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A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems
Authors
Bartosiewicz
Bates
+36 more
Billings
Billings
Biqiang Mu
Box
Chen
Davidson
Dimitrov
Er-Wei Bai
Gourieroux
Haber
Heiser
Henderson
Jennrich
Jia
Kamenski
Klipp
Lehmann
Leontaritis
Ljung
Ljung
Němcová
Němcová
Quanmin Zhu
Sontag
Stoica
Söderström
Söderström
Treloar
Wei Xing Zheng
Zhao
Zheng
Zheng
Zheng
Zhu
Zhu
Zhu
Publication date
1 January 2017
Publisher
'Elsevier BV'
Doi
Cite
Abstract
© 2016 Elsevier Ltd This paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs. Despite its long history, a globally consistent identification algorithm remains illusive. This paper proposes a globally convergent identification algorithm for such nonlinear rational systems. To the best of our knowledge, this is the first globally convergent algorithm for the nonlinear rational systems. The technique employed is a two-step estimator. Though two-step estimators are known to produce consistent nonlinear least squares estimates if a N consistent estimate can be determined in the first step, how to find such a N consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two-step estimators. The technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step. This is achieved by involving model transformation, bias analysis, noise variance estimation, and bias compensation in the paper. Two simulation examples and a practical example are provided to verify the good performance of the proposed two-step estimator
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