The ASI/CGS solutions AWG “Benchmark” Pilot Project R.Devoti, V.Luceri

1. The ASI/CGS solutions AWG “Benchmark” Pilot Project R.Devoti, V.Luceri ILRS Analysis Working Group. 3-4 October 2002, Greenbelt (MD), USA

2. Contribution status Solution types • A solutions: nominal model (Initial orbit, nothing adjusted) • B solutions: Fixed EOP and station coordinates (orbit adjustment) • C solutions: Final orbit ( all adjusted : orbit, station positions, biases, EOP) Contributing agencies

3. Smoothed solA residuals First 3 days Last 3 days

4. Smoothed RMS of solA residuals First 3 days Last 3 days

5. solA residuals statistics Correlation coefficients Gray area: no site ID available for NASDA, the time matching is inferred.

6. RESIDUAL SPECTRA w.r.t. nominal orbit (solA) Four cycles per revolution Once per day Once per revolution I IV Twice per revolution IV II I II III III Three cycles per revolution

7. Range residuals distribution per site (solA) Sites with > 200 NP

8. solB residuals statistics JCET AUSLIG CSR Residuals (m) Residuals (m) Residuals (m) NASDA NERC IAAK ASI Residuals (m) Residuals (m) Residuals (m) Residuals (m)

9. solB residuals statistics (cont.d) Correlation coefficients Gray area: no site ID available for NASDA, the time matching is inferred.

10. Hypothesis testing for solB residuals 2 -test (same distributions) Null hypothesis: two data sets are drawn from the same population distribution. Level of significance: 1% F-test (same variance) Student’s t-test (same mean) Null hypothesis: two data sets are drawn from populations having the same mean. Level of significance: 1% Null hypothesis: two data sets are drawn from populations having the same variance. Level of significance: 1% R: Rejected, the null hypothesis has been disproved. C: Compatible, the null hypothesis has NOT been disproved. C*: Rejected using the full data set, but compatible after a mild outlier editing (<0.2%).

11. solC residuals statistics ASI JCET IAAK Residuals (m) Residuals (m) Residuals (m) NERC DGFI AUSLIG Residuals (m) Residuals (m) Residuals (m)

12. solC residuals statistics (cont.d) Correlation coefficients

13. Hypothesis testing for solC residuals 2 -test (same distributions) Null hypothesis: two data sets are drawn from the same population distribution. Level of significance: 1% F-test (same variance) Student’s t-test (same mean) Null hypothesis: two data sets are drawn from populations having the same mean. Level of significance: 1% Null hypothesis: two data sets are drawn from populations having the same variance. Level of significance: 1% R: Rejected, the null hypothesis has been disproved. C: Compatible, the null hypothesis has NOT been disproved. C*: Rejected using the full data set, but compatible after a mild outlier editing (<0.2%) C**: Rejected using the full data set, but compatible after a strong outlier editing (<10%)..

14. Orbit differences w.r.t. CSR orbit - solA Radial coordinates Cross coordinates Along coordinates RMS of Cross coord. residuals RMS of Radial coord. residuals RMS of Along coord. residuals

15. Orbit differences w.r.t. CSR orbit - solA Radial velocities Cross velocities Along velocities RMS of Radial vel. residuals RMS of Cross vel. residuals RMS of Along vel. residuals

