正态-Gamma先验下粗差探测的Bayes方法  

Bayesian approach for detection of gross errors with normal-gamma priors

作　　者：宫轶松[1] 归庆明[1] 李保利[1] 

机构地区：[1]信息工程大学测绘学院

出　　处：《测绘科学》2008年第2期81-83,87,共4页Science of Surveying and Mapping

基　　金：国家杰出青年科学基金项目(40125013);国家自然科学基金项目(40474007);河南省自然科学基金项目(编号0511010100);“基础地理信息与数字化技术”山东省高等学校省级重点开放实验室课题(SD040202)

摘　　要：本文主要运用Bayes统计推断的基本原理,提出和建立将观测信息与正态——Gamma先验信息融合、基于综合信息判断粗差的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,考虑未知参数的正态-Gamma先验信息,分别给出了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具体计算公式,并给出了相应的粗差的Bayes估算方法。最后提出了基于后验概率进行粗差探测的实施过程和具体步骤。数值试验的结果表明,本文提出的粗差探测的Bayes方法对多个粗差的同时定位和定值是相当有效的。Taking advantage of the basic principle of Bayesian statistical inference, we fuse the observation information and normal-gamma prior information and bring forward a Bayesian method to locate gross errors based on the integrated information. Firstly, based on the basic principle of Bayesian statistical inference, the Bayesian method-posterior probability method-for the detection of gross errors is established. Secondly, considering normal-gamma priors on the unknown parameters, the computational formula of the posterior probability is given for both the mean shift model and the variance inflation model, respectively, under the conditions of unequal weight and independent observations. The Bayesian estimator of gross errors is given. Finally, the implemented procedures and concrete steps for gross errors＇detection based on the posterior probability are suggested. Numerous experiments show that the method given is perfect for sure and effective comparatively for locating and evaluating multiple gross errors simultaneously.

关 键 词：粗差 正态-Gamma先验 后验概率 均值漂移模型 方差膨胀模型 

分 类 号：P207[天文地球—测绘科学与技术]