Data Snooping Algorithm for 3D Datum Transformation with Large Angle
戴鹏洋 1王彬2
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作者信息
1. 同济大学测绘与地理信息学院,上海 200092
2. 南京工业大学测绘科学与技术学院,南京 211800
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摘要
三维基准转换广泛应用于大地测量、摄影测量、点云配准等领域,求解大角度、任意比例尺的三维基准转换参数的研究有很多.然而,当观测值中含有粗差时,得到的转换参数估值会受到不利影响甚至被严重扭曲.为处理含有粗差的大角度三维基准转换问题,本文首先将大角度三维基准转换问题抽象为具有等式约束的最小二乘问题(Constrained least squares,CLS),推导参数在正交约束条件下的最小二乘解.然后,将灵敏度分析方法应用到CLS问题中,研究残差加权平方和对观测值扰动的局部敏感性,并基于这些敏感度指标构造局部检验统计量,进而推导出一个适用于CLS问题的粗差探测算法.最后,为核实该算法的有效性进行了仿真与实测数据实验.实验结果表明:本文提出的基于灵敏度检验统计量的数据探测算法可以降低粗差的负面影响,得到可靠的参数估值,从而有效解决大角度三维基准转换中的粗差处理问题.
Abstract
3D datum transformation is widely used in geodesy,photogrammetry,point cloud registration and many other fields,and there have been many studies of 3D datum transformation problems for large angles and arbitrary scales.When the observations contain gross errors,the estimated transformation parameters are adversely affected and even severely distorted.In order to deal with large-angle 3D datum transformation problems that contain gross errors,this paper first abstracts the large-angle 3D datum transformation problem as constrained least squares(CLS)problem,and derives the least-squares solutions for the parameters under orthogonal constraints.Then,a distinctive sensitivity analysis approach is introduced into this CLS problem.The local sensitivity of the weighted sum of squared residuals to the perturbations of observations in the CLS problem is discussed,and then,the local test statistics are constructed based on these sensitivity indicators,deducing a data snooping algorithm for CLS problem.Finally,simulations and experiments with real data are carried out to verify the effectiveness of the algorithm.The computational results of the simulated and real experiment show that the proposed data-snooping algorithm using the sensitivity-based test statistics can effectually decrease the negative impact of the outliers and derive reliable parameters,which effectively solves the problem of processing gross errors in large-angle 3D datum transformation.
关键词
大角度三维基准转换/约束最小二乘/粗差/数据探测算法
Key words
large-angle 3D datum transformation/constrained least squares/gross error/data snooping algorithm
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