 2 t I I 2 "1 2 I I I I I I I I 2 2 t 2 

-50 ;oF! • 2 2 I 2 2 2 2 3 2 I I I 2 I I I I I I I "1 2 2 I I I 2 I I t 2 2 I I I 2 

-55 + 2 2 I 2 2 2 2 2 2 I I 2 2 I I 2 I 0 I 2 2 I 2 I I I 2 t I I 2 I I I I 2 

-60 

-65 + 

+ 2 2 

I I 

I 

I 

I 

I 

2 

2 

I 

I I 

I 2 

2 2 

I 

I 

I 

2 

I 2 

2 2 

2 2 

2 

2 2 

2 2 

I 

I I 

I 2 

2 

3 3 2 

2 3 3 

3 

3 3 2 

2 2 

2 

I 

I 

I 

2 

I I 

I 

2 2 2 

2 3 2 

I 

I 

I 

I 

I 

I 

2 

I g~ -70 I I I I 2 2 2 2 2 2 2 I I I I I I t I 2 2 3 3 3 3 3 2 I I I 2 2 I 0 I I 

.~; -75 I I I t I 2 2 2 2 I I I I I t I I t I I 2 2 3 3 4 4 3 2 2 2 2 2 2 I I I 

-80 I I I I I I I t 1 I 0 0 0 I I I I I I I 2 2 2 3 3 3 3 2 2 3 3 3 2 2 2 t 

-85 I I I 0 0 0 0 I I I I I I I I I I I t I I I 2 2 "1 2 2 2 2 2 2 2 2 2 2 I 

-90 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 

1--/--1-- --1--/--1--1--1--1--1--1--1--1--1--1--1--1--/--1--1--/--/--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1---

'lONG> 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 

Figure 4-13. GEM-5/MDl One-Half Difference Model, 600-Kilometer Altitude 
UNCERTAINTV IN NONSPIfERICflL GRflVITflTIONflL flCe'!:l ERiI TJON (MGflLI 

"LAT' 

90 9 9 9 9 9 9 9 9 8 8 8 8 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 

85 • 13 13 13 13 12 II 10 9 8 7 6 5 5 4 4 4 3 3 4 4 4 4 5 5 5 6 6 7 8 8 9 9 10 II 12 12 13 

80 + 15 15 15 14 12 II 9 8 6 5 4 3 3 2 2 2 2 2 2 3 3 3 3 4 4 5 5 6 7 8 10 II 12 12 13 14 15 

75 15 15 14 12 10 9 8 6 5 4 3 2 2 I I I I I 2 2 2 2 2 2 2 3 4 4 5 6 8 10 II 12 13 14 15 

70 14 14 12 10 8 7 5 4 3 2 I I I I 0 0 0 I I I I I I I 2 2 3 4 5 7 9 II 12 13 14 

65 + 15 14 II 8 6 4 3 2 2 2 2 I 0 0 0 I I 0 I I I I I I I 2 I 2 3 5 6 8 II 13 15 

60 + 16 14 10 5 3 2 2 2 2 I 2 I 0 0 I I I I I I I I 2 I I 2 2 3 3 5 10 14 16 

55 14 12 8 4 2 I I 2 I I 2 I I I 0 I 2 I I I I I I I I I I I I 4 8 12 14 

50 9 8 6 2 I I I 2 I I 2 I 0 I I I I I I I I I 2 I 2 2 2 I I 3 5 8 9 

45 5 4 2 I I I I 2 2 2 I I 0 I I I I I I 'I I I I I 3 2 I I I 2 2 4 5 

40 6 4 I I 2 I 0 I I I 0 I 0 I I I I I I I 0 I I 0 2 I I I 2 2 I 4 6 

35 6 4 2 I 2 2 I I I I 0 I 0 0 0 0 • I I I I 0 I 0 0 I I I 2 2 I I 5 6 

30 5 3 I 2 2 2 I I I I 0 0 I I 0 0 I I 0 0 I 0 0 0 0 I 2 2 2 2 I 4 5 

25 .. 5 3 2 2 2 2 I I I I I 0 0 I 0 I I I I 0 0 0 0 I I 0 I I 2 3 I 3 5 

20 5 3 I 2 2 2 I I 0 I I 0 0 I I 0 0 0 0 I 0 0 0 I I I I I 2 2 0 3 5 

15 4 2 0 2 2 I I I 0 I I 0 I I I 0 0 0 0 I 0 0 0 I 0 I 0 I 2 I 0 3 4 

10 4 2 I I 2 I 0 0 I I 0 0 I I 0 0 0 I 0 0 I 0 0 0 0 I 0 0 I I 2 I 2 4 

5 3 2 I 2 I I I I 0 I 0 0 0 I 0 I 0 0 0 0 I 0 0 0 0 0 0 I I 2 0 2 3 

0 3 ( 0 I 2 I 0 I 0 I 0 I 0 0 I 0 I I 0 I I I 0 I 0 0 I 0 I 2 I 0 2 3 

-5 2 I 0 I I I 0 0 0 I 0 I I 0 I I I I 0 I I I 0 I 0 I I I 0 I I I 0 I 2 

*'" - 10 2 I 0 I 0 I 0 0 I I 0 0 0 0 I I I I 0 I I 0 0 0 0 I I 0 0 I 0 I 0 I 2 

I - 15 I I 0 0 0 I 0 0 I I 0 0 0 0 I 0 I I 0 I 0 0 0 0 0 I I I 0 0 0 0 0 0 I I 

N -20 I I 0 0 0 I I 0 0 0 0 0 0 0 I 0 I I 0 I I 0 I 0 I I 0 0 0 0 0 0 0 0 I I 

N -25 I I 0 0 0 0 I 0 0 0 I I 0 0 I I I I 0 I I 0 0 0 I I 0 0 0 I 0 0 0 0 I I 

-30 I I I 0 0 0 0 0 0 0 0 0 I 0 0 I I I 0 I I 0 I I 0 0 0 0 I I 0 0 0 0 I I 

-35 I I 0 0 0 0 0 0 0 0 0 0 I 0 0 0 I I 0 I I I I 0 0 0 0 0 0 0 0 0 0 0 I I 

-40 0 I 0 0 0 0 0 0 0 I 0 0 I I I 0 I I 0 I 0 I I I 0 0 0 0 0 0 0 0 0 0 0 0 

-45 I I 0 0 0 0 0 0 0 I 0 0 I I 0 I I I 0 I I 0 0 0 I I 0 0 0 0 0 0 0 0 0 I 

-50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I I I I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-55 0 0 0 I 0 0 0 0 0 0 0 I I 0 I I I I I I 0 I I I 0 0 0 0 0 0 0 0 0 0 0 0 

60 0 0 0 I 0 0 0 0 0 0 0 I I I I I 0 I I I 0 I I I I 0 0 0 I I 0 0 0 0 0 0 0 

-65 0 0 0 0 0 0 0 0 0 I I I I I I I I 0 0 0 I I I I I 0 0 0 0 0 0 0 0 0 0 0 0 

-70 0 0 0 0 0 0 0 0 0 I I I I I I I I I 0 I I I I I I I I 0 0 0 0 0 0 0 0 0 0 

-75 0 0 0 0 0 0 0 0 0 0 0 I I I I I I 0 0 0 I I I I I I I I 0 0 0 0 0 0 0 0 0 

-80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I I I I 0 0 0 0 0 0 0 0 0 

-85 I I I I I I I I I I I I I I I I I I I I I I I I t I I I I I 0 0 0 0 0 0 I 

90 I I I I t I I I I I I I I I I I I I I I I t I I I I I I I I I I I t t t I 

1--1--1--1--1--1- 1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1- 1 - I I -1--1--1--1--1--1--1--1- 1--1--1--1---

"LONG> 0 20 40 60 80 100 120 140 160 180 200 ;120 210 260 280 300 320 340 3150 

Figure 4-14. GEM-9 Standard Deviation Model, 400-Kilometer Altitude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL ACCELERATION IMGALI <LAT> 

90 + 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 

85 + 8 8 8 B 7 7 6 5 5 4 4 3 3 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 5 5 6 6 6 7 7 8 

80 • 9 9 9 9 8 6 5 4 4 3 2 2 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 4 4 5 6 6 7 7 8 9 9 

75 + 9 10 9 B 6 5 4 " 3 2 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 2 2 3 4 5 6 7 8 8 9 9 

70 + 9 9 8 6 5 4 3 2 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 2 3 4 5 7 7 8 9 

65 • 9 9 7 5 4 2 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 2 3 4 5 7 8 9 

60 • 9 8 6 3 2 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 2 2 3 6 8 9 

55 + 8 7 5 2 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 2 5 7 8 

50 + 6 5 3 I 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 2 3 5 6 

45 + 4 3 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 2 3 4 

40 + 4 3 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 3 4 

35 + 4 3 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 3 4 

30 + 3 2 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 I 0 2 3 

25 + 3 2 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 I 1 2 0 2 3 

20 + 3 2 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 2 3 

15 + 3 1 0 I 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 1 1 1 0 2 3 

10 • 2 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 I 1 0 1 2 

5 • 2 1 0 I I 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 2 

0 2 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I 0 I 2 "'" -5 + I I 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I 0 I I I - 10 + I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 1 

N - 15 • I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I 

W -20 + I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 

-25 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-30 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-35 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-45 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-50 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I I I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-55 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-60 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I 0 I I I 0 0 I I 0 0 0 0 0 0 0 0 0 0 0 0 0 

-65 • 0 0 0 0 0 0 0 0 0 0 0 0 0 I I I 0 0 0 0 0 I I I 0 0 0 0 0 0 0 0 0 0 0 0 0 

-70 + 0 0 0 0 0 0 0 0 0 0 0 0 0 I I I 0 0 0 0 I I I I I 0 0 0 0 0 0 0 0 0 0 0 0 

-75 0 0 0 0 0 0 0 0 0 0. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-80 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

-85 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 qo • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1---

<lONG> 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 

Figure 4-15. GEM-9 Standard Deviation Model, GOO-Kilometer Altitude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL ACr,EI ERATION (MGALI <LAT> 

90 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 

85 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 5 6 6 7 7 7 6 6 5 4 3 3 2 2 1 

80 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 4 5 6 7 8 9 8 7 6 5 4 3 3 3 2 2 

75 2 2 2 2 2 3 3 3 3 ;J 3 3 3 2 2 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 6 5 4 3 2 

70 3 3 3 3 3 3 3 3 :3 4 4 6 5 3 2 :3 4 5 5 4 3 :3 4 4 4 ") 2 4 5 6 7 8 8 8 7 4 :3 

65 5 4 4 3 :3 3 3 3 5 5 6 7 6 4 :3 :3 1 3 4 3 2 1 3 4 5 4 2 4 5 5 7 7 7 6 5 5 5 

60 4 3 5 5 4 3 4 4 5 4 3 4 3 3 3 3 2 4 2 2 3 2 3 <I 4 3 5 5 6 5 4 4 3 1 3 3 4 

55 5 3 5 5 2 3 3 4 6 5 1 2 I 2 3 5 4 5 3 2 2 2 4 'i <I 2 4 4 6 5 2 2 2 4 3 3 5 

50 4 4 6 5 3 4 3 4 6 7 3 3 4 2 2 4 3 6 4 2 3 4 7 4 4 4 3 2 5 5 2 1 3 5 6 6 4 

45 4 6 7 6 4 4 2 2 3 6 2 4 4 3 2 2 1 5. 4 2 2 2 6 2 3 3 2 3 4 5 2 1 2 4 5 5 4 40 5 7 5 5 3 3 1 2 4 8 3 4 3 5 3 2 2 6 5 4 3 3 6 2 3 2 2 4 5 6 3 2 3 4 4 4 5 

35 4 6 4 4 2 1 2 2 4 7 5 4 4 5 2 2 4 5 5 3 3 2 4 '1 5 4 3 4 3 4 2 3 4 4 3 4 4 

30 4 6 2 4 2 2 2 2 2 5 6 4 2 4 2 2 2 2 5 2 2 1 4 5 7 6 3 2 2 3 3 2 5 5 3 4 4 

25 4 5 2 2 2 1 2 2 2 5 4 3 2 3 2 2 1 2 6 2 1 2 3 8 8 4 1 2 3 5 2 3 3 3 3 4 4 

20 3 'i 3 3 3 1 4 3 I 3 3 2 3 3 I 3 3 4 6 2 1 1 1 7 6 2 3 3 2 5 3 2 2 2 3 3 3 

15 2 2 1 6 5 2 5 3 3 3 2 2 3 3 I 3 4 4 6 2 1 1 3 7 3 4 3 3 3 3 4 2 4 I 2 3 2 

to 3 3 1 6 4 1 5 4 6 4 I 3 3 I 2 3 4 2 5 2 3 3 4 fi 4 5 5 2 6 I 3 3 4 4 3 2 3 

5 3 4 1 3 4 2 4 8 6 7 2 3 5 I 2 4 5 I 3 3 4 5 7 4 7 3 4 4 7 2 4 2 2 4 3 1 3 

0 2 3 1 3 4 .3 5 8 5 8 5 2 5 2 3 5 3 I 3 4 3 5 6 3 5 4 2 6 5 2 6 4 3 3 4 2 2 

~ -5 2 3 I 2 2 5 7 5 7 6 5 2 4 2 2 4 1 2 3 3 3 3 5 '1 2 3 4 6 4 5 4 3 3 3 3 I 2 

I - 10 2 3 3 4 1 7 4 3 4 3 5 3 3 2 2 3 1 3 3 3 5 2 3 4 '1 <1 4 6 4 7 2 3 4 5 2 2 2 

N - 15 3 3 2 3 2 4 3 3 2 2 5 3 3 2 2 3 2 3 5 4 7 2 2 <1 I 3 4 5 1 6 1 3 3 4 4 5 3 

~ -20 4 3 1 2 3 4 5 2 1 2 3 2 1 2 2 4 3 3 4 5 6 I 2 4 1 2 3 5 3 6 3 5 3 5 4 5 4 

25 3 3 2 2 3 4 5 1 1 2 3 3 4 4 2 4 5 4 3 6 7 3 2 5 2 1 2 5 4 5 3 5 2 5 3 2 3 

30 2 3 2 2 4 3 6 2 2 3 3 4 3 4 2 5 5 5 3 5 5 2 2 <1 1 3 1 3 5 5 4 4 2 6 3 2 2 

-35 2 3 3 2 3 3 3 3 2 4 2 4 4 6 3 3 6 6 3 6 5 2 3 3 1 6 2 1 3 4 5 4 3 5 2 3 2 

-40 I 3 3 I 2 3 1 4 3 5 3 2 4 8 5 4 6 6 4 5 6 4 3 1 1 6 5 2 2 2 4 6 5 4 1 1 1 

-45 1 3 3 2 2 3 1 4 3 5 4 4 4 5 5 4 6 5 4 4 7 6 4 2 2 1 7 2 2 4 5 6 4 4 2 1 1 

-50 1 3 4 3 1 3 4 6 4 4 4 5 4 3 5 4 5 4 4 5 7 5 6 4 3 6 6 2 1 4 5 4 4 5 4 1 1 

55 I 3 5 3 I 3 3 7 6 5 2 4 5 3 4 5 6 4 5 7 6 2 6 5 ") 4 4 2 3 6 6 3 7 6 4 3 1 

60 4 4 3 2 2 2 1 5 7 8 4 4 4 3 4 5 5 7 8 7 6 3 4 <1 <I 5 5 3 4 5 5 3 7 6 2 3 4 

-65 5 4 I 2 2 2 2 5 8 8 6 6 4 2 4 5 4 6 6 3 3 4 3 '1 '1 5 5 4 3 2 3 4 5 4 3 3 5 

70 3 4 4 , 2 I 2 4 6 6 6 6 5 3 3 3 2 2 2 1 2 4 4 <1 4 4 3 3 2 3 4 5 5 4 2 1 3 -~5 <I 4 4 <I 4 <1 4 5 5 5 5 5 5 6 6 5 3 2 2 3 3 4 4 5 5 <1 4 3 4 5 7 8 7 6 5 4 4 

80 6 6 6 6 5 5 4 4 4 3 3 3 4 5 5 5 4 3 3 4 4 4 4 5 'i 4 4 4 4 5 6 6 6 6 6 6 6 

85 6 6 6 6 6 5 4 4 4 4 4 4 4 5 5 6 6 6 6 6 (; 5 5 5 4 4 3 3 2 3 3 4 5 5 6 6 6 

go 5 'i 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 (; 6 5 'i r; <j 5 5 5 5 5 5 5 5 5 5 5 

1--1--1--1- 1--1--1--1--1--1--1--1--1--1--1--1--1- 1--1--1--1--1- - I -1--1--1--1 1--1--1- I - - I - 1--1--1---

~IONG> 0 20 40 60 80 100 120 140 160 180 200 220 74(1 260 280 300 320 340 360 

Figure 4-16. GEM-9 Formal Uncertainties With Random Signs, 200-Kilometer Altitude 
UNCERTAINTV IN NONSPHERICAl GRAVITATIONAL ACCELERATION (MGAl) <LII T> 

90 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 

85 I I I I I I I I I I I 2 2 2 2 2 2 2 2 2 2 2 3 3 3 4 .. 4 3 3 3 2 2 I I I I 80 I I I I I I I I I I I I I I I I I I I I I 2 3 3 4 4 5 .. 4 3 2 2 2 2 1 I 1 

75 I I I I I 2 2 2 I I 2 2 2 I I I 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 2 I 70 2 I 1 2 2 2 2 2 2 2 3 3 3 2 I 1 2 3 3 2 2 2 2 2 2 2 2 3 3 3 .. 5 5 5 4 2 2 

65 2 2 2 2 2 2 2 2 3 3 3 .. 4 2 2 I I 2 2 2 I I 2 2 3 2 2 3 3 3 4 4 4 4 3 2 2 

60 2 2 3 3 2 2 2 2 3 2 2 2 2 2 2 2 I 2 2 I I I 2 2 2 2 2 3 3 3 3 2 2 I 2 2 2 

55 3 2 3 3 I 2 2 2 3 3 0 I I I I 3 2 3 2 1 I I 2 3 3 I 2 2 3 3 1 I 1 2 2 2 3 

50 2 2 4 3 2 2 2 2 3 .. 2 2 2 I I 2 2 3 2 I I 2 .. 2 2 2 I 1 3 3 1 0 I 3 3 3 2 

45 3 3 .. .. 3 3 I I 2 3 2 2 2 2 I I I 3 3 I I I 3 I 2 I I 2 3 3 2 I I 2 3 3 3 

40 3 .. 3 3 2 2 1 1 2 4 2 2 2 3 2 I I 3 3 2 2 I 3 I 2 I I 2 3 .. 2 I 2 2 2 2 3 

35 3 3 2 2 I I I I 2 .. 3 3 2 3 I I 2 3 3 2 2 I 2 I 3 3 2 2 2 3 2 I 2 2 I 2 3 

30 3 3 I 2 I I 1 1 1 3 .. 3 2 2 I 1 2 1 3 1 I 0 2 3 4 3 2 I 1 2 2 1 3 3 2 2 3 

25 2 3 I I 1 1 1 I 1 3 3 2 1 2 1 1 1 I .. 2 1 1 1 .. 5 2 1 1 1 3 1 2 2 1 1 2 2 

20 2 3 I I 2 0 2 2 1 2 2 1 1 2 1 1 2 2 3 2 0 1 1 4 3 1 2 2 1 3 1 1 1 1 1 2 2 

15 I I I 3 3 1 3 2 2 2 I I 2 2 1 2 2 3 .. I I 1 2 4 2 2 2 2 2 2 2 I 2 1 I 2 1 

10 2 2 0 3 2 1 3 3 3 3 0 1 2 0 1 2 2 1 3 1 2 2 2 .. 2 3 3 1 3 1 2 2 2 2 2 1 2 

5 2 2 1 2 2 1 3 5 3 .. 2 I 3 1 2 3 3 0 2 2 2 3 .. 2 4 2 2 2 .. 1 2 2 1 2 2 1 2 

0 • • • • 2 2 4 .. 3 5 3 1 3 I 2 3 2 0 I 2 2 3 3 2 3 2 I 3 3 2 3 2 2 2 2 I I 

"'" -5 I 2 • 1 • 3 4 3 3 .. 3 1 2 1 1 2 1 1 2 1 2 1 2 I 1 2 2 3 3 3 2 2 2 1 2 0 I 

I - .0 • 2 1 2 I .. 2 2 3 2 3 2 2 I 1 2 1 2 2 2 3 • 2 2 I 2 2 3 2 .. 1 2 2 2 1 I 1 

·N - • 5 2 2 • 2 I 2 1 2 1 1 3 2 2 1 • 2 1 2 3 2 4 I 2 2 • • 2 3 1 3 1 2 2 2 2 3 2 

U1 -20 2 2 0 • 2 2 2 1 1 1 2 1 1 1 1 2 2 2 2 3 .. 1 1 2 1 1 2 3 2 3 2 3 2 3 2 3 2 

-25 2 2 • • 2 2 3 0 1 1 2 2 2 2 I 3 3 2 2 3 .. 2 2 :1 I • I 3 2 3 2 2 I 3 I I 2 

-30 I 2 • • 2 2 3 I I 2 I 2 I 2 I 3 3 3 2 3 3 I 2 3 I I I 2 2 2 2 2 I 3 2 1 I -35 I 2 2 • 2 2 2 2 2 2 1 2 2 3 2 2 .. .. 2 3 3 1 2 2 I 3 2 1 2 2 3 3 2 3 1 1 1 

-40 0 2 2 I • 2 I 2 2 3 1 • 2 4 3 2 .. 4 2 3 3 3 2 • • 3 3 I 1 2 3 3 2 2 0 1 0 

-45 0 2 2 I • 2 I 2 2 3 2 2 3 3 3 3 .. 3 2 2 4 4 2 • I 4 4 2 I 2 3 .. 2 2 1 0 0 - 50 1 2 2 2 1 2 2 3 2 2 2 3 3 2 3 2 3 2 2 2 .. 3 3 3 2 3 3 2 0 2 3 3 2 3 2 1 1 

55 • 2 3 2 • 2 2 .. 4 3 2 3 3 2 2 3 3 2 2 3 3 2 .. 3 2 2 3 2 2 3 3 2 4 3 2 1 1 

-60 2 2 2 • • 1 1 3 .. 4 3 2 3 2 3 3 3 .. .. .. 3 2 2 2 2 3 3 2 2 3 3 2 .. 3 2 2 2 

65 2 2 • • • • 1 3 .. ... 4 4 3 2 2 3 3 3 3 2 2 2 2 2 2 3 3 2 1 1 2 2 3 3 2 2 2 

70 2 2 2 2 I • 1 2 3 4 4 .. 3 2 2 2 1 1 I 0 I 2 3 3 2 2 2 I 1 2 3 3 3 2 1 1 2 

75 2 3 3 2 2 2 2 3 3 3 3 3 3 3 3 2 • 1 1 1 2 2 3 3 3 3 2 2 2 3 4 4 4 3 3 2 2 

-90 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3, 3 3 3 2 2 2 3 3 3 4 3 3 3 .. 95 3 3 :1 3 3 :1 3 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 2 2 2 2 1 1 I 2 2 2 3 3 3 3 -'10 3 1 :1 3 :1 3 3 3 :1 3 3 3 3 3 3 3 3 3 3 3 1 3 3 '\ :1 '\ 3 3 2 2 2 3 3 3 3 3 3 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1 - 1 - 1--1--1--1--1--1--1--1--1--1--1--1---

'lONG> 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 

Figure 4-17. GEM-9 Formal Uncertainties With Random Signs, 400-Ki1ometer Altitude 
UNCERTAINTV IN NONSPHERICAL GRAVITATIONAL AC~ELFnATION (MGALI <LilT> 

90 , , , , , I I I I I I I I I I I I I 1 I , , I , , , , I I I I I , I I I I 

85 , , 0 0 , , , , , , I , I , , , I I I , , , , 2 2 2 2 2 2 2 , I , , , I , 

80 , , , 0 , , I , , , I I , , , , , I I I , , I 2 2 2 2 2 2 2 , , , I I I I 

75 I I I , , , I , I , I I , , I I I I I I I I I , 2 2 2 2 2 2 2 2 2 2 2 I , 

70 , , , , , , , , , , 2 2 2 , I , , 2 2 I , , , , 2 , , 2 2 2 2 3 3 3 2 I I 

65 , , , , , , I 2 2 2 2 2 2 , , , I I I , 0 0 I , 2 , I 2 2 2 3 3 3 2 2 , I 

60 , , 2 2 , , 2 2 2 , I , , , I I , I I 0 , 0 , , , , I 2 2 2 2 2 , , I , I 

55 , , 2 , 0 , , I 2 2 0 , I 0 I , I 2 I , , , , 2 2 , , , 2 2 , 0 , , , I , 

50 , , 2 2 , , , , 2 2 , , , , , , I 2 2 I , , 2 , , , , , 2 2 , 0 , , 2 2 , 

45 2 2 3 2 2 2 , 0 , 2 I I , I I I 0 2 2 I , , 2 , , , 0 I 2 2 I I , 2 I 2 

40 2 2 2 2 , , , 0 , 2 , 2 , 2 , , 2 2 , , , 2 , , , , 2 2 I I , , , 2 

35 2 2 , , , , , 0 , 2 2 2 2 2 I I 2 2 I , , , , 2 2 , , 2 , , , , , 2 

30 2 2 , , I , 0 0 I 2 2 2 , I I I I 2 I I 0 , 2 2 2 , I I I 2 I , I 2 

25 , 2 , , , 0 , , , 2 2 , , I , , I 2 I 0 0 , 3 3 , I , 2 I , , I 2 I 

20 , 2 , , , 0 , , I 2 I I , , I , I 2 I 0 0 0 2 2 , I I 2 I , , , I I 

'5 , , 2 2 0 2 , I 2 I I I , I I 2 2 I I I I 2 , , I I I I I I , I I , 0 , 0 2 , 0 2 2 2 2 0 I I 0 I I I 2 I I , I 2 I , I 2 0 I , I I I I 

5 1 1 1 1 1 2 3 2 2 1 I 1 I I 2 0 I I , 2 2 , 2 , I 2 0 1 , 1 , , 1 

0 1 , , 1 , 2 3 2 3 2 , 2 I I 2 0 I I I 2 2 , , , 2 2 I 2 I I , I , 

"'" -5 , 0 , , 2 2 2 2 2 2 I I I I 2 I I I I , I 0 , , 2 2 2 I I 0 I 0 , 

I '0 , , 1 0 2 I 1 1 I 2 I I I 0 I I 1 , 2 0 , 1 0 , 2 , 2 , 2 , , 1 , - '5 , 0 , , , I I I I I I I I I I I I I 2 I I 2 0 , , 0 2 I , I , 2 I tv -20 , 0 0 , , I , I 0 , , , , I , , , 2 2 0 , , 1 , 2 , 2 , , 2 I 2 I 0'1 -25 , 1 0 , , 2 0 I , I I , , I 2 2 I I 2 2 , , 2 I 0 2 I 2 , , 2 I I I 

-30 , , , , , 2 , I I , I I I , 2 2 2 I 2 2 , , 2 , , 0 , , , , I 2 , I I 

35 , , 0 1 , , , , I , I , 2 , , 2 2 I 2 I , , , , 2 , , I , 2 I I , I I 

40 0 , 0 , , 0 , , , , 0 , 3 2 2 3 2 2 2 2 2 , 0 , 2 2 , I , 2 2 , , 0 0 0 

-45 0 , , , , I , , 2 , , 2 2 2 2 2 2 2 , 2 2 , , 1 2 3 1 , , 2 2 , I , 0 0 

-50 0 , , , , I 2 I I 2 2 2 , I , 2 I I , 2 2 2 2 , 2 2 I 0 I 2 2 I I , 0 0 

-55 0 2 , , , , 2 2 2 I 2 2 , , 2 2 I I 2 2 , 2 2 1 , 2 I , 2 2 , 2 2 , I 0 

60 , , , 1 , 0 2 2 3 2 2 2 I 2 2 2 2 2 2 2 1 2 , 1 2 2 2 I 2 I , 2 2 I , I 

-65 , , 0 0 0 , 2 3 3 2 2 2 , 2 2 2 2 2 , , , 2 , , 2 2 , , I , I 2 2 , I , 

70 , 1 , , 0 I , 2 2 2 2 2 I , , , I I 0 , 2 2 2 2 2 , I 0 , 2 2 2 , , , , - 75 2 2 2 2 , 1 1 2 2 2 2 2 1 1 1 1 1 0 I , 1 2 2 2 2 2 2 1 1 2 2 3 2 2 2 , 2 

-80 2 2 2 2 2 2 2 2 , I I I , I , I , " 

, , I 2 2 '] '] 2 2 , , 2 2 2 2 2 2 2 2 -85 2 2 2 2 2 2 I I I I , , I I , , 2 2 2 2 2 2 , t , I , , I t I t , , 2 2 2 

90 I I 1 t 1 t I 1 t t I 2 2 2 2 2 2 ~ 2 I t , t t t t I , I t t 1 I t , t , 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1- 1--1--1--1--1--1--1--1--1--1--1--1--1---

