一种基于自适应点质量的区域(似)大地水准面拟合方法
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摘要
针对传统分频余差点质量模型拟合局部(似)大地水准面时系统偏差大、所需基础数据多、计算效率低等问题,利用位场等效逼近原理,对点质量模型进行改造,提出了一种位置固定、埋深自由的点质量模型,并将该模型应用到局部(似)大地水准面拟合中。利用空间距离最近点最优原则建立了解算点质量模型的迭代算法,并顾及周围点影响提出固定加权点方法和自适应法。实验结果表明,相比于传统模型,所提算法有系统偏差小、无奇异性、所需数据少以及计算效率高等优点,利用该方法进行(似)大地水准面拟合是可行的,而且自适应加权半约束点质量模型效果最好。
Aiming at the problems during the local quasigeoid/geoid determination by traditional residual point mass model, such as large system error, big amount of basic data requirement, low computational efficiency and singularity of inverse process, a new approach is presented in this paper called semi-free position point mass based on the gravity field approximation principle. Compared with the traditional model, the plan coordinates of the new one are stationary, while the depths are free. The method is established by a kind of iterative algorithm using the relationship between the nearest points. Then, the algorithm is optimized using the weights calculated by surrounding points based on their distances from the calculating point, then to obtain the best fitting result, a kind of new adaptive method to determine the optimal weighted point number is presented. Results show that the theories presented in this paper achieve higher accuracy than traditional ways, with the advantage of little system error, less modeling data, no singularity and higher accuracy. In summary, using the method to fit local quasigeoid/geoid is feasible, and the adaptive one is better.
Aiming at the problems during the local quasigeoid/geoid determination by traditional residual point mass model, such as large system error, big amount of basic data requirement, low computational efficiency and singularity of inverse process, a new approach is presented in this paper called semi-free position point mass based on the gravity field approximation principle. Compared with the traditional model, the plan coordinates of the new one are stationary, while the depths are free. The method is established by a kind of iterative algorithm using the relationship between the nearest points. Then, the algorithm is optimized using the weights calculated by surrounding points based on their distances from the calculating point, then to obtain the best fitting result, a kind of new adaptive method to determine the optimal weighted point number is presented. Results show that the theories presented in this paper achieve higher accuracy than traditional ways, with the advantage of little system error, less modeling data, no singularity and higher accuracy. In summary, using the method to fit local quasigeoid/geoid is feasible, and the adaptive one is better.
引文
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[2] Wu Xiaoping.Point-Mass Model of Local Gravity Field[J].Acta Geodaetica et Cartographic Sinica,1984,13(4):11-20 (吴晓平.局部重力场的点质量模型[J].测绘学报,1984,13(4):11-20)
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[4] Antunes C,Pail R,Catalāo J.Point Mass Method Applied to the Regional Gravimetric Determination of the Geoid[J].Studia Geophysica et Geodaetica,2003,47:495-509
[5] Huang Motao,Guan Zheng.Test and Construction of Disturbing Point Masses Model[J].Journal of Wuhan Technical University of Surveying & Mapping,1994,19(4):304-309 (黄谟涛,管铮.扰动质点模型构置与检验[J].武汉测绘科技大学学报,1994,19(4):304-309)
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[7] Wang Jianqiang,Li Jiancheng,Zhao Guoqiang,et al.The Construction and Analysis for Three-tier Point Mass Model of Gravity[J].Acta Geodaetica et Cartographica Sinica,2010,39(5):503-507 (王建强,李建成,赵国强,等.重力三层点质量模型的构造与分析[J].测绘学报,2010,39(5):503-507)
[8] Wu Xiaoping.Structure of Data Distribution in the Determination of the Disturbing Gravity Field Outside the Earth[J].Engineering of Surveying and Mapping,2001,10(3):1-8 (吴晓平.地球外部扰动引力场确定的数据空间分布结构[J].测绘工程,2001,10(3):1-8)
[9] Lin M,Denker H,Müller J.Regional Gravity Field Modeling Using Free-Positioned Point Masses[J].Studia Geophysica et Geodaetica,2014,58(2):207-226
[10] Lehmann R.The Method of Free-Positioned Point Masses-geoid Studies on the Gulf of Bothnia[J].Journal of Geodesy,1993,67(1):31-40
[11] Shu Chanfang,Li Fei,Hao Weifeng.Geoid/Quasigeoid Fitting Based on Equivalent Point Masses[J].Geomatics and Information Science of Wuhan University,2011,36(2):231-234(束蝉方,李斐,郝卫峰.利用等效点质量进行(似)大地水准面拟合[J].武汉大学学报·信息科学版,2011,36(2):231-234)
[12] Wu Yihao,Luo Zhicai.The Approach of Regional Geoid Refinement Based on Combining Multi-satellite Altimetry Observations and Heterogeneous Gravity Data Sets[J].Chinese Journal of Geophy-sics,2016,59(5):1 596-1 607(吴怿昊,罗志才.联合多代卫星测高和多源重力数据的局部大地水准面精化方法[J].地球物理学报,2016,59(5):1 596-1 607)
[13] Wu Yihao,Luo Zhicai,Zhou Boyang.Regional Gravity Modeling Based on Heterogeneous Data Sets by Using Poisson Wavelets Radial Basis Functions[J].Chinese Journal of Geophysics,2016,59(3):852-864(吴怿昊,罗志才,周波阳.基于泊松小波径向基函数融合多源数据的局部重力场建模[J].地球物理学报,2016,59(3):852-864)
[14] Qiu Bin,Zhu Jianjun,Le Kejun.Evaluation and Optimal Selection of High-order Earth’s Gravity Field Models[J].Science of Surveying & Mapping,2008,33(5):25-27(邱斌,朱建军,乐科军.高阶地球重力场模型的评价及其优选[J].测绘科学,2008,33(5):25-27)
[15] Cordell L.A Scattered Equivalent-source Method for Interpolation and Gridding of Potential-field Data in Three Dimensions[J].Geophysics,2012,57(4):629
[16] Zhang Jinming,Guo Liping,Zhang Xiaodan.Effects of Interpolation Parameters in Inverse Distance Weighted Method on DEM Accuracy[J].Journal of Geomatics Science & Technology,2012,29(1):51-56(张锦明,郭丽萍,张小丹.反距离加权插值算法中插值参数对DEM插值误差的影响[J].测绘科学技术学报,2012,29(1):51-56)
[17] Zhang Jinming,You Xiong,Wan Gang.Experimental Research on Optimization of DEM Interpolation Parameters[J].Acta Geodaetica et Cartographica Sinica,2014,43(2):178-185 (张锦明,游雄,万刚.DEM插值参数优选的试验研究[J].测绘学报,2014,43(2):178-185)
[18] Li Zhengquan,Wu Yaoxiang.Inverse Distance Weighted Interpolation Involving Position Shading[J].Acta Geodaetica et Cartographica Sinica,2015,44(1):91-98(李正泉,吴尧祥.顾及方向遮蔽性的反距离权重插值法[J].测绘学报,2015,44(1):91-98)
[19] Fan Zide,Li Jialin,Deng Min,et al.An Adaptive Inverse-Distance Weighting Spatial Interpolation Method with the Consideration of Multiple Factors[J].Geomatics and Information Science of Wuhan University,2016,41(6):842-847(樊子德,李佳霖,邓敏,等.顾及多因素影响的自适应反距离加权插值方法[J].武汉大学学报·信息科学版,2016,41(6):842-847)
[20] Nikolaos K P,Simon A H,Steve C K,et al.The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008) [J].Journal of Geophysical Research,2012,117(B4):531-535
[2] Wu Xiaoping.Point-Mass Model of Local Gravity Field[J].Acta Geodaetica et Cartographic Sinica,1984,13(4):11-20 (吴晓平.局部重力场的点质量模型[J].测绘学报,1984,13(4):11-20)
[3] Chao Dingbo,Ning Jinsheng.Quasi-point Mass Model of Integrated Geodesy[J].Journal of Wuhan Technical University of Surveying & Mapping,1992,17(2):1-7 (晃定波,宁津生.整体大地测量的虚拟点质量模型[J].武汉测绘科技大学学报,1992,17(2):1-7)
[4] Antunes C,Pail R,Catalāo J.Point Mass Method Applied to the Regional Gravimetric Determination of the Geoid[J].Studia Geophysica et Geodaetica,2003,47:495-509
[5] Huang Motao,Guan Zheng.Test and Construction of Disturbing Point Masses Model[J].Journal of Wuhan Technical University of Surveying & Mapping,1994,19(4):304-309 (黄谟涛,管铮.扰动质点模型构置与检验[J].武汉测绘科技大学学报,1994,19(4):304-309)
[6] Huang Motao,Guan Zheng,Ouyang Yongzhong.Accuracy Analysis and Calculation of 1°×1° Point Masses in the Area of China[J].Journal of Wuhan Technical University of Surveying & Mapping,1995,20(3):257-262 (黄谟涛,管铮,欧阳永忠.中国地区1°×1°点质量解算与精度分析[J].武汉测绘科技大学学报,1995,20(3):257-262)
[7] Wang Jianqiang,Li Jiancheng,Zhao Guoqiang,et al.The Construction and Analysis for Three-tier Point Mass Model of Gravity[J].Acta Geodaetica et Cartographica Sinica,2010,39(5):503-507 (王建强,李建成,赵国强,等.重力三层点质量模型的构造与分析[J].测绘学报,2010,39(5):503-507)
[8] Wu Xiaoping.Structure of Data Distribution in the Determination of the Disturbing Gravity Field Outside the Earth[J].Engineering of Surveying and Mapping,2001,10(3):1-8 (吴晓平.地球外部扰动引力场确定的数据空间分布结构[J].测绘工程,2001,10(3):1-8)
[9] Lin M,Denker H,Müller J.Regional Gravity Field Modeling Using Free-Positioned Point Masses[J].Studia Geophysica et Geodaetica,2014,58(2):207-226
[10] Lehmann R.The Method of Free-Positioned Point Masses-geoid Studies on the Gulf of Bothnia[J].Journal of Geodesy,1993,67(1):31-40
[11] Shu Chanfang,Li Fei,Hao Weifeng.Geoid/Quasigeoid Fitting Based on Equivalent Point Masses[J].Geomatics and Information Science of Wuhan University,2011,36(2):231-234(束蝉方,李斐,郝卫峰.利用等效点质量进行(似)大地水准面拟合[J].武汉大学学报·信息科学版,2011,36(2):231-234)
[12] Wu Yihao,Luo Zhicai.The Approach of Regional Geoid Refinement Based on Combining Multi-satellite Altimetry Observations and Heterogeneous Gravity Data Sets[J].Chinese Journal of Geophy-sics,2016,59(5):1 596-1 607(吴怿昊,罗志才.联合多代卫星测高和多源重力数据的局部大地水准面精化方法[J].地球物理学报,2016,59(5):1 596-1 607)
[13] Wu Yihao,Luo Zhicai,Zhou Boyang.Regional Gravity Modeling Based on Heterogeneous Data Sets by Using Poisson Wavelets Radial Basis Functions[J].Chinese Journal of Geophysics,2016,59(3):852-864(吴怿昊,罗志才,周波阳.基于泊松小波径向基函数融合多源数据的局部重力场建模[J].地球物理学报,2016,59(3):852-864)
[14] Qiu Bin,Zhu Jianjun,Le Kejun.Evaluation and Optimal Selection of High-order Earth’s Gravity Field Models[J].Science of Surveying & Mapping,2008,33(5):25-27(邱斌,朱建军,乐科军.高阶地球重力场模型的评价及其优选[J].测绘科学,2008,33(5):25-27)
[15] Cordell L.A Scattered Equivalent-source Method for Interpolation and Gridding of Potential-field Data in Three Dimensions[J].Geophysics,2012,57(4):629
[16] Zhang Jinming,Guo Liping,Zhang Xiaodan.Effects of Interpolation Parameters in Inverse Distance Weighted Method on DEM Accuracy[J].Journal of Geomatics Science & Technology,2012,29(1):51-56(张锦明,郭丽萍,张小丹.反距离加权插值算法中插值参数对DEM插值误差的影响[J].测绘科学技术学报,2012,29(1):51-56)
[17] Zhang Jinming,You Xiong,Wan Gang.Experimental Research on Optimization of DEM Interpolation Parameters[J].Acta Geodaetica et Cartographica Sinica,2014,43(2):178-185 (张锦明,游雄,万刚.DEM插值参数优选的试验研究[J].测绘学报,2014,43(2):178-185)
[18] Li Zhengquan,Wu Yaoxiang.Inverse Distance Weighted Interpolation Involving Position Shading[J].Acta Geodaetica et Cartographica Sinica,2015,44(1):91-98(李正泉,吴尧祥.顾及方向遮蔽性的反距离权重插值法[J].测绘学报,2015,44(1):91-98)
[19] Fan Zide,Li Jialin,Deng Min,et al.An Adaptive Inverse-Distance Weighting Spatial Interpolation Method with the Consideration of Multiple Factors[J].Geomatics and Information Science of Wuhan University,2016,41(6):842-847(樊子德,李佳霖,邓敏,等.顾及多因素影响的自适应反距离加权插值方法[J].武汉大学学报·信息科学版,2016,41(6):842-847)
[20] Nikolaos K P,Simon A H,Steve C K,et al.The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008) [J].Journal of Geophysical Research,2012,117(B4):531-535
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