相关观测的L_1范数最小化方法的比较分析  

Comparative Analysis for L_1 Norm Minimization Method with Correlated Observations

作　　者：赵俊 ZHAO Jun(Xi'an Technical Division of Surveying and Mapping? Xi'an 710054 , China;State Key Laboratory of Geodesy and Earth's Dynamics of Chinese Academy of Sciences, Wuhan 430077, China)

机构地区：[1]西安测绘总站，陕西西安,710054 [2]中国科学院大地测量与地球动力学国家重点实验室，湖北武汉,430077

出　　处：《测绘地理信息》2019年第3期33-37,共5页Journal of Geomatics

基　　金：国家自然科学基金(41074025)

摘　　要：在抵御粗差影响方面,L_1范数最小化方法比最小二乘更具可靠性。求解L_1范数最小化问题,主要有选权迭代法和线性规划法两种方法。针对相关观测,通常采用权阵的对角线元素来构造L_1范数最小化问题的目标函数,这种处理方法容易忽略观测值之间的相关性。如果采用Cholesky分解消去观测值之间的相关性,则容易造成粗差的转移,进而影响抗差功效。本文对上述两种方法进行了比较分析,数值实验结果表明将相关观测转换为独立等权观测,有利于增强线性规划的稳健性,而在探测粗差方面则具有等价性。由于基于选权迭代的方法收敛性较差,故不适合求解L_1范数最小化问题。The L1 norm minimization method is more reliable for resisting outliers compared with the least square method. There are two methods for obtaining the L1 norm solution based on iteratively reweight and linear programming respectively. For correlated observations, the diagonal elements are used to construct the objective function of L1 norm minimization problem, but the dependence of observations is ignored. By adopting the Cholesky decomposing, it can be disposed with the dependent observation with equal weight. The robustness will greatly affected due to the transformations of outliers. The paper compares the two methods for L1 norm minimization. The results show that the way to transform the correlated observations to dependent observations is more robust than the original method for linear programming, but identical in terms of detecting outliers. However, the iteratively reweight method shows the bad convergence, so it is improper for solving the L1 norm minimization problem.

关 键 词：L1范数最小化方法 粗差 相关观测 线性规划 选权迭代 

分 类 号：P207[天文地球—测绘科学与技术]