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Produced by the NASA Center for Aerospace Information (CASI)
NASA CONTRACTOR REPORT 17 7326

(NASA-CR-17.7326) A STUDY OF 3HE APPLICATION N85

OF DIFFERENTIAL TECHNIQUES IC THE GLOBAL

POSITIONING SYSTEM FOR A HELICOPTER

PRECISION APFhOACH (Ohio Univ.) 83 p Unc

HC A05/Mk A01 CSCL 17G G3/04 2464

A STUDY OF THE APPLICATION OF

DIFFERENTIAL TECHNIQUES TO THE GLOBAL POSITIONING SYSTEM

FOR A HELICOPTER PRECISION APPROACH

DARYL L, MCCALL

CONTRACT NAG 2-231

NOVEMBER'1984

^`' .

^^'' u, 

PUG1g$5

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I''' Su'"c^ 419'â"
NASA CONTRACTOR REPORT

A STUDY OF THE APPLICATION OF

DIFFERENTIAL TECHNIQUES TO THE GLOBAL POSITIONING SYSTEM

FOR A HELICOPTER PRECISION APPROACH

DARYL-L, MCCALL

NOVEMBER 1984

PREPARED FOR 

AMES RESEARCH CENTER

UNDER GRANT NAG 2-231 By

OHIO UNIVERSITY

ATHENS, OHIO

NSA

National Aeronautics and

Space Administration

Ames Research Center

Moffett Field, California 94035
A STUDY OF THE APPLICATION OF DIFFERENTIAL

TECHNIQUES TO THE GLOBAL POSITIONING SYSTEM

FOR A HELICOPTER PRECISION APPROACH

Table of Contents

Page

1.0 INTRODUCTION AND SUMI:ARY. ........................................ 1

2.0 BACKGROUND ...................................................... 2

2.1 Global Positioning System (GPS) ............................ 2

2.2 Differential GPS ........................................... 3

2.2.1 The Differential GPS Uplink ......................... 3

2.2.2 The Differential GPS Uplink Using a Pseudolite...... 5

3 4 THE DIFFERENTIAL GPS SIMULATION ................................. 7

3.1 18 Satelli-e Configuration ................................. 7

3.2 DGPS User Flight Path ...................................... 7

3.3 The Navigation Algorithms .................................. 7

3.3.1 Position Fixing Algorithm ........................... 13

3.3.2 Alpha-Beta Tracking Filter .......................... 15

3.4 Simulation of GPS Range Errors..... I ....................... 18

3.4.1 Multipath ........................................... 19

3.4.2 Ionospheric Range Error ............................. 19

3.4.3 Tropospheric Range Error ............................ 24

3.4.4 Receiver Clock Error ................................ 27

3.4.5 Selective Availability Errors ....................... 30

3.5 GPS Simulation Operation. ** ................................ 34

3.5.1 Sequential/ Single Channel Architecture .............. 36

3.5.2 Four Channel Architecture ........................... 38

4.0 SIMULATION RESULTS .............................................. 40

4.0.1 Receiver Performance, Conventional Mode,

No SA Errors ........................................ 40

4.0.2 Receiver Performance, Conventional Mode,

With SA Errors ...................................... 40

4.0.3 Receiver Performance, Fixed Mode,

Without SA Errors .................. I................ 50

4.0.3.1 Diffuse Multipath, Range Correction

Effectiveness .............................. 50

4.0.3.2 Atmospheric Delays, Range Correction

Effectiveness.... * ......................... 50

4.0.3.3 Receiver Performance, Fixed Mode General... 58

4.0.4 Receiver Performance, Fixed Made, With SA Errors.... 58

4.0.5 Receiver Performance, Differential Mode, Without

SA Errors ........................................... 58

4.0.6 Receiver Performance, Differential Mode, With

SA Errors ........................................... 66

4.0.7 Receiver Performance, Differential Mode, With

SA Errors, Using Corrections From Different

Receivers of Different Update Periods ............... 73

5.0 CONCLUSIONS ...................,.................................. 73

6.0 ACKNOWLEDGEMENTS ................................................ 75

7.0 BIBLIOGRAPHY .................................................... 76

at
List of Figures and Tables

Figure 2.2.1.1

Figure 2.2.2.1

Figure 3.1.1

Figure 3.1.2

Figure 3.2.1

Figure 3.2.2

Figure 3.3.1.1

Figure 3.3.2.1

Figure 3.4.1.1

Figure 3.4.2.1

Figure 3.4.2.2

Figure 3.4.2.3

Figure 3.4.3.1

Figure 3.4.4.1

Figure 3.4.5.1

Figure 3.4.5.2

Figure 3.4.5.3

Figure 3.4.5.4

Figure 3.4.5.5

Figure 3.5.1.1

Figure 3.5.2.1

Figure 4.0.1.1

Figure 4.0.1.2

Figure 4.0.1.3

Figure 4.0.1.4

Figure 4.0.1.5

Figure 4.0.1.6

Figure 4.0.2.1

Figure 4.0.2.2

Figure 4.0.2.3

Figure 4.0.2.4

Figure 4.0.2.5

Figure 4.0.2.6

Figure 4.0.3.1

Figure 4.0.3.7.

Figure 4.0.3.3

Figure 4.0.3.4

Figure 4.0.3.5

Figure 4.0.3.6

Figure 4.0.3.1.1

Differential CPS Uplink ............................

Differential CPS Pseudolite Uplink .................

The Uniform 6-Plane, 18-Satellite Configuration....

Phasing of the Uniform 6-Plane, 18 Satellite

Configuration ......................................

Teardrop Flight Path Ground Track ..................

Teardrop Flight Path Altitude Profile ..............

Graphic Re, iresentation of the Pythagorean

Solution c)r Satellite Range .......................

Alpha-Beta Filter Estimation Loop ..................

Diffuse Multipath Range Error ......................

Average Monthly Value of Zenith Propagation

Delay and the Raised Cosine Model ..................

Ionospheric Range Error Model Parameters...........

Ionospheric Range Error ............................

Tropospheric Range Error ...........................

Uncorrected Range Errors Induced by an Imperfect

Receiver Oscillator ................................

Selective Availability Rate Distribution...........

Selective Availability Second Derivative

Distribution .......................................

Selective Availability Model Rate Distribution.....

Selective Availability Model Second Derivative

Distribution .......................................

Selective Availability Range Errors ................

Sequential Single Channel Receiver Simulation

Program Flow .......................................

Four Channel Receiver Simulation Program Flow......

Altitude Errors, Run C-1, without SA ...............

3D Position Error, Run C-1, without SA .............

2D Position Error, Run C-1, without SA .............

Altitude Error, Run C-4, without SA ................

3D Position Error, Run C-4, without SA .............

2D Position Error, Run C-4, without SA .............

Altitude Error, Run C-1, with SA ...................

3D Position Error, Run C-1, with SA ................

2D Position Error, Run C-1, with SA ................

Altitude Error, Run 0-4, with SA ...................

3D Position Error, Run C-4, with SA ................

2D Position Error, Run C-4, with SA ................

Altitude Error, Run F-4, without SA ................

3D Position Error, Run F-4, without SA .............

2D Position Error, Run F-4, without SA .............

Altitude Error, Run F-4, with SA ...................

3D Position Error, Run F-4, with SA ................

2D Position Error, Run F-4, with SA ................

Cross Correlation of Multipath Error ...............

Page

4

6

8

9

11

12

14

17

20

21

22

25

28

29

31

31

32

33

35

37

39

42

43

43

44

45

45

46

47

47

48

49

49

51

52

52

53

54

54

55
List of Tables and Figures (Continued)

Page

Figure 4.0.3.2.1 Cross Correlation of Ionospheric Errors............ 56

Figure 4.0.3.2.2 Cross Correlation of Tropospheric Errors........... 57

Figure 4.0.3.3.1 Cross Correlation of Combined Multipath,

Ionospheric, and Tropospheric Errors ............... 59

Figure 4.0.4.1 Cross Correlation of Selective Availability

Errors ............................................. 60

Figure 4.0.4.2 Cross Corrlation of Combined Selective

Availability, Multipath, Ionospheric, and

Tropospheric Errors ................................ 61

Figure 4.0.5.1 Altitude Errors, Run D-8, without SA ............... 62

Figure 4.0.5.2 3D Position Error, Run D-8, without SA ............. 63

Figure 4.0.5.3 2D Position Error, Run D-8, without SA ............. 63

Figure 4.0.5.4 Single Channel Performance, without SA ............. 64

Figure 4.0.5.5 Four Channel Performance, without SA ............... 65

Figure 4.0.6.1 Altitude Error, Run D-8, with SA ................... 67

Figure 4.0.6.2 3D Position Error, Run D-8, with SA ................ 68

Figure 4.0.6.3 2D Position Error, Run D-8, with SA ................ 68

Figure 4.0.6.4 Single Channel Performance, with SA ................ 69

Figure 4.0.6.5 Four Channel Performance, with SA .................. 70

.Figure 4.0.6.6 Altitude Errors, Run D-6, with SA .................. 71

Figure 4.0.6.7 3D Position Error, Run D-6, with SA ................ 72

Figure 4.0.6.8 2D Position Error, Run D-6, with SA ................ 72

Figure 4.0.7.1 3D Position Errors of a 0.3 sec./dif£. Mode

Receiver, Using Corrections from either a 1.2

Sec. or 2.4 Sec., Fixed Mode Receiver with

Selective Availability Errors ...................... 74

Table 3.1.1 NAVSTAR GPS Orbit Description as Implemented in

the Computer Simulation, Longitude Relative to

Earth and Astronomical Coordinated ................. 10

Table 4.0.1 Basic Receiver Configurations ...................... 41

rte' : .^s
1.0 INTRODUCTION AND SUMMARY

This paper documents the results of a preliminary study of the

application of differential techniques to the NAVSTAR Global Positioning

System for the O.vilian helicopter environment. The results of this study

will be used to assist in the specification of a differential GPS (DGPS)

ground system and in the identification and evaluation of the problem areas

which may inhibit the successful and timely hardware implementation of the

DGPS system.

