Designing Likelihood Function in Block Particle Filter for Beating Curse of Dimensionality

Particle filter (PF) has proven effective for nonlinear identification scenarios; however, its performance in high-dimensional problems is often limited by the curse of dimensionality. To overcome this challenge, block particle filter (BPF) is proposed to reformulate a high-dimensional model into several blocks, so the identification of one high-dimensional system can be simplified into that for many lower-dimensional blocks. However, due to the coupling between blocks, the likelihood function for each state subgroup depends not only on its own state components but also on its neighboring subgroups - a dependency that the BPF does not address. In this work, we extend the BPF by developing likelihood functions that incorporate nuisance components, thereby enabling its application to coupled systems. The performance of the proposed algorithms is demonstrated through a numerical example of a forty-story Bouc-Wen frame structure subjected to ground motion.