The multi-sensor PHD filter: Analytic implementation via Gaussian mixture and effective binary partition

An analytic suboptimum solution is given for the theoretically rigorous multi-sensor probability hypothesis density (MS-PHD) filter due to R. Mahler. Under linear Gaussian assumptions, the propagating formulas for the means, covariances and weights of the constituent Gaussian components of the posterior intensity are given. Furthermore, a method, named “Effective Binary Partition (EBP)”, is proposed for limiting the number of considered partitions to reduce the computational complexity. The EBP method makes it possible to implement the exact MS-PHD filter formulas. The computational complexity of EBP of the proposed two-sensor PHD filter is O(τ(l
₀
) · J
_k|k-1
+ 1), where π(l
₀
) is a constant corresponding to the effective measurement number l
₀
, J
_k|k-1
is the number of predicted targets. Finally, the validity of the proposed algorithm is demonstrated by numerical simulations.