Parallel ODE-solvers for Kalman-Bucy filter with arbitrary initial condition

Despite its wide range of applications, the Kalman-Bucy filter has its weaknesses. One of them is the Gaussian requirement of the initial data. A new direct method for Kalman-Bucy filter with arbitrary initial condition was developed recently by Yau (1994). His result is compared favorably to other methods. In particular, the filtering problem is reduced to a Kolmogorov type partial differential equation (PDE), and a system of 2n+1 differential equations, where n is the dimension of the state space. Since the PDE is independent of the observed data, it can be solved off-line. Hence the key to the success of this novel approach to real-life application would be an efficient algorithm for solving the system of ODE´s. In this paper, we have proposed parallel methods suitable for this system of ODE´s