Particle filters are broadly used to approximate posterior distributions ofhidden states in state-space models by means of sets of weighted particles.While the convergence of the filter is guaranteed when the number of particlestends to infinity, the quality of the approximation is usually unknown butstrongly dependent on the number of particles. In this paper, we propose anovel method for assessing the convergence of particle filters online manner,as well as a simple scheme for the online adaptation of the number of particlesbased on the convergence assessment. The method is based on a sequentialcomparison between the actual observations and their predictive probabilitydistributions approximated by the filter. We provide a rigorous theoreticalanalysis of the proposed methodology and, as an example of its practical use,we present simulations of a simple algorithm for the dynamic and onlineadaption of the number of particles during the operation of a particle filteron a stochastic version of the Lorenz system.
展开▼
