Tracking Coexisting Point and Extended Targets with Unknown Detection Probability Using the PHD Filter

This paper proposes a probability hypothesis density (PHD) filter for coexisting point and extended targets with unknown detection probability, which is referred to as the U-PE-PHD filter. In multi-target tracking (MTT), the target detection probability is usually unknown and time-varying, which leads to bias in the estimation of the target's state and cardinality, affecting the estimation accuracy. Therefore, it is essential to adaptively estimate the detection probability of the target online. In addition, in practical applications, the point targets and extended targets often coexist in the field of view. This paper constructs a generalized measurement model for the coexisting point and extended targets and establishes an intensity function model based on the PHD filter that can accommodate both point targets and extended targets. To obtain a closed-form solution, the intensity function is modeled as a mixture of Beta Gaussian distribution and Beta Gamma Gaussian inverse Wishart (BGGIW) distribution. Furthermore, the U-PE-PHD filter proposed in this paper calculates the probability of the point target, which can be used to determine whether the target is a point target or an extended target. The simulation results show that the proposed U-PE-PHD filter can provide more accurate estimations of the state and detection probability of the coexisting point and extended targets.