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TOR-469(5510-50)-1 

(U) EVALUATION OF GEODETIC CAPABILITY OF 

MOL OPTICAL TRACKING SYSTEM 

Prepared by 

D. R. Speece 

Astrodynamics Department 

J. P. Janus 

Guidance Systems Department 

Guidance and Controls Subdivision 

Electronics Division 

El Segundo Technical Operations 

AEROSPACE CORPORATION 

Contract No. AF 04(695)-469 

24 July 1964 

Prepared for 

COMMANDER SPACE SYSTEMS DIVISION 

AIR FORCE SYSTEMS COMMAND 

LOS ANGELES AIR FORCE STATION 

Los Angeles, California 

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Approved 

22.2- gut., 

C. M. Price, Head 

Astrodynamics Department 

Guidance and Control Subdivision 

Electronics Division 

K. F. fan, H 

Guidance Systems Department 

Guidance and Control Subdivision 

Electronics Division 

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TOR-469(5510-50)-1 

(U) EVALUATION OF GEODETIC CAPABILITY OF 

MOL OPTICAL TRACKING SYSTEM 

Prepared 

D. R. Speece, Astrodynamics Department 

J. P. Janus, Guidance Systems Department 

H. Bernstein, Director 

Group I Studies 

Special Studies Directorate 

Manned Systems Division 

El Segundo Technical Operations 

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CONTENTS 

I. SUMMARY 1 

II. DISCUSSION 3 

APPENDIXES 

I. EPHEMERIS ACCURACY 7 

II. TARGET LOCATION ACCURACY 12 

REFERENCES 23 

FIGURES 

1. Latitude Error -Relative to Ephemeris 

2. Longitude Error Relative to Ephemeris 

3. Altitude Error Relative to Ephemeris 

14 

15 

16 

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SECTION I 

SUMMARY 

The problem was to evaluate the total accuracy to which the geodetic 

coordinates of a surface target could be determined by post-flight reduction 

of the recorded angular orientation of a tracking telescope whose crosshairs were to be kept aligned on the target by the astronaut. In addition, a 

laser might be slaved to the telescope axis to obtain slant range data. 

The following essentially independent sources of error were identified: 

1. The satellite ephemeris errors over the target 

2. The target position resolution errors relative to the ephemeris. 

Based on an extensive post-flight analysis of ephemeris accuracy by 

R. J. Farrar of the Astrodynamics Department, Aerospace Corporation, 

it is concluded that the one-sigma ephemeris errors in one orbital fit to 

16 revs of Satellite Control Facility (SCF) tracking data to a well-behaved 

(non-maneuvering) satellite in a 150 nautical mile (n mi) circular orbit are 

roughly 1000 feet in-track (latitude for a polar orbit), 500 feet cross-track 

(longitude), and 500 feet in altitude. It is suggested that by the use of multiple fitting techniques or by the use of the improved earth models which will 

become available over the next few years, these values can readily be reduced 

to 500 feet in latitude, 300 feet in longitude, and 300 feet in altitude, including 

the errors introduced by the reference ellipsoid parameter errors. Thus, 

the above errors are with respect to true geodetic coordinates. 

By the use of a star tracker reference system, it appears that an 

inertial platform can be aligned to a one-sigma accuracy of roughly 0.1 mr 

(20 seconds of arc). It is assumed that with the combined errors in telescope 

aiming, structural deflection, multiple cross -referencing, platform alignment, 

and data recording, the angular error in target resolution will have a onesigma average value of 0.3 mr. It is assumed that the laser ranging system 

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will have an average one-sigma error of 100 feet. Using these figures, the 

target coordinate errors relative to the local ephemeris are computed for 

target locations within 115 n mi to either side of the satellite ground trace. 

Our resultant estimates of the geodetic coordinate errors in feet are: 

Latitude 

(feet) 

Longitude 

(feet) 

Altitude 

(feet) 

Ephemeris 500 300 300 

Optics 200 200 500 

RMS Total 540 360 600 

Optics with Laser 150 150 150 

RMS Total 520 340 340 

Because of the predominately overhead geometry of the pass, the laser slant 

range is required for good determination of the critical altitude coordinate. 

