Least-Squares Based and Gradient Based Iterative Parameter Estimation Algorithms for a Class of Linear-in-Parameters Multiple-Input Single-Output Output Error Systems

The identification of a class of linear-in-parameters multiple-input single-output systems is considered. By using the iterative search, a least-squares based iterative algorithm and a gradient based iterative algorithm are proposed. A nonlinear example is used to verify the effectiveness of the algorithms, and the simulation results show that the least-squares based iterative algorithm can produce more accurate parameter estimates than the gradient based iterative algorithm.

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Two recursive least squares parameter estimation algorithms for multirate multiple-input systems by using the auxiliary model

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2011.05.014 ◽

2012 ◽

Vol 82 (5) ◽

pp. 777-789 ◽

Cited By ~ 11

Author(s):

Lili Han ◽

Fangxiang Wu ◽

Jie Sheng ◽

Feng Ding

Keyword(s):

Parameter Estimation ◽

Least Squares ◽

Recursive Least Squares ◽

Auxiliary Model ◽

Estimation Algorithms ◽

Multiple Input

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Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

Journal of Applied Mathematics ◽

10.1155/2012/684074 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 13

Author(s):

Weili Xiong ◽

Wei Fan ◽

Rui Ding

Keyword(s):

Parameter Estimation ◽

Nonlinear Systems ◽

Least Squares ◽

Moving Average ◽

Estimation Algorithm ◽

Autoregressive Moving Average ◽

Parameter Estimates ◽

Persistent Excitation ◽

Estimation Algorithms ◽

Parameter Estimation Algorithm

This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

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Recursive Least Squares Identification Algorithms for Multiple-Input Nonlinear Box–Jenkins Systems Using the Maximum Likelihood Principle

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4030387 ◽

2015 ◽

Vol 11 (2) ◽

Cited By ~ 10

Author(s):

Feiyan Chen ◽

Feng Ding

Keyword(s):

Maximum Likelihood ◽

Least Squares ◽

Multiple Input Multiple Output ◽

Recursive Least Squares ◽

Parameter Estimates ◽

Likelihood Principle ◽

Maximum Likelihood Principle ◽

Single Output ◽

Multiple Input ◽

Least Squares Algorithm

Multiple-input multiple-output systems can be decomposed into several multiple-input single-output systems. This paper studies identification problems of multiple-input single-output nonlinear Box–Jenkins systems. In order to improve the computational efficiency, we decompose a multiple-input nonlinear Box–Jenkins system into two subsystems, one containing the parameters of the linear block, the other containing the parameters of the nonlinear block. A decomposition based maximum likelihood generalized extended least squares algorithm is derived for identifying the parameters of the system by using the maximum likelihood principle. Furthermore, a decomposition based generalized extended least squares algorithm is presented for comparison. The numerical example indicates that the proposed algorithms can effectively estimate the parameters of the nonlinear systems and can generate more accurate parameter estimates compared with existing methods.

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The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise

Complexity ◽

10.1155/2017/5292894 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 23

Author(s):

Jiling Ding

Keyword(s):

Least Squares ◽

Identification Problem ◽

Parameter Estimates ◽

Identification Algorithm ◽

Input Output ◽

Iterative Identification ◽

Hierarchical Identification ◽

Output Error ◽

Gradient Based ◽

Simulation Results

This paper considers the identification problem of multi-input-output-error autoregressive systems. A hierarchical gradient based iterative (H-GI) algorithm and a hierarchical least squares based iterative (H-LSI) algorithm are presented by using the hierarchical identification principle. A gradient based iterative (GI) algorithm and a least squares based iterative (LSI) algorithm are presented for comparison. The simulation results indicate that the H-LSI algorithm can obtain more accurate parameter estimates than the LSI algorithm, and the H-GI algorithm converges faster than the GI algorithm.

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Recursive and Iterative Least Squares Parameter Estimation Algorithms for Multiple-Input–Output-Error Systems with Autoregressive Noise

Circuits Systems and Signal Processing ◽

10.1007/s00034-017-0636-0 ◽

2017 ◽

Vol 37 (5) ◽

pp. 1884-1906 ◽

Cited By ~ 49

Author(s):

Jiling Ding

Keyword(s):

Parameter Estimation ◽

Least Squares ◽

Input Output ◽

Estimation Algorithms ◽

Output Error ◽

Multiple Input

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Parameter Estimation in Marketing Models in the Presence of Influential Response Data: Robust Regression and Applications

Journal of Marketing Research ◽

10.1177/002224378402100304 ◽

1984 ◽

Vol 21 (3) ◽

pp. 268-277 ◽

Cited By ~ 3

Author(s):

Vijay Mahajan ◽

Subhash Sharma ◽

Yoram Wind

Keyword(s):

Parameter Estimation ◽

Regression Analysis ◽

Least Squares ◽

Robust Regression ◽

Ordinary Least Squares ◽

Regression Coefficients ◽

Parameter Estimates ◽

Response Data ◽

Marketing Models ◽

Marketing Data

In marketing models, the presence of aberrant response values or outliers in data can distort the parameter estimates or regression coefficients obtained by means of ordinary least squares. The authors demonstrate the potential usefulness of the robust regression analysis in treating influential response values in marketing data.

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Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

ASME 2009 Dynamic Systems and Control Conference, Volume 1 ◽

10.1115/dscc2009-2552 ◽

2009 ◽

Author(s):

James R. McCusker ◽

Kourosh Danai

Keyword(s):

Parameter Estimation ◽

Least Squares ◽

Time Scale ◽

Prediction Error ◽

Nonlinear Least Squares ◽

Integrated Approach ◽

Parameter Estimates ◽

Model Parameters ◽

Single Model ◽

Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

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