稳健估计方法用于测平差的个别问题(英文)

Some Problems of Application of Robust Estimation to Surveying Adjustment

经典的最小二乘方法由于理论严密,计算简单而得到广泛的应用.然而,当测量数据中存在粗差(或称为突出值)时,粗差观测值的残差看上去极象正常值,从而使残差结果检验导致错误.稳健估计方法改善了最小二乘法的不足.文中首次提出了单参数稳健估计方法,解决了Huber估计中β参数的解法,根据大样本理论,文中提出了解决方差矩阵的方法.

The classical Least Squares (LS) method has often been used because of its strict theoretical backgroud, superior regularity and convenient calculation. However, when a few gross errors (or outliers) exist in measurements, they will be smoothed, difficult to be detected, and as a result, degrade the estimation, the robust estimation method has been proven to be effioient in solving these problems.This paper focuses on the deduction of the β constant in the formulation of the calibration parameters for the Huber method, and draws some conclusions by analysing examples. Based on the great sample approximation theory, this paper has also provided the formulation for the solution of the covariance matrix in solving the repeated representation problems.