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1.
现有献对数学期望平移模型的理论分析仅考虑了观测值统计独立的特殊情况，基于现测值统计相关的一般情况，导出了数学期望平移参数估值的简明表达式，在此基础上，采用统计预测理论对△Ｓｉ进行了直观的理论解释，扩展了统计学献中的有关结论。借助于实例，分析了△Ｓｉ与最小二乘残差的本质区别。 相似文献
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构造粗差检验统计量的主要方法有两类。一种是基于观测值数学期望平移参数估值,另一种则是建立在预测残差的基础上。本文对上述两类构造粗差检验统计量的方法进行了理论分析。作者的研究结果表明,当观测值之间不相关时,上述两类方法在理论上是等价的。 相似文献
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采用VB语言与MATLAB语言编程,提取南宁实验GPS控制网观测数据中的原始载波信号,利用小波分析理论在多尺度、多分辨率、可伸缩、可平移等分析方面的优势,分别对提取的原始载波信号、单差观测值、双差观测值采用bd3小波函数进行3层小波分解,研究高频信号特点以及不同差分方法消除噪声的效果。将小波分析理论作为数学工具,实施GPS观测数据小波分解和重组,对于发现并削弱GPS误差具有一定的参考价值。 相似文献
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采用相关平差算法计算导线网中每个观测值的多余观测分量和各类观测值的内可靠性指标，按统计假设检验理论构成观测值的粗差检测统计量，经过探查指出可能含有粗差的观测值。最后给出内可靠性分析的结果，并提出导线网设计和施测要点建议 相似文献
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在测量平差的函数模型和随机模型中，随机误差属正态变量，其数学期望假设为零，即观测值中是不能包含粗差的。一般认为，只要观测者细心，严格按规范操作，观测值的粗差总是可以避免的，但其实并不完全如此，还有其它许多原因。例如，激光测距仪连续多次读数，由于仪器内部原因，其中有的读数超出了偶然误差的限值；归算观测值的改正公式过于粗糙造成参与平差的观测值包含了粗差；由于测量返工的凑合也可能产生粗差等等。因此，不管怎样预防，观测值中还是有可能存在粗差的。包含粗差的观测值是不能参与平差的，然而也不能凭主观任意剔除被认为可疑的观测值，正确的方法是藉助于数理统计理论去发现这种粗差并剔除之，以保证成果的可靠性。 相似文献
6.
黄加纳 《武汉测绘科技大学学报》1997,22(1):51-54
采用相关平差算法计算导线网中每个观测值的多余观测量和各类观测值的内可靠性指标，按统计假设检验理论构成观测值的粗差检测统计量，经过探查指出可能含有粗差的观测值。最后给出内可靠性分析的结果，并提出导线网设计和施测要点建议。 相似文献
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宋力杰 《测绘科学技术学报》2000,17(3):160-162
均值平移模型是处理含粗差观测值的常用模型之一.文中证明了均值平移模型的参数估值及残差二次型与剔除模型的参数估值和残差二次型完全相等,并进一步分析了均值平移模型粗差检验的性质. 相似文献
10.
均值平移模型是处理含粗差观测值的常用模型之一,文中证明了均值平移模型的参数估值及残差二次型与剔除模型的参数估值和残差二次型完全相等,并进一步分析了均值平移模型粗差检验的性质。 相似文献
11.
针对利用最小二乘配置处理多波束测深数据,存在二次曲面数学模型通常无法精确表征海底地形的整体变化趋势以及观测数据存在粗差或异常点时,常规方法给出的协方差函数不能精确表征其统计特性的问题,本文提出了一种抗差最小二乘配置迭代解法。该方法首先进行协方差函数和观测值方差阵初始化,以多面函数拟合趋势项,然后应用等价权抗差估计并通过迭代计算,最终给出稳健的协方差函数参数解及最小二乘配置解。利用本文提出的方法及传统的方法处理实测的多波束测深数据,试验结果表明,相比于传统的方法,本文提出的方法能够较好地表征海底地形的整体变化趋势,一定程度上克服了多波束测深数据中粗差或异常点的影响。相比于传统的抗差方法,本文方法更为有效地识别出测深数据中异常点,推估效果较好,具有稳健性。 相似文献
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推导了精密单点定位含有粗差观测数据的M-LS滤波原理,对等价权阵采用三段降权函数实现抗差。从新息和残差的协方差关系出发,利用对粗差敏感的残差标准差作为抗差因子。通过迭代减弱卫星间载波残差及其抗差因子的相关性。针对载波和伪距观测值不等观测精度和不相关性,采用双抗差因子实现静态抗差卡尔曼滤波（robust Kalman filtering,RKF）。采用标准卡尔曼滤波、基于新息RKF、基于残差的增益矩阵双抗差因子RKF、基于残差的等价权阵双抗差因子RKF等4种模型,分别对一组实测数据解算分析。结果表明,基于新息RKF对精度较高的载波粗差不敏感;基于残差的增益矩阵RKF对载波较小的粗差抗差效果较差,且发生粗差历元时刻的状态参数与真值偏差较大;而基于残差构造的等价权阵双抗差因子RKF可以非常精确和高效地实现抗差,单个卫星粗差对测站位置参数影响小于1 mm。 相似文献
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Robust estimation by expectation maximization algorithm 总被引：2，自引：2，他引：0
Karl Rudolf Koch 《Journal of Geodesy》2013,87(2):107-116
A mixture of normal distributions is assumed for the observations of a linear model. The first component of the mixture represents the measurements without gross errors, while each of the remaining components gives the distribution for an outlier. Missing data are introduced to deliver the information as to which observation belongs to which component. The unknown location parameters and the unknown scale parameter of the linear model are estimated by the EM algorithm, which is iteratively applied. The E (expectation) step of the algorithm determines the expected value of the likelihood function given the observations and the current estimate of the unknown parameters, while the M (maximization) step computes new estimates by maximizing the expectation of the likelihood function. In comparison to Huber’s M-estimation, the EM algorithm does not only identify outliers by introducing small weights for large residuals but also estimates the outliers. They can be corrected by the parameters of the linear model freed from the distortions by gross errors. Monte Carlo methods with random variates from the normal distribution then give expectations, variances, covariances and confidence regions for functions of the parameters estimated by taking care of the outliers. The method is demonstrated by the analysis of measurements with gross errors of a laser scanner. 相似文献
14.
