A Trimmed Moving Total Least Squares Method for Curve and Surface Fitting

Tianqi Gu, Yi Tu, Dawei Tang, Shuwen Lin, Bing Fang

Research output: Contribution to journalArticle

Abstract

The Moving Least Squares (MLS) method has been developed for fitting of the measurement data contaminated with errors. The local approximants of the MLS method only take the random errors of the dependent variable into account, whereas the independent variables of measurement data always contain errors. To consider the influence of errors of dependent and independent variables, the Moving Total Least Squares (MTLS) offers a better choice. However, both MLS and MTLS method are sensitive to outliers, which greatly affects the fitting accuracy and robustness. This paper presents an improved method-Trimmed Moving Total Least Squares (TrMTLS) method, in which Total Least Squares (TLS) method with truncation procedure is adopted to determine the local coefficients in the influence domain. This method can deal with outliers and random errors of all variables without setting the threshold or adding small weights subjectively. The numerical simulation and measurement experiments results indicate that the proposed algorithm has better fitting accuracy and robustness compared with the MTLS and MLS method.
Original languageEnglish
JournalMeasurement Science and Technology
Early online date22 Oct 2019
DOIs
Publication statusE-pub ahead of print - 22 Oct 2019

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Total Least Squares
Surface Fitting
Moving Least Squares
Curves and Surfaces
Curve fitting
curve fitting
least squares method
Least Square Method
Random errors
dependent variables
random errors
Random Error
Outlier
Computer simulation
Robustness
Dependent
Experiments
Truncation
thresholds
coefficients

Cite this

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title = "A Trimmed Moving Total Least Squares Method for Curve and Surface Fitting",
abstract = "The Moving Least Squares (MLS) method has been developed for fitting of the measurement data contaminated with errors. The local approximants of the MLS method only take the random errors of the dependent variable into account, whereas the independent variables of measurement data always contain errors. To consider the influence of errors of dependent and independent variables, the Moving Total Least Squares (MTLS) offers a better choice. However, both MLS and MTLS method are sensitive to outliers, which greatly affects the fitting accuracy and robustness. This paper presents an improved method-Trimmed Moving Total Least Squares (TrMTLS) method, in which Total Least Squares (TLS) method with truncation procedure is adopted to determine the local coefficients in the influence domain. This method can deal with outliers and random errors of all variables without setting the threshold or adding small weights subjectively. The numerical simulation and measurement experiments results indicate that the proposed algorithm has better fitting accuracy and robustness compared with the MTLS and MLS method.",
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A Trimmed Moving Total Least Squares Method for Curve and Surface Fitting. / Gu, Tianqi ; Tu, Yi; Tang, Dawei; Lin, Shuwen; Fang, Bing.

In: Measurement Science and Technology, 22.10.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A Trimmed Moving Total Least Squares Method for Curve and Surface Fitting

AU - Gu, Tianqi

AU - Tu, Yi

AU - Tang, Dawei

AU - Lin, Shuwen

AU - Fang, Bing

PY - 2019/10/22

Y1 - 2019/10/22

N2 - The Moving Least Squares (MLS) method has been developed for fitting of the measurement data contaminated with errors. The local approximants of the MLS method only take the random errors of the dependent variable into account, whereas the independent variables of measurement data always contain errors. To consider the influence of errors of dependent and independent variables, the Moving Total Least Squares (MTLS) offers a better choice. However, both MLS and MTLS method are sensitive to outliers, which greatly affects the fitting accuracy and robustness. This paper presents an improved method-Trimmed Moving Total Least Squares (TrMTLS) method, in which Total Least Squares (TLS) method with truncation procedure is adopted to determine the local coefficients in the influence domain. This method can deal with outliers and random errors of all variables without setting the threshold or adding small weights subjectively. The numerical simulation and measurement experiments results indicate that the proposed algorithm has better fitting accuracy and robustness compared with the MTLS and MLS method.

AB - The Moving Least Squares (MLS) method has been developed for fitting of the measurement data contaminated with errors. The local approximants of the MLS method only take the random errors of the dependent variable into account, whereas the independent variables of measurement data always contain errors. To consider the influence of errors of dependent and independent variables, the Moving Total Least Squares (MTLS) offers a better choice. However, both MLS and MTLS method are sensitive to outliers, which greatly affects the fitting accuracy and robustness. This paper presents an improved method-Trimmed Moving Total Least Squares (TrMTLS) method, in which Total Least Squares (TLS) method with truncation procedure is adopted to determine the local coefficients in the influence domain. This method can deal with outliers and random errors of all variables without setting the threshold or adding small weights subjectively. The numerical simulation and measurement experiments results indicate that the proposed algorithm has better fitting accuracy and robustness compared with the MTLS and MLS method.

KW - Moving least squares

KW - Random errors

KW - Outliers

KW - Local approximants

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