alternative in-flight calibration of the goce gradiometer: esa-l method daniel lamarre

Living Planet Symposium Bergen June 2010 1

Gradiometer In-FlightCalibration

Alternative In-Flight Calibration of the GOCE

Gradiometer: ESA-L Method

Daniel LamarreMichael Kern

ESA



Topics

Differences between TAS-I & ESA-L methods

Comparison between TAS-I & ESA-L results

Improvement of scale factor retrievalwith star tracker combination

Evolution of gradiometer parameters



Two Main Methods for ICM Determination (Note also the ESA-K/Gradnet method: See poster session by C. Siemes)

TAS-I ESA-LImplemented in: Ground segmentOff-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 forall parameters

Linear/angular coupling Assumed null Some info could factors: be retrieved



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.



Comparison with Star Tracker Angular Rates

Star Tracker Gradiometer

Absolute Gain: Perfect Wrong

Gains along 3 axes: Same Same

Reference frame: Perfect Orthogonal but rotatedabout 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



Star Tracker Systematic Errors- FOV dependent errors appear as orbital harmonicson a short time scale

- Impacts retrieval of gradiometer absolute scale factor

- Can be reduced by:

1) Removing orbital harmonics in comparison betweengradiometer & star tracker angular rates

2) Combining readings from 2 (or 3) star trackers



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



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



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



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



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.



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



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



Evolution of In-Line Differential Scale Factors OAG14: Vxx OAG25: Vyy OAG36:Vzz



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

alternative in-flight calibration of the goce gradiometer: esa-l method daniel lamarre

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