The simulated missions used a variety of receiver types;

sequential/single channel, four channel, and various receiver update

periods. Each receiver type was subjected to a variety of degradations of

satellite range, including diffuse multipath, ionospheric delay, tro -

pospheric delay, receiver clock error, and the Department of Defense selec -

tive availability errors. The models used to calculate these values are

presented in this text.

Evaluations of the receiver types are presented by means of performance analyses of representative cases for the three different receiver

modes; conventional, fixed, and differential (corrections applied to the

receiver range measurements). These analyses include the discussion of

position errors, the spatial correlative properties of individual range

error sources, and the filtering algorithm used to smooth the position

data.

The basic findings of this study are:

1) Differential GPS does show significant potential for providing

a precision approach capability, particularly with respect to

lateral guidance.

2) This potential may be increased by the application of some 

type of filtering to the range measurement of the fixed mode

receiver: The high frequency effects of the diffuse multipath

can produce less accurate range corrections, and the removal

of these errors may boost the accuracy of DGPS to 

guidance in altitude.

3) If an uplink rate of 12 seconds or greater is to be imple -

mented in the DGPS ground system, good DGPS user positional

accuracies should be obtainable with a plower (2.4 sec update

period), sequential/single channel receiver implemented in the

ground system.

4) The DGPS differential mode receiver should have a position fix

filtering algorithm capable of tracking accelerative dynamics.

The alpha— beta tracking filter's performance is, at best,

marginal when subjected to levels of acceleration experienced

during the execution of an approach turn maneuver.
2.1 Global Positioning System (GPS)

The Global Positioning System (GPS) is a worldwide, all-weather

navigation system currently under development by the Department of Defense

The baseline space segment configuration will consist of 18 satellites

equally spaced in six orbits. The orbits will be uniformly distributed

about the earth, each inclined 53 0 with respect to the spin axis of the

earth. This baseline system is scheduled to begin deployment in January,

1986 [1].

GPS will offer two systems, the Precise Positioning System (PPS)

which implements the P-code and the Standard Positioning System (SPS) whic

will use the C/A-code. Preliminary studies have shown that the PPS will

provide fixes with an accuracy of 18.1 meters (2 drms) horizontally and

29.7 meters (2 sigma) vertically [2]. In the interest of national

security, the PPS will only be be available for DOD applications and those

users authorized by the DOD. The SPS has been shown to have the potentia

to offer an accuracy of 43.6 meters (1 sigma) horizontally and 23.8 meters

(1 sigma) vertically [3]. This accuracy will, for reasons of security, be

purposely degraded such that available accuracy will be 100 meters (2 drms

horizontally [4]. The DOD will review the practicality of increasing the

accuracy of the SPS annually.

The P-code will be transmitted on two frequencies, L1 - 1575.42

MHz and L2 - 1227.6 MHz. The C/A-code will be transmitted on the LL frequency only. Receivers with the ability to track both carriers will have

the capability to determine the phase/delay and carrier/advance effects of

the atmosphere. Other receivers will have a significantly more inaccurate

determination of the atmospheric effects by means of a model provided in

the GPS navigation message data. Either the two frequency measurements or

the model calculations will be used to correct the time delay of the GPS

signals.

The user can determine position in three dimensions and receiver

clock error by measuring the Zime of propagation of four GPS signals from

four different satellites which provide good geometry. The ideal geometry

would consist of one satellite at zenith and three satellites close to the

horizon, each of the latter uniformly spaced by 120° in azimuth. Because

the effects of the atmosphere are significantly amplified when a satellite

is positioned near the horizon, a mask angle of 5-10° is usually implemented.

The user may compute his position and clock error by tracking

fewer than 4 satellites if he has redundant position informai:ion available

such as knowledge of altitude, differential LORAN-C position fix, etc., or

the user may only track three satellites to compute three dimensions of

position if his receiver possesses an extremely stable frequency standard.

The Genera. Aviation user, with degraded C/A-code compounded by

areas of poor geometry and satellite outages, will be limited to the

-2-
enroute and, perhaps, the non-precision approach environment. Differentia

techniques can be employed to reduce the effects of poor geometry and

expand the possibility of using differential GPS (DGPS) during a precision

approach.

2.2 . Differential GPS

Differential CPS is a technique whereby the certainty of a GPS

user's position is improved by providing, to the user, knowledge as to

either position error or the errors induced in range measurements. Severa

methods have been discussed by others [5, 6) as how these corrections may

be implemented, however only two methods have drawn significant attention

[7]; the uplink method and the uplink method by pseudolite.

2.2.1 The Differential GPS Uplink

The basic components of a DGPS uplink ground unit consist of a GP

receiver, a central processor, and a telemetry unit with the antenna of th

GPS receiver placed at a precisely known location (see figure 2.2.1.1).

The DGPS ground system's processor is programmed with the coordinates of

the receiver's antenna. The central processor is interfaced to the GPS

receiver in such a manner that it can obtain the satellite data block

information stored in the receiver as well as time/Sat ID-tagged

range/range rate information.

With the knowledge of GPS system time, derived either from the

satellite range data or by an external standard, the central processor can

determine the true range from the receiver's antenna to any particular GPS

satellite. The difference between the processor's calculated range and the

receiver's measured range is the range correction provided to the DGPS

user(s) in the local area via a one-way data telemetry uplink. Similarly,

calculations and measurements can be made to provide the user with a range

rate or Doppler correction.

The DGPS nser would have a similar breakdown of basic components

consisting of a GPS receiver, a central processor, and a telemetry

receiver. Once the correction has been received, the central processor 

would then apply them to the user's measured ranges and then proceed to

compute a position fix which is significantly more accurate than those

using conventional GPS. It should be noted that the user's processor would

be less sophisicated than the DGPS ground system's processor. If commercially produced, the user's central processor would probably be shared wit

the GPS receiver.

The corrections could also take the form of position coordinate

corrections. The application of position coordinate corrections to a conventional GPS position fix would only provide consistently improved result

if the correction and the conventional position fix were derived from the

identical selection of satellites. The application of corrections to a

position fix, both of which were calculated from separate sets of satellites, would produce meaningless results.

-3-
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262.2 The Differential GPS Uplink Using a Pseudolite

This method is very similar to the DGPS uplink, however the

distinct advantage to this method comes from the use of a pseudolite (see

figure 2.2.2.1). A pseudolite is a static, ground — based NAVSTAR

transmitter. Its signal format would be identical to that of the space —

based satellites, however the data content of the pseudolite would be

somewhat different. Instead of 2everal complex emphemeris constants, its

position data would consist of three earth centered coordinates. The data

message would also contain the DGPS corrections calculated at the pseudo -

lite. These corrections would be derived using the techniques described in

the uplink method.

The major advantage to the pseudolite uplink comes in the way of

improved geometry due to having a satellite beneath the user. The pseudolite decreases the effects of the residual range errors in the DGPS range

measurements and tends to provide an overall improvement to the altitude

calculation when using either GPS or DGPS.

One problem with the pseudolite uplink is in coverage. The uplink

method without pseudolites could employ the use of transmission frequencies

with enough ground wave to service 100 miles or more over the horizon.

Because the pseudolite will transmit at the NAVSTAR frequencies, there will

be no ground wave, therefore all receptions of the differential information

will be done within line—of—sight of the pseudolite. The coverage of the

pseudolite can not be expanded by merely increasing its transmission power;

to do so would risk saturating the RF front—ends of the all of the GPS

receivers in the immediate area and either degrade or jam the user's

receiving capabilities.

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3.0 THE DIFFERENTIAL CPS SIMULATION

The following is a discussion of the operation of the computer

simulation used ;a derive the results in this paper.

3.1 18 Satellite Configuration [8)

The simulation uses 18 satellites distributed equally into six

circular orbits about the earth (see figure 3.1.1). Each orbit is incline

55 0 with respect to the spin axis of the earth. Each satellite has an

earth centered radius of 14,568 nautical miles and thus the orbital period

of each satellite is approximately 12 hours.

The orbits are sequentially phased 40° in such a way that if a

satellite is directly above the equator, the plane adjacent to the east

will have a satellite 40° ahead and the plane adjacent to the west will

have a satellite 40 0 lagging (see figure 3.1.2). Table 3.1.1 shows the

longitudes of the ascending nodes and the angles of right ascension for

each satellite used. The angles of right ascension, between each orbital

plane, are evenly spaced 60° apart.

3.2 DGPS User Flight Path

The user dynamics used in this simulation were modeled after thos

generally encountered in the GA helicopter terminal/approach environment.

The mission contains six legs, each of which can contain the following

characteristics:

• straight, level, constant velocity paths

• constant heading, constant velocity, constant ascent/descent

paths (descent/ascent speeds varying from 300 fpm to 750 fpm)

• various turns, including a teardrop maneuver

• several different speeds (89- • 120 knots) and accelerations

(-2 knots/second to 5 knots/second)

The final approach to the runway is made using the teardrop maneuver.

Figures 3.2.1 and 3.2.2 depict the ground track and altitude profile of the user. The entire scenario was similar to that used in a study

of degraded CPS for non—precision approaches [9].

3.3 The Navigation Algorithms

The following text describes the position fixing algorithm used t

derive user navigational information given time and four user pseudorange

measurements. A brief discussion is devoted to the alpha—beta tracking

filter employed to smooth the position calculations.

-7-
7

1

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Figure 3.1.1 The Uniform 6-Plane, 18-Satellite Configuration
-9-

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LONGITUDE RIGHT ASCENSION

OF THE OF THE

SATELLITE ORBIT ASCENDING ASCENDING

NUMBER PLANE NODE, DEG. NODE, DEG.*

1 1 0. 180. 0.

2 1 240. 60. 0.

3 1 300. 120. 0.

4 2 260. 80. 60.

5 2 320. 140. 60.

6 2 20. 200. 60.

7 3 340. 160. 120.

8 3 40. 220. 120.

