粗差探测的Bayes方法

Bayesian Method for Detection of Gross Errors

讨论粗差探测的Bayes方法。首先根据Bayes统计推断的基本原理,建立判断粗差的Bayes方法———后验概率法,然后针对测量平差实际,分别给出非等权独立观测条件下基于均值漂移模型和方差膨胀模型的后验概率的计算公式,最后结合一边角网算例,验证本文方法的效果。

Bayesian statistics are widely used in geodetic data processing. However, as for the detection of gross errors by the Bayesian method, there are few achievements. At present, existing methods for gross-error detection are mainly various hypothesis test based on mean shift model. Practice proved, these methods have their individual characteristics and are restricted to certain of application fields. On the whole, it appears that they have a common deficiency, that is, they have not considered or made use of the prior information of the unknown parameters. Neglecting the prior information is a waste; furthermore, it will sometimes lead to unreasonable conclusions. The Bayesian method for gross-error detection with the prior information is discussed in this paper. Firstly, based on the basic principle of Bayesian statistical inference, in the condition of general prior information, the Bayesian method for general form based on alternative distribution of observation errors-posterior probability method-for detection of gross errors is introduced. Here, we assume that observation errors come from two distrihutions, standard distribution and alternative distribution. Secondly, taking surveying adjustment practice into account, in addition, the non-informative priors, the computational formulae of posterior probability are given for mean shift modal and variance inflation model respectively under the condition of unequal weight and independent observations. Finally, as an example, a side-angle adjustment network is computed and analyzed.