Error drift in the ERTS orbit maintenance problem is determined from the actual ground trace errors that the spacecraft experienced over the first 3 1/2 repeat cycles. Actual data are fitted to a parametric model of ground trace error by a least squares method, and initial offsets to these key parameters as well as their rates of change are extrapolated forward analytically to obtain the future ground trace drift in orbital estimates

Fuchs, A. J.

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ERTS ORBIT MAINTENANCE 
Arthur J. Fuchs 
The ERTS orbit maintenance problem arises from the requirements on the ERTS spacecraft 
to repeat its orbit every 18 days to within a tolerance of * 18.5 kilometers for a one-year 
period, and to maintain the orbit in a sun-synchronous mode. In Figure 1 are the error 
sources that might cause the ground trace to drift outside of the tolerance bounds. 
The ERTS requirements, particularly the ground trace requirement, are very sensitive to 
small errors in the orbit and the dynamic model. The first three items, uncertainty in 
orbit determination, orbit adjust performance errors, and dynamic model uncertainties, 
are very common. They give rise to errors in both knowing what the orbit is and in predict- 
ing the orbit drifts. 
Let me dwell for a moment on the fourth item - the unmodeled errors. In designing an 
orbit maintenance procedure, we were concerned about a number of possible unmodeled 
errors, such as fuel leaks in the orbit adjust system, fuel leaks in the attitude control system, 
and uncoupled thrusts in the attitude control system. This last item turned out to be 
extremely important. One approach that we could have taken in maintaining the orbit 
was to choose the best dynamic model possible in the design of an orbit, that would 
satisfy the requirements for a one-year period, and to continually correct to  this orbit if 
we drift outside our tolerances. 
In light of the sensitivity of the requirements to small errors, we felt this procedure would 
require frequent corrections and we looked for another approach. In doing this we asked: 
Is there other information available that we may utilize? Another requirement that we 
have for the ERTS project is to determine the position of the spacecraft in its orbit very 
accurately for the ground data handling system, or specifically for the data processing 
facility. We made use of this information. 
In Figure 2, the solid line on the lower portion of the curve represents the actual ground 
trace errors that the spacecraft experienced over the first 3% repeat cycles. We’ve modeled 
0 UNCERTAINTY IN ORBIT DETERMINAT~O 
0 ORBIT- ADJUST SYSTEM PERFORMANCE ERRORS 
0 DYNAMIC MODEL. UNCERTAINTIES 
0 UNMOOELEO ERRORS 
Figure 1. ERTS requirements error sources. 
129 
https://ntrs.nasa.gov/search.jsp?R=19730019115 2020-03-17T08:56:31+00:00Z
these ground trace errors in terms of some key parameters, namely the mean semi-major 
axis and inclination and their rates of change. We fit the actual data to our model in a 
least squares sense, and deduce from the data the initial offsets to these key parameters as 
well as their rates of change. We can then extrapolate forward analytically what the drift 
in the ground trace is going to be in the future. 
As you can see from Figure 2, the ground trace error rapidly exceeded the 18.5 kilometer 
tolerance. The value of da/dt = 2.79 (times the nominal semi-major axis decay) is 
interesting. The nominal decay is based upon our model of atmospheric drag, solar 
pressure, and so on. The actual data tell us that the spacecraft is experiencing a decay 
almost three tunes this value. Although in implementing this procedure it is not 
necessary to know the cause of the increased rate of change, this can be examined a 
posteriori. We now know that this dynamic behavior is due to the spacecraft attitude 
control system thrusting on a regular basis. How can we use this information? 
In Figure 3, the solid line on the left is the same ground trace error of Figure 2 drawn to a 
different scale. Recall that the tolerance on this error is k 18.5 kilometers. We hypothesize 
that our best estimate of what the orbit is going to do in the future can be based on what 
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Figure 2. Orbit maintenance, least squares solution. 
130 
it has done in the past. By using the dynamic behavior determined over the actual part of 
the orbit, we can easily compute a correction to the orbit. This correction will reverse the 
error drift to keep our requirements within the k 18.5 kilometer bounds. Approximately 
one month prior to the time when the ground trace would have exceeded the bounds, we 
notified the ERTS Project of the drift and decided on a time to make a maneuver. 
The curve which is labeled “best-estimate orbit” is an extrapolation of this correction, 
using the dynamic behavior deduced from the actual data in our analytic model. The 
curved solid line represents actual data points that have been determined since the cor- 
rection was made. As you can see, we’re tracking this curve very well. By implementing 
this procedure we feel that we can limit the frequency of corrections and the amount of 
fuel that we’ll have to use in maintaining the ERTS orbit. 
BEST-ESTIMATE 
REPEAT CYCLES 
Figure 3. Actual and predicted ground trace history. 
131 


ERTS orbit maintenance

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