Title :
Explicit solution of DMZ equation
Author :
Hu, Guo-Qing ; Yau, Stephen S T
Author_Institution :
Dept. of Math. Stat. & Comput. Sci., Illinois Univ., Chicago, IL, USA
Abstract :
We consider the explicit solution of the Duncan-Mortensen-Zakai (DMZ) equation for the finite dimensional filtering system. We show that the nonlinear filtering system under the Hu-Yau conditions can be solved explicitly with an arbitrary initial condition by solving and system of ordinary differential equations and a Kolmogorov-type equation. Let n be the dimension of state space. We show that we need only n sufficient statistics in order to solve the DMZ equation
Keywords :
Kalman filters; Lie algebras; differential equations; filtering theory; nonlinear filters; Duncan-Mortensen-Zakai equation; Hu-Yau conditions; Kolmogorov-type equation; explicit solution; finite dimensional filtering system; nonlinear filtering system; ordinary differential equations; sufficient statistics; Algebra; Differential algebraic equations; Differential equations; Ear; Filtering; Maximum likelihood detection; Nonlinear equations; Nonlinear filters; Partial differential equations; Statistics;
Conference_Titel :
Decision and Control, 1997., Proceedings of the 36th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
0-7803-4187-2
DOI :
10.1109/CDC.1997.649666
