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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 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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slide1

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

Daniel Lamarre

Michael Kern

ESA

Living Planet Symposium Bergen June 2010

slide2

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

slide3

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

slide4

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

slide5

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

slide7

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

slide9

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

slide10

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

slide11

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

slide12

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

slide13

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

slide18

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

slide19

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

slide20

Evolution of In-Line Differential Scale Factors

OAG14: Vxx OAG25: Vyy OAG36:Vzz

Living Planet Symposium Bergen June 2010

slide21

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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