A novel algorithm for adapting the number of particles in particle filtering

In this paper, we propose a novel approach for assessing the convergence of particle filters in online manner. Particle filters sequentially approximate distributions of hidden states of state-space models. The approximations are random measures composed of weighted particles (i.e., samples of the state). A sufficiently large number of particles provides a good quality in the approximation but at the expense of increasing the computational load. We propose to adapt the number of particles in real time based on the convergence assessment of the particle filter. The proposed methodology is based on a model-independent theoretical analysis that is valid under mild assumptions. We present an algorithm that allows the practitioner to operate at a desirable operation point defined by a performance-complexity tradeoff. The algorithm has a small extra cost, and it shows good performance in our numerical simulations.