Data reduction for particle filters

In this paper, we are interested in nonlinear filtering approximations. Approximate filters (such as the extended Kalman filter or particle filters) are known to converge to the optimal filter when the local error (committed at each step of time) vanishes. But this convergence is in general not uniform in time. Error bounds obtained in the general case suggest that the approximation error could grow exponentially with time. This divergent phenomena is actually observed in some simulations. To avoid that divergence of approximate filters with the number of observations, an idea is to reduce the number of observations without losing too much information. This paper proposes an optimal approach to reduce the number of observations for filtering. This new approach is applied to particle filtering and tested in the case of the bearing only tracking problem.