一段圆弧上多点坐标拟合圆心位置的可靠性分析

该文研究分析了通过一段圆弧上多点坐标来进行圆心坐标拟合的问题,列出了圆弧上多点求解圆心的平差模型,并讨论了当测量数据存在粗差时,对圆上多点构成的观测数据运用数据探测法进行可靠性检验并作了相关精度分析。试验假设在施工时只能看到圆形建筑物大概1/2或1/4圆弧,模拟测量了一组实验数据,对其中某点坐标加入适当的粗差后分组组合进行粗差探测并探讨得出了合理的检验显著系数值。试验发现对于1/4圆弧,当观测值存在较小粗差时,结果超限可能性就很大,而对点位分布在大概1/2圆弧上时,如果其中某个观测点的点位误差不超过3倍中误差时,单从得到的平差结果看可能不超限,但通过μ检验法则可以探测到粗差,对实际测量中的数据处理有一定的参考意义。

Reliability Analysis of Multiple Points Coordinates on an Arc to Fitting Circle Center Position

This paper studied and analyzed the fitting of the circle center position by measuring the coordinates of multiple points on an arc,and listed out the adjustment model to solve circle center on multiple points of an arc.When the gross error exist in measurement data,the reliable test is conducted on the observation data of arc multiple points by data snooping method and the accuracy analysis is also made.This experiment is based on an assumption that only about 1/2 or 1/4 circular arc can be seen under construction,then a series of data is measured and simulated,the appropriate gross errors are joined in a point coordinates and made group combination for gross error detection,and finally the reasonable significant coeffcient values are obtained.This test indicates that smaller gross error can be eliminated in 1/4 circular arc,but not for 1/2 arc as the point error no more than three times of square-error.But all of the gross error(one,double or treble of square-error) almost can be discovered by data snooping method.The method has certain reference meaning to the actual data processing.