| 一次范数最小估计的两种算法 |
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| 引用本文： | 赵新秀,王解先.一次范数最小估计的两种算法[J].测绘工程,2010,19(2):13-15,19. |
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| 作者姓名： | 赵新秀 王解先 |
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| 作者单位： | 同济大学测量与国土信息工程系,上海,200092;同济大学测量与国土信息工程系,上海,200092;现代工程测量国家测绘局重点实验室,上海,200092 |
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| 摘 要： | 测量数据服从正态分布情况下,最小二乘估计具有最优统计性质,如果测量数据受到粗差干扰而偏离正态分布,就会使最小二乘估计的最优性受到严重冲击,而且估计失实。然而,若采用一次范数最小估计,则所得结果比较好。介绍一次范数最小估计(L1估计)的两种算法——选权迭代法和线性规划法,并通过Matlab模拟实验比较这两种方法的优缺点,证明L1估计的良好抗差性。
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| 关 键 词： | 稳健估计 L1估计 线性规划 迭代 |
The two algorithms of L1-norm |
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| ZHAO Xin-xiu,WANG Jie-xian.The two algorithms of L1-norm[J].Engineering of Surveying and Mapping,2010,19(2):13-15,19. |
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| Authors: | ZHAO Xin-xiu WANG Jie-xian |
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| Institution: | 1; 2(1.Department of Surveying and Geoinformatics; Tongji University; Shanghai 200092; China; 2.Key Laboratory of Advanced Engineering Survey of SBSM; China); |
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| Abstract: | The least squares estimation has optimal statistical properties when measurement errors obey the normal distribution.If measurement data is deviated the normal distribution by the disturbance of gross errors,the least squares estimation will be brokendown.However,the estimation will be better when using L1-norm.This paper explains the two algorithms of L1-norm,which are called LS iteration method and linear programming method.It compares the two algorithms with simulation experiment in Matlab and proves the... |
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| Keywords: | robust L1-norm estimation linear programming iteration |
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