Validation of the SDP Toolkit Earth Orientation
For Geolocation; Part I - Earth to J2000
Peter D. Noerdlinger
May 14, 1996
This is the first of three reports on the validation of our SDP
Toolkit functions for Earth motion in the J2000 celestial reference
frame. It deals with that topic alone.
The second report (Part II) will deal 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.
Part III will deal with latency problems - the loss of accuracy
attendant on using predicted or out-of-date Earth motion data
or leap seconds data.
---------------------------------------------------------------
SUMMARY
We have validated our Earth position in inertial space (J2000)
to an accuracy of ~6 cm per coordinate against JPL and to about
1 to 16 meters against GSFC, except for problems at GSFC during
leap second intervals, which remain unresolved.
The transformation of velocities was also validated against JPL
to an accuracy of better than a part in a million, which amounts,
for example, to better than 1 cm/s for the spacecraft, or under
3 mm/hour for an Earth point.
In Part II we shall attempt to assess the impact of the GSFC
errors on spacecraft positional data.
Part I depends on the assumption that the Earth motion data file
"$PGSDAT/CSC/utcpole.dat" has been maintained up to date by running,
weekly, the script "$PGSSRC/CSC/update_utcpole.sh", which accesses
Earth rotation data and predictions from the U.S. Naval Observatory.
Therefore, Part III discusses the effect of latency in this process -
the use of out-of-date Earth rotation information due to real-time
processing or to failure to successfully run the script. (Typical
results, hopefully comforting to most users, will be that any
geolocation error due to this cause will be on the order of under
5 meters if the scripts have been run within 90 days).
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INTRODUCTION
The SDP Toolkit has been set up to provide the finest quality
transformation between Earth and Celestial reference frames.
The present report will substantiate that fact.
The transformations we discuss here involve well known
contributions from the precession and nutation of the Earth's
axis, and the steady component of the Earth's diurnal rotation.
These parts are common to virtually all packages of algorithms and
software for orbit determination and geolocation.
Our algorithms and software also take into account the less well
known variable parts of Earth rotation:
1. The deviation of universal time UT1 from UTC, which is
a measure of the deviation of the diurnal axial rotation from
atomic time (a difference that can run up to almost 450 meters).
(Determining UT1 from UTC is equivalent to finding the "Greenwich
Hour Angle." The variation can be visualized as speedups and
slowdowns in axial Earth rotation, interrupted here and there
by 450 m discontinuities in the reference to UTC at leap seconds.)
2. a smaller contribution, called "polar motion," which represents a
shift (about 5 to 17 meters) of the mean solid crust of the Earth in
relation to the true rotation axis or angular momentum vector. In
other words, "Polar Motion" is a displacement of the geographic
North Pole from the more stable rotation pole. It can be visualized
by imagining a flagpole with a pennant affixed to the geographic
North pole - the flagpole will execute an approximate circle about the
rotation pole each day. The size of that circle and the phase of the
motion vary on the timescale of days to a century or more.
The typical range for Polar Motion is about - 6 meters to
+ 5 meters towards Greenwich, and + 5 to + 17 meters at right
angles. (The true rotation pole is displaced -6 to +5 meters
towards Greenwich and 5 to 17 m along 90 degrees West longitude).
Because the true rotation (angular momentum) pole is nearly
stationary, it is far simpler to specify its location in
latitude and longitude than to deal with the diurnal rotation
of the imaginary flagpole. The short term geographic motion
of the true rotation pole is roughly circular, with periods
in the neighborhood of 450 days, so the two components never
add up to more than ~ 17 meters currently, but the mean y
position (90 deg West) has had a more or less steady drift
since 1800 A.D. . If that drift continues, then it will be
all the more important that our Toolkit takes it into account.
The causes of the variations in UT1-UTC and Polar Motion are
geophysical and atmospheric processes.
DATA IMPORTATION
We handle the variable part of the Earth rotation by importing, with
ftp run automatically by a script, data tables from the U.S. Naval
Observatory (seven lines a week).
COMPARISON TO OTHER SYSTEMS
So far as we know, most competitive packages ignore the variable
part of Earth motion, or at best incorporate it by the laborious
and, in principle, error-prone, method of hand copying polynomial
approximations, also from the Naval Observatory.
The cost of operating our system to an accuracy of a few cm is
virtually the same as operating it to an accuracy of 400 meters;
there is little ground in between ignoring the fluctuating part
of Earth motion and bringing in the data tables.
EFFECT ON SPACECRAFT POSITION
Obviously, if the spacecraft ephemeris has been handled or
processed, before we receive it, in a way that uses a different
transformation, then there will be a degradation of the
geolocation functionality. This does not necessarily imply any
failure to meet specifications. Specifications vary from mission
to mission. Our validation work here is mission-independent.
We deliberately aimed for accuracy well beyond what we can
anticipate for the first few EOS and related spacecraft to ensure
upward compatibilty with future missions.
Part II of this analysis will deal with the spacecraft problem.
REFERENCE FRAMES
The Earth frame (which we call "ECR" for "Earth Centered Rotating")
is represented by a Z axis through the geographic North pole
as defined by the International Earth Rotation Service (IERS), an
X axis perpendicular to the Z axis, and through the prime meridian,
and a Y axis forming an orthonormal triad. Conversion to latitude
and longitude is provided by the Toolkit function PGS_CSC_ECRtoGEO(),
and will be accurate to machine precision, although the latitude will
depend on the user's chosen Earth spheroid (such as WGS-84).
