Nonlinear Filtering and Approximation Techniques

Abstract

This research concerned the theory of nonlinear filtering and numerical approximation in nonlinear filtering. The following results were obtained: 1) Under very general conditions it is shown that the conditional density in nonlinear filtering is the unique solution, within an appropriate class of functions, of the Zakai equation. The main conditions is that all coefficients are bounded and smooth. These coefficients are allowed to depend on the history of the observed process; 2) Developed a Lie algebraic criterion for the non-existence of finite dimensional filters; 3) Studied numerical methods for the approximate solution of Zakai's stochastic partial differential equations; 4) Developed approximate finite dimensional filters for high signal to noise ratio problems; and 5) Compared two algorithms for maximizing the likelihood function associated with parameter estimation in partially observed diffusion processes.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1988
Accession Number
ADA202519

Entities

People

  • E. Pardoux

Organizations

  • Institut National de Recherche en Informatique et en Automatique

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Filters
  • Filtration
  • Hidden Markov Models
  • Kalman Filters
  • Markov Chains
  • Mathematical Filters
  • Mathematics
  • Partial Differential Equations
  • Probability
  • Probability Distributions
  • Random Variables
  • Stochastic Processes

Fields of Study

  • Engineering

Readers

  • Calculus or Mathematical Analysis
  • Phased Array Antenna Design.
  • Statistical inference.