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SECTION II 

DISCUSSION 

The basic problem is to evaluate the accuracy to which the geodetic 

coordinates of a surface object can be determined by post-flight analysis 

of optical tracking data from a manned satellite. This problem breaks 

readily into the following sub-problems: 

1. Determine the characteristics and local ephemeris accuracy of 

the satellite orbit. 

2. Determine the characteristics, including accuracy, of the optical 

tracking system. 

3. Evaluate the interface between ephemeris coordinates and geodetic 

coordinates. 

The orbit of interest is a 150 n.mi. circular polar orbit. The satellite 

will be tracked for several weeks time by the USAF satellite control facility 

(SCF). As discussed in Appendix I, results obtained in an extensive postflight study by R. J. Farrar indicate that, with care, a one-sigma ephemeris 

accuracy of 500 ft in-track (latitude), 300 ft cross-track (longitude), and 

300 ft altitude should readily be obtained from 16 rev least squares fits to 

this data using presently available orbit determination programs. We will 

use these figures even though they may be pessimistic by as much as two-toone when applied to 1966 capabilities. 

It can be seen that in the target coordinate determination problem, the 

satellite position errors are truly independent of and can be rms'ed with the 

contribution of the angular tracking system errors in computing the target 

coordinate determination errors. The same is not true of satellite velocity 

errors. But the latter are sufficiently small that their effect during a short 

tracking pass can safely be ignored. Otherwise the ephemeris errors would 

necessarily be larger than they are and change more rapidly than they 

appear to. 

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The tracking system will include a telescope with cross-hairs which 

are to be kept centered on the target by the astronaut. The alignment of the 

telescope axis will be continuously recorded with respect to the MOL reference 

inertial system. The latter may consist of an inertial platform system which 

is kept in alignment by star trackers. 

Several angular reference systems are discussed briefly in Appendix III. 

The state of the art satellite inertial reference accuracy is estimated to be 

0.1 mr (20 arc seconds). This same estimate is given in Reference 5. We 

estimate the inertial angular alignment of the tracking telescope will have a 

one-sigma post-flight computational error of 0. 3 mr. This figure includes 

the combined structural, aiming, referencing, platform alignment, and 

read-out instrumentation errors. 

The MOL tracking telescope is described in Reference 4. It provides 

continuous tracking within a viewing cone which has a 45 degree half-angle 

about an axis which normally leads the vertical by 15 degrees in the direction 

of satellite motion. 

The target coordinates are to be obtained by post-flight analysis of data 

from the above angular tracking system. The contributions of the angular 

errors to target coordinate errors is discussed in Appendix II. With angular 

biases of 0. 3 mr and for passes within 115 n. mi. to the side of the target 

it is shown that latitude and longitude can be determined relative to the 

ephemeris to one-sigma accuracies of roughly 200 feet but that the one sigma 

altitude error will be roughly 500 feet. These results depend primarily on 

the assumed data biases and are only a weak function of the assumed data 

rate, random data noise, and for eward tilt of the tracking cone. It is suggested that the results probably cannot be improved by the use of angular 

rate data in place of angular position data. 

Unfortunately, as indicated in Reference 6, for relatively low-energy 

ICBM trajectories the most serious target coordinate error (in terms of misscoefficient sensitivity) is the target altitude error. It is shown in Appendix II 

that with the addition of a laser ranging system with a one-sigma accuracy of 

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mairifiak 

100 feet, the above errors can be reduced to roughly 150 feet in each 

coordinate. This capability may be necessary to obtain worthwhile ICBM 

targeting information from the system. 

Rms'ing the ephemeris errors with the above targeting errors we 

arrive at the following estimates of the one-sigma errors in the computed 

geodetic coordinates of the target (in feet): 

Latitude Longitude Altitude 

W/o Laser 540 360 600 

With Laser 520 340 340 

as shown, the primary contribution of the laser is in reducing the resultant 

altitude error. 

Let as now examine the significance of the above results in terms of 

the basic meaning of "geodetic coordinates". It must be recognized that all 

reference geodetic constants are in error by some small but unknown amount. 

