加权整体最小二乘算法的改进

摘要

针对EIV模型中系数矩阵含有重复元素的问题,通过考虑系数矩阵元素间的相关性,改进已有的加权整体最小二乘法,使得重复元素的改正数的绝对值相等.并将改进方法应用于直线拟合和解算三维小角度基准转换模型.算例证明,相比以往的参数估计方法,利用改进后的加权整体最小二乘法能够得到更合理的系数矩阵残差阵.%In connection with the problem of EIV model' s coefficient matrix containing repetitive elements, The author improves the available weighted total least squares method through making the repeat element' s correction equal, taking into account the correlation between the elements of coefficient matrix, Then, the improved method is applied to the linear fitting, to solve the small rotation angle of 3D datum transformation model. The examples show that, compared with toprevious parameter estimation methods, the improved weighted total least squares (IWTLS ) method can obtation a more rational residual matrix of coefficient matrix.