基于方差膨胀模型的粗差探测Bayes方法  

Bayesian Approach for Detection of Gross Errors Based on Variance Inflation Model

作　　者：李保利[1] 宫轶松[1] 归庆明[1] 

机构地区：[1]信息工程大学测绘学院

出　　处：《测绘科学技术学报》2007年第6期399-401,405,共4页Journal of Geomatics Science and Technology

基　　金：国家自然科学基金项目(40474007);国家杰出青年科学基金项目(40125013);"基础地理信息与数字化技术"山东省重点开放实验室课题(SD040202);河南省自然科学基金项目(051101010100)

摘　　要：基于方差膨胀模型提出并建立了用观测信息的同时利用先验信息判断粗差的Bayes方法。首先,根据Bayes统计推断的基本原理,建立了判断粗差的Bayes方法——后验概率法;然后针对测量平差实际,考虑未知参数的两种先验信息分别给出了非等权独立观测条件下基于该模型的后验概率的计算公式;最后对模拟算例进行了计算和分析。试验结果表明,用给出的探测粗差的Bayes方法是切实可行的。This paper brought forward the Bayesian method for the detection of gross errors based on the variance inflatilon model, which took advantage of the observation information and the prior information simultaneously. Firstly, based on the basic principle of Bayesian statistical inference, the Bayesian method-posterior probability method for the detection of gross errors was established. Secondly, considering the two kinds of the prior information on the unknown parameters, the computational formulae of the posterior probability were given for the variance inflation model under the condition of unequal weight and independent observations. Finally, as an example, a triangulation network was computed and analyzed. Numerous experiments show that the method given here was feasible.

关 键 词：粗差 无信息先验 正态-Gamma先验 后验概率 方差膨胀模型 

分 类 号：P207[天文地球—测绘科学与技术]