The orbit determination programs presently use the 1960 world geodetic 

survey (WGS-60) as a source of reference ellipsoid parameters and tracking 

station coordinates. It is estimated that the equatorial radius of this reference ellipsoid may be in error by as much as 100 feet. Since the SCF 

stations are referenced to the North American Datum, the orbit determination procedure will tend to force a good fit of the reference ellipsoid to 

this datum with the result that there may be an error of up to 200 feet in 

the computed earth-central radius to the correct satellite position on the far 

side of the earth. 

As pointed out in Appendix I, the estimated radial ephemeris accuracy 

of 300 feet can only, be achieved by the use of a reasonably complete and 

accurate set of longitudinal geopotential harmonics. The most satisfactory, 

fixed set of harmonics which has been investigated by Aerospace is that set 

derived by W. H. Guier of the Applied Physics Lab (APL) by post-flight 

analysis of Transit range rate data (Reference 7). Because the Transit 

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Doppler stations are reasonably well distributed over the earth, the good 

results obtained in the use of this earth model for SCF data reduction provides evidence that the reference ellipsoid parameter errors are not the 

major source of error in orbit determination. Because earth rotation provides good SCF coverage of the orbital arc in the northern hemisphere, it 

is clear that displacements of the reference ellipsoid towards the North 

American datum will contribute to ephemeris errors of the type observed 

by Farrar. Thus, the reference surface errors are already partially 

included in the ephemeris error figures. 

The above discussion suggests the following significant points: 

1. It is basically dangerous to solve for earth model parameters with 

a local tracking net such as the SCF if the results are to be used 

for geodetic purposes. The model parameters thus obtained will 

tend strongly to cancel the contributions of reference ellipsoid 

errors to ephemeris errors at the tracking stations for the given 

orbital inclination and ground track at the expense of magnified 

ephemeris errors far from the reference (local) datum. 

2. It appears that Guier's 1963 harmonic set may permit the computation of ephemerides to an accuracy of roughly 500 feet in-track, 

300 feet cross-track, and 300 feet altitude including the contribution of the geodetic parameter errors. With the ANNA and 

other future geodetic satellite post-flight earth models, there 

should be a significant improvement in these results. With the 

omission of all longitudinal harmonics, the ephemeris errors 

are of the order of 3000 feet in-track, 1000 feet cross-track, 

and 1000 feet altitude. 

3. For there to be an advantage in the precise knowledge of target 

coordinates in the ICBM targeting problem, accurate values of 

the significant geopotential harmonics should be included in 

computing the desired trajectories. 

4. It would appear that a near -optimum way to obtain ICBM target 

coordinates is by sightings from a satellite whose orbital inclination is near that to be used by the ICBM. If the ICBM then 

flies with the same earth-model as was used in satellite data 

reduction there are compensating errors which do not exist in 

the case of the determination of target coordinates by triangulation. 

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APPENDIX I 

EPHEMERIS ACCURACY 

The ephemeris accuracy of low altitude orbits is a function of many 

variables. However, if the vehicle is passive (no significant thrust nor 

attitude control perturbations of either the vehicle frontal area or the 

velocity vector) and if perigee is above 1 20 n mi so that atmospheric density 

fluctuations are not the major source of error, and if typical SCF tracking 

data are available over at least one day's time, then it is possible to obtain 

• 

a realistic estimate of the post flight ephemeris accuracy which can be 

expected. 

Using relatively recent Discoverer data, R. J. Farrar of Aerospace 

has conducted an extensive post flight orbital error analysis. His results 

indicate that with a good least squares orbit determination program (Farrar 

used the Aerospace TRACE program) and with 1 0-to- 20 passes of SCF 

Verlort data taken over 16 orbital revolutions, the major source of ephemeris 

error is the incomplete and incorrect modelling of the geopotential harmonics. 

