New results on particle filters with adaptive number of particles
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In this paper, we present new results on particle filters with adaptive number of particles. First, we analyze a method which is based on generating fictitious observations from an approximated predictive distribution of the observations and where the generated observations are compared to actual observations at each time step. We show how the number of fictitious observations is related to the number of moments assessed between the approximated and the true predictive probability density function. Then, we introduce a new statistic for deciding how to adapt the number of particles in an online manner and without the need of generating fictitious particles. Finally, we provide a theoretical analysis of the convergence of a general class of particle filters with adaptive number of particles.
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