Robust moving total least squares: A technique for the reconstruction of measurement data in the presence of multiple outliers

In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.

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Location and estimation of multiple outliers in weighted total least squares

Measurement ◽

10.1016/j.measurement.2021.109591 ◽

2021 ◽

pp. 109591

Author(s):

Jianmin Wang ◽

Jianjun Zhao ◽

Zhenghe Liu ◽

Zhijun Kang

Keyword(s):

Least Squares ◽

Total Least Squares ◽

Multiple Outliers ◽

Weighted Total Least Squares

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An α-moving total least squares fitting method for measurement data

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405420949758 ◽

2020 ◽

Vol 235 (1-2) ◽

pp. 65-72

Author(s):

Tianqi Gu ◽

Chenjie Hu ◽

Dawei Tang ◽

Shuwen Lin ◽

Tianzhi Luo

Keyword(s):

Least Squares ◽

Geometric Characteristic ◽

Measurement Data ◽

Characteristic Parameter ◽

Negative Influence ◽

Total Least Squares ◽

Least Square ◽

Random Errors ◽

Improved Method ◽

Fitting Accuracy

The Moving Least Squares (MLS) and Moving Total Least Squares (MTLS) method are widely used for approximating discrete data in many areas such as surface reconstruction. One of the disadvantages of MLS is that it only considers the random errors in the dependent variables. The MTLS method achieves a better fitting accuracy by taking into account the errors of both dependent and independent variables. However, both MLS and MTLS suffer from a low fitting accuracy when applied to the measurement data with outliers. In this work, an improved method named as α-MTLS method is proposed, which uses the Total Least Square (TLS) method based on singular value decomposition (SVD) to fit the nodes in the influence domain and introduces a geometric characteristic parameter α to associated with the abnormal degree of nodes. The generated fitting points are used to construct the parameter and quantify the abnormal degree of the nodes. The node with the largest parameter value is eliminated and the remaining nodes are used to determine the local coefficients. By trimming only one node per influence domain, multiple outliers of measurement data can be effectively handled. There is no need to set threshold values subjectively or assign weights which avoids the negative influence of manual operation. The performance of the improved method is demonstrated by numerical simulations and measurement experiment. It is shown that the α-MTLS method can effectively reduce the influence of the outliers and thus has higher fitting accuracy and greater robustness than that of the MLS and MTLS method.

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