Particle filters

Abstract

Subject of this master thesis is the presentation of a methodology, called Particle filters, a class of Sequential Monte Carlo (SMC) methods used to sample sequentially from a sequence of high-dimensional and complex probability distributions. A cloud of particles evolves over time as new observations become available to approximate the posterior distribution of the state variables. From when first introduced from Gordon (1993)[17] , it has been used in a lot of applications that include signal and image processing, predicting economical data, tracking the position of aircraft or cars. In the context of this thesis, the algorithm of particle filters is illustrated, as well as a relatively new technique introduced by Christophe Andrieu, Arnaud Doucet, Roman Holenstein (2010)[8], called Particle Markov Chain Monte Carlo (PMCMC) which combines the MCMC with the SMC methods. PMCMC is used when the state-space model depends on unknown parameters in a case where standard particle filters fail. The main objective of this thesis is to illustrate the basics of those methodologies in theoretical framework together with a simple example.