The geopotential expansion has the form 

oo 00 n 

U = -11 [1 -E J (±)nP (sin 0) +E E rPin(sin 0) cos m (X - 

r nr n n r n 

n=2 n=2 m=1 

where 

u = product of universal gravitational constant and mass of the earth 

r = earth-central radius to satellite 

a = average equatorial radius of earth 

0 = geocentric north latitude of satellite 

X = geocentric east longitude of satellite 

= east longitude of tesseral harmonic 

Jrnn= mass coefficient of harmonic 

Pinn= Legendre polynomial 

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The first of the above series contains the zonal harmonics (oblateness, 

pear shape, etc. ). The double series contains the longitudinal (tesseral) 

harmonics. Those for which n = m are called sectorial harmonics. One 

of the larger of these is the equatorial oblateness term, J. 

In the post-flight solution for the zonal mass coefficients, Jn, a 

technique of long term averaging of the secular effects (such as orbit plane 

and perigee precession rates) may be used. But because of the longitude 

dependence of the tesseral harmonics and because of earth rotation the 

most readily observable effect of the Jn terms is the cyclic oscillation 

n • 

of the orbital elements at a period of l/m day. Because of this it is very 

difficult to separate the effects of those terms of equal period (such as J2, 

2 J3, J4, etc. ) in the combined post-flight solution for the tesseral mass 

coefficients and longitudes and the necessary truncation of the infinite series 

at some arbitrary point results in a folding back of the effects of the higher 

order terms of the same longitudinal frequency into an error in the solution 

for the lower order terms. As a result of this, a set of tesseral harmonics 

derived from an orbit of a given inclination tends to produce more accurate 

ephemeris prediction for orbits of roughly this same inclination than for 

orbits at a significantly different inclination. 

Because of errors in the tesseral harmonics, superior ephemeris 

accuracy is obtained by fitting an integer number of days of tracking data and 

thereby obtaining smoothing over an integer number of cycles of tesseral 

harmonic oscillation. Because of the secular effects of tesseral harmonic 

errors and because of fluctuations in atmospheric density, superior ephemeris 

accuracy may be obtained by one-day (16 rev) fits rather than by fitting data 

taken over two or more days time. In addition, the fits over longer time 

spans require at least proportionately more computing time. 

Based on considerations such as the above, Farrar performed 16 rev 

fits which provided solutions for the initial orbital position, velocity, and 

average drag (the ballistic coefficient). These fits remove most of the 

secular error due to geopotential harmonic errors and atmospheric density 

errors from the subsequent ephemeris computation. In addition, Farrar 

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experimented with the simultaneous solution for several of the lower order 

tesseral harmonics and compared the resultant ephemeris prediction with 

that obtained using several of the presently available sets of harmonics. In 

this study the prime accuracy criterion was the observed period error (that 

solution was assumed to be the most accurate which minimized the time of 

arrival errors at the stations which tracked during the day beyond the end 

of the fitted one-day interval). On this basis, Farrar found that the most 

accurate of the available sets of geopotential harmonics was that set derived 

in 1963 by W. H. Guier of APL, using Transit tracking data (Reference 7). 

Some typical results from Farrar's study are tabulated below: 

Flight Incl. (deg.) Perigee (n mi) Apogee (n mi) 

Prediction Error (ft/day) 

Guier Alternate 

A 65 118 187 9100 21, 000 

B 75 115 223 4600 3, 700 

C 82 164 179 6100 nil 

The above prediction error is the approximate in-track error 16 revs after 

the last fitted tracking pass using Guier's geopotential harmonic set and, 

alternatively, solving for the coefficient and longitude of one 24 hour harmonic 

2 (m = 1) plus J and X. The results for the 65 degree inclination orbit were 

significantly poorer than for the higher inclination orbits as a result of the 

significantly smaller number of tracking passes per day. This, in turn, 

resulted from the reduced number of tracking passes by the northern SCF 

stations. 

Farrar found that even with the 115 n mi perigee, the prediction error 

was less sensitive to a change from the sophisticated Lockeed-Jacchia 

atmospheric model to the crude ARDC 59 model than to changes from one 

geopotential model to another. With the exception of the 65 degree inclination 

orbit, Farrar obtained-superior results when solving for two geopotential 

terms over those which he obtained by the use of Guier's set. The in-track 

error beyond the end of the fitted interval generally increased somewhat 

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parabolically rather than linearly. Thus the initial rate tended to be significantly less than one n mi per day (400 ft per revolution). 

