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PHASE I NAVSTAR/GPS EPHEMERIS 
AND SPACE VEHICLE CLOCK PERFORMANCE SUMMARY 

Albert B. Bierman 
The Aerospace Corporation 


ABSTRACT 

The Navstar/Global Positioning System (GPS) has been under evaluation for more than one year. 
This paper, one of several Major Field Test Objective reports, addresses the issue of Control Seg- 
ment accuracy in predicting Space Vehicle (SV) clock and ephemeris states for broadcast to the user 
community. Both the highly precise ephemeris and clock prediction data blocks and the less precise 
(but longer period of utility) almanac data block are evaluated. 


93 



1. INTRODUCTION 


The Navstar /Global Positioning System (GPS) is a 
satellite-based navigation system that provides extremely 
accurate three-dimensional position, velocity and time 
information to properly equipped users anywhere on or near the 
earth. It is a Joint Service Program, managed by the Air Force 
with deputies from the Navy, Army, Marines, Defense Mapping 
Agency, Coast Guard and NATO with technical support provided by 
The Aerospace Corporation. 

Phase I - Concept Validation - has been undergoing 
test and evaluation in preparation for the second stage of the 
Defense Systems Acquisition Review Council (DSARC-2) in Spring 
1979. An extensive flight test program has been conducted at 
the Yuma Proving Ground in Arizona and, to a lesser extent, off 
the coast of Southern California and at other sites in the 
continental United States. 

While the ultimate objective is to demonstrate 
precision navigation for a wide range of military missions, it 
is equally important to verify the performance of all aspects 
of the GPS system. To accomplish these goals a series of 
papers has been prepared to support major field test objectives 
for DSARC-2. 

1.1 OBJECTIVES 


This paper addresses the accuracy of the ephemeris and 
space vehicle (SV) clock predictions which are vital to the 
user navigation function. The Phase I system specification 
(Ref.l) allocates 3.66 meters (1 sigma) for the ephemeris error 


94 



contribution to the User Equivalent Range Error during the 
twenty-four hour period after the satellite upload message has 
been prepared. Phase I satellites have rubidium frequency 
references as atomic standards. The GPS error budget allocates 
2.74 meters (1 sigma) for the SV clock error during the two 
hour period after the satellite upload message has been 
generated. The Phase I clock error is predicated on a rubidium 
atomic standard with fractional frequency stability of 1 part 
in 10 over a two hour period. Operational satellite clocks 
will be cesium beam tube or hydrogen maser standards. These 
clocks offer frequency stability of 1 part in 10 13 or better 
over 24 hours. Thus the Phase III Operational GPS can be 
expected to provide better than 3 meters (1 sigma) accuracy 
over the twenty-four hour period after the navigation message 
has been prepared. 

1.2 SCOPE 


This assessment will evaluate (1) the ephemeris and SV 
clock error contributions to user ranging error (URE) during 
the two-hour periods following navigation data uploads; (2) the 
error contributions throughout the twenty-four hour period 
following navigation data uploads; and (3) SV almanac data 
accuracy for 2 weeks or more after upload. It is important to 
note that while item (2) addresses twenty-four hour accuracy, 
there is no prescribed Phase I clock error budget beyond two 
hours . 

The adequacy of item (3) will be judged against the 
almanac URE (1 sigma) values (Ref. 2) presented in Table I. 


95 



Table I. Almanac Accuracy 


Time 

User Equivalent Range Error 
estimated by analysis 
(meters) 

1 day 

1000 

1 week 

2500 

2 weeks 

5000 

3 weeks 

10000 

4 weeks 

15000 

5 weeks 

20000 


96 



2. SYSTEM DESCRIPTION 


GPS is comprised of three system components (1) the 
Space Segment, (2) the User Segment, and (3) the Control 
Segment. 


2.1 SPACE SEGMENT 


The Space Segment provides the spaceborne navigation 
payload. Phase I uses four space vehicles in 10,900 nmi 
(20,200 km) altitude circular orbits inclined 63 degrees with 
respect to the equator. The satellites are distributed in two 
inertial planes which provide an hour or more of usable four 
Space Vehicle (SV) geometry for daily user testing at the Yuma 
Proving Ground (YPG) . Table 2 presents a summary of the 
constellation configuration. The orbit periods are controlled 
to cause the ground traces to repeat each day. Fig. 1 
illustrates the repeating satellite geometries. Because of the 
sidereal effect of the earth's motion about the sun, and orbit 
torques by the oblate earth and by sun-moon effects, each day's 
events occur approximately 4 minutes and 3.4 sec earlier than 
the previous day's events. Satellite geometry at the YPG is 
described by the azimuth-elevation time history in Figure 2. 