The celestial reference frame is the inertial reference frame J2000,
which we call "ECI" for "Earth Centered Inertial". This frame is
defined consistently in the Astronomical Almanac and the IERS Standards.
VALIDATION PROCEDURES AND RESULTS
Almost all software packages and documentation explain the
precession and nutation and they will not be discussed separately
here; all tests against competitive packages are accurate essentially
to machine precision (~ a few mm in geolocation). The tests against
JPL validated all components of the system.
Validation of our ECI to ECR transformations was done against two
sources, GSFC FDF (not TONS) and the Planetary Ephemeris (DE200)
group at JPL.
Here is a summary of what we could validate:
----------------- VALIDATION AGAINST GSFC ----------------------
Greenwich Hour Angle (GHA - equivalent to UT1) was available, but not
during leap second intervals, where the GTDS (Goddard Trajectory
Determination System) appeared to encounter difficulties. Validation
was satisfactory at either side of the 1992 and 1994 leap seconds, but
GSFC could not provide comparisons in Feb, 1996 around the Dec 1995 leap
second, nor reliable validation during any leap second interval.
GSFC comparisons during the 1992 and 1994 leap seconds were confusing
and were referred by GSFC to a contractor.
Our GSFC FDF contact was unable to provide any validation of polar motion.
Subsequently, we have been informed that a polar motion correction is
present in the TONS system; that will be discussed in the second part
of our validation discussion (spacecraft-dependent).
We did not attempt to validate precession, nutation, or the transformation
of velocity against GSFC.
----------------- VALIDATION AGAINST JPL ----------------------
At JPL - Greenwich Hour Angle and Polar Motion were validated at essentially
all times. Actually, even JPL normally does not run its ECR to ECI software
during leap seconds, but they validated our results on each side to 0.0001
second of time in UT1 (100 microseconds) and found no fault with our
continuous and smooth results during the leap seconds.
The 3-coordinate validations against JPL were by actual transformation
of space vectors and velocities from ECR to ECI. We have previously
validated reversibility of our ECR to ECI transformation to machine
accuracy. There is every reason to believe that all our differences
from JPL are due to slight differences in our data tables - the Naval
Observatory frequently improves its older solutions for Earth motion
and we have not seen fit to determine whether we or JPL has the "latest
and greatest" - the errors being so small in any case.
Because the JPL validation was end-to-end on vectors, it includes
precession and nutation as well as UT1 and polar motion.
The following results are expressed in equivalent geolocation error.
Spot checks on velocity against JPL gave at least six figures
agreement.
One second arc translates to 30 Meters Earth position.
----------------- OVERALL VALIDATION RESULTS ------------------
(RMS means root mean square one sigma error)
GSFC
_____________________________________________________________
Greenwich Hour Angle Total ECR-ECI
RMS 54 cm see Note A
Worst Case 1.25 meters (see Note B) see Note A
JPL
_____________________________________________________________
Greenwich Hour Angle Total ECR-ECI
RMS 5.7 cm 10 cm
Worst Case 16 cm 24 cm
Note A: GSFC declined to validate Polar Motion. If we ignore
the omission of polar motion we can multiply the GHA error of
54 cm by the statistical factor 1.732 which results in ~ 1m
error, 3 coordinates; else if we assume that all the polar
motion error propagates to GSFC results, we could assume that
the error is up to 17 m. This problem will be discussed further
in Part II. If the problems during leap seconds persist the
potential error at those times is up to 450 m.
Note B: Because the worst case was almost 4 times worse than the
typical ones, we requested separate validation from JPL for
this exact time, June 21, 1995 at 18 hours UTC. The comparison
ran, for the GHA in degrees:
Goddard 179.462844
SDP Toolkit 179.462833
JPL DE200 group 179.462833
All these errors are relatively small compared to the specifications
for spacecraft ephemeris error, and even more so compared to terrain
effects.
Final Comments on Solar/Lunar/Planetary Positions and Nutation
Note that by providing a most accurate Earth-sky relation,
we guarantee that celestial body positions in Earth centered
coordinates will be virtually of astrometric accuracy. We
are, in that regard, good to 0.03 " arc, each coordinate,
one sigma. 90% of that error is in the error of the 1980
IAU nutation model, which could also be corrected if that
were important - any users who wish to do so can contact us.
Every package of algorithms and software that has come to my
attention assumes that the IAU 1980 (or an even earlier, inferior)
nutation model is valid. Therefore, it was decided early
on that there is no point in importing further coefficients
amounting to <~ 0.03" arc, or less than 1 m equivalent Earth
motion, to "correct" the nutation theory. To do so would put us
OUT of registration with all other workers in this field, such
as GSFC, and put us in the same arena as specialists in space
geodesy and astrometry. In other words, we would have to read
in 2 more coefficients per day but our registration against JPL
would deteriorate from 6 cm per coordinate to 1 m, and against
GSFC the comparison would also deteriorate. The only thing that
would improve is the registration of Earth position against
star catalogs and the like.
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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