Finite-dimensional filters with nonlinear drift X: Explicit solution of DMZ equation

Authors
Citation
Sst. Yau et Gq. Hu, Finite-dimensional filters with nonlinear drift X: Explicit solution of DMZ equation, IEEE AUTO C, 46(1), 2001, pp. 142-148
Citations number
25
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN journal
00189286 → ACNP
Volume
46
Issue
1
Year of publication
2001
Pages
142 - 148
Database
ISI
SICI code
0018-9286(200101)46:1<142:FFWNDX>2.0.ZU;2-#
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 filtering system ((partial derivativef(j)/partial derivativex(i)) - (parti al derivativef(i)/partial derivativex(j)) = 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. L et n be the dimension of state space. We show that we need only n sufficien t statistics in order to solve the DMZ equation.