In a number of cases, Farrar cross-compared ephemerides obtained 

by fitting alternate 16 rev spans. Based on the results of these tests and 

other results Farrar has estimated that the one-sigma ephemeris errors 

within the interval of the 16 rev fits may be as large as 1000 ft in-track and 

500 feet in the cross-track and altitude coordinates. The in-track errors 

at the tracking stations within the 16 rev spans were generally smaller than 

500 ft but, because data from these stations were included in the process of 

the least squares orbit determination, this number is a lower limit estimate 

of the average in-track error. This is true if, as found by Farrar, the 

major source of ephemeris error is the earth model error and not tracking 

Station survey errors. 

It is not unreasonable to postulate a two-to-one reduction within the 

next few years in the contribution of earth model errors to ephemeris errors. 

This can be obtained with improved knowledge of the geopotential mass coefficients and/or by the development of techniques to reduce the effects of 

model errors on ephemeris prediction (such as Farrar's solution for model 

terms). Alternatively, given several days tracking data to a well behaved 

orbit, a two-to-one post-flight improvement over the accuracy of a single 

16 rev fit could very probably be obtained by the following technique: 

1. Perform 16 rev fits to revs 1-16, 2-17, 3-18, etc. 

2. Generate ephemerides at the desired time points 

within each of these fits. 

3. Using these multiple estimates of the satellite's 

position at a given time, compute the mean and 

variance of the coordinate errors. 

4. The above mean values are the best estimates 

of the ephemerides. The variances provide a 

lower limit estimate of resultant accuracy. It 

is a lower limit because the sliding 16 rev fits 

do not completely average out the contribution 

of a given component of model error (or station 

location or drag error) to the resultant estimate. 

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Based on Farrar's results plus considerations such as the above, we 

have taken 500 ft in-track, 300 ft cross-track, and 300 ft altitude as conservative estimates of the one-sigma ephemeris errors which can be expected 

several years hence from careful post-flight massage of the SCF data obtained 

from several days tracking of a well-behaved satellite in a 150 n mi circular 

orbit. It must be emphasized that future improvements in ephemeris accuracy 

from the Farrar type fits depend on the development of more accurate geopotential mass coefficients and/or improved orbit determination techniques. 

Relatively little improvement can be obtained by improving basic sensor 

accuracy. But greater accuracy can be obtained by improved orbital coverage 

such as would result if additional tracking stations were added to the net. 

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Our present problem is to evaluate the accuracy to which the coordinates 

of a surface object can be determined relative to the 150 n. mi. MOL orbit 

by post-flight analysis of the tracking telescope angular readings. 

To simplify the problem, let us assume that the angular readings have 

a constant bias of 0.3 mr (one minute of arc) and, that tracking occurs 

over a . 45 degree (half-angle) cone about the vertical. The geometry of a 

zenith pass over the targets with approximate dimensions in feet is given in 

the following sketch: 

SATELLITE 

It is immediately apparent that the two extreme measurements alone pin down 

both the in-track coordinate (latitude) and the altitude to an accuracy of 

roughly 400 feet (RcrE) and that the minimum range reading pins down the 

longitudinal coordinate to a one- sigma accuracy of better than 300 feet 

(RcrE again). 

To verify the above estimates of accuracy it was decided that the 

FEIGN error analysis program should be used to simulate the least squares 

determination of geodetic coordinates in the presence of measurement noise 

and bias. It was concluded that the assumptions of a noise and bias of 0.3 mr 

each at a data rate (quantization increment) of 120 measurements per minute 

would suffice for this study. 

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APPENDIX II 

TARGET LOCATION ACCURACY 
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The results of the FEIGN study are presented graphically in Figures 

1, 2, and 3. The curves show the coordinate accuracies which would result 

from the least squares reduction of all data taken prior to the times given 

for the five representative cases. The passes had a nominal length of 1.2 

minutes. 

The curves indicate that data taken prior to midpass (0. 6 minute) will 

permit the computation of target latitude and longitude to one- sigma 

accuracies of roughly 200 feet. With angles only data, the altitude error is 

400-to-600 feet depending on the cross-track displacement of the target. 

