带球约束的平差算法及应用  

Adjustment Algorithm with Spherical Constraint and Application

作　　者：左廷英[1,2] 陈邦举 宋迎春 ZUO Tingying;CHEN Bangju;SONG Yingchun(School of Geosciences and Info-Physics,Central South University,932 South-Lushan Road,Changsha 410083,China;Key Laboratory of Mineralization Prediction and Geological Environmental Monitoring,Ministry of Education,932 South-Lushan Road,Changsha 410083,China)

机构地区：[1]中南大学地球科学与信息物理学院,长沙市410083 [2]有色金属成矿预测与地质环境监测教育部重点实验室,长沙市410083

出　　处：《大地测量与地球动力学》2020年第1期71-76,共6页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(41674009,41574006,41674012)~~

摘　　要：针对测量数据处理中由于观测信息不充分以及对参数物理信息和先验信息的利用不充分引起的病态问题,利用先验信息对参数加以约束,将测量平差问题转化为凸二次规划问题,提出一种带有球约束的平差模型。根据最优化理论,基于Kuhn-Tucker条件,研究球约束下的平差问题,并针对该模型提出解算方法。模拟数值实验和测边网实例应用结果表明,该方法在处理病态问题上具有明显的更优估计,可以广泛应用于大地测量病态数据处理。Aiming at solving the ill-conditioned problem caused by inadequate observation,inadequate utilization of parameter physical information and prior information in measurement data processing,this paper transforms the measurement adjustment problem into a convex quadratic programming problem by constraining the parameters with prior information,and proposes an adjustment model with spherical constraints.Based on the optimization theory and Kuhn-Tucker condition,the adjustment problem under spherical constraints is studied,and a solution method is proposed for the model.The results of numerical simulation and practical application of trilateration network show that this method has obvious better estimation in dealing with ill-conditioned problems,and can be widely used in geodetic ill-conditioned data processing.

关 键 词：球约束 最小二乘 病态问题 KUHN-TUCKER条件 先验信息 

分 类 号：P207[天文地球—测绘科学与技术]