9 3 100. 280. 120.

10 4 60. 240. 180.

a 11 4 120. 300. 180.

12 4 180. 0. 180.

13 5 140. 320. 240.

14 5 200. 20. 240.

15 5 80. 260. 240.

16 6 220. 40. 300.

17 6 280. 100. 300.

18 6 160. 340. 300.

r.:

* Referenced to astronomical coordinates of 1950.0 as of 0 hr 0 min GHT

the simulation does not allow the right ascending node to regress.

Table 3.1.1. NAVSTAR CPS Orbit Description as Implemented

in the Computer Simulation, Longitude Relative

to Earth and Astronomical Coordinates

-10-

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Figure 3.2.1 Teardrop Flight Path Ground Track
0

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Figure 3.2.2 Teardrop Flight Path Altitude Profile

-12-

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3.3.1 Position Fixing Algorithm

The following discussion is based upon the information presented

by Noe and Myers (10).

The algorithm used to calculate the user's position requires the

inputs of time, an estimate of the user's position and four user

pseudorange measurements. To assist in the discussion of this algorithm,

assume that the pseudorange is equal to the true range between the user and

a satellite, plus user clock error.

The following expression relates the user's position (u , u , u )

and receiver clock bias (b), i th satellite position (x il, x12 1 x13)nd 3

the measured pseudorange ri;

3

Eq. 3.3.1.1 E(xif

— uj ) 2

° ( ri— b) 2 , for i = 1, 2, 3, 4

J=1

Figure 3.3.1.1 expresses graphically the Pythagorean relations used to

derive the earth centered user's position.

Expanding the equation and solving for r i , the following

expression is obtained;

Eq. 3.3.1.2 ri °. 3 ( xil—ul) 2 + (xi2—u2) 2 + (x,3—u3) 2 + b

To obtain the desired navigation algorithm, it is first necessary

to Taylor series expand the pseudorange measurement r i about the user posi 

tion estimate U. This results in the following equation;

2 1 air

Eq. 3.3.1.3 ri = 'L- + ari 6U + 1

a 

ri 6 2 U + i 63U+

au ) _ 21 aU2

31 aU3

U U U

This equation can now be linearized by deleting all of the partial

derivatives of an order greater than one, giving the expression;

ari

_ 6U or

Eq. 3.3.1.4 ri = ri +

au U

—13—
USI

(UTA

POSITION OF Ith SATELLITE

(XI 'X2'X3)

Figure 3.3.1.1 Graphic Representation of the Pythagorean Solution for Satellite Range.

-14-
i

Eq. 3.3.1 .5

[(:71

)riariarir

dri dU

3 U2)

 au au ab I 

Where Sr ° ri — ri and dU = U — U.

Define dr as follows;

Eq. 3.3.1.6 Sri ° hi d U

whe re hi is the row vector of first order partial derivatives;

I ari

ari ( ri

ari) 1

Eq. 3.3.1.7 hi

L 1

3u2)

au \ 3au 0 I U

Now, replace ri in the hi row vector with Eq. 3.3.1.2, expand the partial

derivatives, substitute ri — b from Eq. 3.3.1.2, and obtain;

Eq. 3.3 .1 .8hi I 

(Uil

ri xib I

(r1i

—Xi

bJ

I urix bl 1 I U

This may now be expanded to four pseudorange measurements and solved

for the user position vector U;

[hl ]

h2

SR = h3 dU ° HSU

h4

Eq. 3.3. 1.10 dU = H71 SR

Now, given time, four pseudorange measurements, and an user position

estimate, this algorithm will provide a user position and clock bias

update.

3.3.2 Alpha—Beta Tracking Filter

The data output from the position fix algorithm is filtered using

a simple, fixed gain alpha—beta tracking filter. This is the same filter

used in the GPS non—precision approach study simulations developed for the

-15-

Eq. 3.3.1.9

- >t ...

.=-fir F

OJ'»'.'• Y 
Department of Transportation. The following discussion is paraphrased from

the documentation of that study (11).

Figure 3.3.2.1 depicts the alpha-beta filter estimation loop and

its corresponding system equations. Rearranging these filter equations

yields;

UP (t+ T) - Up (t) AU

Eq. 3.3.2.1 _ + Vp(t + T)

T T

VP

 (t+ T) - Up(t) 00

Eq. 3.3.2.2

T T2

where U p is the predicted user position component, V is the predicted user

velocity component, T is the update period, AU is the position update from 

the position fix algorithm, and alpha and beta are the filter gain

constants.

These equations can be approximated by the following differential 

equations;

dUp aAU

Eq. 3.3.2.3 dt = T + V 

dUp _ A

Eq. 3.3.2.4 dt - 

T22

and then converted to these integral equations;

aAU

Eq. 3.3.2.5 Up - T + V dt

U

Eq. 3.3.2.6 V

P

= V 

HA

T2 dt

By means of the Laplace Transform and deriving the transfer function of this system, it is possible'to obtain the characteristic equation

to determine the relationship of the filter gain constants to the damping

ratio of the system. A damping ratio of unity was chosen for the non-

-16-
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precision approach study to compromise between filter rise time, overshoot,

and ringing of the transient response. This gives the relationship between

alpha and beta;

Eq. 3.3.2.7 a2 - 48

Again, using the transfer function of the system, the unit step

response of the filter is found to be;

at at at

Eq. 3.3.2.8 1 *2T e

2T- e 2

Now define a time constant Tf such that at t - 2T f , the step response

is within 13.5% (e 2 ) of the final value of the unit step response, this

yields;

aT aTf aaTf

Eq. 3.3.2.9 e2. e - T e - L

This differential equation can be solved and found to have at least one

real solution;

.72T

Eq. 3.3.2.10 Tf '- a

The values used for the DOT simulations were found by experimentation. "Reasonable performance" was achieved for alpha - .2 and beta =

.01 for a dwell time of 1.2 seconds. This gave an overall time constant of

Tf -4.3 seconds. These filter gain constants were used throughout this

simulation, regardless of receiver update rate. Therefore, Tf was allowed

to vary proportional to the receiver update rate, a receiver with a shorter

update period filtered its position data using a filter with a faster reaction time. A receiver with an update rate of 0.3 seconds had a time

constant of approximately 1.075 seconds and a receiver with an update rate

of 2.4 seconds had a time constant of 8.6 seconds.

3.4 Simulation of GPS Range Errors

The following is a discussion of the error models used in this

study and their derivations.

e

-18-

lei
3.4.1 Multipath

Multipath can take on two basic forms of interference to GPS

signals, specular and diffuse multipath. Specular multipath produces a

delayed replica of the direct path GPS signal and, depending upon the medi

from which it is reflected, can be received at various signal levels. Thi

degradation can be substantial if the receiver does not lock on the

earliest received signal; usually this can only occur If the signal delay

is greater than one pseudorandom (PRN) code chip width. Specular multipat

was not included in the simulation. The diffuse multipath was modeled as

described in the following text.

Diffuse multipath produces a random wide—band interference rathe

than inducing a large range offset. The diffuse multipath is caused by th

addition of the many indirect signals, reflected mainly from the user's

vehicle surface. These errors have an rms value of 1.0 to 3.0 meters for

the P—code and 10.0 to 30.0 meters for the C/A—code (12].

The error values generated by the

mean gaussian distribution with a standard

multiplying the elements of the distribuci,

This produces a sequence of random numbers

is then scaled to the appropriate units of

A typical diffuse multipath error sequence

simulation by calling a zero

deviation of one and then

)n by ten (see Eq. 3.4.1.1).

with an rms value of ten, which

measure used by the simulation.

is shown in figure 3.4.1.1.

Eq. 3.4.1.1 Multipath Error . 10.0 * N(0,1)

Where N(0,1) denotes a sequentially accessed zero mean

Gaussian number sequence, with a unity standard deviation.

3.4.2 Ionospheric Range Error

The delay caused by the ionosphere , is due to the free electrons

encountered by the signal along the ray path between the satellite and the

user. The delay encountered when a satellite is at zenith varies from

about 5 nanoseconds during the evening to a peak of 35 nanoseconds during

the middle of the day for the L—band frequencies. A plot of the average

value of zenith propagation delay versus time, over a 24 hour period, is

shown in figure 3.4.2.1.

Superimposed with the ionospheric data is a plot of the raised

cosine model approximation of the ionosphere. This model was developed by

Klobuchar (13) and has been incorporated into the GPS simulation to calculate the ionospheric propagation delay, at zenith, given the time and

location at the point where the ray path, between the user and the

satellite, pierces the bottom of the ionospheric layer. This location is

called the local ionospheric point (-'see figure 3.4.2.2).

The local ionospheric point is calculated from the satellite's

earth angles, elevation and azimuth angle as viewed from the user, and the

-19-
1 9

M

L

W

V

`oLW

O

OlC

D' C

Time, Hours

Figure 3.4.1 .1 Diffuse Multipath Range Error

-20-
0

30

HONG KONG

AUNeIgGe

2a

--ACTUAL DATA

---COa INE MODEL

z

u 30

t

y

to

K -- J

W

O I O ^ 1,

r

a

G

4

G 4 e Iz to zo 24

LOCAL TIYC

Figure 3.4,2,1 Average Monthly Value of Zenith Propagation Delay

and the Raised Cosine Model (Taken from Klo6uchar).

-21-
RAY PATH TO

SATELLITE

LOCAL IONOSPHERIC

POINT

1

Lis

A LT11

Figure 3.4.2.2 Ionospheric Range Error Model Parameters

-22-
use

s ocatousg a at eatappoato. y appyg a ew spe

trigonometric rules and identities to the triangle depicted in figure

3.4.2.2, the earth angle A can be found to be described by the following

equation;

r +alt /I 1

Eq. 3.4.2.1 A - 90° — el — aresin U Icos ell

It0 + h 111111

The location of the local ionospheric point may now be calculated using;

Eq. 3.4.2.2 4'I = ^p + A cos Az

A sin AZ

Eq. 3.4.2.3 aI = X + cos ft

Where ^1I is the user's latitude, a is the user's longitude,

Az is Che satellite's azimuth angle, 0I is the latitude of the

local ionospheric point, and XI is the longitude of the local

ionospheric point.

