On weighted total least-squares adjustment for linear regression

Schaffrin, Burkhard; Wieser, Andreas

doi:10.1007/s00190-007-0190-9

Cited by 248 publications

(151 citation statements)

References 9 publications

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“…has been chosen such as to allow a comparison of our MTLS to the "exact solution" reported by Neri et al [14] and the solution reported by Schaffrin and Wieser [17]. In fact, the results indicate that the estimated line parameters are the same and coincide with the exact solutions as reported by Neri et al [14] and Schaffrin and Wieser [17]. Therefore, it is possible to find exact results for a regression line analysis affected by errors, without requiring any kind of approximation.…”

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%

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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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Section: Numerical Examplesmentioning

confidence: 99%

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 way of taking this noise into account is suggested in Schaffrin and Wieser (2008), in which the Errors-in-Variables model is used, given by…”

Section: Post-transform Optimizationmentioning

confidence: 99%

Enhanced Hydroacoustic Range Robustness of Three-Stage Position Filter based on Long Baseline Measurements with Unknown Wave Speed**This work is supported by the Center of Autonomous Marine Operations and Systems (AMOS), grant no. 223254.

2016

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This paper considers the problem of constructing a globally convergent positionand velocity estimator with close-to-optimal noise properties using hydroacoustic long baseline measurements. Three ways of improving the range robustness of the three stage filter for long baseline measurements with unknown wave speed are suggested. One addition is employing depth measurements in addition to pseudo-range measurements, thus increasing range noise robustness and relaxing requirements for transponder placement from not co-planar to not colinear. Furthermore, a Kalman Filter with a linear measurement model is used, instead of a pseudo-linear time-varying measurement model and a step solving an optimization problem is also added. The proposed scheme is validated through simulation and compared to a standard Extended Kalman Filter and a perfect (non-implementable) Linearized Kalman Filter using real states as linearization point. Simulations suggest that the improved three stage filter will have similar stationary performance as the EKF while having significantly better transient performance and stability subjected to inaccurate initial estimates.

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“…Now, there are many researches about the total least squares in algorithms such as the singular value decomposition (SVD) algorithm (Golub and Van Loan [2]) and the algorithm based on the Lagrange function (Schaffrin and Wieser [12]). For more information about the methodology of TLS, one can refer to Huffel et al [3,4].…”

Section: Introductionmentioning

confidence: 99%

Total Least Squares Algorithms for Fitting 3d Straight Lines

Guo¹,

Peng²,

Li³

2017

Int. J. Appl. Math. Mach. Learning

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To address the problem of fitting a 3D straight line, the TLS method based on the Lagrange function is used to solve it. The number of parameter to be estimated is decreased from six to four by changing the standard equation of the straight line into the projective equation of it. The problem of fitting a 3D straight line is converted to the problem of fitting two 2D straight lines with errors in both coordinates. And then the total least square (TLS) and least square (LS) method are employed to fit the two 2D straight line. A simulated example is carried out to demonstrate the effectiveness and applicability of proposed algorithms.

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On weighted total least-squares adjustment for linear regression

Cited by 248 publications

References 9 publications

On Mixed Total Least Squares for Parameter Estimation

On Mixed Total Least Squares for Parameter Estimation

Enhanced Hydroacoustic Range Robustness of Three-Stage Position Filter based on Long Baseline Measurements with Unknown Wave Speed**This work is supported by the Center of Autonomous Marine Operations and Systems (AMOS), grant no. 223254.

Total Least Squares Algorithms for Fitting 3d Straight Lines

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