Stochastic Filtering Solutions for Ill-Posed Linear Problems and Their Extension to Measurable Transformations.

Abstract

An ill-posed linear problem Ax=y in Hilbert space is considered as a filtering problem AX+Z=Y for Hilbert space valued random elements. Depending on the models for the signal X and the noise Z, the solutions of this problem are discussed in the context of cylinder measures on hilbert spaces and their radification by the Abstract Wiener space concept. Extensions of the solutions to measurable transformations are given explicity. The filtering solution is related to the solution of the problem Ax=y obtained by Tichonov's regularization method.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1987
Accession Number
ADA186016

Entities

People

  • R. Brigola

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Banach Space
  • Computational Science
  • Cross Correlation
  • Data Science
  • Equations
  • Functional Analysis
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • Integral Equations
  • Mathematical Filters
  • Probability
  • Random Variables
  • Statistical Estimation
  • Statistical Inference
  • Stochastic Processes
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra

Technology Areas

  • Space