Square-Root Algorithms for the Continuous-Time Linear Least Squares Estimation Problem.

Abstract

A simple differential equation for the triangular square-root of the error covariance of the linear state estimator is derived. Previous algorithms involved an antisymmetric matrix in the square-root differential equation. In the constant model case, Chandrasekhar-type equations are shown to constitute a set of fast square-root algorithms for the derivative of the error variance. Square-Root algorithms for the smoothing problem are presented and as in the discrete case, an array method for handling continuous square-roots is developed. This method also yields very naturally the usual normalizations of stochastic calculus, suggesting extensions to more general stochastic equations, even to estimators for nonlinear models. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1977
Accession Number
ADA050305

Entities

People

  • B. Levy
  • M. Morf
  • Thomas Kailath

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Covariance
  • Differential Equations
  • Electrical Engineering
  • Engineering
  • Equations
  • Estimators
  • Filters
  • Linear Systems
  • Mathematical Filters
  • New York
  • Nonlinear Dynamics
  • Numbers
  • Riccati Equation
  • Space Navigation
  • Square Roots

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.