Fitting variogram models by weighted least squares

The method of weighted least squares is shown to be an appropriate way of fitting variogram models. The weighting scheme automatically gives most weight to early lags and down-weights those lags with a small number of pairs. Although weights are derived assuming the data are Gaussian (normal), they are shown to be still appropriate in the setting where data are a (smooth) transform of the Gaussian case. The method of (iterated) generalized least squares, which takes into account correlation between variogram estimators at different lags, offer more statistical efficiency at the price of more complexity. Weighted least squares for the robust estimator, based on square root differences, is less of a compromise.     

地震序列较强余震灰色及最小二乘拟合预测方法的应用研究

在收集、整理1966年～2002年8月我国(主要为大陆地区)183个5级以上地震序列资料的基础上，应用灰色预测和最小二乘拟合预测方法，对每一地震序列较强(显著)余震发震时间进行“硬性”检验预测。结果表明，2种预测方法对7级以上地震序列和6级地震序列的较强(显著)余震具有较好的预测效能，预测效能分别为76．2％和64．7％；而对5级地震序列预测效果则不甚明显。因此，灰色预测和最小二乘拟合预测方法主要着眼于对大(强)地震的较强(显著)余震预测，可望在地震现场大(强)震应急工作中发挥积极作用。     

砂土的抗剪强度与干密度的曲线拟合

利用曲线拟合的最小二乘法原理，确定砂土在某垂直压力下的抗剪强度与干密度的关系，并绘制曲线图，可避免人工处理数据的随意性，减小了误差。     

Hybrid Estimation of Semivariogram Parameters

Two widely used methods of semivariogram estimation are weighted least squares estimation and maximum likelihood estimation. The former have certain computational advantages, whereas the latter are more statistically efficient. We introduce and study a “hybrid” semivariogram estimation procedure that combines weighted least squares estimation of the range parameter with maximum likelihood estimation of the sill (and nugget) assuming known range, in such a way that the sill-to-range ratio in an exponential semivariogram is estimated consistently under an infill asymptotic regime. We show empirically that such a procedure is nearly as efficient computationally, and more efficient statistically for some parameters, than weighted least squares estimation of all of the semivariogram’s parameters. Furthermore, we demonstrate that standard plug-in (or empirical) spatial predictors and prediction error variances, obtained by replacing the unknown semivariogram parameters with estimates in expressions for the ordinary kriging predictor and kriging variance, respectively, perform better when hybrid estimates are plugged in than when weighted least squares estimates are plugged in. In view of these results and the simplicity of computing the hybrid estimates from weighted least squares estimates, we suggest that software that currently estimates the semivariogram by weighted least squares methods be amended to include hybrid estimation as an option.     

A Least-squares Window Curves Method for Interpretation of Magnetic Anomalies Caused by Dipping Dikes

We have developed a least-squares method to determine simultaneously the depth and the width of a buried thick dipping dike from residualized magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the half-width of the source and a combination of windowed observations. The relationship represents a family of curves (window curves). For a fixed window length, the depth is determined for each half-width value by solving one nonlinear equation of the form f (z) = 0 using the least-squares method. The computed depths are plotted against the width values representing a continuous curve. The solution for the depth and the width of the buried dike is read at the common intersection of the window curves. The method involves using a dike model convolved with the same moving average filter as applied to the observed data. As a result, this method can be applied to residuals as well as to measured magnetic data. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to theoretical data with and without random errors. The validity of the method is tested on airborne magnetic data from Canada and on a vertical component magnetic anomaly from Turkey. In all cases examined, the model parameters obtained are in good agreement with the actual ones and with those given in the published literature.     

遗传算法与最小二乘法相结合的遥感图像子像素匹配

图像匹配在计算机视觉和数字摄影测量中都是一项十分重要的任务。为了加速匹配并为高精度子像素匹配提供稳健而相对精度的初值，本文提出了一种基于遗传算法（GA）和最小二乘法匹配（LSM）相结合的遥感图像子像素匹配算法。实验表明：基于遗传算法的匹配算法比序贯相似度度量（SSDA）和经典的平均绝对差（MAD）方法要快得多。以我们的实验数据为例，MAD与GA在相关计算总量上的比至少为36：1。本文从理论上证明了这一点。     

抗差最小二乘法在卫星测高数据处理中的应用

在采用1992年10月至1998年10月的Topex/Poseidon卫星测高资料进行海平面变化研究，将抗差最小二乘法引入到数据处理时，计算了平均海面高，海平面变化量和海平面的升降速率及其主要周期项的振幅和相位，同时给出采用经黄最小二乘法计算的结果，将将两种结果进行了比较，最后通过对计算结果的分析，揭示了海平面变化的一些规律，实证了海平面变化与厄尔尼诺现象之间的联系。     

非线性最小二乘参数平差迭代算法

在非线性最小二乘问题现有的3类主要算法－－高斯－牛顿法、阻尼最小二乘法和最小二乘的拟牛顿法的基础上，引入了综合性能更优的非线性规划的SQPM（序列二次规划法）算法，并且为进一步提高SQPM算法迭代的收敛性，对其步长策略进行了改进。改进的SQPM算法成为无需精确计算参数概略值的非线性最小二乘参数平差的实用和有效算法。     

高精度局部区域GPS水准计算方法的探讨

针对现有各种 GPS水准存在的缺陷 ,我们运用现代计算数学的最新研究成果 ,提出了一种新的 GPS水准 B样条最小二乘拟合法。通过对我国西南某地区的 GPS测量成果进行处理的具体结果可以看出 ,该方法是一种更适用于高精度 GPS水准的拟合方法     

SEMIAUTOMATIC BUILDING EXTRACTION FROM STEREO IMAGE PAIR BASED ON LINES GROUPING AND LEAST SQUARES MATCHING

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