"-LONG> 0 20 40 60 80 100 '20 140 160 '80 200 220 240 260 280 300 :320 340 360 

Figure 4-18. GEM-9 Formal Uncertainties With Random Signs, 600-Kilometer Altitude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL IIcrE' fRATION (MGALI .... L 1\ T" 

90 3 3 3 J :I :I 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 :I 

85 I I I I 2 2 :I :I 4 4 5 5 5 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 4 4 :I :I 2 I 

80 2 2 3 4 4 5 5 5 4 :I 2 :I 4 5 5 5 6 6 6 6 6 5 4 4 :I :I :I 4 4 3 3 3 2 2 2 2 2 75 , 2 2 J 4 5 5 4 4 4 :I :I 4 5 5 4 :I 2 :I 4 5 7 7 7 6 5 4 4 :I 3 :I 2 2 I I I I 

70 I I I 2 :I :I :I :I 4 5 5 4 4 4 5 7 8 8 6 5 5 6 7 7 6 6 6 4 :I :I 2 2 2 I I 2 I 

65 2 :I 4 3 3 6 7 6 5 4 :I I 3 5 5 8 I I 10 7 4 2 2 4 5 4 6 7 6 5 4 2 2 4 4 3 3 2 

60 2 :I 5 6 8 6 6 7 6 5 :I :I 4 5 5 6 7 9 7 2 :I :I 4 4 :I 5 6 4 6 5 5 4 6 6 4 4 2 

55 2 1 C; 7 II 5 4 8 5 4 4 4 :I 4 5 4 :I 10 10 :I :I 4 :I 4 4 7 6 , 6 6 8 6 5 5 I 4 2 

50 4 4 4 <I 7 5 4 6 5 4 4 4 :I 5 6 :I :I 9 8 :I :I 4 :I :I 4 7 8 :I 6 8 7 4 :I 5 4 6 4 

45 5 6 4 <I 6 5 2 4 6 3 2 4 3 4 5 2 3 6 4 2 4 5 4 2 2 4 4 4 6 8 5 2 3 5 3 3 5 

40 5 6 4 3 5 5 2 2 :I 3 I :I 3 2 3 2 4 6 4 4 3 4 4 I I :I :I 4 6 6 :I 2 4 5 :I 3 5 

35 4 5 5 2 3 4 I I 2 4 I 2 2 2 2 2 4 4 I 3 3 2 2 2 2 :I 6 5 5 6 4 I I 5 2 3 4 

30 3 4 .1 <I 2 3 I I 3 2 I 2 :I 4 4 3 4 <I 3 5 2 2 I :I 3 2 6 4 3 5 5 2 2 5 2 2 :I 

25 I 1 2 3 2 2 2 2 5 4 2 I 3 5 6 5 4 3 6 5 I 2 2 2 2 I 3 :I 3 5 6 3 2 6 2 I I 

20 I 3 1 2 2 2 2 2 6 7 4 2 5 :I 5 3 4 2 6 7 :I I 2 I I I 2 4 :I 4 6 :I I 3 2 I I 

15 I 3 4 3 2 2 I I 2 5 5 4 5 5 4 :I 4 4 3 9 4 I :I 2 2 2 I 5 :I :I 4 I 2 3 I 2 I 

10 4 2 2 3 2 4 2 :I 2 4 6 7 5 6 5 4 2 5 :I 7 4 2 2 2 2 I I 4 :I 4 4 :I :I :I :I 2 4 

5 5 :I 2 2 2 5 2 4 2 4 7 9 6 7 6 :I :I 4 5 5 4 2 4 2 4 4 2 :I :I :I I 4 :I 2 4 :I 5 

0 6 4 3 I 2 :I 2 3 2 :I 7 6 5 6 7 2 :I 4 4 5 :I :I 4 2 4 :I 5 :I I 2 I 5 4 2 3 :I 6 

01::00 -5 8 <I I 2 2 :I :I :I I I 5 5 6 6 7 4 :I 3 4 4 3 6 2 2 I I 5 6 2 3 2 5 4 I 2 3 8 

I - 10 5 C; 2 2 3 2 2 :I I I 2 4 3 :I 8 5 2 2 :I 4 :I 5 I :I , I 2 5 I 4 4 4 2 :I :I :I 5 

IV - 15 4 4 2 I 4 2 2 5 I I 2 :I :I I 7 :I 2 I :I :I 2 3 2 4 :I 0 2 6 2 5 4 4 5 :I :I 5 4 

-...J -20 5 5 2 , 5 I 4 4 I I 2 4 :I 4 7 2 2 I :I :I :I :I I 4 6 2 2 4 4 3 6 3 6 3 I 3 5 -25 4 4 I 3 7 2 3 3 2 3 3 4 3 5 7 2 3 <I 5 4 5 3 I 2 4 2 4 2 5 I 5 3 4 2 I 2 4 - )0 6 :I , 3 4 :I 2 I 2 2 2 :I 4 4 4 3 2 4 5 4 4 3 2 2 4 :I 4 I 2 2 3 4 3 2 2 :I 6 

-35 6 4 2 2 2 :I 3 I 2 I I 2 3 3 3 4 2 2 4 5 2 3 3 I 3 2 :I 2 3 3 2 4 4 5 :I 3 6 

-<10 4 :I I 2 2 3 4 2 2 2 2 I 2 2 :I 5 :I I :I 4 I I 4 2 2 2 :I :I 6 4 4 :I 4 5 :I 3 4 -45 3 3 2 3 3 5 4 3 2 3 3 2 2 I 4 5 3 2 4 3 2 4 6 3 2 2 4 I 5 4 5 3 3 4 I 3 3 

-50 3 2 3 <I 5 7 3 2 2 2 4 3 2 2 4 5 2 4 5 5 4 6 6 4 3 3 4 4 6 3 5 2 3 :I 3 4 3 

-55 7 4 3 3 4 6 4 4 5 3 2 3 3 I 3 5 3.4 4 4 4 7 6 :I 4 4 5 6 6 5 8 6 3 2 4 6 7 

-60 8 5 2 2 4 7 7 5 6 3 I 4 5 4 3 2 I 3 4 3 3 5 4 I 4 5 5 5 3 4 8 7 4 3 5 7 8 

-65 5 :I I 3 5 7 6 3 3 4 4 6 8 6 3 2 2 3 4 3 4 5 4 3 4 Ii 4 2 I 2 4 3 4 4 5 5 5 

-70 2 2 2 3 4 5 4 2 3 5 5 6 7 7 5 4 4 4 2 I :I 4 3 2 3 .. 5 4 3 2 2 :I 4 5 4 :I 2 -75 :I :I 2 3 3 3 3 3 3 4 4 3 3 4. 5 6 6 5 4 4 5 5 4 J 4 5 7 6 6 5 5 6 8 7 6 4 3 

-80 3 2 , ( , 2 2 2 2 3 3 2 2 3 3 4 5 5 6 7 7 7 7 Ii Ii 7 7 7 7 6 6 7 7 7 6 4 3 

-85 :I 2 2 2 2 2 2 2 2 2 :I :I 3 :I :I 4 4 4 5 5 6 6 6 6 6 6 6 6 6 6 5 5 5 4 4 3 3 

-90 4 4 <I <I 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 <; !i C; 5 5 5 5 5 5 4 4 4 4 4 

1-"1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1- 1--1--1--1--1--1--1--1--1--1--1--1--1--1---

<, ONG" 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 

Figure 4-19. GEM-9 Formal Uncertainties ~'li th RandoJTl Phase, 200-Kilometer 

Altitude 
UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL ACCEl£RAlION (MGALI <l4'> 

90 2 2 2 2 2 2 2 2 2 2 2 '2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 

85 I I I I I I 2 2 2 2 3 3 3 3 3 ~ ~ ~ ~ 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 I I I 

80 I I '2 2 3 3 3 3 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 '2 2 '2 2 2 2 2 2 2 I I I I I 

75 I I I '2 2 3 3 3 2 2 I I 2 3 3 2 2 2 2 3 3 ~ ~ 4 4 3 3 2 2 2 2 I I I I I I 

70 I I 0 I '2 2 2 2 2 2 2 2 2 3 3 ~ 5 5 ~ 3 3 ~ ~ .. 4 3 3 3 2 '2 I I I I I I I 

65 I 2 2 I '2 3 4 .. 3 2 I I 2 3 3 5 6 6 4 2 2 2 3 3 3 3 4 3 3 2 I I 2 2 2 2 I 

60 I 2 3 3 5 4 3 4 3 2 2 2 2 3 3 3 4 5 4 I I 2 2 3 2 3 3 3 4 3 3 2 3 3 2 2 I 

55 I '2 3 3 6 3 2 4 3 2 2 2 2 2 3 2 2 6 6 2 2 2 2 3 3 4 4 I 3 4 4 3 3 3 I 2 I 

50 2 3 2 2 4 3 2 3 3 2 2 2 '2 3 3 '2 2 5 5 2 2 2 2 '2 '2 4 4 2 4 5 4 2 2 3 2 3 2 

45 3 4 2 2 4 3 I 2 3 2 I 2 2 2 3 I 2 ~ 2 I 3 3 2 I '2 2 3 4 5 3 2 2 3 2 2 3 

40 3 3 2 2 3 3 I I 2 2 0 2 2 I I I 2 3 2 2 2 2 2 I 2 I 3 4 4 2 1 2 3 2 2 3 

35 2 3 '2 I 2 2 I 1 2 2 1 I I I I I 2 2 0 2 2 I I I 2 3 3 3 .. 2 1 I 3 I 2 2 

30 2 2 '2 2 1 I I 1 2 2 I 1 2 2 2 2 2 2 2 3 I I I '2 I 3 3 2 3 3 I I 3 I 1 2 

25 I '2 I I I I 1 1 3 2 2 1 2 2 3 3 '2 2 3 3 I I I I I 2 2 2 3 ~ 2 2 3 I 1 I 

20 0 2 '2 I I I I 1 3 4 3 I 3 I 3 '2 2 1 3 ~ 2 I I 0 I I 2 2 3 4 2 I 2 I I 0 

15 1 2 '2 I I 1 1 0 I 3 3 2 3 3 3 2 2 2 2 5 2 0 I I I I 3 2 2 3 0 I 2 1 I 1 

10 + 2 I I 2 1 2 1 2 1 3 4 4 3 4 3 2 1 2 2 4 2 I I I I 0 2 2 2 2 1 I I 2 2 2 

5 3 2 I I I 2 I 2 I 2 4 5 4 4 4 2 2 2 2 3 2 I 2 2 2 I I 2 2 I 2 2 I 3 2 3 

0 3 2 2 I I 2 I 2 1 2 4 ~ 2 ~ 4 2 2 2 2 3 2 2 2 2 2 2 I I 1 1 3 2 I 2 2 3 

"'" -5 4 2 I I I 2 2 1 1 I 2 2 3 3 .. 2 2 2 2 3 2 3 I I I 2 3 I 2 2 3 2 I 2 2 .. I - 10 3 3 I 1 2 I I 2 1 I 1 2 2 2 5 3 1 1 2 2 2 3 I 0 0 I 3 I 3 2 2 I I 2 2 3 

N - 15 2 2 I I 2 1 1 3 I 0 1 2 2 I 4 2 1 1 1 2 I 2 I 2 0 I 3 I 3 2 2 2 2 2 3 2 

ex) -20 2 3 I I 3 I 2 2 I I I '2 '2 '2 .. I I I I '2 '2 '2 I '2 3 I I 3 2 '2 3 I 3 '2 I '2 2 

-25 2 2 I I 4 I 1 I I 1 1 2 2 3 4 I I 2 2 2 3 2 I I 2 I 2 I 3 I 3 2 2 I I I 2 

-30 3 2 I 2 2 2 1 I 1 I 1 2 2 3 3 1 I 2 2 2 2 2 1 I 2 2 2 1 2 I 2 3 2 I 1 2 3 

-35 3 3 I 2 I I 2 1 1 0 1 1 2 2 2 2 I 1 '2 3 I '2 '2 I 2 I I I '2 '2 '2 '2 3 3 '2 2 3 

-40 2 2 I I I I '2 2 I 1 I 1 I 1 2 '2 2 0 2 2 0 I 3 I I I I I 3 2 2 2 2 3 2 2 2 

-45 2 2 I 2 I 3 2 2 . I 2 2 1 I 1 '2 3 I 1 '2 '2 I 2 3 2 I 2 2 1 3 2 3 2 2 2 1 2 '2 

-50 2 I 2 2 2 4 2 I I I 2 2 I 1 3 3 I 2 3 3 3 3 3 2 2 2 3 3 3 I 3 1 2 2 2 '2 2 

-55 4 2 2 2 2 3 2 2 3 2 1 2 2 0 2 3 2 2 3 3 3 4 3 I 2 3 3 4 3 3 4 3 2 2 3 3 4 

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1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1- I - 1--1--1--1--1--1--1--1--1--1--1--1--1---

'-LONG> 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 

Figure 4-20. GEH-9 Formal Uncertainties with Random Phase, 400-Kilometer 

Altitude 
UNCERTAINTV IN NONSPHERICAl GRAVITATIONAL ACCELfRAllON (MGAL) 

<LAT> 

90 I I I t t I I I t I I I I I I I t t I I t I I I t I I I I I I I I I I I I 

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'LONG> 0 20 40 60 80 100 120 140 160 180 200 220 '''0 260 280 300 320 340 360 

Figure 4-21. GEr1-9 Formal Uncertainties \'lith Random Phase, 600-Kilometer 

Altitude 
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90 • 13 13 13 12 12 12 12 12 12 12 II II II II II 10 10 10 10 10 10 10 10 10 II II II II 12 12 12 12 12 12 12 13 13 

85 • 18 18 17 17 16 16 15 14 14 13 13 12 II 10 9 8 7 7 6 6 6 7 8 9 10 II 12 13 14 15 16 17 17 18 18 18 18 

80 • 25 23 21 20 18 17 16 16 15 14 14 13 12 II 9 8 6 5 5 5 6 7 8 II 13 15 18 20 21 23 24 26 27 27 27 26 25 

75 • 29 25 22 19 18 17 16 16 15 14 14 13 13 12 IQ 9 7 7 7 7 7 8 10 13 18 23 26 29 30 31 33 35 37 37 36 33 29 

70 • 30 24 20 16 15 16 17 18 18 18 17 16 14 13 12 10 9 8 8 8 9 12 14 17 23 30 35 38 38 38 39 41 43 43 41 36 30 

65 + 28 21 17 14 12 15 18 20 22 23 24 22 19 16 14 13 12 8 5 7 12 18 21 20 24 32 40 43 43 40 39 41 43 42 39 34 28 

60 + 24 19 17 14 II 15 19 21 22 25 27 26 24 20 17 15 14 8 2 6 13 22 24 18 18 28 38 43 43 39 37 38 39 37 34 30 24 

55 • 20 20 19 16 13 17 20 21 23 25 26 26 26 23 21 19 16 10 4 7 12 21 22 14 9 20 31 38 39 34 34 36 36 34 31 25 20 

50 • 19 24 23 20 19 23 24 21 28 33 29 27 27 25 23 21 16 II 5 8 12 18 20 13 I II 21 29 30 26 30 36 37 36 32 22 19 

45 + 21 27 25 24 27 28 27 19 30 41 35 30 29 25 21 19 17 14 8 7 II 16 20 18 8 6 12 18 17 18 27 35 40 40 33 20 21 

40 + 25 24 24 25 30 27 25 16 21 37 36 31 31 28 20 16 18 17 II 9 II 16 20 23 16 6 8 12 II 21 26 34 42 42 27 23 25 

35 • 26 19 19 21 28 21 19 14 6 22 28 29 31 31 22 17 18 19 13 12 12 14 17 24 22 10 7 12 15 29 27 32 41 38 20 27 26 

30 • 20 20 17 13 25 18 17 16 II 3 19 28 29 27 26 21 17 18 13 14 14 12 3 22 25 15 6 12 19 35 27 30 34 26 18 28 20 

25 + 12 21 16 9 24 19 20 21 23 16 15 28 29 23 27 25 16 16 12 16 16 13 2 17 25 20 8 12 21 38 29 27 25 18 21 2 I 12 

20 • 12 17 16 II 21 22 28 34 35 32 21 30 33 24 25 26 16 15 8 15 14 13 4 16 24 21 12 13 22 36 30 25 19 18 25 13 12 

15 + 14 14 18 14 18 26 35 49 50 41 29 36 40 30 27 24 17 16 6 14 II 12 6 19 23 18 12 16 22 29 27 30 19 18 25 12 14 

10 • 14 14 19 14 18 28 35 55 63 46 32 40 47 38 30 25 19 16 8 9 10 12 5 20 24 16 II 17 22 24 26 34 23 15 21 16 14 

5 + 16 15 22 II 20 29 33 53 66 51 35 40 49 42 31 27 23 II 8 2 9 14 3 15 22 16 8 15 21 23 26 31 24 15 17 19 16 

0 16 14 24 8 23 28 29 53 62 49 37 41 43 37 37 28 25 13 8 3 8 13 4 9 15 12 3 14 20 23 24 24 22 14 16 18 16 ~ -5 14 7 22 9 24 25 26 51 55 42 36 40 37 33 43 33 26 20 14 7 9 II 5 7 6 6 3 15 2 I 27 24 20 15 12 16 14 14 

I - 10 • II 5 18 17 24 19 26 42 46 38 33 35 34 34 42 39 29 26 24 13 9 12 3 8 4 3 6 16 22 33 25 18 9 10 16 10 II 

W - 15 + 8 12 18 21 25 17 25 33 38 36 32 32 33 35 39 41 30 33 32 20 10 12 4 10 6 3 10 13 20 35 25 18 6 10 16 6 8 

I-' -20 • 9 15 19 22 23 19 21 29 35 32 33 33 31 33 36 37 28 36 33 24 12 10 3 10 6 5 II 7 16 31 24 19 8 10 q 5 9 

-25 + 12 13 19 20 19 21 19 25 31 29 32 32 30 32 31 31 24 31 31 23 12 8 3 8 6 4 6 2 13 24 21 16 9 II II 6 12 

-30 + 10 7 16 18 17 22 20 22 26 27 31 30 30 35 29 25 22 28 27 20 10 9 I 6 9 5 3 4 13 19 17 13 II II 9 ., 10 

-35 • 5 6 15 15 21 26 22 21 22 25 31 30 29 34 29 22 21 28 25 19 12 9 8 7 10 7 6 9 13 16 16 14 13 12 12 9 5 

-40 + 3 10 14 14 25 29 23 21 22 23 27 30 26 28 26 20 20 24 25 21 14 7 8 9 7 6 6 10 14 16 14 16 14 13 15 10 3 

-45 • 5 10 12 16 25 30 24 19 24 24 22 23 21 21 18 17 18 20 26 21 14 10 10 II 8 4 6 12 15 14 II 16 17 15 15 10 5 

-50 • 7 II 14 16 24 29 23 20 25 23 17 16 18 17 10 15 19 20 29 26 14 12 10 10 9 5 9 14 14 10 9 15 18 14 12 II 7 

-55 + 8 12 16 13 22 26 20 23 25 21 17 16 18 17 12 14 19 24 33 31 18 10 8 5 7 8 II 14 13 12 15 17 19 13 II 14 8 

-60 5 10 12 9 17 21 19 24 25 20 19 19 19 18 16 15 19 24 31 31 22 14 12 9 8 II 13 14 15 18 20 21 22 14 8 II 5 

-65 + 6 II 13 14 19 22 23 26 26 23 22 22 21 21 20 18 20 23 27 28 25 22 21 19 16 15 15 15 17 20 22 22 20 13 6 6 6 

-70 • 13 18 22 26 28 30 30 30 29 27 26 26 26 27 27 27 26 26 28 29 29 28 28 26 23 20 19 18 18 19 20 18 15 10 7 9 13 

-75 + 18 23 27 31 33 34 33 33 32 30 30 30 31 32 32 32 32 31 30 30 29 29 28 26 24 21 19 18 17 16 15 13 II 10 10 13 18 

-80 • 19 23 26 28 30 31 32 32 31 31 31 31 31 31 32 32 31 30 29 28 27 26 24 23 21 19 17 15 14 13 12 II II 12 14 16 19 

-85 • 19 21 22 24 25 26 26 27 27 27 28 28 28 27 27 27 26 26 25 24 23 22 21 20 19 18 17 16 15 14 14 14 15 16 17 18 19 

-90 + 20 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 22 22 21 21 21 21 20 20 20 20 20 20 20 19 20 20 20 20 20 20 

1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1--1---

<LONG> 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 

Figure 4-23. Gravity f-1ap at a 200-Kilometer Altitude for the Nonaxisynunetric 

Portion of GEM-9 
of the GEM-9 spherical harmonic coefficients. The maps 

dep1ct the follow1ng: 

• As expected, gravity errors for every model decrease with altitude. 

• In addition to the anomalous distribution of gravity errors discussed for the GEM-9 standard deviation mOdel, 

difference models involving the MDI and a GEM model show a 

bana of large differences at latitudes near the Equator. 

• The GEM-9 uncorrelated model predicts a very uniform distribution of errors with a magnitude around 

4 milligals (mgals) (10- 5 m/sec 2 ) at 200 km. The GEM-9 

standard deviation model predicts errors, apart from the 

anomalous region, at·a level considerably smaller than those 

given by the other models. The other models generally give 

rise to errors from 1 to 10 mgals and show much greater 

fluctuations from one location to another. 

4.3 NAVIGATION AND ORBIT PREDICTION ERRORS INTRODUCED BY 

GEOPOTENTIAL UNCERTAINTY 

The interest in geopotential error models is not so much in 

the gravity errors themselves but in their effect on satellite navigation accuracy. Satellite navigation error 

analyses were thus conducted using the SEA program to evaluate, under postulated navigation scenarios, the expected 

orb1t determination and prediction errors resulting from the 

geopotential errors given by different error models. The 

baseline scenario considered was for low-altitude Earth 

satel11te navigation based on a sequential filter uS1ng continuous TDAS range and Doppler track1ng data sampled at 

3-min intervals for 1 day, followed by 5 days of propagat10n 

without tracking. Navigation at 200 and 600 km and at 28-

and 57-deg inclinations was considered. No process noise 

was introduced in the filter: thus, the 5-day propagation 

results should agree with those based on a batch orbit 

4-32 

0112 
determination process. The expected navigation errors resulting from geopotential uncertainties are summarized in 

Table 4-1 for the d~fferent geopotential error models. 

4.4 COMPARISON wITH LANDSAT-5 ORBIT DETERMINATION RESULTS 

Some results on Landsat-5 orbit determination using GSTDN 

and single-TDRS tracking data are presented in Reference 4-12. Measures of orbit accuracies are provided by 

• Overlap ephemeris comparisons of definitive orbit 

solutions (34-hour data arcs with 10 hours of overlap) 

• Ephemeris comparisons of definitive and predictive 

orbit solutions (1- or 2-day predictions based on 

34-hour data arcs) 

The overlap compar~sons of definitive solutions derived from 

TDRS data have maximum differences of 82, 71, 35, 74, and 

35 m. One-day predictions have maximum differences of 186, 

131, 40, 172, and 79 m from definitive solutions. Two-day 

predictions have maximum differences of 412 and 172 m. Although these differences, or errors, result from a combination of geopotential and atmospheric uncertainties and 

tracking errors, it is expected that geopotential uncerta~nties playa major role. These numbers can thus serve as 

bases for the calibration of geopotential error models. For 

this purpose, error analyses were set up to evaluate, under 

the same tracking and batch orbit determination scenario, 

orbit errors resulting from the GEM-9/SAO one-half difference error model and the GEM-9/MDI one-half difference 

model. The GEM-9/SAO error model predicts a maximum pos~­

tion error of 57 m during the tracking period and maximum 

errors of 184 and 236 m during I-day and 2-day propagat~ons. These numbers appear quite reasonable compared with 

actual orbit determinat~on results quoted above. The GEM-9/ 

MDI error model predicts a maximum position error of 77 m 

4-33 

0112 
Table 4-1. Navigation Errors Resulting From Geopotentlal 

Uncertainties 

ORBIT POSITION ERROR 

(meters) 

ORBIT GEOPOTENTIAL ERROR 

CHARACTERISTICS MODEL MAXIMUM DURING MAXIMUM DURING 

24 HOURS OF 5-DAY 

TRACKING PREDICTION 

2OO-km ALTITUDE, GEM-9 STANDARD DEVIATION 21 205 

28-deg INCLINATION 

}l GEM-9/SAO DIFFERENCE 149 481 

}l GEM-9/MD-l DIFFERENCE 168 3209 

}l GEM-5/MD-l DIFFERENCE 186 3495 

RANDOM SIGN 148 496 

RANDOM PHASE 108 575 

2OO-km ALTITUDE, GEM-9 STANDARD DEVIATION 56 1171 

57-deg INCLINATION 

}l GEM-9/SAO DIFFERENCE 126 1271 

}l GEM-9/MD-l DIFFERENCE 253 44886 

}l GEM-5/MD-l DIFFERENCE 227 42745 

RANDOM SIGN 105 4562 

RANDOM PHASE 238 2511 

6OO-km ALTITUDE, GEM-9 STANDARD DEVIATION 9 71 

28-deg INCLINATION 

}l GEM-9/SAO DIFFERENCE 60 246 

}l GEM-9/MD-l DIFFERENCE 73 597 

}l GEM-5/MD-l DIFFERENCE 71 576 

RANDOM SIGN 68 154 

RANDOM PHASE 44 118 

6OO-km ALTITUDE, GEM-9 STANDARD DEVIATIONS 14 235 

57-deg INCLINATION 

}l GEM-9/SAO DIFFERENCE 58 686 

}l GEM-9/MD-l DIFFERENCE 81 1537 

}l GEM-5/MD-l DIFFERENCE 77 2330 

RANDOM SIGN 35 395 

RANDOM PHASE 44 118 

4-34 
during the tracking period but unrealistic, smaller maXlmum 

errors of 58 and 64 m during propagatlons. 

4.5 CONCLUSIONS 

The results described in the preceolng sections show that 

the choice of an appropriate model is very difficult. The 

models studied may be classified into two categories: those 

dependent on internal accuracy estimates and those dependent 

on comparisons with other models. 

Error models based on internal accuracy estimates run the 

r1sk of being unduly optimistic. This weakness can, however, be remedied by a calibration scale factor. The real 

difficulty is the need to consider correlations between 

errors in the geopotential coefficients. This 1S impractical because of the large computational requirements. . 

Short of actually considering the correlations, the GEM-9 

uncorrelated standard deviation model seems to be the most 

appropriate, although correlations do exist. However, even 

this model is computationally prohibitive. Comparison of 

the error map of this model with those of the geopotential 

difference models shows that the geographical fluctuation of 

the error as predicted by this model may be too mild. On 

the other hand, based on the same comparisons, it seems that 

the predicted gravity error magnitude for GEM-9, approximately 5 mgals at a 200-km altitude, is reasonable. 

The random-sign and random-phase models, which are simple to 

implement, give rise to gravity error maps that seem reasonable, w1th local error fluctuations possibly somewhat excessive. The orbit determination errors based on these models 

also appear reasonable, although the error growths during 

predict10n do not clearly exh1bit the distinct character ist1C of a sinusoidal variation superimposed on a linear 

growth. The main objection to these models is that they are 

empirical models without sound theoretlcal just1f1cations. 

4-35 

0112 
The GEM-9 standard deviation model, when compared with other 

models, shows gravitational errors that are too low in the 

Southern Hemisphere and near the Equator. Therefore, its 

predict10n of orbit errors for low-inclination satellites 1S 

too optim1st1c. On the other hand, this model has an unrealistic concentration of large errors near O-deg longitude 

and 65-deg latitude that may give rise to anomalous orbit 

error spikes near these regions. This model is definitely 

faulty and should not be used. 

A comparison between different geopotential models provides 

information about the accuracies of the individual models. 

The geopotential difference error models use the weighted 

differences of the spherical harmonic coefficients of two 

geopotential models as error coeffic1ents. rf one of the 

geopotent1al models is considerably more accurate than the 

other, the straight difterence of the two models can be considered, w1th good confidence, as representative of the 

errors of the less-accurate model. If the two models are 

derived from independent sources, there is some justification in using their weighted differences as characterizing 

the accuracies of individual models, although the justification is weak and cannot be rigorously proven. 

SAO and MDI are models independent of GEM-9. GEM-9 was derived several years after SAO and MOl, and there should be 

no disagreement that GEM-9 is a considerably improved 

model. Thus, the GEM-9/SAO and GEM-9/MOI difference models 

serve as good error models for the SAO and MDI geopotential 

models. Doubling the numbers shown in Figure 4-5, which are 

for one-half the model differences, implies that the gravitational errors for the SAO model at a 200-km altitude vary 

from 2 to 26 mgals. The error map shows local fluctuations 

but not any particularly recognizable features. Similarly, 

it m1ght be said that Figure 4-2, with the errors doubled, 

describes the accuracy of the MOl model. It should be noted 

4-36 

0112 
that, 1n Figure 4-2, there is a band of large errors at 

equatorial latitudes reaching, at a 200-km altitude, as 

large as 60 mgals (1n accuracy), which is comparable in magnitude to the total contribution of the nonaxisymmetric 

portion of GEM-9. This band and its large magnitude is 

bothersome, because no ready explanations exist. Away from 

th1s band, the error distribution appears reasonable. 

