| 顾及框架点坐标误差的三维基准转换严密模型 |
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| 引用本文： | 曾安敏,明锋.顾及框架点坐标误差的三维基准转换严密模型[J].测绘学报,2017,46(1):16-25. |
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| 作者姓名： | 曾安敏 明锋 |
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| 作者单位： | 1. 地理信息工程国家重点实验室, 陕西 西安 710054;2. 信息工程大学地理空间信息学院, 河南 郑州 450001 |
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| 基金项目： | 国家重点研发计划，国家863计划，国家自然科学基金(41474015;41274040)The National Key Research and Development Program of China，The National High-tech Research and Development Program of China (863 Program)，The National Natural Science Foundation of China |
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| 摘 要： | 框架点坐标是由观测数据通过平差得到的,不可避免地受到观测误差的影响。针对原框架和目标框架坐标均存在误差、非公共点与公共点间存在相关性,以及转换系数矩阵中仅部分元素存在误差的实际情况,提出了同时考虑框架内误差以及转换点间相关性的基准转换严密模型,该模型将公共点和非公共点联合处理,同时计算坐标转换参数和所有点的坐标转换值,推导出了新的严格坐标转换公式,该公式为传统坐标转换公式基础上增加一改正量的形式;进一步,推导了原框架和目标框架坐标的方差不一致情况下的坐标转换模型的自适应解法;最后,利用"陆态网络工程"2000个区域站的实测坐标进行坐标转换验证,结果表明,这种严密模型较传统坐标转换模型具有更高的坐标转换精度。
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| 关 键 词： | 坐标转换 相似变换 自适应估计 联合统一模型 框架协方差 |
| 收稿时间： | 2016-06-14 |
| 修稿时间： | 2016-11-30 |
The Rigorous Model for Similarity Transformation under Intra-frame and Inter-frame Covariance |
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| ZENG Anmin,MING Feng.The Rigorous Model for Similarity Transformation under Intra-frame and Inter-frame Covariance[J].Acta Geodaetica et Cartographica Sinica,2017,46(1):16-25. |
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| Authors: | ZENG Anmin MING Feng |
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| Institution: | 1. State Key Laboratory of Geo-information Engineering, Xi'an 710054, China;2. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China |
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| Abstract: | The coordinates are obtained from observations by using least-squares method,so their precision should be contaminated by observation errors and the covariance also exists between common points and non-common points.The coordinate errors don't only exist in the initial frame but also in the target frame.But the classical stepwise approach for coordinate frame transformation usually takes the coordinate errors of the initial frame into account and overlooks the stochastic correlation between common points and non-common points.A new rigorous unified model is proposed for coordinate frame transformation that takes into account both the errors of all coordinates in both fame and inter-frame coordinate covariance between common points and non-common points,and the corresponding estimator for the transformed coordinates are derived and involve appropriate corrections to the standard approach,in which the transformation parameters and the transformed coordinates for all points are computed in a single-step least squares approach.The inter frame coordinate covariance should be consistent to their uncertainties,but in practice their uncertainties are not consistent.To balance the covariance matrices of both frames,a new adaptive estimator for the unified model is thus derived in which the corresponding adaptive factor is constructed by the ratio computed by Helmert covariance component estimation,reasonable and consistent covariance matrices are arrived through the adjustment of the adaptive factor.Finally,an actual experiments with 2000 points from the crustal movement observation network of China (abbreviated CMONOC) is carried out to verify the implement of the new model,the results show that the proposed model can significantly improve the precision of the coordinate transformation. |
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| Keywords: | coordinate transformation similarity transformation adaptive estimation unified rigorous model intra-frame and inter-frame covariance |
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