# A Sector-Matching Probability Hypothesis Density Filter for Radar Multiple Target Tracking
###### Abstract  
The development of high-tech, dim, small targets, such as drones and cruise missiles, brings great challenges to radar multi-target tracking (MTT), making it necessary to extend the beam dwell time to obtain a high signal-to-noise ratio (SNR). In order to solve the problem of radar sampling time variation exacerbated by extending the beam dwell time when detecting weak targets, a sector-matching (SM) PHD filter is proposed, which combines the actual radar system with a PHD filter and quantifies the relationship between the beam dwell time, the false alarm rate and the detection probability. The proposed filter divides the scanning area into small sectors to obtain actual multi-target measurement times and rederives the prediction and update steps based on the actual sampling time. Furthermore, a state correction step is added before state extraction. Applying the SM structure to the basic Gaussian mixture PHD (GM-PHD) filter and labeled GM-PHD filter, the simulation results demonstrate that the proposed structure can improve the accuracy of multi-weak-target state estimation in the dense clutter and can continuously generate explicit trajectories. The overall real-time performance of the proposed filter is similar to that of the PHD filter. multi-target tracking; radar; random finite sets; sampling time variety; weak targets +
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proposed which combines prediction and updating into one step and reduces the computational complexity. The GLMB filter [20; 21; 22] has difficulty generating the correct multi-target trajectories in good real-time performance. The trajectory Poisson multi-Bernoulli filter and the trajectory Poisson multi-Bernoulli hybrid filter proposed in [23] have better filtering accuracy and real-time performance than the joint GLMB filter. Ref. [24] proposed message-passing-based multitarget tracking methods which can cope with clutter, missed detections, and unknown associations between targets and measurements. Based on the general coordinate ascent variational filtering framework, an online VB-AbNHPP tracker was proposed in [25], which is superior to other competing methods in terms of implementation efficiency and tracking accuracy. Ref. [26] provided an algorithm for approximating the inference in this model using a Markov chain Monte Carlo (MCMC)-based auxiliary variable particle filter, which significantly reduced the computational cost per iteration of the Markov chain. Ref. [27] introduced two new methods (the peak-fusion method and the group-target track-before-detect algorithm) for OTHR tracking, which significantly improved the ability to follow maneuvers. Ref. [28] brought different schools of the tracking community together by demonstrating that PGFLs are very precise and succinct models of the combinatorial probability structures are involved in multitarget tracking. All results of these filters [23; 24; 25; 26; 27; 28] have shortcomings in terms of real-time performance. How to construct a PHD filter suitable for trajectory generation has become the focus of MTT in recent years, as PHD filters have lower computational complexities. Based on the output estimates of a PHD filter, a data association step was performed in [29; 30] to generate multi-target trajectories. In [31; 32], labels were added to the state estimation of the PHD filter. In [33], a trajectory probability hypothesis density (TPHD) filter was proposed which used the trajectory set as the state for MTT. In [34], a Gaussian mixture trajectory PHD filter was proposed, which allowed trajectory estimation of surviving targets without adding labels; however, it has difficulty in shielding against the interference from clutter nearby the targets. In [35], a labeled Gaussian mixture PHD (LGM-PHD) filter was proposed to shield against the interference and achieve trajectory maintenance by attaching labels to Gaussian components and introducing an update matrix to obtain target tracking information.