A nonlinear filtering algorithm based on an approximation of the conditional distribution

An effective form of the Gaussian or moment approximation method for approximating optimal nonlinear filters with a diffusion signal process and discrete-time observations is presented. Various computational simplifications reduce the dimensionality of the numerical integrations that need to be done. This process, combined with an iterative Gaussian quadrature method, makes the filter effective for real-time use. The advantages are illustrated by a model that captures the general flavour of modeling the highly uncertain behavior of a ship near obstacles such as a shore line into which it cannot go, and must manoeuvre away in some unknown fashion. The observations are of very poor quality, yet the filter behaves well and is quite stable. The procedure does not rely on linearization, but attempts to compute the conditional moments directly by approximating the integrations used by the optimal filter.