Including the data from the second half of the pass improved the computed 

latitude and longitude by a factor of roughly 4-to-1 but apparently caused 

some degradation in .the computation of altitude from a zenith pass of 

angular data. In fact, the use of the full zenith pass resulted in a one-sigma 

altitude error of 665 feet versus only 565 feet for a pass 115 n. mi. to the 

side of the orbital plane or when using only the first and last 0.2 minutes of 

data from the zenith pass. These results deserve some explanation and 

qualification. 

The two angles with which FEIGN specifies target direction from the 

satellite are downward elevation (which goes from 45 degrees through 90 and 

back to 45 for a zenith pass) and azimuth which is measured clockwise from 

the north and goes through a 180 degree switch at zenith. In the least-squares 

fit to a zenith pass of angular data, it is the time of this azimuth switch 

which provides the prime indication of the zenith position and, hence, of the 

in-track target coordinate (latitude). As shown in Figure 1, the mid-pass 

improvement in latitude determination did not occur for the pass 115 n. mi. 

to the side of zenith and was less pronounced for that zenith pass which 

included range measurements. 

It should be noted that the FEIGN constant bias in elevation is geometrically detrimental to the determination of target altitude but not necessarily 

to the determination,of latitude and longitude. For an equal amount of tracking 

on each side of the minimum range point, the effect of the elevation bias 

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Figure 1. Latitude Error Relative to Ephemeris 

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Figure 2. Longitude Error Relative to Ephemeris 

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Figure 3. Altitude Error Relative to Ephemeris 

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beyond mid-pass cancels the effect along the corresponding arc ahead of 

midpass in the solution for latitude and longitude but re-inforces the error 

in the altitude computation. By picturing the geometrical effect of the elevation bias on the least squares fit, it can readily be understood why the 

omission of the midpass data for the zenith pass resulted in the reduction 

in the altitude error illustrated in Figure 3 (case 3). 

To investigate the sensitivity of the above results to data rate and 

noise, both of these parameters were changed by a factor of two-to-one on 

separate additional runs. As expected, since granularity is not a problem 

at the 120 point per minute data rate, the effect of reducing the data rate to 

60 points per minute was very similar to the effect of doubling the assumed 

data noise. Because of the smoothing provided by the high data rate, the 

least squares fit was relatively insensitive to two-to-one changes in the 

assumed data rate and noise. This is illustrated by case 2 of Figures 1, 2, 

and 3. 

Because of the dynamic error introduced by a high azimuth-tracking 

rate, the MOL tracking telescope is not designed to operate in an azimuthelevation coordinate 'system. Instead, its angular orientation will be 

continuously recorded in terms of inertial platform direction cosines. In 

this case (or any other realistic case) the bias smoothing evidenced in the 

FEIGN runs will be much less pronounced. Nonetheless, the fit to a full 

pass of angular data will tend to result in an improved estimate of latitude 

and longitude but negligible improvement in altitude over the results obtained 

by simply fitting the end points of the pass. 

Based on the geometry and the above considerations, we estimate that 

the midpass results of Figures 1, 2, and 3 are representative of the 

accuracies which can be expected from careful post-flight reduction of the 

tracking telescope data. Thus, for either an overhead or a side pass, 

latitude and longitude can be resolved to an accuracy of roughly 200 feet. To 

obtain altitude to an accuracy of better than 400 feet, range data are needed. 

With a zenith pass the altitude can be determined to roughly the accuracy of 

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the ranging system. We have conservatively estimated that a laser-ranging 

device will have a one-sigma bias of 100 feet. This figure includes the error 

due to uncertainty in the exact target point from which the laser return is 

received. Then, for the more representative case of a pass 115 n. mi. to 

the side of the target, we estimate that the one- sigma accuracy of relative 

target coordinate determination will be 200 feet in latitude and longitude and 

500 feet in altitude with 0. 3 mr angular data but that this can be reduced to 

a spherical position uncertainty of 150 feet by the addition of a 100 foot 

ranging capability. In connection with this latter estimate it should be noted 

that in the FEIGN study the range data were not subjected to the same unreasonably favorable bias smoothing as were the angular data. 

