非等权观测的Householder参数估计方法

当设计矩阵Ａ“病态”（ 强复共线） 时，正则矩阵ＡＴＡ 亦“病态”，而且更为严重，导致参数的最小二乘解极不稳定。Ｈｏｕｓｅｈｏｌｄｅｒ 方法，是用一镜像映射矩阵Ｈ（ 对称、正交） 对误差方程（ 等权） 进行正交变换，将Ａ变换为上三角阵Ｒ，直接解算参数，避免了ＡＴＡ 的“病态”性对参数最小二乘解的影响。本文解决了在非等权观测情况下，如何应用Ｈｏｕｓｅｈｏｌｄｅｒ 方法进行参数估计的问题。因而，本文扩展了Ｈｏｕｓｅｈｏｌｄｅｒ 方法，并使其在测绘数据处理中更具有实用价值。

The Method of Parameters Estimation with Householder to Unequal Weight Observations

It will result in more serious ill conditoned A TA and will lead to affect the parameter quality of solution of the Least Squares if designed matrix A is ill conditioned one. The method of Householder to parameters estimation, is to make orthographical of transformation observation equations (equal weight) and to transform A into an upper triangular matrix R and to solve parameters directly, avoiding the effect of ill conditioned A TA on solution of the Least Squares. This paper offers how to use the method of Householder for parameter estimation of unequal weight observation equations, develops the method of Householder and improves the application of the method in data processing of surveying.