Strongly consistent coefficient estimate for errors-in-variables models

For the single-input-single-output (SISO) errors-in-variables system it is assumed that the system input is an ARMA process and that the driven noise of the system input and the observation noise are jointly Gaussian. The two-dimensional observation made on system input and output is represented as...

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Bibliographic Details
Published in:Automatica (Oxford) 2005-06, Vol.41 (6), p.1025-1033
Main Authors: Chen, Han-Fu, Yang, Jun-Mei
Format: Article
Language:English
Subjects:
Applied sciences
ARMA
Computer science
control theory
systems
Control theory. Systems
Convergence rate
Errors-in-variables
Exact sciences and technology
Identifiability
Modelling and identification
Strong consistency
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Summary:For the single-input-single-output (SISO) errors-in-variables system it is assumed that the system input is an ARMA process and that the driven noise of the system input and the observation noise are jointly Gaussian. The two-dimensional observation made on system input and output is represented as a two-dimensional (2D) ARMA system of minimum phase driven by a sequence of 2D i.i.d. Gaussian random vectors (innovation representation). It is shown that the resulting ARMA system is identifiable, i.e., its coefficients are uniquely defined under reasonable conditions. Recursive algorithms are proposed for estimating coefficients of the ARMA representation including those contained in the original SISO system. The estimates are proved to be convergent to the true values with probability one and the convergence rate is derived as well. The theoretical results are justified by numerical simulation.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2004.12.007