Constrained Extended Target Tracking With Random Matrix and Approximate Projection

Constrained target tracking problem has received widespread attention in sensor systems. In this problem, targets are required to satisfy specific constraints imposed by physical laws or other restrictions. As a typical approach to the constraint tracking problem for point targets, the constraint projection method has shown strong compatibility and given rise to many variants. Meanwhile, in the extended target tracking problem arisen from high-resolution sensors, the random matrix (RM) model has demonstrated outstanding stability and low computational complexity. However, research on constrained tracking of extended targets is limited. To address this problem, this article proposes an approximate projection approach that projects the state of the RM model to satisfy prescribed constraints. First, the RM model is transformed into the corresponding elliptical parameter state to facilitate the constraint construction since the RM model does not explicitly represent the physical shape parameters of the target. Then, the mean square error of the transformed state is approximated to determine the weight matrix for projection. Finally, the parameter state of the projected target expansion is reconstructed as an RM that adheres to the Bayesian conjugate prior form via moment matching. Building on this approach, two constrained extended target tracking methods are proposed within the estimate projection (EP) and the constrained minimum mean square error (CMMSE) frameworks. Experiments using both simulated and real data demonstrate that the proposed constrained extended target tracking methods based on EP and CMMSE framework have superior performance compared to the unconstrained RM tracking method.