Breadcrumb
Generalized particle filters
Fri 22 February 2013, 15:40
Dan Crisan
Imperial College
Organisers: Nick Whiteley, Feng Yu
ABSTRACT
The ability to analyse, interpret and make inferences about evolving dynamical systems is of great importance in different areas of the world we live in today. In general, the dynamical systems are not directly observable, quite often only partial information, which is deteriorated by the presence noise, is available. This naturally leads us to the area of stochastic filtering, which is defined as the estimation of dynamical systems whose trajectory is modelled by a stochastic process called the signal, given the information accumulated from its partial observation. A class of numerical methods called particle filters have proved the most successful methods to-date. These methods produce approximations of the posterior distribution of the current state of the signal by using the empirical distribution of a cloud of particles that explore the signal's state space. In this talk, I discuss a more general class of numerical methods which involve generalised particles, that is, particles that evolve through spaces larger than the signal's state space. Such generalised particles can include Gaussian mixtures, wavelets, orthonormal polynomials, and finite elements in addition to the classical particle methods.
This is joint work with Kai Li (Imperial College London)