Adaptive Meshfree Backward SDE Filter

An adaptive meshfree approach is proposed to solve the nonlinear filtering problem based on forward backward stochastic differential equations. The algorithm relies on the fact that the solution of the forward backward stochastic differential equations is the unnormalized filtering density as required in the nonlinear filtering problem. Adaptive space points are constructed in a stochastic manner to improve the efficiency of the algorithm. We also introduce a Markov chain Monte Carlo resampling method to address the degeneracy problem of the adaptive space points. Numerical experiments are carried out against the auxiliary particle filter method in the rugged double well potential problem as well as the multitarget tracking problem to demonstrate the superior performance of our algorithm.