Improving Regularised Particle Filters

Christian Musso, Nadia Oudjane, François Le Gland

Abstract: The optimal filter computes the posterior probability distribution of the state in a dynamical system, given noisy measurements, by iterative application of prediction steps according to the dynamics of the state, and correction steps taking the measurements into account. A new class of approximate nonlinear filter has been recently proposed, the idea being to produce a sample of independent random variables, called a particle system, (approximately) distributed according to this posterior probability distribution. The method is very easy to implement, even in high-dimensional problems, since it is sufficient in principle to simulate independent sample paths of the hidden dynamical system.