Of course, it is not the errors for these older models but 

the accuracy of GEM-9 that is of interest here. Since, at 

best, only the level of orbit determination error resulting 

from geopotential uncertainty can be expected, it may not be 

unreasonable to take the scaled d1fference of GEM-9 and a 

less accurate model as an error model for GEM-9, with the 

scale factor determined from some means of calibration. For 

instance, it might be speculated that GEM-9 is twice as accurate as MOl and that therefore one-half of the GEM-9/MOl 

difference would serve as an error model for GEM-9. This 

is, of course, not completely satisfactory because gravity 

errors are expected to become more uniformly distributed for 

higher order and more accurate models. The band of large 

errors, shown in Figure 4-2, is probably reflective of the 

nonuniform inaccuracies of MOl, and a simple scaling of the 

error model that preserves this feature of concentrated 

error would not be a good error model for GEM-9. The same 

consideration also appli~s to the GEM-9/SAO difference 

model. However, as shown in Figure 4-5, this difference 

model has a more random error distribution devoid of particular unexplainable features. Thus the GEM-9/SAO difference 

model, with a proper scaling factor, appears to be a reasonable error model for GEM-9. 

The primary interest is not in the global gravity error distribution itself but in the effect of geopotential errors on 

orb1t determination accuracies. Table 4-1 shows the orbit 

determination and prediction errors according to the 

4-37 

0112 
d1fferent geopotential error models. The follow1ng may be 

observed from the results presented in the table: 

• W1th the exception of the GEM-9 standard deviation 

model, the orbit determination errors predicted by the different models do not differ by a factor greater than two 

during the tracking period. The error of the GEM-9 standard 

deviation model is too low. Greater differences occur for 

orbit propagation beyond the tracking period. 

• The GEM-9/MDI and GEM-5/MDI one-half difference 

models are similar. Perhaps as a result of the large band 

of anomalous errors discussed earlier, the orbit determination errors predicted by these models are erratic (The exceSS1ve errors for the 200-km-altitude, 57-deg-inclination 

orbit and the small propagation errors for Landsat-5 as discussed 1n Section 4.4.) 

It may be concluded from this study that the GEM-9 standard 

deviation model and GEM-9/MDI and GEM-5/MDI difference models 

are all faulty and should not be used. The random-sign and 

random-phase models are difficult to justify theoretically 

and do not seem to offer any advantage over the GEM-9/SAO 

difference model. Although the GEM-9 uncorrelated model has 

not been extensively studied, it is not expected to be much 

more accurate than the GEM-9/SAO difference model, yet the 

computational burden is much greater. It appears, from this 

llmited study, that the scaled GEM-9/SAO difference model is 

the best error model for GEM-9. A scaling factor of onehalf 1S tentatively suggested before the availabil1ty o~ 

add1t1onal calibration. 

4.6 REFERENCES 

4-1. F. J. Lerch et al., "Gravity Model Improvement Using 

GEOS-3 Altimetry (GEM lOA and lOB), paper presented at 

AGU Annual Meet1ng, Miami Beach, Flor1da, April 1978 

4-38 

0112 
4-2. Goddard Space Fl~ght Center, X-552-76-77, Mathematical 

Theory of the Goddard Trajectory Determ~nation System, 

J. O. Cappellari, C. E. Velez, and A. J. Fuchs (ed~­

tors), April 1976 

4-3. --, X-921-77-246, Gravity Model Improvement Us~ng 

GEOS-3 (GEM 9 & 10), F. J. Lerch et al., September 1977 

4-4. C. F. Martin and N. A. Roy, "Error Model for the SAO 

Standard Earth," The Uses of Artificial Satellite for 

Geodesy, AGU Monograph 15, washington, DC, 1970 

4-5. Computer Sciences Corporation, CSC/TM-81/6033, Feas~­

bility Study on Altimeter Measurements as Supplemental 

Data for Upper Atmospheric Research Satell~te Orb~t 

Determ~nat~on, B. T. Fang and J. R. Kuhn, January 1981 

4-6. Stanford Telecommunications, Inc., STI/E-TR-25066, 

Tracking and Data Acquisition System (TDAS) for the 

1990's, Volume VI TDAS Navlgat~on System Architecture, 

B. D. Elrod et al., May 1983 

4-7. C. A. Wagner and F. J. Lerch, "The Accuracy of Geopotential Models," Planetary and Space Science, December 

1978 

4-8. EG&G Washington Analytical Services Center, Inc., 

Applied Systems Department, Report No. 003-78, Gravitv 

Model Improvements and Implications for Operational 

Orb~t Determ~nat~on, B. T. Fang, October 1978 

4-9. --, Planetary Sciences Department, Report No. 001-80, 

Orbital Error Analysis Studies for GRO and Landsat-D 

Using One-Way and Two-Way Measurements, 

J. J. McCarthy, May 1980 

4-10. Smithsonian Astrophysical Observatory, Special Report 315, 1969 Smithsonian Standard Earth (II), 

E. M. Gaposchkin and K. Lambeck, May 18, 1970 

4-11. B. T. Fang, "Satellite-to-Satellite Tracking Orbit 

Determination," Journal of Guidance and Control, 

January-February 1979 

4-12. Computer Sciences Corporation, CSC/TM-85/6731, Flight 

Dynamics Divislon Single-TORS S-Band Navigation Certi- ficat~on Plan and Cert~fication Results for Early 

Tracking and Data Relay Satell~te System Users, 

J. O. Cappellari, Jr., et al., September 1985 

4-39 

0112 
SECTION 5 - ORBIT SMOOTHER PROCESS NOISE STUDY 

Because the batch method of orbit determination is a subset 

of an orbit smoother, an improved orbit determ1nation accuracy would be expected with a smoother. As discussed in 

Appendix A, the SEA program now has the capability of evaluating the performance of orbit smoothers. Limited investigations using this new capability have been performed as an 

exploratory study of orbit smoothers and also to validate 

the fading memory process noise option of the SEA smoother 

capability. Two different orbit determination scenar10S are 

considered: 

• The baseline TDAS navigation scenario for a 600-kmaltitude, 28-deg inclination satellite considered 

in Section 3 

• The 34-hour arc Landsat-5 orbit determination 

scenario referred to in Section 4.4 (This investigation is undertaken in part to determine if the 

degradation of Landsat-5 orbit accuracy discussed 

in Section 2 results from geopotential errors compounded by the reduct10n in track1ng coverage.) 

The TDAS navigation smoother results are summarized in 

Table 5-1. Two process noise options are considered: the 

linear growth option and the fading memory option. The 

linear growth option assumes that, 1n addition to the 

modeled evolution ot the covariance matrix, there is an additive increase (noise) in the variances of the Cartes1an 

veloc1ty components proportional to the time elapsed since 

the last measurement. The fad1ng memory option assumes a 

mult1p11cative 1ncrease of the whole covar1ance matr1X. The 

orb1t smoother does indeed improve the performance over that 

of a batch orbit determination process for this particular 

TDAS scenario. The major error sources are geopotential 

5-1 

0112 
errors and clock acceleration; the TDAS ephemeris errors are 

secondary, and other error sources are negligible. Although 

the fading memory option has not been invest1gated 1n as 

much detail as the linear growth option, the former does not 

appear to offer any advantage over the latter. 

Table 5-1. Orbit Smoother Performance for the TDAS 

~avigation Scenario 

Process Noise Option 

Linear Growth Rate 

-16 2 10 (m/sec) /sec 

-14 2 10 (m/sec) /sec 

-12 2 10 . (m/sec) /sec 

10-10 (m/sec}2/sec 

-8 2 10 (m/sec) /sec 

Faaing Memory Multiplicative Factor 

1.1 

1.25 

1.5 

Orbit Pos1tion Errors (m) 

Maxima 

104 

78 

67 

40 

42 

61 

63 

98 

Root Mean Square 

46 

41 

33 

24 

23 

24 

36 

38 

The Landsat-5 results are presented in Table 5-2. Tracking 

aata cons1st of single TDRS and ground station data. The 

only error source considered is the one-half the GEM-9/SAO 

geopotential difference discussed 1n Section 4. Generally, 

1ncreasing the process noise tends to decrease dynam1c error 

at the expense of measurement error. Although measurement 

noise is excluded, Table 5-2 shows that an opt1mum noise 

level exists above which the dynamic error also increases. 

Another 1nteresting result shown in Table 5-2 1S that, with 

the add1t1on of ground tracking data, orbit errors actually 

increase it process noise is not introduced. This 1S not a 

generally valid conclus1on but shows that the behavior of 

5-2 

0112 
dynaruic error is difficult to predict. On the other hand, 

Table 5-2 shows that, with the use of process noise, orbit 

errors are decreased when more tracking 9ata are available. 

Table 5-2. Landsat-5 Orbit Smoother Error Caused by 

One-Half GEM-9/SAO Differences 

Process Noise 

Linear Growth Orbit Position Error 

Rate 

(m) 

Trackl.ng Data 2 (m/sec) /sec Maximum Root Mean Sguare 

Single TDRS and 

Lanasat-5 ground 

tracking stations 

As above with addition of several 

Landsat-4 ground 

tracking stations 

10-8 

10-10 

10-12 

0 

10-12 

0 

69 24 

56 20 

47 24 

57 28 

42 17 

69 30 

Other results not shown in Tables 5-1 and 5-2 include the 

following: 

0112 

• Maximum errors generally occur near two ends of the 

data arc where smoothing has smaller effects. 

• Orbit solutions propagated beyond the data arc are 

generally less accurate for smoothed solutions than 

for batch solutions. This 1S not unexpected because the process noise introduced in an orbit 

smoother is artl.ficl.al rather than physical. 

5-3 
SECTION 6 - CONCLUSIONS 

Several tOP1CS related to 10w-alt1tude satellite orbit determination have been investigated. The topics stud1ed and 

maJor conclus10ns reached are summarized below. 

• Landsat-S Orbit Determinat10n using GPSPAC data--

Landsat-S orbit solutions computed from GPSPAC deltapseudorange (Doppler) data are good. Maximum differences 

between GPSPAC and GSTDN solutions are generally under 

70 m. Maximum differences between partially overlapping 

GPSPAC solutions are even smaller. There is a good possibillty that the GPSPAC solutions are superior to the G5TDN 

solutions in accuracy. 

For orbit determination instead of real-time navigation, 

s1multaneous data from four GPS satellites are not necessary. The ~tudy results indicate that approximately 3 hours 

of data from a single GPS satellite. are sufficient to resolve Landsat-S orbit and clock. A study of a randomly selected sample shows that the Landsat-S orbit solut10ns based 

on lndividual GPS satellites agree to within 80 m, and 

typically less than 40 m. 

As with Landsat-4 GPSPAC data, some inconsistencies exist 

between the Landsat-S GPSPAC pseudo range and deltapseuQorange data. Landsat-S solutions derived from pseudorange data generally differ from the GSTDN solutions by 

maximas over 100 m. Furthermore, large, GPS-independent 

range observation residuals of over 100 m are seen in 

delta-pseudorange Landsat-S GPSPAC data solutions. Based on 

these, it may be concluaed that the pseudoranges have systemat1c errors on the order of 100 m in addition to the expected clock errors. The causes of these systematic errors 

6-1 

0112 
have not been determined, although bad data from an individual GPS satellite and several easily committed preprocess1ng 

errors have been elim1nated as possible reasons. 

In connection with the GPSPAC study, the computation of 

Landsat-5 orbits from GSTDN data was undertaken. Unfortunately, there are not as many ground tracking stations for 

Landsat-5 as for Landsat-4, and the accuracy of the resulting Landsat-5 orb1t solutions is not as good as the corresponding Landsat-4 solutions. Investigations show that this 

degradat10n cannot be attributed solely to dynamic modeling 

errors accentuated by the sparsity of tracking coverage. 

• TDAS Simulation--Simulated TDAS one-way Doppler 

data were generated. The data, with errors added, were input to an extended Kalman filter in R&D GTDS for the navigation of low-altitude Earth satellites. Comparisons with 

truth models yielded information about the navigation performance. The results showed very good agreement with those 

obtained earlier from error analysis using the SEA program. 

The agreement provides confidence in the TDAS capabilities 

of both programs and indicates that TDAS navigation performance can be studied economically using SEA instead of the 

computationally expensive simulations. 

• Error Model for GEM-9--Several candidate error 

models for GEM-9 were studied. Although the specification 

of an appropriate model was difficult, the use of the 

GEM-9/SAO difference model with a proper scaling factor is 

recommended. A scaling factor of one-half is tentat1vely 

suggested before the availability of add1t10nal calibrat1on. 

• Orbit Smoothers--Some exploratory study of orbit 

smoothers was conducted using SEA. The fading memory process n01se option of SEA was validated. However, this option 

does not seem to offer particular advantages over the l1near 

growth option. This l1mited study showed that an orbit 

6-2 

0112 
smoother can indeed outperform a batch orbit determ1nation 

process in accuracy. The following two observations may be 

made concerning orbit smoothers: (1) If accuracy is of primary concern, a smoothed orbit near the ends of the data arc 

can be discarded because smoothing action is less at the 

ends and orbit errors are generally greater. (2) Because 

process noises are generally artificial rather than physical, 

orbit propagation beyond the data arc from a smoothed orbit 

is generally not as accurate as the propagation from a batch 

solution. 

• Validation of the SEA Smoother/TDAS Capability--The 

SEA Smoother/TDAS capability was fully validated by testing. An inconvenience of the SEA smoother is that it will 

not output smoother error analysis results at times not coincident with a measurement. It 1S poss1ble to trick the 

program into outputting results by 1ntroducing dummy measurements wlth negligible data weights, i.e., large measurement varlances. 

6-3 

0112 
APPENDIX A - VALIDATION AND VERIFICATION OF THE SEA SMOOTHER/ 

TDAS CAPABILITY 

The Sequential Orbit Determ1nation Error Analysis (SEA) Program has been enhanced to incorporate error analysis capabilities for the following orbit determination scenarios: 

• Orbit determination using the smoother method 

• Orbit determination using the proposed Tracking and 

Data Acquisition System (TDAS) data 

These enhancements to SEA were designed and implemented in 

1984 under Task 42100. 

Th1S appendix outlines the results of the validation and 

verification testing of these enhancements. For the convenience of discussion, the enhanced SEA program w111 be 

referred to as SEA Version 4.1 to distinguish it from the 

unenhanced SEA Version 3.1. 

The testing to validate and verify the SEA ~nhancements was 

divided into three phases: 

• Phase 1 tests ensured that the enhancements have 

not corrupted the integr1ty of the original capabilities of 

SEA Version 3.1. 

• Phase 2 tests compared the SEA Version 4.1 error 

analysis results with those of the independent Orbit Analysis (ORAN) Program. (ORAN is an error analysis program for 

the batch orbit determination method, which can be considered a subset of an orbit smoother. Thus, ORAN can be 

used to verify some, but not all, of the SEA smoother capabi11ties.) 

• Phase 3 tests focused on the smoother algor1thm's 

numerical stability and expected behavior under controlled 

operating conditions. 

A-l 

0112 
These three test phases and their results are described in 

more detail in Sections A.l, A.2, and A.3, respectively. 

During the course of test1ng several software modificat10ns 

or corrections were required. After they were implemented, 

the testing sequence was rein1tialized. These modificat10ns 

or corrections are described in the sections describing the 

test1ng phases dur1ng which they occurred. 

Finally, all keyword deck setups and associated Job control 

language (JCL) used in testing have been archived so that 

they may be used as prototype benchmarks for future modifications to SEA. For reference, the listings of all deck 

setups are reproduced in Section A.5. References to setups 

are made in Sections A.l, A.2, and A.3. The convention for 

labeling a particular setup is as follows: P1SjRk, where i, 

j, and k are integers associated with the phase, a given 

- scenario, and a given run number, respectively, for which 

the test was performed. For brevity, the corresponding SEA 

Version 3.1 control runs used in Phase 1 of the testing are 

not listed. 

A.l PARALLEL FUNCTIONAL VERIFICATION 

A.l.l TESTING DESCRIPTION 

Th1S phase of testing ver1fied the functional integrity between SEA Version 3.1 and SEA Version 4.1 for nonsmoother 

options. It was undertaken to ensure that the smoother and 

TDAS enhancements had not corrupted the eX1st1ng SEA options 

and processing. Parallel funct10nal verification was performed under four different track1ng scenarios: 

1. Direct tracking of a low-altitude satellite from 

10 ground stations--The satellite orbit is at a 200-km altitude and 28-deg inclination. An effective drag coeffic1ent 

is alternately a solve-for or a cons1der parameter 1n the 

orbit determination process. Tracking data are available 

A-2 

0112 
whenever the satell~te is v~sible to a station (deck setup 

P1S1Tl) • 

2. Tracking of a user satellite by six Global Positioning System (GPS) satellites. The user orbit is at a 

400-km altitude and 57-deg inclination. Tracking data are 

available during periods of v~sibility. Several different 

geopotent~al error models are considered (deck setup P1S2Tl) • 

3. Scheduled relay tracking of a user satellite 

through two Tracking and Data Relay Satell~te System (TDRSS) 

relays. The user satellite ~s at a 600-km alt~tude and a 

98-deg inclination (deck setup P1S3Tl) • 

4. Cont~nuous beacon tracking of a user satellite 

through three TDAS satellites (one backside, two frontside)--The user satellite is at a 600-km altitude and a 

28-deg incl~nation (deck setup P1S4Tl) • 

Each of these four tracking scenar~os const~tuted more than 

one test run. In the test runs performed for this phase, 

most nonsmoother options were tested, although not in all 

possible combinations. 

SEA Version 3.1 does not include either the smoothing or 

TDAS options; thus, the basis for compar~son in this phase 

of test~ng was the forward-filtered results and those reports that are smoother/TDAS independent. In testing associated with the TDAS scenario, th~s comparison was slightly 

modified: the forward-filtered results of SEA Version 4.1 

were compared with a TDAS-only modification of SEA Version 3.1. This was to test for any interference that might 

be present when the TDAS and smoother updates were comb~ned 

in SEA Version 4.1. In addit~on, the SEA Vers~on 4.1 tests 

were run with and w~thout requesting the smoother option to 

test for any smoother-introduced inconsistency ~n the 

forward-f~ltered results. 

A-3 

0112 
A.l.2 TESTING RESULTS 

All tests performed us~ng SEA Version 3.1 agreed with their 

correspond~ng SEA Vers~on 4.1 runs. It may be concluded 

that t,he smoother/TDAS updates have not corrupted any of the 

many options preexisting in SEA. 

Th~s agreement is demonstrated by the output list~ngs shown 

in F~gures A-I and A-2, both of wn~ch are assoc~ated w~th 

the GPS tracking scenario. Figure A-I displays the forwardfiltered error budget at 1440 min past epoch result~ng from 

the nonupdated SEA Vers~on 3.1. Figure A-2 displays the 

corresponding output resulting from SEA Version 4.1 (run 

PIS3Tl). Although only three decimal places of accuracy are 

output, the length of propagation is long enough (I day) so 

that any divergence would be displayed. 

A.2 INDEPENDENT VERIFICATION 

A.2.l TESTING DESCRIPTION 

For the independent verif~cation phase, the smoother error 

analysis results of SEA Version 4.1 were compared and contrasted w~th correspond~ng results from the batch orb~t determ~nation error analysis program ORAN. SEA and ORAN are 

two independent programs with different capab~lities; comparisons were thus made under restr~cted condit~ons ~n wh~ch 

correspondence or near correspondence between the two programs exists. In particular, th~s means that no TDAS track-

~ng and no process noise were introduced ~nto this phase of 

testing. Also, clock errors ~n SEA Version 4.1 were emulated by measurement biases in ORAN. 

Under these restrictions, the same geopotential error models, 

measurement errors, and tracking systems were considered. 

However, the atmospheric drag models for the two programs 

are somewhat d~fferent. SEA uses the Harris-Pr~ester model, 

and ORAN uses the Jacchia model. 

A-4 

0112 
:t-' I 

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.0 

.7210-0J 

RSS-VEL 

METI'S!:.C 

.0 

.6520·0J 

• 106 

.0 

.0 

.0 

.8620-0J 

.0 

.10b 

~~ "nCO) 0-

Figure A-2. SEA Version 4.1 Forward-Filtered Error Budget 

at 1440 Minutes. User Tracking Trhough Six 

GPS Satellites 

o~ :UrI()~ 

~Ci) r-trJ 

~ii) 
Because the two programs use different error analysis algorithms, some differences in the results produced were expected even if the 1nitial conditions and 1nput values were 

the same. Spec1al attention was therefore accorded the degree of disagreement between SEA and ORAN results to ensure 

that d1screpancies were not larger than bounds established 

by physical considerations. 

Independent verification was performed under two different 

tracking scenarios using corresponding SEA and ORAN setups: 

1. D1rect tracking of two TORS-type spacecraft through 

a single ground tracking station--Dynamic errors cons1dered 

are lumped geopotential modeling errors (GEM-9 15x15 - GEM-l 

8x8) and grav1tational constant. Measurement bias errors 

are considered on both range and range-rate data (deck setups P2S1Tl and P2S1TIO (the 0 indicates the ORAN run». 

2. Relay tracking of a user satellite through two 

TDRSS-type satellites--The user satellite is at a 400-km 

altitude and a 28-deg 1nclination. Dynamic and measurement 

errors are of the same type as those in the previous 

scenar10. In addition, an effective drag uncertainty is 

considered (deck setups P2S2Tl through P2S2T20). 

In th1s pnase of testing, the smoother results of SEA VerS10n 4.1 were compared w1th the batch results from ORAN. In 

addit1on, correspond1ng observat1on measurements and propagated ephemerides between SEA Version 4.1 and ORAN served as 

add1tional bases for comparison. 

A.2.2 TESTING RESULTS 

In the course of test1ng, it was found that the two programs 

usually agree quite well: two to three decimal digits were 

quite common for most numer1C results. 

tween the two programs was ach1eved in 

scenario. Figures A-3 and A-4 display 

A-7 

0112 

Close compar1son bethe direct track1ng 

the error budget 
~ 

I 

00 

TJ Ir" ,1''''11 [r>~rH PI ',PJlITF'> = lnAO. 

r,rHl \!r 'Jr r 

lIl'o'P, ) "1r ~ <;r. T "r II ,r T ... ror tI<::r> I 0' 

'[A<'. t 4 f) '> c; 

r,n,.'Jr'1rr 

LlJ' ',lr J ~·FII~.I 1 " [,' ~I'" T " 

~'f"/\<;'~I :: "'r A<;"" T ' .. 

flS, 

F" R R 0 R R U 1'1 r. E T 

'>~T.nllt ,AT.otC C:;AT.nll R'\C;.POS 'AT.01Hn - C:;AT.01cn 

.,ETFIl' "',TrRS '~ETrRC:; WF"Tf'lC; "'T/'\Er. MET/'\"'r. 3. 11 , •• ?lP .21'.' ?A.O:; .?070 .. 0? .1?A'1 .. 03 •• ?7n .~7;' 2.11 ?15 •• 1610 ... 03 .15&0.04 •• ;'070·01 •• 1'\9 .20." 110." .\49n.0:? .92"n·04 

I'J .n n ~n _ • 0 .n • '.'1 • '1.1 .40." • 1." .?<J60.02 .1;"I4n.03 

0 .0 II .0 .n .n ~.')Q '1.1 ~, .1, F.?' .'\91n.02 .':'7'\n.03 

c;:. T.'l;>H ,t.T,n2C <;AT.02l RC;S.POS c:;AT·02HIl SAT;c~cn 

"~TP~' '-'rTF RC; l~rTf"R C; IlF"Tfg,\ M['f/c:;~r. N[T/C;~r. 

."i4 .I'?1 21'.'\ ?R.7 •• ?O O.,.o~ •• I'uo·03 .",,, '.'1 6.<J4 7.71 •• "1150.03 •• 430;n.04 

.0 • n ~n . .n . .0 .0 _ 

.17"['.'1] .'\C}" cO." ?n." •• 150n':'n2 •• <JOln.04 

" .01 0 .n .0 .n .!.'J' 1.'\9 .~'.7 '4.n .\8Bn.02 •• 19:m .. 02 

4.<)7 '.[\1 if?q 4'\.'\ .'22n.02 • \9"n.02 

Figure A-3. SEA Version 4.1 Smoothed Error Budget at 

1080 Minutes. Direct Tracking on Two 

TDRS-Type Spacecraft 

C;AT.OlLD RSC;.VEl 

MF"T/SEr MET/'>Ec: 

.?62n.0, 

.1360.04 

.2090.02 

.162n.03 

.4270.05 .150n.02 

.0 

•• ,\870·03 .0 

.305n·02 

.0 . .468n.03 .0 

.4001).02 

SAT .. 02ID RSS·VEL 

MET/SEr 

.?54n·0,\ 

"IET/'>Ec 

.210l).n2 •• 159n.04 .51Bn.03 

.0 

..166n.05 .0 

.150n.02 .n .0 .7820.04 .269n.02 

.2660.03 .376n.02 
)I 

I 

\0 

Of"l T A I~ 

1"·Tf"R"'1 

'.4;J44 

•• ,78';1 •• 1".26160.n1 

o 

'.1973 

.0 

'.53n .('33';9 

.0 

.14"'50."1 

o .~. 4491 

r::~TIIo1ATEO HCI F"RROR F:lR ARC NO. , OIlE Tn IINIiOnn EO PARAIo1EH'~c; 

orLTA C nrLTA L 1"Tf"R~1 (V.TrR~1 R~~ P:lc; nF"LTa HonT nf"LTa rO~T 

(Io1F"TF"R~1 IrM/~F"r' (rM/~F"CI nELTA LOOT 

I rl"~F"e I 

TlIoIr = 108n.Oo MTNIITf"S vYl4l1on HHNN ~~.~ = 80n"ln1 t800 o.n _.1f,~I\R 

_'7:I'l~ 

_,.1'R75 

.0 

·'O.CJ'l2 

.0 

.914C17 

~.';'04 

.n 

_6""'''0 

.0 

,."t..4 

_~R.'24 

~.1tg~ 

_'0."17':' 

.0 

-40.?&7 

.0 

'8 1 47,- (, • .,,"1'-

.0 

?0.48':' 

.0 _,3.47" 

Figure A-4. 

SATF"lI TTE 1 - • 'R.5~1 .207,6. .1'n71~7Q_n1 .~'-'429RQ.01 

'.15"1C1 •• 1(,139n_01 ~14qO~S'0_02 .1~('4660J_O? 

?0.37(' .14C118 ,.10004"10_01 ~4~5(,97<1n_03 

.0 .0 .0- .0_ :;1.3'0 .• 2C14<11 _';""\9"1&n-01 -. ~A6(,051,,-01 

.0 .0 .0 .0 

SATF"lI TTr 2 - . - • 'P.709 _.20R"3. -.1'''105040_01 .'~44&3nJ.01 

7.747? _.51,,_9n.01 -,.4"'''10ARn.02 _.1"6'814"_02 .0 .0 .0 _ .0 _ ?0.497 _.1"on, -_9(,(,(,0(,AO.02 •• 1'~"I914n_C3 

.0 .0 .0 .0 - _ ".8"10 .1A~t..R -.lA607('R .R1R15&4".02 

ORAN Batch Error Budget at 1080 Minutes. 

Tracking on Two TORS-Type Spacecraft 

R<;S Vf"L (rM/~f"CI 

.'0948. 

.16?(,~n_n1 

.149"1 

:g04"'1 

.0 

.'10S0. 

.518"90.01 

.0 

.1~0"l'l 

:g6300 

Direct 

UNAO.III<;TEO 

PARAIlf"TF"R 

"RAVeo M01_MO? GRAV 

RNGRtAc;1 

Rr~GRU<;2 

ROOTRIAS1 

RDOTRIAS2 

"RAVeO 

M01_M02 GRAV 

RrJGRJA<;l 

RNGRU'i2 

ROOTRIAS1 

RDOT1HAS2 

00 

"11~ 

"tJ B 

02 

O;D 

::or 

,0"'0 

C:):! 

):.C) 

r-m 

~Cil 
output from SEA VerS10n 4.1 and ORAN (setups P2S1Tl and 

P2S1T10) at 1080 min after epoch. 

In the relay track1ng scenario, a limitation in ORAN complicated the process of comparison between the two programs. 

ORAN does not model the TDRSs directly as relay satellites 

with given orbits; an artifice has to be used to make ORAN 

s1mulate the relay role of the TDRSS.l Naturally, greater 

d1spar1ties should be expected between the results. 

