Multi-sensor PHD by space partitioning: Computation of a true reference density within the PHD framework

In a previous paper, the authors proposed an extension of the Probability Hypothesis Density (PHD), a well-known method for single-sensor multi-target tracking problems in a Bayesian framework, to the multi-sensor case. The true expression of the multi-sensor data update PHD equation was constructed using finite sets statistics (FISST) derivative techniques on functionals defined on multi-sensor observation and state space named "cross-terms". In this paper, an equivalent expression in a combinational form is provided, which allows an easier interpretation of the data update equation. Then, using the joint partitioning proposed by the authors in the previous paper, an exact multi-sensor multi-target PHD filter is efficiently propagated on a benchmark scenario involving 10 sensors and up to 10 simultaneous targets where the brute force approach would have been extremely burdensome. The availability of a true reference PHD then allows a validation of the classical iterated-corrector approximation method, albeit limited to the scope of the implemented scenario.