Trajectory PHD and CPHD Filters for the Pulse Doppler Radar

Abstract

Different from the standard probability hypothesis density (PHD) and cardinality probability hypothesis density (CPHD) filters, the trajectory PHD (TPHD) and trajectory CPHD (TCPHD) filters employ the sets of trajectories rather than the sets of the targets as the variables for multi-target filtering. The TPHD and TCPHD filters exploit the inherent potential of the standard PHD and CPHD filters to generate the target trajectory estimates from first principles. In this paper, we develop the TPHD and TCPHD filters for pulse Doppler radars (PD-TPHD and PD-TCPHD filters) to improve the multi-target tracking performance in the scenario with clutter. The Doppler radar can obtain the Doppler measurements of targets in addition to the position measurements of targets, and both measurements are integrated into the recursive filtering of PD-TPHD and PD-TCPHD. PD-TPHD and PD-TCPHD can propagate the best augmented Poisson and independent identically distributed multi-trajectory density approximation, respectively, through the Kullback–Leibler divergence minimization operation. Considering the low computational complexity of sequential filtering, Doppler measurements are sequentially applied to the Gaussian mixture implementation. Moreover, we perform the L-scan implementations of PD-TPHD and PD-TCPHD. Simulation results demonstrate the effectiveness and robustness of the proposed algorithms in the scenario with clutter.

Keywords

• multi-target tracking
• pulse Doppler radars
• sets of trajectories
• trajectory PHD filter
• trajectory CPHD filter