王乐洋, 余航. 附有相对权比的加权总体最小二乘联合平差方法[J]. 武汉大学学报 ( 信息科学版), 2019, 44(8): 1233-1240. DOI: 10.13203/j.whugis20170265
引用本文: 王乐洋, 余航. 附有相对权比的加权总体最小二乘联合平差方法[J]. 武汉大学学报 ( 信息科学版), 2019, 44(8): 1233-1240. DOI: 10.13203/j.whugis20170265
WANG Leyang, YU Hang. Weighted Total Least Squares Method for Joint Adjustment Model with Weight Scaling Factor[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1233-1240. DOI: 10.13203/j.whugis20170265
Citation: WANG Leyang, YU Hang. Weighted Total Least Squares Method for Joint Adjustment Model with Weight Scaling Factor[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1233-1240. DOI: 10.13203/j.whugis20170265

附有相对权比的加权总体最小二乘联合平差方法

Weighted Total Least Squares Method for Joint Adjustment Model with Weight Scaling Factor

  • 摘要: 采用不同类数据联合平差时,不仅观测向量含有误差,其对应的系数矩阵也通常受到误差的影响。将加权总体最小二乘方法应用于多类观测数据的联合平差模型,推导相应迭代计算方法,以相对权比权衡各类数据参与联合平差的比重。设计了多种方案,并给出了确定相对权比的判别函数最小化方法。结果表明,验前单位权方差法与总体最小二乘方差分量估计方法具有一定的局限性,当验前信息不准确或者总体最小二乘方差分量估计方法不可估时,判别函数为\mathop \mathop \sum \limits_i = 1 \limits^n_1 \left| \widehat \bar e_1_i \right| + \mathop \mathop \sum \limits_j = 1 \limits^n_2 \left| \widehat \bar e_2_j \right|的判别函数最小化法能取得较优的参数估值结果。

     

    Abstract: In regard to the joint adjustment problem with different types of dataset, the functional model of each type of dataset is affected by random errors, which indicates the observation vector and coefficient matrix are not error-free. In this paper, the weight total least squares (WTLS) method is applied to joint adjustment model. An iterative WTLS method for joint adjustment model is derived, which uses the weight scaling factor to adjust the contribution of each type of dataset. In view of the determination of the weight scaling factor, more schemes are designed, which includes the minimum discrimination function method. The results show that the prior unit weight variance method and the total least squares variance component estimation (TLS-VCE) method have their limitations. When the prior information is inaccurate or the variance components are not estimable while using the TLS-VCE method, the minimum discriminate function method with \mathop \mathop \sum \limits_i = 1 \limits^n_1 \left| \widehat \bar e_1_i \right| + \mathop \mathop \sum \limits_j = 1 \limits^n_2 \left| \widehat \bar e_2_j \right| as its discriminate function can achieve the relative effective results.

     

/

返回文章
返回