16. Nerc CRL Spectral analysis (radial, cross, along) solA

17. Orbit differences w.r.t. CSR orbit - solA Pos. rms Agency Min Max Mean rms Min Max Mean rms Min Max Mean rms 6.374 CRL -0.827 0.842 0.008 0.347 -12.93 0.420 -5.253 6.274 -2.069 2.295 0.008 1.068 3.344 AUSLIG -0.106 0.114 0.003 0.050 -6.139 0.523 -2.669 3.244 -1.443 1.403 0.000 0.810 3.344 JCET -0.105 0.114 0.003 0.050 -6.137 0.529 -2.669 3.244 -1.447 1.408 0.000 0.810 3.373 IAA -0.056 0.068 0.003 0.027 -5.997 -0.020 -2.913 3.349 -0.894 0.855 -0.006 0.398 2.963 NERC -0.102 0.109 0.003 0.045 -5.367 -0.069 -2.555 2.946 -0.810 0.768 -0.007 0.317 1.794 NASDA -0.163 0.166 0.002 0.064 -3.737 0.197 -1.405 1.754 -0.865 0.842 -0.010 0.374 Agency Mean rms Vel. rms Mean rms Mean rms CRL 0.002580 0.003068 0.003414 -0.000057 0.001028 -0.000101 0.001090 AUSLIG 0.001312 0.001594 0.001635 0.000008 0.000356 -0.000064 0.000068 JCET 0.001312 0.001594 0.001635 0.000008 0.000356 -0.000064 0.000068 IAA 0.001432 0.001646 0.001653 0.000002 0.000143 -0.000022 0.000029 NERC 0.001256 0.001448 0.002027 0.000006 0.000927 -0.000022 0.001075 NASDA 0.000690 0.000860 0.000868 -0.000006 0.000115 -0.000015 0.000038 Position: Radial (m) Cross-track (m) Along-track (m) Velocity: Radial (m/s) Cross-track (m/s) Along-track (m/s)

18. Orbit differences w.r.t. CSR orbit - solA Semi-major axis Eccentricity Inclination Node Perigee+mean anomaly

19. Spectral analysis solA (keplerian elements)

20. Orbit differences w.r.t. CSR orbit - solA Agency Mean rms Mean rms Mean rms Mean rms Mean rms Agency Scale X (mas) Y(mas) Z(mas) CRL -0.578 6.347 -0.0365 0.4011 -0.01856 0.02778 -0.00255 0.03034 -0.08971 0.10725 CRL 0.000739 1.058 1.290 -52.158 AUSLIG -0.366 0.372 -0.0234 0.0240 -0.01648 0.01737 0.00018 0.00620 -0.04501 0.05515 AUSLIG 0.000270 0.538 0.863 -27.585 JCET -0.366 0.372 -0.0234 0.0240 -0.01648 0.01737 0.00018 0.00620 -0.04501 0.05515 JCET 0.000272 0.538 0.863 -27.591 IAA -0.120 0.145 -0.0078 0.0095 0.00099 0.00591 -0.00137 0.00642 -0.04976 0.05713 IAA 0.000268 0.556 0.896 -28.942 -0.0078 0.3989 NERC -0.120 6.322 0.00050 0.01843 0.00005 0.02839 -0.04313 0.05108 NERC 0.000222 0.392 0.730 -26.365 -0.0054 0.0095 NASDA -0.084 0.129 -0.00361 0.00594 -0.00312 0.00492 -0.02500 0.03074 NASDA 0.000167 0.371 0.498 -12.111 Axis(m) Ecc (arcsec) Incl (arcsec) Node (arcsec) W+M (arcsec) Scale and rotation parameters

21. Orbit differences w.r.t. CSR orbit - solB Radial coordinates Cross coordinates Along coordinates RMS of Cross coord. residuals RMS of Radial coord. residuals RMS of Along coord. residuals

22. Orbit differences w.r.t. CSR orbit - solB Radial velocities Cross velocities Along velocities RMS of Radial coord. residuals RMS of Cross coord. residuals RMS of Along coord. residuals

