A new variant of the differential gravimetry approach

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A new variant of the differential gravimetry approach

Matthias Weigelt, Tonie van Dam Tamara Bandikova

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Geometry of the GRACE system

2

Differentiation Integration

Rummel et al. 1978

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Solution strategies

3

Variational equations In-situ observations

Classical

(Reigber 1989, Tapley 2004)

Celestial Mechanics approach

(Beutler et al. 2010, Jäggi 2007)

Short-arc method

(Mayer-Gürr 2006)

…

Energy Integral

(Han 2003, Ramillien et al. 2010)

Differential gravimetry

(Liu 2010)

LoS Gradiometry

(Keller and Sharifi 2005)

…

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DIFFERENTIAL GRAVIMETRY

THE STANDARD APPROACH

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Differential gravimetry

5

Range observables:

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5

Range observables:

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5

Range observables:

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5

Range observables:

Multiplication with unit vectors in along- track, cross-track and radial direction:

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5

Range observables:

Multiplication with unit vectors in along- track, cross-track and radial direction:

GRACE

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Relative motion

6

Epoch 1

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Relative motion

6

absolute motion neglected!

Epoch 2

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Relative motion

6

Epoch 2

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Relative motion

6

Epoch 2

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Relative motion

6

Epoch 2

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Relative motion

6

Epoch 2

K-Band

GPS

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Relative motion

6

Epoch 2

K-Band

GPS

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A VARIANT BASED ON ROTATIONS

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Instantaneous relative reference frame

Remember:

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Remember:

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Remember:

Definition:

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Remember:

Definition:

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Remember:

Definition:

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Remember:

Definition:

CoM LOS

CoM

A B

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Need for moving frame quantities:

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What about ?

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What about ?

defined by the Cartan-Matrix:

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Differential gravimetry in the IRRF

Inertial:

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Inertial:

IRRF:

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Inertial:

IRRF:

with and introducing :

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Inertial:

IRRF:

with and introducing :

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INSTANTANEOUS RELATIVE

REFERENCE FRAME

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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

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Most useful implementation at the current stage:

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Best approximation at the current stage:

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Note the similarity:

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Relation cross-track to East-West direction

>5

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Relation cross-track to East-West direction

>5

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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: ?

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A new variant of the differential gravimetry approach

Matthias Weigelt, Tonie van Dam Tamara Bandikova

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