基于F-范数的不确定性平差模型的解算方法
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摘要
为提高基于F-范数的不确定性平差模型的解算效率,给出直接迭代算法进行参数估计。该算法无需SVD,解算过程简单且易于编程计算,同时给出迭代不收敛时的SVD-解方程算法。二元线性拟合及沉降观测AR模型的算例结果表明,这2种算法正确可行,与SVD-迭代算法具有等价性。当迭代收敛时,宜使用直接迭代算法,收敛速度更快,解算效率更高;当迭代不收敛时,可釆用SVD-解方程算法。
In order to improve the calculation efficiency of adjustment models with uncertainty based on F-norm,a directly iterative algorithm is developed.The algorithm does not use singular value decomposition(SVD),is simple in the concept,and is easy to program.Another algorithm of SVD-equations is also given when the iterative algorithm is divergent.The results of the binary linear fitting and AR model in settlement observation illustrate that the two proposed algorithms could be practiced and are equivalent to the algorithm of SVD-iteration.The directly iterative algorithm is more suitable when the iterative algorithm is convergence,which has faster convergence rate and higher calculation efficiency.Moreover,the algorithm of SVD-equations can be used when the iterative algorithm is divergent.
In order to improve the calculation efficiency of adjustment models with uncertainty based on F-norm,a directly iterative algorithm is developed.The algorithm does not use singular value decomposition(SVD),is simple in the concept,and is easy to program.Another algorithm of SVD-equations is also given when the iterative algorithm is divergent.The results of the binary linear fitting and AR model in settlement observation illustrate that the two proposed algorithms could be practiced and are equivalent to the algorithm of SVD-iteration.The directly iterative algorithm is more suitable when the iterative algorithm is convergence,which has faster convergence rate and higher calculation efficiency.Moreover,the algorithm of SVD-equations can be used when the iterative algorithm is divergent.
引文
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[2]宋迎春,金昊,崔先强.带有不确定性的观测数据平差解算方法[J].武汉大学学报:信息科学版,2014,39(7):788-792(Song Yingchun,Jin Hao,Cui Xianqiang.Adjustment Criterion and Algorithm in Adjustment Model with Uncertainty[J].Geomatics and Information Science of Wuhan University,2014,39(7):788-792)
[3]Ghaoui L E,Lebret H.Robust Solutions to Least-Squares Problems with Uncertain Data[J].Siam Journal on Matrix Analysis&Applications,1997,18(4):1 035-1 064
[4]Chandrasekaran S,Golub G H,Gu M,et al.Parameter Estimation in the Presence of Bounded Modeling Errors[J].Signal Processing Letters,IEEE,1997,4(7):195-197
[5]Chandrasekaran S,Golub G H,Gu M,et al.Parameter Estimation in the Presence of Bounded Data Uncertainties[J].Siam Journal on Matrix Analysis&Applications,1998,19(1):235-252
[6]杨智慧,毛剑琴,魏可惠.基于LMI的具有一类不确定性数据的参数估计[J].北京航空航天大学学报,2000,26(4):481-484(Yang Zhihui,Mao Jianqin,Wei Kehui.Parameter Estimation Based on LMI with Bounded Data Uncertainties[J].Journal of Beijing University of Aeronautics and Astronautics,2000,26(4):481-484)
[7]邹渤,宋迎春,唐争气,等.沉降观测AR模型的不确定性平差算法[J].大地测量与地球动力学,2016,36(8):686-688(Zou Bo,Song Yingchun,Tang Zhengqi,et al.Adjustment Algorithm on AR Model with Uncertain in Settlement Observation[J]Journal of Geodesy and Goedynamics,2016,36(8):686-688)
[8]邱卫宁,陶本藻,姚宜斌,等.测量数据处理理论与方法[M].武汉:武汉大学出版社,2008(Qiu Weining,Tao Benzao,Yao Yibin,et al.The Theory and Method of Surveying Data Processing[M].Wuhan:Wuhan University Press,2008)
[9]Cryer J D,Chan K S.Time Series Analysis with Applications in R[M].Berlin:Springer-Verlag,2008
[10]鲁铁定.总体最小二乘平差理论及其在测绘数据处理中的应用[D].武汉:武汉大学,2010(Lu Tieding.Research on the Total Least Squares and Its Applications in Surveying Data Processing[D].Wuhan:Wuhan University,2010)
[11]武汉大学测绘学院测量平差学科组.误差理论与测量平差基础[M].武汉:武汉大学出版社,2015(Surveying Adjustment Group of School of Geodesy and Geomatics of Wuhan University.Error Theory and Foundation of Surveying Adjustment[M].Wuhan:Wuhan University Press,2015)