A Scattering Theory Framework for Fast Least-Squares Algorithms
1976 (English)In: Proceedings of the 4th International Symposium on Mulitvariate Analysis, 1976Conference paper (Refereed)
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
Signal processing, Riccati equation, Linear systems, White noise, Differential Equations
IdentifiersURN: urn:nbn:se:liu:diva-100803ISBN: 978-0720405200OAI: oai:DiVA.org:liu-100803DiVA: diva2:663737
4th International Symposium on Mulitvariate Analysis, Dayton, OH, USA, 16-21 June, 1976