An example of the relay tracking scenar10 results is shown 

1n Figures A-S and A-6, in which the error budget outputs 

for 180 m1n past epoch are shown for SEA and ORAN, respectively (deck setups P2S2Tl and P2S2T10). All error budgets 

agree quite well except for the errors caused by the gravity 

coeff1cient uncertainty and the drag uncertainty. The ORAN 

result shows considerably greater effect for the gravity 

coeff1cient uncertainty. This was expected because, in the 

artifice of ORAN simulation, this uncertainty also accounts 

for part of the TDRSS ephemeris errors. In other words, the 

ORAN result includes both the dynamic effect of gravity coeff1C1ent uncerta1nty and the geometr1c effect of TDRSS 

ephemeris error that can be attributed to grav1ty coefficient uncertainty in deriving the TDRS orbits. The drag 

uncertainty effects from the two programs are d1fferent 

because, as discussed above, two different atmospheric drag 

models were used. 

A comparison between SEA and ORAN was also performed for the 

scenario in which all three satellite orbits are solved for 

s1multaneously. Figures A-7 and A-8 demonstrate the results 

of setups in wh1ch both relay and direct track1ng of the 

lEG&G Wasnington Analyt1cal Services Center, Inc., TDRSS 

Era Orbit Determ1nation System Review Study, B. T. Fang and 

B. P. G1bbs, December 1975. 

A-10 

0112 
~ 

I 

I-' 

I-' 

Tl'~r FRn'l EPOrH IN '-IUJlJTES = tAo.n 

F' A R 0 A Run .. F' T 

C;AT.O'-H C;AT;ntC SAT ... oiL RC;'i·POS C;AT·01Hn SAT;01CD "TTrAC; ~'F'TrAS MGTF'AS oIF'TfQC; '~F'T Ic;~r • "'fT/"rc IJSrIlI'R~G .17A '.40 ~ .!lIS 9.80; .li6 n .. 02 •• ,73n·02 GkAvrOI'"F .""10 .'1780.01 •• 107 .(,60 .527n .. 04 •• qOOD.03 I I JprO .14.4 f,0;.(, ~3f1.4 7'1.7 .'I60n .. [ll .'I4qn.Ol r'~!1 C;R I 1 .2.'1'1 .'1.'11 1.0;'1 4.30; •• li15n.03 • 'I7:m.02 .IEt.<:;pI ? .7'1'1 '.?7 3.tA '1.9" ~.t51n.02 .,,67n.02 r~rt.C;RI 'I •• 10nn~05 .4090.02 •• 39"0;0' .'17nn.o, .422n.o'1 •• ,"07n.05 "f!lc;qI 4 •• '9'1n.03 •• 'IF.60~n' •• q4'10.n'l .'I7qn.O? .t43n.05 .44An.05 

p<;c: 14.F. f,o;.!! 3,.n 74." • "3n.Ol .'I5An.Ol 

Figure A-5. SEA Version 4.1 Smoothed Error Budget at 

180 Minutes. Relay Tracking of 

400-Kilometer-Altitude Spacecraft 

Through Two TDRSs 

SAT·OllD 

"'ET/SEr. 

•• 204,,~03 

.545n~03 

.206n.01 

.261n.02 

•• R61'l~03 

.679n.07 

.313n.o(' 

.20AI').01 

~o 

.... ~ 

;Je 

o~ :aro~ fC) 

r-1'1 

~Ci) 

RSS~VEl 

MET/s~r .10 n.Ol 

.105n.02 

.5420.01 

.464n.02 

·l10n.02 

• 39n.05 

.472n.05 

.558n.ol 
~ 

I 

I-' 

tv 

'If"l T, II ('~rTric ) 

.1."lC'd 

.111 ,:>c:r 

.A!.,lh'i".n1 

.:>.'I'I~] 

.1J'I~~ 

•• ·'11:>7r'l.,,:; •• ,:><j;>Q( rl.03 

~.541:> 

•• 13111; •• '\] 1:>111'.11" •• "I<)('Il'n.'1"\ • :>'Io 1Qr.,,5 .:''11'11.'''.('11.1 

.':>?"I42f'.n:! 

'1.4'17Q 

1. Cj'lH •• :>11'\RI,').r!: • ;>U .. I~')').,,5 

• >S114 U n. /I') 

•• ~,~cPI"r:.,,-3 

."?O~4'.r': 

on TA C ItJ~TrR<:1 

" .. 1\1n1 F.>I ~~'3 

l.f?t."i 

.~.~104 

':> ?7111 

.4n Q I20.0:> •• "~"<)<\n.n;> 

1 "'''1,\1 •• {I''':><)').n1 

.]'1]<)'10.04 

• .31~A ~ 7n. 04 

.'101'-1'10.0 4 

.h'11"'IO.nA •• l Q 'l7"1n.n 7 

.1."1'1]1 

.:>.71':>' 

.1'\1\"I~n.04 

.:>'11'\7n.04 

• :>fl 9:> On. Oil 

.1:>'I Q 'In.n7 •• t4"1':'n.'l7 

f'"<:TI"HEo Ilrl 

'):-LTA 1 

("F"T[RC::I 

TT"F" = 1e'l.0'lO 

".51'17 

.,:>1,'1":> 

.4.w"S"', 

1.5"1'~7 

'I 1A~<) 

•• ~9~4:.').n':> •• Q4"'lJ(D.n~ 

.2"."'i" 1.nOn'l _ •• ':>5'1"111).0" ... ".7~1:>O.o':' 

•• 1CJ"",:1.n" 

.444""°.01> 

•• '\71'41>').nl'l 

,1\."1<;'1 

1 I, "ollq •• '\3'1I1Q').0". 

.11A:>r,D.,,"o 

•• 1'14'l"n.0'i •• t~n:>'IJ.'l7 

.A4:>7')D.nA 

rRRQR FJI' ~PC Nn. 1 OIlE Tn WJIIIOr'ln E,) PARAMETr~<: 

')fLTa LonT 

(C'4/<:rc, R<:~ P1~ r'lf'"LTa HonT (qrT~R<:1 ,r~/<:rCI 

on Tft rD'lT 

'T~UTF"S YY~MOO 

B.1 2r." 71~. 91'1 7 

4.'i0"\('I 

1I.'5:>F. 

:'I.QAO'\ 

."'~97r').0:> 

• 'I190''m.O:> 

::In.91t/) 

1.00'11 

.. 1'141:>r'l.04 

.1t4<JF.:>n.:'Ili 

.'10'11 "In.04 

.7,\"il"n.o'l 

.:>(\'1'1""'1.07 

'.j.'~1 

111.9'1" 

.. 1F.8"11n.OIl 

.~"I'I(j;!"'I.04 

."l<jQQ7n.t')4 

.I'114CJO.07 

.11'.9Q1n.07 

~nrll TTf'" •• ~'I7q1 

'1.'17"'; 

.41l0:l7 

•• Q'''Q':>n.01 -.1"71'i_ 

.4':>:>000.0'1 

.11l'l'l~'l.0'l 

snr~1 TTE .211R7 

_.7:>qQ~0.02 

.q:>'1CJO'l.nR 

•• 5n1]1"\0.nl1 

.'3'-"'5:>:3.0R 

-.2"7':>70.10 

.34<)17".10 

'>ATrll TTF" 

-.210(.1; 

_.ln71':>_ 

.3"'840.07 

_.4'-CJ77D.nA 

.1:>11'00.07 

.i!A';74~.11l 

_.6,,'-46r.l0 

(rM I<:~C' 

HHM~ ~q.q = A1l0~01 

1 

300 0.0 

·.4'1n'l'19 

'I.""nh'l3 

·.1"4 D 46 

.'11:>'19'12 

.~~I;CJ?A'I 

•• F.nr,<I"Iuln.1l3 

.4 .. 1\1 &\7<1".(\3 

2 - •• R:>I\'1'1CJn.n2 •• 'I&<lF.1790./)2 

.. Q"0F.~"'An.n7 

."'1'1:120hU.07 

.7o;~1CJ?7'.07 

•• p"''II>(\'n.l0 

.1n7'1:>Qon_n9 

3 - • '1'-'1'171l 'ir'l. 02 •• 1~77"o14n.Ol 

.. "7''-lluon.07 

.""'1"'''''?'.'18 .:>:)'\4"077'.07 

.R"'I'IfI"<lr).10 

•• ~7:>CJ47(,"1.10 

.'7lJOR9R 

?n41]('67. 

•• I\<lI\CJ H"o"'l.02 .:>~1449'1_ 

•• AQ"i561::3.01 

.~771l5'l<)".n'\ 

.31':>F.497"'1.114 

.'U6<J03'10.01 

.qU1'127"o~.O'l 

.~nn:>93<):3.08 

.?n""'IOII::3.07 

.1'-774?1:3.07 

.(':>7t,4f,4~.11 

•• 1"''1457'.10 

.?"''1'\1210.01 

•• 7""F.R7'1:l.0? 

.1'1?':>60nQ.07 

.1A71;71'1Cl./)7 

.1<)<)'797:3.07 

.1411?1''I:3.10 

•• 1'1:>'1'19''''1.10 

I?q.. vrL Ir"/<:~CI 

.5';7117 

'1.'41'\ 

.45900 

.4&414 

.709'l2_ 

.7'19:>'\::).03 

.471F.O~,.03 

.;>10"14 

.777(}5').0, 

.CJ,,7000.07 

."o7'1r.'1~.07 

.772"'~.07 

• CJ 04<1<)0.10 .11'1AA"'.n9 

.?1''1'1 

.10R41_ 

.(,'J')1RO.07 

.?044'1C.07 

.3'3:>3c.07 

.1'4,-tO.09 

.';7A09"'.10 

Figure A-6. ORAN Batch Error Budget at 180 Minutes. Relay 

Tracking of 400-Kilometer-Altitude Spacecraft 

Through Two TDRSs 

UNI\O III'>TEO 

PAR A\~F"TF"R 

r,RAVCO 

MD1.MD2 GRAV 

ORAr. 

RNGRU<;l 

RNr.RIAS' 

RnOTRIAS1 

ROOTRIAS2 

r,RAvro 

Wll.MD;> G~AV 

ORAr. 

RNGRTA<;l 

RNr,PU,>' 

ROOTRIAS1 

ROOTQIAS2 

r.RAvro 

~101.MD' GRAV 

ORAr. 

RNr.PIAQ1 

RtJr.RtA<;2 

RDOTRlAS1 

ROOTRtAS2 
~ 

I 

I-' 

LV 

TIME FROM EPOCH-IN MINUTES = .0 

SAT-OIH 

METERS 

MEASOI I -1.~7 

MEASOI 2 1.19 

MEASOI 3 -.~1~0-02 

MEA 501 4 -.8890-02 

RSS 1.90 

SAT-02H 

METERS 

HEASOI I -1.42 

HEASOI 2 -.2JO 

MEASOI 3 -.3810-01 

MEASOI It .5420-01 

RSS 1.44 

SAT-OJH 

METERS 

MEA SO I 1 -1.52 

MEASOI 2 -1.95 

MEAsal 3 -.6100-02 

MEAsal 4 .~820-02 

RSS 2.47 

Figure A-7. 

ERR a A a U D G E-T - ------

SAT-OIC SAT-OIL Rss-pas 5AT-ClIHO SAT-OICD 

METERS METERS METEAS MET"SEC "U "SEC - -2. Olf -1.Ol 2.72 -.172D-02 • '~~D-02 

2.86 -1.86 3.61 .2790-02 • 9~8D-02 

-.IJOO-Ol ___ -.8610-01 ___ .1r720-0L _____ .~19D-O~ _____ ~.~~IO-0~ 

-.1f320-02 .1f230-01 .~350-01 -.1'~0-05 .2~50-01f 

3.51 2.12 1f.52 .328D-02 .1270-01 

SAT-02C SA T-02L Rss-pas SA'-02HO SAT-02CO 

METERS METERS METERS MET"SEC "ET"SEC 

23.4 -3.62 2J.7 .791f0-01f .1810-02 __ 12.6 -~.7~ __ ~J.5 _________ 1870-03 _____ 1620-02 

.252 .112 .278 -.5920-05 -.29150- Olf -.~81 -.9270-01 .~95 .5860-015 .1700-01f 

26.6 5.97 27.3 .20l0-01 • 2 If If 0-02 

SAT-Ole SAT-03L Rss-pas SAT-Cl1HO SAT-OlCO 

METERS METERS METERS MH "SfC MET "SEC 

19.9 5.92 _ 20.8 __ -.5000-0l .13~0-02 

18.l -.109 18.1f -.'570-0~ .1660-02 

-.296 -.l58 .~65 .2320-01f .2500-04 

.170 .236 .291 -.1590-01f -.9010-05 

27.1 5.95 27.8 .5080-0l .2130-02 

SEA Version 4.1 Smoothed Error Budqet at Epoch. Relay 

Tracking Scenarios in Which User and Relay Orbits Are 

Solved for Simultaneously 

SAT-OILO 

MET "SEC 

.1590-02 

-.1 ~3O-02 

.5970-05 

.9520-05 

.211f0-02 

SAT-OlLO 

MET "SEC 

.1040-0J 

.2900-01t 

.21t6o-00; 

-.3610-05 

.1090-03 

SAT-OlLO 

MET"SEC 

.126o-0J 

• 1 If If 0-03 

-.lIf50-06 

.2060-06 

.1920-0] 

RSS-VEL 

IoIET/SEC 

.6760-02 

.9960-02 

.68JO-0~ 

.264o-01f 

.13Jo-OI 

RSS-VEL 

MET"SEC 

.18Jo-02 

.16JO-02 

.3050-04 

.163O-01f 

.2460-02 

RSS-VEL 

MET/SEC •. 141t0-02 

.1670-02 

.34IO-0~ 

.18JO-01f 

.2200-02 

~~ - C,b 

~~ 

.:0,-

g~ .:be) 

r-1Tl 

~Ci) 
:t:' 

I 

I-' 

~ 

r""rL T,. II 

I 'oTr '<:, 

., 117Cjlf 

, : l 'J '1" 

_.'Jlh41 r _ r ." 

_.l .. ht iii _"' .... 

.1.'1:'111 

_.""R1C"f 

_. ~~'1 '''''r._,1 .<,414' lr.r.l 

_1. ., 0 '";f 

.1.'i1. 7'1 

•• r..ll1"'r,.ro~ • ~, ~A ':,'F'"\_'1? 

r-~TIVf\Tf~J 'le' r-PIHlP r-C1R f.rtC rln. , nilE Tn "NIIOn.1 EO PARAI4ET.QC; 

',rIT,r r~LTAI P~<'P:1" nr-tTal·mnT I"l.LTArDnT nELTALnnT 

,'<"T.o.,=\ (' •• T£I-<:, (," •• T.RC;, Irl~/<:.r' (N4/<:I"C1 (C'4/C;.C1 

..... "" 1 l4 ? u 7; _ .. I ...... I "'"... _Ii' •• I ~ II -•• " • n ~ 

,: ... , (' "I 

, ;> • r ~ , .. '"'";' ..,,.., •• ..1 1 '>.., 1 

, t: • ~ r q 

, -.-~~' _ .. " - .... rl·' .~h'noTJ"f" = '.0 

., .l·,74 

.1 .,G o;~ ... 

•• "Ih177n.", 

... ,,,'1110.('11 

-... .;~;, 

_1'.71+'14 "","1 _:1~Ul\qn.n' 

". q,., g' _ .. ~:::-r"l , 

_.7,5r, ln .:?31;1~ 

r.qlllJTrs vYl'Mnn 

SATl"lI TTf '.7~n' .17'06 '.~On~ .279~1 .. .~7'4~n.n1 .5,Q,:?,_n' .1I,C;l~n-nl -.lqo~1n_n' 

S6Tl"lI HE ?~.72~ .9n",n_o' ,~.50' .lR7~7n.n1 

.'7~'4 -.'\G171o.n' .4q4'~ .5R4~ln.n' 

.., r. • Il" 

11'.4'19 

.41;4~P 

.'90"7 

SATl"lI TTF 

-.4QA77o-nl 

_.fl4:"';0_n' 

.?'1 !I'Io.n:? 

-.1',9,Sn-o:? 

H~~~ C;S.C; = 8nn,n, o o.n 1 

.A44nn4 

.947<;101 . _.4404'R10.0? 

.'4I1Al~2n.n2 

2 

.IR"4Q2 

• H>"4"~. -.'9R7~'ltl_n2 

.17nnA,f,fI_02 

3 

.1~'F.3D6 

.1"<;f.15' 

.'~0F.l1(,I).n2 

·.qo,~oq31"l-n3 

.10;9'187 

..14:>711l3n. 

.0;9/197:>4::J.O'\ 

.94R'67"".03 

.104'l11IJo.01 

.'1)9n'3Rf').O:> 

.~~o;7167c_03 

•• '''nq09~n_n' 

• 1 27790RO.Ol .1~30;A7RO.Ol 

.,.,441'2'10_011 

.'02492:?"-04 

RC;/i vEL 

(rM/c,.CI 

./170;97 

.99qn6. 

.(,R'41D_02 

.:?F."'''_n:? 

.183(" 

.1(,34'1_ 

.300)1530.n:? 

.lIn4'\n_n2 

.11J~21 

.1(,f.~'1_ 

.'414<;0.n' 

.lA'00n-02 

Figure A-B. ORAN Batch Error Budget at Epoch. 

Scenarios in Which User and Relay 

Solved for Simultaneously 

Relay Tracking 

Orbits Are 

tJrJAO.IIIC; TED I"ARA,~rTrR 

RNr,~TASI 

RNG~IA'i2 

RnOTIlJAS1 

ROOTIlJAS2 

R"JGRtASl 

RNGRJAc;2 

RJOTRIASI 

ROOTRJAC)' 

R~GRIA'>l 

Rr-Jr;lltAC;2 

RnOTRIASl 

RDOTRIAS2 

~~ 

::or-

~~ 

,0-0 

c:l:> 

~~ 

~u; 
relays are present (deck setups P2S2T2 and P2S2T20). These 

figures display the error budgets for all three satellites 

at the epoch or start~ng time and show very good agreement. 

A.3 FUNCTIONAL PERFORMANCE VALIDATION 

A.3.1 TESTING DESCRIPTION 

As mentioned in Section A.2.1, the SEA smoother capability 

cannot be ver~fied in the presence of process noise by 

examining the agreements between SEA and ORAN. Thus, the 

final phase of testing concentrated on the effects of process noise on the smoother behavior. (See Section 5 for a 

related study.) 

If the smoother was implemented correctly, the following 

results should be observed in the tests: 

• The smoothed state variances should be smaller than 

the corresponding filtered state variances. This should be 

true irrespective of the magnitude of the process nolse. 

• The smoothed state variances should increase with 

the increase of the process noise. 

• The process no~se should introduce a fading memory 

feature into an estimator. Thus, the effect of dynamic 

errors is attenuated w~th the use of process noise whereas 

the effect of measurement noise is amplified. Furthermore, 

the filter is a one-sided fading memory estimator whereas 

the smoother is a two-sided fading memory f~lter. The fluctuation of errors with time is thus considerably smaller for 

a smoother than for a filter. 

Th~s phase of testing was performed us~ng the following 

tracking scenar~os with controlled process noise parameters: 

1. Scheduled relay tracking of a user satellite through 

two TDRSs--The user satellite was at a GOO-km altitude and a 

28-deg incl~nation. A nominal velocity variance process 

A-15 

0112 
no~se of 1 x 10-9 

m

2

/sec 3 and several variations were used 

(deck setup P3S1Tl) • 

2. Continuous tracking of a user' satell~te through 

three TDAS satell~tes (one backs~de, two frontside)--The user 

satell~te ~s at a 600-km altitude and a 28-deg inclination. 

A nominal velocity variance -9 2 process noise of 1 x 10 m / 

sec 3 - and severa 1" var~at~ons were used (deck setup P3S2Tl). 

A.3.2 TESTING RESULTS 

During the course of this phase of testing, the following 

errors relating to the process noise in backward f~ltering/ 

smoothing were uncovered and corrected: 

• The process noise variance had an incorrect sign 

because the elapsed t~me was computed based on 

backward time differences. 

• The process noise variance was not propagated using 

the backward transition matrix. This was a subtle 

error that was int~mately related to the method 

chosen to model the process noise in forward 

filtering. 

• The backward f~lter/smoother executive did not include the backward process no~se added since the 

last measurement, when ~t computed the smoothed 

error results. 

After these corrections were made, tests performed conf~rmed 

that all process noise effects listed ~n Sect~on A.3.1 were 

indeed observed, thus providing confidence that the SEA 

smoother capability was working correctly. Figures A-9 

through A-12 show some sample error analys~s results at 

1140 min of a 1440-min TDAS tracking arc (run corresponding 

to Scenar~o 2 of Sect~on A.3.1). The reduct~on of error 

from filtering (Figure A-9) to smooth~ng (Figure A-IO) and 

the decrease ~n dynamic error (lumped geopotent~al) and 

A-16 

0112 
~ 

I 

...... 

~ 

11M!:. ,COM EI'Oelt IN MINUTES = 1140. 

SOLIUO I 

GRAVClEf 

LUMPED 

A(eEL I 

I4EASBI I 

NEASBI 2 

MEAsel J 

MEAsel 411 

MEASBI 5 

MEASBI 6 

EPHEMERR 

RSS 

ERR 0 R 8 U 0 G E: , 

SAT-Olti--- -- -iA'-OI~ SAT Oft RSS-POS SA~8 5A'-~IC9 ~H.9 ASS-VU.---

MEfERS METERS METERS METERS METI'SEC MET.lSEC METI'SEC METI'SEC 

-.'190-02 -.2880-0J .2210-02 .'750-02 -.'390-05 -.1060-05 .5250-05 .6930-05 

.557 .681 -.5150-01 .1181 -.941t50-0' -.3350-03 .5810-03 - .6770-03 

-'."7 -16.4It 10.2 19.8 -.5520-02 -.1860-01 .4It280-02 .1980-01 

1.13 __ 10.' ________ ~1.1.7 _ 17.2 __ .122D-01 -.8010-02 -.2060-02 .1"70-01 

-.'120-01 .101 .6741t0-Ol .110 -.5110-04lt .5630-0' .14lt00-04lt .8"50-0' 

.'07 -.'290-01 -.1181 .971 .7980-03 -.7850-03 -.1680-03 .1180-02 

-.5150-01-----•• ~ • fl8D-iH ---..' 83-- ----- - .... 320-05 - --.......-9060-0"---. ~25D-O<4lt-- - --.-96"0-0" 

-.J16 1.08 -.5"1 1.25 .1850-0J -.2590-03 .2150-03 .381t0-03 

-.8110-02 .641t60-01 -.121 .118 .4It8110-0" -.14It70-03 -.1"20-05 .1550-03 

.6100-01 .1810-01 - .363-- - .369 -.2500-04lt .2210-03 -.5620-0" .2290-01 

.865 1.89 14It.0 1".5 -.1050-01 .6210-02 -.1010-02 ,.1220-01 __ '.75 19.8.... _______ 22a1______ 30.0 .1700-01 .2120-01 .4It910-02 .2160-01 

USERDRA6- - -i;l=ttBI---t----iHHA'--iI:---

SOLRAO I .J'00-05 .6,,70-02 -.2600-06 

GRAVCOEf .7170-0" 5.62 - -.7290-0' 

LUMPED -.6860-04lt -"5.6 .7"10-01 

ACCEL __ 1 __ ."52D~03 ___ 21.1- -a.'O~D~L _____ . MEAS81 I .1020-01 -1'.1 -.2820-01 

MEAS81 2 -.2"70-0" 2."8 -.2000-04lt MEA58I-J------.-I-H~-_3r10 .allD 0' 

MEAS81 ,. .12"0-01 1.09 -.6120-0" 

MEAS81 5 .2110-0" -15.9 .2110-03 

MEASBI- 6 "06230-0' -- -- 6;3~---- --..-;-V2CJO-CJ'----· 

EPHEMERR .5180-0J -11.2 -.3190-01 

RSS .12"10-03_ _ _ 92.3_ _ ___ .~QID=-OL __ _ 

S I AND A R 0 o E V A I I a N COR R E L A , I o N M A I R I II 

5AT-01ll 5U-Oly---- --- SAt-Oil SA '-01 liD SAT-OI'lD 

SA 1- o lit .975 .'31 .113 -.177 .ltl" 

SAT-DIY ." 31 • ~9" .4II01t .202 .887 

SAl-Oil .111 .'0'1 .916 .255 .61t0 

SAI-OlxO -.177 .202 .255 .5520- 01 .156 

SAt-OIYD .ltllt .887 .6'0 .156 .1260-02 

SAt-OllO • J1I .615 • "9" -.11' ."87 

USERORAG -.1120-02 .332()-0~ .3510-02 -.241t70-02 .3910-02 

CLKBI I .IJ7D-OI -.5110-02 .1820-01 • '''80- 04lt .2300-01 

DR If t I -.6'00-0 I -.126 -.1"6 -.121 -.288 

USERORAG CLKSI ORIF' 

SAt-OlK -.312D-02 .IJ7D-OI -.6'OD-01 

SAt-OIY .312D-02 -.5130-02--- --- - - -.126 

SAT-Oil .1510-02 .1820-01 -.I~IC~ 

SA r- aUD -.2' 10-02 .'480-01t -.123 

SAT-DIY" .19ID-.)2 .2100-01 -.288 

SA T-OIll) .1510-02 -.12Z0-01 -.19, USER()~AG .25011-01 .1~20-02 -.]510-02 

CLK61 I .15Z()-02 ' • .19 -.519 

O~IF' I -.3510-:12 -.579 .1100-01 

Figure A-9. SEA Version 4.1 Forward-Filtered Error Budget 

at 1140 Minutes. Nominal Velocity Variance 

Rate Process Noise of 1 x 10-9 Meter2j 

Second3 

SAT-OIlO 

.1.11 

.615 

.'94 

-.IIIt 

.1t81 

.1160-02 

.3530-02 

-.1220-01 

-.194 

o~ "i! ';;;.Jl 

--. 

~f2 aS; 

~!r~ 

tIE) -0 

c: ;J" I:ai 

~cn 
:t>' 

I 

...... 

IX) 

SOLRA') I 

GRAVCOEF 

LUMPED 

ACCEL I 

MEASOI I 

MEASOI 2 

MEASOI 3 

MEASOI It 

MEA~BI 5 

MEASBI 6 EPHEMER~ 

RSS 

SULRAO 1 

GRAVCOEF 

LUMPED 

ACCEL I 

MEASBI I 

MEASBI 2 

MEASOI 3 

MEASBI It 

"'EASOI 5 

MEASOI 6 

EPHEMERR 

RSS 

SA 1-011( 

SA I-OIY 

SAr-Oll 

SAr-01l(0 

SAr-OlVll 

SA T-OIlI) 

USER!>RAC. 

CLKOI I 

DRIFT 1 

SA '-OIX 

SAT-OI't 

SAl-Oil 

SA'-OlXD 

5AI-OIYO 

SA '-Olll> 

USERORAG 

CLKI:U I 

DRIF' I 

SAT-OIH 

METERS 

-.2~ID-OII 

.689 

-5.50 

I.~O 

-.2060-01 

.198 

.ZIIO-Ol 

-.I'rtI 

-.O\Z8D-03 

.5680-01 

I. ZI 

5.93 

USEAOAA6--

ERR 0 Ff BUD GET 

--SAT-GIC -----SU--Oll:---- FfSS-POS-----5AJ-OIHD--- &AT-OICo 

METEAS METEFfS METEAS MET'SEC MET/SEC 

.8870-05 -.8120-0~ .8510-0ll -.le720-06 -.llIII0-05 

.736 .3V60-01 1.01 -.5700-05 -.17leO-Ol 

-13.2 5.0V 15.5 -.2850-02 -.6l150-02 

10\.0 -1.80 16.1 .9110-02 -.9760-02 

.58VO-02 .]610-01 .lI200-01 -.25'0-Oll -.2360-0le 

.5VI -.512 .806 .lI960-03 -.1680-0] 

-.8070-01 -.lI8V&-01- -.9670-01- -.lI250-oll- .1370-0le 

.557 -.lIo\2 .725 .lII60-03 .lIIOO-Oll 

.7leVO-01 -.8500-01 .111 .6790-0ll .9910-05 

.3l100-01 .113 .1leO -.1860-03 -.7050-03 

.V17 13.8 1'.8 -.1050-01 .2560-02 

19.3 16.9 26.3 .llI20-01 .1200-01 

-<LKlH-1-- OluF-.r--I----

.0\1]0-05 .61ll0-02 -.9320-07 

.5760-011 5.97 -.7J90-0ll 

-.1010-02 -lI5.6 .6650-03 

-.1070-0l 37.5 -.leOlO-OI 

.1020-03 -llI.J -.2790-03 

-.o\'OO-Oll 2.6' -.39]0-Ole 

SAT-01LO 

MET'SEC 

.3810-06 

.5200-03 

.0\150-02 

-.IZ8D-02 

.190\0-011 

-.1920-03 

-.2380-011 

.1600-03 

.11320-05 

-.7600-011 

-.1160-02 

.le5l1D-02 

-.1150-03----3.15- .le83&-0.-- ---------------- -- ------ .8060-011 2.1~ -.IIS80-0le 

.1230-0ll -15.9 .2110-0] • 8220-01t 6.37 -.9390-0le 

.6720-0] -'0.8 -.2660-0] 

.1250-02 95:2 .le03D-01 

S TAN 0 II R 0 OEVArlON COR A E L A T ION MAT R I X 

ASS-VEL 

MET'SEC 

.1560-05 

.6'10-03 

.8190-02 

.13l10-01 

.3980-011 

.5570-03 

.5060-011 

.111170-03, 

.6870-0" 

.7330-03 

.1080-01 

.1910-01 

SAT-OtIC ----- - - - SAf-Gtv------- SAf-OIZ-------,-- SAf-OIilO---------SAf-OtYD--- ---- - SAT-OllO 

.120 

• 50'~ 

.202 

-.637 

.61t' 

.1186 

.509 .202 

-.lIl10--- -,8500-01 

-.85VD-OI .5l13 

.109 .llO 

.607 .JIO 

.3l8 .251 

-.637 

.100 

.130 

.1I610-0J 

-.Il] 

-.28l 

.61111 

.607 

.310 

- --- -.17,0-03--

.1070-01 

-.1190-02 

-----.-IS&D-G3------- -,.ZI20-03 --.510\0-03---

-.1]] 

.5110-03 

.9100-01 

--.-1700-03--- - .IIZI0-01 

-.Z800-02 

USERORAG 

-.17'0-Ol 

.1580-0] 

.212D-I)] 

.5IltO-0] 

.1700-0] 

.Z"70-0] 

.2500-01 

.]5~0-02 

-.5500-0" 

Figure A-IO. 

