Applications of the Multigrid Algorithm to Solving the Zakai Equation of Nonlinear Filtering with VLSI Implementation

An important question for us is: If the Zakai equation is defined in R^n, what is the maximum dimension n we can expect to allow, for real-time signal processing? We conduct an analysis of this question using the methods of R. W. Hockney for estimating performance of general computing systems. We find that dimensions no higher than about six or seven can be reasonably treated in conventional real-time signal processing environments, which is usually on the order of about one millisec, a time bound suggested by research on signal processing for the one-dimensional Zakai equation.