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A Scattering Theory Framework for Fast Least-Squares Algorithms
Stanford University, CA, USA.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1976 (English)In: Proceedings of the 4th International Symposium on Mulitvariate Analysis, 1976Conference paper (Refereed)
Abstract [en]

 In scattering theory the Riccati equation arises in a natural family of equations evolving forwards as well as backwards in time. The authors show how this framework allows an interesting derivation of the fast Chandrasekhar-type equations for linear least-squares filtering of processes generated by a time-invariant, finite-dimensional linear system driven by white noise. The processes are not required to be stationary. The same ideas can be used to obtain Levinson- and Cholesky-type differential equations for the impulse responses of the whitening filter and the innovations representation of such processes. The scattering framework brings out clearly both the significance of the time-invariance of the parameters of the underlying finite-dimensional system and of the associated family of nonstationary processes. For stationary processes, it also becomes clear that the assumption of finite-dimensionality is unnecessary, but the proper extension of the nonstationary class of processes raises some interesting questions.

Place, publisher, year, edition, pages
Keyword [en]
Signal processing, Riccati equation, Linear systems, White noise, Differential Equations
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-100803ISBN: 978-0720405200OAI: diva2:663737
4th International Symposium on Mulitvariate Analysis, Dayton, OH, USA, 16-21 June, 1976
Available from: 2013-11-12 Created: 2013-11-12 Last updated: 2013-11-12

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Automatic ControlThe Institute of Technology
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