Multi-beam Bathymetry Data Processing Using Iterative Algorithm of Robust Least Squares Collocation

doi:10.11947/j.AGCS.2017.20160491

Abstract

Abstract: In the process of dealing with multi-beam bathymetry data by least squares collocation, the quadric curved mathematical model of trend term can not express accurately the whole variation trend of seafloor topography in general. Moreover, the covariance function estimated by general method is incapable of accurately expressing statistical characteristics with the multi-beam bathymetry data contains gross errors or outliers. So the iterative algorithm of robust least squares collocation is proposed in this paper. Firstly, the initial weight matrix of observations and the initial parameters of covariance function are both given in this method, then the trend term is fitted by polyhedral function and equivalent weights scheme is applied into robust estimation in this method. Finally, the robust parameters of covariance function and solutions of least squares collocation are iteratively calculated. The experimental results show that the method proposed in this paper can express well the whole variation trend of seafloor topography and overcome the effect of gross error or outlier in multi-beam bathymetry data to a certain extent. Compared with the conventional robust method, the proposed method in this paper more effectively probes the outliers in bathymetry data with the robust and better predicted results.

Key words: least squares collocation, seabed terrain generation, covariance function, robust, trend term

CLC Number:

P229

WANG Leyang, CHEN Hanqing. Multi-beam Bathymetry Data Processing Using Iterative Algorithm of Robust Least Squares Collocation[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(5): 658-665.

