为提高多元总体最小二乘问题参数估值的解算效率,推导了基于牛顿法的多元加权总体最小二乘算法;分析比较了基于牛顿法的多元加权总体最小二乘解和基于拉格朗日乘数法多元加权总体最小二乘解之间的关系,根据协因数传播律给出了多元总体最小二乘平差的16种协因数阵的近似计算公式。新算法能够解决观测矩阵和系数矩阵元素具有相关性的问题,并且可以把观测矩阵和系数矩阵的随机元素和常数元素纳入到一个协因数阵中进行处理。算例结果表明,本文提出的多元总体最小二乘问题的牛顿解法可行且收敛速度更快。
In order to improve calculation efficiency of parameter estimation, an algorithm for multivariate weighted total least squares adjustment based on Newton method is derived. The relationship between the solution of this algorithm and that of multivariate weighted total least squares adjustment based on Lagrange multipliers method is analyzed. According to propagation of cofactor, 16 computational formulae of cofactor matrices of multivariate total least squares adjustment are also listed. The new algorithm could solve adjustment problems containing correlation between observation matrix and coefficient matrix. And it can also deal with their stochastic elements and deterministic elements with only one cofactor matrix. The results illustrate that the Newton algorithm for multivariate total least squares problems could be practiced and have higher convergence rate.
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