Design of the ordinary differential equation solver in the Yau filtering system

Kalman and Bucy (1961) proposed an important filtering system. However, in the extended Kalman filter, one needs to solve the Riccati equations and the initial data must be assumed to be in Gaussian distribution. There is no theorem to ensure the estimated result converges. Yau (1990) presented a new filtering system that uses a new direct method to solve nonlinear filtering systems with arbitrary initial condition; this system is called the Yau filter. The Yau filter guarantees that the final solutions will converge for any assumption of initial distribution. Therefore, the Yau filtering system is powerful and the realization of the Yau filtering system is valuable. We present a circuit system for solving the ordinary differential equations (ODEs) of the Yau filter. The Runge-Kutta method is used to create the data flow structure for the circuit system. An optimization method is then used to compress the circuit system. Experimental results are shown to demonstrate the performance of the circuit system.