On weak distance between distributions in application to tracking

In this paper, we consider the general problem of assessing accuracy losses associated with converting distributions from one representation to the other. Based on distribution theory, we argue that any such quality metric is intrinsically problem-specific, and that the choice of the so-called probe functions is unavoidable. We discuss the meaning of these definitions in the context of tracking, and how probe functions may encode valuable a priori assumptions about sensors and the tracking quality. Based on these ideas, we suggest two novel algorithms: one to prune Gaussian mixtures (GMs) and the other to perform a weighted sampling of GMs. Finally, we compare the tracking quality between identical trackers where GM pruning is done with the suggested and the conventional algorithms.