Since the above results were dictated almost entirely by the assumed 

data biases, let us consider the possibility of fitting rate data rather than 

position data. This appears inadvisable for the following reasons: 

1. The FEIGN study assumed constant biases for convenience only. 

Actually, much of the systemmatic error in computing the 

tracking telescope direction cosines is sensitive to changes in 

telescope alignment. This will produce a ramp-type error of 

significant magnitude in the angular measurements whose effect 

will be greatly accentuated by fitting to angular rate data rather 

than position data. 

2. The effects of high frequency data noise and orbital velocity 

errors will be accentuated by the use of rate data rather than 

position data. 

3. Rate data provides a weak solution for position coordinates. If 

rate data rather than position data are used then that component 

of error which results from poor convergence of the target 

coordinate computational procedures will be accentuated. This 

component is also accentuated by the increase in data noise 

level which results from differentiation of the position data. 

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APPENDIX III 

SATELLITE ANGULAR REFERENCE SYSTEMS 

The following is an outline of several present and potential satellite 

angular reference systems with short discussions of approximate accuracy, 

system problems, and some potential interfaces with a manned system. 

1. Gyrocompassing--Rate Gyros plus Horizon Sensor 

This is a proven satellite attitude control technique. The horizon sensor 

maintains the orbital pitch rate while rate gyros prevent roll and yaw misalignments. The fundamental lack of definition of the horizon to an accuracy 

of better than 5 mr is a major limitation on system accuracy. At a target 

slant range of 200 n mi this alone dictates a position prediction error of one 

nautical mile. 

2. Three-Axis Star Reference 

This could be three separate instruments or one instrument which used 

star map (correlation) techniques. In either case, initial positive alignment 

and maintaining alignment can present problems. But an accuracy of better 

than 0. 1 mr (100 ft at 200 n mi) is potentially available. Unfortunately, the 

angles between the stars are essentially the same from anywhere within the 

solar system. The star reference system requires an independent vertical 

reference to the earth. If a horizon sensor is used, then its 5 mr accuracy 

is again the limiting system accuracy. 

3. Three-Axis Gyro System 

Because of drift (at least .1 mr/day) and the initial alignment problem, 

this system is of primary value in providing smoothing and stable aiming of 

other angular reference equipment. A stable table might provide a good 

reference for obtaining and maintaining star-tracker lock-on. Whether used 

alone or with star trackers, the gyro system requires a separate vertical 

reference system. If the gyrocompas sing technique is used, star-trackers 

• are not required. 

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Because the primary need of the above systems is for a good vertical 

reference to the earth, let us now consider alternate techniques for satisfying 

this requirement. 

1. Crude Vertical Reference Systems 

The vertical has been obtained by both magnetic field and gravity 

gradient techniques. These suffer from the small magnitude of the effects. 

Neither technique has an accuracy of better than 50 mr. Both methods are 

degraded by placing a man aboard the satellite and allowing him to move either 

during or after initial alignment. 

2. Horizon Sensors 

The basic problems with the horizon reference from a near-earth 

satellite are the uneven distribution of cloud heights and the day-night illumination problem. The limiting accuracy appears to be roughly 5 mr. Considerably more accurate alignment to the sun and moon can be obtained but, 

when reflected back to a computed local vertical to the earth, the error 

is much greater than 5 mr. 

3. Computed Vertical 

With star trackers or gyros for an inertial angular reference and 

satellite ephemerides computed by an orbit determination program, the 

direction of the vertical with respect to the inertial reference at any given 

time can be computed. With one-day's tracking data to a well behaved 150 

n mi orbit the accuracy is limited to the 500 foot accuracy to which the 

ephemerides can presently be computed. At lower altitudes where atmospheric 

drag errors become significant, the accuracy is poorer. It is also possible 

to compute target positions from certain reconnaissance data without the need 

for angular reference data. 

4. Monopulse Altimeter 

Ocean return radio-altimeter data holds considerable promise for 

improving ephemeris prediction accuracy. In addition, a monopulse capability 

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could provide a vertical determination to an accuracy of better than 1 mr. 

