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1.
The cause of the formal difference ofp-norm distribution density functions is analyzed, two problems in the deduction ofp-norm formulating are improved, and it is proved that two different forms ofp-norm distribution density functions are equivalent. This work is useful for popularization and application of thep-norm theory to surveying and mapping.
Supported by Scientific Research Fund of Human Province Education Department (No. 03C483). 相似文献
2.
APPROXIMATE REPRESENTATION OF THE p-NORM DISTRIBUTION 总被引：1，自引：0，他引：1
SUN Haiyan 《地球空间信息科学学报》2001,4(3)
1 ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｓｕｒｖｅｙｉｎｇｄａｔａｐｒｏｃｅｓｓｉｎｇ ,ｉｔｉｓｏｆｔｅｎｓｕｐｐｏｓｅｄｔｈａｔｏｂｓｅｒｖａｔｉｏｎａｌｅｒｒｏｒｓｄｉｓｔｒｉｂｕｔｅｎｏｒｍａｌｌｙ .Ｉｆｏｂ ｓｅｒｖａｔｉｏｎｓｃｏｍｅｆｒｏｍｔｈｅｎｏｒｍａｌｄｉｓｔｒｉｂｕｔｉｏｎａｌｃｌａｓｓ ,ｔｈｅｍｅｔｈｏｄｏｆｌｅａｓｔｓｑｕａｒｅｓｃａｎｇｉｖｅｔｈｅｍｉｎｉ＿ＰｒｏｊｅｃｔｓｕｐｐｏｒｔｅｄｂｙｔｈｅＳｕｓｔｅｎｔａｔｉｏｎＰｌａｎｆｏｒＯｕｔｓｔａｎｄｉｎｇＴｅａｃｈｅｒｓｏｆＡ… 相似文献
3.
p—范分布的近似表示 总被引：8，自引：0，他引：8
孙海燕 《武汉大学学报(信息科学版)》2001,26(3):222-225
p-范分布是一个包含拉普拉斯分布、正态分析、均匀分布等常见分布的分布族。用p-范分布描述观测误差的统计特性，只需假定误差的分布为单峰、对称，因此、p-范分布似然平差可以避免事先假定误差的具体分布模式，而在平差过程中确定未知参数及误差的分布具有自适应的特点。但是p-范分布的密度函数比较复杂，不利于理论分析和实际应用。 的研究表明，p-范分布可以近似地表示为拉普拉斯分布与正态分析或正态分布均均匀分布的线性组全。p-范分布与本文给出的近似分布具有相的前四阶矩。由于拉普拉斯分布。正态分布。均匀分布的密度函数都比较简单，用近似分布代替p-范分布会使相关的问题得到简化。 相似文献
4.
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。 相似文献
5.
Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness 总被引：3，自引：1，他引：3
Peiliang Xu 《Journal of Geodesy》2005,79(1-3):146-159
The findings of this paper are summarized as follows: (1) We propose a sign-constrained robust estimation method, which can
tolerate 50% of data contamination and meanwhile achieve high, least-squares-comparable efficiency. Since the objective function
is identical with least squares, the method may also be called sign-constrained robust least squares. An iterative version
of the method has been implemented and shown to be capable of resisting against more than 50% of contamination. As a by-product,
a robust estimate of scale parameter can also be obtained. Unlike the least median of squares method and repeated medians,
which use a least possible number of data to derive the solution, the sign-constrained robust least squares method attempts
to employ a maximum possible number of good data to derive the robust solution, and thus will not be affected by partial near
multi-collinearity among part of the data or if some of the data are clustered together; (2) although M-estimates have been
reported to have a breakdown point of 1/(t+1), we have shown that the weights of observations can readily deteriorate such results and bring the breakdown point of
M-estimates of Huber’s type to zero. The same zero breakdown point of the L
1-norm method is also derived, again due to the weights of observations; (3) by assuming a prior distribution for the signs
of outliers, we have developed the concept of subjective breakdown point, which may be thought of as an extension of stochastic
breakdown by Donoho and Huber but can be important in explaining real-life problems in Earth Sciences and image reconstruction;
and finally, (4) We have shown that the least median of squares method can still break down with a single outlier, even if
no highly concentrated good data nor highly concentrated outliers exist.
An erratum to this article is available at . 相似文献
6.
