等价条件闭合差的方差-协方差分量估计解析法  

Analytical Method for VCE Using Equivalent Condition Misclosure

作　　者：刘志平[1] 

机构地区：[1]中国矿业大学国土环境与灾害监测国家测绘地理信息局重点实验室,江苏徐州221116

出　　处：《测绘学报》2013年第5期648-653,共6页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金青年项目(41204011);中央高校基本科研业务费专项(2010QNA20);江苏高校优势学科建设工程资助项目(SZBF2011-6-B35)

摘　　要：分析指出现有方差-协方差分量估计(VCE)方法在计算效率与χ2统计量性质两方面的固有缺陷。利用零空间算子消去概括平差模型中的参数向量,建立等价条件平差模型。由此定义等价条件闭合差(ECM),并导出了以ECM表示的χ2统计量计算式。顾及对称性和可逆性构造了新的方差分量模型,进而基于等价条件闭合差提出方差-协方差分量估计的无偏解析法,简称为VCE-ECM法。同时,给出对应4种基本平差模型的VCE-ECM法简化计算式。实例与仿真结果表明,VCE-ECM法与现有残差型VCE方法的估计效果相当,并有效地克服了现有VCE方法的固有缺陷。The defects of the existed methods for variance-covariance component estimation （VCE）, including both computational efficiency and statistical properties of Chi-squared test statistic, are analyzed and investigated in this paper. The equivalent condition adjustment model is established from the generalized adjustment model by null-space operator, based on which both the equivalent condition misclosure （ECM） and the formula of Chi-squared test statistic are given. Moreover, theinvertiblevariance-covariancecomponent model instead of thenoninvertible variance-covariancecomponent model is constructed creatively and the analytical method for VCE is proposed using both ECM and invertiblevariance-covariancecomponent model （short for VCE-ECM method）. Meantime, the simplified formulas of VCE-ECM method are provided for four basic adjustment models correspondingly. Finally, Theoretical and computational results show there was no statistically significant difference in variance-covariance components between proposed method and existed VCE methods, and the analytical method presented here could overcome the inherent defects in existed VCE methods.

关 键 词：零空间算子 等价条件闭合差 可逆方差分量模型 VCE-ECM法 

分 类 号：P207[天文地球—测绘科学与技术]