Approximate solution of nonlinear filtering problems by direct implementation of the Zakai equation

Numerical methods for the solution of the robust version of the Duncan-Mortensen-Zakai partial differential equation are considered. Both semidiscretization and complete discretization schemes are included. Direct implementation of such schemes via array processors is proposed as a design method for nonlinear filters. The importance of existence, uniqueness and tail behavior of solutions is related to properties of such implementations.