-.1690-01 .5Z80-01 -.1I120-0Z 

-.1t0'0-02 -.1760-03 -.15l10-02 

CLKOI 1 DRIFT 1 

.IG10-01 -.1190-02 - -. t69f}-GI -- -- -- ----.110110-02 

.5280-01 -.176D-Ol 

-."120-02 -.151t0-02 

.4210-01 -.280D-G2 

-.17ltO-01 -.1020-0] 

.]550-02 -.5500-011 

It.]6 -.1510-01 

-.1510-01 .'220-02 

SEA Version 4.1 Smoothed Error Budget at 

1140 Minutes. Nominal Velocity Variance 

Rate Process Noise of 1 x 10-9 Meter2/ 

Second 3 

.1186 

.J38 

.251 

-.26l 

.9100-0 I 

.6060-0] 

.21t70-0~-

-.17110-01 

-.7020-0] 
~ 

I 

I-' 

1.0 

11 .... 10 f~U~ L.-'JCH 1"4 'HNUfES = 114J. 

SAf-OIH :. ... T-OIC 

'4EfE~i l4E:rE:QS 

.. OL~AJ I .4Il0-0" .1110-0) 

Gq "iClt::f .557 .ol~ 

LUMIlL) -J.6) -7.l" 

"CCt.L -1.08 6.01 

"E ... ~tll • 6600- 0 I -.J(01)-01 

IoICA~OI ~ .6700-01 .l71 '4E"'~dl J -.)lJO-Ol -.16~ 

loll A ~11I .. -.107 1.14 

l4eASOI :i -.31t7rl-01 • .!05 

MfOA .. dl to -.5060-0 I -.d~J 

cPHCMERR -. )50 - 5. I It 

£lSi 1.~5 II.Z 

USEiWRAG CLIi:ill 

:iULllAD I ~96i)-·)9 - --- .l750-03 

"~A"CLlCF -.2910-06 1.5b 

LUMPeu -.6Il0-06 -1.dO 

ACCeL I -.2970-0~ 16.7 "EA,,~I I -.175'>-06 -I'.).l 

'4EA-,IH Z -.1620-06 I.J'.) 

MEASdl ) -.8570-07 1.12 .... E ... 501 ~ -.IOOU-Ob 1.7~ 

-Mn-~ar- .;--- ----;~MU--()6----;-1 ~-; 2 ----

IoIEA::ial 6 -.20JO-06 5.60 t.PHEM!~~ -.1190-05 -90.5 

kSS .JZ90-05 95.5 

ERR 0 £l 

:iAr-OIL 

METE~S 

-.1110-01t 

-.ZI9 

-1.02 

-18.6 

-.6550-01 

-.481 

.179 

-I.)) 

-.11) 

.Z14 

15.a 

24.6 

ORIF T 

--.4230-08 

-.1070-0" 

.15~0-0" 

-.)9~0-01 

-.2600-0J 

-.1910-04 

-.1550-0" 

-."520-0" 

BUOGET 

RSS-PUS 

ME TE £lS 

.14)O-0} 

.862 

6.17 

lO.O 

.101 

.5513 

.248 

1.75 

.2)7 

.898 

16.6 

27.) 

-.2751)---0]--- ---

-.6150-0" 

.7150-04 

.)9~0-01 

S"'T-OIHO 

ME:TJ'SEC 

- .3180-06 

-.713 70-04 

.l680-0l 

.731t0-02 

-.2i20-04 

.4120-0J 

-.alOO-04 

.5060-0J 

.1080-0) 

-.)200-0J 

-.1110-01 

.1)60-01 

Sf" N C A ~ J o E V A T ION C 0 ~ R E L A flO N 

SAT-OlCO 

ME T J'SEC ---';li510-0~ 

-.2990-0) 

.1t540-02 

-.8110-02 

.1640-0J 

-.1)40-02 

-.2140-0) 

.1150-02 

.5040-04 

-.6670- 0) 

.l850-02 

• ')940-02 

... A f R I x 

SAT-OILO RSS-VEL 

I4ETJ'SEC ~ETJ'SEC 

---.1290-06 --- ---.7 160-06 

.64JO-0) .7130-0J 

.4750-0) .5290-02 

.)940-02 .1160-01 

-.7570-04 .1820-0) 

.19JO-0) .1"10-02 

.1")0-04 .2)00-03 

.2500-0) .1"60-02 

.6140-04 .1140-0] 

-.1270-0) .7510-03 

-.7770-0) .1150-01 

.4110-02 .11)0-01 

SAT-aU SAT-OIY SAT -OIl SAf-OIXO SAT-OIYO SAT-OIlO 

5AI_ul)(--U-U- IJ.-, .)00 -~21iFlf2- -.lor----------~4 .liY-Z------

~Af-OH .31'>1 11 • .1 -.90Z0-01 .126 -.5180-01 .361 -~I-Ol.L __________ --". l'.Ju-:l~ _____ -"'. gaZll,,"O I _______ I ~. a _ • l45 __ .6120-.01__ .46 <;i0- 01 

SAr-OI)(,) -.261 .120 .J,.s .17"0-01 .568 -.J900-01 

S ... T-OIYU -.44" -.5IltO-01 .'!Ilc!O-OI .566 .6060-02 -.21] ~Ar-Ollj - --- .41? - - --- - - -.361- .4890-01 -.]'l00-01 --- .. 23.1 ----- .2890·01 

U .. EfHHAu -.1500-')4 .1160-04 -.'t240-0~ .1070-04 .1140-04 .2850-05 

CLI<JI I .I'>ZO-JI .221J-J2 .6Z30-0Z -.4150-02 .1650-01 -.1980-02 -u~ln I -----~)J)--.;-)I-----;.7T1-S_- ---- • 72110..-0Z-------;;-;-246D-<n- ~7Z[T-OZ-------..-.32eO-·lJt---

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USE:H"'~A" 

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-.37 .. 0-,)5 -- --.107D--JIi-

.1I40-il4 

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.ISZO-()4 

-.]'.)1()-1)'S 

Figure A-II. 

CL"tll 

---.1520-01---- • Z270-02 

.62JLJ-02 

-;4150-02 

.165",-01 

-.IJdO-02 

.1520-04 

3 I. 6 

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'>RIFT 

-.16)0-0 1-

-. liS 

• 720D-O~ 

-- ~~ 2460-0,-- .------------ -.9120-02 

- • .12'10-01 

-.]570-05 

-.109 

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SEA Version 4.1 Smoothed Error Budget at 

1140 Minutes. Velocity Variance Rate Process 

Noise of 1 x 10- 6 Meter2/Second 3 

OCl 

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000 000 -1II1t1t\J()ItI~OO<O 

00<P ... 1ll1tI ... ",0,.. ,...,.t)ol\l~""'_U'\ · ..... . , " ,,, 

000 I\j '" 

• I I 

000 

-""_U')~O"'..o"'" 

"'''''''''''''''<0,..''' 

"'-"'~,.,,.,,....-- ..... 

--III Q ,=,00 

, I I , 

o 000 «,,-o""Ln~"'-o.o"'" C ......... ItII\jIll""'" 1t')"'_""C"'''''~_ · ....... . I I , I I 

-t\J .... nC'o 

I I I 

:l00 -.,..._ .... O"'~".f\J 

1'\,I.o""""O"'''''t\I-

~"''''''J,...~U''-"" ..... . .... I 

__ "'~""'v~"""1 

______ f"-' 

o"':)":)ooo~_ ... 

• I • I I I t'l:~LL. ............... -.LJ\LCCCcfC(oC.II...J:r 

"c.l'tV'1 • ."v'JV'1:)U":\ 

... 

I&. 

0:: 

o 

III 

w: 

...J 

U 

"'111111"'111"'..,-111 

0000~0000 

• I I , • I , I , 

000000000 

t\I,....,....OOf'\la)~1'\I -111111,...,.",,,,0'" 

,....--.l'J-",U"-#' · ....... . , , , " I I 

"'-:)It":) "'000 0 

" " I I , 

00 OOCIO 0 ~'O..oI(')"',"-3'O'# 

1\j..,"'OO"lCOOOO !'\ID __ r'-al", ... 

· . . .. ,., . • I I 

--"\IN-"'''''''''' 00':>0':)0000 

, I I ,1" I , • 

CO('OCOOOC 

.r-C""~"'~"\J"'4'" 

", ~J 00 '" 0 '"' '" ~ ", .. ""'''O ...... '''Il1ll' · .. , ..... . I, 1" I I 

I~..,., '"' __ )C"~ ...... lI(>"""'<I( 

~ooooo~-

------I'l" ... I fl' • I a1l1.L. 

~-"'''''''~!JJ~­ cf oC C oC "f C _, ...J :r 

"',,"''''''' JI:l.J:l 

Ul X 

C (J) 

O+Jr-i 

-r-i ::s 

UlC4-I 

).,j-r-i 0 (J)~ 

:::-

~ 

(J) 

o Ul 

"" .r-i ~ r-I 0 

CJ)r-IZ 
increase in measurement error (TDAS ephemeris error and 

others) as the process noise ~ncreases (Figure A-10, A-ll, 

and A-12), should be noted. 

A.4 CONCLUSIONS 

The following conclusions can be drawn from the ser~es of 

tests perform~d: 

• The SEA smoother/TDAS enhancements were implemented 

successfully. The only major errors uncovered were those 

process noise errors described in Sect~on A.3.2. 

• The SEA smoother/TDAS capabil~lity is now fully 

validated and ready for use. 

• The close agreement between the process-noise-free 

SEA smoother results and the batch ORAN results verifies 

that SEA now also has the error analysis capabil~ty for a 

batch orbit determination process. Because SEA is a wellstructured, well-documented, and easily enhanced program, it 

can be easily modif~ed to analyze new tracking systems and 

data types, whether these are used in a sequential or batch 

orbit determination mode. 

One of the lim~tations of a smoother (or a smoother error 

analysis program) is that, for discrete t~me measurements, 

smoothed states (or smoother errors) are only available at 

those measurement times peculiar to the tracking scenario. 

This means that the smoother results will not be output during data gaps between tracking passes. Smoother output from 

SEA dur~ng data gaps can be obtained by entering fictitious 

measurements at the desired output times. These artificially introduced, fictit~ous measurements are given large 

standard deviations so that they do not affect the error 

analysis accuracy. 

A-21 

0112 
A.5 LISTING OF TEST DECK SETUPS 

The following pages contain listings of representat1ve deck 

setups used 1n the va11dation and verification of the SEA 

smoother/TDAS capabilit1es. 

A-22 

0112 
O~f3~~i~1. F_~GE ~S 

OF POOR QU?JJ..mr 

IIZBPAP1T1 uOB (GC002,311H,FFF), 'SEA P1S1T1',MSGLEVEL=(1,1), 

II MSGCLASS=A,TIME=30,CLASS=C, NOTIFY=ZBPAP 

l*uOBPARM LINES=30 

I*ROUTE PRINT PRTSS 

II*MEMBER P1S1T1 DATA IN TESTPAN LIBRARY 

II*DIRECT TRACKING OF A 200-KM 28 DEG INC SIC, W/DRAG A SOLVE-FOR 

II*RANGE AND RANGE RATE MEASUREMENTS EVERY 180 0 SECONDS 

II*DETERMIN TRACKING SCHEDULE, FOR 13 TRACKING STATIONS, FOR 24 HRS 

II*USING SMTHDU5M SEA SMOOTHER/TDAS UPDATES, SEA VER 4 1 KEYWORDS 

II*WITH SMOOTHING 

IISTEP1 EXEC PGM=PAN'1,REGION=300K,COND=(1,LE) 

IIPANDD1 DO DSN=GCDEV.MVT SEA.PANLIB DATA,UNIT=DISK,DISP=SHR 

IIPANDD2 DO DSN=&&SEAUPD,UNITrVIO,SPACE&(CYL,(2,1),RLSE), II DISP~(NEW,PASS),DCB-(RECFM=FB,LRECL=80,BLKSIZE=3600) 

IISYSPRINT DO SYSOUT-. 

IISYSPUNCH DO DUMMY 

IISYSIN DO DSN=ZBPAP SMTHDU5M DATA,UNIT=DISK,DISP=SHR 

II EXEC FORTRANH,PARM='XREF' 

IISYSLIN DO SPACE=(CYL,(2,1» 

IISOURCE.SYSTERM DO DUMMY 

IISOURCE.SYSPRINT DO DUMMY 

IISYSIN DO DSN=&&SEAUPD,UNIT=VIO,DISP=(OLD,DELETE) II EXEC LINK,PARM-'LET,LIST,MAP,SIZE=(200K,20K)',REGION=250K 

IISYSLIB DO DSN=SYS2 FORTLIB,DISP-SHR II DO DSN-GCDEV SEAMVS LDAD,DISP=SHR 

IISYSPRINT DO SYSOUT=* 

IISYSUT1 DO SPACE=(TRK,(55,1,1» 

IISYSLIN DO 

II DO * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

IIGO EXEC PGM=GSFC,REGION=400K 

IISTEPLIB DO DSN-&&LODMOD,DISP=(OLD,DELETE) 

IIFT01F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), II SPACE=(CYL,(5,1» SORTING FOR TRACKING DATA SCHEDULE 

IIFT02F001 DO UNIT=DISK,OCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), 

II SPACE-(CYL,(1,1» MERGING FOR TRACKING OATA SCHEDULE 

IIFT03F001 DO UNIT=DISK,DCB-(RECFM=VBS,LRECL=44,BLKSIZE=4404, II BUFNO-1),DISP-(NEW,PASS),SPACE=(CYL,(1,1», 

II DSN-&&SORTRK SORTED TRACKING DATA SCHEDULE 

IIFT05F001 DO DDNAME=DATA5 TRACKING SCHEDULE CARD INPUT 

II*FT06F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT06F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(3,1),RLSE), 

II DSN=&&PRTOUT SEA PRINTER OUTPUT 

II*FT08F001 DO DDNAME=INPCRD SEA KEYWORD CARD INPUT 

II*INPCRD DO * 

IIFT08F001 DO * 

EPOCHTIM 0 99 

USERSATO 1 11 1 

USERSATO 1 12 1 

SATELITE 2 11 0 

SATELITE 2 12 0 

SATELITE 3 11 0 

SATELITE 3 12 0 

STATIONS 1 0 0 

STATIONS 2 0 0 

STATIONS 3 0 0 

STATIONS 5 0 0 

STATIONS 6 0 0 

STATIONS 8 0 0 

STATIONS 11 0 0 

STATIONS 12 0 0 

STATIONS 13 0 0 

STATIONS 4 0 0 

STATIONS 7 0 0 

STATIONS 9 0 0 

STATIONS 10 0 0 

EARTH 15 15 

SPCPARAM 1 0 0 

EBOUTPUT -99 2 

CLKBIAS 1 1 

CLKDRIFT 1 1 

861101 

6578140. 

o 

42166750. 

358 

42163592 42 

228 

323003.857 

352029.642 

352029 642 

283029.905 

-075717.371 

322105 001 

220734.461 

283029.774 

352031.937 

402719.656 

-330903.596 

385954 656 

131838.265 

0.00272 

1440 0 

1000000 

200 0 

SEA KEYWORD CARD INPUT 

000000 0000 

o 0001 

o 

0.0004 

o 

o 0004 

o . 

2532329 162 

2430737 214 

2430735 042 

2791826.183 

3454022.570 

2952031 937 

2002005 439 

2791823 853 

2430735 561 

3554953.596 

2892001 065 

2830926 161 

1444412 524 

30 0 

o 000001 

A-23 

28.8 

o 

5 0 

o 

5.0 

o 

1441 37 

150 0 

2 0 

30 0 

o 9133100+03 

o 9187100+03 

-0 5582000+02 

o 5283700+03 

-0 3375000+02 

o 1139750+04 

-0 5445000+02 

o 9127100+03 

o 8089900+03 

o 7066100+03 

-0 2500000+01 

o 1159500+03 
USERDRAG 1 o 1 

GRAVCOEF -1 0.25 

1* 

II DO UNIT=OISK,OSN=ZBBTF ZBEXS.GEM DATA(RECOEF2),DISP=SHR 

II DO * 

SATSOLPR 1 -1 1 

MEASBIAS 2 -1 2000000010002. 10.0 

MEASBIAS 3 -1 13000000010013. 001 

MEASBIAS 2 -1 10000000010000. 10 0 

MEASBIAS 3 -1 10000000010000 .001 

MEASBIAS 2 -1 5000000010000. 10 0 

MEASBIAS 3 -1 12000000010000 .001 

EPHEMERR 1 25.0 23 0 40 0 

EPHERROR 99 

CLKACCEL -1 .11574 

COVARANC 1 

2.50+05 2.50+05 2 50+05 1.00+00 1 00+00 1 00+00 

NOISECOV 1 0 

0 O. 0 000000-10 1.000000-10 000000-10 

1* 

II*FT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(2,1),RLSE), 

II DSN=&&NOMOUT SATELLITE NOMINAL TRA~ECTORY OUTPUT 

II*FT10F001 DO SYSOUT=*, DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT10F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(2,1),RLSE), 

II DSN=&&MEASOUT PROCESSED MEASUREMENTS PRINTER OUTPUT 

IIFT20F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, 

II DSN=&&FESUM SEQUENTIA~ ERROR BUDGET SUMMARY 

IIFT21F001 DO DISP~(NEW,PASS),SPACE=(CYL,(1,1», 

II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&SESUM BACKWARD SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DO UNIT=DISK,DCB=(RECFM-VBS,LRECL=196,BLKSIZE=1964, II BUFNO=1),DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DSN=&&AKKHIN VISIBLE TRACKING DATA SCHEDULE 

IIFT40F001 DO UNIT=DISK,DCB=(RECFM=FB,LRECL=1688,BLKSIZE=18568), 

II DISP=(NEW,DELETE),SPACE=(CYL,(2,1),RLSE), 

II DSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

IIGO SYSUDUMP DO DUMMY 

II*SYSUDUMP DO SYSOUT=*,SPACE=(TRK,1), 

11* DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922) IIGO DATA5 DO * 

3 

100020001 

o 00 

100030001 

o 00 

100000002 

o 00 

200000001 

638 0 

200000001 

638 0 

300000001 

638 0 

300000001 

638.0 

500000001 

365 0 

552.0 

500000001 

365 0 

552 0 

600000001 

665 0 

861101000000 0000 

3 1800.0 10000.0 

1440.0 

3 1800.0 

1440.0 

2 1800.0 

1440 0 

2 

640 0 

3 

640 0 

2 

640 0 

3 

640 0 

2 

369 0 

556 0 

3 

369.0 

556 0 

2 

668 0 

20 0 

20 0 

20.0 

20 0 

20 0 

20.0 

20 0 

10000 0 

1.5 

1 5 

732.0 

0 002 

732 0 

1.5 

732.0 

o 002 

732 0 

1.5 

459.0 

646.0 

o 002 

459 0 

646 0 

1 5 

A-24 

733 0 

733.0 

733 0 

733 0 

463 0 

649 0 

463 0 

649 0 

-1 
600000001 3 20 0 0 002 

665 0 668 0 

700000001 2 600 0 5 

1200 0 1440.0 

700000001 3 600 0 0.002 

0.00 240 0 

800000001 2 20.0 1 5 

369 0 373.0 462 0 466 0 

556 0 559 0 

800000001 3 20.0 0 002 

369 0 373.0 462.0 466 0 

556 0 559 0 

1100000001 2 20 0 1.5 

627 0 631.0 721.0 724 0 

815.0 817 0 

1100000001 3 20 0 0 002 

627.0 631 0 721 0 724 0 

815 0 817 0 

1200000001 2 20 0 1 5 

365 0 369 0 459 0 463 0 

552 0 556 0 646 0 649 0 

1200000001 3 20 0 0 002 

365 0 369 0 459 0 463 0 

552.0 556 0 646 0 649 0 

1300000001 2 20 0 1.5 

638.0 640 0 732 0 733 0 

1300000001 3 20 0 0 002 

638 0 640 0 732 0 733 0 

6 

1* 

I/NTSO EXEC PGM=NOTIFY.COND=EVEN 

II 

A-25 
.IIZBPAP2T1 uOB (GCOO2,311H,FFF), 'SEA P1S2T1',TIME=30, II MSGCLASS=X,MSGLEVEL=(1,1),NOTIFY=ZBPAP,CLASS=C 

l*uOBPARM LINES=30 

II*ROUTE PRINT RMT6 

II*MEMBER P1S2T1.DATA IN TESTPAN LIBRARY 

11*6 GPS'S TRACKING A 400-KM 57 DEG INC SIC, 

II*RANGE AND RANGE RATE MEASUREMENTS EVERY 300 0 SECONDS 

II*USING SMTHDU5M SEA SMOOTHER/TDAS UPDATES, SEA VER 4 1 KEYWORDS 

II*WITH SMOOTHING 

I/STEP1 EXEC PGM=PAN'1,REGION=30OK,COND=(1,LE) 

IIPANOD1 DD DSN=GCDEV.MVT.SEA PANLIB DATA,UNIT=DISK,DISP=SHR 

IIPANOD2 DO DSN=&&SEAUPD,UNIT=VIO,SPACE=(CYL,!2,1),RLSE), II DISP=(NEW,PASS),DCB=(RECFM=FB,LRECL=80,BLKSIZE=3600) 

IISYSPRINT DD SYSOUT=* 

IISYSPUNCH DD DUMMY 

IISYSIN DO DSN=ZBPAP.SMTHDU5M DATA,UNIT=DISK,DISP=SHR 

/1 EXEC FORTRANH,PARM='XREF' 

I/SYSLIN DD SPACE=(CYL,(2,1» 

IISOURCE.SYSTERM DO DUMMY 

IISOURCE.SYSPRINT DO DUMMY 

IISYSIN DO DSN=&&SEAUPD,UNIT=VIO,DISP=(OLD,DELETE) II EXEC LINK,PARM='LET,LIST,MAP,SIZE=(200K,20K)',REGION=250K 

I/SYSLIB DD DSN=SYS2.FORTLIB,DISP=SHR II DD DSN=GCDEV.SEAMVS.LOAD,DISP=SHR 

IISYSPRINT DD DUMMY 

IISYSUT1 DD SPACE=(TRK,(55,1,1» 

I/SYSLIN DO 

II DO * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

llGO EXEC PGM=GSFC,REGION=400K 

IISTEPLIB DO DSN-&&LODMOD,DISP=(OLD,DELETE) 

I/FT01FOO1 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), II SPACE=(CYL,(5,1» SORTING FOR TRACKING DATA SCHEDULE 

IIFT02FOO1 DD UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), 

/1 SPACE=(CYL,(1,1» MERGING FOR TRACKING DATA SCHEDULE 

IIFT03F001 DD UNIT=DISK,DCBa(RECFM=VBS,LRECL=44,BLKSIZE=4404, II BUFND-1),DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DSN=&&SORTRK SORTED TRACKING DATA SCHEDULE 

IIFTOSFOO1 DD DDNAME*DATA5 TRACKING SCHEDULE CARD INPUT 

II*FT06FOO1 DD SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT06FOO1 DO SYSOUTa*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), 

1/ SPACE=(CYL, (3,1) ,RLSE), II DSN=&&PRTOUT SEA PRINTER OUTPUT 

1/*FT08FOO1 DD DDNAME=INPCRD SEA KEYWORD CARD INPUT 

II*INPCRD DO * 

IIFT08FOO1 DO * 

EPOCHTIM 2 1-9 

USERSATO 1 11 1 

USERSATO 1 12 1 

SATE LITE 2 11 

SATELITE 2 12 

SATELITE 3 11 

SATELITE 3 12 

SATELITE 4 11 

SATELITE 4 12 

SATE LITE 5 11 

SATELITE 5 12 

SATELITE 6 11 

SATELITE 6 12 

SATELITE 7 11 

SATELITE 7 12 

EARTH 4 4 0 

SPCPARAM 1 0 0 

GRAVCOEF 0 0-1 

1* 

860101. 

6978140. 

O. 

26560123.0 

120.0 

26560123.0 

120.0 

26560123.0 

120.0 

26560123.0 

240.0 

26560123 0 

240.0 

26560123.0 

240.0 

.0 

.0117618 

1.0 

SEA KEYWORD CARD INPUT 

000000.0000 

0.0005 

O. 

.001 

0.0 

.001 

o 0 

.001 

o 0 

.001 

o 0 

001 

o 0 

001 

0.0 

.0 

.0 

II DO DSN=ZBBTF.ZBEXS.GEM.DATA(RECOEF4),DISP=SHR,UNIT=DISK 

II DO * 

USERDRAG 1 

CLKBIAS 1 

CLKDRIFT 1 

CLKACCEL 1 

MEASBIAS 2 

o -1 

o 1 

o 1 

o -1 

-1 

0.25 

10000. 

10000 

.0001 

200010000. 5.0 

A-26 

57.0 

o 

63.0 

100 0 

63.0 

140.0 

63.0 

180 0 

63 0 

60 0 

63.0 

100 0 

63 0 

140.0 

2 0 

o 
MEASBIAS 2 -1 300010000. 5 0 

MEASBIAS 2 -1 400010000. 5 0 

MEASBIAS 2 -1 500010000 5 0 

MEASBIAS 2 -1 600010000 5.0 

MEASBIAS 2 -1 700010000 5 0 

MEASBIAS 3 -1 200010000 0 .001 

MEASBIAS 3 -1 300010000 0 .001 

MEASBIAS 3 -1 400010000 0 001 

MEASBIAS 3 -1 500010000.0 .001 

MEASBIAS 3 -1 600010000.0 001 

MEASBIAS 3 -1 700010000.0 .001 

EPHEMERR 1 0 0 10 0 10.0 20 0 

EPHERROR 0 0 0 99.0 .0 0 

EBOUTPUT o 99 2 1440.0 30 0 30 0 

COVARANC 1 0 0 

100000.0 100000 0 100000 0 1.0 1 0 1 0 

NOISECOV 1 0 

0 O. 0 1 00000D-10 1.00000D-10 1.00000D-10 

1* 

1* 

II*FT09F001 DD SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT09F001 DD SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), 

1/ SPACE= (CYL, (2,1) ,RLSE) , II DSN=&&NOMOUT SATELLITE NOMINAL TRAuECTORY OUTPUT 

II*FT10FOO1 DD SYSOUT=*, DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT10F001 DD SYSOUT8*,DCB=(RECFMzVBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(2,1),RLSE), II DSN=&&MEASOUT PROCESSED MEASUREMENTS PRINTER OUTPUT 

IIFT20F001 DD DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&FESUM SEQUENTIAL ERROR BUDGET SUMMARY 

IIFT21F001 DD DISP=(NEW,PASS),SPACE=(CYL,(1,1». II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&SESUM BACKWARD SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DD UNIT=DISK,DCB=(RECFM=VBS,LRECL=196,BLKSIZE=1964, II BUFNO=1),DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

/ I . DSN-&&AKKHIN VISIBLE TRACKING DATA SCHEDULE 

IIFT40F001 DD UNIT=DISK,DCB=(RECFM=FB,LRECL=1688,BLKSIZE=18568), II DISP=(NEW,DELETE),SPACE=(CYL,(2.1),RLSE), II DSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

llGO SYSUDUMP DD DUMMY 

II*SYSUDUMP DD SYSOUT=*,SPACE=(TRK,1), 11* DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922) 

lIGO.DATA5 DD * 

3 

20001 

o 00 

20001 

0.00 

30001 

0.00 

30001 

0.00 

40001 

0.00 

40001 

0.00 

50001 

0.00 

50001 

0.00 

60001 

0.00 

60001 

000 

70001 

o 00 

70001 

0.00 

1* 

860101000000.0000 

2 300.0 1.0 

1440.0 

3 300 0 

1440 0 

2 300.0 

1440.0 

3 300.0 

1440.0 

2 300.0 

1440.0 

3 300 0 

1440 0 

2 300.0 

1440.0 

:I 300.0 

1440.0 

2 300 0 

1440.0 

:I 300.0 

1440.0 

2 300.0 

1440 0 

3 300.0 

1440.0 

0.001 

1.0 

0.001 

1.0 

0.001 

1 0 

0.001 

1 0 

o 001 

1.0 

0.001 

A-27 

-1 
IINTSO EXEC PGM=NOTIFY,CONO=EVEN 

II 

A-28 
IIZBPAP3T1 uOB (GC002 311H.FFF), 'SEA P1S3T1' .MSGLEVEL=(1.1 I. 

