Generalized Two-Stage Particle Filter for High Dimensions

In this paper, we proposed a novel generalized two-stage particle filter for high dimensions that can be applied to all model setups, regardless of the dimension sizes of the states and data. The new filter modifies the proposal distribution in the first stage, similar to the two-stage particle filter, but uses partitioning and predictions of the rest of the state components to carry on. Additionally, we derived a recursive expression for the posterior distribution of the tempering coefficient, which serves in the construction of the new proposal distribution in the first stage. The proposed filter tracks well even with a small number of particles. Moreover, it has no limitation in minimum number of particles used like the multiple particle filter, and its performance wins over the topologically-weighted random partitioning multiple particle filter in higher dimensions, especially in the cases where the dimension of the data is smaller than that of the states.