| 多维随机变量的熵不确定度 |
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| 引用本文： | 李大军,程朋根,龚健雅,熊助国.多维随机变量的熵不确定度[J].计量学报,2006,27(3):290-293. |
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| 作者姓名： | 李大军 程朋根 龚健雅 熊助国 |
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| 作者单位： | 1. 东华理工学院测量系,江西,抚州,344000
2. 武汉大学,测绘遥感信息工程国家重点实验室,湖北,武汉,430079 |
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| 基金项目： | 国家重点基础研究发展计划(973计划);东华理工学院校科研和教改项目 |
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| 摘 要： | 通过引入信息熵理论，将一维随机变量的熵不确定度指标推广到二维、三维和N维情况，提出了熵不确定椭圆、熵不确定椭球和熵不确定超椭球指标，以此作为二维、三维及多维随机点的不确定度指标。所提的熵指标具有惟一确定、不受置信水平选取的主观性影响的特点，比较适合于作为GIS中信息点的位置不确定性度量指标。
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| 关 键 词： | 计量学 信息熵 多维随机变量 熵不确定度 |
| 文章编号： | 1000-1158（2006）03-0290-04 |
| 收稿时间： | 2004-10-20 |
| 修稿时间： | 2004-12-25 |
Entropy Uncertainty of Multi-dimensional Random Variable |
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| LI Da-jun,CHENG Peng-gen,GONG Jian-ya,XIONG Zhu-guo.Entropy Uncertainty of Multi-dimensional Random Variable[J].Acta Metrologica Sinica,2006,27(3):290-293. |
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| Authors: | LI Da-jun CHENG Peng-gen GONG Jian-ya XIONG Zhu-guo |
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| Affiliation: | 1. Department of Surveying, East China Institute of Technology, Fuzhou, Jiangxi 344000, China ; 2. State Key Lab for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, Hubei 430079, China |
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| Abstract: | With the introduction of the theory of information entropy, the entropy uncertainty indices of one-dimensional random variable are extended to the circumstances of two-dimensional, three-dimensional and N-dimensional. The indices of entropy uncertainty ellipse, entropy uncertainty ellipse sphere and super entropy uncertainty ellipse sphere are presented, which can be considered as the indices of uncertainty degree of two-dimensional, three-dimensional and multi-dimensional random points. The entropy indices presented in this paper are sole and not effected by the objective selection of the confident level. They are suitable for measurement of the positional uncertainty of information points in GIS. |
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| Keywords: | Metrology Information entropy Multi-dimensional random variable Entropy uncertainty |
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