Given time, in GMT hours at the user's location, and the calculated longi -

tude of the local ionospheric point, the time at the local ionospheric

point is calculated from;

aI

Eq. 3.4.2.5 t = 1Y + GMT

Note: t - t —24, if t is greater than 24 hours

Now that time is known at the local ionospheric point, the zenith

propagation delay can now be computed using the raised cosine model. For

values of local time at the ionospheric point between 0600 and 2200 hours,

the zenith propagation delay can be represented by;

- ^72,r

Eq. 3.4.2.6 Ion Zenith Delay = DC + A cos 

(Lt

P

)

Where DC = nighttime component of the zenith propagation

delay, approximately 5 nanoseconds; A = the peak zenith

propagation delay, 30 nanoseconds; 2 = period of the

-23-

.
cosine model, 32 hours; and t is the local time at the

local ionospheric point.

For all other times, the delay will equal the nighttime component only.

Thus far, the computation of the ionospheric delay has only buen

concerned with a signal ray path at zenith, however rarely are there any

satellites available exactly at zenith. For those ray paths not coincidi

with zenith, a slant factor or obliquity factor must be calculated. The

slant factor is defined as the secant of the zenith angle, Z, at the loca

ionospheric point. The angle Z is equal to;

r +alt

Eq 3.4.2.7 Z = aresin It 0 cos el) a + h ( J

which, if user altitude is considered negligible, is approximately;

Eq. 3.4.2.8 Z = aresin[ .94792 cos(el) J

The slant factor, SF, is then equal to;

Eq. 3.4.2.9 SF = sec [ Z ]

The propagation delay, due to the true signal ray path, is then

calculated to be a product of the zenith propagation delay and the slant

factor (see Eq.3.4.2.10).

Eq. 3.4.2.10 Total Time Delay = SF * Ion Zenith Delay

Figure 3.4.2.3 shows typical ionospheric range error produced by

this model.

3.4.3 Tropospheric Range Error 

This particular error model was developed by Altshuler and

Kalaghan [14]. The inputs required for this model. included user altitude

satellite elevation angle, and the season or month of the year. The basic

equation used is;

Eq. 3.4.3.1 AR(9,h,Ns) = GO) H(h)'F(h,Ns)

-24-
C

u

w

a

ba

Time, Hours

Figure 3.4.2.3 Ionospheric Range Error

-25-

\{u

.. ^ .a SKI ^S^/.l l

M. n^
Where G ( 0) is a function of satellite elevation angle,

H(h)' is a function of user altitude, and F ( h,Ns) is a

function of user height and surface refractivity Ns.

The functions of the tropospheric range error are found from the followin

equations;

Eq. 3.4 . 3.2 G(8) _ ( g 0 + g 1 0-1 + g 20 2 + g 3 0-3 ) Igo + g 6 (6-g 5)21

Where 6, is valid only for 6 > 5°.

Eq. 3.4 . 3.3 H(h) _ [(b0+b1(h+8.6286) - 1+b2(h+8 . 6286) -2+b3(h+8.6286)-3))

Eq. 3.4 . 3.4 F(h,Ns) - c 0

c

+ c2 (h+c o ) + cps-c4 -c 5 (Ns c6)2 Ll

Eq. 3.4 . 3.5 Ns ( h , L , M) = a0 + a h + a L + a3 hs 2 + a4Ls 2 + a5 hc + a6Le

1 2

Where L is the user ' s latitude in degrees and;

Eq. 3.4.3.6 a - sin (

n

12M)

R

Eq. 3.4.3.7 c - cos ( 12M)

Good results can be obtained by using an average global surface refractivi

value of 324.8 N units and deleting the calculation of Ns.

The constants required for these equations are as follows:

0.1556 b = 0'.00970 c - 3.28084 a = 369.0300

S

-

0 = 138.8926 b0 - -2.08809 co = 6.81758 a0 -.01553

1 g = -105.0574 b1 = 122.73592 c1 = 0.30480 a1 0.92442

92 - 31.5070 b2 703.82166 c2 0.00423 a2 = 0.00160

3 94

1.000 3 c3 = 1.33333 a3 = 0.19361

= 30.000 c 4 = 1.41723X10 -6 a4 0.00063

g6X = 1.0 10-4

c^ = 315.00000 a6 = -0.05958

-26-
Season M Value (Month Number)

Winter 1.5

Spring 4.5

Summer 7.5

Fall 10.5

The error values are calculated for each satellite by supplying to

these equations the necessary data and scaling the results to the required

units for the simulation to process the range measurements. Figure 3.4.3.1 

depicts the error profile generated by this model for the teardrop flight

path, notice the deviation due to the change in altitude. The tropospheric 

error behaves in much the same manner as the ionospheric error with respect

to elevation angles. The tropospheric error induced by a satellite close

to the horizon may be as much as an order of magnitude greater than that

exhibited by a satellite located near zenith.

3.4.4 Receiver Clock Error

The receiver clock error model used in this simulation calculates

an instantaneous clock offset biased upon a starting clock offset (SO),

frequency error based upon clock temperature stability (TS), and frequency

drift based upon aging race (AR) characteristics. Given SO, TS, and AR,

the clock parameters are derived using the following equations;

Eq. 3.4.4.1 Freq. Error = FE = TS * DELT * C

Eq. 3.4.4.2 Freq. Drift = FD = AR/86400. * .5 * DELT**2 * C

Where 86400. scales the aging rate from days to seconds,

DELT is the update period of the receiver, and C is the

speed of light.

The clock bias is then calculated to be;

Eq. 3.4.4.3 Clock Bias = SO + FE * TIM + FD * TIM**2 + SS

Where TIM is the number of elapsed update rates and SS is

a short term stability term derived from a gaussian random

sequence of N(O,SS). SS is assigned a value of 50 nanoseconds

thus gives the quassian sequence a stand deviation of 50.

Figure 3.4.4.1 shows the output of the clock error model for the following

values;

SO = 1000 nanoseconds

-27-

=3x 7
e

d

r

W

m

m

0

iQ

O

Time, Hours

Figure 3.4.3.1 Tropospheric Range Error

_28_

N
C

m

m

2-

W `x

m

C

O

K

v

Time, Hours

Figure 3.4.4.7 Uncorrected Range Errors Induced by

on Imperfect Receiver Oscillator

-29-
-30-

TS . 5.E-07

AR - 1.0E-07

3.4.5 Selective Availability Errors

A statistical analysis has been performed by Kalafus, to determine

the characteristics of the selective availability errors to be induced by

the Department of Defense. These studies were performed upon unclassified

samples of the SA error, given the original. premise that the error was to

induce a 500 meter (2d rms) horizontal position error. This has been

lowered by a factor of five so now the expected horizontal position error

will now be 100 meters (2d rms).

The SA model used in this study was scaled to the 100 meter criteria and maintained the dynamic characteristics found by Kalafus. These

dynamics are characterized by the probability density functions, as derived

by Kalafus, and are shown in figures 3.4.5.1 and 3.4.5.2.

These statistical characteristics are closely modeled by the

following equation;

Eq. 3.4.5.1 SA Error(i) = SA Error(i-1) + VEL * DELT + 0.5 * ACC * DELT**

Where VEL is a constant and ACC is a random walk generated from

the summation of a gaussian random number sequence of N(O,SIGA).

SIGA was assigned a value of 0.07 feet, this value was achieved

through experiment.

The calculation of ACC was as follows;

Eq. 3.4.5.2 ACC - ACC + SIGA * N(0,1)

Figures 3.4.5.3 and 3.4.5.4 show the typical statistical characteristics of

the SA error rate and accelerations,as computed by the model, for one

satellite.

Comparing the statistics of the model and those found by Kalafus,

some discrepancies can be seen. The velocity distribution does not appear

entirely gaussian. However, if the model is allowed to run for longer

periods of time, it is found that the distribution takes-on a more, zero

mean, gaussi.an appearance. Another discrepancy can be seen by comparing

the endpoints of the distributions between those found by Kalafus and those

generated by the model.

The accelerative values of the error generated by the model can

take on values double those found by Kalafus, during a significant portion

of the mission. Also, the velocity values generated by the model are

somewhat lower than those calculated from the SA samples. The standard
h

h

g

5

wm I UI IUb1 LIIJZIUJd

(3NI1 0314SU01 LN33939 '1115NIn 111'11OUanai

a,., r v1 o+11 annadaJa Ail 1JUMMUd JAIlN"IDNNJ

-31-

yd-O

E

^Lb

QcO O

>19

N

w o

Jn

d'

CV)

rn

{1.

ON

OF POOR QUALITY

^o c

c v

o=

0 

N

c

^. O

.O ..O a F

•^ N

a> ° u >^

>

w >,

^r •c

Nd^ ^

N

M

d

U.
-32-

Slope (NS/S)

Figure 3.4.5.3 Selective Availability Model Rate Distribution

.50

I?a0

B

a_
Z.

M

C

a

Q

0Ld

ORMWAL PAk:j

OF POOR QUALITY

N

Second Derivative (NS/S/S)

Figure 3.4.5.4 Selective Awilability Model Second Derivative Distribution 

—33—
deviation of the random number sequence used to generate the accelerative

random walk, was scaled until the error statistics best matched those found

by Kalafus. Although the accelerative values are excessive, it was felt

that the velocity values were representative of those to be encountered in

the field. Figure 3.4.5.5 displays the data output of this model for four

satellites.

3.5 GPS Simulation Operation

Thus far, programming tools have been defined which can compute;

1) User/Receiver Position, given time

2) Satellite Position and Range to User, given time and the

user's position

3) Satellite Range Error Values, given time, satellite's observed

azimuth and elevation angles, and the user's position

4) Position fix and user clock error estimate based upon the bes

estimate of four satellite ranges

These basic tools can be used together to emulate either a

sequential/single channel receiver or a four channel receiver. Each archi

tecture is able to operate in a conventional, fixed, or differential GPS

mode. These architectures were constructed to perform at 0„3, 1.2, and 2.

second range update periods.

