Stability and approximation of nonlinear filters using the Hilbert metric, and applications to particle filters
Résumé
The stability of the optimal filter w.r.t. its initial condition and w.r.t. the model, is studied in a general hidden Markov model using the Hilbert projective metric. These stability results are then used to prove the uniform convergence of the interacting particle filter to the optimal filter, as the number of particles goes to infinity.