大旋转角的空间直角坐标转换方法的改进

An Improved Method for Spatial Rectangular Coordinate Transformation with Big Rotation Angle

针对现有大旋转角空间直角坐标转换方法存在的问题,基于尺度参数的SVD估计提出改化模型,并推导了参数解估计的方向余弦法、单位四元数法及罗德里格矩阵法。最后,基于奇异点、模型条件数、中误差及迭代次数等指标,通过文献算例和大旋转角仿真算例比较分析了3种方法在七参数模型与本文改化模型的坐标转换效果。结果表明,旋转矩阵的SVD初值优于单位阵初值,改化模型优于七参数模型,方向余弦法优于其他两种方法。

To accomplish spatial rectangular coordinate transformation with big rotation angles, the improved coordinate transformation model is proposed. This model is based on scale parameter estimation using the ma- trix singular value decomposition （SVD）. Three estimation methods, including direction cosine, unit quater- nion and Rodrigues are presented for the improved coordinate transformation model. Finally, simulated and practical experiments of coordinate transformation with big angle are tested to compare and analyze the adapta- bility of the three methods using the total number of singular points, the condition number of normal matrix, the number of iterations and the RMS, etc. Experimental results show that the improved model is better than the extant seven parameters model, that the SVD solution of rotation matrix is superior to unit matrix as an initial value, and that the direction cosine method is preferable to the other two methods.