The satellite positions at 1 January 1979/1700 GMT are shown on 
Figs. 1 and 2. At that time, the opportunity for four 
satellite navigation at YPG was nearing termination due to the 
fade of Navstar 4. 

The major elements comprising the navigation payload 
are the pseudo random noise sub assembly (PRNSA) , atomic 
frequency standard, processor, and L-band antenna. The PRNSA 
includes the baseband generator, which produces the P (precise) 
and C/A (coarse/ acquisition) ranging codes and encodes naviga- 
tion data from the processor onto the pseudo random noise (PRN) 


97 



Table II. Navstar Phase I Orbits at First 
Ascend ing Node on 1 Jan. 1979 


SATELLITE 

IDENTIFIER 

NODAL 

PERIOD, 

min 

INCLINATION, 

deg 

LONGITUDE OF 
FIRST ASCENDING 
NODE, deg 

RIGHT ASCENSION OF 
ASCENDING N00E<1*. 
deg 

TIME OF FIRST 
ASCEN0ING NODE. 
GMT 

ECCENTRICITY 

ARGUMENT OF 
PERIGEE, deg 

DATE OF 
LAUNCH 

NS-1 

717.982 

63.12 

46.12 

218.06 

0448:18 

0.0034 

345.5 

21 FEB 1978 

NS -2 

717.983 

63.41 

331.61 

100.25 

0155:30 

0.0051 

93.4 

12 MAY 1978 

NS “3 

717.985 

63.03 

352.81 

98.15 

0022:18 

0.0015 

350.4 

7 OCT 1978 

NS-4<» 

717.988 

63.13 

95.71 

217.67 

003148 

0.0008 

77.4 

10 DEC 1978 


(1) Referenced to astronomical coordinates of 195010 

(2) Data for 15 January 1979 




LATITUDE 




1509 Z 

300°i 


YPGH^s 


.222 Z 


T) SE 
r 225' 


200 ° 1 
rise' 

1517 Z 


180° ,8 ° 0 DICC 

' iao° 170 RISE 

SET SET 1203 Z 

2133 Z 1957 Z 


NOTE: 1. TIMES SHOWN ARE GREENWICH MEAN TIME 

2. SATELLITE LOCATIONS INDICATE POSITIONS 
AT 1700Z ON 1 JAN 1979 

3. RISE - SATELLITE APPEARANCE ABOVE HORIZON 
SET - SATELLITE DISAPPEARANCE BELOW HORIZON 


Figure 2. Satellite Geometries at the Yuma Proving Ground 








ranging signal; the amplifier /modulator units that supply the 
(1575.42 MHz) and L 2 (1227.6 MHz) carrier frequencies 
modulated by the PRN ranging signals; and the high-power 
amplifiers that amplify the carrier signals for transmission. 

2.2 USER SEGMENT 


The User Segment consists, in part, of navigation 
avionics which measure pseudo range and delta (pseudo) range 
using the navigation signal from each satellite. Pseudo range 
is the true distance from the satellite transmitter to the user 
antenna phase center plus an offset due to the user's clock 
bias. Similarly, delta range is the incremental range change 
over a specified time interval plus an offset due to the user's 
frequency bias. Each signal carries ephemeris data and system 
timing information modulated at 50 bps. The low data rate 
information forms the navigation message, which permits the 
user receiver /processor to convert pseudo range and delta range 
measurements to user three-dimensional position and velocity. 

Navigation message data consists of five subframes 
each containing 300 bits of data (Pig. 3) . Subframe 1 


Subframe 1 

Subframe 2 

Subframe 3 

Subframe 4 

Subframe 5 

SV Clock 
Data 

SV Ephem- 
eris Data 

SV Ephem- 
eris Data 

Special 

Messages 

Almanac Data 

Single 
Frequency 
Ionospheric 
Model Data 





Data Block I 

U ^ 

Data 

U 

Block II 



Data Block III 

U 


Figure 3. Navigation Message Structure 

101 




contains data to establish system time and a set of 
coefficients with which a single frequency user can model the 
signal delay due to the ionosphere. The data in subframe 1 is 
also referred to as data block I. Subframes 2 and 3 contain 
data from which the satellite position and velocity can 
accurately be determined. These two subframes are referred to 
as data block II. Subframe 4 contains alpha numeric data 
irrelevant to navigation. Subframe 5 provides data similar to 
data block II but of reduced accuracy. Every thirty seconds 
the almanac, of a different satellite appears in data block III. 

2.3 CONTROL SEGMENT 


The Control Segment consists of a Master Control 
Station (MCS) , an Upload Station (ULS) , and monitor stations 
(MS) located in Hawaii, Guam, Alaska, and at Vandenberg AFB, 
California. The monitor stations passively track all 
satellites in view and accumulate pseudo ranging data, which is 
transmitted to the MCS where it is processed to provide 
estimates of the satellite ephemerides and clock offsets. At 
least once a day these estimates are extrapolated forward in 
time to provide predictions of the SV ephemeris and clock 
states. These predictions are the basis of the new navigation 
message that is transmitted by the upload station to the 
satellites for subsequent downlink transmission encoded on the 
carrier signals. The MCS, ULS, and the Vandenberg monitor 
station are co-located. 

