A class of fast exact Bayesian filters in dynamical models with jumps

Yohan Petetin (1) , François Desbouvries (2, 3, 4)

1 LADIS (CEA, LIST) - Laboratoire d'analyse des données et d'intelligence des systèmes (CEA, LIST)
2 TSP - CITI - Communications, Images et Traitement de l'Information
3 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications
4 CNRS - Centre National de la Recherche Scientifique

We address the statistical filtering problem in dynamical models with jumps. When a particular application is adequately modeled by linear and Gaussian probability density functions with jumps, a usual method consists in approximating the optimal Bayesian estimate (in the sense of the Minimum Mean Square Error (MMSE)) in a linear and Gaussian Jump Markov State Space System (JMSS). Practical solutions include algorithms based on numerical approximations or on Sequential Monte Carlo (SMC) methods. In this paper, we propose a class of alternative methods which consists in building statistical models which, locally, similarly model the problem of interest, but in which the computation of the MMSE estimate can be computed exactly (without numerical nor SMC approximations) and at a computational cost which is linear in the number of observations

Mots clés: NP-hard problems; Pairwise Markov chains; Conditional pairwise Markov chains; Exact Bayesian filtering; Hidden Markov chains; Jump Markov state space systems

Domaines: Statistiques [math.ST]; Traitement du signal et de l'image [eess.SP]

Yohan Petetin, François Desbouvries. A class of fast exact Bayesian filters in dynamical models with jumps. IEEE Transactions on Signal Processing, 2014, 62 (14), pp.3643 - 3653. ⟨10.1109/TSP.2014.2329265⟩. ⟨hal-01262437⟩