三维坐标转换的总体最小二乘拟合推估

Total Least Squares Fitting Estimation Model of Three-Dimensional Coordinate Conversion

最小二乘的Gauss-Markov误差模型在三维坐标转换参数求解中存在缺陷,而求取坐标转换参数的目的是计算非公共点在目标坐标系的坐标,因此提出了一种三维坐标转换的总体最小二乘拟合推估法。考虑了原坐标系中公共点坐标和非公共点坐标的相关性以及非公共点在原坐标系中的坐标误差对模型的影响,对计算坐标转换参数和计算非公共点在目标坐标系中的坐标进行联合处理,推导出三维坐标转换的总体最小二乘拟合推估模型和求解方法。算例表明,利用新方法计算结果相比其他2种方法更加精确,均方根误差降低至0.077 3,相对百分误差降低至1.54%,证明了新方法的有效性和可靠性。

Gauss-markov error model of least squares has some defects in solving 3d coordinate transformation parameters,and the purpose of obtaining coordinate transformation parameters is to calculate the coordinates of non-common points in the target coordinate system.Considering the common point coordinates in the coordinate system and the common point coordinates of relevance and the common points in the original coordinate system of the coordinate error of the model,the influence of the coordinate transformation parameters and calculates the common point in joint coordinates of target coordinate system,and deduced the three-dimensional coordinate conversion of total least squares fitting to estimate model and solving method.The results show that the new method is more accurate than the other two methods,and the root-mean-square error is reduced to 0.077 3 and the relative percentage error is reduced to 1.54%,which proves the effectiveness and reliability of the new method.