Max-Sum-Based Data Associations for Tracking Point and Extended Targets

For multitarget tracking applications, data association is a fundamental problem of assigning measurements to their corresponding targets. In this article, we propose two algorithms for tracking point and extended targets, respectively, based on factor graph representations of the joint probability density functions. Both employ the max-sum (MS) algorithm to find the maximum a posteriori assignment such that the state of each target is updated with the most probable measurement(s). We model the single target densities as Gaussian distribution for point targets and gamma Gaussian inverse Wishart distribution for extended targets. Under linear Gaussian assumptions on the target models, the proposed algorithms provide analytical solutions to multitarget tracking problems. Specifically, the messages flowed in the factor graphs, existence probabilities and states of the targets are analytically calculated. These two algorithms have reduced computational load compared to the particle-based sum-product (SP) algorithms and avoid gating or clustering used by traditional multitarget tracking methods. We compare the proposed MS-based algorithms (MSAs) with the Poisson multi-Bernoulli mixture filters and the SP-based algorithms, and simulation results show that the MSAs have comparable or improved tracking performance.