Joint Bayesian estimation of local covariances and gravity field functionals
21/09/2016 | 11:00 | Session 3: Recent Development in Theory and Modelling
Author(s): Mirko Reguzzoni, Martina Capponi, Andrea Gatti, Fernando Sansò, Jan Martin Brockmann and Wolf-Dieter Schuh
Mirko Reguzzoni, Martina Capponi, Andrea Gatti, Fernando Sansò, Jan Martin Brockmann and Wolf-Dieter Schuh
The problem of estimating a data covariance model and using it to predict gravity field functionals is customarily treated by collocation by sharply separating the two steps, hoping that estimation errors in the covariance modelling have a little influence to the final gravity field solution. In particular, the first step is typically performed under the hypothesis of homogeneous and isotropic random fields, determining a set of locally adapted degree variances from the data. In 2003, a study to merge these two steps into a unique estimation theory was presented at the fifth Hotine-Marussi symposium, suggesting a suitable Bayesian predictor working at global level with isotropic covariances. However, the problem is that the anisotropic nature of the signal cannot be generally ignored in the analysis of local data. Yet, the experience gained in the GOCE data processing suggests that a reasonable anisotropic covariance model can be constructed by simply allowing different variances for each individual spherical harmonic coefficients of the potential, thus only slightly increasing the number of degrees of freedom. In this work, the previously mentioned Bayesian predictor is generalized in this direction, proposing a numerically feasible solution. In particular, individual coefficient variances are modelled as independent random variables, each of them with an inverse gamma prior distribution having a mean equal to the corresponding locally adapted degree variance. The local gravity field estimates, together with the resulting covariance modelling, are obtained by maximizing the posterior distribution. This is basically the same as an iterative collocation solution coupled with the equations for the covariance estimation. A numerical simulation in the case of local geoid determination is here presented, showing similarities and differences with respect to the standard collocation approach.