Title :
Finite-dimensional filters with nonlinear drift. III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for the linear filtering system and the Benes filtering system
Author :
Shing-Tung Yau ; Yau, Stephen S T
Author_Institution :
Dept. of Math., Harvard Univ., Cambridge, MA, USA
Abstract :
We consider the Duncan-Mortensen-Zakai (DMZ) equation for the Kalman-Bucy filtering system and Benes filtering system. We show that this equation 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; probability; Benes filtering; Duncan-Mortensen-Zakai equation; Kalman-Bucy filtering; Kolmogorov-type equation; arbitrary initial condition; finite-dimensional filters; linear filtering; nonlinear drift; ordinary differential equations; statistics; Algebra; Differential algebraic equations; Differential equations; Filtering; Maximum likelihood detection; Nonlinear equations; Nonlinear filters; Partial differential equations; State-space methods; Statistics; Stochastic processes;
Journal_Title :
Aerospace and Electronic Systems, IEEE Transactions on