As previously described, the satellite-station 
geometries repeat, occurring somewhat less than 4 minutes 
earlier each day. Fig. 4 presents the tracking contacts for 1 
January 1979. Tracking opportunities for some SV-MS pairs 
occur 23 hours per day with as many as 12 satellite-station 


102 



VANDENBERG 

MONITOR 

STATION 


HAW A 1 1 
MONITOR • 
STATION 


GUAM 
MONITOR - 
STATION 


ALASKA 

MONITOR 

STATION 


NS-1 
NS -2 
NS -3 
NS -4 




NS-1 
NS -2 
NS -3 
NS -4 


NS-1 
NS -2 
NS -3 
k NS -4 


□ 


NS-1 
NS -2 
NS -3 
. NS -4 


i i i i i i i i i i i i i < i i i i 1 1 1 ' 1 1 1 

0 2 4 6 8 10 12 14 16 18 20 22 24 

GMT - 1 JAN 1979 


Figure 4 


Monitor Station Tracking Schedules 




contacts occurring simultaneously, e.g., 1600 GMT. Yuma 
Proving Ground can be considered to have the same tracking 
opportunities as Vandenberg monitor station because of their 
proximity. Thus, the opportunity for four SV tracking at Yuma 
occurs between 1515 and 1725 GMT on 1 January 1979 where the 
earlier time is determined by the rise of Navstar 1 while the 
later time is determined by the fade of Navstar 4. The 
desirability of incorporating Vandenberg tracking data prior to 
preparing the upload further reduces the available test window. 


104 



3. EVALUATION METHODS 


Control Segment operations have been supporting Phase I 
satellites for nearly two years. Much of this time has been 
used to integrate the system, de-bug hardware and software, and 
to refine system parameters in order to optimize performance. 
Sufficient data have been accumulated during the last year to 
enable the Phase I Control Segment evaluation. Evaluation 
activities fall into two categories: (1) Master Control 

Station system performance evaluation and (2) independent 
validation activity. 

3.1 Master Control Station System Performance Evaluation 

Within the Master Control Station software is a 
program for system performance evaluation. This program 
performs various computational checks and comparisons to 
monitor Control Segment performance. These checks generally 
involve comparisons of parameters or functions generated some 
time in the past with corresponding parameters or functions at 
current ("real") time. In particular, two computations 
involving the navigation message have proved useful as a 
measure of Control Segment performance: (1) measurement 

residuals and (2) user range error (URE) . 

3.1.1 Measurement Residuals 


Throughout a satellite pass, raw monitor station 
measurements (pseudo range and delta range) are edited; 
corrected for such physical phenomena as tropospheric and 
ionospheric delays, relativity, satellite lever arms, and light 
transit time delay; and smoothed to yield a current measure of 
the slant range between the satellite and the monitor station. 
Using the applicable data block I and II portions of the 


105 



navigation message which were last uploaded to the satellite , 
one can compute the corresponding (predicted) slant range to 
the satellite. The difference between the smoothed and 
predicted measurement represents the range error due to the 
navigation message errors. Pig. 5, is a simplified 
illustration of the measurement residual computations. 

3.1.2 User Range Error 

The navigation message is prepared and uploaded during 
the time when the Vandenberg monitor station is tracking. 

After upload, the satellite is tracked for at least another 
hour (SV4) and for as much as another five hours (SV2) . The 
newest data represents the best (real time) information on the 
satellite clock and epheroeris. A predicted pseudo range 
measurement to a stationary site at Yuma Proving Ground, 

Arizona is computed from the applicable navigation message (see 
Fig. 6). A corresponding pseudo range measurement is computed 
using the current (real time) satellite clock and ephemeris 
estimates. The difference between these pseudo range 
computations represents the user range error (URE) attributable 
to the Control Segment (i.e., navigation message). 

3.2 INDEPENDENT VALIDATION 

In support of the Phase I activities. The Aerospace 
Corporation has performed independent evaluations of Control 
Segment performance (see, for example. Reference 3) . 

Evaluation efforts involve post flight ephemeris and clock 
reconstruction using GPS-supplied data as well as S-band 
ranging data collected by the Air Force Satellite Control 
Facility (AFSCF) . Also, extensive simulation activity where 
the truth is precisely known has been used to validate Control 
Segment performance. 


