Gaussian Particle Flow Implementation of PHD Filter

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