The Performance of the Time-wise Semi-analytical Inversion of Satellite Gravity Gradients

The development of procedures for the estimation of the gravity field from satellite gravity gradients is one of key problems in preparation of the GOCE mission to be launched in 2005. Different strategies are currently being developed and implemented. Standard least-squares estimation requires sophisticated algorithms in order to handle the huge number of observations and unknowns, the ill-conditioning of the normal matrix and the colored observation noise, just to mention some of the numerous challenging problems. Therefore, an approximation to the least-squares estimator has been developed, which significantly reduces the numerical costs but is non-optimal in the least-squares sense. This approach is known as time-wise semianalytical method. It has been used extensively for error propagation in mission design studies, and, in the course of the last years, has been extended to allow for the estimation of potential coefficients from measured gravity gradients. The objective of this research is to investigate the performance of the time-wise semi-analytical method. This question has become increasingly important since the time-wise semi-analytical method may also be used as quicklook analysis tool during the GOCE mission. As a quick-look tool it should be very fast compared to exact least-squares solutions but should also be sufficiently accurate. Results from very extensive and realistic simulations are presented and compared with the exact least-squares solution. The analysis shows that the semi-analytical solution does not differ much from the exact least-squares solution, but is a factor 2 – 3 faster. A further improvement by a factor 10 is achieved if the time-wise synthesis step is replaced by a combination of classical spherical harmonic synthesis using Legendre functions and 3D-interpolation.