Finite-dimensional filters with nonlinear drift. XV. New direct method for construction of universal finite-dimensional filter
Guoqing Hu, Stephen S.‐T. Yau · IEEE Transactions on Aerospace and Electronic Systems · 2002
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.