# Canonical input-output representation of linear multivariable stochastic systems and joint optimal parameter and state estimation.

G. Salut; J. Aguilar-Martín; S. Lefevre

Stochastica (1979)

- Volume: 3, Issue: 1, page 17-38
- ISSN: 0210-7821

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topSalut, G., Aguilar-Martín, J., and Lefevre, S.. "Canonical input-output representation of linear multivariable stochastic systems and joint optimal parameter and state estimation.." Stochastica 3.1 (1979): 17-38. <http://eudml.org/doc/38804>.

@article{Salut1979,

abstract = {In this paper a complete presentation is given of a new canonical representation of multi-input, multi-output linear stochastic systems. Its equivalence with operator form directly linked with ARMA processes as well as with classical state space representation is given, and a transfer matrix interpretation is developed in an example. The importance of the new representation is mainly in the fact that in the joint state and parameters estimation problem, all unknown parameters appear linearly when an input-output record is available. Moreover, if noises are Gaussian and their statistics are known, a conditionally time varying Kalman-Bucy type filter gives the recursive optimal estimation of parameters and state. Historical comments and remarks about the adaptive version of this algorithm are given. Finally an illustrative low order example is described.},

author = {Salut, G., Aguilar-Martín, J., Lefevre, S.},

journal = {Stochastica},

keywords = {Procesos estocásticos; Modelo input-output; Control multivariable; Estimación de estado; Estimación paramétrica; Filtro kalman; canonical input-output representation; linear multivariable stochastic systems; state estimation; state space representation; transfer matrix},

language = {eng},

number = {1},

pages = {17-38},

title = {Canonical input-output representation of linear multivariable stochastic systems and joint optimal parameter and state estimation.},

url = {http://eudml.org/doc/38804},

volume = {3},

year = {1979},

}

TY - JOUR

AU - Salut, G.

AU - Aguilar-Martín, J.

AU - Lefevre, S.

TI - Canonical input-output representation of linear multivariable stochastic systems and joint optimal parameter and state estimation.

JO - Stochastica

PY - 1979

VL - 3

IS - 1

SP - 17

EP - 38

AB - In this paper a complete presentation is given of a new canonical representation of multi-input, multi-output linear stochastic systems. Its equivalence with operator form directly linked with ARMA processes as well as with classical state space representation is given, and a transfer matrix interpretation is developed in an example. The importance of the new representation is mainly in the fact that in the joint state and parameters estimation problem, all unknown parameters appear linearly when an input-output record is available. Moreover, if noises are Gaussian and their statistics are known, a conditionally time varying Kalman-Bucy type filter gives the recursive optimal estimation of parameters and state. Historical comments and remarks about the adaptive version of this algorithm are given. Finally an illustrative low order example is described.

LA - eng

KW - Procesos estocásticos; Modelo input-output; Control multivariable; Estimación de estado; Estimación paramétrica; Filtro kalman; canonical input-output representation; linear multivariable stochastic systems; state estimation; state space representation; transfer matrix

UR - http://eudml.org/doc/38804

ER -

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