Convolution Kernels based Sequential Monte Carlo Approximation of the Probability Hypothesis Density (PHD) Filter

The probability hypothesis density (PHD) filter is a practical alternative to the optimal Bayesian multi-target filter based on random finite sets. It propagates the posterior intensity (or a first-order moment) of the random sets of targets, from which the number as well as individual states can be estimated. Furthermore, a number of sequential Monte Carlo (SMC) approximations of the PHD filter (also known as SMC-PHD filter) have been proposed to overcome its computational intractability in nonlinear and non-Gaussian models/appications. However, the SMC-PHD filters are limited in practice when the observation likelihood is analytically unknown or the observation noise is small. In this paper, we propose a new SMC implementation of the PHD filter based on convolution kernels to overcome the aforementioned limitations of the SMC-PHD filter. For illustration purposes, the tracking performance of the new filter is presented in the presence of small observation noise.