Covariance analysis of gravity models for land navigation

Abstract

Gravity compensation errors are significant error contributors for high-accuracy land navigation systems. Their effect on performance can be mitigated by incorporating a statistical gravity model into the on-board Kalman filter which resets the navigation state from external updates. System performance analysis can be complicated for this application because gravity compensation errors are in general spatially correlated according to vehicle position, and may have to satisfy statistical constraints imposed by physical geodesy. An analysis method is presented here for propagating navigation error covariances when a sub-optimal Kalman filter for external update incorporation models gravity as a Markov process, while actual errors are correlated according to an arbitrary spatially correlated model. The approach is based on the Edwards nested integrals concept, but the computations are arranged in a storage-efficient form. The adjustments required for handling filter resets of the navigation state, and filter mismodeling of instrument errors, are described explicitly. A simulation example for a land navigation scenario is given, showing improvement obtainable by adjusting filter gravity model parameters. Actual gravity errors are assumed correlated according to the Sperry Three-Dimensional Algebraic Gravity (STAG) model, and errors are reset with velocity updates at periodic stopping points. Filter gravity estimation improvement by means of position update incorporation is presented.