Abstract

Although, sequential Monte Carlo based particle filters and smoothers, in principle, provide the Bayesian solution to any dynamic estimation problem presentable in probabilistic state space form, they are not flawless. In particular, as the state dimension grows, the required number of particles quickly becomes high. Furthermore, plain particle filters and smoothers cannot be used for inferring static or slowly varying parameters. One way to overcome these problems is to resort to Gaussian approximations for the full state posteriors or parts of the posteriors. Sigma-point and numerical cubature integration based filters and smoothers are a recently developed class of methods for robust computation of such Gaussian approximations. Rao-Blackwellization refers to partial closed form marginalization, which can be used for avoiding sampling of Gaussian or approximately Gaussian parts of the state state, or for marginalizing the static parameters of the model in closed form. In this talk I will discuss the sigma-point, numerical integration and Rao-Blackwellization based filtering and smoothing methods, and present applications of the methods.