A Numerically Robust Bayesian Filtering Algorithm for Gaussian Mixture Models

Abstract

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement update steps. In addition, a numerically robust square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems, including the state estimation for a challenging non-linear system.