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."
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