Generalized Recursive Track-Before-Detect with Proposal Partitioning for Tracking Varying Number of Multiple Targets in Low SNR

Track-before-detect (TBD) algorithms incorporate unthresholded measurements to track targets under low signal-to-noise ratio (SNR) conditions. In this paper, we generalize a single target recursive TBD tracking algorithm to track a time-varying number of targets in low SNR and cluttered environments. This algorithm is important, for example, in tracking scenes involving multiple, closely spaced targets moving along the same direction such as a convoy of low observable vehicles moving through a forest, or multiple targets moving in a crisscross fashion. The proposed multi-mode, multi-target TBD (MM-MM-TBD) algorithm is based on estimating the probabilities of all possible combinations of target existence scenarios to obtain the joint multi-target posterior probability density function in a recursive Bayesian framework. We implement the algorithm recursively using particle filtering to also incorporate nonlinear/non-Gaussian tracking models. As the number of target existence combinations dynamically increases with the number of targets, we also propose an efficient proposal density function through partitioning of the multiple target space in order to decrease the number of particles and thus improve the approximation accuracy of the particle filter. We employ a heuristic decision-directed based approach to keep the computational complexity as a linear function of the maximum number of possible targets by exploiting the information obtained from the estimated mode probabilities.