Joint Detection and Tracking for Multipath Targets: A Variational Bayesian Approach

Different from traditional point target tracking systems assuming that a target generates at most one single measurement per scan, there exists a class of multipath target tracking systems where each measurement may originate from the interested target via one of multiple propagation paths or from clutter, while the correspondence among targets, measurements, and propagation paths is unknown. The performance of multipath target tracking systems can be improved if multiple measurements from the same target are effectively utilized, but suffers from two major challenges. The first is multipath detection that detects appearing and disappearing targets automatically, while one target may produce $s$ tracks for $s$ propagation paths. The second is multipath tracking that calculates the target-to-measurement-to-path assignment matrices to estimate target states, which is computationally intractable due to the combinatorial explosion. Based on variational Bayesian framework, this paper introduces a novel probabilistic joint detection and tracking algorithm (JDT-VB) that incorporates data association, path association, state estimation and automatic track management. The posterior probabilities of these latent variables are derived in a closed-form iterative manner, which is effective for dealing with the coupling issue of multipath data association identification risk and state estimation error. Loopy belief propagation (LBP) is exploited to approximate the multipath data association, which significantly reduces the computational cost. The proposed JDT-VB algorithm can simultaneously deal with the track initiation, maintenance, and termination for multiple multipath target tracking with time-varying number of targets, and its performance is verified by a numerical simulation of over-the-horizon radar.