References

[1] 朱庆, 李德仁. 多波束测深数据的误差分析与处理[J]. 武汉测绘科技大学学报, 1998, 23(1):1-4, 46. ZHU Qing, LI Deren. Error Analysis and Processing of Multibeam Soundings[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1998, 23(1):1-4, 46.
[2] 陆秀平, 黄谟涛, 翟国君, 等. 多波束测深数据处理关键技术研究进展与展望[J]. 海洋测绘, 2016, 36(4):1-6, 11. LU Xiuping, HUANG Motao, ZHAI Guojun, et al. Development and Prospect of Key Technologies for Multibeam Echosounding Data Processing[J]. Hydrographic Surveying and Charting, 2016, 36(4):1-6, 11.
[3] 王海栋, 柴洪洲, 王敏. 多波束测深数据的抗差Kriging拟合[J]. 测绘学报, 2011, 40(2):238-242, 248. WANG Haidong, CHAI Hongzhou, WANG Min. Multibeam Bathymetry Fitting Based on Robust Kriging[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(2):238-242, 248.
[4] BORRE K. Mathematical Foundation of Geodesy:Selected Papers of Torben Krarup[M]. Berlin Heidelberg:Springer, 2006.
[5] MORITZ H. Advanced Physical Geodesy[M]. Karlsruhe:Wichmann, Abacus Press, 1980.
[6] WOLF H.Über Verallgemeinerte Kollokation[J]. Zeitschrift für Vermessungswesen, 1974, 99(11):475-478.
[7] EL-FIKY G S, KATO T. Continuous Distribution of the Horizontal Strain in the Tohoku District, Japan, Predicted by Least-squares Collocation[J]. Journal of Geodynamics, 1998, 27(2):213-236.
[8] 柴洪洲, 崔岳, 明锋. 最小二乘配置方法确定中国大陆主要块体运动模型[J]. 测绘学报, 2009, 38(1):61-65. DOI:10.3321/j.issn:1001-1595.2009.01.011. CHAI Hongzhou,CUI Yue,MING Feng.The Determination of Chinese Mainland Crustal Movement Model Using Least-squares Collocation[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(1):61-65. DOI:10.3321/j.issn:1001-1595.2009.01.011.
[9] 江在森, 刘经南. 应用最小二乘配置建立地壳运动速度场与应变场的方法[J]. 地球物理学报, 2010, 53(5):1109-1117. JIANG Zaisen, LIU Jingnan. The Method in Establishing Strain Field and Velocity Field of Crustal Movement Using Least Squares Collocation[J]. Chinese Journal of Geophysics, 2010, 53(5):1109-1117.
[10] YANG Y X,ZENG A M,ZHANG J.Adaptive Collocation with Application in Height System Transformation[J]. Journal of Geodesy, 2009, 83(5):403-410.
[11] JARMOLOWSKI W. Least Squares Collocation with Uncorrelated Heterogeneous Noise Estimated by Restricted Maximum Likelihood[J]. Journal of Geodesy, 2015, 89(6):577-589.
[12] YOU R J, HWANG H W. Coordinate Transformation between Two Geodetic Datums of Taiwan by Least-Squares Collocation[J]. Journal of Surveying Engineering, 2006, 132(2):64-70.
[13] 徐卫明, 刘雁春. 海道测量中非定位点的精密确定方法[J]. 系统仿真学报, 2007, 19(20):4612-4615. XU Weiming, LIU Yanchun. Methods of Determining Non-Position Points in Hydrographic Survey[J]. Journal of System Simulation, 2007, 19(20):4612-4615.
[14] 王海栋, 柴洪洲, 赵东明. 基于抗差最小二乘配置的海底地形生成研究[J]. 系统仿真学报, 2010, 22(9):2091-2094, 2099. WANG Haidong, CHAI Hongzhou, ZHAO Dongming. Research on Seabed Terrain Generation Based on Robust Least-squares Collocation[J]. Journal of System Simulation, 2010, 22(9):2091-2094, 2099.
[15] 王海栋. 多波束系统测深异常处理理论与方法研究[D]. 郑州:信息工程大学, 2010. WANG Haidong.Research on the Theories and Algorithms of Processing the Bathymetry Outlier in Multibeam Echosounder System[D]. Zhengzhou:Information Engineering University, 2010.
[16] 薛树强, 杨元喜. 广义反距离加权空间推估法[J]. 武汉大学学报(信息科学版), 2013, 38(12):1435-1439. XUE Shuqiang, YANG Yuanxi. Generalized Inverse Distance Weighting Method for Spatial Interpolation[J]. Geomatics and Information Science of Wuhan University, 2013, 38(12):1435-1439.
[17] 黄维彬. 近代平差理论及其应用[M]. 北京:解放军出版社, 1992:92-118. HUANG Weibin. Theory of Adjustment and Its Applications in Geodesy[M]. Beijing:The PLA Press, 1992:92-118.
[18] YANG Yuanxi. Robustfying Collocation[J]. Manuscripta Geodaetica, 1992, 17(1):21-28.
[19] HARDY R L. Multiquadric Equations of Topography and Other Irregular Surfaces[J]. Journal of Geophysical Research, 1971, 76(8):1905-1915.
[20] HARDY R L. The Application of Multiquadric Equations and Point Mass Anomaly Models to Crustal Movement Studies[R]. NOAA Technical Report NOS 76 NGS 11. Rockville, Maryland:US Department of Commerce, National Oceanic and Atmospheric Administration, National Ocean Survey, National Geodetic Survey, 1978.
[21] 谢曦霖, 许才军, 温扬茂, 等. 一种基于多面函数的改进最小二乘配置方法[J]. 武汉大学学报(信息科学版). DOI:10.13203/j.whugis20150664. XIE Xilin, XU Caijun, WEN Yangmao, et al. A Refined Least Squares Collocation Method Based on Multiquadric Function[J]. Geomatics and Information Science of Wuhan University. DOI:10.13203/j.whugis20150664.
[22] 杨元喜. 抗差估计理论及其应用[M]. 北京:八一出版社, 1993. YANG Yuanxi. Robust Estimation Theory and Its Applications[M]. Beijing:Bayi Publishing House, 1993.
[23] SCHAFFRIN B, BOCK Y. Geodetic Deformation Analysis Based on Robust Inverse Theory[J]. Manuscripta Geodaetica, 1994, 19(1):31-44.
[24] 刘念. 协方差函数的抗差拟合[J]. 测绘科学, 2001, 26(3):25-28. LIU Nian. Robust Fitting of Covariance Function[J]. Science of Surveying and Mapping, 2001, 26(3):25-28.
[25] BROUNS G, DE WULF A, CONSTALES D. Multibeam Data Processing:Adding and Deleting Vertices in a Delaunay Triangulation[J]. Hydrographic Journal, 2001(101):3-9.