Particle Filter with Unknown Noise Statistics and with Prior Knowledge

Particle filters have been widely used as a solution to the Bayesian filtering problem, propagating in time a Monte Carlo (MC) approximation of the a posteriori filtering measure. In many situations, the exact statistics of the noises is not known, but some prior information is available. We consider here the estimation of the noise parameters by sampling from the a posteriori distribution of the unknown parameters given the measure data incorporated to the prior information using the Metropolis-Hastings MCMC algorithm. In order to compute the likelihood function, which is needed in the MCMC algorithm to sample from the a posteriori distribution, a factor-graph based approach is used.