REaldatenAnaLyse GOCE (REAL GOCE) 5. Projekttreffen
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1 REaldatenAnaLyse GOCE (REAL GOCE) 5. Projettreffen Michael Murböc, Claudia Stummer Institut für Astronomische und Physialische Geodäsie, TU München Stuttgart, 10/10/2011 REAL GOCE Projettreffen: Stuttgart, 10/10/2011
2 Overview GOCE real data GOCE gradient analysis and gravity field computation Focus on orbital gradients WP 110 GOCE gravity gradients: a new satellite observable (IAPG, DGFI) WP 150 Topography and gravity gradients (GIK) Internal calibration Spectral analysis 2 Semi-analytical gravity field analysis Rotation of gravity gradient tensor Comparison Improvements and combination Level 1b of gravity gradiometer gradients withprocessing: satellite altimetry Topographic-isostatic Angular rate reconstruction reduction Attitude reconstruction Star sensor combination Internal calibration REAL GOCE Projettreffen: Stuttgart, 10/10/2011
3 Angular Rate Reconstruction Optimal combination of gradiometer (EGG) and star sensor (STR) angular rates by Wiener filtering filter design in frequency domain w(str) = ;w(egg) = ;w(str) 0 = 1 P(EGG) P(STR) P(EGG) + P(STR) P(EGG) + P(STR) assumed noise of angular rates weights of Wiener filters PSD of STR ~ f PSD of EGG ~ 1 / f 2 Stummer C, Fecher T, Pail R: Alternative method for angular rate determination within the GOCE gradiometer processing. Journal of Geodesy 85: , DOI: /s , 2011 REAL GOCE Projettreffen: Stuttgart, 10/10/2011
4 Angular Rate Reconstruction Realization for official gradiometer processor in frequency domain assumed noise P(EGG) w(str) = P(EGG) + P(STR) P(STR) w(egg) = P(EGG) + P(STR) w(str) = 0 1 PSD of STR ~ f PSD of EGG ~ 1 / f 2 weights of Wiener filters in time domain STR EGG h(str) n h(egg) n ( ) = IFFT w(str) ( ) = IFFT w(egg) Characteristics of filters symmetric 8401 sec long cross-over frequency between STR and EGG at about 2.7 x 10-4 Hz REAL GOCE Projettreffen: Stuttgart, 10/10/2011
5 Angular Rate Reconstruction Optimal combination of gradiometer (EGG) and star sensor (STR) angular rates by Wiener filtering σ (EGG) σ (STR) h(str) = = σ (EGG) σ (STR) σ (EGG) σ (STR) 2 2 ; h(egg) STR EGG 5 + combination Wiener lowpass filter Wiener highpass filter REAL GOCE Projettreffen: Stuttgart, 10/10/2011
6 Angular Rate Reconstruction PSD of gravity gradient tensor trace SGG-only gravity field solution geoid heights [m] (d/o ) 6 REAL GOCE Projettreffen: Stuttgart, 10/10/2011
![solution geoid heights [m] (d/o 10 200 ) 6](/docs-images/43/15815072/images/page_6.jpg "REAL GOCE Projettreffen: Stuttgart,")
7 Star sensor fusion Attitude about boresight axis is ten times worse than about axes in the focal plane Star sensors point in different directions Always at least two star sensors available Optimal combination in least squares sense of all available star sensors 7 star sensor 1 + star sensor 2 combination REAL GOCE Projettreffen: Stuttgart, 10/10/2011
8 Star sensor fusion PSD of gravity gradient tensor trace SGG-only gravity field solution geoid heights [m] (d/o ) 8 REAL GOCE Projettreffen: Stuttgart, 10/10/2011
![field solution geoid heights [m] (d/o 10](/docs-images/43/15815072/images/page_8.jpg "200 ) 8 REAL GOCE Projettreffen:")
9 Internal Calibration (WP 110) Comparison with reference gradients (EGM2008) has shown that the gravity gradient Vyy is affected by the variation of the differential scale factor in y-direction of gradiometer arm 2-5 (dsf25y). Temporal development of differential scale factors is almost linear. Linear interpolation of Inverse Calibration Matrices (ICMs) Nominal ICM Development of dsf25y 9 Interpolated ICM Vyy minus Vyy_ref (from EGM2008), Nov.+Dec. 2009, pre-whitening filtered, ascending tracs REAL GOCE Projettreffen: Stuttgart, 10/10/2011
10 Internal Calibration (WP 110) Linear interpolation of ICMs PSD of gravity gradient tensor trace SGG-only gravity field solution geoid heights [m] (d/o ) 10 REAL GOCE Projettreffen: Stuttgart, 10/10/2011
![SGG-only gravity field solution geoid heights [m]](/docs-images/43/15815072/images/page_10.jpg "(d/o 10 200 ) 10 REAL GOCE Projettreffen: Stuttgart,")
11 Attitude Reconstruction Optimal combination of gradiometer (EGG) and star sensor (STR) quaternions by Wiener filtering σ (EGG) σ (STR) h(str) = = σ (EGG) σ (STR) σ (EGG) σ (STR) 2 2 ; h(egg) STR integrated GAR 11 + combination Wiener lowpass filter Wiener highpass filter REAL GOCE Projettreffen: Stuttgart, 10/10/2011
12 Attitude Reconstruction PSD of gravity gradient Vxz, comparsion with reference gradient and with Quic-loo residuals SGG-only gravity field solution geoid heights [m] (d/o ) 12 PSD of Vxz [me/sqrt(hz)] Frequency [Hz] REAL GOCE Projettreffen: Stuttgart, 10/10/2011
![gravity field solution geoid heights [m] (d/o 10 200 ) 12 PSD of](/docs-images/43/15815072/images/page_12.jpg "Vxz [me/sqrt(hz)] Frequency [Hz] REAL GOCE Projettreffen:")
13 Total effect of improved Level 1b processing SGG-only gravity field solution geoid heights [m] (d/o ) original processing vs. EGM2008 Improvement in formal errors 13 new processing vs. EGM2008 Stummer C, Siemes C, Pail R, Frommnecht B, Floberghagen R: Upgrade of the GOCE Level 1b gradiometer processor. Paper submitted to Advances in Space Research, 2011 REAL GOCE Projettreffen: Stuttgart, 10/10/2011
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