PDE, Differential Geometric, Wavelet and Algebraic Methods in Nonlinear Filtering

Abstract

We have found the best solution to Duncan-Mortensen-Zakai (DMZ) equation for Yau filtering system, which is the most general filtering system and includes both linear filtering and exact filtering systems. 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 the state space. We show that we need only n sufficient statistics in order to solve DMZ equation. In the other direction, we prove that if the estimation algebra is finite dimensional of maximal rank, then the Wang's matrix has constant structures. this theorem plays a fundamental role in the classification of finite dimensional estimation algebra of maximal rank in fact we have classified all these Lie algebras for statespace dimension less than or equal to 6.

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Document Details

Document Type
Technical Report
Publication Date
Mar 23, 1999
Accession Number
ADA365262

Entities

People

  • Stephen Sik-Sang Yau

Organizations

  • University of Illinois at Chicago

Tags

Communities of Interest

  • Human Systems
  • Space

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Classification
  • Differential Equations
  • Equations
  • Filters
  • Filtration
  • Kolmogorov Equations
  • Linear Filtering
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Polynomials
  • Quadratic Equations
  • Statistics
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Image Processing and Computer Vision.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space