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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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.

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20106

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 20108

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June Comparison of ad14x (Vxx) ICM rows: Absolute Values ESA-L Values: SHK3: SHK4: SHK5: SHK6: TAS-I Values: SHK3: SHK4: SHK5: SHK6: ESA-L Variations (ppm): SHK4vs3: SHK5vs4: SHK6vs5: TAS-I Variations (ppm): SHK4vs3: SHK5vs4: SHK6vs5: ESA-L vs TAS-I (ppm): SHK3: SHK4: SHK5: SHK6:

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June Comparison of ad14x (Vxx) ICM rows: Relative values (ie each row divided by CSF) ESA-L Values: SHK3: SHK4: SHK5: SHK6: TAS-I Values: SHK3: SHK4: SHK5: SHK6: ESA-L Variations (ppm): SHK4vs3: SHK5vs4: SHK6vs5: TAS-I Variations (ppm): SHK4vs3: SHK5vs4: SHK6vs5: ESA-L vs TAS-I (ppm): SHK3: SHK4: SHK5: SHK6:

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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.

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June ICM Comparison: ESA-L 6 th vs 3 rd Shakings, STRV. Difference (ppm) OAG Vxx  OAG Vyy  OAG Vzz 

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

Gradiometer In-Flight Calibration Living Planet Symposium Bergen June 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