Multiple Integral Expansions for Nonlinear Filtering.

Abstract

Multiple stochastic integral expansions are applied to the problem of filtering a signal observed in additive noise. It is shown that the optimal mean-square estimate may be represented as a ratio of two multiple integral series. A formula for expanding the product of two multiple integrals is developed and applied to deriving equations for the kernels of best, finite expansion approximations to the optimal filter. These equations are studied in detail in the quadratic case. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1981
Accession Number
ADA103873

Entities

People

  • Daniel Ocone

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Counter IED

DTIC Thesaurus Topics

  • Applied Mathematics
  • Differential Equations
  • Equations
  • Filters
  • Filtration
  • Gaussian Processes
  • Integral Equations
  • Integrals
  • Markov Processes
  • Mathematical Filters
  • Mathematics
  • Probability
  • Random Variables
  • Scientific Research
  • Statistics
  • Stochastic Processes
  • United States

Fields of Study

  • Engineering
  • Mathematics

Readers

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  • Fluid Dynamics.