Closed Form PHD Filtering for Linear Jump Markov Models

In recent years there has been much interest in the probability hypothesis density (PHD) filtering approach, an attractive alternative to tracking unknown numbers of targets and their states in the presence of data association uncertainty, clutter, noise, and miss-detection. In particular, it has been discovered that the PHD filter has a closed form solution under linear Gaussian assumptions on the target dynamics and birth. This finding opens up a new direction where the PHD filter can be practically implemented in an effective and reliable fashion. However, the previous work is not general enough to handle jump Markov systems (JMS), a popular approach to modeling maneuvering targets. In this paper, a closed form solution for the PHD filter with linear JMS is derived. Our simulations demonstrate that the proposed PHD filtering algorithm provides promising performance. In particular, the algorithm is capable of tracking multiple maneuvering targets that cross each other