Data analysis for the GOCE mission

We investigate the time-wise approach to the data anlaysis for the GOCE mission. The number of observations collected during the mission, the number of potential coefficients to be estimated, and the complexity of the mathematical model for the time-wise approach require a special strategy, which has to reduce the CPU-time and storage requirements considerably. Our approach is based on (1) the iterative solution of the normal equations using a Richardson-iteration scheme and (2) the approximation of the design matrix in order to assemble the right-hand side in each iteration step efficiently. We demonstrate the performance of the approach for white noise and coloured noise observations along a simulated GOCE orbit up to degree and order 180. We provide error estimates anal show that the solution is unbiased. We also prove that the method does not converge to the solution of the normal equations. However, the approximation error can be neglected in our simulations.