106 




Figure 5 


System Performance Evaluation Measurement Residual 





3.2.1 


Best Fit Ephemeris and Clock 


Absolute satellite ephemeris and clock accuracies are 
difficult to establish. To accomplish post flight 
reconstruction, a special version of the TRACE program (Ref. 4) 
has been used to generate best fit ephemeris and clock (BPE/C) 
estimates. For evaluation purposes, BFE/C estimates are 
considered to be the closest representations of the "truth" 
currently available. Three types of data have been used for 
post flight reconstructions: MCS generated smoothed ranging 

data (SRTAP) , Aerospace generated smoothed ranging data (named 
APOLY, after the software which generates it) and AFSCF radar 
ranging data. 

3. 2. 1.1 SRTAP Data 


The Master Control Station generates smoothed pseudo 
range and delta range measurements every fifteen minutes when 
monitor station tracking data exists. These data referred to 
as SRTAP data, are the input to the linearized Kalman filter 
which computes the real time satellite ephemeris corrections 
and clock states. In addition, this same data is forwarded to 
the Naval Surface Weapons Center/Dahlgren Laboratories where a 
reference trajectory for the MCS Kalman filter linearization is 
generated weekly. 

3. 2.1.2 APOLY Data 


As an alternative to using MCS prepared smoothed data, 
The Aerospace Corporation has developed a program (named APOLY) 
which converts raw monitor station (6 second interval 
measurement) ranging data into smoothed data. Moreover, APOLY 
uses integrated delta range rather than polynomial generated 


109 



range differences to complement the pseudo range data. By 
doing their own editing, correcting, and smoothing. Aerospace 
Analysts have absolute control over which data are used and 
obtain explicit measures of the quality of the data. 

3. 2. 1.3 AFSCF Data 

As part of AFSCF support, the GPS satellites are 
tracked with S-band radars from Satellite Control Facility 
(SCF) sites extending from the Indian Ocean to northeastern 
United States. Six daily contacts of 10 minute minimum 
duration (the Indian Ocean site often gathers as much as one 
hour) , while sparse vis-a-vis GPS tracking densities, provide 
tracking coverage over more of the orbit than the four GPS 
monitor station network. The GPS sites stretch only from Guam 
to Vandenberg AFB. 

3. 2. 1.4 Ephemeris Comparisons 

Best Fit Ephemerides (BFE) for the period 16-30 August 
1978 were generated: one based on SRTAP data, a second based on 
APOLY data, and a third based on SCF data. The solution 
trajectories of each fit were differenced with each other. 
Agreement between the BFEs was quite good. Figure 7 is an 
example of the differences between Navstar 2 BFEs using SCF and 
SRTAP data. Estimated differences in terms of URE are 
approximately three meters (one sigma) . These results are more 
notable when one considers that Navstar 2 experienced roll 
momentum dumps on the twentieth and the twenty sixth day of 
August. 


The momentum dumping process was performed with a 
coupled-pair of 0.1 lb reaction control jets. The location of 
these jets caused a plume impingement onto the space vehicle. 


110 



CROSSTRACK, m INTRACK, m RADIAL, 




producing an intrack position error of about one hundred meters 
impulsive per day. A judicious choice of fit parameters to 
include in-track thrusts in the BFE solutions removed 
essentially all of the intrack error due to this source. 

3.2.2 Ephemeris End Around Check 

The ephemeris end around check (EEAC) involves a 
sophisticated simulation of GPS data inputs and outputs (see 
Ref. 5) . Some aspects of the activity are still not 
completed. When they are, they will be documented. For now, 
two aspects of EEAC will be useful to this presentation: (1) 
best fit ephemeris and clock solutions, and (2) monitor station 
location solutions (geodetic survey) . Monitor station survey 
will be discussed in Para. 4.3. The best fit activity is cited 
here to demonstrate the efficacy of the post flight 
reconstruction methodology since in this case the truth is 
precisely known. 

One case (Case 3.X) involved the simulation of two 
Phase I satellites and four monitor stations. Reference 5 
gives specific details of all the simulated effects. Briefly, 
one satellite was characterized by a cesium frequency standard 
and Navy's Navigation Technology Satellite II (NTS II) the 
solar pressure force model, while the second satellite had a 
rubidium frequency standard and a Navstar solar pressure force 
model. Force model errors were introduced into the solar 
pressure and geopotential force models. Other simulated errors 
included monitor station location coordinates, pole wander 
values, monitor station clock instabilities based upon ground 
cesiums, SV random and deterministic clock errors, tropospheric 
and ionospheric refraction corrections, and white noise on all 
measurement links. 


