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

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**Scattering theory and linear least squares estimation : Part I: Continuous-time problems.** / Ljung, Lennart; Kailath, Thomas ; Friedlander, Benjamin .

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift

### Harvard

*Proceedings of the IEEE*, vol. 64, nr. 1, s. 131-139. https://doi.org/10.1109/PROC.1976.10074

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*Proceedings of the IEEE*,

*64*(1), 131-139. https://doi.org/10.1109/PROC.1976.10074

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*Proceedings of the IEEE*. 1976, 64(1). 131-139. https://doi.org/10.1109/PROC.1976.10074

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TY - JOUR

T1 - Scattering theory and linear least squares estimation

T2 - Part I: Continuous-time problems

AU - Ljung, Lennart

AU - Kailath, Thomas

AU - Friedlander, Benjamin

PY - 1976

Y1 - 1976

N2 - 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.

AB - 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.

U2 - 10.1109/PROC.1976.10074

DO - 10.1109/PROC.1976.10074

M3 - Article

VL - 64

SP - 131

EP - 139

JO - Proceedings of the IEEE

JF - Proceedings of the IEEE

SN - 0018-9219

IS - 1

ER -