On optimal sampling for particle filtering in digital communication

Particle filtering has been successfully used to approximate the fixed-lag or fixed-interval smoothing distributions in digital communication and to perform approximate maximum likelihood inference. Because the state-space is finite, it is possible at each step to consider all the offsprings (path) of any given particle. Because each particle has typically several possible offsprings, the population of offsprings is larger than the initial population; it is thus required to construct a novel particle swarm by selecting, among all these offsprings, particle positions and computing appropriate weights. We propose here a novel unbiased selection algorithm, which minimizes the expected loss with respect to general distance functions. In a blind deconvolution setting, the selection schemes associated to the Chi-Square distance and the Kullback-Leibler divergence are compared by simulations to the deterministic scheme that keep only the best weights.