112 



This data was fit using the same methodology applied 
to real data. Figures 8 and 9 present the differences between 
the best fit solutions and the truth. All the error components 
display the twelve hour periodic structure typical of GPS 
orbits. Radial errors have amplitudes between one and two 
meters. Horizontal errors (the root sum square of intrack and 
crosstrack errors) are approximately fifteen meters for Navstar 
1 and ten meters for NTS II. As a result of the altitude of 
the GPS orbits only between zero (at zenith) and twenty four 
percent (on the horizon) of the horizontal error maps into the 
user range error. Hence , the estimated contribution to the 
user ranging error is about three meters (one sigma) . 

3.3. DATA COLLECTION 


Although Control Segment data is collected daily, 
special data collection periods have been designated for the 
purpose of performance evaluation. Table III presents a 
summary of these special periods. The SEG tests (CS-SEG-1) 
were intended to verify Control Segment performance in support 
of one, two, and three satellites. Each test was nominally 
scheduled for four weeks of normal operations. As evidenced in 
Table III, none of the SEG tests had four consecutive weeks of 
normal operations. The CS-S-1 (S-l) test was a four satellite 
full system evaluation. Initially scheduled for 17 January to 
13 February, 1979, it was rerun from 26 February to 25 March, 
1979. This latter period was devoid of significant anomalies 
and is considered to be representative of normal operations. 

During these test periods extensive data collections 
were performed and forwarded to General Dynamics/Electronics 
Division in San Diego, California and The Aerospace Corporation 
in El Segundo, California for analysis, it is primarily the 
results of these data analysis activities that are reported in 
the following section. 


113 



CROSSTRACK, m INTRACK, m RADIAL, 



o 


■I 


28 29 30 31 1 2 3 4 


9 10 11 


OCTOBER 


Figure 9 


5 6 7 8 

NOVEMBER 

DAY OF 1978 


Best Fit Ephemeris Errors for Simulated 
Navstar 1 Satellite Data 


115 


Table III. Special Data Collection Periods 


TEST 


CS-SEG-1 (1 SV) 


CS-SEG-1 (2 SV) 


CS-SEG-1 {3 SV) 


CS-S-1 (4 SV) 


15 MAY 


15 AUG 


13 NOV 


29 JAN 


26 FEB 


PERIOD 


- 12 JUNE 1978 


- 12 SEPT 1978 


- 20 DEC 1978 


- 23 FEB 1979 


- 25 MAR 1979 




4. RESULTS 


This section summarizes Phase I Control Segment 
performance to date. For more details see Refs 6-9. The 
results will address the following issues: ephemeris and 
satellite clock prediction accuracy, i.e., data block I (SV 
clock) and data block II (ephemeris); almanac accuracy, i.e., 
data block III* 


4.1 EPHEMERIS AND SATELLITE CLOCK PREDICTION ACCURACY 


4.1.1 Master Control Station System Performance Evaluation 

As described in Section 3, this activity is performed 
with the MCS software. The results reported in Sections 

4.1.1. 1 and 4. 1.1. 2 have been supplied by General Dynamics 
Electronics Division. The remainder of Section 4 is based on 
analyses performed at The Aerospace Corporation. 

4. 1.1.1 Measurement Residuals 


Satellite positions predicted from the navigation 
messages are used by the GPS Master Control Station System 
Performance Evaluation software to compute a predicted range 
from a given satellite to a Control Segment monitor station 
currently tracking that satellite. Corrected smoothed pseudo 
range measurements are then converted into a measured range by 
subtracting the predicted satellite clock offset and the 
current estimate of the monitor station clock offset. The 
difference between these measured and predicted ranges provides 
a direct indication of the accuracy of the GPS navigation 
message. 


117 



Fig. 10 summarizes the predicted range residuals to 
the Vandenberg monitor station for the four GPS satellites. 

The data presented are the root-mean-square (rms) of the 
predicted range residuals based on data collected during four 
satellite testing in February 1979. The daily residuals were 
shifted along the horizontal axis so the data could be 
evaluated relative to upload time. Note that the residuals for 
the four SVs before the daily upload are of the order 3-30 
meters. At the upload time, the residuals drop towards zero 
and then begin to disperse. The residuals are not identically 
zero at upload time because of the timing involved in computing 
the evaluation parameter. The navigation message is 
constructed based upon filter estimates at a particular epoch. 
These data must be uploaded to the satellites and verified by 
the Control Segment monitor stations before it is available for 
evaluation. Hence, the message has aged a minimum of fifteen 
minutes (the nominal Phase I evaluation interval) before 
measurement data are available for residual formation. 

4. 1.1.2 User Range Error 

Section 3.1.2 described the URE computation performed 
by the MCS System Performance Evaluation. The CS-S-1 test % 
performed from 26 February through 25 March 1979 was a period 
of stable GPS operation. Daily URE data were accumulated for 
the four satellites. The root-mean- square (rms) of these URE 
values are plotted in Fig. 11 as a function of time since the 
navigation message was uploaded to the satellite. It should be 
added that the mean value of the URE for each satellite is less 
than 1.5 meters; hence the rms value can also be interpreted 
as the standard deviation with no significant error. 

