Weighted total least squares: necessary and sufficient conditions, fixed and random parameters

Fang, Xing

doi:10.1007/s00190-013-0643-2

Cited by 122 publications

(54 citation statements)

References 32 publications

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“…WLSM has been widely used in many fields by researchers: e.g. Veraart et al used WLSM to estimate the diffusion MRI parameters [12]; Zhuang et al proposed an improved meshless Shephard and WLSM possessing the delta property [13]; Fang did a complete analysis of the WLSM problem considering fixed and random parameters [14]; Mahboub and Sharifi developed a WLSM with linear and quadratic constraints [15]; Ciucci adopted WLSM to revisit parameter identification in electrochemical impedance spectroscopy [16]; Wang et al used WLSM to make Multi-Gaussian fitting for pulse waveform [17]; Khatibinia et al assessed seismic reliability of RC structures including soil-structure interaction using WLSM [18]; Parrish et al used WLSM to analyse the acceleration of coupled cluster singles and doubles [19]; Stanley and Doucouliagos did WLSM meta-analysis for neither fixed nor random conditions [20]; and Einemo and So used WLSM for target localization in distributed MIMO radar [21].…”

Section: Weighted Least Square Methodsmentioning

confidence: 99%

Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

Zhang¹,

Guo²,

Xi³

2017

PROMET

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Section: Weighted Least Square Methodsmentioning

confidence: 99%

Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

Zhang¹,

Guo²,

Xi³

2017

PROMET

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“…In order to demonstrate the performance of Algorithm 1, in this section, the algorithm will be applied to a straight line fitting problem representing the MEIV problem, compared with the general WLS algorithm and the algorithm proposed by Fang [6]. The observed data and their corresponding weights are listed in Table 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…An appropriate approach to solve EIV models is the total least squares (TLS) method. Now, there are many researches about the total least squares in algorithms such as the singular value decomposition (SVD) algorithm (Golub and Van Loan [8]) and the algorithm based on the Lagrange function (Schaffrin et al [16,17]; Fang [6]). For more information about the methodology of TLS, one can refer to Huffel et al [10,11].…”

Section: Introductionmentioning

confidence: 99%

On Mixed Total Least Squares for Parameter Estimation

Guo¹,

Peng²,

Li³

2017

Int. J. Appl. Math. Mach. Learning

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A mixed weighted total least squares (MWTLS) method is presented for an errors-invariables (EIV) model with some fixed columns in the coefficient matrix. An iterative algorithm is derived based on the proposed MWTLS method. Compared with the classical WTLS method, the method represented in this paper improves the computing speed of the estimated parameter, while the fixed columns of the coefficient matrix keeps unperturbed.Furthermore, a simulated example is carried out to demonstrate the performance of the proposed algorithm.

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“…A typical EIV model is similar to a GaussMarkov (GM) model but all the variables are subject to random errors. For further reading, see e.g., Van Huffel and Vandewalle (1991), Schaffrin and Wieser (2008), Felus (2004), Schaffrin et al (2012a, b), Mahboub et al (2012), Fang (2013Fang ( , 2014, Snow and Schaffrin (2012), Snow (2012) and Mahboub (2014), etc. Meanwhile, some other researchers investigated this problem traditionally; see e.g., Neitzel (2010) and Shen et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Adjustment of non-typical errors-in-variables models

2015

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In this contribution, non-typical errors-in-variables (EIV) model is introduced as a more general form of the so-called EIV model which is highly relevant for geodetic data processing. Total least-squares (TLS) algorithms within a typical EIV model cannot deal with the non-typical EIV models since the first order moment/mean of the random design matrix in a non-typical EIV model is not linear. In this paper, we propose a new algorithm besides a standard solution to deal with this model. To achieve this goal, first we review a classic algorithm in order to solve this problem using traditional non-linear leastsquares method within a non-linear mixed model. Then by comparison, weighted TLS algorithm within the typical EIV model can be replaced by the proposed approach after some slight modifications which results in an excellent approximate solution. This foundation is important because there is no need for linearization in the TLS algorithms. The proposed way is not sensitive to the approximate initial values of the unknown parameters and it is applicable to curve fitting, surface reconstruction or other non-typical EIV models. Here we employ it to the curve fitting. Also two examples convincingly demonstrate that the standard TLS solution of the non-typical EIV model is not admissible when it is incorrectly considered as a typical EIV model; i.e., the non-linear relationships of the elements of the random design matrix are neglected.

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Weighted total least squares: necessary and sufficient conditions, fixed and random parameters

Cited by 122 publications

References 32 publications

Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

On Mixed Total Least Squares for Parameter Estimation

Adjustment of non-typical errors-in-variables models

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