Validation of the SDP Toolkit Earth Orientation For Geolocation; Part II - Spacecraft Ephemeris Considerations Peter D. Noerdlinger May 16, 1996 This is the second of three reports on the validation of our SDP Toolkit functions for Earth motion in the J2000 celestial reference frame. It deals with our understanding of how the TRMM and AM1 spacecraft ephemeris data are processed before we receive them, and how that processing relates to our transformation between Earth and J2000 Celestial coordinates -i.e. with the impact on the accuracy of the spacecraft position in relation to Earth. Thus, the report can be viewed as an attempt to estimate any part of the spacecraft positional error that can be attributed to different assumptions or algorithms between the Toolkit and the providers. Because this report is based on conversations with and exchange of e-mail with FDF, TDRSS, and TONS personnel at GSFC it is less definitive than Part I, which was based on actual numerical computations. Nevertheless, it is believed that the statements herein are reliable. In Part I it was explained that our Earth position in relation to inertial space (J2000) is accurate to 10 cm, 3 coordinates, 1 sigma, provided that the Earth motion data files are up to date. Part III will deal with the effect of using predicted or out- of-date Earth motion data. --------------------------------------------------------------- SUMMARY AM1: From study of the TDRSS On Board Navigation System (TONS) handbook and discussions with the TONS and TDRS Orbit Determination staff, it is concluded that the error in locating the AM1 spacecraft in relation to Earth points due to the combined effect of our SDP Toolkit transformations between Earth centered rotating (ECR) and the methods used by TONS to reduce the original ephemeris data to J2000 will generally amount to about 1 meter or less, 1 coordinate, 1 sigma. This error is basically a TONS estimate of the effect of polar motion on the TONS system and is included in the TONS error budget. Users should therefore refer to the overall AM1 error budget as expressed elsewhere - the present discussion mainly confirms that our Toolkit transformations are basically consistent with the AM1 orbit determination system. Nevertheless, the Goddard Trajectory Determination System is used for portions of the TDRSS orbit determination, and it is our impression, as explained in Part I, that said system, which depends on hand entry of polynomial coefficients, is susceptible to further random error of about 0.5 - 1.2 meters and larger, transient problems at leap seconds, always in the East- West direction. Therefore, although the averaging processes inherent in orbit fitting will tend to smooth away any resulting error, and we express overall confidence in the TDRSS system, it is not possible with the information at hand to independently set an absolute upper bound on the error. TRMM: From discussions with FDF and the TDRSS orbit determination staff, it appears likely that a considerable part - perhaps all - of the error in neglecting Polar Motion for TRMM will propagate from an error in Earth position within J2000 to an error in spacecraft ephemeris. It is possible that this could represent an error of up to 17 meters in addition to whatever was previously included in the TRMM error budget. Because the spacecraft position and velocity will already have been reduced in the absence of the polar motion correction, there does not appear to be an opportunity to correct them after the fact. Similar remarks about additional errors due to use of polynomials and at leap seconds pertain as above for AM1. --------------------------------------------------------------- INTRODUCTION To understand the analysis, please keep in mind that the spacecraft data are in both cases (AM1 and TRMM) obtained in some way through the use of the TDRS spacecraft. In turn, the TDRS positions are, and in fact must be, determined in J2000, because programs that model spacecraft orbits such as TRDS depend on fitting integrations in inertial space to measurements from ground stations. In turn, the instantaneous inertial positions of ground stations in J2000 will be as accurate as the underlying determination of Earth position. Cognizant of this situation, the TDRS staff have endeavored to include the effects of polar motion and UT1 - UTC (as explained in Part I) in their orbit determination. We can expect that their accuracy for the TDRS orbit is of the order of ~ 1m most of the time, perhaps a bit worse at leap seconds. Because orbit fitting schemes generally average over some time, the problem of transients at leap seconds can be expected to be greatly mitigated. Therefore we have no reason to question the quoted TDRS orbit accuracies beyond our general, minor, reservation on the use of hand copied polynomials. Given that the TDRS orbits are quite accurate, then the orbit determination accuracy for AM1 and TRMM depends on the details of the telemetry links and the reduction of the resulting data. We will be given the AM1 positions directly in J2000, which minimizes any possible problems, because our Toolkit uses all spacecraft ephemeris data in J2000. Since the TRMM ephemeris will come to us in True of Reference Coordinates, there is opportunity for error not only in the original data, but in any inconsistency between the way the TRMM processing system handles its Earth position data in inertial space and the way we do in the SDP Toolkit. DETAILS FOR THE AM1 and TRMM SPACECRAFT TONS and AM1: The TONS system depends on two-way ranging that is said to be quite insensitive to errors from UT1 - UTC or polar motion. According to TONS analysis, for example, only the change in the polar motion contribution to the Doppler measurement during the 16 second averaging interval contributes to actual error in TONS. That is in part because a two-way Doppler measurement is used. TRMM and White Sands: On the other hand, the TRMM orbits are determined by ranging from White Sands through TDRS to TRMM. As a backup method (in case of problems in contact via TRDS - such as line-of- sight or transmission problems) direct ground station ranging may be used. Since neither White Sands nor FDF corrects the ground station position for polar motion in TRMM operations, the backup method would appear to bring in polar motion as an error. But this method would be used infrequently at most. Consider, then, the method utilizing TDRS. To the best of our information, even though the TDRS position (see above under AM1) is corrected for polar motion, because one-way ranging through TDRS to TRMM is used, the ground station position error can still propagate to error in the TRMM ephemeris. According to FDF, polar motion is only of order + or - 5 meters. But according to our data tables (from the U.S. Naval Observatory) and to the I.E.R.S. 1995 Annual Report, the maximum polar motion in recent years was a 17 meter displacement. We can then expect that there may be an error of up to 17 meters in the TRMM position, which may have been budgeted as a 5 meter error or not have been included in the budget. Further inquiries on this would have to be referred to FDF. We have entered this area with some reservations, because it is not within our purview to assess the accuracy of incoming spacecraft data. But because we do transform the data in certain ways, we have felt it necessary to ascertain if our processing is consistent or not with prior processing. Because the transformations between True of Date or True of Epoch and J2000 are so widely understood and agreed upon, we do not anticipate any inconsistency in that part of handling the TRMM data. It is to be emphasized again that the Earth motions embodied in UT1-UTC and polar motion are entirely distinct from the transformations between True of Date or True of Epoch and J2000. Obviously, since we carry within the Toolkit the daily values for UT1 - UTC and Polar Motion (Part I), it would in principle be possible for us to correct the TRMM ephemeris for the error in polar motion, if it were a simple displacement in two angles. But the error is certainly convolved with the method of orbit determination in a way that we could not unravel, and it is not within our scope to attempt to correct incoming spacecraft data. Peter D. Noerdlinger [Senior Scientist - EOSDIS Project] Applied Research Corp. c/o HITC 1616 McCormick Drive Upper Marlboro, MD 20774-5372 tel: (301) 925-0776 FAX: (301) 925-0321 (Telephone to confirm - machine is unattended) e-mail: pnoerdli@eos.hitc.com "Take care of the nanoseconds and the milliseconds will take care of themselves."