As a consequence of the satellite geometries (see 
Section 2) , Navstar 4 is visible to Yuma for less than 2 hours 


118 




Figure 10. RMS of Predicted Range Residuals at Vandenberg 


USER RANGING ERROR, 1 



Figure 11. User Ranging Error Based on MCS System 
Performance Evaluation 


120 



after the fourth satellite (Navstar 2) rises. During the first 
two hours after upload Navstars 1, 2, and 3 better the required 
accuracy by more than one meter. Although Navstar 4 exceeds 
the one hour error budget by 0.1 meters (4.0 vs 3.9 meters) , 
the difference is quite small. In general, all four satellites 
better the Phase I accuracy requirements during the entire 
period they are visible to Yuma after upload. 

4.1.2 Independent Validation 

The twenty-six navigation messages broadcast by the 
satellite (one message each hour) predict the position and SV 
clock offset around the entire orbit, actually extending two 
hours into the next day. These predictions have been compared 
against the "truth" solution (BPE/C) prepared by The Aerospace 
Corporation (see Section 3.2) during the special data 
collection periods. Figures 12 and 13 present the Navstar 1 
and 2 ephemeris and clock errors as determined from the upload 
messages on 16 Aug 1978 (day 228) . The small data loss in the 
first hour is due to the MCS computation lag between the time 
the navigation message is prepared and the time it is uploaded, 
verified, and then broadcast. During this time the satellite 
is broadcasting the navigation message uploaded previously. 

Radial and crosstrack ephemeris errors have a 
characteristic twelve hour periodicity. Intrack errors, while 
also of twelve hour periodicity, have a secular error growth in 
addition. Clock errors, on the other hand, should look more 
like a random walk. However, the clock errors on 16 August 
show some periodic characteristics. This appears to be a 
result of (1) relative paucity of data due to unavailability of 
Guam tracking station, (2) induced correlations between clock 
state and ephemeris state estimates due to high altitude (4.2 
earth radii) of GPS orbits, and (3) induced correlations due to 
best fit clock processing. 


121 



CLOCK, m CROSSTRACK, m INTRACK, m RADIAL, 



TIME FROM UPLOAD, hr - 16 AUG 1978 


Figure 12. Navstar 1 Ephemeris and Clock Prediction 
Errors for 16 Aug 1978 


122 


CLOCK, m CROSSTRACK, m INTRACK, m RADIAL, 



TIME FROM UPLOAD, hr - 16 AUG 1978 


Figure 13. Navstar 2 Ephemeris and Clock Prediction 
Errors for 16 Aug 1978 


123 


Next, the epheraeris and clock errors are converted to 
user ranging errors by mapping the contributions onto the 
line-of-sight to (fictional) uniformly distributed users on the 
earth's surface. At each time point, the range errors for the 
uniformly distributed user population are computed and the 
corresponding statistics are tabulated. Fig. 14 presents the 
68 percent error curves for Navstars 1 and 2 for 16 Aug 1978. 

To interpret this result, remember that 68 percent of all users 
who can see the satellite (masking angle is five degrees for 
these computations) will incur errors equal to or less than the 
value indicated by the curve. On 16 Aug, the maximum global 
user range error was 10 meters during the first two hours and 
about 22 meters during the twenty four hour period after upload. 

4. 1.2.1 Two Vehicle Testing 

A similar activity was done for each day during which 
an upload was generated during the CS-SEG-1 (2 SV) test 
period. A total of 10 days between 16 and 31 August had 
acceptable uploads (weekends were excluded, and two days had 
some difficulties) . Cumulative error statistics for the 
two-week test period are presented in Fig. 15. Two curves - 
one for the first two hour period after the upload message was 
generated and the second for the twenty-four hour period after 
the upload message was generated - summarize the Control 
Segment ephemeris and SV clock prediction performance. To 
interpret the figure, given a point on either curve » URE, 

Y1 * probability) , one states that for the indicated time span 
(i.e., 0-2 hours or 0-24 hours) there is a probability of y x , 
that a user will incur a URE less than or equal to x^ Ergo, 
there is a 68 percent probability that the user ranging error 
is less than 6.5 meters during the first two hours after 
upload. While this value is almost two meters beyond the error 
budget it is a very positive result when one considers that at 
this point in time: 


124 



URE 68 PERCENT, 



Figure 14. Global User Range Error Statistics 




Figure 15. Cumulative Error Distribution From Ephemeris 
and SV Clock for All Satellites 


126 



• Navstar 2 incurred intrack velocity impulses 
during the attitude control system roll momentum 
dumping process. This phenomenon was caused by 
plume impingement during the firing of the 0.1 lb 
reaction control thrusters. The momentum dump 
impingement anomaly was identified during the BFE 
processing - a month or more after the test 
period. 

