Abstract

Stochastic filtering is defined as the estimation of a partially observed dynamical system. A massive scientific and computational effort has been dedicated to the development of numerical methods for approximating the solution of the filtering problem. Approximating with Gaussian mixtures has been very popular since the 1970s, however the existing work is only based on the success of the numerical implementation and is not theoretically justified.

We fill this gap and conduct a rigorous analysis of a new Gaussian mixture approximation to the solution of the filtering problem. In particular, we construct the corresponding approximating algorithm, deduce the L2-convergence rate and prove a central limit type theorem for the approximating system. In addition, we show a numerical example to illustrate some features of this algorithm. This is joint work with Dan Crisan (Imperial College London).

References: [1] D. Crisan, K. Li, A central limit type theorem for Gaussian mixture approximations to the nonlinear filtering problem, ArXiv1401:6592, (2014).

[2] D. Crisan, K. Li, Generalised particle filters with Gaussian mixtures, accepted by Stochastic Processes and their Applications, ArXiv1306:0255, (2013).

[3] D. Crisan, K. Li, Generalised particle filters with Gaussian measures, Proceedings of 19th European Signal Processing Conference, Barcelona, Spain, pp. 659-663, (2011).