Title :
Finite-dimensional filters with nonlinear drift X: explicit solution of DMZ equation
Author :
Yan, S.S.-T. ; Hu, Guo-Qing
Author_Institution :
Dept. of Math. Stat. & Comput. Sci., Illinois Univ., Chicago, IL, USA
fDate :
1/1/2001 12:00:00 AM
Abstract :
In this note, we consider the explicit solution of Duncan-Mortensen-Zakai (DMZ) equation for the finite-dimensional filtering system. We show that Yau´s (1990, 1994) filtering system (δfj/δxi)-(δfi /δxi)=cij=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 :
differential equations; filtering theory; multidimensional systems; nonlinear filters; DMZ equation; Duncan-Mortensen-Zakai equation; Kolmogorov-type equation; explicit solution; finite-dimensional filtering system; finite-dimensional filters; multidimensional state space; nonlinear drift; ordinary differential equations; Algebra; Convergence; Differential equations; Filtering; Job shop scheduling; Nonlinear equations; Nonlinear filters; Queueing analysis; Statistics; Stochastic processes;
Journal_Title :
Automatic Control, IEEE Transactions on
