一种无参数的圆拟合快速迭代算法  

A Fast Iterative Algorithm for Circle Curve Fitting Without Parameters

作　　者：廖有祺 康雄华[1] 曾文宪[1] 雷杨 LIAO Youqi;KANG Xionghua;ZENG Wenxian;LEI Yang(School of Geodesy and Geomatics,Wuhan University,Wuhan 430079,China;Hubei Spatial Planning Institute,Wuhan 430064,China)

机构地区：[1]武汉大学测绘学院,湖北武汉430079 [2]湖北省空间规划研究院,湖北武汉430064

出　　处：《测绘地理信息》2023年第6期32-35,共4页Journal of Geomatics

基　　金：国家自然科学基金(42174049)。

摘　　要：针对圆拟合的间接平差方法难以确定参数初始值的问题,提出了一种无需参数的快速迭代算法。该算法根据相同弧段对应圆周角相等的关系建立条件方程,迭代解算观测点坐标及圆曲线参数。该方法涉及的矩阵求逆运算的次数、阶数较间接平差方法更小,故在高阶次迭代中计算量更小。实验结果表明,该方法对圆曲线的拟合效果良好。与间接平差方法相比,该无参数方法解算结果相同、收敛速度相近且省去了计算参数初始值的步骤。圆曲线拟合的无参数快速迭代算法对于非线性拟合算法的编写有一定的参考价值,在工程放样等领域有着广阔的应用前景。Aiming at the difficulty to determine the initial val⁃ue of parameters in fitting circular curve by indirect adjustment method,this paper presents a parameterless algorithm based on conditional adjustment.According to the conditional equa⁃tions based on the relation that equal arcs correspond to equal circle angles are,this method iteratively solves observation points coordinates and parameters of circle curve.The analy⁃sis shows that the number and order of matrix inversion are smaller than those of indirect adjustment method,so the calcu⁃lation amount is smaller in higher order iteration.Results of experiments show the method fitting well on circle curve.Compared to indirect adjustment method,non-parametric one gets same results and similar convergence rate,leaving out the step to compute initial value of parameters as well.The parameterless fast iterative algorithm for circle curve fitting has reference value for writing similar nonlinear fitting al⁃gorithm and broad application areas in fields like engineer⁃ing lofting.

关 键 词：圆曲线拟合 条件平差 最小二乘准则 收敛速度 

分 类 号：P207[天文地球—测绘科学与技术]