Alternatives to the Tracking and Data Relay Satellite (TDRS) orbit estimation procedure were studied to develop a technique that both produces more reliable results and is more amenable to automation than the prior procedure. The Earth Observing System (EOS) Terra mission has TDRS ephemeris prediction 3(sigma) requirements of 75 meters in position and 5.5 millimeters per second in velocity over a 1.5-day prediction span. Meeting these requirements sometimes required reruns of the prior orbit determination (OD) process, with manual editing of tracking data to get an acceptable solution. After a study of the available alternatives, the Flight Dynamics Facility (FDF) began using the Real-Time Orbit Determination (RTOD(Registered TradeMark)) Kalman filter program for operational support of TDRSs in February 2007. This extended Kalman filter (EKF) is used for daily support, including within hours after most thrusting, to estimate the spacecraft position, velocity, and solar radiation coefficient of reflectivity (C(sub R)). The tracking data used are from the Bilateration Ranging Transponder System (BRTS), selected TDRS System (TDRSS) User satellite tracking data, and Telemetry, Tracking, and Command (TT&C) data. Degraded filter results right after maneuvers and some momentum unloads provided incentive for a hybrid OD technique. The results of combining EKF strengths with the Goddard Trajectory Determination System (GTDS) Differential Correction (DC) program batch-least-squares solutions, as recommended in a 2005 paper on the chain-bias technique, are also presented

Blizzard, Mike

Dang, Ket D.

Jenkins, Greg

Slojkowski, Steve

Ward, Douglas T.

NASA Technical Reports Server

 1 
TRACKING AND DATA RELAY SATELLITE (TDRS) ORBIT 
ESTIMATION USING AN EXTENDED KALMAN FILTERΨ 
 
Douglas T. Ward, Ket D. Dang, and Steve Slojkowski 
a.i. solutions, Inc. 
Lanham, MD  20706 
 
Mike Blizzard and Greg Jenkins  
Honeywell Technology Solutions, Inc. 
Columbia, MD  21046 
 
 
 
ABSTRACT 
 
Alternatives to the Tracking and Data Relay Satellite (TDRS) orbit estimation procedure were 
studied to develop a technique that both produces more reliable results and is more amenable to 
automation than the prior procedure.  The Earth Observing System (EOS) Terra mission has 
TDRS ephemeris prediction 3σ requirements of 75 meters in position and 5.5 millimeters per 
second in velocity over a 1.5-day prediction span.  Meeting these requirements sometimes 
required reruns of the prior orbit determination (OD) process, with manual editing of tracking 
data to get an acceptable solution.   
 
After a study of the available alternatives, the Flight Dynamics Facility (FDF) began using the 
Real–Time Orbit Determination (RTOD®) Kalman filter program for operational support of 
TDRSs in February 2007.  This extended Kalman filter (EKF) is used for daily support, 
including within hours after most thrusting, to estimate the spacecraft position, velocity, and 
solar radiation coefficient of reflectivity (CR).  The tracking data used are from the Bilateration 
Ranging Transponder System (BRTS), selected TDRS System (TDRSS) User satellite tracking 
data, and Telemetry, Tracking, and Command (TT&C) data. 
 
Degraded filter results right after maneuvers and some momentum unloads provided incentive 
for a hybrid OD technique.  The results of combining EKF strengths with the Goddard Trajectory 
Determination System (GTDS) Differential Correction (DC) program batch-least-squares 
solutions, as recommended in a 2005 paper on the chain–bias technique, are also presented. 
 
 
1.  INTRODUCTION 
 
This paper discusses a continuation of the work described in Reference 1, documenting the 
continued progress toward the two goals of meeting the 75–meter (3σ) predicted accuracy 
requirement for Tracking and Data Relay Satellites (TDRSs) in support of the                         
                                                 
Ψ
 This work was supported by the National Aeronautics and Space Administration (NASA) – Goddard Space Flight 
Center (GSFC) under contract number NN-G-04-DA01-C 
https://ntrs.nasa.gov/search.jsp?R=20080012722 2019-08-29T19:06:49+00:00Z
 2 
Earth Observing System (EOS) Terra mission, and the continued progress toward increased 
automation of the daily OD solutions.   
 
