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Alternative In-Flight Calibration of the GOCE Gradiometer: ESA-L Method Daniel Lamarre

Alternative In-Flight Calibration of the GOCE Gradiometer: ESA-L Method Daniel Lamarre Michael Kern ESA. Topics Differences between TAS-I & ESA-L methods Comparison between TAS-I & ESA-L results Improvement of scale factor retrieval with star tracker combination

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Alternative In-Flight Calibration of the GOCE Gradiometer: ESA-L Method Daniel Lamarre

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  1. Alternative In-Flight Calibration of the GOCE Gradiometer: ESA-L Method Daniel Lamarre Michael Kern ESA Living Planet Symposium Bergen June 2010

  2. Topics Differences between TAS-I & ESA-L methods Comparison between TAS-I & ESA-L results Improvement of scale factor retrieval with star tracker combination Evolution of gradiometer parameters Living Planet Symposium Bergen June 2010

  3. Two Main Methods for ICM Determination (Note also the ESA-K/Gradnet method: See poster session by C. Siemes) TAS-I ESA-L Implemented in: Ground segment Off-line Retrieval per: OAG Whole grad’r Computes: ICMs Grad’r parameters Equations: 9 12 Scale factors (SF) found 6 1 by comparing with STR: STR vs Grad’r Misalignment: Assumed null Retrieved Baselines (Lx Ly Lz): Assumed known Assumed known Convergence criteria: Per parameter Simultaneous for all parameters Linear/angular coupling Assumed null Some info could factors: be retrieved Living Planet Symposium Bergen June 2010

  4. The 12 Equations Used by ESA-L Method Gradients cannot be expressed as linear combination of linear and angular accelerations acting on the spacecraft: Vxx=0 Vyy=0 Vzz=0 Bandwidth Vxy=0 Vxz=0 Vyz=0 (50 to 100mHz) Estimates of linear accelerations from different OAGs are the same (Michael Kern’s equations): ax14 = ax25 = ax36 Bandwidth ay14 = ay25 = ay36 (50 to 100mHz) az14 = az25 = az36 These and the assumed knowledge of the 3 baselines, ensure coherence between all 18 accelerometer gain estimations. Living Planet Symposium Bergen June 2010

  5. Comparison with Star Tracker Angular Rates Star TrackerGradiometer Absolute Gain: Perfect Wrong Gains along 3 axes: Same Same Reference frame: Perfect Orthogonal but rotated about 3 axes By best fit are retrieved: Gradiometer single scale factor Fixed rotations of grad’r about x, y and z Best fit performed in bandwidth: ~ 0.7 to 2.0mHz Living Planet Symposium Bergen June 2010

  6. Living Planet Symposium Bergen June 2010

  7. Star Tracker Systematic Errors - FOV dependent errors appear as orbital harmonics on a short time scale - Impacts retrieval of gradiometer absolute scale factor - Can be reduced by: 1) Removing orbital harmonics in comparison between gradiometer & star tracker angular rates 2) Combining readings from 2 (or 3) star trackers Living Planet Symposium Bergen June 2010

  8. Living Planet Symposium Bergen June 2010

  9. Calibrations Performed in Latest Configuration Shaking Date Available Star Trackers #3 Oct/2009 STR1, STR2 #4 Jan/2010 STR1, STR3 #5 Mar/2010 STR1, STR2 #6 May/2010 STR1, STR2 Merging of the 2 available star trackers with a least square algorithm from C. Siemes  Yields a ‘virtual star tracker’ STRV Living Planet Symposium Bergen June 2010

  10. Comparison of ad14x (Vxx) ICM rows: Absolute Values ESA-L Values: SHK3: 0.0175226 0.0000121 -0.0000082 1.0237767 -0.0000237 0.0000577 SHK4: 0.0176962 0.0000123 -0.0000068 1.0239178 -0.0000294 0.0000638 SHK5: 0.0177480 0.0000120 -0.0000066 1.0236419 -0.0000240 0.0000558 SHK6: 0.0178763 0.0000116 -0.0000051 1.0235056 -0.0000286 0.0000640 TAS-I Values: SHK3: 0.0172522 0.0000126 -0.0000110 1.0075948 0.0000000 0.0000366 SHK4: 0.0180007 0.0000129 -0.0000099 1.0416350 0.0000000 0.0000366 SHK5: 0.0177637 0.0000125 -0.0000093 1.0246993 0.0000000 0.0000359 SHK6: 0.0181930 0.0000126 -0.0000083 1.0417186 0.0000000 0.0000368 ESA-L Variations (ppm): SHK4vs3: 174 0 1 141 -6 6 SHK5vs4: 52 0 0 -276 5 -8 SHK6vs5: 128 0 1 -136 -5 8 TAS-I Variations (ppm): SHK4vs3: 749 0 1 34040 0 0 SHK5vs4: -237 0 1 -16936 0 -1 SHK6vs5: 429 0 1 17019 0 1 ESA-L vs TAS-I (ppm): SHK3: 270 0 3 16182 -24 21 SHK4: -305 -1 3 -17717 -29 27 SHK5: -16 0 3 -1057 -24 20 SHK6: -317 -1 3 -18213 -29 27 Living Planet Symposium Bergen June 2010

