Communications in Information and Systems

Volume 8 (2008)

Number 3

New Algorithms in Real Time Solution of the Nonlinear Filtering Problem

Pages: 303 – 332



Stephen S. T. Yau


It is well known that the filtering theory has important applications in both military and commercial industries. The Kalman-Bucy filter has been used in many areas such as navigational and guidance systems, radar tracking, solar mapping, and satellite orbit determination. However, the Kalman-Bucy filter has limited applicability because of the linearity assumptions of the drift term and observation term as well as the Gaussian assumption of the initial value. Therefore there has been an intensive interest in solving the nonlinear filtering problem. The central problem of nonlinear filtering theory is to solve the DMZ equation in real time and memoryless way. In this paper, we shall describe three methods to solve the DMZ equation: Brockett-Mitter estimation algebra method, direct method, and new algorithm method. The first two methods are relatively easy to implement in hardware and can solve a large class of nonlinear filtering problems. We shall present the recent advance in the third method which solves all the nonlinear filtering problems in a real-time manner in theory.

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