Un nouvel algorithme de filtrage dans les modèles de Markov à saut linéaires et Gaussiens

In this paper, we focus on the statistical filtering problem in linear and Gaussian Jump Markov State Space Systems (JMSS). In such models, the computation of the optimal Bayesian estimate (in the sense of the mean square error) is an NP hard problem. Suboptimal solutions include algorithms based on numerical approximations or based on Sequential Monte Carlo methods. We propose an alternative option which consists in approximating the linear and Gaussian JMSS by a statistical model which keeps the same physical properties but in which the computation of the optimal estimate can be done at a computational cost which is linear in the number of observations.