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Summary of the processing details  

The LUH-GRACE2018 monthly solutions are obtained using the variational equations approach. The estimation process consists of two steps as follow:

1- In the first step the initial state vector along with the accelerometer bias parameters are estimated by fitting the integrated orbit to the GNV1B orbit products. The adjustment process is usually converged after 2 or 3 iterations.

2- In the second step, the gravity field parameters up to d/o N=80 are added to the unknown parameters of the first step. In this step a total number of 6557 common parameters and 9 arc-dependent parameters for each arc are estimated. In this step the orbit (pseudo) observations are combined with the range rate data with a relative weighting of 1 x 1010 .

No regularization or prior information are used in the estimation process. Hence the GRACE-LUH2018 solutions are unconstrained.

The estimated gravity field solutions show a very good agreement with the official solutions from GFZ, CSR and JPL. Figure below show the typical errors of the GFZ, CSR and the LUH-GRACE2018 solutions for January 2007.


The force models used for the dynamic orbit integration are listed in table below. 

Force model


Earth’s gravity

GIF48, maximum d/o: 300

Direct tides

Moon and Sun, ephemerides: DE405

Solid Earth tides

IERS Conventions 2010

Ocean tides

EOT11a, maximum d/o: 80

Solid Earth pole tides

IERS Conventions 2010

Ocean pole tides

IERS Conventions 2010, maximum d/o: 60

Relativistic effects

IERS Conventions 2010


AOD1B RL05, maximum d/o: 100




Error degree standard deviations of CSR, GFZ and LUH solutions reference to model GIF48.