We propose the use of a novel Mahalanobis distance for comparing point processes in the context of multi-target tracking and sensor fusion. In drawing on methods analogous to free field theory, we derive analytic expressions for key models such as the Poisson and Bernoulli point processes. Moreover, we present efficient Monte Carlo integration schemes that enable practical computation in cases where the point processes are represented by Gaussian mixtures. Simulation results confirm that our proposed distance can be applied in practice.

A conditional multi-target mean and covariance are calculated based on a Gaussian random field approximation of point processes. We derive a particular solution based on a multi-target model commonly used for multi-target tracking. The resulting conditional mean is shown to coincide with the classical first-order filter, while the posterior covariance–owing to the Gaussian approximation–exhibits a refined, localized representation of spatial correlations that contrasts with previous point process derivations. The proposed framework opens new avenues for interdisciplinary research in multi-target tracking, bridging point process theory and field theoretic methods.

The ability to rapidly select an optimal subset of sensors is of critical importance in massive multi-sensor target tracking. Various information metrics exist for selecting the subset of sensors that is most informative with respect to the target being tracked. Moreover, information bounds were proposed as approximate metrics in order to speed up the selection algorithms. In this paper, we provide an analysis on the information loss and its impact on the subset selection problem when employing an information upper bound instead of the exact mutual information metric. We design several greedy sensor-selection algorithms that sequentially evaluate the exact mutual information between a set of sensors and the target. Subsequently, we compare these algorithms with a sensor-selection method that employs an information upper bound and highlight situations where the latter finds sub-optimal solutions.