Simulation and Computation Research on Nonlinear Filtering

摘要

We have found the best solution to Duncan-Mortensen-Zakai equation for Kalman-Bucy filtering system with arbitrary initial condition. We show that this equation can be solved explicitly with an arbitrary initial condition by solving a system of ordinary differential equations and a Kolmogorov type equation. The Kolmogorov equation can be computed off time. We have given several algorithms to do parallel computation for the system of ordinary differential equations. As a result, we achieve the real-time solution to Duncan-Mortensen-Zakai equation for Yau filtering system with initial condition. Under Yau's direction, Professor Yeu-Tai Lai and his students in the Department of Electrical Engineering, National Cheng Kung University, Taiwan, has successfully implemented an ODEs solver for the Yau filtering system in hardware.