Unscented Auxiliary Particle Filter Implementation of the Cardinalized Probability Hypothesis Density Filters

The probability hypothesis density (PHD) filter suffers from lack of precise estimation of the expected number of targets. The Cardinalized PHD (CPHD) recursion, as a generalization of the PHD recursion, remedies this flaw and simultaneously propagates the intensity function and the posterior cardinality distribution. While there are a few new
approaches to enhance the Sequential Monte Carlo (SMC) implementation of the PHD filter, current SMC implementation for the CPHD filter is limited to choose only state transition density as a proposal distribution. In this paper, we propose an auxiliary particle implementation of the CPHD filter by estimating the linear functionals in the elementary symmetric functions based on the unscented transform (UT). Numerical simulation results indicate that our proposed algorithm out performs both the SMC-CPHD filter and the auxiliary particle implementation of the PHD filter in difficult situations with high clutter. We also compare our proposed algorithm with its counterparts in terms of other metrics, such as run times and sensitivity to new target appearance.