Particle filtering with transformed weights

Particle filters are simulation-based algorithms for computational inference in dynamical systems that have become very popular over the years in many areas of science and engineering. They are derived from Bayes´ theorem and the technique of importance sampling (IS), which entails the approximation of probability measures by way of weighted random samples in the space of interest. As a consequence, particle filters suffer from problems related to the degeneracy of these weights, a limitation shared with other IS-based methods. In practice, the weight degeneracy implies that in some scenarios (typically when the dimension of the state space is high or when the likelihood function of the system is sharp) classical particle filters become numerically unstable and fail to converge. In this paper we investigate the application of a recently proposed technique, termed nonlinear importance sampling (NIS), to the design of particle filters. We show how the standard particle filter can be easily modified to incorporate transformed weights computed according to the NIS scheme, then provide a concise proof of convergence of the resulting algorithm, and finally present computer simulation results to illustrate the potential improvement in performance that can be attained.