Non-Linear and Robust Filtering: From the Kalman Filter to the Particle Filter

摘要

This report presents a review of recent non-linear and robust filtering results for stochastic systems. We focus on stability and robustness issues that arise in the filtering of real systems. Issues such as numeric stability and the effect of non-linearity are also considered. The report begins by introducing the famous Kalman filtering problem before proceeding to introduce the extended Kalman filter and related stability results. Robust forms of the Kalman filter and extended Kalman filter are also considered and finally a particle filtering approach is presented. The report is intended to lead readers with a familiarity of the Kalman filtering problem through some of the more important recent (and not so recent) results on stability and robust filters in non-linear filtering problems.