基于岭估计的粗差探测

Outlier Detection Based on Ridge Estimation

针对测量平差Gauss-M arkov模型中法矩阵的病态性和观测值的粗差同时存在问题,把岭估计和粗差探测两者的优点结合起来提出了基于岭估计的粗差探测方法。该方法把岭估计看成具有伪观测值的最小二乘估计,然后运用基于最小二乘估计的粗差探测技术探讨岭估计意义下的奇异点,并给出奇异点的检验统计量和判断方法。数值实验表明,新方法在克服病态性的同时能够有效地识别出可疑(可能含粗差)的观测值。

In order to solve the problem of both ill-conditioning in the normal matrix and outlier existing simultaneously in Gauss-Markov model, a new method called outlier detection based on ridge estimation is proposed by combining the advantages of the ordinary ridge estimation and outlier detection. At first, the method regards the ordinary ridge estimation as least square （LS） estimation with pseudo-observations. Then the outlier and the corresponding statistic in the meaning of the ordinary ridge are discussed in detail by using the LS outlier detection technique. Numerical examples illustrate that the new method not only can overcome the ill-conditioning effectively, but also detect the outlier successfully.