Stochastic Realization and Invariant Directions of the Matrix Riccati Equation.

Abstract

Invariant directions of the Riccati difference equation of Kalman filtering are shown to occur in a large class of prediction problems and to be related to a certain invariant subspace of the transpose of the feedback matrix. The discrete time stochastic realization problem is studied in its deterministic as well as probabilistic aspects. In particular a new derivation of the classification of the minimal markovain representations of the given process z is presented which is based on a certain backward filter of the innovations. For each markovian representation which can be determined from z, the space of invariant directions is decomposed into two subspaces, one on which it is possible to predict the state process without error forward in time and one on which this can be done backward in time. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1979
Accession Number
ADA070972

Entities

People

  • Michele Pavon

Organizations

  • University of Kentucky

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Difference Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Estimators
  • Filters
  • Invariance
  • Kalman Filters
  • Markov Processes
  • Mathematical Filters
  • Numbers
  • Rational Functions
  • Riccati Equation
  • Stochastic Processes
  • Transfer Functions
  • White Noise

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers