A Backward Doubly Stochastic Differential Equation Approach for Nonlinear Filtering Problems (Communications in Computational Physics, 2018)
A backward doubly stochastic differential equation (BDSDE) based nonlinearfiltering method is considered. The solution of the BDSDE is the unnormalizeddensity function of the conditional expectation of the state variable with respect tothe observation filtration, which solves the nonlinear filtering problem through theKallianpur formula. A first order finite difference algorithm is constructed to solve theBSDES, which results in an accurate numerical method for nonlinear filtering problems.Numerical experiments demonstrate that the BDSDE filter has the potential tosignificantly outperform some of the well known nonlinear filtering methods such asparticle filter and Zakai filter in both numerical accuracy and computational complexity.