23. Spectral analysis (radial, cross, along) solB

24. Orbit differences w.r.t. CSR orbit - solB Mean rms Pos. rms Agency Mean rms Mean rms 0.000 0.035 0.043 CRL 0.000 0.005 0.003 0.025 0.056 0.300 0.371 AUSLIG 0.001 0.094 0.002 0.196 0.036 0.269 0.343 JCET 0.000 0.094 0.001 0.193 -0.005 0.065 0.083 IAA 0.000 0.016 0.000 0.049 0.002 0.033 0.043 0.000 0.028 NERC 0.000 0.005 0.084 0.258 0.394 0.005 0.284 NASDA 0.001 0.088 Agency Mean rms Mean rms Mean rms Vel. rms CRL 0.000000 0.000017 0.000001 0.000919 -0.000027 0.001075 0.001414 AUSLIG -0.000027 0.000125 -0.000000 0.000073 0.000006 0.000041 0.000151 JCET -0.000017 0.000107 0.000000 0.000075 0.000006 0.000041 0.000137 IAA 0.000002 0.000029 0.000001 0.000044 -0.000028 0.000029 0.000060 0.000001 0.000918 NERC -0.000001 0.000016 -0.000027 0.001075 0.001414 -0.000001 0.000123 NASDA -0.000041 0.000104 -0.000004 0.000041 0.000166 Position: Radial (m) Cross-track (m) Along-track (m) Velocity: Radial (m/s) Cross-track (m/s) Along-track (m/s)

25. Orbit differences w.r.t. CSR orbit - solB Semi-major axis Eccentricity Inclination Node Perigee+mean anomaly

26. Orbit differences w.r.t. CSR orbit - solB (without NERC and CRL) Semi-major axis Eccentricity Inclination Node Perigee+mean anomaly

27. Spectral analysis (keplerian elements) Semi-major axis Eccentricity Inclination Node Perigee+mean anomaly

28. Orbit differences w.r.t. CSR orbit - solB Agency Mean rms Mean rms Mean rms Mean rms Mean rms CRL -0.160 6.321 -0.0101 0.3988 -0.00095 0.01781 -0.00013 0.02787 -0.00006 0.01042 AUSLIG 0.035 0.045 0.0021 0.0070 0.00024 0.00131 0.00036 0.00433 0.00108 0.00556 Agency Scale X (mas) Y(mas) Z(mas) JCET 0.038 0.048 0.0023 0.0071 0.00037 0.00131 0.00021 0.00431 0.00067 0.00491 CRL -0.00000600 -0.01492 0.23543 0.04877 IAA -0.166 0.168 -0.0105 0.0106 -0.00072 0.00124 0.00011 0.00128 -0.00004 0.00119 AUSLIG 0.00005559 0.04111 0.35402 0.31044 -0.0100 0.3989 NERC -0.159 6.323 -0.00094 0.01779 -0.00035 0.02788 -0.00010 0.01047 JCET 0.00004332 0.02035 0.34329 0.21007 NASDA -0.019 0.087 -0.0012 0.0083 -0.00093 0.00343 -0.00023 0.00589 0.00132 0.00496 IAA 0.00001460 0.09166 0.41094 -0.13016 NERC 0.00000328 -0.06537 0.26682 0.24845 NASDA 0.00007115 0.13963 0.24991 1.04482 Axis(m) Ecc (arcsec) Incl (arcsec) Node (arcsec) W+M (arcsec) Scale and rotation parameters

29. Remarks • General: • The model parameters MUST be common to all groups. The adoption of exactly the same parametrization is mandatory to allow a homogeneous comparison. • Common reference frame, e.g. in a reduction run Geodyn never computes orbits in the ECEF frame! To avoid confusion (from external S/W bugs) a common TOD-ECEF transformation routine should be adopted in the benchmark.

30. Remarks (cont.d) RANGE RESIDUALS solA: Geodyn users have best ‘unbiased’ residuals (tailor effect!). CSR has the best long term rms (1.5 m), followed by ASI and NASDA (2 m) and finally NERC, IAAK, AUSLIG and JCET (2.8 m). solB: substantial disagreement in the residual distributions due to different modelization, Geodyn users are consistent. solC: as in solB, differences due to modelization. Geodyn users are moderately consistent. • ORBITS • solA: consistent radial positions with the exception of CRL, ‘anomalous’ cross-track positions for CRL, AUSLIG and JCET. NERC and CRL have a strong once-per-day (and their linear combinations with the once-per-revolution) oscillations in the cross- and along-track velocity. The NASDA solution demonstrate a long-term (15 days?) ondulation. • solB: positions agree within 1 m, roughly two consistent groups: 1) NASDA, AUSLIG and JCET, 2) IAAK, NERC and CRL. Velocities, same behaviour as for solA.