A generalized instrumental variable estimation method for errors-in-variables identification problems

Söderström, Torsten

doi:10.1016/j.automatica.2011.05.010

Cited by 65 publications

(23 citation statements)

References 14 publications

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“…We have found, cf Söderström (2009), Hong, Söder-ström, andZheng (2007) and Söderström (2011) that many biascompensating schemes can be formulated as the general estimator (41)-(45), by appropriate choices of z 1 (t), z 2 (t) and W . We exemplify such choices in the next section.…”

Section: General Frameworkmentioning

confidence: 95%

“…Details are provided in Diversi et al (2003), where this approach was first proposed. It is shown in Söderström (2011) that it corresponds to…”

Section: Various Examplesmentioning

confidence: 99%

“…the Frisch scheme) require that some of the defining equations are exactly satisfied. The relations between the BCLS methods have been analyzed in Hong and Söderström (2009) whereas in Söderström (2011) it is shown how these methods can be put into a general framework, resulting in a Generalized Instrumental Variable Estimator (GIVE). The GIVE framework provides also a general accuracy analysis leading to the asymptotic covariance matrix of the parameter estimates (Söderström, 2011).…”

Section: Introductionmentioning

confidence: 99%

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A unified framework for EIV identification methods when the measurement noises are mutually correlated

2014

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Section: General Frameworkmentioning

confidence: 95%

“…Details are provided in Diversi et al (2003), where this approach was first proposed. It is shown in Söderström (2011) that it corresponds to…”

Section: Various Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A unified framework for EIV identification methods when the measurement noises are mutually correlated

2014

Self Cite

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“…The IV method [47], [48] is to reduce the bias of the OLS estimate and yields the following estimate:θ…”

Section: Problem Formulationmentioning

confidence: 99%

System Identification in Presence of Outliers

Wang

Zhang

et al. 2016

IEEE Trans. Cybern.

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The outlier detection problem for dynamic systems is formulated as a matrix decomposition problem with low rank and sparse matrices, and further recast as a semidefinite programming problem. A fast algorithm is presented to solve the resulting problem while keeping the solution matrix structure and it can greatly reduce the computational cost over the standard interior-point method. The computational burden is further reduced by proper construction of subsets of the raw data without violating low-rank property of the involved matrix. The proposed method can make exact detection of outliers in case of no or little noise in output observations. In case of significant noise, a novel approach based on under-sampling with averaging is developed to denoise while retaining the saliency of outliers, and so-filtered data enables successful outlier detection with the proposed method while the existing filtering methods fail. Use of recovered "clean" data from the proposed method can give much better parameter estimation compared with that based on the raw data.

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“…The method may not work well when the input is not a true auto regressive moving average (ARMA) process. In one study, 13 the author puts several methods into a general framework, resulting in a Generalized Instrumental Variable Estimator. [5][6][7][8][9][10] The Frisch estimation method is based on the assumption of white input and white output measurement noise.…”

Section: Introductionmentioning

confidence: 99%

Identification of errors‐in‐variables systems: An asymptotic approach

Liu

Zhu

2017

Adaptive Control & Signal

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This work studies the identification of errors-in-variables (EIV) systems. An asymptotic method (ASYM) is developed for the EIV system. Firstly, an auto regressive with exogeneous (ARX) model estimation method is proposed, which is consistent for EIV systems. Then the asymptotic variance expression of the estimated high-order ARX model is derived, which forms the basis of the ASYM method. In parameter estimation, the ASYM starts with a high-order ARX model estimation followed by a frequency domain weighted model reduction. The obtained model is consistent, and its efficiency needs to be investigated. Besides parameter estimation, a criterion for model order selection is proposed, which is based on frequency domain considerations, and the frequency domain error bound is established that can be used for model validation. Simulations and comparisons with other methods are used to illustrate the performance of the method. KEYWORDSARX model, asymptotic method, Box-Jenkins model, errors-in-variables models, input noise variance 1 1126

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A generalized instrumental variable estimation method for errors-in-variables identification problems

Cited by 65 publications

References 14 publications

A unified framework for EIV identification methods when the measurement noises are mutually correlated

A unified framework for EIV identification methods when the measurement noises are mutually correlated

System Identification in Presence of Outliers

Identification of errors‐in‐variables systems: An asymptotic approach

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