Space-wise approach to satellite gravity field determination in the presence of coloured noise

For many years the gravity field of the Earth was only seen by satellite geodesy as the main factor affecting the orbit and consequently it was retrieved together with a number of other perturbations. It is since the advent of a new generation of accelerometers that non gravitational perturbations could be separated from the gravity effects and a new era of gravity field estimates from space was born. In the preparatory work of data analysis for the new missions, performed by the geodetic community, three approaches have been proposed and numerically tested: the brute force method (direct approach), the semi analytical (time-wise) method and the space-wise method. In particular, the time-wise method takes advantage of the incoming time flow of data and, after performing a Fourier transform of the observation equations, exploits the prevailing block diagonal structure of the normal equations to estimate the harmonic coefficients of the gravity field. Complementary to it, the spacewise approach has been developed, which goes back to the traditional computation of the harmonic coefficients by some integration technique or by collocation. Some advantages and disadvantages are peculiar of both methods; particularly the space-wise approach has for long ignored the marked signature of the noise spectrum due to the specific measuring conditions of space-born accelerometers. The application of a proper Wiener filter, exploiting the correlation along the orbit, embedded into an iterative scheme seems to be the right answer. In the paper the solution of this major problem of the space-wise approach is illustrated and simulation results are discussed.