Asymptotic stochastic analysis of a gravity model for inertial navigation systems

Abstract

Inertial navigation systems require a precise knowledge of gravity to function properly. The inability of models to account for the small amplitude, short wavelength components of the gravity field leads to errors which are frequently viewed as random; these random errors can introduce a significant cumulative impact on system performance.

A model is studied which, in the context of an appropriate scaling, consists of a gravity field having a known deteministic long scale behavior and an unknown random short scale behavior. The short wavelength random fluctuations are assumed to satisfy a strong mixing (asymptotic independence) property; no a priori stationary or isotropy assumptions are made. Results of Khas'minskii (Theory of Probability and Its Applications, Vol. XI, No. 2, 1966, pp 211-228) are extended and applied. In an appropriate asymptotic limit, the vehicle motion is approximated by the sum of a deterministic trajectory and a Gauss-Markov fluctuation process.