The Flight Dynamics Facility (FDF) at the Goddard Space Flight Center (GSFC) currently uses 
two software systems for orbit determination/estimation (OD) of the TDRSs.  One is the 
Goddard Trajectory Determination System (GTDS) Differential Correction (DC) program, which 
was developed within the GSFC and which obtains batch-least-squares solutions.  The second is 
the Real–Time Orbit Determination (RTOD®) system, which implements an Extended Kalman 
filter (EKF).  RTOD® is a commercial product currently marketed and supported by Northrop 
Grumman. 
 
The background section of this paper discusses a description of the OD techniques and a review 
of prior performance.  More recent results of the EKF are then discussed, along with coincident 
changes.  The operational results obtained from applying the EKF are presented, followed by an 
overview of operational automation advances, and concluding with a summary and 
recommendations. 
 
2.  BACKGROUND 
 
In 2005, studies were completed to improve the accuracy of TDRS OD and the ability to 
automate this process through improved analytic and numeric techniques and tools        
(Reference 1).  Since the completion of those studies, which are summarized in this section, 
efforts have continued to assess and improve the TDRS OD process to address.  This paper is a 
follow-on study to Reference 1, which describes TDRS OD techniques with increased accuracy 
and automation potential relative to the prior GTDS Single–Bias (SB) technique.  The two newer 
OD techniques detailed in Reference 1 are an enhanced technique modeling the biases in 
equipment chains and the EKF.  Each of the three techniques is summarized below. 
 
Most TDRSs and Space–to–Ground–Link Terminals (SGLTs) at the White Sands Complex 
(WSC) have three different service type and antenna combinations that may be used.  These are 
the S-band SA 1 (SSA1) service (with chains A and B), the S-Band SA 2 (SSA2) service (with 
chains A and B), and the MA service (with chains 1 to 6).  For TDRS–3 and –10, the GTDS 
methods also use TT&C tracking data.  Since Reference 1 was written, we have learned that 
Forward and Return chains need not be identical for SA, which potentially doubles the possible 
number of SA chains from four to eight.  The MA forward link also has a backup, which 
potentially doubles the possible number of MA chains from six to twelve.  The prior operational 
GTDS technique, the GTDS SB, estimates or applies one composite range bias for all chains of 
BRTS data taken through the same SGLT. 
 
The enhancement to the GTDS DC, the Chain–Bias (CB) technique, assigns hybrid station 
indices depending on which Single Access (SA) or Multiple Access (MA) service and chain are 
recorded at the tracking station for Bilateration Ranging Transponder System (BRTS) events.   
 
The EKF was the third technique evaluated for TDRS OD.  Because an EKF updates the 
estimates of all solve-for parameters at each observation, it possesses an inherent capability to 
determine time–dependent biases. The FDF installation of the EKF does not assign a separate 
 3 
bias to each service type and chain.  For the period reported here, the EKF was configured to 
solve for range biases for each BRTS transponder, to model the transponder delay in range data.  
The BRTS transponder biases are treated as Gauss-Markov parameters and the supplied BRTS 
transponder delay establishes the a priori range bias.  The estimated bias then floats from this 
value based on the bias uncertainty model and the tracking data received.  Because this bias is 
intended to model the BRTS transponder delay, all service types and chains for any TDRS 
supported by that BRTS are modeled within it.    
 
