A discrete nonlinear filter for fast sampled problems based on vector quantization

The Chapman-Kolmogorov equation and Bayes' rule provide a conceptually simple solution to the discrete nonlinear filtering problem. Unfortunately these equations involve high order multiple integrals which are, in general, computationally intractable. Here we exploit recent results on an incremental form of the discrete nonlinear filter to develop a novel algorithm which is computationally straightforward at high sample rates.We illustrate performance by a two examples.