Numerical techniques for large least-squares problems with applications to GOCE

Abstract

The development of space-borne measurement sensors and powerful computer hardware, in combination with improvements in mathematical and physical modelling, allow us to determine the Earth’s gravity field with increasing resolution and accuracy. The huge amount of data and unknowns and the stringent accuracy requirements pose the limits for simplifications of the functional and stochastic model and for the numerical and approximation errors introduced in the course of the least-squares data processing. This requires the design of sophisticated numerical algorithms despite of the increasing computer power. This paper addresses a number of computational problems that one frequently encounters in least-squares gravity field determination: i) how to set-up and solve the normal equations efficiently, ii) how to deal with instabilities, iii) how to model the observation noise correctly, iv) how to find optimal weights for different types or groups of observations? Possible solutions to these problems are presented and supported by simulations. The gravity field determination from satellite gravity gradients serves as an example, but the presented solutions may be used for other types of satellite data, as well. Moreover, some developments may also be relevant for other data acquisition techniques such as airborne gravimetry.