Presently, the EKF technique provides operational FDF support for the EOS Aqua and Aura 
missions.  The FDF implementation of the EKF performs simultaneous state estimation for a 
constellation of satellites.  The current implementation includes eleven satellites:  the five 
operational TDRSs and six TDRSS User satellites [Aqua, Aura, Terra, the Hubble Space 
Telescope (HST), the Rossi X–Ray Timing Explorer (RXTE), and the Tropical Rainfall 
Measurement Mission (TRMM)].  The EKF configuration uses BRTS range and Doppler, TT&C 
range, Ground Network (GN) Doppler, and TDRSS User range and Doppler tracking data in its 
state update. The EKF potentially provides advantages over GTDS by dynamically estimating 
drag, solar radiation coefficient of reflectivity (CR), and observation biases, and by providing the 
capability to use all TDRSS User data in TDRS OD. 
 
Both the EKF and the GTDS CB were seen to have advantages over the prior technique.  The 
tentative choice of the GTDS CB for the automation process was made.  The comparison of the 
three techniques has continued beyond that of the initial study, and the results of this follow-up 
work are presented throughout the remainder of this paper.  
 
3.  RECENT EKF RESULTS 
 
Evaluation of results collected in more recent analysis showed significantly improved 
performance of the EKF as compared with the GTDS CB technique.  Table 1 displays both the 
GTDS CB and the EKF results for all operational TDRSs for daily cases in the first 8 months of 
2006, excluding solution arcs over thrust periods for GTDS CB. 
  
Table 1.  Predicted Ephemeris Accuracy for 1.5 Days 
January 2006 to August 2006 
Techniques GTDS CB EKF 
# of cases 1044 796 
# of cases over 75 meters 9 3 
Normalized “over 75 meters” 
Failures per Case 0.009 0.004 
Failure Rate Percentage (%) 0.862 0.377 
 
The results suggested that the EKF would meet the Terra requirements near the 3σ level (a 
failure rate of 0.27%).  This improvement is coincident with and is attributed to four factors: 
 
1. A decrease in solar activity from September 2005 to August 2006 allows more accurate 
OD using the EKF constellation. 
 4 
2. A shorter compare span (1.5 days instead of 2 days) seemed to help EKF more than it 
helped GTDS.  This change was done to exactly match the Terra requirement span. 
3. Three satellite-missions [the Earth Radiation Budget Satellite (ERBS), the Upper 
Atmosphere Research Satellite (UARS), and the Ocean Topographic Experiment 
(TOPEX/POSEIDON)] were removed from the EKF simultaneous-solution processing, 
as their active mission phases terminated.  The estimation of the first two had worse 
accuracies than many spacecraft in the filter because of their highly drag–perturbed 
orbits. 
4. Ephemeris generation was changed from the EKF smoothed ephemeris to a GTDS 
propagator. 
 
Because of this marked improvement in accuracy and the relative ease for automation with the 
EKF, the EKF was implemented as the prime FDF system for routine TDRS OD on February 20, 
2007.  The EKF solution vectors are propagated to yield ephemerides with future maneuvers and 
momentum unloads (MUs) modeled as impulses.  These ephemerides also serve as reference 
data for comparisons. 
 
Table 2 and Figures 1 through 5 present the predicted accuracies of the EKF solutions for periods 
of normal, nonmaneuver support, for February through June 2007.  The EKF can be seen as 
having a good success rate, with three times out of 521 when the 75–meter requirement was 
exceeded.  This failure rate was 0.576%. 
 
Table 2.  Predicted Ephemeris Accuracy for 1.5 Days in 2007 
 
  
TDRS-3 
 
TDRS-4 
 
TDRS-5 
 
TDRS-6 
 
TDRS-10 
 
Mean (km) 
 