II MSGCLASS=X,TIME=30,CLASS=C,NOTIFY=ZBPAP 

l*uOBPARM LINES=40 

II*ROUTE PRINT PRTSS 

II*MEMBER P1S3T1.DATA IN TESTPAN LIBRARY 

II*TDRSS TRACKING OF A 600-KM 98 DEG INC SIC 

II*RANGE AND RANGE RATE MEASUREMENTS EVERY 180 0 SECONDS 

II*USING SMTHDU5M SEA SMOOTHER/TDAS UPDATES, SEA VER 4.1 KEYWORDS 

II*WITH SMOOTHING 

IISTEP1 EXEC PGM=PANN1,REGION=300K,COND=(1,LE) 

IIPANDD1 DO DSN=GCDEV MVT SEA PANLIB DATA,UNIT=DISK,DISP=SHR 

IIPANDD2 DO DSN=&&SEAUPD,UNIT=VIO,SPACE=(CYL,(2,1),RLSE), 

II DISP=(NEW,PASS),DCB=(RECFM=FB,LRECL=80,BLKSIZE=3600) 

IISYSPRINT DO SYSOUT=* 

IISYSPUNCH DO DUMMY 

IISYSIN DO DSN=ZBPAP SMTHDU5M DATA,UNIT=DISK,DISP=SHR 

II EXEC FORTRANH,PARM='XREF' 

IISYSLIN DO SPACE=(CYL,(2,1» 

IISOURCE.SYSTERM DD DUMMY 

IISOURCE.SYSPRINT DD DUMMY 

IISYSIN DD DSN=&&SEAUPD,UNIT=VIO,DISP=(OLD,DELETE) 

II EXEC LINK,PARM='LET,LIST,MAP,SIZE=(200K,20K)',REGION=250K 

IISYSLIB DO DSN=SYS2 FORTLIB,DISP=SHR II DO DSN=GCDEV.SEAMVS.LOAD,DISP=SHR 

IISYSPRINT DO SYSOUT=* 

IISYSUT1 DO SPACE=(TRK,(55,1,1» 

IISYSLIN DD 

I I DD * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

IIGO EXEC PGM=GSFC,REGION=400K 

IISTEPLIB DD DSN=&&LODMOD,DISP=(OLD,DELETE) 

IIFT01F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), 

II SPACE=(CYL,(5,1» SORTING FOR TRACKING DATA SCHEDULE 

IIFT02F001 DD UNIT=DISK,DCB=(RECFM·VBS,LRECL=44~BLKSIZE=4404), 

II SPACE=(CYL,(1,1» MERGING FOR TRACKING DATA SCHEDULE 

IIFT03F001 DD UNIT=DISK,DCB-(RECFM=VBS,LRECL=44.BLKSIZE=4404, 

II BUFNO=1),DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II DSN=&&SORTRK SORTED TRACKING DATA SCHEDULE 

IIFT05F001 DO DDNAME=DATA5 TRACKING SCHEDULE CARD INPUT 

II*FT06F001 DO SYSOUT=*,DCBa(RECFM*VBA,LRECL=137,BLKSIZE=3990), 

IIFT06F001 DD SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), 

II SPACE=(CYL, (3,1) ,RLSE), II DSN=&&PRTOUT SEA PRINTER OUTPUT 

II*FT08F001 DO DDNAME-INPCRD SEA KEYWORD CARD INPUT 

II*INPCRD DD * 

IIFT08F001 DO * 

EPOCHTIM 1 99 

USERSATO 1 11 1 

USERSATO 1 12 1 

SATELITE 2 11 1 

SATELITE 2 12 1 

SATELITE 3 11 0 

SATELITE 3 12 0 

SATELITE 4 11 0 

SATELITE 4 12 0 

SATELITE 5 11 0 

SATELITE 5 12 0 

STATIONS 1 0 0 

STATIONS 3 0 0 

STATIONS 4 0 0 

STATIONS 6 0 0 

STATIONS 7 0 0 

STATIONS 8 0 0 

STATIONS 10 0 0 

STATIONS 11 0 0 

STATIONS 12 0 0 

STATIONS 13 0 0 

EARTH 

SPCPARAM 1 0 0 

EBOUTPUT -99 2 

MEASRMNT 

CLKBIAS 

851101. 

6978140. 

O. 

6778140. 

160 0 

42166750. 

358 

42163592.42 

228 

42163592 42 

113 

323003 857 

385953.936 

402719 656 

-075717 371 

-330903.596 

322105 001 

131838 265 

220734 461 

283029.774 

352031 937 

o 0011765 

1020 0 

1000000 

SEA KEYWORD CARD INPUT 

000000.0000 

0.0001 

O. 

0.0017 

o 

o 0004 

O. 

o 0004 

o 

o 0004 

O. 

2532329.162 

2830929 141 

3554953.596 

3454022.570 

2892001.065 

2952031 937 

1444412 524 

2002005 439 

2791823 853 

2430735 561 

2 0 

30 0 

1020' 

A-29 

98 8 

o 

28 

o 

5.0 

o 

5 0 

o 

5 0 

o 

1441 37 

150 0 

2.0 

30.0 

o 400000D+01 

o 8089900+03 

o 5283700+03 

o 7066100+03 

-0.3375000+02 

o 1159500+03 

o 1139750+04 

-0 5445000+02 

0.9127100+03 
CLKORIFT 

USERORAG 

GRAVCOEF 

1* 

1 

1 

-1 

200 0 o 000001 

o 1 

o 25 

II DO UNIT=OISK,OSN=ZBBTF.ZBEXS.GEM OATA(RECOEF2),OISP=SHR 

1 

2 

2 

3 

2 

3 

1 

II DO * 

SATSOLPR 

MEASBIAS 

MEASBIAS 

MEASBIAS 

MEASBIAS 

MEASBIAS 

EPHEMERR 

EPHERROR 

CLKACCEL 

COVARANC 1 

1.00+05 

COVARANC 2 

1 00+06 

O. 

O. 

o 

O. 

-1 

-1 

-1 

1 

-1 

-1 

.1 

1000300010000. 

6000000010000 

10000000010000. 

7000000020000. 

3000000020000. 

25.0 

-1 

99. 

.11574 

1 00+05 

1 

o 

1 00+06 

o 

o 

5 00-01 

1 00-06 

o 

1.00+05 

o 

O. 

1.00+06 

1 00-06 

O. 

1 00-06 

o 00001 

10.0 

001 

10 0 

001 

23,0 

00+00 

O. 

O. 

1,00-06 

5.00+00 

O. 

5 00-09 

00+00 

o 

5 00-01 

o 

o 

5 00+00 

5 00-09 

40.0 

00+00 

1 00-06 

1 00-06 

1 00-06 

5 00-09 

5 00-09 

1 00-06 5 00+00 

NOISECOV 1 

o o o 000000-10 000000-10 1.000000-10 

NOISECOV 2 1 0 

1 000000-12 1.000000-12 1.000000-12 

1* 

o o 

II*FT09F001 DO SYSOUT=*,OCB-(RECFM=VBA,LRECL=137,BLKSIZE=3990), IIFT09F001 00 SYSOUT=*,OCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(2,1),RLSE), 

o 

II - OSN*&&NOMOUT SATELLITE NOMINAL TRA~ECTORY OUTPUT 

II*FT10F001 DO SYSOUT=*,OCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT10F001 DO SYSOUT=*,OCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(2,1),RLSE), II DSN=&&MEASOUT PRDCESSED MEASUREMENTS PRINTER OUTPUT 

IIFT20F001 000ISP=(NEW,PASS),SPACE=(CYL,(1,1», II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=OISK, II DSN=&&FESUM SEQUENTIAL ERROR BUDGET SUMMARY 

IIFT21F001 DO OISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II OCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=OISK, 

II OSN=&&SESUM BACKWARD SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DD UNITaDISK,DCS-(RECFM-VSS,LRECL=196,BLKSIZE=i964, II BUFNO·1),OISP-(NEW,PASS),SPACE=(CYL,(1,1», 

II DSN=&&AKKHIN VISIBLE TRACKING DATA SCHEDULE 

IIFT40F001 00 UNIT=OISK,OCB=(RECFM=FB,LRECL=1688,BLKSIZE=18568), II OISP*(NEW,OELETE),SPACE=(CYL,(2,1),RLSE), II OSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

IIGO SYSUOUMP DO DUMMY 

II*SYSUOUMP 00 SYSDUT=*,SPACE=(TRK,1), 

11* OCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922) 

IIGO.OATA5 00 * 

3 861101000000.0000 

100030001 2 180.0 30.0 

o 00 1440 0 

100030001 3 180 0 

o 00 1440 0 

100040001 2 180 0 

0.00 1440 0 

100040001 3 180 0 

o 00 1440 0 

1000400050002 2 180.0 

0.00 120.0 

100000002 2 60.0 

30 0 39.0 

1218.0 1227.0 

100000002 

30 0 

3 60.0 

39.0 

1218 0 1227 0 

300000002 2 60 0 

0.01 

30 0 

0.01 

30 0 

1.5 

1122.0 

1317 0 

o 002 

1122 0 

1317 0 

1 5 

A-3D 

1128 0 

1323 0 

1128 0 

1323 0 

-1 
1128 0 1134.0 1032.0 1038 0 

300000002 3 60 0 o 002 

1032.0 1038.0 1128.0 1134 0 

400000002 2 60 0 1.5 

852.0 861.0 

400000002 3 60.0 o 002 

852 0 861 0 

600000002 2 60 0 1 5 

354.0 363.0 453 0 462 0 

552.0 558 0 1245 0 1254.0 

1344.0 1350 0 

600000002 3 60.0 o 002 

354 0 363 0 453.0 462 0 

552 0 558.0 1245 0 1254 0 

1344 0 1350.0 

700000002 2 60.0 1.5 

237.0 255 0 339 0 348.0 

435.0 447 0 534 0 543 0 

700000002 3 60 0 o 002 

237.0 255 0 339 0 348 0 

435.0 447 0 534 0 543 0 

800000002 2 60 0 1 5 

936.0 942 0 1032 0 1041 0 

1131 0 1140.0 1230 0 1236 0 

800000002 3 60.0 0.002 

936 0 942 0 1032 0 1041 0 

1131.0 1140.0 1230 0 1236 0 

900000002 2 180.0 1 5 

60.0 30.0 

1000000002 2 60.0 1.5 

3 00 12 0 102 0 111 0 

201 0 207 0 300.0 306 0 

399.0 405 0 495.0 504 0 

594 0 603.0 1389 0 1395 0 

1000000002 :I 60.0 o 002 

3.00 12 0 102 0 111 0 

201.0 207.0 300.0 306.0 

399 0 405.0 495 0 504 0 

594.0 603.0 1389 0 1~95.0 

1100000002 2 60.0 1.5 

18 0 27.0 114 0 126 0 

213 0 225.0 312 0 321 0 

1206.0 1212.0 1305 0 1311 0 

1401 0 1410 0 

1100000002 3 60.0 0.002 

18.0 27 0 114 0 126 0 

213 0 225 0 312 0 321 0 

1206 0 1212 0 1305 0 1311 0 

1401 0 1410.0 

1200000002 2 60.0 1 5 

933 0 939 0 1029 0 1038 0 

1028.0 1034.0 1224 0 1233 0 

1323 0 1329 0 

1200000002 3 60.0 0.002 

933 0 939.0 1029.0 1038 0 

1028.0 1034.0 1224 0 1233 0 

1323 0 1329.0 

1300000002 2 60 0 1 5 

27 0 36 0 1218.0 1224 0 

1314 0 1320.0 1413 0 1419 0 

1300000002 3 60 0 o 002 

27 0 36 0 1218 0 1224 0 

1314 0 1320.0 1413 0 1419 0 

A-31 
1* 

IINTSO EXEC PGM=NOTIFY,COND=EVEN 

II 

A-32 
IIZBPAP4T1 uOB (GC002,311H,FFFI,'SEA P1S4T1', 

II MSGCLASS=X,TIME=30,MSGLEVEL=(1,1),NOTIFY=ZBPAP,CLASS=C 

l*uOBPARM LINES=30 

II*ROUTE PRINT RMT6 

II*MEMBER P1S4T1 DATA IN TESTPAN LIBRARY 

II-USING SMTHDU5M SMOOTHER/TDAS UPDATES, SEA VER 4 1 KEYWORDS 

II*TDAS TRACKING SCENARIO, CONTINUOUS BEACON TRACKING 

IISTEP1 EXEC PGM=PAN#1,REGION=300K,COND=(1,LE) 

IIPANDD1 DO DSN=GCDEV MVT SEA PANLIB DATA,UNIT=DISK,DISP=SHR 

IIPAND02 DO DSN=&&SEAUPD,UNIT=VIO,SPACE=(CYL,(2,1),RLSE), 

II DISP=(NEW,PASS),DCB=(RECFM=FB,LRECL=80,BLKSIZE=3600) 

IISYSPRINT DO SYSOUT=* 

IISYSPUNCH DO DUMMY 

IISYSIN DO DSN=ZBPAP SMTHDU5M DATA,UNIT=DISK,DISP=SHR 

II EXEC FORTRANH,PARM='XREF' 

IISYSLIN DO SPACE=(CYL,(2,1») 

IISOURCE SYSTERM DO DUMMY 

IISOURCE SYSPRINT DO DUMMY 

IISYSIN DO DSN=&&SEAUPD,UNIT=VIO,DISP=(OLD,DELETE) II EXEC LINK,PARM='LET,LIST,MAP,SIZE=(200K,20K)',REGION=250K 

IISYSLIB DO DSN=SYS2 FORTLIB,DISP=SHR II DO OSN=GCDEV SEAMVS LOAD,DISP=SHR 

IISYSPRINT DO SYSOUT=* 

IISYSUT1 DO SPACE=(TRK,(55,1,1)1 

IISYSLIN DO 

I I DO * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

IIGO EXEC PGM=GSFC,REGION=400K 

IISTEPLIB DO OSN=&&LODMOO,DISP=(OLD,DELETE) 

IIFT01F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), 

II SPACE=(CYL,(5,1» SORTING FOR TRACKING DATA SCHEDULE 

IIFT02F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), II SPACE=(CYL,(1,1) MERGING FOR TRACKING DATA SCHEDULE 

IIFT03F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404, 

1/ BUFNO=1),DISP=(NEW,PASS),SPACE=(CYL,(1,1), 

II DSN=&&SORTRK SORTED TRACKING DATA SCHEDULE 

I/FT05F001 DO DDNAME=DATA5 TRACKING SCHEDULE CARD INPUT 

1/*FT06F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT06F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(3,1),RLSE), 

II DSN=&&PRTOUT SEA PRINTER OUTPUT 

/1*FT08F001 DO DDNAME=INPCRD SEA KEYWORD CARD INPUT 

II*INPCRD DO * 

SEA KEYWORD CARD INPUT 

120000 0000 

/IFT08F001 DO * 

EPOCHTIM 3 

USERSATO 1 11 

USERSATO 1 12 

SATELITE 2 11 

SATELITE 2 12 

SATELITE 3 11 

SATELITE 3 12 

SATELITE 4 11 

SATELITE 4 12 

EARTH 15 15 

1 

1 

1 

o 

o 

o 

o 

o 

o 

840805 

6681144 o 00078765 57 01940796 

96 4218 

42166750 

360 

42163592 42 

240 

42163592 42 

240 

SPCPARAM 1 0 0 0 00214 

STATIONS 1 0 0 323003 857 

GRAVCOEF -1 1 

360 

o 0004 

160 

o 0004 

60 

o 0004 

60 

2532329 162 

o 

5 0 

292 

5 0 

22 

5 0 

292 

150 0 

2 2 

1441 37 

II DO UNIT=DISK,DSN=ZBBTF ZBEXS GEM DATA(RECOEF),DISP=SHR 

II DO * 

USERDRAG 

CLKDRIFT 

CLKACCEL 

SATSOLPR 

EPHEMERR 

EPHERROR 

EBOUTPUT 

COVARANC 1 

1 

1 

-1 

-1 

99 

2 

1. 

1000 

o 12 

1. 

10 0 

1320 

1 00+06 

o 

1 00+06 

20 0 50 0 

10 10 

1 00+06 1 00+00 1 00+00 1 00+00 

NOISECOV 1 

o o o 1 000000-10 000000-10 1 000000-10 

1* 

II*FT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

A-33 
IIFT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(2,1 ),RLSE), 

II DSN=&&NOMOUT SATELLITE NOMINAL TRAJECTORY OUTPUT 

II*FT10F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

IIFT10F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), 

II SPACE=(CYL,(2,1),RLSE1, 

II DSN=&&MEASOUT PROCESSED MEASUREMENTS PRINTER OUTPUT 

IIFT20F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, 

II DSN=&&FESUM SEQUENTIAL ERROR BUDGET SUMMARY 

IIFT21F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=28841,UNIT=DISK, 

II DSN=&&SESUM BACKWARD SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=196,BLKSIZE=1964, 

II BUFNO=1),DISP=!NEW,PASS),SPACE=(CYL,(1,1», 

II DSN=&&AKKHIN VISIBLE TRACKING DATA SCHEDULE 

IIFT40F001 DO UNIT=DISK,DCB=(RECFM=FB,LRECL=1688,BLKSIZE=18568), II DISP=(NEW,DELETE1,SPACE=!CYL,(2,1),RLSE), 

II DSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

IIGO SYSUDUMP DO DUMMY 

II*SYSUDUMP DO SYSOUT=*,SPACE=(TRK,1), 

11* DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922) IIGO DATA5 DO * 

3 

000100020001 

o 

840805120000 0000 

3 180 0 01 

185 

380 

570 

760 

960. 

1160 

000100030001 

30 

230 

430. 

625. 

820 

1030 

1225 

25 

215 

415 

610. 

795 

985 

1190 

80 

285. 

. 475 

660 

860 

1055 

3 

1245. 

0001000300040001 3 

25 30 

215 230 

415. 430. 

610 625 

805 820 

995 1030 

1190 1220. 

/* 

180 

180 

80 

285 

475 

665. 

860. 

1055 

1265. 

130 

335. 

525 

720. 

925 

1125. 

120. 

310 

515. 

705 

900 

1090 

1300 

IINTSO EXEC PGM=NOTIFY,COND=EVEN 

II 

0 01 

0 01 

A-34 

120 

310 

515 

700 

890 

1090 

1285 

185 

380 

565. 

755 

960 

1150 

130 

335 

525 

720 

925 

1120 

1320 

-1 
IIZBPAPSOR ~OB (GC002.311H.FFF). 'SEA P2S1T1',MSGLEVEL=(1,1), II MSGCLASS=A,TIME=30,CLASS=C,NOTIFY=ZBPAP I*~OBPARM LINES=30 

I*ROUTE PRINT RMT6 

11* MEMBER P2S1T1 IN TESTPAN 

11* SOLVE FOR ONLY TWO SATELLITES, PROPOGATE FOR 1 DAY 

11* WITH 15X15 GEM9 - 8X8 GEM1 MISMATCH, GM (DATA CUT-OFF AT 144OMIN) 

11* USE ZBPAP SMTHDU5M.DATA TO UPDATE THE SEA SOURCE 

IISTEP1 EXEC PGM=PAN#1.REGION=300K.COND=(1,LE) 

IIPANDD1 DO DSN=GCDEV.MVT.SEA.PANLIB.DATA,UNIT=DISK,DISP=SHR 

IIPANDD2 DO DSN=&&SEAUPD.UNIT=VIO,SPACE=(CYL.(2,1),RLSE). I I DISP= ( •• EW, PASS), DCB=(RECFM=FB. LRECL=80, BLKSIZE=3600) 

IISYSPRINT DO SYSOUT=* 

IISYSPUNCH DO DUMMY 

IISYSIN DD DSN=ZBPAP.SMTHDU5M.DATA,UNIT=DISK.DISP=SHR II EXEC FORTRANH.PARM='XREF'.TERM='*' 

IISYSLIN DO SPACE=(CYL,(2,1» 

IISYSPRINT DO DUMMY 

IISYSIN DO DSN=&&SEAUPD.UNIT=VIO,DISP=(OLD.DELETE) II EXEC LINK,PARM='LET,LIST,MAP.SIZE=(20OK.2OK) ',REGION=25OK, 

II NBLK=100 

IISYSLIB DO DSN=SYS2.FORTLIB,DISP=SHR II DD DSN=GCDEV.SEAMVS.LOAD,DISP=SHR 

IISYSPRINT DO SYSOUT=* 

IISYSUT1 DO SPACE=(TRK,(55,1,1» 

IISYSLIN DD 

II DO * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

llGO EXEC PGM=GSFC,REGION-50OK 

/IGO.STEPLIB DO DSN"'&&LODMOD.DISP=(OLD,DELETE) 

IIFT01F001 DO UNIT=DISK,DCB-(RECFM-VBS,LRECL=44.BLKSIZE=4404). II SPACE=(CYL,(5,1» SORTING FOR TRACKING DATA SCHEDULE 

II FT02FOO 1 DO UNIT=DISK,DCB-(RECFM=VBS.LRECL=44,BLKSIZE=4404). II SPACE=(CYL,(1,1» MERGING FOR TRACKING DATA SCHEDULE 

IIFT03F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE-4404, II BUFNO-1).DISP-(NEW,PASS),SPACE-(CYL,(1,1», II DSN=&&SORTRK SORTED TRACKING DATA SCHEDULE 

IIFT05F001 DO DDNAME*DATAS TRACKING SCHEDULE CARD INPUT 

II*FT06F001 DO SYSOUT-*,DCB-(RECFM=VBA,LRECL=137,BLKSIZE-1922), 

I IFT06FOO 1 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE*(CYL,(1,1),RLSE), 

II DSN=&&PRTOUT SEA PRINTER OUTPUT 

I/*INPCRD DO * 

II*FT08F001 DO DDNAME"'INPCRD SEA KEYWORD CARD INPUT 

1 800301. 

IIFT08F001 DO * 

EPOCHTIM 1 

USERSATO 1 11 

USERSATO 1 12 

SATELITE 2 11 

SATELITE 2 12 

EARTH 8 8 

GRAVCOEF 

1 42166663.0 

1 319. 

1 42166663.0 

1 189. 

SEA KEYWORD CARD INPUT 

000000 0000 

0.2499 

O. 

0.17865865 

O. 

0-7 7.0 

158.92521261 

0-7 7. 

158.9521261 

40.0 

-1 0.25 

1* 

II DD UNIT=DISK,DSN=ZBBTF.ZBEXS.GEM.DATA(RECOEF),DISP=SHR 

II DD * 

SPCPARAM 1 0 0 

SPCPARAM 2 0 0 

MEASBIAS 2 -1 

MEASBIAS 2 -1 

MEASBIAS 3 -1 

MEASBIAS 3 -1 

- 0.036 1 5 

1.5 

5.0 

5 0 

STATIONS 1 0 0 

EBOUTPUT 1 2 

COVARANC 1 

0.036 

0001000100000001. 

0001000200000001 

0001000100000001. 

0001000200000001 

323003.857 

1440. 

0.0005 

0.0005 

2532329.162 

180. 

1441 37 

30.0 

1.00+06 1.00+06 1.00+06 1 00+00 1.00+00 

1* 

II*FT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137.BLKSIZE=1922), 

IIFT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137.BLKSIZE=141). 

II SPACE=(CYL.(1,1).RLSE). 

1.00+00 

II DSN=&&NOMOUT SATELLITE NOMINAL TRA~ECTORY OUTPUT 

II*FT10F001 DO SYSOUT=*,DCB=(RECFM=VBA.LRECL=137,BLKSIZE=1922), 

IIFT10F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137.BLKSIZE=141), 

A-35 
II SPACE=(CYL,(1,1),RLSE), 

II DSN=&&MEASOUT PROCESSED MEASUREMENTS PRINTER OUTPUT 

IIFT20F001 DD DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, 

II DSN=&&FESUM SEQUENTIAL ERROR BUDGET SUMMARY 

IIFT21F001 DD DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, 

II DSN=&&SESUM BACKWARD SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DD UNIT=DISK,DCB=(RECFM=VBS,LRECL=196,BLKSIZE=1964, 

II BUFNO=1),DISP=(NEW,PASS),SPACE=(CYL, (1,1», 

II DSN=&&AKKHIN VISIBLE TRACKING DATA SCHEDULE 

IIFT40F001 DD UNIT=DISK,DCB=(RECFM=FB,LRECL=1688,BLKSIZE=18568), II DISP=(NEW,DELETE),SPACE=(CYL.(2.1).RLSE), 

II DSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

IIGO SYSUDUMP DD DUMMY 

II*SYSUDUMP DD SYSOUT=*.SPACE=(TRK,1), 11* DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922) 

/IGO DATA5 DD • 3 800301000000.0000 

00010001 

o 0 

240.0 

480.0 

720.0 

960.0 

1200. 

1440. 

00010001 

0.·0 

240 0 

480.0 

720.0 

960.0 

1200 

1440 

00010002 

1.0 

241 0 

481.0 

721.0 

961 0 

1201. 

00010002 

1 0 

241.0 

481.0 

721.0 

961.0 

1201. 

1* 

0001 2 10 30.0 

1 0 

241.0 

481 0 

721.0 

961.0 

1201 

1440. 

0001 3 

1.0 

241.0 

481.0 

721 0 

961 0 

1201. 

1440. 

'0001 2 

2.0 

242 0 

482.0 

722.0 

962.0 

1202 

10. 

10. 

0001 3 10 

2.0 

242.0 

482.0 

722.0 

962.0 

1202. 

120 0 

360.0 

600 0 

840.0 

1080 

1320. 

0.003 

120 0 

360 0 

600.0 

840.0 

1080. 

1320. 

30.0 

121.0 

361.0 

601.0 

841.0 

1081. 

1321. 

0.003 

121.0 

361.0 

601 0 

841.0 

1081. 

1321. 

IINTSO EXEC PGM=NOTIFY,COND=EVEN 

II 

A-36 

121.0 

361.0 

601.0 

841.0 

1081. 

1321 

121.0 

361.0 

601.0 

841.0 

1081. 

1321. 

122.0 

362.0 

602.0 

842.0 

1082. 

1322. 

122.0 

362.0 

602.0 

842.0 

1082. 

1322 

o 
IIZBPAP2S2 uOB (GC002,311H,FFF),'SEA P2S2T1',MSGLEVEL=(1,1), II MSGCLASS=X,TIME=30,CLASS=C,NOTIFY=ZBPAP 

l*uOBPARM LINES=30 

I*ROUTE PRINT RMT6 

11* MEMBER P2S2T1 I .. TESTPAN 

11* SOLVE FOR ONLY ONE OF 3 SATELLITES, PROPOGATE FOR 1 DAY 

11* USE ZBPAP.SMTHDUSM.DATA TO UPDATE THE SEA SOURCE 

IISTEP1 EXEC PGM=PAP'N1,REGION=300K,COND=(1,LE) 

IIPANDD1 DD DSN=GCDEV MVT.SEA.PANLIB.DATA,UNIT-DISK,DISP=SHR 

IIPANDD2 DD DSN=&&SEAUPD,UNIT=VIO,SPACE=lCYL,(2,1),RLSE), II DISP=(NEW,PASS),DCB=(RECFM=FB,LRECL=80,BLKSIZE=3600) 

IISYSPRINT DO SYSOUT=* 

IISYSPUNCH DD DUMMY 

IISYSIN DD DSN=ZBPAP.SMTHDUSM.DATA,UNIT=DISK,DISP=SHR 

II EXEC FORTRANH,PARM='XREF',TERM='*' 

IISYSLIN DD SPACE=(CYL,(2,1» 

IISYSPRINT DD DUMMY 

IISYSIN DD DSN=&&SEAUPD,UNIT=VIO,DISP-(OLD,DELETE) II EXEC LINK,PARM='LET,LIST,MAP,SIZE=(200K,2OK)',REGIDN=2SOK, II NBLK=100 

IISYSLIB DD DSN=SYS2.FORTLIB,DISP=SHR II DD DSN-GCDEV.SEAMVS.LOAD,DISP=SHR 

IISYSPRINT DD SYSOUT=* 

IISYSUT1 DD SPACE=(TRK,(SS,1,1» 

IISYSLIN DD 

II DD * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

llGO EXEC PGM=GSFC,REGION=SOOK _ lIGO.STEPLIB DD DSN=&&LODMOD,DISP=(OLD,DELETE) 

IIFT01F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), II SPACE=(CYL,(S,1» SORTING FOR TRACKING DATA SCHEDULE 

IIFT02F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), II SPACE=(CYL,(1,1» MERGING FOR TRACKING DATA SCHEDULE 

IIFT03F001 DO UNIT=DISK.DCB-(RECFM-VBS,LRECL-44,BLKSIZE-4404, 

II BUFNO=1),DISP=(NEW.PASS),SPACE-(CYL,(1,1», II DSN=&&SORTRK SORTED TRACKING DATA SCHEDULE 

IIFTOSF001 DO DDNAME-DATAS TRACKING SCHEDULE CARD INPUT 

II*FT06F001 DO SYSOUT·*,DCB-(RECFM-VBA,LRECL-137,BLKSIZE=1922), 

IIFT06F001 DD SYSOUT-*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), 

II SPACE-(CYL,(1,1),RLSE), II DSN=&&PRTOUT SEA PRINTER OUTPUT 

1/*FT08F001 DO DDNAME=INPCRD SEA KEYWORD CARD INPUT 

1 800301. 

