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

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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=0Vyy=0Vzz=0 Bandwidth

Vxy=0Vxz=0Vyz=0(50 to 100mHz)

Estimates of linear accelerations from different OAGs are the same (Michael Kern’s equations):

ax14 = ax25 = ax36Bandwidth

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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

  • 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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

  • 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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

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


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

Evolution of In-Line Differential Scale Factors

OAG14: Vxx OAG25: Vyy OAG36:Vzz

Living Planet Symposium Bergen June 2010


Alternative in flight calibration of the goce gradiometer esa l method daniel lamarre

  • 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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