A BAYES FILTER IN FRIEDLAND FORM FOR INS/GPS VECTOR GRAVIMETRY

Abstract

We introduce a dynamic linear model in which the observation equations are perturbed by a form that has constant (over time), non-random coefficients and may represent the disturbing gravity field under investigation. Because of its non-random behaviour, their form cannot be determined using Friedland's generalization of the Kalman filter. However, after putting it in dual form ('Bayes filter'), Friedland's approach can be further generalized to also cover the present case. This (apparently new) filter version is then employed to estimate the disturbing gravity vector from airborne INS/GPS data, following the ideas of Jekeli & Kwon (1999) for the combined analysis. Thus, the filter acts on the integration of INS and GPS acceleration vectors where the discrepancies are simultaneously modelled in terms of random system 'biases', i.e. self-calibration, and the local non-random disturbing gravity vector. We do not introduce a second filter step ('cascaded filter'), owing to problems with neglected correlations in a two-step procedure. The new results are eventually compared with those of a related algorithm that may be interpreted as Kalman filtering with 'partial regularization', effectively using a stochastic gravity field representation. Improvements of between 10 per cent ('down' direction) and 60 per cent (north direction) were achieved, which we attribute in large part to the use of the disturbing gravity vector as a non-stochastic quantity.