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

In this study, we propose a novel information theoretic reward function based on the statistical Hölder divergence (HD). The Hölder divergence is the generalization of Cauchy–Schwarz divergence (CSD). We extended Hölder divergence to the finite set statistics (FISST) densities, thus making it possible to use in the multiobject applications based on the random finite set (RFS) theory. We derive the analytic expressions for the extended Hölder divergence (EHD) for the case when the multitarget densities have the form of Poisson RFSs and apply it to the probability hypothesis density (PHD) filter in a sequential Monte Carlo (SMC) implementation. We evaluated the performance of the proposed reward function in a multitarget 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 the optimal subpattern assignment (OSPA) metric, and it is shown that the proposed reward function is superior to other similar reward functions in multitarget sensor management literature. We also show that it is possible to adapt the management algorithm to different situations, such as static and dynamic environments.