Title: Particle filtering for truncated noise densities
Authors: Elisabeth Leoff - Fraunhofer ITWM (Germany) [presenting]
Tom Ewen - Fraunhofer ITWM (Germany)
Abstract: Particle filters are a popular class of Monte Carlo methods used for state estimation in general state space models, where the filter is not explicitly known. They work online to approximate the marginal distribution of the signal as observations become available. Importance sampling is used at each time point to approximate the distribution with a set of particles, each with a corresponding weight. When the density of the observation noise has finite support, it can happen that all weights are zero and the filter diverges. We present an approach where repeated sampling of all particles is applied, similar to the (partial) rejection control from literature. We demonstrate that this method is valid in the sense that it approximates the correct conditional expectation. If repeated sampling still leads to vanishing weights, it can be combined with smoothing out the noise density, which allows the filter to continue. Numerical examples for both concepts are presented.