Stability of the discrete time filter in terms of the tails of noise distributions

Institute of Mathematics, Tampere University of Technology, Finland

Abstract

Recently, it has been pointed out by several authors that the uniform convergence of the stochastic discrete time filter approximations, such as particle filters, is closely related to the stability of the exact filter. This work provides easily verifiable conditions on the signal and observation model that ensure a certain level of stability for the exact filter. Essentially, the conditions are imposed on the tails of the signal and observation noise distributions. For sufficiently light tailed observation noise, the filter is shown to be stable.