When operating in the conventional mode, the GPS receiver uses th

range measurements to compute the receiver's position, without any corrections except for those intrinsic to operating with four satellites. The

conventional mode also uses the flight path simulator to predetermine the

position and velocity of the receiver.

When operating in the fixed mode, the GPS receiver collects range

measurements as in the conventional mode. However, the fixed receiver and

its antenna are positioned at a precisely known location, allowing the

fixed receiver to compute its true range from a particular satellite at a

given time. .The difference between the true range and measured range is

computed and provided to the differential receiver at specified uplink

rate. The rate used in these studies is one correction every 12 seconds.

The differential mode incorporates many of the characteristics of

the conventional mode and the application of the corrections generated by

the fixed receiver. The differential receiver applies a range correction

to each one of its measurements to obtain a better position fix. This

correction is updated at the rate specified by the fixed receiver's uplink

rate. For these experiments, the flight path and dynamics incurred during 

the conventional mode and the differential mode are identical.

-34-
Cu

^ o

U_ W

its C N

C

C0

0

p

. mil'

W '- C

po^ C N

a

a

C

w0

p

^ + N

C

W

O 

^'q^ C "• Oa

a

M

C = W

o ^

c

0

a

O

ei Time, Hours

N

o Time, Hours .

Time, Hours

Figure 3.A.5.5 Selective Availability Range Errors

-35-
3.5.1 Sequential/Single Channel Architecture

The flowchart for the sequential/single channel receiver is shown

in figure 3.5.1.1. The following text elaborates upon the program flow;

1) First the program is initialized, defining the initial time,

receiver update rate, mission-end time, initial receiver

position/velocity, the four satellites to be tracked and specified as KTN-one through four, initial error values, and the

initialization of any program subroutines as required. the

initialization defines satellite KTH-1 to be the first

satellite tracked.

2) Next the true position of the receiver is determined. This

position is determined by the flight path generator, given

time.

3) With the knowledge of the receiver's position and time, the

position fo the KTN satellite can be determined and the

resulting range between the satellite and the receiver.

4) The programmer selected range errors are now computed for the

current KTN satellite given time, receiver position, and the

observed satellite azimuth and elevation angles. These errors

can include diffuse multipath, ionospheric delay, trcpospheric

delay, receiver clock error, and a selective availability

error.

5) Differential Mode —• If the receiver is operating in the 

differential mode, the receiver obtains the most recent range

correction from the fixed receiver and applies it to the most 

recent estimate of the corresponding range measurement.

Fixed Mode — If the receiver is operating in the fixed mode

and one uplink period has elapsed, the receiver will compute

a correction for the most recent satellite measurement, and

then provide the most recent corrections of all of the

selected satellites to the differential receiver. The minimum

number of satellites to be serviced by the fixed receiver is

four.

Conventional Mode — If operating -in the conventional mode,

once the necessary range and range error calculations have

been made and properly combined, the program will then proceed

to calculate a CPS position fix based upon the degraded range

measurementa.

6) A position fix is not calculated by the sequential receiver

until at least four separate range measurements are available

Once four satellite ranges have been computed, a new position

fix is made with every new range measurement. Therefore, the

position fix calculation is made with ranges that are either 

instantaneous, or one, two, or three update periods old.

-36-
YES

D FI

OBTAIN CURRENT

CORRECTI ONS

APPLY CORRECTION

TO KTH SAT

INITIALIZE

KTH = I

COMPUTE TRUE

RECEIVER POSITION

COMPUTE TRUE RANGE

OF SAT KTH

DEGRADE SAT KTH

MEASUREMENT

*PUTE

YES

FD<ED J

COM

NAL CORRECTION

AND STORE 

YES

COMPUTE

STATISTICS

STOP

COMPUTE GPS

POSITION

INCREMENT

TIME

T ^TMAX SEQUENCE KTH

(1,2,3,4,1,2,3'....)

FIGURE 3.5.1.1

SEQUENTIAL SINGLE CHANNEL RECEIVER

SIMULATION PROGRAM FLOW
7) Next, time is incremented by one receiver update period.

8) If time is equal to of treater than the mission-end t}me, a

subroutine is called to generate the statistical data and

desired plot files for post program execution evaluation.

Program execution is terminated after this subroutine call.

If the mission-end time has not been reached, the value of KTH

is sequenced and the process recycles beginning with step two.

3.5.2 Four Channel Architecture

The operation of the four channel set is very similar to that of

the sequential/single channel receiver. The subroutines used in both

programs are almost identical. The difference between the two architectures is the sequential/single channel receiver measures one satellite

range each update period and the four channel receiver can measure four

separate satellite ranges during the same period.

The program steps executed for the four channel receiver is shown

in figure 3.5.2.1. The explanation of this flowchart is the same as the

sequential/single channel receiver with the exception of the computation of

satellite range and range errors. Each time the program is sequenced

through the satellite position/range and satellite range error subroutines,

new values for each of the four satellites are calculated. Likewise in the

differential or fixed mode, either four of the latest corrections are

applied or calculated at one time.

The calculation of the true receiver position, GPS position fix,

time, and program statistics for both receiver types are identical.

-38-
' INITIALIZE

KTH = I

COMPUTE TRUE

RECEIVER POSITION

COMPUTE TRUE RANGE

OF SAT KTH

DO KTH =1,4 I

I

DEGRADE SAT KTH

MEASUREMENT

YES

DIFFERENTIAL DIFF ?

OBTAIN CURRENT NO

CORRECTIONS IXED YES

AND T-TCORR FIXED

V

NO COMPUTE

CORRECTION CONVENTIONAL CORRECTION

[

APPLY

O 4 RANGES AND STORE

COMPUTE GPS

POSITION

INCREMENT

TIME

YES T %TMAX

COMPUTE

STATISTICS FIGURE 3.5.2.1

FOUR CHANNEL RECEIVER. SIMULATION

PROGRAM FLOW

STOP

—39—
4.0 SIMULATION RESULTS

Shown in Table 4.0.1, are the basic receiver configurations used

for the three different modes of operation. Two sets of data were

collected for each run, one set of data was collected with the Selective

Availability error evoked and the second set was run without the SA error.

The entire file of statistics generated in these experiments is

not presented. This is in an attempt to Lower the amount of data to be

assimilated by the reader and to avoid the presentation of redundant information. Only selections of representative data and data of particular

interest are shown and discussed.

4.0.1 Receiver Performance, Conventional Mode, No SA Errors

Figures 4.0.1.1, 4.0.1.2, and 4.0.1.3 show the altitude errors,

three dimensional errors, and two dimensional errors encountered during the

entire teardrop scenario using a sequential/ single channel receiver, with

an update period of 0.3 seconds, and operating in the conventional mode

(run ID # C-1). Figures 4.0.1.4, 4.0.1.5, and 4.0.1.6 depict the same scenario and mode, however this receiver has four channels with an update

period of 0.3 seconds (run ID # C-4).

Because the four channel receiver's measurements are more

accurate, the errors induced by the alpha-beta cracking filter are

amplified, particularly in figure 4.0.1.6. At times equal to approximately

0.039-0.053, 0.162-0.108, and 0.284-0.293 hours, one can see the peaks

recorded in the two dimension error plots. These peaks occur during the

three turns incurred during the teardrop flight path. The alpha-beta

tracking filter does perform well in constant velocity dynamics. However,

when submitted to the rates of velocities induced by these turns, the performance of this fixed gain filter is degraded considerably.

4.0.2 Receiver Performance, Conventional Made, With SA Errors

Figures 4.0.2.1, 4.0.2.2, and 4.0.2.3 depict the positional errors

encountered during the teardrop flight path while operating in the conventional mode, with a sequential/single channel, and an update period of 0.3

seconds with the SA error evoked (run ID # C-1). Figures 4.0.2.4, 4.0.2.5,

and 4.0.2.6 depict the same type of errors for a similar receiver type with

Four tracking channels (run ID U C-4).

The cause for the increasing magnitudes of all of the positional

errors during the second half of the mission, is evident if compared with

the individual satellite SA errors shown in Figure 3.4.5.5. in Section

3.4.5. This increase corresponds with a significant increase in range

error for three of the four satellites during this time frame. These

errors may also be amplified by a slight increase in PDOP/GDOP. These

values increase respectively from 2.44/2.67 at the beginning of the mission

to the final values of 2.78/3.01 at'the mission-end time.

The effects of the alpha-beta tracking errors are still noticeable

in the 3D and 2D error plots, however the net effect of these errors are

diluted somewhat by the large positional errors induced by the SA errors.

