基于最优迭代初值的坐标转换全局最优组合算法
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摘要
针对坐标转换7参数求解过程中出现的参数不稳定问题,从全局最优解的角度分析了获取稳定参数解的方法,提出了适合坐标转换7参数求解的基于最优迭代初值的全局最优算法.在消除平移参数和尺度参数影响下,分析了旋转参数初值的选取对于参数解不稳定的影响,同时验证了3个角度参数在一个周期范围内有2个等价全局最优解.结果表明:该算法可得到稳定的转换参数,受测量误差影响较小.
Aimed at solving the problem of unstable result in coordinate transfer,we analyzed the way of obtaining the stable solution referring to the view of global optimization,and put forward a method suitable for the calculation of 7parameters in coordinate transfer based on global optimization of iterative initial value.After eliminating the influence of shift and scale parameters,we made a detailed study on the influence of selected initial values of angle parameters and also verified that there are two equivalent global optimizations within the periodic range of three angle parameters.From the results of the experiment data,we can see that this algorithm can get stable transformation parameters which are little influenced by measurement error.
Aimed at solving the problem of unstable result in coordinate transfer,we analyzed the way of obtaining the stable solution referring to the view of global optimization,and put forward a method suitable for the calculation of 7parameters in coordinate transfer based on global optimization of iterative initial value.After eliminating the influence of shift and scale parameters,we made a detailed study on the influence of selected initial values of angle parameters and also verified that there are two equivalent global optimizations within the periodic range of three angle parameters.From the results of the experiment data,we can see that this algorithm can get stable transformation parameters which are little influenced by measurement error.
引文
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[2]王解先.7参数转换中参数之间的相关性[J].大地测量与地球动力学,2007,27(2):43-46.WANG Jiexian.Correlations among parameters in seven-parameter transformation model[J].Journal of Geodesy and Geodynamics,2007,27(2):43-46.
[3]吴杰,李明峰,余腾.测量数据处理中病态矩阵和正则化方法[J].大地测量与地球动力学,2010,30(4):102-104.WU Jie,LI Mingfeng,YU Teng.Ill matrix and regularization method in surveying data processing[J].Journal of Geodesy and Geodynamics,2010,30(4):102-104.
[4]沈云中,胡雷鸣,李博峰.Bursa模型用于局部区域坐标变换的病态问题及其解法[J].测绘学报,2006,35(2):94-98.SHEN Yunzhong,HU Leiming,LI Bofeng.Ill-posed problem in determination of coordinate transformation parameters with small area’s data based on Bursa model[J].Acta Geodaetica et Cartographica Sinica,2006,35(2):94-98.
[5]王乐洋,许才军,鲁铁定.病态加权总体最小二乘平差的岭估计解法[J].武汉大学学报:信息科学版,2010,35(11):1346-1350.WANG Leyang,XU Caijun,LU Tieding.Ridge estimation method in ill-posed weighted total least squares adjustment[J].Geomatics and Information Science of Wuhan University,2010,35(11):1346-1350.
[6]赵志凯,钱建生,程健,等.基于流形正则化的多元时间序列半监督回归[J].中国矿业大学学报,2011,40(3):492-498.ZHAO Zhikai,QIAN Jiansheng,CHENG Jian,et al.Manifold regularization based semi-supervised regression on multivariate time series[J].Journal of China University of Mining&Technology,2011,40(3):492-498.
[7]舒蕾,郝志峰,林大瀛.基于频率矩阵的多样性策略在遗传算法中的应用[J].华南理工大学学报:自然科学版,2003,31(8):23-26.SHU Lei,HAO Zhifeng,LIN Daying.Application of diversity strategy based on frequency matrix in genetic algorithm[J].Journal of South China University of Technology:Natural Science Edition,2003,31(8):23-26.
[8]潘凤萍,巩敦卫,孙晓燕,等.一种自适应遗传算法研究[J].中国矿业大学学报,2003,32(1):68-70.PAN Fengping,GONG Dunwei,SUN Xiaoyan,et al.Research on novel adaptive genetic algorithm[J].Journal of China University of Mining&Technology,2003,32(1):68-70.
[9]崔永利,魏君.SA法在求解非线性约束优化问题中的应用[J].大连大学学报,2003,24(6):5-8.CUI Yongli,WEI Jun.Application of SA algorithm to solving problem of non-linear constraint optimization[J].Journal of Dalian University,2003,24(6):5-8.
[10]李爽,许才军,王新洲.一种求解约束条件下多变量非线性函数所有全局最优解的区间算法[J].武汉大学学报:理学版,2003,49(5):556-560.LI Shuang,XU Caijun,WANG Xinzhou.An Interval algorithm for finding all global minimizers of a constrained nonlinear function with several variables[J].Journal of Wuhan University:Natural Science Edition,2003,49(5):556-560.
[11]王海军,曹德欣,李苏北,等.非线性等式约束全局优化问题的区间算法[J].中国矿业大学学报,2003,32(2):204-208.WANG Haijun,CAO Dexin,LI Subei,et al.An interval algorithm for problems of nonlinear equality constrained global optimization[J].Journal of China University of Mining&Technology,2003,32(2):204-208.
[12]姜爱萍,濮定国.一种改进的填充函数法[J].同济大学学报:自然科学版,2008,36(6):837-840.JIANG Aiping,PU Dingguo.A modified filled function method[J].Journal of Tongji University:Natural Science,2008,36(6):837-840.
[13]XU Peiliang.A hybrid global optimization method:the one-dimensional case[J].Journal of Computational and Applied Mathematics,2002,147:301-314.
[14]XU Peiliang.A hybrid global optimization method:the multi-dimensional case[J].Journal of Computational and Applied Mathematics,2003,155:423-446.