Uniform approximations of discrete-time filters

Throughout recent years, various sequential Monte Carlo methods, i.e. particle filters, have been widely applied to various applications involving the evaluation of the generally intractable stochastic discrete-time filter. Although convergence results exist for finite-time intervals, a stronger form of convergence, namely, uniform convergence, is required for bounding the error on an infinite-time interval. In this paper we prove easily verifiable conditions for the filter applications that are sufficient for the uniform convergence of certain particle filters. Essentially, the conditions require the observations to be accurate enough. No mixing or ergodicity conditions are imposed on the signal process.