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Scattering theory and linear least squares estimation : Part II: Discrete-time problems

Friedlander, Benjamin ; Kailath, Thomas and Ljung, Lennart (1976) p.71-82
Abstract
A certain "star-product" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g., the distinctions between time and measurement updates, predicted and filtered estimates, etc. Several other applications of the scattering framework are presented, including doubling formulas for the error covariance, a change of initial conditions formula, equations for a backwards Markov state model, and a new derivation of the Chandrasekhar-type equations for the constant parameter case. The differences between the... (More)
A certain "star-product" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g., the distinctions between time and measurement updates, predicted and filtered estimates, etc. Several other applications of the scattering framework are presented, including doubling formulas for the error covariance, a change of initial conditions formula, equations for a backwards Markov state model, and a new derivation of the Chandrasekhar-type equations for the constant parameter case. The differences between the discrete-time and continuous-time are noted. (Less)
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author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes
pages
71 - 82
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
DOI
10.1109/CDC.1975.270648
language
English
LU publication?
no
id
c39921f9-b80d-4df3-a16d-9bd168121bea
date added to LUP
2018-12-27 11:59:13
date last changed
2020-07-07 11:33:51
@inproceedings{c39921f9-b80d-4df3-a16d-9bd168121bea,
  abstract     = {{A certain "star-product" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g., the distinctions between time and measurement updates, predicted and filtered estimates, etc. Several other applications of the scattering framework are presented, including doubling formulas for the error covariance, a change of initial conditions formula, equations for a backwards Markov state model, and a new derivation of the Chandrasekhar-type equations for the constant parameter case. The differences between the discrete-time and continuous-time are noted.}},
  author       = {{Friedlander, Benjamin and Kailath, Thomas and Ljung, Lennart}},
  booktitle    = {{1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes}},
  language     = {{eng}},
  pages        = {{71--82}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Scattering theory and linear least squares estimation : Part II: Discrete-time problems}},
  url          = {{http://dx.doi.org/10.1109/CDC.1975.270648}},
  doi          = {{10.1109/CDC.1975.270648}},
  year         = {{1976}},
}