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Scattering theory and linear least squares estimation : Part I: Continuous-time problems

Ljung, Lennart ; Kailath, Thomas and Friedlander, Benjamin (1976) In Proceedings of the IEEE 64(1). p.131-139
Abstract
The Riccati equation plays as important a role in scattering theory as it does in linear least squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. This framework is shown to be appropriate for estimation problems and makes possible simple derivations of known results as well as leading to several new results. Examples include the derivation of backward equations to solve forward Riccati equations, an analysis of the asymptotic behavior of the Riccati equation, the derivation of backward Markovian representations of stochastic processes, and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equations.
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Proceedings of the IEEE
volume
64
issue
1
pages
131 - 139
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:0016884199
ISSN
0018-9219
DOI
10.1109/PROC.1976.10074
language
English
LU publication?
no
id
ff2d792c-da55-4699-a05e-2dfbf65fcc73
date added to LUP
2018-12-27 11:48:31
date last changed
2025-04-04 15:29:41
@article{ff2d792c-da55-4699-a05e-2dfbf65fcc73,
  abstract     = {{The Riccati equation plays as important a role in scattering theory as it does in linear least squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. This framework is shown to be appropriate for estimation problems and makes possible simple derivations of known results as well as leading to several new results. Examples include the derivation of backward equations to solve forward Riccati equations, an analysis of the asymptotic behavior of the Riccati equation, the derivation of backward Markovian representations of stochastic processes, and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equations.}},
  author       = {{Ljung, Lennart and Kailath, Thomas and Friedlander, Benjamin}},
  issn         = {{0018-9219}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{131--139}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{Proceedings of the IEEE}},
  title        = {{Scattering theory and linear least squares estimation : Part I: Continuous-time problems}},
  url          = {{http://dx.doi.org/10.1109/PROC.1976.10074}},
  doi          = {{10.1109/PROC.1976.10074}},
  volume       = {{64}},
  year         = {{1976}},
}