根据残差与真误差的Bahadur型关系,L1范估计中, 粗差几乎完全反映到相应的残差上,这就是L1范估计能正确定位粗差的原因.对L2范估计,粗差只是部分地反应到相应残差上,由此会导致粗差误判.根据L1范估计的残差及其方差, 构造了L1范估计的巴尔达检验统计量, 并讨论了L1范估计的可靠性.与L2范估计的可靠性比较,L1范估计的可靠性受多余观测的影响小. 相似文献
7.
同震滑动分布参数与地表形变间的线性关系依赖于格林函数矩阵的构造,格林函数矩阵元素与破裂面位置、几何参数、破裂方式及位错模型假设等因素有关。本文尝试考虑格林函数矩阵元素的误差来补偿上述原因在一定程度上对反演参数的影响,采用同时顾及系数矩阵(格林函数矩阵)和观测向量两者误差的总体最小二乘方法反演同震滑动分布。首先确定了系数矩阵元素和观测向量的协因数矩阵,考虑到格林函数矩阵的病态性(秩亏),借助拉普拉斯二阶平滑得到正则化矩阵,采用总体最小二乘正则化法反演同震滑动分布。并对2009年意大利中部拉奎拉(L’Aquila)Mw6.3级地震实例进行同震滑动分布反演研究。结果表明,拉奎拉地震的走向为144.37°,倾角为59.06°,滑动分布的最大滑动量为0.95m,平均滑动角为-96.4°,主要滑动深度为4~15km的范围,地震矩为3.63×10~(18)N·m,对应的矩震级为Mw6.34。总体最小二乘与最小二乘法的滑动分布解存在一定差别,但差别的量级在10-4以内。 相似文献
8.
J. Marshall 《Journal of Geodesy》2002,76(6-7):334-344
Several pre-analysis measures which help to expose the behavior of L
1 -norm minimization solutions are described. The pre-analysis measures are primarily based on familiar elements of the linear
programming solution to L
1-norm minimization, such as slack variables and the reduced-cost vector. By examining certain elements of the linear programming
solution in a probabilistic light, it is possible to derive the cumulative distribution function (CDF) associated with univariate
L
1-norm residuals. Unlike traditional least squares (LS) residual CDFs, it is found that L
1-norm residual CDFs fail to follow the normal distribution in general, and instead are characterized by both discrete and
continuous (i.e. piecewise) segments. It is also found that an L
1 equivalent to LS redundancy numbers exists and that these L
1 equivalents are a byproduct of the univariate L
1 univariate residual CDF. Probing deeper into the linear programming solution, it is found that certain combinations of observations
which are capable of tolerating large-magnitude gross errors can be predicted by comprehensively tabulating the signs of slack
variables associated with the L
1 residuals. The developed techniques are illustrated on a two-dimensional trilateration network.
Received: 6 July 2001 / Accepted: 21 February 2002 相似文献
9.
半参数回归与模型精化 总被引：31，自引：4，他引：31
就一般情况给出了半参数平差的算法，并结合一种特定的情况，讨论了正规化矩阵半正定时的计算方法，给出了相应的公式，最后构造了一个模拟的平差问题，对半参数法和最小二乘法的计算结果进行了比较，计算表明，半参数法能够发现并识别模型误差或观测值中的系统误差。 相似文献
10.
根据Laplace分布的概率密度函数公式，推导了了中位数的概率密度，在此基础上证明了L1－范估计的无偏性。 相似文献
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在已有的极化合成孔径雷达(PolSAR)图像恒虚警(CFAR)检测方法中,存在着高分辨下杂波模型适用性差的难题。为解决此问题,提出了一种G_0分布下虚警概率具有闭合解析表达形式的CFAR检测方法,并定义虚警损失率(CFAR Loss, C_L)参数用以量化评估CFAR检测方法的恒虚警保持效果。首先,在乘积模型框架下,引入了逆Gamma纹理变量假设,推导出了多视极化白化滤波(MPWF)检测量的概率密度函数(PDF)。然后,对MPWF检测量的概率密度函数积分得到了虚警概率关于CFAR检测阈值的解析表达式,并设计了相应的CFAR检测流程。最后,采用仿真数据和AIRSAR实测数据对已有方法和新方法进行了算法运行时间、检测量拟合性能及目标检测性能对比。实验结果表明,方法运行时间比已有方法缩短3至30倍,具有良好的实时性;日本玉野地区的AIRSAR实测数据结果表明G_0分布对高分辨不均匀海区具有良好的拟合性能,且新方法在G_0分布和非G_0分布海区均能有效检测出目标,鲁棒性较强,相比其他检测方法品质因数(FoM)平均高出15.78%;C_L分析结果表明新方法具有良好的恒虚警保持性能,同时指出杂波对数累积量散点距离G_0分布曲线越近,新方法的恒虚警保持效果越好。 相似文献
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文中在平面网平差中应用整体最小二乘理念.在最小二乘模型中,为了消除观测方程系数误差和未知参数系统误差,加入系数改正数和参数改正数,并提出三原则整体最小二乘模型.研究平差两大步骤,用最小二乘多次改用"参考点组"而选出w个稳定点;用最小二乘多次改用"近似坐标"而消除系数误差和参数系统误差.三原则整体最小二乘适用于平面自由网... 相似文献
15.
