1. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20101 Alternative In-Flight Calibration of the GOCE Gradiometer: ESA-L Method Daniel Lamarre Michael Kern ESA

2. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20102 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

3. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20103 Two Main Methods for ICM Determination (Note also the ESA-K/Gradnet method: See poster session by C. Siemes) TAS-IESA-L Implemented in:Ground segmentOff-line Retrieval per:OAGWhole grad’r Computes:ICMsGrad’r parameters Equations:912 Scale factors (SF) found61 by comparing with STR: STR vs Grad’r Misalignment:Assumed nullRetrieved Baselines (Lx Ly Lz):Assumed knownAssumed known Convergence criteria:Per parameterSimultaneous for all parameters Linear/angular couplingAssumed nullSome info could factors:be retrieved

4. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20104 The 12 Equations Used by ESA-L Method Gradients cannot be expressed as linear combination of linear and angular accelerations acting on the spacecraft: V xx =0V yy =0V zz =0 Bandwidth V xy =0V xz =0V yz =0(50 to 100mHz) Estimates of linear accelerations from different OAGs are the same (Michael Kern’s equations): a x14 = a x25 = a x36 Bandwidth a y14 = a y25 = a y36 (50 to 100mHz) a z14 = a z25 = a z36 These and the assumed knowledge of the 3 baselines, ensure coherence between all 18 accelerometer gain estimations.

5. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20105 Comparison with Star Tracker Angular Rates Star TrackerGradiometer Absolute Gain:PerfectWrong Gains along 3 axes:SameSame Reference frame:PerfectOrthogonal 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

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7. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20107 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

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9. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20109 Calibrations Performed in Latest Configuration ShakingDateAvailable Star Trackers #3Oct/2009STR1, STR2 #4Jan/2010STR1, STR3 #5Mar/2010STR1, STR2 #6May/2010STR1, STR2 Merging of the 2 available star trackers with a least square algorithm from C. Siemes  Yields a ‘virtual star tracker’ STRV

10. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 201010 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

11. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 201011 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

12. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 201012 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

13. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 201013 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.

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18. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 201018 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

19. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 201019 ICM Comparison: ESA-L 6 th vs 3 rd 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

20. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 201020 Evolution of In-Line Differential Scale Factors OAG14: Vxx OAG25: Vyy OAG36:Vzz

21. Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 201021 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