附有相关权的Householder参数估计方法  

The Method of Estimation of Parameters with Householder to Correlated Observations.

作　　者：卢秀山[1] 吉星升[2] 张金榜 

机构地区：[1]山东矿业学院 [2]攀枝花大学 [3]德州市房屋综合开发公司

出　　处：《矿山测量》1999年第3期4-7,59,共4页Mine Surveying

摘　　要：正则矩阵 Ａ Ｔ Ａ 的列向量呈强复共线性（“病态”）时，将影响参数最小二乘解的质量。应用 Ｈｏｕｓｅｈｏｌｄｅｒ 方法进行参数估计，可以减弱 Ａ Ｔ Ａ 的“病态”性对参数最小二乘解的影响。由于该方法基于等权的线性方程组，因此其在测绘数据处理中的应用受到了限制。本文提出对相关权阵进行平方根分解和用上三角阵变换误差方程组，将相应的相关权阵变换为单位阵，并使其定理化，从而扩展了史赖伯约化法则，为 Ｈｏｕｓｅｈｏｌｄｅｒ 方法在测绘数据处理中的应用奠定了基础。这一方法对于 Ｇ Ｐ Ｓ差分快速基线解算，具有明显的应用前景。文中给出了 Ｇ Ｐ Ｓ差分基线解算的算例。n case of stronger multi-colinearity among column vectors in regular matrix A TA,the quality of the least squares solution will be affected.Using the method of househlder for estimation of parameters may lead reduced effect of ill-conditioned A TA on solution of least squares.However as a method based on equal weight linear equations,it can find only limited applications in survey data processing.It is therefore proposed in the paper to carry out Cholesky's resolution to correlated weight matrix transform observation equations with super-triangular matrix,and transform the correlated weight matrix into theorem-based unit one,for further extending the Schraiber's Reduction Law,so as to lay a sound foundation for use of the Householder method in obervation data processing.The method also offers a good prospect for differential GPS quick solution of baseline for which typical cases are cited in the paper.

关 键 词：参数估计 复共线性 相关权阵 H-矩阵 测绘数据 

分 类 号：P208[天文地球—地图制图学与地理信息工程]