• Chinese Journal of Lasers
  • Vol. 50, Issue 6, 0604004 (2023)
Xuece Miao1, Keliang Ding1、*, Tao Luo2, Xiaoye He2、**, Wei Wang2, and Guimin Liu3
Author Affiliations
  • 1School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
  • 2National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, Anhui, China
  • 3School of Physics, Sun Yat-sen University, Guangzhou 510275, Guangdong, China
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    DOI: 10.3788/CJL221239 Cite this Article Set citation alerts
    Xuece Miao, Keliang Ding, Tao Luo, Xiaoye He, Wei Wang, Guimin Liu. Self-Adaptive Weighted Rank-Defect 3D Bundle Adjustment of Laser Tracker[J]. Chinese Journal of Lasers, 2023, 50(6): 0604004 Copy Citation Text show less

    Abstract

    Objective

    China is currently planning on building several 4th-generation light source facilities that are larger in scale and have highly complex equipment. Therefore, higher alignment and global control point accuracies are required to ensure the robust and stable operation of the facility. The accuracy requirement has reached the measurement accuracy limit of laser trackers. It is of great significance for the construction and development of 4th-generation light source facilities to explore high-precision and stable data processing methods for laser trackers. In this study, an improvement on the existing adjustment method for the control network, which can retain the extremely high accuracy of laser tracking data while avoid some small and unidentifiable gross errors that will affect the overall processing results, is proposed.

    Methods

    Based on robust estimations, an adaptive weighting strategy for rank-defect weighted 3D bundle adjustment that can adaptively adjust the weight matrix of the observed values and weight matrix of the datum equation to achieve robust estimation is employed in this study. Simultaneously, due to data processing using routine robust estimation without any gross error, gross error misjudgment can also be avoided. First, after the first iteration of adjustment, the sum of the residuals less than or equal to the product of the mean value of the two selected weight thresholds and mean square error is calculated. If this value is less than half of the total numbers of observations, the thresholds are considered to be set too low, and vice versa. The two thresholds are corrected proportionally by multiplying them with a specific correction factor when the threshold is high and dividing them by the same factor when the threshold is low. Along with the iteration process, the selected weight thresholds are dynamically and adaptively adjusted to allow the dynamic and adaptive adjustment of the weight of the observed values. This process ends when the changes in the threshold are less than 0.001. Simultaneously, according to the corresponding relationship between the parameters of the datum equation and observed values, the sum of the weight values of all the observed values corresponding to each point in the parameters is calculated and divided by the numbers of respective observed values to obtain the weight matrix of the parameters of the datum equation. Thus, the adaptive adjustment of the weight matrix of the reference equation is realized (Fig. 1) owing to the progress of adjustment iterations and the adaptive adjustment of the weight matrix of the observed values.

    Results and Discussions

    The robustness and stability of the self-adaptive weighted bundle adjustment are verified using simulation data. Based on the accelerator alignment measurement scene and characteristics of the laser tracker, the alignment control point measurement data are simulated (Figs. 2-4), and the minimum norm adjustment method, the unified spatial metrology network (USMN) of SpatialAnalyzer software, and the method used in this study are used to adjust the simulated data. The error range and change trend of the treatment results are close, which conforms to the actual measurement experience (Fig. 5). The accuracy of the proposed method is basically equivalent to that of the USMN, with a deviation of about 0.002 mm (Table 1). To verify the ability to handle gross errors, a gross error of 1 mm is added to a point observed at the fifth station to simulate the gross error observation in the measurement process. This method maintains the processing stability in all three directions, avoids the influence of gross error observation, and has an overall accuracy equal to that of the USMN. When conducting data processing for two groups, the weight selection thresholds decrease proportionally with increased numbers of iterations and tend to be stable after eight iterations. Moreover, after the addition of gross error observations, the threshold must be decreased to ensure the stability of the selected observation range (Fig. 7). The measured data are processed in the Hefei Advanced Light Facility (HALF), and the results obtained are similar to those of mature commercial software (Figs. 9 and 10). The deviation is approximately 0.02 mm, which is within the accuracy requirements of the 4th-generation light facilities.

    Conclusions

    In this study, an adaptive weighting method for adjusting the weighted rank-defect bundle is proposed. Based on the weight selection and actual accuracy of the observed values, the weight selection thresholds are dynamically and adaptively adjusted to realize the adaptive adjustment of the weight matrix of the observed values. Simultaneously, the parameters of the weight matrix of the datum equation are adaptively adjusted according to the weight matrix of the observed values. In the adjustment process of the high-precision data of laser tracker and data with a slight gross error, the observed values are not misjudged as gross error during processing and the influence of the gross error can be simultaneously avoided. The simulation data and measured data show that the proposed method has a stability and robustness of adjustment similar to those of commercial software processing and can be a basic reference for studies on accelerator alignment.

    Xuece Miao, Keliang Ding, Tao Luo, Xiaoye He, Wei Wang, Guimin Liu. Self-Adaptive Weighted Rank-Defect 3D Bundle Adjustment of Laser Tracker[J]. Chinese Journal of Lasers, 2023, 50(6): 0604004
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