基于整体最小二乘的空间直线拟合算法

Spatial Straight Lines Fitting Algorithm Based on Total Least Squares

首先通过一定方式的转换将空间直线六参数拟合问题简化为平面直线四参数拟合问题,然后将方程组进行矩阵化,有利于利用整体最小二乘理论进行算法计算,最后分别利用本算法和最小二乘法对实测数据进行空间直线拟合计算,并对2种算法的结果进行比较,初步验证了本算法的可靠性和精确性.同时,将计算结果与不同文献的研究结果相比,证明了本算法的有效性与正确性.

First of all,the problem of six-parameter fitting of the spatial line is simplified into a four-parameter fitting of the planer line by certain means of transition.Then,the equation set has been matrixed,which is beneficial to the calculation by using the total least squares theory.Finally,the least squares algorithm and this algorithm are used to calculate the spatial linear fitting for the measured data respectively,and the results of these two algorithms are compared to preliminarily verify the reliability and accuracy of this algorithm.By comparing the calculation results with the research results of different literatures,the validity and correctness of this algorithm are proved in this paper.