• The Control Segment software was still in a state 
of checkout. Several corrections have since been 
made - primarily in the data base. 


The twenty-four hour URE statistics are impressive 
when one realizes that the SV rubidium clock should contribute 
nearly 37 meter (1 sigma) to the URE. According to the curve, 
for the 16-31 Aug. time period, the 68 percent probability 
yields a URE of 14 meters - which includes ephemeris and clock. 


4. 1.2. 2 Three Vehicle Testing 

A similar exercise was performed for the CS-SEG-1 (3 
vehicle) test period. Seventeen days in the period 14 November 
to 8 December had uploads included in the cumulative error 
statistics shown in Figure 16. Again, two curves are used to 
summarize the Control Segment ephemeris and SV clock prediction 
performance; the first depicts performance for the first two 
hours after an upload while the second is for the twenty four 
hour period after the upload. 


A procedural change strongly affected the character of 
these results. In an attempt to obtain ephemerides independent 
of GPS data, the previously referenced tracking data from the 
Air Force Satellite Control Facility was used as the basis for 
generating the BFE used in this comparison. This data was not 
corrected for ionospheric propagation effects at all, and was 
corrected for tropospheric propagation effects by use of a 
procedure different from that used at the MCS. While the 


127 




Figure 16. Cumulative Error Distribution From Ephemeris and 
SV Clock for All Satellites - Three Vehicle Test 


128 


long— arc fits to these AFSCF data appeared of acceptable 
quality, it was subsequently demonstrated that their predict 
performance was noticeably poorer than those obtained from 
GPS-obtained data. This poorer predictive capability is 
sharply evident in these three satellite test results. 


Additional problems hampered these analyses; 


• A different clock was employed on Navstar 2 
during this test than was used on the 2 vehicle 
test. This clock exhibited a 56 sec-period 
oscillation throughout this test. Additionally, 
this clock at that time manifested some as yet 
unexplained frequency excursions typically of 
many minutes duration and of several tens of 
meters' magnitude in pseudo range. These factors 
have led to worsening of Navstar 's prediction 
performance by a factor of 2 or more. 

• Guam monitor station was not operational 

• Navstar 2 had a 56 second period anomalous 
oscillation in the 1575.42 Mhz carrier signal 
with amplitude 50 times greater than expected 

• Navstar 1 had emerged from its eclipse season 
just prior to the 3 vehicle test span. It has 
been observed throughout these analyses that 
orbit and clock prediction are relatively worse 
in and near eclipse seasons than between eclipse 
seasons. 

• Plume impingement during roll momentum dump 
firings was again a problem during this test. If 
anything, the number of momentum dumps was larger 
in this interval than during the two vehicle test. 


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4. 1.2. 3 Four Vehicle Testing 


Four vehicle data for the period 29 January - 12 
February 1979 was employed to examine the predictive 
capabilities of that configuration. Ten days of valid uploads 
are included in this sample. Cumulative error statistics are 
given in Figure 17, as before, in the four vehicle 2 hour and 
24 hour prediction curves. 

These data were reduced using a GPS data based BFE 
Predict Performance characteristics of this configuration and 
seen to be smaller than the two vehicle data presented 
earlier. The two hour value of less than 5.5 in with a 68 
percent probability is closer to the specification error budget 
than previously reported values. In this two week interval 
there were two cases of anomalous clock performance, and the 
previously noted 56 second oscillation on Navstar 2*s clock 
continued to plague the analysis. However, by the use of the 
magnetic torque momentum control system the incidence of 
thrusting to control momentum was eliminated. A change in the 
MCS data case process noise values resulted in more accurate 
predictions during this period, as is shown in Figure 17. 

Table IV summarizes the 68% values for each of the 
three described here. It presents data by Navstar vehicle as 
well as points from the composite curves, Figures 15-17. The 
specific problems addressed earlier are clearly reflected in 
the summary. 

The four vehicles analyzed here were part of a 
preliminary examination of four vehicle test results. Both the 
individual Navstar SV results and the composite are very 
encouraging as steps toward meeting the specification of 5 
meters in 2 hours, 68% of the time. A preliminary look at the 


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Figure 17. Cumulative Error Distribution From Ephemeris And 
SV Clock for All Satellites - Four Vehicles 


131 


Table IV. Test Summaries 




Two 

Vehicle 

Cumulative Summary 




NAV 1 

NAV 2 

ALL (B Chart) 

68%, 

0-2 

7.3m 

5.5m 


6 . 5m 

68%, 

0.24 

14.1m 

12.4m 


14 m 



Three Vehicle Cumulative Summary 




NAV 1 

NAV 2 

NAV 3 

ALL 

68%, 

0-2 

13.5m 

12 m 

10 m 

13.5m 

68%, 

0-24 

. 23.5m 

29 m 

12 m 

20.5m 



Four 

Vehicle 

Cumulative Summary 




NAV 1 

NAV 2 

NAV 3 NAV 4 

ALL 

68%, 

0-2 

5 m 

6 m 

4 m 7.5m 

5 . 5m 

68%, 

0-24 

11.5m 

27 m 

12 m 6 m 

11.5m 


CS-S-1 (see Table III) data indicates it is of higher quality 
and more nearly free of annoying anomalies. It is anticipated 
that all vehicles will meet specification value during this 
period . 