-40-
CONVENTIONAL NODE RECEIVER CONFIGURATIONS

RECEIVER UPDATE

RUN ID RECEIVER TYPE PERIOD

C-1 SEQ/SINGLE CHAN. 0.3 seconds

C-2 SEQ/SINGLE CHAN. 1.2 seconds

C-3 SEQ/SINGLE CHAN. 2.4 seconds

C-4 FOUR CHANNEL 0.3 seconds

C-5 FOUR CHANNEL 1.2 seconds

C-6 FOUR CHANNEL 2.4 seconds

FIXED MODE RECEIVER CONFIGURATIONS

RECEIVER UPDATE

RUN ID RECEIVER TYPE PERIOD

F-1 SEQ/SINGLE CHAN. 0.3 seconds

F-2 SEQ/SINGLE CHAN. 1.2 seconds

F-3 SEQ/SINGLE CHAN. 2.4 seconds

F-4 FOUR CHANNEL 0.3 seconds

F-5 FOUR CHANNEL 1.2 seconds

F-6 FOUR CHANNEL. 2.4 seconds

DIFFERENTIAL MODE RECEIVER CONFIGURATIONS

RECEIVER UPDATE FIXED RECEIVER MOD

RUN ID RECEIVER TYPE PERIOD RUN ID 

SEQ/SINGLE MAN. 0.3 seconds

SEQ/SINGLE CHAN. 0.3 seconds

SEQ/SINGLE CHAN. 1.2 seconds

SEQ/SINGLE CHAN. 1.2 seconds

SEQ/SINGLE CHAN. 2.4 seconds

SEQ/SINGLE CHAN. 2.4 seconds

FOUR CHANNEL 0.3 seconds

FOUR CHANNEL 0.3 seconds

FOUR CHANNEL 1.2 seconds

FOUR CHANNEL 1.2 seconds

FOUR CHANNEL 2.4 seconds

FOUR CHANNEL 2.4 seconds

SEQ/SINGLE CHAN. 0.3 seconds

FOUR CHANNEL 0.3 seconds

SEQ/SINGLE CHAN. 0.3 seconds

FOUR CHANNEL 0.3 seconds

SEQ/SINGLE CHAN. 0.3 seconds

FOUR CHANNEL 0.3 seconds

SEQ/SINGLE CHAN.' 0.3 seconds

FOUR CHANNEL 0.3 seconds

TABLE 4.0.1 Basic Receiver Configurations

D-1

D-2

D-3

D-4

D-5

D-6

D-7

D-8

D-9

D-10

D-11

D-12

D-13

D-14

D-15

D-16

D-17

D-18

D-19

D-20

F-1

F-4

F-2

F-5

F-3

F-6

F-1

F-4

F-2

F-5

F-3

F-6

F-2

F-2

F-5

F-5

F-3

F-3

F-6

F-6

-41-
0

W

t—W

s

Q

d

cc

W

WQ

r

1-.1

Q

TIME, HOURS

Figure 4.0 .1 .1 Altitude Errors, Run C-1, without SA

-42-
0

n ABrnrern.•

TIME, HR5

o

Figure 4.0.1.2 3D Position Error, Flan Cpl, with SA

Seq/Single Chan., 0.3 sec.

TIME. HAS

Figure 4.0.1.3 2D Position Error, Run C-1, without SA

Sag/Single Chan., 0.3 sec.

-43-
o 

Figure 4.0.1.4 Altitude Error, Run C-4, without SA

Four Channel, 0,3 sec.

-44-
0

^o

o= .

w o

w

Ut^1GGidld@. G^i^'C'aA ;vt

,F pooh QtJ^11 l it

^o

Er- V

w

0io

mr;

0

1b, 00 ,10' , w0 30 , 40 5[

TIME, HRS

o Figure 4.0.1 .5 3D Position Error, Run C-4, without SA

Figure 4.0.1 .b 2D Position Error, Run C-4, without SA

Four Channel, 0.3 sec.

—45—
VI

1.^

1. 1

1^h

WE

O

Ui

W

0

h

r

Cr

Figure 4.0.2.1 Altitude Error, Run C-1, with SA

Seq/Single Chan., 0.3 sec.

-46-

`— --—
CO C3

=o

W Co.

t--'

W

O

-o

!L

rc

W

Cl e

to No

n Or POOR QUALITY

I Figure 4.0.2.2 3D Position Error, Run C-1, with SA

- Seq/Single Chan., 0.3 sec.

C3 ly 1..

`x,00 .1^ 0 —.2030 .80 .50.

TIME, HHS

Figure 4.0.2.3 2D Position Error, Run C-1, with SA

Scq/Single Chan., 0.3 sec.

-47-
0

Figure 4.0.2.4 Attitude Error, Run. C-4, with SA

Four Channel, 0.3 sec.

-48-
Q

I

m

W

IW

O

0=

tI:

W

k TIME, HHS

Figure 4.0.2.5 3D Position Error, Run C-4, with SA

o Four Channel, 0.3 sec.

Vj a

a=o

Wm

t- .

W

-o

^-o

Oy

fY: '

W

cu

G7o

to

0

'0.00 .10 ~.20, .30 .80 -.50

TIME, HHS

Figure 4.0.2.6 2D Position Error, Run C •-4, with SA

Four Channel, 0.3 sec.

-49—

_____ ----

...;.
4.0.3 Receiver Performance, Fixed Mode, Without SA Errors

Figures 4.0.3.1-3 and 4.0.3.4-6 depict the positional errors

calculated at the fixed receiver with and without the SA error model ev

respectively. It is interesting to see that the errors induced by the

alpha—beta tracking filter, as seen the dynamic cases, are no longer pr

sent.

The performance of the fixed receiver is best measured by the

quality of its calculated range corrections. This comparison is rendere

by the cross—correlation of the range errors experienced at the fixed

receiver and those experienced at the airborne receiver for a particula

satellite. The following cross correlation functions are presented in 

form of plots with the computed Rxy(T) versus the uplink period. The

cross correlation coefficient is related to the uplink period due to the

fact that the higher uplink periods provide under—sampled corrections a

as a result produce a lower cross correlation coefficient.

4.0.3.1 Diffuse Multipath, Range Correction Effectiveness

The cross correlation of multipath errors experienced at the fi

receiver and at the airborne receiver is shown in Figure 4.0.3.1.1. Th

plot clearly shows, that in the case of diffuse multipath, there is no

correlation between the errors experienced at the two receivers. This

should be expected as the paths taken by the many indirect signals signa

cannot possibly be the same for two spatially separated antenna and the

fore the addition of those indirect signals should not be identical.

4.0.3.2 Atmospheric Delays, Range Correction Effectiveness

The delays induced by the ionosphere and the troposphere are v

similar in that both are very correlative over relatively long periods o

time. The differences lie within the diurnal dynamic properties of the

ionosphere and the sensitivity of tropospheric error to receiver altitud

Figure 4.0.3.2.1 shows the correlation between the ionospheric

errors measured at the fixed receiver and those measured at the airborne

receiver. The correlation between the two measurements are nearly cons

over an uplink period of instantaneous corrections (uplink period =

receiver update period) to a value of almost 5 minutes.

The cross correlation coefficients for the tropospheric errors 

almost as well behaved as shown in Figure 4.0.3.2.2. The correlation b

ween the two receiver measurements is fairly constant over the range fr

instantaneous to five minute uplink periods.

It is clear from these correlation plots that the corrections p

vided by the fixed receiver can produce significant improvements when

applied to the range measurements at the airborne receiver.

-50-
Or.. POOR QUALI I V

0

.40 50 TIME. HOURS

Figure 4.0.3.1 Altitude Error, Fun F-4, without SA

Four Channel, 0.3 sec.

-51-
i

W

E—

W

k `

O

tr

I ^W

O

1 N

U

TIME, HRS

Figure 4.0.3.2 3D Position Error, Run F-4, without SA

o Four Channel. 0.3 sec.

Figure 4.0.3.3 2D Position Error, Run F-4, without SA

Four Channel, 0.3 sec.

-52-
O

Figure 4.0.3.4 Altitude Error, Pun F-4, with SA

Four Channel, 0.3 sec.

-53-
C) Figure 4.0.3,5 3D Position Error, Run F-4, with SA

TIME. HHS

Figure 4.0.3.6 2D Position Error, Run F-4, with SA

Four Channel, 0.3 sec.

.54—
?S

Z

O

F+

UjW

C

K

OU

N

N

OC

U

10.0

UPLINK PERIOD, SECONDS

Figure 4.0.3.1.1 Cross Correlation of Multipath Error 

-55-
z

O

W

OU

NN

O

adV

.Q 

UPLINK PERIOD, SECONDS

Figure 4.0.3.2.1 Cross Correlation of Ionospheric Errors

—56—
Z

O

u.T

o:

n:

O

U

cn

w

O

a

V

.0

0

UPLINK PERIOD, SECONDS

Figure 4.0.3.2.2 Cross Correlation of Tropospheric Errors

-57-

--- mow.; Y;
a1.

4.0.3.3 Receiver Performance, Fixed Mode, General

Although a period of 12 seconds is recommended by the RTCM Spec

Committee (171, these results imply that comparable improvements could b

expected with higher uplink periods, given the above conditions. Figure

4.0.3.3.1 displays the correlative properties of the combined multipath 

atmospheric range errors between the two receivers. This also shows tha

uplink periods greater than 12 seconds could provide an equally good

correction. The 12 second uplink period does provide a better capabilit

when the system is subjected to SA errors.

,F4.0.4 Receiver Performance, Fixed Mode, With SA Errors

The cross correlation plot of the Selective Availability errors 

shown in Figure 4.0.4.1. This plot shows that the SA error is highly

correlative, but does show significant decreases in correlation for highe

uplink periods. The decrease in correlation appears to be linear for fi

60-90 seconds and then begins to degrade with an some type of exponential

decay—like function, however, continuing with the decreasing tendency

displayed by the 60-90 second linear function. This phenomenon is most 

likely due to the fixed receiver providing under —sampled corrections at 

high uplink periods (i.e., aliasing).

The effect of injecting the SA errors with the diffuse multipath

ionospheric delay, and tropospheric delay is shown in the cross correlati

plot shown in Figure 4.0.4.2. As seen in the previous section, the

resulting correlation plot reflects the culmination of the more negative

characteristics of the error models. In this case the correlative prope

ties are degraded by the white noise induced by the diffuse multipath and

the decreasing tendency of the SA correlation function.

4.0.5 Receiver Performance, Differential Mode, Without SA Errors

The positional errors shown in Figures 4.0.5.1-3 are for a four

channel, differential mode, 0.3 second update period receiver using corre

tions provided by a four channel, fixed mode, 0.3 second update period

receiver (run ID # D-8). New corrections are provided to the differenti

set once every 12 seconds. These results are indicative of the statisti

characteristics of the other receiver types, the differences lie mainly i

alpha— beta tracking filter's inability to track turns especially for the

2.4 second update period receivers.

