Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering†

Using Bayes' theorem the conditional mean of the posterior probability density function is estimated via Monte Carlo techniques. Multi-stage, non-linear filtering requires the solution of high dimensional integrals. The new feature of the approach presented is that a combination of analytical and numerical methods yields a variance reduction which can also be interpreted as an accuracy improvement of approximate non-linear filter equations. Theorems are derived to prove zero sampling variance for the linear Gaussian case and experimental results indicate that the proposed estimators are feasible in non-linear situations.