PDE, Differential Geometric and Algebraic Methods for Nonlinear Filtering.

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.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1996
Accession Number
ADA310330

Entities

People

  • Stephen Sik-Sang Yau

Organizations

  • University of Illinois at Chicago

Tags

Communities of Interest

  • Human Systems
  • Space

DTIC Thesaurus Topics

  • Algebra
  • Algebraic Geometry
  • Algorithms
  • Applied Mathematics
  • Classification
  • Complex Variables
  • Differential Equations
  • Equations
  • Geometry
  • Kolmogorov Equations
  • Mathematics
  • Partial Differential Equations
  • Polynomials
  • Probability
  • Statistics
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space