一种附非负约束秩亏平差模型的迭代算法  

An iterative algorithm for non-negative constrained rank defect adjustment model

作　　者：郝天恒 左廷英 赵邵杰[1,2] HAO Tianheng;ZUO Tingying;ZHAO Shaojie(Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring(Central South University),Ministry of Education,Changsha 410083,China;School of Geosciences and Info-Physics,Central South University,Changsha 410083,China)

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

出　　处：《测绘科学》2020年第10期22-26,40,共6页Science of Surveying and Mapping

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

摘　　要：针对附非负约束秩亏平差的问题,该文先将最小二乘问题转化为线性互补问题,然后利用极大熵函数的性质对其进行迭代求解,建立了一种附非负约束秩亏平差模型的迭代算法。它充分利用了测量中符号约束的先验信息,只需参数具有非负约束或先将参数转化为非负约束,无须对矩阵求逆,计算简便。文中还针对算法的收敛性进行了分析,并模拟了GPS网平差的算例。数值实验表明,与其他秩亏平差算法相比,该文算法在精度和计算效率方面均具有一定的优势。In order to solve the problem of non-negative constrained rank defect adjustment,in this paper,the least squares problem was transformed into a linear complementarity problem,and then the maximum entropy function was used to solve the problem iteratively. It made full use of the prior information of sign constraint in measurement,and only required that the parameters had non-negative constraint or first converted the parameters into non-negative constraint,without the need of matrix inversion,and the calculation was simple. The convergence of the algorithm was also analyzed,and an example of global positioning system(GPS) network adjustment was simulated. Numerical experiments showed that the proposed algorithm was superior to other rank-deficit adjustment algorithms in terms of accuracy and computational efficiency.

关 键 词：非负约束 秩亏 线性互补问题 极大熵函数 

分 类 号：P2O7[天文地球—测绘科学与技术]