Accession Number : ADA310330

Title :   PDE, Differential Geometric and Algebraic Methods for Nonlinear Filtering.

Descriptive Note : Final rept. 15 Oct 92-14 Oct 95,

Corporate Author : ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF MATHEMATICS STATISTICS AND COMPUTER SC IENCE

Personal Author(s) : Yau, Stephen S.

PDF Url : ADA310330

Report Date : FEB 1996

Pagination or Media Count : 25

Abstract : We have found the best solution to Duncan-Mortensen-Zakai (DMZ) equation for linear filtering system and exact 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. In the other direction, we prove that if the estimation algebra is finite dimensional and of maximal rank, then the matrix is linear in the sense that all the entries are degree one polynomials. This theorem plays a fundamental role in the classification of finite dimensional estimate algebra of maximal rank.

Descriptors :   *LINEAR FILTERING, *PARTIAL DIFFERENTIAL EQUATIONS, MATHEMATICAL MODELS, ALGORITHMS, STOCHASTIC PROCESSES, MATRICES(MATHEMATICS), MATHEMATICAL FILTERS, NONLINEAR SYSTEMS, POLYNOMIALS, SYSTEMS ANALYSIS, MAPPING(TRANSFORMATIONS), NONLINEAR PROGRAMMING.

Subject Categories : Numerical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE