顾及系数矩阵中误差项的三维坐标转换参数总体最小二乘迭代算法
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摘要
在求解三维坐标转换参数过程中,观测误差直接影响着系数矩阵中相关元素的精确性,从而影响到坐标转换参数的最终结果。传统的总体最小二乘算法认为由平面坐标组成的系数矩阵中所有元素都含有误差,忽略了常数项的存在。因此,提出了一种只针对系数矩阵中含有误差元素改正的总体最小二乘迭代算法。该算法对系数矩阵中的常数项和含有误差的元素分别进行处理,利用某地实测数据对本算法的可靠性和精确性进行了验证,并将计算结果与其他四种常用算法进行比较。数值分析结果表明:算法能够实现坐标转换参数的精确计算,可靠性较高。
In the process of solving 3D coordinate transformation parameters,the observation error directly affects the accuracy of related elements in the coefficient matrix,and then affecting the final result of transformation parameters. It considers that all elements in the coefficient matrix composed of plane coordinates contain errors in the traditional total least-squares algorithm without considering the existence of constant terms in the matrix. Therefore,a new iterative algorithm of only for the elements of error correction in coefficient matrix based on total least squares is proposed,and the constant term and the term contained errors are respectively processed in this algorithm. The reliability and accuracy of this algorithm is verified by using the measured data and the calculation results are compared with other four commonly algorithm. The results of numerical analysis shows that this algorithm can realize accurate calculation of coordinate transformation parameters and has high reliability.
In the process of solving 3D coordinate transformation parameters,the observation error directly affects the accuracy of related elements in the coefficient matrix,and then affecting the final result of transformation parameters. It considers that all elements in the coefficient matrix composed of plane coordinates contain errors in the traditional total least-squares algorithm without considering the existence of constant terms in the matrix. Therefore,a new iterative algorithm of only for the elements of error correction in coefficient matrix based on total least squares is proposed,and the constant term and the term contained errors are respectively processed in this algorithm. The reliability and accuracy of this algorithm is verified by using the measured data and the calculation results are compared with other four commonly algorithm. The results of numerical analysis shows that this algorithm can realize accurate calculation of coordinate transformation parameters and has high reliability.
引文
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12崔立鲁,张涌,安家春.超宽巷组合辅助电离层残差法北斗周跳探测与修复[J].科学技术与工程,2018,18(15):1-5Cui Lilu,Zhang Yong,An Jiachun.Detection and repair of BDSbased on ionosphere residual method combined with ultra-wide lane carrier[J].Science Technology and Engineering,2018,18(15):1-5
13崔立鲁,朱贵发.冰后回弹对南极地区冰盖质量变化影响的研究[J].科学技术与工程,2015,15(28):107-111Cui Lilu,Zhu Guifa.The research on the effects of ice rebound for the quality change of antarctic ice caps[J].Science Technology and Engineering,2015,15(28):107-111
14崔立鲁,朱贵发.利用重力卫星数据恢复地球质量迁移方法的研究[J].科学技术与工程,2015,15(14):106-109Cui Lilu,Zhu Guifa.The research on using the method to restore earth’s mass migration based on gravity satellite data[J].Science Technology and Engineering,2015,15(14):106-109
15崔立鲁,杜石.北斗三频无几何相位组合实时周跳探测与修复[J].科学技术与工程,2018,18(29):7-12Cui Lilu,Du Shi.The real-time detection and repair of beidou triple-frequency cycle slip based on geometry-free phase combination[J].Science Technology and Engineering,2018,18(29):7-12
2 Van Huffel S,Vandeualle J.The total least squares problem[J].Conmputational Aspects and Analysis,Frontiers in Applied,Mathematics,SIAM,Philabelphia,1991(9):34-35,84-86
3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,2010Lu Tieding.Research on the total least squares and its applications in surveying data processing[D].Wuhan:Wuhan University,2010
4丁海勇,孙景领.GPS高程转换的总体最小二乘方法研究[J].大地测量与地球动力学,2013,33(3):52-55Ding Haiyong,Sun Jingling.Research on total least-square methods for transformation of GPS elevation[J].Journal of Geodesy and Geodynamics,2013,33(3):52-55
5陆珏,陈义,郑波.总体最小二乘法在三维坐标转换中的应用[J].大地测量与地球动力学,2008,28(5):77-80Lu Jue,Chen Yi,Zheng Bo.Applying total least square to three-dimensional datum transformation[J].Journal of Geodesy and Geodynamics,2008,28(5):77-80
6邱德超,鲁铁定.基于Partial EIV模型的三维坐标转换参数求解方法[J].江西科学,2017,35(3):355-359Qiu Dechao,Lu Tieding.Three-dimensional coordinate conversion parameters method based on Partial EIV model[J].Jiangxi Science,2017,35(3):355-359
7崔立鲁.观测噪声对重力场数据融合方法的影响[J].成都大学学报(自然科学版),2016,35(2):183-186Cui Lilu.Influence of observation noise on gravity field data fusion method[J].Journal of Chengdu University(Natural Science),2016,35(2):183-186
8崔立鲁,罗志才,钟波,等观测噪声对频域输入输出法数据融合的影响[J].大地测量与地球动力学,2009,29(1):79-82Cui Lilu,Luo Zhicai,Zhong Bo,et al.Effect of observation noise on data fusion by frequency domain input-output method[J].Journal of Geodesy and Geodynamics,2009,29(1):79-82
9姚宜斌,黄书华,张良,等.求解三维坐标转换参数的整体最小二乘新方法[J].武汉大学学报:信息科学版,2015,40(7):853-857Yao Yibin,Huang Shuhua,Zhang Liang,et al.A new method of TLS for solving the parameters of three-dimensional coordinate transformation[J].Geomatics and Information Science of Wuhan Unversity,2015,40(7):853-857
10 Shen Y Z,Chen Y,Zheng D H.A quaternion-based geodetic datum transformation algorithm[J].Journal of Geodesy,2006,80:233-239
11 Akyilmaz O.Total least-squares solution of coordinate transformation[J].Survey Review,2007(1):68-80
12崔立鲁,张涌,安家春.超宽巷组合辅助电离层残差法北斗周跳探测与修复[J].科学技术与工程,2018,18(15):1-5Cui Lilu,Zhang Yong,An Jiachun.Detection and repair of BDSbased on ionosphere residual method combined with ultra-wide lane carrier[J].Science Technology and Engineering,2018,18(15):1-5
13崔立鲁,朱贵发.冰后回弹对南极地区冰盖质量变化影响的研究[J].科学技术与工程,2015,15(28):107-111Cui Lilu,Zhu Guifa.The research on the effects of ice rebound for the quality change of antarctic ice caps[J].Science Technology and Engineering,2015,15(28):107-111
14崔立鲁,朱贵发.利用重力卫星数据恢复地球质量迁移方法的研究[J].科学技术与工程,2015,15(14):106-109Cui Lilu,Zhu Guifa.The research on using the method to restore earth’s mass migration based on gravity satellite data[J].Science Technology and Engineering,2015,15(14):106-109
15崔立鲁,杜石.北斗三频无几何相位组合实时周跳探测与修复[J].科学技术与工程,2018,18(29):7-12Cui Lilu,Du Shi.The real-time detection and repair of beidou triple-frequency cycle slip based on geometry-free phase combination[J].Science Technology and Engineering,2018,18(29):7-12