激光跟踪仪自适应加权秩亏三维光束法平差

Self-Adaptive Weighted Rank-Defect 3D Bundle Adjustment of Laser Tracker

针对激光跟踪仪光束法平差,基于稳健估计理论中的选权迭代法,提出一种自适应加权秩亏三维光束法平差解法,通过对观测值选权判定阈值与秩亏平差基准方程权的自适应调整,能够准确识别粗差并抵御其影响。通过仿真实验验证了方法的可行性,并在合肥先进光源预研平台进行了实测验证,实验结果与SpatialAnalyzer软件的处理结果精度相当,可为准直测量数据处理提供抗差结果参考。

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.