Hölder Divergence Based Reward Function for Poisson RFSs and Application to Multi-Target Sensor Management

In this study, we propose a novel information theoretic reward function based on the statistical Hölder divergence. The Hölder divergence is the generalization of Cauchy-Schwarz divergence. We extend the Hölder divergence to the FISST densities, thus making it possible to use in the multi-object applications based on the RFS theory. We derive the analytic expressions for the extended Hölder divergence (EHD) for the case when the multi-target densities have the form of Poisson RFSs and apply it to the PHD filter in a sequential Monte Carlo implementation. We evaluated the performance of the proposed reward function in a multi-target sensor management problem where the next position of a moving observer is decided according to the value of the EHD-based reward function. The performance of the algorithm is compared against, in terms of OSPA metric, and it is shown that the proposed reward function is superior to other similar reward functions in multi-target sensor management literature. We also show that it is possible to adapt the management algorithm to different situations, such as static and dynamic environments.