Algebraic Structure and Finite Dimensional Nonlinear Estimation,

Abstract

Optimal recursive state estimators have been derived for very general classes of nonlinear stochastic systems. The optimal estimator requires, in general, an infinite dimensional computation to generate the conditional mean of the system state given the past observations. This computation involves either the solution of a stochastic partial differential equations for the conditional density or an infinite set of coupled ordinary stochastic differential equations for the conditional moments. However, the class of linear stochastic systems with linear observations and white Gaussian plant and observation noises has a particularly appealing structure, because the optimal state estimator consists of a finite dimensional linear system -- the Kalman-Bucy filter. In this paper the authors exploit the algebraic structure of certain other classes of systems, in order to prove that the optimal estimators for these systems are finite dimensional.

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1975
Accession Number
ADA012019

Entities

People

  • Alan S. Willsky
  • Steven I Marcus

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Computational Complexity
  • Computations
  • Differential Equations
  • Equations
  • Estimators
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Observation
  • Optimal Estimators
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Statistical inference.