<title>Nonlinear filtering with quasi-Monte Carlo methods</title>

Abstract

We describe a new hybrid particle filter that has two novel features: (1) it uses quasi-Monte Carlo samples rather than the conventional Monte Carlo sampling, and (2) it implements Bayes' rule exactly using smooth densities from the exponential family. Theory and numerical experiments over the last decade have shown that quasi-Monte Carlo sampling is vastly superior to Monte Carlo samples for certain high dimensional integrals, and we exploit this fact to reduce the computational complexity of our new particle filter. The main problem with conventional particle filters is the curse of dimensionality. We mitigate this issue by avoiding particle depletion, by implementing Bayes' rule exactly using smooth densities from the exponential family.