Stability and Uniform Particle Approximation of Nonlinear Filters in Case of Non Ergodic Signals

In this paper, we propose a new approach to study the stability of the optimal filter w.r.t. its initial condition in introducing a “robust filter, ” which approximates the optimal filter uniformly in time. This approach allows us to prove, in some cases, when the signal is nonergodic, the stability of the optimal filter in mean over the observations and the uniform convergence in mean over the observations of a special interacting particle filter to the optimal filter.