谢建;姚学恒;周璀;

• 1:湖南科技大学煤炭资源清洁利用与矿山环境保护湖南省重点实验室
• 2:海南省大数据管理局
• 3:中南林业科技大学理学院

摘要(Abstract)：

针对不等式约束PEIV模型的参数估计问题,在整体最小二乘准则下,将其转化为约束非线性最优化问题,并提出积极约束法求解。由于积极约束法需要重复求解等式约束PEIV模型,首先利用Lagrange乘子法推导了等式约束PEIV模型的迭代算法;然后提出了积极约束法解不等式约束PEIV模型的算法,包括初值的选取、搜索方向和步长因子的确定方法;最后给出两个数值模拟算例和不等式约束平面拟合实例。结果表明,该文提出的积极约束法具有良好的计算效率和广泛的适用性。

关键词(KeyWords)： 部分EIV模型;不等式约束;整体最小二乘;积极约束法;平面拟合

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(41704007,41604012)

作者(Authors): 谢建;姚学恒;周璀;

DOI: 10.16251/j.cnki.1009-2307.2020.09.006

参考文献(References)：

• [1] GOLUB G H,VAN Loan.An analysis of the total least-squares problem[J].SIAM J Num Anal,1980,17(6):883-893.
• [2] SCHAFFRIN B,LEE I,FELUS Y,et al.Total least-squares for geodetic straight-line and plane adjustment[J].Bollettino di Geodesia e Scienze Affini,2006,65(3):141-168.
• [3] SCHAFFRIN B,WIESER A.On weighted total least-squares adjustment for linear regression[J].Journal of Geodesy,2008,82(7):415-421.
• [4] SHEN Yunzhong,LI Bofeng,CHEN Yi.An iterative solution of weighted total least-squares adjustment[J].Journal of Geodsy,2011,85(4):229-238.
• [5] FANG Xing.Weighted total least squares:necessary and sufficient conditions,fixed and random parameters[J].Journal of Geodesy,2013,87(8):733-749.
• [6] XU Peiliang,LIU Jingnan,SHI Chuang.Total least squares adjustment in partial errors-in-variables models:algorithms and statistical analysis[J].Journal of Geodesy,2012,86(8):661-675.
• [7] SHI Yun,XU Peiliang,LIU Jingnan,et al.Alternative formulae for parameter estimation for partial errors-in-variables models[J].Journal of Geodesy,2015,89(1):13-16.
• [8] 王乐洋,余航,陈晓勇.Partial EIV模型的解法[J].测绘学报,2016,45(1):22-29(WANG Leyang,YU Hang,CHEN Xiaoyong.An algorithm for Partial EIV model[J].Acta Geodaetica et Cartographica Sinica,2016,45(1):22-29.)
• [9] SCHAFFRIN B,FELUS A Y.An algorithmic approach to the total least-squares problem with linear and quadratic constraints[J].Studia Geophysica et Geodaetica,2008,53(1):1-16.
• [10] FANG Xing.Weighted total least squares with constraints:a universal formula for geodetic symmetrical transformations[J].Journal of Geodesy,2015,89(5):459-469.
• [11] ZHANG Sonlin,TONG Xiaohua,ZHANG Kun.A solution to EIV model with inequality constraints and its geodetic applications[J].Journal of Geodesy,2013,87(1):23-28.
• [12] FANG Xing.On non-combinatorial weighted total least squares with inequality constraints[J].Journal of Geodesy,2014,88(8):805-816.
• [13] 曾文宪,方兴,刘经南,等.附有不等式约束的加权整体最小二乘算法[J].测绘学报,2014,43(10):1013-1018.(ZENG Wenxian,FANG Xing,LIU Jingnan,et al.Weighted total least squares algorithm with inequality constraints[J].Acta Geodaetica et Cartographica Sinica,2014,43(10):1013-1018.)
• [14] ZENG Wenxian,LIU Jingnan,YAO Yibin.On partial errors-in-variables models with inequality constraints of parameters and variables[J].Journal of Geodesy,2015,89(2):111-119.
• [15] 陈宝林.最优化理论与算法[M].北京:清华大学出版社,2005.(CHEN Baolin.Theory and algorithms of optimization[M].Beijing:Press of Tsinghua University,2005.)