The overall positive effect of differential GPS can be seen in

Figures 4.0.5.4 and 4.0.5.5. The plots contained in these figures are b

ken up into four columns of three bars each; column one contains the 3D

approach results while operating in the conventional mode, column two con 

tains the 3D positional information generated by the fixed mode receiver

during the approach, column three displays the 3D positional approach

information while operating in the differential mode with corrections pro

vided by a sequential/single channel fixed receiver with a common update

rate, and column four displays the 3D data from a receiver operating in 

differential mode using corrections from a four channel fixed receiver wi

-58-
a

ORMNAL: PAM I5

OF POOR QUALITY

0

i

O

1=

s

W.

W

O

V

tnV)

O

o: V

UPLINK PERIOD, SECONDS 

Figure 4.0.3.3.1 Cross Correlation of Combined Multipath, 

Ionospheric, and Tropospheric Errors.

—59—
Z

O

W

O

U

y

N

K

U

C

UPLINK PERIOD, SECONDS

It 0

Figure 4.0.4.1 Cross Correlation of Selective Availability Errors.

-60-
b

z

0

W

O

V

Ln

N

0

V

OF POOPS QUALIV

C

UPLINK PERIOD, SECONDS

Figure 4.0.4.2 Cross Correlation of Combined Selective Availability,

Multipath, Ionospheric, and Tropospheric Errors.

—61—
C)

Figure 4.0.5.1 Altitude Errors, Run D-8, without SA

Four Channel, 0.3 sec.

-62-
N

m

W

^o

O ^

LU 

Q

io m,

to

LU

t—

T

Q

LU

Q

i N

OUC+MAL k

",:;. ^.

OF POOR QtfE;^.i"a'v

o 1 ' s '

Y 1' '' 1 yyW ^'1'In 1 'I" I

.20' ,30 .40 5f

TIME:, HAS

Figure 4.0.5.2 3D Position Error, Run D-8, without SA

C Four Channel. 2.4 sec.

Figure 4.0.5.3 2D Position Error, Run D-8, without SA

Four Channel, 0.3 sac.

-63-
URIGIVAL PUAL.iP`!

OF POQR 4 2 MERN

CI R M 8

^1vv77

ST

S

. DEV.

N iC^ Xr CO

N ti Ill Q ^ ?

D-L D-2

Ditt. Made ear.

Dirt. mods car.

rearioor trop D.]/ reasiaee tram

I tacle e6anael 0.2/4 aaaanel

7

p9

O

`s' s$ N

P

n ^

°R

C3

C-1 t-L

conventional R;ed 'lade

made

y^y

V^

•b

^g

=R

aril

^a

10

CamnrMiarl fixed Nails DIIf. Made Car Dili Nails co,

Made "C"ans from 1.2/4 raarlan from 1.2/

Channel single dmmml

a

Comernlaml Fl,d Mods Dlff. h4.d+ Car Dlff. Made Cot.

Mils n ioe (mm 2.4/ Replan Rom

single thomwl 2.414 ab.nel

Figure 4.0.5.4 Single Channel Performance, without SA

-64-
Cb

uu

ORIGINAL Pti4;.L 44j

np onno ril tal Wd,

W".

o

N

dA

c=mc1crAL PLXed VW,

.We

9 MERN

q RMS

U3 11 N

N M CY rn H A

Dirr. MDde Car- DLf.'. Mode Cwmccio= C4m 0.3/ m-!= r=

SIM10 cr^L 0•3/4 ct^-j

Cmvencimel Pixel N5d* Diff. Mode ^ MC.- lode Carrods re=IM fr= 1.2./4 1= chm 1.4/

ah^l sisal. WW=L

0

C-6 F-61 D-U. D-12

Ca tlm,, Mad 143de our. .1ble car- D=. MAD rnrftdl Mein! c4 21 4l

recc:= ftm

single ==='. 2.4/4 em l

Figure 4.0.5.5 Four Channel Performance, without SA

-65-
a common update rate. Each of the columns are labeled with the appropriate

receiver configuration run ID number shown in table 4.0.1 of Section 4.0

and the differential data are Labeled with their respective abscissa values

in meters.

The data displayed by these bar charts, and those that follow,

contain the 3D positional information relevant to the approach segment of

the teardrop flight path. This was done to eliminate the negative effects

of the alpha—beta tracking filter. The dynamics of the approach involve

constant velocities and therefore the tracking filter can perform reasonably well and provide an indication of the accuracies obtainable by using

differential GPS.

The most impressive results were obtained by the 0.3 second update

period, four channel, differential mode receiver. The values of one standard deviation for along—track error, cross —track error, and altitude error

were equal to or less than 2.8 meters and were generally about 2 meters or

less. The values for the sequential/single channel receiver were good but

not nearly ad impressive with a one standard deviation value for each

dimension of error not exceeding 10 meters.

4.0.6 Receiver Performance, Differential Mode, With SA Errors

The data output for the four channel, 0.3 update period, differential mode receiver using a four channel, 0.3 update period, fixed mode

[r eceiver, both subjected to SA errors, is shown in Figures 4.0.6.1,

4.0.6.2, and 4.0.6.3. Again, the results are good except when the alpha— 

beta tracking filter is expected to track the receiver's position during

turns.

Figures 4.0.6.4 and 4.0.6.5 show the same type of bar graphs as

described in the previous s^ction, except these results reflect the effects

of the Si-. range errors. When compared with the bar graphs in Section

4.0.5, it can be seen that for an uplink period of 12 seconds, the posi -

tional accuracies obtainable with DGPS are comparable whether or not the SA

errors are present. The value of standard deviation never exceeded 2.3

meters for along track (ATE), cross track (CTE), or altitude error for the 

four channel, 0.3 update period, differential mode receiver. The standard

deviation for the ATE and altitude errors incurred by the longer update

period receivers never exceeded 10.5 meters and the GTE never exceeded 15.7

meters. 

The dequential/single channel, 2.4 update period, differential

mode receiver was the most suseptible to the position errors due to the

alphabets filter. These prevalent deviations can be seen in Figures

4.0.6.6, 4.0.6.7, and 4,.0.6.8. The large deviations, which appear in the

3D and 2D errors, directly correspond with the execution of turns in the

teardrop flight path.

-66-
ORIG."'NAI: Ppmi E°"^

OF POOR QUALI"*w

a

TIME HOURS

Figure 4.0.6.1. Altitude Error, Run D-8, with SA
cr

W

I--

Uj

d

Uj

i

m

W

LU

Ltl

C3

1

N

is

0

TIME, HRS

Figure 4.0,6.2 3D Position Error, Run D-8, with SA

Figure 4.0.6.3 2D Position Error, Run D-8, with SA

-68-
e

9 9

SOW

C

ng tic

— A

C1

—a

t

ga.r

M ^

91 MEAN

a^ 11 RMS

ST. OEV-

^e

Mill ^ c

e; m :..

3s

a m

c 14

CM H U;

o

/

O C-I

Cam.ndaml

F-1 0.1

Y=d 01((. Mod.

0•e

01R, Mad.

Mad. Can.tti. (mm 4. 7/A than. Mod. Comalant (tamJ.7/11n214 Chun.

O

01(F. Mud. DIR. Mad. Conn wloml Mod. Ft..d Mode Catr Wf. (tun 1 .1/a(rglo than. Co ,tlat+(mm 1.1/4 dwn.

C« Mloml Mod. F1..d Mud. 01R. Mod.

C.R.CH.I. (mn 1.4/dtgl. Chan. Camtt(em from 1.4/4 than.

Figure 4.0.6.4 Single Channel Performance, with SA

-69-
c

c

0

s 6

N p

r 19

p

c

e

W

C

Y O

Y w

w e6

Y Q

N .'J

ER MEAN

q RMS

0 9T.OEV.

0

^a

con

upi

e ..

^y 2

Ry

^ O ON p

p

C-4

Camrencienal

Made

F-4

Fixed Fade

m N b m s ^

N m n N P1 N

D-7 04

Difr. Mode Cor- arr. Mode Ccc

reccicm r-m 0.3/ mciav flxm

aingL! charnel 0.3/4 charnel

cammicnal Fixed twde Darr. Mode Cox- oit': Mode C=-

M:de reeoiau fr= 1.2/4 reeti= rr= 1.2/

ch=el eir8le chm=1

w r-o ^-u. u-ie

Cenvemir^ml Fixed Mode Riff. Mode cc Dlrr. Mode Qum

Mode recoi= fig 2.4/ teoeiau frm

eir.Sle cmm+ l 2.4/4 charnel

Figure 4.0.6.5 Four Channel Performance, with 5A

r70-

•- -s ... .max ^.^.,w^: = ti
en

rU.1

LL.1

Fti

Q

0

r

p

Figure 4.0.6.6 Altitude Errors, Run D-6, with SA

Seq/Single Chan., 2.4 see.

-71-
TIME, HRS

rt

o

Figure 4.0.6.7 3D Position Error, Run D-6, with SA

Figure 4.0.6.8 2D Position Error, Run D-6, with SA

Seq/Single Chan., 2.4 sec.

-72-
4.0.7 Receiver Performance, Differential Mode, With SA Errors, Using

Corrections From Different Receivers of Different Update Periods

The problems of using a receiver with an update period larger than

0.3 seconds have been presented for the dynamic case. This set of experiments were conducted to see the effects of using fixed receivers of longer

update periods than that used by the airborne unit. In each case, the dif -

ferential mode airborne unit was either a sequential/single channel or four

channel receiver with an update period of 0.3 seconds. The fixed mode

receiver varied in both channel number and update period, the period being

either 1.2 seconds or 2.4 seconds.

Figure 4.0.7.1 displays the 3D position errors incurred by the 0.3

update period, differential mode receiver when using correction data provided by a fixed receiver of a slower update period. The performance of

the differential mode, sequential/single channel receivers (run ID numbers

D-13, D-15, D-17, and D-19) are comparable with mean error values of

11.3-13.3 meters, rms error values of 12.5-14.7, and standard deviation

error values of 5.4-6.4 meters. These values correlate well with the previously discussed 0.3 update period, sequential/single channel, differen -

tial mode receivers. Likewise, the four channel, differential mode

receiver errors (run ID numbers D-14, D-16, D-18, and D-20) correlated well

and performed comparably to the previously mentioned 0.3 update period,

four channel, differential mode receivers.

