SMC-PHD algorithm based on squared cubature particles

Most of the conventional sequential Monte Carlo probability hypothesis density (SMC-PHD) approaches adopt the state transition density as importance sampling function. When targets are with nonlinear motions, such a selection makes few particles with large weights, leading to inaccurate estimation and particle divergence. To avoid such problems, a novel importance sampling function approximation approach with the squared cubature Kalman filter (SCKF) and statistical gating method was proposed. To design such an importance sampling function, the mean and covariance of importance sampling function were predicted at first. Then, the statistical gating method were utilized to extract observations associated with the importance sampling particle from the current observation set. Merging the extracted observations with corresponding weights, the mean and covariance of importance sampling function were updated. Using the designed importance sampling function, the intensity of particles can be predicted and updated, according to the conventional SMC-PHD method. At last, the states and number of multi-target can be approximated by the intensity of particles. The simulation results demonstrate that the proposed approach has the advantages of high accuracy and stable estimation in nonlinear target tracking.