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Stochastic Systems: Modeling, Identification and Optimization, I pp 116–123Cite as

A reduced dimensionality method for the steady-state Kalman filter

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Part of the Mathematical Programming Studies book series (MATHPROGRAMM,volume 5)

Abstract

We consider the standard Kalman filtering problem in which the dimension of the output (measurement) vector is p, while the dimension of the state-space for the process model is n. The usual approach to determination of the steady-state gain matrix involves solving an algebraic Riccati equation consisting of n(n+1)/2 quadratically nonlinear equations. In this article, we present an alternate equation for the optimal gain matrix, itself, continuing only np quadratically nonlinear components. Numerical results comparing the efficiency of the new equation with the standard approach are also given.

Keywords

  • Riccati Equation
  • Gain Function
  • Algebraic Riccati Equation
  • Reduce Dimensionality Method
  • Observation Process

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Authors and Affiliations

  1. International Institute for Applied Systems Analysis, Laxenburg, Australia

    J. Casti

Authors
  1. J. Casti
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Editor information

Roger J.- B. Wets

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© 1976 The Mathematical Programming Society

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Casti, J. (1976). A reduced dimensionality method for the steady-state Kalman filter. In: Wets, R.J.B. (eds) Stochastic Systems: Modeling, Identification and Optimization, I. Mathematical Programming Studies, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120769

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  • DOI: https://doi.org/10.1007/BFb0120769

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00783-5

  • Online ISBN: 978-3-642-00784-2

  • eBook Packages: Springer Book Archive

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