5.0 CONCLUSIONS

The simulation data shows that differential CPS does have potential to provide a precision approach capability, at least for lateral navi -

gation. The 1982 Federal Radionavigation Plan (FRP) states the lateral 

accuracy of a localizes to be t 7.6 meters at the threshold. The simulated

DGPS approach data revealed accuracies of this type for the entire

approach. The 2 sigma repeatable and relative lateral navigational accura—

cies for a Cat I approach is 9.1 meters. The 2 sigma values for the 0.3

update period, differential mode receivers came very close to this figure,

the worse case exceeding it by 4.7 meters. 

It also appears that, for an uplink period of 12 seconds, a

sequential channel receiver with update periods slower than the Z—set (1.2

seconds) will function quite well as the fixed mode receiver. If ever pro -

duced as a part of the airway system, this characteristic alone could

result in a significant savings. The slower update period and the 12

second uplink period would also reduce the computational power required for

the DGPS ground system. The idle processing time gained could be spent in

monitoring the integrity of the DGPS ground system and the visible NAVSTAR

satellites. The DGPS ground system could serve a two fold service; 1) pro -

vide an increased accuracy to DGPS equipped users and 2) provide a net of

remote monitoring systems to monitor the integrity of the entire NAVSTAR

constellation..

During a constant velocity flight path the alpha-beta filter performs well and provides smoothed, well behaved data even for the longer

-73-
Cf^ pciDi^ QUALIiV,

0 MEAN

C3 1-1 CI R M S

S

N rMl ~

m

N

N

n pi^,7^ ST. DEY.

O

Q M

in

o in Ln c`oo m ti

mw

Mc^1

Co

I

N M 4

H

NCI

H IT) C

C

/ N 9^^ N mlalig D-13 D-14 D-15 D-16

Diff. Mode Diff. IL--de Diff. Made DIM Mode

Seq./Single 4 channel Seq./Single 4 channel

channel channel

a

8.

v N

m

o

^^Y

C

c

~

M ti

^

co .^ ly

~^

b L`

m N

N N

N m 4

aW N

'i

D

D-17 D-18 0.19 D-20

Diff. Mode Diff. Male Diff. Mode 11 Diff. Mode

Seq./Single 4 channel Seq./Single 4 channel

channel channel

Figure 4.0.7.1 3D Position Errors of a 0.3 sec. /diff. Mode Receiver, Using Correctio

from either 1,2 sec, or 2.4 sec., Fixed Mode Receiver, with

Selective Availability Errorto
up.tate periods. However, if accelerative platforms are to be used, a mo

sophisticated filtering algorithm should be implemented. This addition

alone could lower the lateral errors of the DGPS airborne unit to meet o

exceed the current Cat I requirements and significantly improve the DGPS

altitude guidance.

The range corrections provided to the differential receiver wer

not filtered by any means. The implementation of a filtering algorithm 

the fixed receiver, to reduce the high frequency noise induced by the di

fuse multipath, may improve the final accuracy of the airborne DGPS

receiver. Considering the high correlative characteristics of the

ionospheric delay, the tropospheric delay, and the Selective Availabilit

the highest source of range correction uncertainty is due to the white

noise injected into the correction as an effect of the diffuse multipath

This may also be compounded in the hardware implementation by the noise

injected by the receiver tracking loops. Considering the two sources ar

independent random variables, the addition of the two would serve to

increase the standard deviation of the range measurement error and the

resulting calculated range correction.

6.0 ACKNOWLEDGEMENTS

This work was supported under NASA Grant NAG-2-231, sponsored b

NASA Ames Research Center, Moffett Field, California.

The author wishes to thank Mr. Fred Edwards, NASA/Ames Technica

Monitor, for his helpful suggestions during this work; members of the Oh

University Avionics Engineering Center NASA/Ames Project: Messrs. Dennis

Scanlon, Graduate Research Assistant, Howard B. Maidlow, Undergraduate

Intern, and Andrew Nelson, Undergraduate Intern, these gentlemen have

assisted me In the development of the DGPS programs and performed most o

the data collection presented in this work.

Additional thanks go to Dr. Robert W. Lilley, Associate Directo

and Mr. James D. Nickum, my co—engineer, for reviewing this document and

Ms. Alleys. Shade and Ms. Michele Nutter for the extra hours they put in 

the production of this paper.

-75-

._ _ -- 
7.0 BIBLIOGRAPHY

[1] Kruh, P., Brady, W.E., and Schmitt, D.G., "A Strategy f

to the Operational NAVSTAR GPS Constellation," Institute of Navigation

National Aerospace Meeting, Arlington, Virginia; March 22-25, 1983.

(2) "Radionavigation System Characteristics," Federal Radionavigatio

Plan, DOD -4650.4-P-III and DOT-TSC-RSPA-81-12-I11, Vol. 3; March, 1982.

(31 Campbell, Steven D., and LaFrey, Raymond R., "Flight Test Results

for an Experimental GPS C/A-code Receiver in a General Aviation Aircraft,"

NAVIGATION, Journal of the Institute of Navigation, Vol. 30, No. 4, pp.

350-368; Winter 1983-Ig84.

(4) "Defense Department Boosts Civil NAVSTAR Precision," Aviation We

and Space Technology, p. 24; June 27, 1983.

[5] Beser, Jacques and Parkinson, Bradford W., "The Application of

NAVSTAR Differential GPS in the Civilian Community," Institute of

Navigation Thirty--Seventh Annual Meeting, Annapolis, MD.; June 9-11, 1981

(61 Magnavox Advanced Products and Systems Company, "Civil

Applications of Differential GPS Using a Single Channel Sequential

Receiver," NASA Contractor Report 166168; May, 1981.

[71 Kalafus, Rudolph M., "Synopsis and Recommendations of the TSC

Workshop on Differential Operation of NAVSTAR GPS," Transportation Systems

Center, Cambridge, MA., (DOT-TSC-RSPA-83-10, October, 1983); June 9-10,

1983.

181 Kruh, Pierre, "The NAVSTAR Global Positioning System Six-Plane

18-Satellite Constellation," The 1981 National Telecommnications Conferenc

of the IEEE, pp. E9.3.1-E9.3.8; November, 1981.

191 Shively, Curtis A., "A Real ;lime Simulation for Evaluating a

Low-Cost GPS Navigation," MITRE/METREK, McLean, VA., Report MTR-SOW00081;

April, 1980.

[101 Noe, Philip S., and Myers, Kenneth A., "A Position Fixing

Algorithm for the Low-Cost GPS Receiver," IEEE Trans. Aerospace and

Electronics Systems, Vol. AES-12, No. 2, pp. 295-297; March 1976.

[111 Shively, Curtis A., op. cit., Appendix B.

(121 Martin, E.H., "GPS User Equipment Error Models," NAVIGATION,

Journal of the Institute of Navigation, Vol. 25, No. 2, pp. 201-210; 

Summer, 1978.

(131 Klobuchar, J.A., "Ionospheric Time-Delay Corrections for Advance

Satellite Ranging Systems," AGARD Conference Proceedings No. 209 on

Propagatiou Limitations of Navigation and Positioning Systems,

Electromaguetic Wave Propagation Panel Specialists Meeting, Istanbul,

pp.3-1 - 3-13; October 20-22, 1976.

-76-
.

[141 Altshuler, Edward E. and Kalaghen, Paul M., "Tropospheric Range

Error Corrections for the NAVSTAR System," U.S. Air Force Cambridge

Research Laboratories, L.G. Hanscom Field, Bedford, MA., Report No.

AFCRL-TR-74-0198; April 16, 1974.

[151 Shively, Curtis A., op. cit., Appendix C.

[161 Kalafus, Rudolph M., "NAVSTAR CPS Accuracy Study," Proceedings of

the Surface Transportation Navigation User ' s Conference, Washington, D.C.;

November 16-17, 1982

[171 Kalafus, Rudolph M., "Synopsis...," op. cit.

-77-

_. 
e

,

1. Report No.

s cR ^"1732

2. Government Accession No. 3, Recipient's catalog No,

4. Title and Subtitle

A Study of the Application of'Differential

8. Report Date

November 1984

S. Performing Organleation Coda

FSN

Techniques to the Global Positioning System for a

7. Aollrar(e1 . 8. Performing Orgsniaatlon Report No

Daryl L. McCall

10. Work unit No.

T3771 9. Performing Organintlon Name and Address

Avionics Engineering Center

11. Contract or Grant No.

NAG2-231

Dept of Electrical & Computer Engineering

Ohio University, Athens, OH 45701

13. Type of Report and Period Covme

Contractor Report 12, Sponsoring Agency Name and Address

National Aeronautics & Space Administration

Washington, D.C. 20546

14, Sponsoring Agency Code

532-01-11

15, Supplementary Notes Point of Contact: Technical Monitor, Fred G. Edwards

M.S. 210-9, Ames Research Center, Moffett Field, CA 94035

415-694-5437 or FTS 464-5437

18. Abstract

This report documents the results of a simulation study to define the

functional characteristics of a airborne and ground reference GPS receiver

for use in a Differential GPS system. The operations of a variety of

receiver types (sequential-single channel, continuous multi-channel, etc.)

are evaluated for a typical civil helicopter mission scenario. The math

model of each receiver type incorporated representative system errors

including intentional degradation. The results include the discussion of

the receiver relative performance, the spatial correlative properties of

individual range error sources, and the navigation algorithm used to

smooth the position data.

17. Key Words ISuggetted by Authm(c1) 18. Distribution Statement

NAVSTAR GPS Unclassified - Unlimited

Differential GPS

Helicopter GPS STAR Category 04

GPS Simulation

19. Security Classif. (of this reports

Unclassified

20. Security Classil. (of this Pagel

Unclassified

21, No, of Pages

80

22. Rica'

'For sale by the National Technical Information Service, Springfield, Virginia 22101