最小二乘法的改进算法辨识棱镜摄谱仪定标多项式

提出了采用最小二乘法的改进算法拟和一元非线性函数，并用该算法辨识棱镜摄谱仪的定标多项式-数值计算结果表明：采用改进的算法，非常显著地降低了求解定标多项式系数方程组的系数矩阵的条件数，定标多项式能更精确地反映谱平面坐标和谱线波长的定量关系。     

Determining Rayleigh damping parameters of soils for finite element analysis

Soil damping ratio is an important parameter for modelling the dynamic behaviour of soil embankment structures, especially for the micro‐vibration analysis of hospitals and high‐tech industries, which have a very severe construction requirement for vibration. This paper explores using a least‐squares method to evaluate the Rayleigh damping parameters for the finite element analysis of wave propagation in soils. The least‐squares method was first used in Bornitz's equation to calculate the absorption coefficients of soils. Afterward, the best‐fit Rayleigh damping parameters were obtained using those coefficients in the least‐squares scheme again. Both three‐dimensional finite element analyses and field experiments were performed to validate the accuracy of this method. The comparison between experimental and finite element results demonstrates that the accuracy of this least‐squares method is acceptable. Copyright © 2007 John Wiley & Sons, Ltd.     

反演奇异模型的参数估计的通用公式

将大地测量反演问题中的线性模型，综合为一般模型，称为反演奇异模型。运用最小二乘统一理论给出了反演奇异模型的参数和单位权方差通用估计公式，给出了这种模型的验前验后方差一致性检验方法。讨论了反演参数估计的有关问题。     

阻尼最小二乘法在射线追踪中的应用

利用弯曲法进行有倾角的层状介质的两点射线追踪，并采用改进的阻尼最小二乘法迭代求解。为了减小迭代初值的影响，采用分段线性插值调整迭代初值，使这种方法具有较好和较快的收敛性，对不同层数和倾角的层状介质均适用。     

THE PERFORMANCE OF LEAST SQUARES AND ROBUST REGRESSION IN THE CALIBRATION OF ANALYTICAL METHODS UNDER NON-NORMAL NOISE DISTRIBUTIONS

By means of Monte Carlo simulations a comparison has been made between ordinary least squaresregression and robust regression. The robust regression procedure is based on the Huber estimate and iscomputed by means of the iteratively reweighted least squares algorithm. The performance of bothprocedures has been evaluated for estimation of the parameters of a calibration function and fordetermination of the concentration of unknown samples. The influence of the distributionalcharacteristics skewness and kurtosis has been studied, and the number of measurements used forconstructing the calibration curve has also been taken into account, Under certain conditions robustregression offers an advantage over least squares regression.     

基于配置法的局部重力场延拓模型构建与应用分析

在大地坐标系下利用Forsberg局部扰动位协方差模型（即DPM模型）导出了实用的局部重力异常协方差模型（即GAC模型）和局部扰动重力协方差模型（即GDC模型）,两种模型形式完全一致.针对GAC模型,提出了两种模型参数的拟合方法,即按照泊松积分向上延拓获得的不同高度数据进行拟合以及按照测量区域的平面实测数据进行拟合,通过某地区的实测数据检验得出两种参数拟合方法得到的参数值相差不大,这种差别在向上和向下延拓过程中的影响可以忽略.依据本文的算例,GAC模型作为配置法的协方差模型用于延拓时,其向上延拓的精度在1.8×10^－5 m·s^-2左右,向下延拓的精度在5×10^－5 m·s^-2左右,完全满足局部重力场在中等山区的延拓要求.通过对不同高度下GAC模型用于延拓效果的对比,可以得出基于GAC模型的延拓精度随着高度的增加而衰减,在满足测量精度要求下其最大向下延拓高度约为7 km.总体而言,本文推导的GAC模型能够很好地利用地形数据,较好地满足了航空重力测量在局部重力场的延拓要求.     

最小二乘谐波估计对GNSS坐标时间序列多路径效应提取能力的研究

在对比分析单元谐波估计与多元谐波估计这2种最小二乘谐波估计方法的数学原理及实现方法基础上,基于实际监测点的GNSS坐标时间序列,通过实验对比2种方法在提取多路径效应方面的效果.结果表明,单元谐波估计和多元谐波估计均能较好地提取多路径效应;在未发生数据中断的情况下,相比于单元谐波估计,多元谐波估计的去噪效果更明显,E、N...     

Test of statistical means for the extrapolation of soil depth point information using overlays of spatial environmental data and bootstrapping techniques

Hydrological modelling depends highly on the accuracy and uncertainty of model input parameters such as soil properties. Since most of these data are field surveyed, geostatistical techniques such as kriging, classification and regression trees or more sophisticated soil‐landscape models need to be applied to interpolate point information to the area. Most of the existing interpolation techniques require a random or regular distribution of points within the study area but are not adequate to satisfactorily interpolate soil catena or transect data. The soil landscape model presented in this study is predicting soil information from transect or catena point data using a statistical mean (arithmetic, geometric and harmonic mean) to calculate the soil information based on class means of merged spatial explanatory variables. A data set of 226 soil depth measurements covering a range of 0–6·5 m was used to test the model. The point data were sampled along four transects in the Stubbetorp catchment, SE‐Sweden. We overlaid a geomorphology map (8 classes) with digital elevation model‐derived topographic index maps (2–9 classes) to estimate the range of error the model produces with changing sample size and input maps. The accuracy of the soil depth predictions was estimated with the root mean square error (RMSE) based on a testing and training data set. RMSE ranged generally between 0·73 and 0·83 m ± 0·013 m depending on the amount of classes the merged layers had, but were smallest for a map combination with a low number of classes predicted with the harmonic mean (RMSE = 0·46 m). The results show that the prediction accuracy of this method depends on the number of point values in the sample, the value range of the measured attribute and the initial correlations between point values and explanatory variables, but suggests that the model approach is in general scale invariant. Copyright © 2009 John Wiley & Sons, Ltd.     

基于Hough变换的航空影像建筑物半自动提取

针对Hough变换不能检测直线段的缺点,提出了一种改进的Hough变换用于影像中矩形建筑物的半自动提取。同传统Hough变换相比,改进的Hough变换充分利用了Hough变换的参数空间数据,将Hough变换的“投票”过程和直线段的检测过程融为一体,获得直线段的端点坐标。根据直线段的端点坐标消除虚假直线段的过连接,并根据直线段的角度、距离条件合并直线段。最后通过直线段上的若干点利用最小二乘法拟合出一条最佳直线,通过计算最佳直线的交点确定建筑物的角点坐标,完成影像中建筑物的半自动提取。实验结果表明:用改进的Hough变换算法提取出的航空影像中建筑物边缘结果是正确的,定位精度较高。     

地磁场日变数据处理方法的探讨

基于地磁场日变规律的基本特性,介绍利用最小二乘法对其日变规律进行具体的讨论,并对其拟合精度进行评定;就短时间内而言,该方法对日变规律的模拟与外推,具有推广应用价值.