以三维坐标转换为例解算稳健总体最小二乘方法

Performing 3D Similarity Transformation by Robust Total Least Squares

稳健最小二乘方法能够有效解决平差计算中观测值存在粗差的情况,因此广泛应用于各种实际问题中。在最小二乘方法中,系数矩阵被认为是不含有误差的。然而在实际情况中,系数矩阵中的变量往往也包含观测值,因此不可避免地会被误差污染。为同时考虑系数矩阵和观测向量中的误差,同时对粗差进行探测和定位,本文提出基于选权迭代的稳健总体最小二乘方法,并以三维相似坐标变换为例展示解算过程。通过模拟计算,证明采用本文提出的稳健总体最小二乘方法,能够较好地达到粗差探测和定位的目的,获得稳健的参数解。

The robust least squares （LS） adjustment has been extensively studied and successfully applied in the real applications to resist the influence of gross errors in observation. However in theLSadjus^ment, the coefficient matrix is considered as non-error. Unfortunately, variables in coefficient matrix are inevitably error-contaminated when they come from the real observations. Considering the random errors and gross errors may exist both in the observation vector and the coefficient matrix, the robust total least squares （TLS） solution is studied in this paper. The reweighting iteration method is used to detect and identify the gross errors. At the end of the paper, the simulated experiments of three-dimensional similarity coordinate transformation are investigated to prove that using the robust TLS method, the influence of the gross errors can be resisted, and the reliable solution can be obtained.