Adapting sample size in particle filters through KLD-resampling

An adaptive resampling method is provided. It determines the number of particles to resample so that the Kullback-Leibler distance (KLD) between the distribution of particles before resampling and after resampling does not exceed a pre-specified error bound. The basis of the method is the same as Fox´s KLD-sampling but implemented differently. The KLD-sampling assumes that samples are coming from the true posterior distribution and ignores any mismatch between the true and the proposal distribution. In contrast, the KLD measure is incorporated into the resampling in which the distribution of interest is just the posterior distribution. That is to say, for sample size adjustment, it is more theoretically rigorous and practically flexible to measure the fit of the distribution represented by weighted particles based on KLD during resampling than in sampling. Simulations of target tracking demonstrate the efficiency of the method.