Nonlinear filtering in discrete time : a particle convolution approach

Vivien Rossi (1) , Jean-Pierre Vila (2)

1 ASPI - Applications of interacting particle systems to statistics
2 ASB - Analyse des Systèmes et Biométrie

In this paper a new generation of particle filters for nonlinear disrete time processes is proposed, based on convolution kernel probability density estimation. The main advantage of this approach is to be free of the limitations encountered by the current particle filters when the likelihood of the observation variable is analytically unknown or when the observation noise is null or too small. To illustrate this convolution kernel approach the counterparts of the well-known sequential importance sampling (SIS) and sequential importance sampling-resampling (SIS-R) filters are considered and their stochastic convergence to the optimal filter under different modes are proved. Their good behaviour with respect to that of these filters is shown on several simulated case studies.

Mots clés: RESAMPLING; SEQUENTIAL IMPORTANCE SAMPLING

Mots clés: CONVOLUTION KERNELS; PARTICLE FILTER; PROBABILITE

Domaines: Mathématiques [math]; Informatique [cs]

Vivien Rossi, Jean-Pierre Vila. Nonlinear filtering in discrete time : a particle convolution approach. Annales de l'ISUP, 2006, 50 (3), pp.71-102. ⟨hal-02665573⟩