1 6778140. 

1 O. 

SEA KEYWORD CARD 

000000.0000 

0.0017 

O. 

INPUT 

28. 

o 

II*INPCRD DO * 

IIFT08F001 DO * 

EPOCHTIM 1 

USERSATO 1 11 

USERSATO 1 12 

SATELITE 2 11 

SATELITE 2 12 

SATELITE 3 11 

SATELITE 3 12 

EARTH 8 8 

SPCPARAM 1 0 0 

SPCPARAM 2 0 0 

SPCPARAM 3 0 0 

STATIONS 1 0 0 

42166683.0 

319 

42168683.0 

189. 

0.2499 

O. 

0.1788S86S 

O. 

D-77.0 

1S8.92S21261 

0-7 7. 

USERDRAG -1 

GRAVCOEF -1 

1* 

0.0011765 

0.036 

0.036 

323003.857 

0.25 

0.25 

158 9521261 

1.5 2 0 

0.00000000000000001 0.000000000000001 

0.00000000000000001 0.000000000000001 

2532329.162 1441.37 

II DD UNIT=DISK,DSN-ZBBTF.ZBEXS.GEM.DATA(RECOEF),DISP=SHR 

II DO * 

MEASBIAS 2 

MEASBIAS 2 

MEASBIAS 3 

MEASBIAS 3 

EBOUTPUT 

COVARANC 1 

1.0D+OS 

1* 

-1 

-1 

-1 

-1 

1 2 

0001000200010000. 

0001000300010000. 

0001000200010000. 

0001000300010000. 

1440.0 

1.00+05 1.0D+05 

S 0 

5.0 

0.0005 

0.0005 

180.0 

1.00+00 

30.0 

1.00+00 

II*FT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922), 

I/FT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), 

II SPACE=(CYL,(1,1),RLSE), 

A-37 

1.0D+00 
II DSN=&&NOMOUT SATELLITE NOMINAL TRA~ECTORY OUTPUT 

II*FT10F001 DO SYSOUT=*,DCB=(RECFM=YBA,LRECL=137,BLKSIZE=1922), 

IIFT10F001 DO SYSOUT=*,DCB=(RECFM-YBA,LRECL-137,BLKSIZE=141), II SPACE=(CYL,(1,1),RLSE), II DSN=&&MEASOUT PROCESSED MEASUREMENTS PRINTER OUTPUT 

IIFT20F001 DO DISP=(NEW,PASS),SPACE~(CYL,(1,1», 

II DCBc(RECFM-YBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&FESUM SEQUENTIAL ERROR BUDGET SUMMARY 

IIFT21F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DCB-(RECFM=YBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&SESUM BACKWARD SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DO UNIT=DISK,oca=(RECFM=YBS,LRECL=196,BLKSIZE=1S64, II BUFNO=1),DISP-(NEW,PASS),SPACE=(CYL,(1,1», 

II DSN-&&AKKHIN YISIBLE TRACKING DATA SCHEDULE 

IIFT40F001 DO UNIT=DISK,DCB=(RECFM=FB,LRECL=1688,BLKSIZE=18568), II DISP=(NEW,DELETE),SPACE=(CYL,(2,1),RLSE), 

II DSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

lIGO.SYSUDUMP DO DUMMY 

II*SYSUDUMP DO SYSOUT=*,SPACE=(TRK,1), 11* DCB=(RECFM=YBA,LRECL=137,BLKSIZE=1922) 

lIGO.DATAS DO - 3 

000100020001 

10. 

800301000000.0000 

2 600. 30. 

000 10002000 1 

10 

000 10003000 1 

10. 

00010003000 1 

10. 

1* 

360. 

3 600. 

360. 

2 600. 

360. 

3 600. 

360. 

IINTSO EXEC PGM=NOTIFY,COND=EYEN 

1/ 

0.3 

30. 

0.3 

A-38 

o 
IIZBCPYSOT uOB (Gu002,311H,FFF),'SEA P2S2T2',MSGLEVEL=(1,1), 

II MSGCLASS=X,TIME=30,CLASS=C,NOTIFY=ZBCPY 

l*uOBPARM LINES=30 

I*ROUTE PRINT PRTSS 

11* MEMBER P2S2T2 IN TESTPAN 

11* SOLVE FOR ALL THREE SATELLITES, PROPOGATE FOR 1 DAY 

11* **** USING EQUAL WEITHTS FOR A DATA TYPE- REGARDLESS OF SIC 

11* USE ZBCPY.SMTHDU5M DATA TO UPDATE THE SEA SOURCE 

IISTEP1 EXEC PGM=PANH1,REGIONz30OK,COND=(1,LE) 

IIPANDD1 DO DSN=GCDEV.MVT.SEA.PANLIB.DATA,UNIT=DISK,DISP=SHR 

IIPANDD2 DO DSN&&&SEAUPD,UNIT=VIO,SPACE=(CYL,(2,1),RLSE), II DISP=(NEW,PASS),DCB=(RECFM=FB,LRECL=80,BLKSIZE=3600) 

IISYSPRINT DO SYSOUT=* 

IISYSPUNCH DO DUMMY 

IISYSIN DO DSN=ZBCPY SMTHDU5M.DATA,UNIT=DISK,DISP=SHR 

II EXEC FORTRANH,PARM='XREF',TERM='*' 

IISYSLIN DO SPACE=(CYL,(2,1» 

IISYSPRINT DO SYSOUT=* 

IISYSIN DO DSN=&&SEAUPD,UNIT=VIO,DISP=(OLD,DELETE) II EXEC LINK,PARM='LET,LIST,MAP,SIZE=(200K,2OK)',REGION=25OK, 

II NBLK=100 

IISYSLIB DO DSN=SYS2.FORTLIB,DISP=SHR 

II DO DSN=GCDEV.SEAMVS.LOAO,DISP=SHR 

IISYSPRINT DO SYSOUT=* 

IISYSUT1 DO SPACE=(TRK,(55,1,1» 

IISYSLIN DO 

II DO * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

llGO EXEC PGMsGSFC,REGION=50OK 

lIGO.STEPLIB DO DSN-&&LODMOD,DISP-(OLD,DELETE) IIFT01F001 DO UNIT*DISK,DC8=(RECFM*VBS,LRECL=44,BLKSIZE=4404), II SPACEz(CYL,(5,1» SORTING FOR TRACKING DATA SCHEDULE 

IIFT02F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), II SPACE=(CYL,(1,1) MERGING FOR TRACKING DATA SCHEDULE 

IIFT03F001 DD UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404, II BUFNO&1),DISP&(NEW,PASS),SPACE=(CYL,(1,1», II DSN*&&SORTRK SORTED TRACKING DATA SCHEDULE 

IIFT05FOO1 DD DDNAME=DATAS TRACKING SCHEDULE CARD INPUT 

II*FT06F001 DD SYSOUT=*,DCB-(RECFM*V8A,LRECL=137,BLKSIZE=1922), 

IIFT06FOO1 DO SYSOUT=*,DCB-(RECFM-VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(1,1),RLSE), II DSN=&&PRTOUT SEA PRIN?ER OUTPUT 

IIFT08F001 DO DDNAME=INPCRD SEA KEYWORD CARD INPUT 

II*FT09F001 DO SYSOUT=*,DC8=(RECFM=VBA,LRECL=137,BLKSIZE=1922), 

IIFT09FOO1 DO SYSOUT=*,DCB=(RECFM-VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(1,1),RLSE), II DSN=&&NOMOUT SATELLITE NOMINAL TRAuECTORY OUTPUT 

II*FT10F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922), 

IIFT10F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(1,1),RLSE), II DSN=&&MEASOUT PROCESSED MEASUREMENTS PRINTER OUTPUT 

IIFT20F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», 0 

II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&FESUM SEQUENTIAL ERROR BUDGET SUMMARY 

IIFT21F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&SESUM BACKWARD SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=196,BLKSIZE=1964, II BUFNO=1),DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DSN=&&AKKHIN VISIBLE TRACKING DATA SCHEDULE 

IIFT40FOO1 DO UNIT=DISK,DCB=(RECFM=FB,LRECL=1688,BLKSIZE=18568), II DISP=(NEW,DELETE),SPACE=(CYL,(2,1),RLSE), II DSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

lIGO.SYSUDUMP DD DUMMY 

II*SYSUDUMP DD SYSOUT=*,SPACE=(TRK,1), 11* DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922) IIINPCRD DO * 

EPOCHTIM 1 

USERSATO 1 11 

USERSATO 1 12 

SATELITE 2 11 

SATELITE 2 12 

1 800301. 

1 6778140. 

1 0 

1 42166663.0 

1 319, 

000000.0000 

0.0017 

o 

o 2499 

O. 

A-39 

28. 

O. 

0-7 7 0 

158.92521261 
SATEl.ITE 3 11 1 42166663.0 . 0 17865865 

SATEl.ITE 3 12 1 189 _ O. 

EARTH 8 8 

SPCPARAM 1 0 0 0.0011765 2.0 

SPCPARAM 2 0 0 0.036 1.5 

SPCPARAM 3 0 0 0.036 1.5 

STATIONS 1 0 0 323003 857 2532329 . 162 

MEASBIAS 2 -1 0001000200010000. 5.0 

MEASBIAS 2 -1 0001000300010000. 5 0 

MEASBIAS 3 -1 0001000200010000 0.005 

MEASBIAS 3 -1 0001000300010000 0.005 

EBOUTPUT 0 2 1440. 180. 

COVARANC 1 

1.00+05 1.00+05 1.00+05 1 00+00 

1* 

IIGO.OATAS DO * 

3 800301000000.0000 

000100020001 2 600 30 

10. 360. 

000100020001 3 600. o 3 

10. 360. 

000100030001 2 600. 30. 

10. 360. 

000100030001 3 600. 0.3 

10. 360. 

00010002 0001 2 10. 30.0 

0.0 1.0 120 0 121 0 

240.0 241.0 360.0 361 0 

480.0 481.0 600.0 601.0 

720.0 721.0 840.0 841.0 

960.0 961 0 1080. 1081. 

1200. 1201. 1320. 1321. 

1440. 1440. 

00010002 0001 3 10. 0.3 

0.0 1.0 120.0 121.0 

240.0 241.0 360.0 361.0 

480.0 481.0 600.0 601.0 

720.0 721.0 840.0 841.0 

960 0 961.0 1080. 1081. 

1200. 1201. 1320. 1321. 

1440. 1440. 

00010003 0001 2 10. 30.0 

1.0 2.0 121.0 122.0 

241.0 242.0 361.0 362.0 

481.0 482.0 601.0 602 0 

721.0 722.0 841.0 842 0 

961.0 962.0 1081. 1082. 

1201. 1202. 1321. 1322. 

00010003 0001 3 10. 0.3 

1.0 2.0 121.0 122.0 

241.0 242.0 361.0 362.0 

481.0 482.0 601'.0 602.0 

721.0 722.0 841.0 842 0 

961 0 962 0 1081 1082. 

1201 1202 1321. 1322. 

1* 

IINTSO EXEC PGM=NOTIFY.CONO=EVEN 

II 

A-40 

0-7 7 

158 9521261 

40 0 

2.0 

1441 37 

30.0 

1.00+00 00+00 
IIZBPAPSWN ~OB (GC002,311H,FFF), 'SEA P3S1T1',MSGLEVEL=(1,1), 

II MSGCLASS=A,TIME=30 ,CLASS=C, NOTIFY=ZBPAP I*~OBPARM LINES=30 

I*ROUTE PRINT PRTSS 

11* MEMBER P3S1T1 UI TESTPAN 

11* SOLVE FOR ONLY ONE OF 3 SATELLITES, PROPOGATE FOR 1 DAY 

11* WITH VELOCITY PROCESS NOISE OF 1 00-09 ON STATE VELOCITIES 

11* USE ZBPAP.SMTHDU5M.DATA TO UPDATE THE SEA SOURCE 

II. SMTHDUP3 MODIFIED TO SET VAR DELTAT WITH THE OPPOSITE SIGN 

IISTEP1 EXEC PGM=PANN1,REGION=300K,COND=(1,LE) 

IIPANDD1 DO DSN=GCDEV.MVT.SEA.PANLIB.DATA,UNIT=DISK,DISP=SHR 

IIPANDD2 DO DSN=&&SEAUPD,UNIT=VIO,SPACE=(CYL,(2,1),RLSE), II DISP=(NEW,PASS),DCB=(RECFM=FB,LRECL=80,BLKSIZE=3600) 

IISYSPRINT DO SYSOUT=* 

IISYSPUNCH DO DUMMY 

IISYSIN DO DSN=ZBPAP.SMTHDU5M DATA,UNIT=DISK,DISP=SHR II EXEC FORTRANH,PARM='XREF',TERM='*' 

IISYSLIN DO SPACE=(CYL,(2,1» 

IISYSPRINT DO DUMMY 

IISYSIN DO DSN=&&SEAUPD,UNIT=VIO,DISP=(DLD,DELETE) II EXEC LIN<,PARMa'LET,LIST,MAP,SIZE=(200K,2OK)',REGION=250K, II NBLK=1oo 

IISYSLIB DO DSN=SYS2.FDRTLIB,DISP=SHR II DO DSN=GCDEV.SEAMVS.LOAD,DISP=SHR 

IISYSPRINT DO SYSOUT=a 

IISYSUT1 DO SPACE=(TRK,(55,1,1» 

IISYSLIN DO 

II DO * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

/100 EXEC PGMaGSFC,REGION=50OK 

IIOO.STEPLIB DO DSNa&&LODMOD,DISP=(OLD,DELETE) 

IIFT01F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), II SPACE=(CYL,(5,1» SORTING FOR TRACKING DATA SCHEDULE 

IIFT02F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44,BLKSIZE=4404), II SPACE=(CYL,(1,1» MERGING FOR TRACKING DATA SCHEDULE 

IIFT03F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=44~BLKSIZE=4404, 

II BUFNQ=1),DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DSNa&&SORTRK SORTED TRACKING DATA SCHEDULE 

IIFT05F001 DO DDNAMEaDATAS TRACKING SCHEDULE CARD INPUT 

II*FT06F001 DO SYSOUT=*,DCBa(RECFMaVBA,LRECL=137,BLKSIZE=1922), 

IIFTOSF001 DO SYSOUTa*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(1,1),RLSE), II DSN=&&PRTOUT SEA PRINTER OUTPUT 

II*FT08F001 DO DDNAME=INPCRD SEA KEYWORD CARD INPUT 

800301. 

6778140. 

SEA KEYWORD CARD 

000000.0000 

0.0017 

O. 

INPUT 

28 

o 

II*INPCRD DO • 

IIFT08F001 DO * 

EPOCHTIM 1 

USERSATO 1 11 

USERSATO 1 12 

SATE LITE 2 11 

SATELITE 2 12 

SATELITE 3 11 

SATELITE 3 12 

EARTH 8 8 

SPCPARAM 1 0 0 

SPCPARAM 2 0 0 

SPCPARAM 3 0 0 

STATIONS 1 0 0 

GRAVCOEF -1 

I· 

O. 

42166663.0 

319. 

42166663.0 

189 

0.2499 

O. 

0.17865865 

o 

0-7 7 0 

158.92521261 

0-7 7 

o 0011765 

0.036 

0.036 

323003.857 

0.25 

1 5 

1.5 

2532329 162 

158 9521261 

o 00000000001 

1441 37 

II DO UNIT=DISK,DSN=ZBBTF.ZBEXS.GEM.DATA(RECOEF),DISP=SHR 

II DO * 

MEASBIAS 2 

MEASBIAS 2 

MEASBIAS 3 

MEASBIAS 3 

EBOUTPUT 

COVARANC 1 

1 00+05 

NOISECOV 1 1 

0.00+00 

1* 

-1 

-1 

-1 

-1 

2 

0001000200010000. 

0001000300010000. 

0001000200010000. 

0001000300010000. 

360. 

1.00+05 

o 

0.00+00 

1 00+05 

0.00+00 

5.0 

5.0 

0.0005 

0.0005 

30. 

1.00+00 

1.00-09 

A-41 

30.0 

00+00 1.00+00 

00-09 1 00-09 
II*FT09F001 DO SYSOUT=* ,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922 I , IIFT09F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141I, II SPACE=(CYL,(1,1),RLSE), II DSN=&&NOMOUT SATELLITE NOMINAL 7RAuECTORY OUTPUT 

II*FT10F001 DO SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922), 

IIFT10F001 DD SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(1,1),RLSEI, II DSN=&&MEASOUT PROCESSED MEASUREMENTS PRINTER OUTPUT 

IIFT20F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&FESUM SEQUENTIAL ERROR BUDGET SUMMARY 

IIFT21F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, II DSN=&&SESUM BACKWARD SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=196,BLKSIZE=1964, II BUFNO=1I,DISP=(NEW,PASS),SPACE=(CYL,(1,1)I, II DSN=&&AKKHIN VISIBLE TRACKING DATA SCHEDULE 

IIFT40F001 DO UNIT=DISK,DCB=(RECFM=FB,LRECL=1688,BLKSIZE=18568), II DISP=(NEW,DELETE),SPACE=(CYL,(2,1),RLSE), II DSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

IIGO.SYSUDUMP DD DUMMY 

II*SYSUDUMP DD SYSOUT=*,SPACE=(TRK,1), 11* DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922) 

IIGO.DATA5 DO * 

3 800301000000.0000 0 

000100020001 2 600 30. 

10. 360 

000100020001 3 600 0.3 

10. 360 

000100030001 2 600. 30 

10 360 

000100030001 3 600. 0.3 

10 360 

1* 

IINTSO EXEC PGM=NOTIFY,COND=EVEN 

II 

.A-42 
IIZBCPYSTS ~DB (G~002,311H,FFF),'SEA P3S2T1',TIME=30, 

II MSGCLASS=X,MSGLEVEL=(1,1),NDTIFY=ZBCPY,CLASS=C I*~DBPARM LINES=100 

I*ROUTE PRINT PRTSS 

II*MEMBER P3S2T1 IN TESTPAN 

II*BEAKON TRACKING (FLBT) FOR A SPACE TELESCOPE MISSION MODEL 

II*RANGE AND RANGE RATE MEASUREMENTS EVERY 180 0 SECONDS 

II*USING SMTHDU5M SEA SMOOTHER/TDAS UPDATES, SEA VER 4 1 KEYWORDS 

II*WITH SMOOTHING 

II*WITH LOW ACCCURACY TRACKING EYERY 30 MINUTES TO INCREASE THE 

II*NUMBER OF SMOOTHED ERROR BUDGETS 

IISTEP1 EXEC PGM=PN'N1,REGION=30OK,COND=(1,LE) 

IIPANDD1 DD DSN=GCDEY.MVT.SEA.PANLIB.DATA,UNIT=DISK,DISP=SHR 

IIPANDD2 DD DSN=&&SEAUPD,UNIT=YIO,SPACE=(CYL,(2,1),RLSE), II DISP=(NEW,PASS) ,DCB= (RECFM=FB ,LRECL=80, BLKSIZE=3800) 

IISYSPRINT DD SYSOUT=* 

IISYSPUNCH DD DUMMY 

IISYSIN DD DSN=ZBCPY.SMTHDU5M.DATA,UNIT=DISK,DISP=SHR 

II EXEC FORTRANH,PARM='XREF',TERM='*',OUT='*' 

IISYSLIN DD SPACE=(CYL,(2,1» 

IISOURCE.SYSTERM DD SYSDUT=* 

IISOURCE.SYSPRINT DD DUMMY 

IISYSIN DD DSN=&&SEAUPD,UNIT=YIO,DISP=(OLD,DELETE) II EXEC LINK,PARM='LET,LIST,MAP,SIZE=(2ooK,20K)',REGION=250K 

IISYSLIB DD DSN=SYS2.FORTLIB,DISP=SHR II DD DSN=GCDEY.SEAMVS LOAD,DISP=SHR 

IISYSPRINT DD SYSOUT=* 

IISYSUT1 DD SPACE=(TRK,(55,1,1» 

IISYSLIN DD 

II DD * 

INCLUDE SYSLIB(SEA) 

ENTRY MAIN 

II EXEC PGM-GSFC.REGION=40OK 

IISTEPLIB DD DSN=&&LODMOD,DISP=(OLD,DELETE) 

IIFT01F001 DO UNIT=DISK,DCB=(RECFM=YBS,LRECL=44,BLKSIZE=4404), II SPACE = (CYL, (5, 1» SORTING FOR TRACKING DATA SCHEDULE 

IIFT02F001 DD UNIT-DISK,DCB=(RECFM=YBS,LRECL=44,BLKSIZE=4404), II SPACE-(CYL,(1,1» MERGING FOR TRACKING DATA SCHEDULE 

IIFT03F001 DD UNIT-OISK,DCB-(RECFM-YBS,LRECL=44,BLKSIZE-4404, II BUFNO-1),DISP=(NEW,PASS),SPACE-(CYL,(1,1», II DSN-&&SORTRK SORTED TRACKING DATA SCHEDULE 

IIFT05F001 DO DDNAME=DATA5 TRACKING SCHEDULE CARD INPUT 

II*FTOSF001 DD SYSOUT=*,DCB=(RECFM-YBA,LRECL=137,BLKSIZE=3990), 

11* DSN=&&PRTOUT SEA PRINTER OUTPUT 

IIFT06F001 DO SYSOUT=-, II DCB=(RECFM=YBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(3,1),RLSE) 

II*FT08F001 DD DDNAME-INPCRD SEA KEYWORD CARD INPUT 

II*INPCRO DD - IIFT08F001 DD * 

EPOCHTIM 3 -1 

USERSATO 1 11 1 

USERSATO 1 12 1 

SATELITE 2 11 0 

SATELITE 2 12 0 

SATELITE 3 11 0 

SATELITE 3 12 0 

SATELITE 4 11 0 

SATE LITE 4 12 0 

STATIONS 1 0 0 

EARTH 15 15 

SPCPARAM 1 0 0 

EBOUTPUT -1 2 

CLKBIAS 1 1 

CLKDRIFT 1 1 

USERDRAG 1 1 

GRAYCOEF -1 

1* 

881101. 

8978140. 

O. 

42186750 

358 

42163592.42 

228. 

42163592 42 

113. 

323002.887 

0.00272 

1440.0 

1000000. 

200.0 

.025 

0.25 

SEA KEYWORD CARD INPUT 

000000.0000 

0.0001 

O. 

0.0004 

o 

o 0004 

o 

0.0004 

O. 

2532329. 163 

30.0 

0.000001 

28 8 

O. 

5.0 

o 

5 0 

O. 

5 0 

O. 

1441 37 

150.0 

2.0 

30.0 

II DD UNIT=DISK,DSN=ZBBTF.ZBEXS.GEM.DATA(RECOEF2),DISP=SHR 

II DD * 

SATSOLPR 1 

MEASBIAS 2 

MEASBIAS 3 

-1 

-1 

-1 

1 

1000200010000. 

1000200010000. 

10.0 

.001 

A-43 
MEASBIAS 2 

MEASBIAS 3 

MEASBIAS 2 

MEASBIAS 3 

EPHEMERR 1 

EPHERROR 

CLKACCEL 

COVARANC 1 

-1 1000300010000 

-1 1000300010000. 

-1 1000200040001. 

-1 1000200040001 . 

25.0 

99 

-1 .11574 

2.50+05 

o 

2.50+05 

10 0 

.001 

10.0 

.001 

23 0 40.0 

2.50+05 1 00+00 1 00+00 1 00+00 

NOISECOV 1 

o O. O. 000000-10 1.000000-10 1.000000-10 

1* 

II*FT09F001 00 SYSOUT=*,OCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

11* DSN=&&NOMOUT SATELLITE NOMINAL TRA~ECTORY OUTPUT 

IIFT09F001 DO SYSOUT=*, 

II OCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), 

1/ SPACE=(CYL, (2,1) ,RLSE) 

II*FT10F001 00 SYSOUT=*,DCB=(RECFM=VBA,LRECL=137,BLKSIZE=3990), 

11* DSN=&&MEASDUT PROCESSEO MEASUREMENTS PRINTER OUTPUT 

IIFT10F001 00 SYSOUT=*, 

II OCB=(RECFM=VBA,LRECL=137,BLKSIZE=141), II SPACE=(CYL,(2,1),RLSE) 

IIFT20F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=DISK, 

II DSN=&&FESUM SEQUENTIAL ERROR BUDGET SUMMARY 

IIFT21F001 DO DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II DCB=(RECFM=VBS,LRECL=144,BLKSIZE=2884),UNIT=OISK, 

II DSN=&&SESUM BACKWARO SMOOTHER ERROR BUDGET SUMMARY 

IIFT27F001 DO UNIT=DISK,DCB=(RECFM=VBS,LRECL=196,BLKSIZE=1964, II BUFNO=1),DISP=(NEW,PASS),SPACE=(CYL,(1,1», 

II DSN=&&AKKHIN VISIBLE TRACKING DATA SCHEDULE 

IIFT40F001 DO UNIT-DISK,DCB=(RECFM-FB,LRECL=1888,BLKSIZE=18568), II DISP=(NEW,DELETE),SPACE=(CYL,(2,1),RLSE), 

II DSN=&&SMSTOR SMOOTHER INFORMATION STORAGE FILE 

IIGO.SYSUOUMP DO DUMMY 

I/*SYSUDUMP DD SYSDUT-*,SPACE=(TRK,1), II- DCB=(RECFM=VBA,LRECL=137,BLKSIZE=1922) 

lIGO.DATA5 DO - 3 

100020001 

0.00 

200.3333 

407.8686 

812.3333 

819.6686 

1028.3333 

1233.6666 

1439 6666 

100020001 

0.00 

200.3333 

407 6686 

812.3333 

819.8688 

1028.3333 

1233.6666 

1439.6666 

100030001 

63.6666 

268.6666 

475 3333 

684.3333 

890.3333 

1095.6666 

1304.0 

100030001 

63 6668 

268.6666 

475.3333 

684.3333 

890.3333 

1095.6666 

861101000000.0000 

2 180.0 

2.7 

235.7 

443.7 

650.0 

856.0 

1064.0 

1271.0 

1440.0 

3 180.0 

2.7 

235.7 

443.7 

650.0 

·856.0 

1064.0 

1271 0 

1440 0 

2 180.0 

95.0 

304.4 

509.7 

715.0 

924.0 

1131 0 

1336.0 

3 

95.0 

304.4 

509.7 

715.0 

924.0 

1131.0 

180 0 

1.88867 

95.3333 

304.8686 

510.0 

715.3333 

924.3333 

1131. 3333 

1336.3333 

0.00186667 

95.3333 

304.6686 

510.0 

715.3333 

924.3333 

1131 3333 

1336 3333 

1 66667 

166.3333 

371.6666 

580.0 

787 6666 

992.6866 

1199.6666 

1408.6866 

0.00166667 

166.3333 

371.6666 

580.0 

787 6666 

992.6666 

1199.6666 

A-44 

132.0 

339 7 

547.0 

753 0 

959 7 

1167.7 

1374.4 

132.0 

339 7 

547 0 

753 0 

959 7 

1167 7 

1374 4 

200 0 

407 4 

612.0 

819.4 

1028.0 

1233.4 

1439.4 

200 0 

407 4 

612.0 

819 4 

1028.0 

1233.4 

-1 
1304.0 1336.0 1408 6666 1439.4 

1000200040001 2 180.0 1 66667 

3 00 63.4 132 3333 166.0 

236.0 268.4 340.0 371.4 

444 0 4.75.0 547.3333 579.7 

650.3333 684.0 753 3333 787.4 

856.3333 890.0 960 0 992 4 

1064.3333 1095.4 1168.0 1199.4 

1271.3333 1303.7 1374.6666 1408.4 

1000200040001 3 180 0 0.00166667 

3.00 63.4 132.3333 166.0 

236.0 268.4 340 0 371 4 

444.0 475 0 547 3333 579.7 

650.3333 684 0 753.3333 787.4 

856.3333 890.0 960.0 992.4 

1064.3333 1095.4 1168 0 1199.4 

1271.3333 1303.7 1374.6666 1408 4 

100020001 3 1800.0 10000.0 

0.00 1440.0 

100030001 3 1800.0 10000 0 

0.00 1440 0 

1000200040001 3 1800.0 10000.0 

0.00 1440.0 

/* 

//NTSD EXEC PGM=NDTIFY,COND=EVEN 

II 

A-45 
APPENDIX B - UTILITIES FOR GEOPOTENTIAL ERROR MODEL STUDIES 

ThlS appendix describes two utllities adapted from the Sequential Error Analysis (SEA) program for geopotentlal error 

model studies. Both utilities compute the gravitational 

acceleration errors that result from a given geopotentlal 

error model. The first utility outputs the magnitudes of 

the acceleration errors as a function of geocentric latitude 

and longitude at a fixed altitude. The second utility outputs the magnltudes as well as the acceleratlon components 

in the radial, alongtrack, and crosstrack directlons as the 

satellite travels in its orbit. These two utilities are 

described in more detail in Sectlons B.l and B.2. 

