Abstract: We propose a divide-and-conquer approach to filtering. The proposed approach decomposes the state variable into low-dimensional components, to which standard particle filtering tools can be successfully applied, and recursively merges them to recover the full filtering distribution. This approach is less dependent on factorizing transition densities and observation likelihoods than are competing approaches, and can be applied to a broader class of models. We compare the performance of the proposed approach with that of state-of-the-art methods on a benchmark problem, and show that the proposed method is broadly comparable in settings in which the other methods are applicable, and that it can be applied in settings in which they cannot.

Key words and phrases: Data assimilation, marginal particle filter, particle filtering, spatio-temporal models, state-space model.