The observations of theIRIS network are used to study the stability of the determination ofERP fromVLBI. It is concluded that the uncertainties in the initial values ofERP, the errors of other parameters and analyst noise are at the same level as the formal errors in the determination ofERP. The geometric effect on the determination ofERP is important and gives rise to systematic errors. The geometric effect on polar motion is greate than onUT1, and much greater for the continental network. The stability of the determination ofERP fromVLBI can be improved either by creating new stations at reasonable locations in a network or by creating new networks.
At last a comparison is provided between the determinations ofERP from theIRIS andTEMPO networks. 相似文献
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地图扫描矢量化误差的最小二乘配置法处理研究 总被引：3，自引：0，他引：3
屏幕扫描数字化是地图数字化的常用方法。在数字化过程中,由于地图本身的变形、扫描仪分辨率等系统误差会影响数字化的结果。仿射变换是实现栅格数据向矢量化数据转换的常用方法之一,研究表明基于最小二乘的仿射变换只可以消除整体变形,而不能消除局部变形。为此作者提出采用最小二乘配置。采用最小二乘配置可以在计算转换参数的同时估计局部系统变形信号,可以消除或减弱以上误差的影响,改善数字化精度。实例分析表明,是提高扫描数字化的有效方法。 相似文献
18.
Accurate relative positioning via dynamic satellite methods is a complicated process. In an attempt to simplify this process
a semidynamic method has been investigated in a real data environment. In this method quasi-simultaneous observations from
pairs of stations are transformed to Simultaneous Range Differences(SRD's). With this transformation it is anticipated to reduce the effects of orbital and observational residual biases and, therefore,
to obtain baselines the accuracy of which is less sensitive to the overall orbital accuracy and yet compatible to that of
the observations. Using laser range observations to Lageos collected during theMERIT Main Campaign, baselines have been estimated via both theSRD and the geometric methods. Baselines estimated via the geometric method are independent of orbital errors and any inconsistencies
affecting the implementation of the Terrestrial Reference Frame, and therefore they have been used in the present study as
standards of comparison. From this comparison it was concluded that for baselines of regional extent, theSRD method is very efficient and at least as accurate as the more complex dynamic methods. 相似文献
19.
GNSS坐标时间序列中不可避免地含有粗差,未剔除的粗差将会导致参数估计有偏。因此,粗差探测与剔除是GNSS坐标序列分析中一项重要的数据预处理工作。针对GNSS坐标时间序列特点,提出了一种将L1范数(L1-norm)估计与四分位距统计量IQR(interquartile range)组合的移动开窗粗差探测算法,称之为L1_Mod IQR。该方法的主要思想是,首先利用L1范数估计得到较"真实"的残差,然后再对残差采用IQR统计量进行粗差探测。将L1_Mod IQR法与"3σ"法、基于最小二乘的τ检验法等粗差探测算法进行了模拟计算与对比,验证了该算法的有效性。进一步采用L1_Mod IQR算法对中国区域10个IGS站的高程时间序列进行了分析,结果表明中国区域IGS站高程序列的粗差剔除率最小为0.1%,最大为2.6%。并且以WUHN站为例与SOPAC提供的结果进行了对比,结果表明SOPAC提供的"Clean"数据仍含有大量的粗差,而L1_Mod IQR算法能够有效地剔除粗差。 相似文献
20.
本文利用经典平差方法对鑫诺卫星的观测数据进行处理,采用偏度、峰度正态假设检验其残差值是否服从偶然分布,进而判断参数估计结果可靠与否。检验结果表明,残差时间序列的频率直方图不服从正态分布,最小二乘平差方法在处理此观测数据所得到的估计结果是不可靠的。鑫诺卫星观测数据不仅含有偶然误差,还存在系统误差等。本文采用数字滤波方法模型化系统误差及迭代平差的方法,达到提高数据处理精度的目的。 相似文献