A Split-Step Solution of the Fokker-Planck Equation for the Conditional Density
Hendrick C. Lambert, Fred E. Daum, John Weatherwax · 2006
We have developed and tested a new algorithm, which we call the "wave filter," that solves the nonlinear filtering problem with discrete-time measurements by solving the Fokker-Planck equation for the conditional probability density function using a split-step technique. The wave filter uses fast convolution to compute the effect of process noise at discrete times. Between measurements, the conditional density is propagated by solving a system of ordinary differential equations. Measurement update is carried out via Bayes' rule. We propose the "adjoint method" to reduce the computational complexity of the algorithm by adaptively varying the mesh size.