This assumes an 8 Kmc frequency with a 2 ft antenna. General Electric has 

proposed an 8 Kmc altimeter in a 24 lb package with an average power level 

of 30 watts. A disadvantage is the disruptive effect of the high instantaneous 

power level of the transmitted pulses on other satellite electronics. 

5. Interferometer Angular Reference 

The vehicle angular alignment over tracking stations could be determined by interferometer methods using multiple satellite sensors and a cw 

ground signal. Such a system has been proposed by Cubic Corporation and a 

similar system has been designed by Bendix for commercial airliner use. 

Unfortunately, the knowledge of the vertical beyond the alignment point is 

again dependent on computed ephemeris accuracy. But this system could 

provide gyro reference alignment. The Cubic system had a computed accuracy 

of better than 1 mr. 

Let us now consider how a man could help or hinder the operation of the 

above systems. It is clear that, because of his motion, angular aiming of all 

instruments could be made more difficult. But either the instruments or the 

entire satellite could be provided with a good attitude stabilization system. 

It is also clear that the man could provide improved target selectivity. The 

following points appear pertinent: 

1. The man could be of value in obtaining and maintaining alignment 

of star trackers and/or other instruments. 

2. The man could telescopically track known landmarks and thereby 

provide a new source of angular alignment information. He could 

also maintain instrument alignment during target tracking. 

3. By identification of unsuspected targets and selectivity in data 

collection the man could significantly improve system yield. There 

would be less danger of missing pre-selected targets because of 

angular aiming or ephemeris errors. 

4. With the aid of charts and pre-selected logic the man could provide a significant on board decision making capability. He could 

add in a major way to the system flexibility and quick reaction 

capability. 

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5. The man could provide back-up in varying degrees to all on-board 

systems. He could try to repair failed systems or switch to 

alternate systems. He could provide on-the-spot evaluation of 

aiming accuracy and requirements at each target area. 

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REFERENCES 

1. Manned Tracking Study Progress Report, by R. H. Leatherman, 

ATM 64(4107-40)-1. 

2. Application of the Weiner-Kalman Filter to MOL Manned 

J. E. Lesinski (Rough Draft). 

3. Comparison of Possible MOL Tracking Filters, by R. H. 

(Rough Draft). 

4. Design Study and Analysis of a Three-Inch Aperture Variable Power 

Pointing and Tracking Telescope, by S. Brewer, A. Mandl and 

L. Watson, ATM 64(4107-40)-2. 

5, Trip Report, MIT Instrumentation Lab (Project Apollo), by B. Adams, 

J. Alder, and K. Steffan, A-65-2511-7. 

6. The Effect of Geophysical and Geodetic Uncertainties at Launch Area on 

Ballistic Missile Impact Accuracy, by R. C. Gore, TDR-269(4922)-2. 

7. Determination of the Non-Zonal Harmonics of the Geopotential from 

Satellite Doppler Data, by W. H. Guier, Nature, 1963. 

Tracking, by 

Leatherman 

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Internal 

(2) 

J. R. Allder 

S. D. Crane 

P. Diamond 

R. J. Farrar 

T. P. Gabbard 

E. U. Gambaro 

E. A. Goldberg 

R. C. Gore 

N. S. Hall 

L. Hirschl 

J. R. Janus 

H. K. Karrenberg 

F. L. Keller 

R. H. Leatherman 

J. L. LeMay 

J. E. Lesinski 

E. Levin 

E. E. Loft 

D. R. S. McColl 

D. MacPherson 

J. E. Michaels 

H. Nakamura 

J. C. Peale 

C. R. Precious 

P. R. Schultz 

C. W. Sarture 

• 

D. R. Speece 

K. F. Steffan 

S. M. Tennant 

J. S. Thompson 

D. W. Whitcombe 

C. M. Price 

AOCRC Files 15 + vellum 

J. S. Meditch 

B. P. Leonard 

H. Bernstein 

N. L. Anderson 

J. M. Baker 

B. H. Billik 

R. W. Bruce 

A. Grossman 

P. T. Guttman 

H. E. Hogfors 

W. M. Kaula 

R. D. Lliders 

A. H. Milstead 

D. E. Regan 

H. L. Roth 

I. B. Russak 

L. J. Tedeschi 

W. Nordyke 
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