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 Part III will deal with latency problems - the loss of accuracy attendant on using predicted or out-of-date Earth motion data or leap seconds data.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 Therefore, Part III discusses the effect of latency in this process - the use of out-of-date Earth rotation information due to real-time processing or to failure to successfully run the script.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). --------------------------------------------------------------- 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."