Multiple particle filtering for inference in the presence of state correlation of unknown mixing parameters

We present a novel Rao-Blackwellized multiple particle filtering method for inference of correlated latent states observed via nonlinear functions. We adopt a state-space framework and model the dynamic correlated states using a mixing matrix, embedded in white Gaussian noise. The critical challenges in practice are the lack of knowledge about the mixing parameters and the possibly large dimensionality of the state. We address these issues by implementing Rao-Blackwellization of the unknown parameters and adopting a divide-and-conquer approach. The former strategy amounts to marginalizing out some of the variables; the latter breaks the space of the system in subsystems, and runs a separate particle filter for each of them. The resulting Rao-Blackwellized multiple particle filtering accurately estimates the correlated latent states, as shown by the provided simulation results.