A linear complexity particle approach to the exact multi-sensor PHD

Recently it has been shown that the Multi-Sensor Probability Hypothesis Density (MS-PHD) has some optimality properties in the regime of large number of sensors [1, 2], achieving the same performance of the Bayes multi-sensor/multi-target posterior in the Random Finite Set (RFS) framework [3]. However, when the number of sensors N is relatively large, the traditional PHD filter loses its computational efficiency, the complexity being exponential in N. On the other hand, the complexity of the full Bayes posterior is only linear in N, and this paper suggests an idea for its computation using Sequential Monte Carlo (SMC) methods. The MS-PHD is then evaluated, and numerical examples show that it is possible to deal with a scenario where the number of sensors is very large while targets, appearing and disappearing, evolve in time.