  11. Comparison of ad14x (Vxx) ICM rows: Relative values (ie each row divided by CSF) ESA-L Values: SHK3: 0.0171156 0.0000118 -0.0000080 1.0000000 -0.0000232 0.0000563 SHK4: 0.0172828 0.0000120 -0.0000067 1.0000000 -0.0000287 0.0000623 SHK5: 0.0173381 0.0000117 -0.0000064 1.0000000 -0.0000234 0.0000545 SHK6: 0.0174658 0.0000113 -0.0000050 1.0000000 -0.0000279 0.0000625 TAS-I Values: SHK3: 0.0171221 0.0000125 -0.0000109 1.0000000 0.0000000 0.0000364 SHK4: 0.0172812 0.0000124 -0.0000095 1.0000000 0.0000000 0.0000352 SHK5: 0.0173355 0.0000122 -0.0000091 1.0000000 0.0000000 0.0000350 SHK6: 0.0174644 0.0000121 -0.0000079 1.0000000 0.0000000 0.0000354 ESA-L Variations (ppm): SHK4vs3: 167 0 1 0 -6 6 SHK5vs4: 55 0 0 0 5 -8 SHK6vs5: 128 0 1 0 -4 8 TAS-I Variations (ppm): SHK4vs3: 159 0 1 0 0 -1 SHK5vs4: 54 0 0 0 0 0 SHK6vs5: 129 0 1 0 0 0 ESA-L vs TAS-I (ppm): SHK3: -6 -1 3 0 -23 20 SHK4: 2 0 3 0 -29 27 SHK5: 3 0 3 0 -23 20 SHK6: 1 -1 3 0 -28 27 Living Planet Symposium Bergen June 2010

  12. Comparison of Results ESA-L vs TAS-I - Excellent agreement for differential parameters - Excellent agreement for common misalignments - ESA-L retrieved common scale factors much more stable Living Planet Symposium Bergen June 2010

  13. Why should we use the ESA-L retrieved scale factors ? • In principle, ESA-L method is more robust because only 1 scale factor is retrieved, and grad’r vs star tracker misalignment is retrieved as well. • ESA-L gives more stable results, property more often associated with more accurate method than with less accurate method. • ESA-L gives results more in-line with expected stability. • ESA-L results are more consistent with the variation of differential parameters. • ESA-L results are ‘validated’ by external calibration investigations. Living Planet Symposium Bergen June 2010

  14. Living Planet Symposium Bergen June 2010

  15. Living Planet Symposium Bergen June 2010

  16. Living Planet Symposium Bergen June 2010

  17. Living Planet Symposium Bergen June 2010

  18. Conclusion wrt Comparison with Star Tracker • Fusion of data from 2 star trackers improves significantly scale factor & misalignment retrieval • Filtering of orbital harmonics helps a lot if data from only 1 star tracker is available Living Planet Symposium Bergen June 2010

  19. ICM Comparison: ESA-L 6th vs 3rd Shakings, STRV. Difference (ppm) OAG14 271 5 -6 -354 1 -3 -4 851 0 0 -224 3 6 0 259 3 -2 -249 Vxx -354 1 -3 271 5 -6 0 -224 3 -4 851 0 3 -2 -249 6 0 259 OAG25 521 -9 1 141 -2 -1 8 474 -1 1 190 1 0 1 925 3 -1 81 141 -2 -1 521 -9 1 Vyy  1 190 1 8 474 -1 3 -1 81 0 1 925 OAG36 653 -1 -3 15 1 1 0 1181 1 0 -17 1 2 -1 624 0 -1 10 15 1 1 653 -1 -3 0 -17 1 0 1181 1 Vzz  0 -1 10 2 -1 624 Living Planet Symposium Bergen June 2010

  20. Evolution of In-Line Differential Scale Factors OAG14: Vxx OAG25: Vyy OAG36:Vzz Living Planet Symposium Bergen June 2010

  21. Conclusion Concerning Grad’r Evolution • Alignment is very stable • Common scale factor variation ~< 100 ppm/month • Differential scale factor variation seems continuous: • Vxx < 50 ppm/month • Vyy < 30 ppm/month • Vzz < 2 ppm/month • Interpolation between shakings should be investigated: • - Eg external calibration, or ESA-K (Gradnet) method • - Can take advantage of stable alignment Living Planet Symposium Bergen June 2010

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