Of special interest are the 24 hour predict values, 

which are much better than had been anticipated from analyses 

12 

assuming a 1 part in 10 fractional frequency stability 
clock . 


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4.2 


ALMANAC EVALUATION 


The methodology for evaluating the almanac (data block 
III) message is quite similar to that used for the independent 
validation of the ephemeris and SV clock messages (see section 
4.1.2) . Data block III has only one message per satellite per 
day. Moreover, it is intended to be useful (to much less 
accuracy) over extended time periods (see Table I) . Thus, in 
evaluating almanac messages, the time scale is in days rather 
than hours. Here, as in section 4.1.2, the evaluation is based 
on data collected from 16 to 31 August 1978. 

Fig. 18 presents the results of the almanac evaluation 
for messages generated during the CS-SEG-1 (2 SV) test. These 
messages spanned the period 16 to 31 August. If the one sigma 
values of Table I are interpreted as 68 percent probable URE, 
the almanac accuracies during the 2 SV SEG test appear to 
satisfy the error budget over the five week evaluation interval. 


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PROBABILITY 



Figure 18. Cumulative Error Distribution for Almanac Message 


134 



5. CONCLUSIONS 


Control Segment test evaluations have occurred during 
Spring 1978 (1 SV) , Summer 1978 (2 SV) , Fall 1978 (3 SV) , and 
Winter 1979 (4 SV) . The one SV test period was of little value 
because of many anomalous conditions. The two SV test period 
during Summer 1978 had two weeks' usable data. The three SV 
test period had over three weeks of usable data. Two weeks of 
4 vehicle tracking were examined as a preliminary look at the 
formal four vehicle test data. Analysis on these periods forms 
the basis of this paper. 

GPS system checkouts were still occurring in summer 
1978. The evolution of Monitor Stations capability and 
reliability has increased continually from that period to the 
present. Plume impingement during momentum wheel unloading, 
which were causing in-track satellite perturbation approaching 
100 meters a day, were identified in the course of these 
analyses. This problem has been removed through the use of 
magnetic torque for momentum wheel unloading. The checkout 
operations included a large number of problems solved, 
anomalies identified, fixes devised, work-arounds installed, 
and general systems development. Throughout it all, (perhaps 
despite it all) , the Control Segment continued to perform its 
functions extremely well. Specifically: 

• Control Segment user ranging error contributions 
were only about 1 meter over the specified values 
(i.e., 5.5 meters vice 4.6 meters) for the two 
hour period following upload. 

• Twenty-four hour URE values were below what was 
anticipated from the Phase I rubidium SV clocks. 

• Almanac accuracy met the URE budget. 


135 



6 . REFERENCES 


(1) System Specification for The Navstar Global 
Positioning System , SS-GPS-101B, 15 April 1974. 

(2) Space Vehicle Navigation Subsystem and NTS PRN 
Navigation Assembly/Pser System Segment and Monitor 
Station Interface Control Document , MH08-00002-400 , 
Revision F, 13 April 1977. 

(3) H. Bernstein, Global Positioning System (GPS) Phase I 
Accuracy Analysis Concept , Report No. 

TOR-0076 (6474-01)-3, The Aerospace Corporation, El 
Segundo, California, 25 July 1975. 

(4) R. H. Prislin, and D. C. Walker, TRACE 66 Trajectory 
Analysis and Orbit Determination Program , Report No. 
TR-0059 (9320) -1, Vol. I, The Aerospace Corporation, El 
Segundo, California, 15 August 1971. 

(5) D. A. Conrad, Data Base for GPS Ephemeris End Around 
Check , TOR-0079 (4473-04) -3, 1 April 1979. 

(6) Post Launch CS/SV Test, CS-SEG-1 Category II Final 
Test Report , Revision B, 11 December 1978 

(7) Post Launch CS/SV Test, CS-SEG-1 (2 SV) , Category II 
Final Test Report , Revision B, 5 March 1979 

(8) Post Launch CS/SV Test, CS-SEG-1 (3 SV) Category II 
Final Test Report , 30 March 1979 (Draft) . 

(9) Post Launch CS/SV Test, CS-S-1, Category II Final Test 
Report , To Be Delivered 


136