0.0174 
 
0.0273 
 
0.0209 
 
0.0140 
 
0.0250 
Standard 
Deviation 
(km) 
 
0.0150 
 
0.0180 
 
0.0090 
 
0.0085 
 
0.0152 
Maximum 
Value (km) 
 
0.0740 
 
0.0904 
 
0.0586 
 
0.0479 
 
0.0713 
 
# of Cases 
 
105 
 
105 
 
106 
 
104 
 
101 
# of Cases 
over 75 
meters 
 
0 
 
3 
 
0 
 
0 
 
0 
Failure Rate 
Percentage 
(%) 
 
0 
 
2.86 
 
0 
 
0 
 
0 
 
 
 5 
06-May-07, 0.0740
0.000
0.025
0.050
0.075
0.100
02/17/07 03/01/07 03/13/07 03/25/07 04/06/07 04/18/07 04/30/07 05/12/07 05/24/07 06/05/07
Predicted Generation Date
M
ax
 
Po
si
tio
n
 
D
iff
er
en
ce
 
(km
) Max Delta-R
 
Figure 1.  TDRS-3 Predicted Accuracy for 1.5–days 
 
 
0.000
0.025
0.050
0.075
0.100
02/17/07 03/01/07 03/13/07 03/25/07 04/06/07 04/18/07 04/30/07 05/12/07 05/24/07 06/05/07
Predicted Generation Date
M
ax
 
Po
si
tio
n
 
D
iff
er
en
ce
 
(km
)
Max Delta-R
 
Figure 2.  TDRS-4 Predicted Accuracy for 1.5–days 
 
 
0.000
0.025
0.050
0.075
0.100
02/17/07 03/01/07 03/13/07 03/25/07 04/06/07 04/18/07 04/30/07 05/12/07 05/24/07 06/05/07
Predicted Generation Date
M
ax
 
Po
si
tio
n
 
Di
ff
er
en
ce
 
(km
)
Max Delta-R
 
Figure 3.  TDRS-5 Predicted Accuracy for 1.5–days 
 
 
 6 
0.000
0.025
0.050
0.075
0.100
02/17/07 03/01/07 03/13/07 03/25/07 04/06/07 04/18/07 04/30/07 05/12/07 05/24/07 06/05/07
Predicted Generation Date
M
ax
 
Po
si
tio
n
 
D
iff
er
en
ce
 
(km
)
TDRS-6 Max Delta-R
 
Figure 4.  TDRS-6 Predicted Accuracy for 1.5–days 
 
 
 
0.000
0.025
0.050
0.075
0.100
02/17/07 03/01/07 03/13/07 03/25/07 04/06/07 04/18/07 04/30/07 05/12/07 05/24/07 06/05/07
Predicted Generation Date
M
ax
 
Po
s
iti
o
n
 
D
iff
er
en
ce
 
(km
) Max Delta-R
 
Figure 5.  TDRS-10 Predicted Accuracy for 1.5–days 
 
 
When the EKF process is not expected to reliably accommodate maneuvers or MUs, GTDS is 
used.  An MU within 2 hours of the normal solution run time automatically triggers the use of 
the GTDS CB.  For stationkeeping maneuvers within 11 to 16 hours of 1300 Greenwich Mean 
Time (GMT), the default EKF epoch time, the GTDS SB alternative is used for all five 
operational TDRSs.  Further automation work is described in the next section. 
 
 
4.  AUTOMATION 
 
As experience was gained in using the EKF, enhancements were made to the automated TDRS 
daily production process.  In particular, added quality assurance (QA) tests were implemented to 
guard against problems from thrusting or range bias shifts.  These tolerances must be passed 
before an automated delivery occurs.  An operational engage-disengage option was also added to 
prevent degraded, EKF deliveries to the Terra Project.  This option keys on both the elapsed time 
since the last thrusting event and the type of thrusting.  If thrusting was too recent, a skip or 
nonoperational condition is enabled, which makes the GTDS solution prime.  Additional 
 7 
adjustments were made to ephemeris comparison tolerances to prevent unnecessary interruption 
to automated Terra deliveries; some of those tolerances were either re-categorized as warnings 
(non-failures) or relaxed and augmented with warnings. 
 
