Three Methods in Solving the Nonlinear Filtering Problem
January 27, 2010 3pm, 206 SEC
Abstract
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
theoretically.
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