Performing 3D Similarity Transformation Using the Weighted Total Least-Squares Method

Lu, Jing; Chen, Y.; Fang, Xing; Zheng, Bing

doi:10.1007/978-3-319-10828-5_11

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…In the 3D similarity transformation model with large rotation angles, the nine elements in the rotation matrix are treated as the unknown parameters in addition to the three translation and one scale parameters. The nine elements need to be estimated, rather than the three rotation angles (Lu et al 2015)…”

Section: D Similarity Transformation Model With Large Rotation Anglesmentioning

confidence: 99%

“…Both the computation of the transformation parameters and the transformation of the coordinates of non-common points were integratively implemented. In Lu et al (2015), the weighted total least squares (WTLS) algorithm based on the nonlinear Gauss-Helmert model (Neitzel 2010) was applied in the 3D similarity transformation with large rotation angles. However, the method of Lu et al (2015) has potential numerical instability because of the existing of the rank-defect problem (Yang et al 2017).…”

Section: Introductionmentioning

confidence: 99%

“…In Lu et al (2015), the weighted total least squares (WTLS) algorithm based on the nonlinear Gauss-Helmert model (Neitzel 2010) was applied in the 3D similarity transformation with large rotation angles. However, the method of Lu et al (2015) has potential numerical instability because of the existing of the rank-defect problem (Yang et al 2017). For this reason, Chang (2016) derived the closed-form least-squares solution, but the method would only be applied in the case with rotational invariant covariance structure.…”

Section: Introductionmentioning

confidence: 99%

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Performing 3d Similarity Transformation With Large Rotation Angles Using Constrained Multivariate Total Least Squares

2020

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3D similarity transformation is frequently encountered operation in the field of geodetic data processing, and there are many applications that involve large rotation angles. In previous studies, the errors of the coefficient matrix were usually neglected and a least squares algorithm was applied to calculate the transformation parameters. However, the coefficient matrix is composed of the point coordinates in source coordinate system, i.e., the coefficient matrix is also contaminated by errors. Therefore, a total least squares algorithm should be applied. In this paper, a new method is proposed to address the 3D similarity transformation problem with large rotation angles. Firstly, the scale factor and rotation matrix are put together as the parameter matrix to avoid the rank-defect problem. Then, the translation vector is removed and the multivariate model is constructed. Finally, the constraints are introduced according to the properties of the parameter matrix and the constrained multivariate total least squares algorithm is derived to obtain the transformation parameters. The experimental results show that the proposed method has a high computational efficiency.

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Section: D Similarity Transformation Model With Large Rotation Anglesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Performing 3d Similarity Transformation With Large Rotation Angles Using Constrained Multivariate Total Least Squares

2020

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An advanced multiple outlier detection algorithm for 3D similarity datum transformation

Liu

2020

Measurement

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Fixing positions and orientations of laser trackers during bundle adjustment in multi-station measurements

Wang¹,

Luo²,

Wang³

et al. 2020

Meas. Sci. Technol.

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The accumulated errors in multi-station measurements make it challenging to meet higher precision requirements for annular or straight tunnel measurements in the accelerator alignment field. In this paper, a study on fixing positions and orientations of laser trackers during the bundle adjustment is presented. First, we adopt the mixed least squares-total least squares algorithm to calculate the spatial-transformation parameters. Then, according to the principle of bundle adjustment based on laser trackers, we design four schemes and compare them to determine which scheme results in the highest precision. Experimental results show that fixing each station’s position and orientation can considerably decrease the absolute point errors from 0.130 to 0.069 mm within 15 m × 10 m × 3 m, and fixing stations’ orientations is better than fixing their positions. This research can derive high-precision schemes that effectively reduce accumulated errors in annular or straight tunnel measurements, and it can apply to other robotic sensors as well.

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Performing 3D Similarity Transformation Using the Weighted Total Least-Squares Method

Cited by 3 publications

References 8 publications

Performing 3d Similarity Transformation With Large Rotation Angles Using Constrained Multivariate Total Least Squares

Performing 3d Similarity Transformation With Large Rotation Angles Using Constrained Multivariate Total Least Squares

An advanced multiple outlier detection algorithm for 3D similarity datum transformation

Fixing positions and orientations of laser trackers during bundle adjustment in multi-station measurements

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