Second Order Subspace Statistics for Adaptive State-Space Partitioning in Multiple Particle Filtering

One of the main challenges in nonlinear Bayesian filtering is the so-called curse of dimensionality, that is, the computational complexity increase and associated performance degradation in high-dimensional systems. In the context of particle filtering (PF), a possible solution to mitigate such performance loss is the multiple PF (MPF) approach, where the original state is partitioned into several lower dimensional subspaces, and a set of interconnected PFs are used to characterize the marginal subspace posteriors. Two key issues are: i) how to partition the state, which is application dependent, and ii) how to let the filters (i.e., subspaces) fuse or merge depending on the time-varying conditions of the system, in order to improve the overall estimation performance. We propose a probabilistic approach to the adaptive state-partitioning problem within the MPF, which is based on the computation of subspace second order statistics. An illustrative multiple target tracking example is considered to support the discussion.