Gaussian particle flow implementation of PHD filter

Particle ïlter and Gaussian mixture implementations of random ïnite set ïlters have been proposed to tackle the issue of jointly estimating the number of targets and their states. The Gaussian mixture PHD (GM-PHD) ïlter has a closed-form expression for the PHD for linear and Gaussian target models, and extensions using the extended Kalman ïlter or unscented Kalman Filter have been developed to allow the GM-PHD ïlter to accommodate mildly nonlinear dynamics. Errors resulting from linearization or model mismatch are unavoidable. A particle ïlter implementation of the PHD ïlter (PF-PHD) is more suitable for nonlinear and non-Gaussian target models. The particle ïlter implementations are much more computationally expensive and performance can suï€er when the proposal distribution is not a good match to the posterior. In this paper, we propose a novel implementation of the PHD ïlter named the Gaussian particle ï?ow PHD ïlter (GPF-PHD). It employs a bank of particle ï?ow ïlters to approximate the PHD; these play the same role as the Gaussian components in the GM-PHD ïlter but are better suited to non-linear dynamics and measurement equations. Using the particle ï?ow ïlter allows the GPF-PHD ïlter to migrate particles to the dense regions of the posterior, which leads to higher eïciency than the PF-PHD. We explore the performance of the new algorithm through numerical simulations.