处理高杠杆异常值的抗隐差型Bayes方法 总被引：1，自引：1，他引：0
给出了一种剔除初始子集中高杠杆异常值的方法。首先根据高杠杆异常值在总观测值集中所占的比例选出若干组观测值,使得至少有一组不含高杠杆异常值的概率很高;然后根据残差最小准则从中选出不含高杠杆异常值的那组作为初始子集;最后用这种初始子集确定方法结合Gibbs抽样给出了相应的Bayes多粗差定位算法。 相似文献
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The authors address the issue of statistical testing in least squares collocation (LSC) in two stages. The first stage concerns the extension and focusing of theLSC equations to the task of statistical testing. The second stage deals with statistical testing titself and is introduced in
the second portion of the paper. The paper commences with an overview of the development ofLSC and its relationship to least squares adjustment (LSA). Expressions for the various random variables and their corresponding covariance matrices are derived and in some instances
are gleaned from the literature for the following quantities: (i) corrections to the unknown parameters with a priori covariance information; (ii) estimated signal at both the observation and computation points; and (iii) the noise at the observation points. Some of the needed covariance matrices are either obscurely hidden in the literature
or not available at all, but, nevertheless are given in the paper. Also given are expressions for the estimated variance factor
which forms the basis of various statistical tests. The paper closes with an overview and enumeration of possible statistical
tests for detection of outliers in the observations. 相似文献
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当观测值不含粗差、观测误差服从零均值分布时,最小二乘算法是最优无偏估计。若观测值包含粗差,由于最小二乘不具备抗差性,往往采用以M估计为代表的稳健估计方法,选权迭代算法是应用最为广泛的稳健估计方法之一。目前,选权迭代算法的每一步都需要对模型的稳健正交矩阵求逆,其运算复杂度是矩阵维数的三次方,在未知参数或粗差个数较多的情况下,计算量大、计算时间长。本文基于矩阵逆的运算法则,对现有选权迭代算法进行了改进,改进的选权迭代算法在迭代计算过程中仅需计算更新权阵后的解的改正项,不需要对正交矩阵求逆,显著提高了算法的效率。 相似文献
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粗差探测拟准检定法的核心是拟准观测的选取。提出了L1范数和中位数相结合的方法选取拟准观测值,并设计了相应的准则。首先利用L1范数方法得到稳健的残差,将其中残差接近于零时对应的观测值直接确定为拟准观测值,然后将余下残差形成新的残差向量,并计算其绝对值的中位数,拟准观测值即为那些余下残差绝对值小于中位数所对应的观测值。GPS网平差和GPS单点定位计算结果表明本文提出的选取拟准观测值的方法有效可行。 相似文献
18.
Behzad Behnabian Masoud Mashhadi Hossainali Ahad Malekzadeh 《Journal of Geodesy》2018,92(11):1329-1350
The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points. 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.
W. Prószyński 《Journal of Geodesy》1994,68(3):162-167
An approach to analysis of internal reliability of linear least squares models is presented. It is based on the relationship between a single observational disturbance, i.e. a gross error or a blunder, and the model response being a certain pattern of distortions in the least squares residuals. Rigorous formulae describing this relationship in terms of internal reliability characteristics are derived both for the models with uncorrelated and correlated observations. A specific case of decorrelated observations is also taken into consideration. Finally, the criteria for the evaluation of the model internal reliability are proposed for all the above cases. It is worth mentioning that the criteria are obtained without resorting to any particular method of statistical testing. The theory is illustrated with two numerical examples, using simple measuring schemes. 相似文献