TY - JOUR
T1 - Parametric identification of ARMAX models with unknown forming filters
AU - Escobar, Jesica
AU - Poznyak, Alexander
N1 - Publisher Copyright:
© 2021 The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
PY - 2022/3/1
Y1 - 2022/3/1
N2 - In this paper, we present the parameter estimation algorithm for the class of an extended ARMAX model containing a 'coloured' noise sequence, formed by an unknown finite-dimensional linear filter. This algorithm represents the extended versions of residual whitening method and least squares method, working in parallel, to identify the extended parameters obtained after the suggested linear model transformation. The strong consistency of the suggested method (convergence with probability one of the obtained extended parameters to their exact values) is proven. A good performance of the proposed method is illustrated by a numerical example with all polynomials containing unknown parameters.
AB - In this paper, we present the parameter estimation algorithm for the class of an extended ARMAX model containing a 'coloured' noise sequence, formed by an unknown finite-dimensional linear filter. This algorithm represents the extended versions of residual whitening method and least squares method, working in parallel, to identify the extended parameters obtained after the suggested linear model transformation. The strong consistency of the suggested method (convergence with probability one of the obtained extended parameters to their exact values) is proven. A good performance of the proposed method is illustrated by a numerical example with all polynomials containing unknown parameters.
KW - extended least squares method
KW - forming filter
KW - generalized error
KW - parameter estimation
UR - http://www.scopus.com/inward/record.url?scp=85126719894&partnerID=8YFLogxK
U2 - 10.1093/imamci/dnab042
DO - 10.1093/imamci/dnab042
M3 - Artículo
AN - SCOPUS:85126719894
SN - 0265-0754
VL - 39
SP - 171
EP - 184
JO - IMA Journal of Mathematical Control and Information
JF - IMA Journal of Mathematical Control and Information
IS - 1
ER -