A Probabilistic Approach for Adaptive State-Space Partitioning

The multiple Bayesian filtering approach is based on the partitioning of the state-space in several lower dimensional subspaces, combined with a set of parallel filters that characterize the marginal subspace posteriors. This solution has been shown to perform well and solve some of the problems typically suffered by standard Bayesian filters, such as the curse-of-dimensionality, in some scenarios. An inherent problem in the application of multiple Gaussian filters (MGF) and multiple particle filters (MPF) proposed in the literature is how to partition the state-space. A closed answer does not exist because this is an application-dependent problem. In this contribution we further elaborate on the multiple filtering approach, and propose a probabilistic adaptive state-partitioning strategy based on the crosscorrelation computed at each filter.