基于罗德里格矩阵的抗差迭代坐标转换算法研究

针对大旋转角坐标转换模型线性化复杂、计算量大等问题,并顾及数据粗差对计算结果的影响,根据反对称矩阵和罗德里格矩阵的性质,探讨一种基于罗德里格矩阵和稳健抗差估计理论进行迭代解算的高精度空间直角坐标转换方法,推导基于罗德里格矩阵进行空间直角坐标转换的七参数模型、线性化误差方程及抗差迭代计算的严密公式。通过计算与分析,表明该方法适用于任意旋转角的坐标转换,能有效抵抗数据粗差对转换结果的影响,计算精度高,收敛速度快,是一种有效、实用的坐标转换方法。

Research of resistance iteration algorithm based on Lodrigues matrix in coordinate transformation

Aiming at the problems of the model used in large rotation angle coordinate transformation,such as complex linearization,large amount of computation,and taking the impact of the data containing the severe error on the calculation results into account,this paper proposes a high accuracy space cartesian coordinate transformation method by iterative calculation based on Lodrigues matrix and robust estimation theory.On the basis of the properties of Antisymmetric matrix and the Lodrigues matrix,this paper deduces the seven-parameter model,the linearized error equation and the robust formula of the robust iterative calculation,which are based on the Rodrigue matrix.This method is an effective and practical coordinate transformation method is showed through calculation and analysis,which is suitable for the coordinate transformation of arbitrary rotation angle.The method can resist the influence effectively of gross error contained in data on the conversion result.And the calculation accuracy is high and the convergence speed is fast.