Some simulated noise inversion studies of satellite geopotential missions involving “criterion functions” in the frequency domain

Summary

In connection with the problem of optimally combining the results of a global geopotential mission using (1) a gravity gradiometer and (2) an on-board GPS receiver, we propose a technique operating in the frequency domain using “criterion functions”, which describe the precision of each inversion solution as a function of degreen and orderm of its spherical harmonic expansion.

We propose a formalism for term-wise averaging in the frequency domain, which is both unbiased and optimal in a global least-squares sense.

Software for deriving a “criterion function” for the geopotential coefficient recovery errors from both GPS-tracking and gradiometry was developed. This function gives a simple description, using a few parameters only, of the error behaviour of various observation types and geometries.

Criterion functions derived for various simulated missions are described, analytically converted to degree variance functions, and compared with results by others. For one case, criterion function dependence on mission parameters is studied.