Refined instrumental variable methods for identification of Hammerstein continuous-time Box-Jenkins models

Laurain, Vincent; Gilson, Marion; Garnier, Hugues; Young, Peter C.

doi:10.1109/cdc.2008.4738853

Cited by 26 publications

(30 citation statements)

References 29 publications

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“…An instrumental variable (IV) method using the nonlinear transformed instruments has been studied to improve the estimates' consistency [17]. For Hammerstein Box-Jenkin models, a refined IV method has been reported based on the extended framework [18]. Although the IV methods are consistent, the parameter reduction step and the regularization of nonlinear basis functions were not discussed.…”

Section: Most Of the Iterative Identification Methods Transform The Omentioning

confidence: 99%

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Regularized estimation of Hammerstein systems using a decomposition-based iterative instrumental variable method

Saini¹,

Dewan²

2017

Turk J Elec Eng & Comp Sci

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This paper presents a two-step instrumental variable (IV) method to obtain the regularized and consistent parameter estimates of the Hammerstein ARMAX model based on the bilinear parameterized form. The two-step identification method consists of estimating the bilinear parameters in the first step, followed by parameter reduction in the second step. An iterative identification method is proposed, based on the idea of separating the bilinear form in the two separable forms with partial parameters and solving the decomposed model forms iteratively. The IV-based estimation is integrated into the formulated decomposed structure by introducing the instruments constructed from the estimated auxiliary model outputs. It is shown that in a stochastic environment the proposed IV method produces consistent estimates in the presence of correlated noise disturbances. The validity of the proposed algorithm is verified with the help of extensive simulations using a Monte Carlo study.

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Section: Most Of the Iterative Identification Methods Transform The Omentioning

confidence: 99%

“…For this the coefficient of the first basis function is assumed to be 1, i.e. d 1 = 1 [1,7,[11][12][13][14][15][17][18]. Then the estimates of the coefficient vectors a and β can be obtained by considering the following minimization problem:…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Regularized estimation of Hammerstein systems using a decomposition-based iterative instrumental variable method

Saini¹,

Dewan²

2017

Turk J Elec Eng & Comp Sci

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“…Whilst there would appear to be an issue associated with the estimates of the over-parameterised B( β ) in (32), whereby b¯s and b s are combined within one vector, it was shown in [41] that b¯s can be directly obtained from …”

Section: Considering Zero Initial Conditions the Laplace Transform Omentioning

confidence: 99%

“…The refined instrumental variable method for linear continuous-time systems was first proposed by Young and Jakeman [39] and extended for the fractional-order systems in [40]. It has also been successfully extended to estimate the parameters of the Hammerstein and Wiener models [38,41] in which the static output non-linear function is assumed to be invertible [38].…”

mentioning

confidence: 99%

Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

Allafi

Zajic

Uddin

et al. 2017

IET Control Theory & Applications

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This study proposes a direct parameter estimation approach from observed input-output data of a stochastic singleinput-single-output fractional-order continuous-time Hammerstein-Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input-output data by considering the system to be a multi-input-single-output linear fractional-order continuoustime model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input nonlinear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein-Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein-Wiener output model.

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“…The main reason of this increasing interest is that IV methods offer a similar performance to the extended Least Square (LS) methods or other Prediction Error Minimization (PEM) methods (see Ljung (2009), Rao and Garnier (2004)) and provide consistent results even for an imperfect noise structure which is the case in most practical applications. These approaches have been used in many different frameworks such as direct continuous-time (Garnier & Wang, 2008;Rao & Garnier, 2004), nonlinear (Laurain, Gilson, Garnier, & Young, 2008) or closed-loop identification (Gilson, Garnier, Young, & Van den Hof, 2009;Gilson & Van den Hof, 2005) and lead to optimal estimates in the LTI linear case if the system belongs to the model set defined.…”

Section: Introductionmentioning

confidence: 99%

Refined instrumental variable methods for identification of LPV Box–Jenkins models

et al. 2010

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a b s t r a c tThe identification of linear parameter-varying systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive colored noise. In the Box-Jenkins and output-error cases, it is shown that the currently available linear regression and instrumental variable methods from the literature are far from being optimal in terms of bias and variance of the estimates. To overcome the underlying problems, a refined instrumental variable method is introduced. The proposed approach is compared to the existing methods via a representative simulation example.

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Refined instrumental variable methods for identification of Hammerstein continuous-time Box-Jenkins models

Cited by 26 publications

References 29 publications

Regularized estimation of Hammerstein systems using a decomposition-based iterative instrumental variable method

Regularized estimation of Hammerstein systems using a decomposition-based iterative instrumental variable method

Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

Refined instrumental variable methods for identification of LPV Box–Jenkins models

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