DocumentCode
1928469
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
Volume
5
fYear
1997
fDate
10-12 Dec 1997
Firstpage
4455
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;
fLanguage
English
Publisher
ieee
Conference_Titel
Decision and Control, 1997., Proceedings of the 36th IEEE Conference on
Conference_Location
San Diego, CA
ISSN
0191-2216
Print_ISBN
0-7803-4187-2
Type
conf
DOI
10.1109/CDC.1997.649666
Filename
649666
Link To Document