Orthogonal Transformation (Square-Root) Implementations of the Generalized Chandrasekhar and Generalized Levinson Algorithms

  • T. Kailath
  • A. Vieira
  • M. Morf

Abstract

In recent work, we have shown how least-squares estimation problems for arbitrary nonstationary processes can be speeded up by using the notion of an index of nonstationarity and a corresponding generalized Levinson algorithm. It was also shown that when the nonstationary processes have constant-parameter state-space models, the generalized Levinson algorithms reduce to the generalized Chandrasekhar equations. In this paper we shall show that the explicit equations of the above algorithms can be replaced by certain implicitly defined J-orthogonal transformation procedures, where J is a signature matrix (zero everywhere except for ±l’s on the diagonal). In the state-space case, these methods yield the previously-derived fast square-root algorithms of Morf and Kailath.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • T. Kailath
    • 1
  • A. Vieira
    • 1
  • M. Morf
    • 1
  1. 1.Information Systems Laboratory, Department of Electrical EngineeringStanford UniversityStanfordUSA

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