Marginalized particle filters for Bayesian estimation of Gaussian noise parameters

The particle filter provides a general solution to the nonlinear filtering problem with arbitrarily accuracy. However, the curse of dimensionality prevents its application in cases where the state dimensionality is high. Further, estimation of stationary parameters is a known challenge in a particle filter framework. We suggest a marginalization approach for the case of unknown noise distribution parameters that avoid both aforementioned problem. First, the standard approach of augmenting the state vector with sensor offsets and scale factors is avoided, so the state dimension is not increased. Second, the mean and covariance of both process and measurement noises are represented with parametric distributions, whose statistics are updated adaptively and analytically using the concept of conjugate prior distributions. The resulting marginalized particle filter is applied to and illustrated with a standard example from literature.