多视角理解约束平差法  

Understanding constrained adjustment from multiple perspectives

作　　者：常国宾 张书毕[1] 刘志平[1] CHANG Guobin;ZHANG Shubi;LIU Zhiping(School of Environmental Science and Spatial Informatics,China University of Mining and Technology,Xuzhou 221116,China)

机构地区：[1]中国矿业大学环境与测绘学院,江苏徐州221116

出　　处：《海洋测绘》2022年第6期14-20,共7页Hydrographic Surveying and Charting

基　　金：国家自然科学基金(42074001);江苏省高等教育教改研究项目(2019JSJG260);中国矿业大学教学研究项目(2021YB035)。

摘　　要：为了深层次地揭示附有限制条件的间接平差(本文简称约束平差)的性质,以便更好地发挥约束平差在实际测量数据处理中的重要作用,从多个视角对约束平差这一基础平差方法进行理论分析。研究结果如下:给出了约束平差问题的间接平差法求解过程;推导出了结论更简单、结构更清晰的约束平差两步法算法;从“新息”角度分析了两步法约束平差与序贯平差、Kalman滤波的有趣联系;采用Fisher-Neyman分解定理证明了无约束解是原始观测的充分统计量;将无约束解视作“伪观测”,可以为理解约束平差提供新的视角;从条件正态分布的角度对两步法约束平差进行了重新推导;证明了约束解为无约束解在约束方程所定义子空间上的正交投影;介绍了一种观测方程不可解的情况下获得无约束解的新方法,从而扩展了两步法约束平差的适用范围。研究表明:拥有诸多优良性质的约束平差将在处理海量、复杂、动态的测绘数据时发挥更大作用。In order to deeply reveal the properties of constrained adjustment(CA),the important role of CA in the actual measurement data processing can be better played.Theoretical analysis of the CA is conducted from multiple viewpoints.The findings are as follows:it is shown that CA problem can be solved as a plan adjustment problem;a two-step algorithm for CA,with simpler formulae and clearer structure,is proposed;with innovative vector as a tool,the interesting link between the two-step CA and the recursive adjustment/Kalman filtering is analyzed;based on Fisher-Neyman factoring theorem,it is proved that the unconstrained solution is exactly a sufficient statistic of the raw measurements in parameter estimation;regarding the unconstrained solution as a set of pseudo measurements can provide new perspectives for understanding CA;it is shown that the two-step algorithm can be derived using the conditional normal distribution theorem;it is shown that the constrained solution is the orthogonal projection on to the subspace defined by the constraint equations;finally we proposed a method to get an unconstrained solution when the original measurement equation is unsolvable,and this improves the applicability of the proposed two-step algorithm.It is shown that,due to its multiple good properties,the CA will find more important applications in processing huge,complex and dynamic surveying data.

关 键 词：测量平差 约束平差 理论分析 两步法 不可估问题 

分 类 号：P207[天文地球—测绘科学与技术]