A new variant of the differential gravimetry approach
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1 A new variant of the differential gravimetry approach Matthias Weigelt, Tonie van Dam Tamara Bandikova
2 Geometry of the GRACE system Rummel et al Differentiation Integration 2
3 Solution strategies Variational equations Classical (Reigber 1989, Tapley 2004) In-situ observations Energy Integral (Han 2003, Ramillien et al. 2010) Celestial Mechanics approach (Beutler et al. 2010, Jäggi 2007) Differential gravimetry (Liu 2010) Short-arc method (Mayer-Gürr 2006) LoS Gradiometry (Keller and Sharifi 2005) 3
4 DIFFERENTIAL GRAVIMETRY THE STANDARD APPROACH
5 Differential gravimetry Range observables: 5
6 Differential gravimetry Range observables: 5
7 Differential gravimetry Range observables: 5
8 Differential gravimetry Range observables: Multiplication with unit vectors in alongtrack, cross-track and radial direction: 5
9 Differential gravimetry Range observables: Multiplication with unit vectors in alongtrack, cross-track and radial direction: GRACE 5
10 Relative motion Epoch 1 6
11 Relative motion absolute motion neglected! Epoch 2 6
12 Relative motion absolute motion neglected! Epoch 2 6
13 Relative motion absolute motion neglected! Epoch 2 6
14 Relative motion absolute motion neglected! Epoch 2 6
15 Relative motion absolute motion neglected! GPS K-Band Epoch 2 6
16 Relative motion absolute motion neglected! GPS K-Band Epoch 2 6
17 A VARIANT BASED ON ROTATIONS
18 Instantaneous relative reference frame Remember:
19 Instantaneous relative reference frame Remember:
20 Instantaneous relative reference frame Remember: Definition:
21 Instantaneous relative reference frame Remember: Definition:
22 Instantaneous relative reference frame Remember: Definition:
23 Instantaneous relative reference frame Remember: Definition: A B CoM LOS CoM
24 Instantaneous relative reference frame Need for moving frame quantities:
25 Instantaneous relative reference frame Need for moving frame quantities:
26 Instantaneous relative reference frame Need for moving frame quantities:
27 Instantaneous relative reference frame Need for moving frame quantities: What about?
28 Instantaneous relative reference frame Need for moving frame quantities: What about? defined by the Cartan-Matrix:
29 Differential gravimetry in the IRRF Inertial:
30 Differential gravimetry in the IRRF Inertial: IRRF:
31 Differential gravimetry in the IRRF Inertial: IRRF: with and introducing :
32 Differential gravimetry in the IRRF Inertial: IRRF: with and introducing :
33 INSTANTANEOUS RELATIVE REFERENCE FRAME
34 What is the optimal choice for the IRRF? Obviously given: Ambiguity for : radial direction of GRACE A radial direction of GRACE B radial direction of midpoint Other considerations: accessibility accuracy simplification physical meaning
35 Instantaneous relative reference frame Most useful implementation at the current stage:
36 Instantaneous relative reference frame Best approximation at the current stage:
37 Instantaneous relative reference frame Best approximation at the current stage:
38 Instantaneous relative reference frame Best approximation at the current stage: Note the similarity:
39 Relation cross-track to East-West direction >5
40 Relation cross-track to East-West direction >5
41 Summary Derivation of the acceleration approach based on rotations creating the chance of using star cameras instead of GPS (Free) choice of the moving frame allows for optimisation Determination of and allows for a second (observed) component. Explanation of the low East-West sensitivity Necessity for GPS observations (determination of the frame) Open questions: Can be determined by the star camera (accuracy)? Is it possible to find a frame which also fulfils:?
42 A new variant of the differential gravimetry approach Matthias Weigelt, Tonie van Dam Tamara Bandikova
43
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