B.l GEOPOTENTIAL ACCELERATION ERROR WORLD-MAP UTILITY 

This SEA utility computes the uncertainty in the gravitatlonal acceleration due to nonspherical effects of the Earth 

at a specified alt~tude for a given geopotential error 

model. The utility computes and prints out the global distributlon of gravitational acceleration uncertainties in 

meters per second squared for latitudes between -89 deg and 

+89 deg l with S-deg increments and longitudes varying between a deg and 360 deg with 10-deg increments. 

The utility also generates a global dlstribution plot of the 

gravitational acceleration uncertainties in milligals (lO-Sm/ 

sec

2) rounded to the nearest integer, with longitude as 

abscissa and latitude as ordinate. 

lThe geopotential computation subroutine is adapted from 

the corresponding GTDS subroutine, WhlCh has a singularity 

at the poles (+90 deg). The use of +89 deg avoids this program deflciency. 

B-1 

0112 
B.l.l INPUT DATA SETUP 

This ut~l~ty can be executed us~ng the SEA keyword cards 

setup, and no special keyword cards are requ~red. The geopotential error model is provided by the LUMPGEOP keyword 

card followed by the corresponding set of RECOEF cards if 

other than the default model--GEM-9 formal uncertainties--is 

desired. The coefficients of any geopotential error model, 

except the default model, can be scaled using the first real 

field of the LUMPGEOP keyword card. The altitude for which 

geopotential accelerat~on uncertainties are computed is 

based on the orbital elements provided on the USERSATO card. 

B.l.2 MODIFICATIONS TO SEA PROGRAM 

Modifications are made in subroutines RDKEYS and SPART to 

adapt SEA to function as described in Section B.l. In subroutine RDKEYS, which reads in keyword cards, modifications 

are made so that the first real field (Rl) on the LUMPGEOP 

keyword card can be used as a scaling factor (multiplication 

factor) to the s~ne and cosine coefficients uncertainties of 

an input geopotential error model. This provides a convenient means to scale down or scale up the coeff~c~ents to 

study the effects of an error model. 

Subrout~ne SPART, which normally computes the grav~tational 

accelerations due to a geopotent~al model, is modified to 

compute the acceleration uncertainties resulting from a geopotential error model instead. A nested DO-loop for lat~­

tudes and longitudes is added so that the subroutine 

computes and outputs the global distribution of gravitational acceleration uncertainties. These uncertainties are 

calculated based on the orbital radius of the user satell~te 

as provided by the orbital elements in the USERSATO card. 

The subrout~ne also converts the accelerat~on uncertaint~es 

from meters per second squared to mill~gals (rounded to the 

nearest integer) and generates a global d~str~bution plot of 

B-2 

0112 
grav~tational acceleration uncertaint~es. After printing 

out the above results, the program execution is allowed to 

terminate instead of execut~ng the rest of the normal SEA 

program. 

B.l.3 REQUIRED CODING UPDATES TO SEA PROGRAM 

The following is the listing of Panvalet updates to the 

Panvalet SEA source program stored in the data set 

GCDEV.MVT.SEA.PANLIB.DATA. To create an updated SEA program 

load module, the updates that follow must be compiled and 

linked to the existing SEA load module GCDEV.SEAMVS.LOAD. 

B-3 

0112 
++UPDATE RDKEYS,1,TEMP 

++C 229.229 

DPMAP(ILUMP) = 1 000 

IF (R1 NE. 0.000 ) DPMAP(ILUMP) = R1 

++C 251,252 

CSIG(I1, 12+1 ) = R1 * DPMAP(ILUMP) 

CSIG(31-I1, 33-12 ) = R2 * DPMAP(ILUMP) 

++WRITE WDRK,RDKEYS 

++UPDATE SPART,1,TEMP 

++C 69,S9 

CDMMON/CONST I AE, GM, DUM(3), THETG, DTR 

++C 73,73 

COMMON/FMODEL/CSIG(30, 33) ,C(30,33) ,MAXDEG.MAXDRD,NMAX,M MAX 

++C 7S 

C 

LOGICAL*1 HORZ(11S),VERT,SLASH 

INTEGER*2 PLOT(40,40),A1(40),A2(40) 

DATA DLAT/S DOl, DLON/10 DOl, FACTOR/1.DSI 

DATA HORZ/11S*'-'I, VERT/'+'I, SLASH/'I'I 

DO 50 ICOL = 1,112,3 

HORZ(ICOL) = SLASH 

50 CONTINUE 

++0 93,94 

C 

WRITE(S,10IR 

10 FORMAT! '1' III,' *** ENTER SPART TO GENERATE WORLD MAP " 

* '- USE GEOP UNCER"S TO CALC ACCELERATIONS ***',111, 

*' THE SIZE OF THE GEOPOTENTIAL UNCERTAINTY IS SPECIFIED BY , * 'THE "EARTH" KEYWORD',II. 

*' THE ORBITAL RADIUS FOR WHICH THIS WORLD MAP IS BEING ' 

* 'CALCULATED IS R =' 025 15,1/////, 

* ' THE C ARRAY CONTAINING THE GEOPOTENTIAL UNCER"S IS.' I 

C PRINT OUT THE C ARRAY CONTAINING THE GEOPOTENTIAL UNCER'S 

C 

C 

C 

CALL OUTCOF(C,MAXDEG,MAXORD,1) 

INDO = 180 DO/OLAT + 

IND1 = 360.DO/DLON + 

C ENTER LATITUDE LOOP 

C 

WRITE!S,390) 

390 FORMAT! '1 NON-SPHERICAL ACCELERATION AS A FUNCTION', 

C 

• ' OF LATITUDE AND LONGITUDE' ) 

ALAT = (DLAT + 90 001 

DO 1000 I=1,INDO 

IF ( MOD(I,2) .NE 0 AND. I GT 1 ) WRITE!6,401) 

401 FORMAT!' 1 ' ) 

WRITE(S,400) 

400 FORMAT! I) 

ALAT = ALAT - OLAT 

A, \ I) = ALAT 

ALAT1 = ALAT 

IF ( ALAT GE. 90.00 ALAT1 = ALAT - 0 

IF (ALAT LE -90 DO ) ALAT1 = ALAT + 0 

SINP = DSIN(OTR*ALAT1) 

COSP = DCOS(DTR*ALAT1) 

++C 112,112 

C 

C ENTER LONGITUDE LOOP 

C 

ALON = -(DLON + 0 DO) 

DO 2000 J = 1,IND1 

ALON = ALON + DLON 

A2( J I = ALON 

ALAM = DTR*ALON 

-+C 205 

PLAMDA = PLAMDA I ! R ~ COSP) 

++C 209 

PPSI = PPSI/R 

C 

C COMPUTE ACCELERATION 

B-4 
C 

C 

ACC = DSQRTIPS*PS + PLAMDA*PLAMDA + PPSI*PPSIJ 

WRITE(6,SOO) ALAT1,ALDN,ACC 

500 FORMAT(' ALAT=',G14 8,' ALON=',G14 8,' ACC=',G14 8) 

C 

C LOAD PLOT ARRAY 

C PLOT(I,~) = ACC*FACTOR + 0.5 

C 

2000 CONTINUE 

C 

1000 CONTINUE 

C 

C ****.*** GENERATE PLOT *****.** 

C 

WRITEt6,700J 

700 FORMAT( '1',II,T36,' UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL', 

* ' ACCELERATION (MGALJ'.I,2X,'<LAT>' 3X,/) 

C 

DO 800 I=1,INDO 

WRITE(6,7S0) A1(I),VERT,(PLOT(I,~),~=1,IND1J 

750 FORMAT(3X,I3,3X,A1,40I3) 

800 CONTINUE 

C 

WRITEIS,770) HORZ,IA2(I).I=1,IND1,21 

770 FORMAT(/,T10,11SA1,II,2X, '<LONG>',2X,I3.19IS) 

IF ( 5 NE 0 )STOP 

++WRITE WORK,SPART 

B-5 
B.2 UTILITY FOR COMPUTING GRAVITATIONAL ACCELERATION UNCERTAINTIES ALONG THE TRAJECTORY OF A USER SATELLITE 

This SEA ut1lity computes the grav1tational acceleration 

uncertaint1es that result from a given geopotential error 

model as a user satel11te travels in its orbit. The uti11ty 

computes and prints out a table of radial, crosstrack, and 

alongtrack components: the magnitudes of the gravitational 

acceleration uncertainties: and the latitude and longitude 

of the ground trace of the satellite, for each error budget 

time requested. 

The data are then presented 1n five separate plots. The 

first four plots show the radial (height), crosstrack, and 

alongtrack components and the magnitudes of the gravitational acceleration uncertainties, respectively, as a function of t1me from epoch. The last plot shows the magnitudes 

of the gravitational acceleration uncertainties as the 

satel11te moves in its orbit as a funct10n of latitude an~ 

longitude. 

B.2.1 INPUT DATA SETUP 

This utility can be executed using the SEA keyword cards 

setup, and no special keyword cards are required. The geopotent1al error model can be set up the same way as described in Section B.l.l. 

B.2.2 MO~IFICATIONS TO SEA PROGRAM 

In subroutine RDKEYS, which reads in keyword cards, modifications are made so that the first real f1eld (Rl) on the 

LUMPGEOP keyword card can be used as a sca11ng factor 

(multiplication factor) to the S1ne and COS1ne coefficients 

uncertainties of an input geopotent1al error model. This 

prov1des a conven1ent means to scale down or scale up the 

coeff1cients to study the effect of an error model. 

B-6 

0112 
In subroutine FORCE, wh1ch calculates force per unit mass 

acting on the satel11te for the integration of the nom1nal 

trajectory, adait10nal cod1ngs are added to print out a 

table of time from epoch; latitude; longitude; radial, 

crosstrack, and alongtrack components; and the magn1tudes of 

the gravitational acceleration uncertainties whenever current t1me equals error budget time. This subroutine 1S 

modified so that, for each error budget t1me, SPART is 

called tW1ce: the first time for computing the geopotential 

accelerat10n uncertainties due to the geopotential error 

model; the second time to help in computing the nominal trajectory of the user satellite. The acceleration uncertainties computed are stored in separate arrays for later 

plotting purpose. To be able to recognize the error-budget 

time, the call1ng sequence of FORCE is also modified to include the input of the variable EBTIME. 

Subrout1ne FORCE is called from subroutine INTAG for each of 

the integration steps for the propagation of the satellite 

traJectory. Coding modification is therefore required in 

INTAG whenever FORCE is invoked using the modified calling 

sequence. The calling sequence (argument list) of I~TAG is 

also modified with the addition of the variable EBTIME, to 

be able to transfer the error-budget time to FORCE. 

Subroutine SEQUEN, wh1ch controls the forward sequential 

filter computation, specifies the variable EBTIME, which is 

passed to subroutine INTAG through its calling sequence. 

Modifications are made to suppress the error-budget and 

standard deviation correlat10n output reports. In addit10n, 

a new subroutine, GTPLOT, is added at the end of the filter 

computation to generate five separate plots (Section B.2). 

GTPLOT uses the arrays previously loaded in subroutine FORCE 

to generate the required plots. 

B-7 

0112 
Minor modifications are also made in subroutine SEAOl to 

suppress the error summary reports and error plots. In addit~on to the nonspher~cal gravitational accelerat~ons or 

acceleration uncertainties, the calling sequence of subrout~ne SPART is modified to pass the latitude and longitude of 

the user satellite to the calling subroutine, FORCE. 

Subroutine THCL is also mod~fied to output the 3 by 3 transformation matrix for transforming the gravitational acceleration uncerta~nties from inertial coordinates to height, 

crosstrack, and alongtrack coordinates. 

B.2.3 REQUIRED CODING UPDATES TO SEA PROGRAM 

The following is the listing of Panvalet updates to the 

Panvalet SEA source program stored in the data set 

GCDEV.MVT.SEA.PANLIB.DATA. To create an updated SEA program 

load module, the updates that follow must be compiled and 

linked to the existing SEA load module GCDEV.SEAMVS.LOAD. 

B-8 

0112 
~+UPDATE FORCE,1,TEMP 

++C 1,1 

SUBROUTINE FORCE ( T , ISAT , D2Y , ACCEL , EBTIME) 

++C 40 

LOGICAL*1 LTOOUT 

++C 45,45 

COMMON/CONST / AE, GM, DUMMY(5), RTD 

COMMON/FMODEL/C(30,33),CSIG(30,33) . COMMON/GTRACK/GTM~N(96),GALAT(96),GALAM(96),GGRAV(96,3),GG(96), 

* IGCNT 

DIMENSION CTEMP(30,33) 

DATA OEBTIM / -1 ODO / 

++C 50 

DIMENSION GRAV(3),TR(3,3) 

C LTOOUT - TRACKING ORIENTED OUTPUT FLAG 

LTOOUT = .FALSE 

C IS EBTIME A NEW ERROR BUDGET TIME 

IF ( EBTIME NE. OEBTIM ) LTOOUT = TRUE 

++0 72 

C 

C GENERATE THE TRACKING ORIENTED OUTPUT ONLY DURING ERROR 

C BUDGET REQUEST TIMES 

C 

C 

IF ( T .NE EBTIME) GO TO 550 

IF ( NOT. LTOOUT ) GO TO 550 

C FIND THE ACCELERATION DUE TO GEM UNCERTAINTIES CONTAINES IN CSIG 

C - BUT FIRST STORE THEM IN ARRAY C BECAUSE THIS IS THE ARRAY ACTED 

C UPON BY SUBROUTINE SPART 

C 

DO 510 IROW = 1,30 

DO 515 ICOL =1,33 

CTEMP(IROW,ICOL) = C(IROW,ICOL) 

C(IROW,ICOL) = CSIG(IROW,ICOL) 

515 CONTINUE . 510 CONTINUE 

CALL SPART(X,XDD,ALAT,ALAM) 

DO 530 IROW = 1,30 

00 535 ICOL =1,33 

C(IROW,ICOL) = CTEMP(IROW,ICOL) 

535 CONTINUE 

530 CONTINUE 

CALL THCL1(STATE(1,ISAT),TR) 

CALL MATMUL(TR,XDO,GRAV,3,3,1) 

G = OSQRT(GRAV(1)*GRAV(1)+GRAV(2)*GRAV(2)+GRAV(3)*GRAV(3» 

ALAT • RTO * ALAT 

ALAM = RTD • ALAM 

IF ( ALAM GE 0 000 ) GO TO 537 

IMULT = 1.000 + DABS(ALAM / 360 DO) 

ALAM = ALAM + DFLOAT(IMULT) * 360 000 

537 TMIN = T / 60 000 

C 

C LOAD ARRAYS USED LATER FOR PLOTTING 

C 

C 

IGCNT = IGCNT + 1 

GTMIN(IGCNT) = TMIN 

GALAT(IGCNT) = ALAT 

GALAMCIGCNT) = ALAM 

GGRAV(IGCNT,1) = GRAV(1) 

GGRAV(IGCNT,2) = GRAV(2) 

GGRAVCIGCNT,3) = GRAV(3) 

GG( IGCNT) = G 

WRITEC6,500) TMIN,ALAT,ALAM,GRAV,G 

500 FORMATC' TMIN=',G17 10,' ALAT=',G14 8,' ALAM=',G14 8, 

+ ' GRAV= ',3(G14 8,1X),' G=',G14 8) 

OEBTIM = EBTIME 

550 CALL SPARTCX,XDD,ALAT,ALAM) 

++WRITE WORK,FORCE 

++UPDATE INTAG,1,TEMP 

++C 1,1 

SUBROUTINE INTAG(T1,T2,PXX,TXU,PXZ,D2Y,YDY,YDY1,RK,ACCEL,EBTIME) 

++C 244,244 

B-9 
CALL FORCE';,1SAT,D2Y,ACCEL,EBT1~E' 

...... C 2S9 299 

CALL FORCE\T,ISAT,C2Y,ACCEL,EBTIME) 

++WR1TE WORK,INTAG 

++UPDATE RDKEYS,1,TEMP 

++C 229,229 

DPMAP(ILUMP) = 1 000 

IF C R1 NE a ODO l DPMAP(ILUMP) = R1 

++C 251,252 

CSIG(I1, 12+1):: R1" DPMAPCILUMP) 

CSIG(31-I1, 33-12 ) :: R2 ,. DPMAP(ILUMP) 

++WRITE WORK,RDKEYS 

++UPDATE SEQUEN,1,TEMP 

++C 167 

COMMON/GTRACK/GTMIN(96),GALAT(96),GALAMC96),GGRAV(96,3),GG(96), 

* IGCNT 

++C 176,177 

++C 207 

IGCNT = a 

++C 292,292 

95 CALL INTAG(TIME,TTO,PXX,TXU,PXZ,D2Y,YDY,YDY1,RK,ACCEL,EBTIME) 

++0 343,346 

++0 412,413 

++C 458,459 

C 

C GENERATE GEOPOTENTIAL TRACK ERROR PLOTS 

C 

800 CALL GTPLOTCEBSTOP) 

++WRITE WORK,SEQUEN 

++UPDATE SEA01,1,TEMP 

++C 216,216 

C SUPPRESS ERROR SUMMARY REPORT AND PLOT, BECAUSE THIER EXECUTION 

C IN COMBINATION WITH THESE UPDATED, RESULTS IN A SOC1 ABEND 

C 

C CALL OUTRSS 

++C 220,220 

C CALL PLTHLC 

++WRITE WORK,SEA01 

++UPDATE SPART,1,TEMP 

++C 1,1 

SUBROUTINE SPART ( X, XDD, ALAT, ALAM ) 

++C 93 

ALAT = DARSINCSINP) 

++WRITE WORK,SPART 

++UPDATE THCL,1,TEMP 

++C 4,4 

SUBROUTINE THCL1 X, T ) 

++R 17, ,/6,6/3,31 

++0 35,37 

++0 55,61 

++WRITE WORK,THCL 

++INSERT WORK 

SUBROUTINE GTPLOTCEBSTOP) 

C 

C 

IMPLICIT REAL*8(A-H,~-Z) 

COMMON/GTRACK/GTMIN(96),GALAT(96),GALAMC96l,GGRAV(96,3),GGI96), 

,. IGCNT 

C 

C 

,. 

,. 

,. 

,. 

OIMENSION TPLOT(53,103),XLINE(101),YLINE(53) 

DIMENSION XLAB(11),SYM(4) 

DIMENSION PLOT(40,111),DIGITSC36) 

LOGICAL"1 HDRZ(113),VERT,SLASH 

INTEGER,.2 A1(40),A2(40) 

DATA DLAT/5 DOl, OLON/10 DOl, FACTOR/1 05/ 

DATA HORZ/113"'-'I, VERTI'I'I, SLASHI' 'I 

DATA SYM I 'H', 

'e' . 'L' , 

'R'I 

DATA DOT I' 'I, 

DASH 1'-'1, 

B-IO 
C 

C 

C 

:t. 

:0 

~ 

'" '" '" '" '" 

,. '" 

ANILET ,I'! I 

BLANK , " , I , 

OVERFL /':r.' I 

DATA DIGITS/'O', '1', '2','3', '4', 

'5', '6', '7', 'S', '9', 

I A', 'B', 'e' , '0' , 'E I, 

'F', 'G', 'H', 'I I, 'u'. 

'K', 'L', 'M' ,'N','O', 

'P', 'Q', 'R/t/S/t/T', 

'U', 'V', 'W', 'X', 'V', 

'Z'/ 

DO 5 ICOL = 4,112,S 

HORZ(ICOL) = SLASH 

5 CONTINUE 

HORZ( 1) = VERT 

HORZ(113) = VERT 

DO 7 I= 1,40 

DO 8 0.1=1,111 

PLOT(I,o.I) = BLANK 

8 CONTINUE 

7 CONTINUE 

C BUILD XLINE AND VLINE 

C 

DO 10 I = 1 , 101 

10 XLINE(II = DASH 

DO 20 1-=1,101,10 

20 XLINE(I) = DOT 

DO 30 1=1,53 

30 VLINE(I) = ANILET 

DO 40 1=2,52,5 . 40 VLINE (I) = DOT 

C 

C INITIALIZE ARRAY TPLOT AND LOAD AXlES 

C 

C 

DO 50 ICOL=2, 102 

DO SO IROW=2,s2 

TPLOT(IROW,ICOL) = BLANK 

SO CONTINUE 

50 CONTINUE 

DO 80 1=2,102 

TPLOT(1 ,I) = XLINE(I-1) 

TPLOT(s3,I) = XLINE(I-1) 

80 CONTINUE 

DO 90 1=1,53 

TPLOT ( I , 1 ) = YLINE ( I ) 

TPLOT(I,103) = YLINE(I) 

90 CONTINUE 

C FIND MAX AND MIN OF THE GEOPOTENTIAL ACCELERATIONS 

C 

AMAX = -1 00-50 

AMIN = 1 00+50 

DO 200 I=1,IGCNT 

IF (GG(I) GT. AMAX ) AMAX = GG(I) 

DO 210 ISET=1,3 

IF (GGRAV(I,ISET) LT AMIN) AMIN = GGRAV(I,ISET) 

210 CONTINUE 

200 CONTI NUE 

WRITE(S,4000)AMAX,AMIN 

4000 FORMAT('O"'''''''''' AMAX = ',025 15,' AMIM = ',025 15,/) 

C 

C FIND SCALING FOR THE X AXlES 

C 

lEBEC = EBSTOP/BO 000 + 500 

IEBST = 0 0 

IXSCAL = ( ( OFLOAT(IEBEO) - OFLOAT(IEBST»/100 000 ) + 9999900 

XSCAL = IXSCAL 

IXMIN = IEBST 

WRITE(S,4010)EBSTOP,IEBEO,IEBST,XSCAL,IXMIN 

4010 FORMAT('O***"'* EBSTOP =',014 7,' IEBED = ',IB,' IEBST :',1B, 

B-ll 
.' XSCAL =' ,014 7,' IXMIN =',16,/1 

C 

C FIND SCALING FOR THE Y AXlES 

C 

YRANGE = ( AMAX - AMIN ) * 1 005 

YSCAL = YRANGE 1 SO 000 

YTEMP = YSCAL * 5 000 

C ROUND YTEMP UP TO NEAREST 1 MG 

IYTEMP = ( YTEMP * 10 000 ) + 9999900 

YTEMP = DFLOAT(IYTEMP) 1 10 00 

YSCAL = YTEMP 1 5 000 

YMIN = ( ( AMIN * 1.005 ) 1 YRANGE ) * YSCAL * SO 000 ) 

C ROUND YMIN DOWN TO NEAREST .1 MG 

IYTEMP = YMIN * 10 DO 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

IF (YMIN LT 0 000 ) IYTEMP = ( YMIN * 10 DO ) - 9999900 

YMIN = OFLOAT(IYTEMP) 1 10 DO 

YMAX = YMIN + 50 000 * YSCAL 

WRITE(6,4020)YRANGE,YSCAL,YMIN,YMAX 

4020 FORMAT('O**** YRANGE =',014 7,' YSCAL =' ,014 7,' YMIN =' ,014 7, 

*' YMAX =',014 7,/) 

LOOP OVER ALL FOUR PLOTS 

WHERE. ISET = 1, HEIGHT PLOT (HI 

2, CROSS TRACK PLOT (C) 

3, ALONG TRACK PLOT (L) 

4, RSS PLOT (R) 

DO 500 ISET = 1,4 

LOAD INDIVIDUAL POINTS IN TO ARRAY TPLOT 

YCOR = YMIN 1 YSCAL 

WRITE(6,4040) ISET,YCOR 

4040 FORMAT('O**** ISET =' ,13,' YCOR =',014 7,1) 

DO 600 I = 1,IGCNT 

C 

C 

C 

* 

* 

4050 

600 

IXCOL = ( GTMIN(I) 1 XSCAL ) + 500 

IF ( ISET LT 4) 

IYROW = ( (GGRAV(I,ISET) * 1 ODS ) 1 YSCAL - YCOR + 5 

IF (ISET EQ. 4 ) 

IYROW = ( (GG(I) * 1 ODS) 1 YSCAL - YCOR + 5 

WRITE(6,40S0)IYROW,IXCOL,SYM(ISET) 

FORMAT(' **** IYROW =',15,' IXCOL =',15,' USING SYMBOL->',A1) 

TPLdT(52-IYROW,IXCOL+2) = SYM(ISET) 

CONTINUE 

PRINT OUT ARRAY TPLOT ONE ROW AT A TIME 

WRITE(6,2000) 

2000 FORMAT("',T10, 'PLOT OF TRACK ACCELERATIONS FROM THE' 

.'GEOPOTENTIAL UNCERTAINTY, IN MGAL',II) 

YVAL = YMAX + 5.0 * YSCAL 

DO 700 IROW = 1,53 

WRITE(6,2010) (TPLOT(IROW,ICOL),ICOL=1,103) 

2010 FORMAT(' ',T14,103A1) 

IF (MOO(IROW-2,5) NE 0 ) GO TO SOD 

YVAL = YVAL - 5 0 * YSCAL 

WRITE(6,2050)YVAL 

2050 FORMAT('+',T3,F10.2) 

SOO CONTINUE 

C LATER ON ONE MAY WISH PLACE HERE THE CODE TO GIVE 

C Y-AXIS LABELS 

C 

700 CONTINUE 

IXVAL = IXMIN - 10 * IXSCAL 

DO 900 1=1,11 

IXVAL = IXVAL + 10 * IXSCAL 

XLAB(I) = IXVAL 

900 CONTINUE 

WRITE(6,2100)XLAB 

2100 FORMAT(' ',TS,11F10 2,II,T47, 

* 'TIMES FROM EPOCH IN MINUTES') 

C BEFORE PRINTING NEXT PLOT, BLANK OUT TPLOT ARRAY 

C 

B-I2 
-, 

C 

IF , ISEi EO 4 I GO TO 500 

DO 100e ICO~=2.102 

DO 1010 IROW=2,S2 

TPLOTCIROW,ICOL) = BLANK 

1010 CONTINUE 

1000 CONTINUE 

500 CONTINUE 

C LOAD PLOT ARRAY TO GENERATE LONGITUDE LATITUDE PLOT 

C 

C 

C 

DO 1020 II=1,IGCNT 

I = 19 500 - ( GALAT(II) / DLAT ) 

ALAMT = GALAMCII) 

uCOL = ( ALAMT / 3 333300 ) + 3.500 

AMGAL = GG(II) * FACTOR + 0 5 

IMGAL = AMGAL 

IF ( IMGAL LE 36 ) GO TO 1018 

PLOT(I,uCOL) = OVERFL 

GO TO 1020 

1018 CONTINUE 

WRITEC6,4060lII,GTMINCII),II,GALATCII),ALAMT,AMGAL,I,uCOL 

4060 FORMAT(' **** GTMIN( ',I2,')=',F7.2,' GALAT(',I2, ')=', .. 014.7,' ALAMT=',D147,' AMGAL=',F62,' 1=',13,' uCOL=',I3) 

PLOT(I,uCOL) = DIGITS ( IMGAL + 1 ) 

1020 CONTINUE 

C 

C GENERATE LATITUDE/LONGITUDE PLOT 

C 

C 

C 

INDO = 180 000 / OLAT + 1 

IND1 = 360 000 / OLON + 1 

ILONGV = 0 

lLATV = 90 

DO 1025 1=1,40 

A1( I) • ILATV 

ILATV = ILATV - 5 

A2(I) = ILONGV 

ILONGV = ILONGV + 20 

1025 CONTINUE 

WRITE(S,1030) HORZ 

1030 FORMAT('l',//,T3S,' UNCERTAINTY IN NONSPHERICAL GRAVITATIONAL', * ' ACCELERATION (MGAL)',1,2X,'<LAT>',3X,I, * 9X,115A1) 

DO 1040 I=1,INDO 

WRITE(6,1050) Al(I),VERT,(PLOT(I,u),u=l,l11),VERT 

1050 FORMAT(3X,I3,3X,A1,111A1,Al) 

1040 CONTINUE 

WRITECS,1060) HORZ,(A2(I),I=1,191 

10S0 FORMAT(' ',T10,113Al,//,10X,I3,18I6,//,60X, 

* '<LONG>') 

RETURN 

END 

B-13 
End of Document