Reducing manual intervention and allowing cost savings are continual incentives for increased 
automation.  Weekend labor reduction or elimination is an added benefit.  The logic flow for 
daily automated deliveries is shown in Figure 6.  After the automation begins, a check for a 
recent maneuver or MU is done.  If thrusting was too recent, GTDS will be used for the delivery 
if its QA checks pass.  If there was no recent thrusting, the EKF will be used for the delivery if 
its QA checks pass.  Once a delivery is done, analysts are notified by pager and/or email. 
 
Begin at
1300 GMT
Recent
MUs and/or
Maneuvers
No
Yes
Pager/Email
Status
Deliver 
Products
GTDS 
Pass
Fail
Manual 
Note:
- All non-routine jobs are done outside TDRS production
- GTDS is for contingency purposes
EKF
Pass
Manual 
Fail
 
 
Figure 6.  Process Flow of TDRS Automation 
 
Based on empirical results, limits were established on the use of EKF in general and during 
special circumstances following MUs or maneuvers.  Required threshold criteria are used in 
monitoring the acceptable percentage of data used by the EKF, which would have avoided at 
least two of the three high TDRS–4 comparisons in Figure 2.  Had that been done, the failure rate 
would have been no more than 1 case in 521, or 0.19%, which is within the 3σ requirement.  For 
the first day after stationkeeping maneuvers, manual intervention is currently necessary.   
 
Beginning in April 2007, Figure 7 shows the progress of the TDRS automation for Terra 
deliveries.  The percentage of daily Terra deliveries that were made automatically for Terra is 
displayed by month.  The July automation rate was 65%.  Maneuvers are expected to limit the 
current automation success rate to 80 or 90%.  Full autonomous daily support, including 
unattended weekend support, began on June 12, 2007. 
 
 8 
 
 
0%
20%
40%
60%
80%
100%
April May June July
  
Figure 7.  Percentage of Autonomous TDRS Deliveries for Terra since April 2007 
 
Work continues to increase the efficiency, the accuracy, and the robustness of the automated 
process.   
 
5.  SUMMARY AND RECOMMENDATIONS 
 
The EKF technique was chosen for the automation of TDRS support because of the relative ease 
for automation of the EKF.  The EKF was implemented as the prime FDF system for routine 
TDRS OD on February 20, 2007.  Automated deliveries to Terra became predominant in July 
2007.  Except for the first day after stationkeeping maneuvers, fully autonomous daily support 
has been in use since June 12, 2007. 
 
The automated process will continue to be refined as experience is gained in its use.  One 
consideration is to investigate further the procedures and techniques applied during periods of 
TDRS orbit perturbation, principally the maneuvers and momentum unloads.  Momentum unload 
modeling may improve with recalibration based on more accurate OD with the EKF.  Another 
investigation might be on improving the solar radiation pressure modeling in the filter, as the 
GTDS modeling is seen to be more responsive. 
 
The decline of the 11–year solar cycle was coincident with the improvement of the EKF 
performance.  A natural question is how the EKF will be affected by the next maximum of the 
11–year solar cycle, when there will be increasing variations in the solar flux and geomagnetic 
indices, which will directly affect TDRSS User OD.   
 
The results presented here show that the accuracies achieved by the automated operational 
support procedures, combining the strengths of both the EKF and GTDS, can meet the TDRS 
 9 
accuracy requirement of 75 meters, 3σ.  The automation also has the additional benefit of 
reducing the needs for both manual processing and weekend labor. 
 
 
6.  REFERENCES 
 
1. K. Dang, D. Ward, S. Slojkowski, J. Dunham, and M. Blizzard, Tracking And Data Relay 
Satellite (TDRS) Orbit Determination Using Chain-Dependent Range Biases, 2005 Flight 
Mechanics Symposium, Greenbelt, Maryland, October 18–20, 2005, NASA/CP–2005–
212789, Session 4, Paper No. 4. 


Tracking and Data Relay Satellite (TDRS) Orbit Estimation Using an Extended Kalman Filter

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server