Title :
Finite-dimensional filters with nonlinear drift. XV. New direct method for construction of universal finite-dimensional filter
Author :
Hu, Guo-Qing ; Yau, Stephen S T
Author_Institution :
Illinois Univ., Chicago, IL, USA
fDate :
1/1/2002 12:00:00 AM
Abstract :
We consider the explicit solution of Duncan-Mortensen-Zakai (DMZ) equation for the finite-dimensional filtering system. We show that under certain conditions, the nonlinear filtering system 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 :
Kalman filters; differential equations; multidimensional systems; nonlinear filters; state-space methods; Benes filters; DMZ equation; Duncan-Mortensen-Zakai equation; Kalman-Bucy filters; Kolmogorov-type equation; arbitrary initial condition; finite-dimensional filtering system; finite-dimensional filters; finite-dimensional nonlinear filters; nonlinear drift; nonlinear filtering system; ordinary differential equations; state space dimension; sufficient statistics; universal finite-dimensional filter construction; Algebra; Differential algebraic equations; Differential equations; Information filtering; Information filters; Nonlinear equations; Nonlinear filters; Partial differential equations; State-space methods; Statistics;
Journal_Title :
Aerospace and Electronic Systems, IEEE Transactions on
