多波束测深数据处理的抗差最小二乘配置迭代解法

doi:10.11947/j.AGCS.2017.20160491

测绘学报 ›› 2017, Vol. 46 ›› Issue (5): 658-665.doi: 10.11947/j.AGCS.2017.20160491

多波束测深数据处理的抗差最小二乘配置迭代解法

王乐洋^1,2,3, 陈汉清^1,2

1. 东华理工大学测绘工程学院, 江西南昌 330013;
2. 流域生态与地理环境监测国家测绘地理信息局重点实验室, 江西南昌 330013;
3. 江西省数字国土重点实验室, 江西南昌 330013

收稿日期:2016-10-17 修回日期:2017-04-13 出版日期:2017-06-20 发布日期:2017-06-05
作者简介:王乐洋(1983-),男,博士,副教授,主要研究方向为大地测量反演及大地测量数据处理。E-mail:wleyang@163.com
基金资助:
国家自然科学基金（41664001；41204003）；江西省杰出青年人才资助计划项目（20162BCB23050）；国家重点研发计划（2016YFB0501405）；江西省教育厅科技项目（GJJ150595）；江西省数字国土重点实验室开放研究基金（DLLJ201705）

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

WANG Leyang^1,2,3, CHEN Hanqing^1,2

1. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China;
3. Key Laboratory for Digital Land and Resources of Jiangxi Province, Nanchang 330013, China

Received:2016-10-17 Revised:2017-04-13 Online:2017-06-20 Published:2017-06-05
Supported by:
National Natural Science Foundation of China (Nos.41664001;41204003);Support Program for Outstanding Youth Talents in Jiangxi Province (No.20162BCB23050);National Key Research and Development Program(No.2016YFB0501405);Science and Technology Project of the Education Department of Jiangxi Province (No.GJJ150595);the Project of Key Laboratory for Digital Land and Resources of Jiangxi Province(No.DLLJ201705)

摘要/Abstract

摘要： 针对利用最小二乘配置处理多波束测深数据，存在二次曲面数学模型通常无法精确表征海底地形的整体变化趋势以及观测数据存在粗差或异常点时，常规方法给出的协方差函数不能精确表征其统计特性的问题，本文提出了一种抗差最小二乘配置迭代解法。该方法首先进行协方差函数和观测值方差阵初始化，以多面函数拟合趋势项，然后应用等价权抗差估计并通过迭代计算，最终给出稳健的协方差函数参数解及最小二乘配置解。利用本文提出的方法及传统的方法处理实测的多波束测深数据，试验结果表明，相比于传统的方法，本文提出的方法能够较好地表征海底地形的整体变化趋势，一定程度上克服了多波束测深数据中粗差或异常点的影响。相比于传统的抗差方法，本文方法更为有效地识别出测深数据中异常点，推估效果较好，具有稳健性。

关键词: 最小二乘配置, 海底地形生成, 协方差函数, 抗差, 趋势项

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

中图分类号:

P229

王乐洋, 陈汉清. 多波束测深数据处理的抗差最小二乘配置迭代解法[J]. 测绘学报, 2017, 46(5): 658-665.

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.

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多波束测深数据处理的抗差最小二乘配置迭代解法

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

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