Title :
New direct method for Yau filtering system with arbitrary initial conditions
Author :
Yau, Stephen S -T ; Hu, Guo-Qing
Author_Institution :
Dept. of Math., Stat. & Comput. Sci., Illinois Univ., Chicago, IL, USA
Abstract :
In this paper we consider the explicit solution of the Duncan-Mortensen-Zakai (DMZ) equation for the finite dimensional filtering system. We show that the Yau filtering system (∂fj /∂xi-∂fi/∂xj=c ij=constant for all i,j) can be solved explicitly with an arbitrary initial condition by solving a 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 :
Lie algebras; differential equations; filtering theory; multidimensional systems; Duncan-Mortensen-Zakai equation; Kolmogorov-type equation; Yau filtering system; direct method; finite dimensional filtering system; ordinary differential equations; sufficient statistics; Algebra; Differential algebraic equations; Differential equations; Filtering; Mathematics; Nonlinear equations; Nonlinear filters; Partial differential equations; Riccati equations; Statistics;
Conference_Titel :
Decision and Control, 1996., Proceedings of the 35th IEEE Conference on
Conference_Location :
Kobe
Print_ISBN :
0-7803-3590-2
DOI :
10.1109/CDC.1996.573479
