Bayesian Filtering using Galerkin-Methods for Nonlinear Prediction and Measurement Updates

This article addresses sequential Bayesian filtering for nonlinear and stochastic dynamical systems. We extend a Galerkin-approach that was previously used for the prediction of non-Gaussian probability density functions, to incorporate linear and non-linear measurement updates. The proposed method results in a linear pipeline of prediction and update steps, which are computed as sparse matrix operations on the finite-dimensional coefficient vector. The performance of our approach is demonstrated in numerical experiments for nonlinear dynamical 2D- and 4D-systems, using results of a standard particle filter as reference, both in terms of accuracy and computational expenses.