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Explicit solution of DMZ equation in nonlinear filtering via solution of ODEs

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2 Author(s)
S. S. -T. Yau ; Dept. of Math., Univ. of Illinois, Chicago, China ; Y. -T. Lai

In this note, we develop a real-time and accurate solution for nonlinear filtering problems based on the Gaussian distribution. Specifically, we present an explicit solution of the Duncan-Mortensen-Zakai (DMZ) equation of the Yau filtering system, which includes the linear filtering system and exact filtering system. The solution is given in terms of a solution of a system of ordinary differential equations. In particular, our method can be implemented in hardware. The complexity of our algorithms is the same as those of Kalman-Bucy filters in the case of linear filtering systems.

Published in:

IEEE Transactions on Automatic Control  (Volume:48 ,  Issue: 3 )