使用正交多项式核的密度导数估计

研究出一种正交多项式核函数，具有限支撑而在全实轴连续。用它构造的密度导数估计保持连续性和较好的收敛速度，且多项式次数不随求导次数改变。     

满足水位改正要求的观测时间间隔探讨

本文通过利用我项式最小二乘拟合法对水位观测数据进行拟合、内插,主要对其进行了精度估计,依此对水位观测的观测时间间隔和拟事多项式次数进行分析,得到比较适当的预测时间间隔和拟合多项式次数。     

地图投影的最小二乘二元多项式拟合的误差估计

探讨了在地图投影的最小二乘二元多项式拟合中参考点的分布对拟合误差的影响,提出了一种基于矩阵的秩亏的方法来判断参考点是否在指定次数的二元多项式空间的代数曲线上,并导出在极小范数最小二乘意义下的拟合多项式的误差估计式,公式表明拟合误差和参考点的最小二乘误差无关。     

基于RBF神经网络的GPS精密星历卫星坐标插值

GPS卫星坐标插值的主要方法有Lagrange多项式插值、Chebyshev多项式插值、三角函数多项式插值等,这类方法会出现Runge现象,即当多项式次数较高时,数据的两端会出现振荡现象。提出采用RBF(radial basis function)神经网络对GPS卫星坐标进行插值来避免Runge现象的方法,并分别针对不同时间段、不同卫星的数据进行处理,结果表明该方法能有效地避免Runge现象的发生,且兼顾了插值的精度与计算效率。     

GPS高程拟合方法的研究

本文选取某地区74个已知点(大地高和高程异常值已知)作为实验数据,选择46个点作为建模点,选择28个点作为外检验点,选择多项式曲面拟合模型和双次多项式曲面拟合模型及泰勒多项式拟合模型的方法来建立该地区GPS高程拟合模型,并研究不同模型对拟合精度的影响。通过VB程序设计语言实现拟合模型的建立并进行精度比较。通过实验证明,在多项式曲面拟合模型中二次曲面模型拟合效果最好,次数增加时出现龙格现象;在双高次曲面拟合模型及泰勒多项式曲面拟合模型中双三次拟合和泰勒二次多项式拟合效果最佳。通过实验比较,可以得出在多项式曲面拟合模型中双三次曲面拟合模型的拟合效果最好。     

点质量模型计算空间扰动引力的多项式拟合研究

本文通过对点质量模型计算各频段空间扰动引力矢量随高度变化的分析,提出了点质量模型的代数多项式拟合逼近模型。通过对多项式拟合函数与点质量模型计算空间扰动引力矢量结果的比较,确定了各频段适合实际计算的多项式函数次数,从而建立起能够替代点质量模型的分段多项式拟合函数模型。所建立的拟合函数模型能够贴切地反映出空间扰动引力各频段的变化特征,而且函数形式简单,有利于实现空间扰动引力的实时、快速计算。     

TLS强度数据的入射角及距离效应改正方法

通过分离目标反射率、入射角及距离三个因素,利用Weierstrass定理,将激光强度表示成三个因素多项式函数的乘积形式,提出一种新的地面三维激光扫描（terrestrial laser scanning,TLS）激光强度改正模型。利用不同反射率的漫反射目标,设计入射角与距离实验,确定各个多项式的次数及系数,求取改正后激光强度值。实验结果表明,与现有改正模型进行比较,本文模型能精确地对激光强度值进行改正,并可以推广到自然目标强度数据的改正。     

基于多项式表达模型的多角度覆盖率反演研究

冠层光谱的多项式表达模型是理解叶片／土壤系统内的光线散射过程，描述植被的冠层光谱与组分光谱间非线性关系的一种新的方法。冠层光谱的多项式表达模型用高阶多项式的形式表达了系统内的各组分对入射光的散射过程，多项式中每一项系数表达了各组分对入射光多次散射的可能性有多少，这与冠层的结构，包括作物的覆盖率、叶倾角、垄行结构等有关。因此，多项式系数具有反演冠层结构参数的潜力。本次研究首先使用SAILH模型得到玉米全生长期的BRDF波谱以及模型计算过程的中间变量冠层多角度覆盖率，建立多项式系数与多角度覆盖率之间的经验关系。最后，设计了一次野外BRDF观测试验，对经验关系进行验证。     

经验模式分解的尺度阈值滤波在变形分析中的应用

本文将信号处理领域的经验模式分解算法应用于变形信息的提取中,通过引入阈值函数,建立了基于经验模式分解的尺度阈值滤波模型,采用优化模型确定了经验模式分解的次数。分别通过模拟试验和实测数据与小波阈值法和多项式拟合法进行了比对,分析表明:在低噪声情况下,三种方法都有一定的滤波效果;在高噪声情况下,经验模式分解的尺度阈值滤波法具有与小波阈值去噪法相等的精度,而且瞬时强噪声识别能力更好,优于多项式拟合法。     

灰色系统模型在卫星钟差预报中的应用

分析了二次多项式模型在卫星钟差长期预报中的缺陷，依据灰色系统理论和卫星钟差的变化规律，以较少的观测样本建立了预报卫星钟差的灰色预测模型，并将其与二次多项式预测模型进行分析比较。计算结果表明，两者的短期预报精度基本相当，而灰色系统模型的长期预报精度要明显地优于二次多项式模型，更适合于实际应用。     

Improved convergence rates for the truncation error in gravimetric geoid determination

 When Stokes's integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary regions. An important observation is that the rate of decay of the coefficients of the series expansion for the truncation error in terms of Legendre polynomials is determined by the smoothness properties of the error kernel. Previously published deterministic modifications of Stokes's integration kernel involve either a discontinuity in the error kernel or its first derivative at the spherical cap radius. These kernels are generalised and extended by constructing error kernels whose derivatives at the spherical cap radius are continuous up to an arbitrary order. This construction is achieved by smoothly continuing the error kernel function into the spherical cap using a suitable degree polynomial. Accordingly, an improved rate of convergence of the spectral series representation of the truncation error is obtained. Received: 21 April 1998 / Accepted: 4 October 1999     

A support vector machine classifier based on a new kernel function model for hyperspectral data

The kernel function is a key factor to determine the performance of a support vector machine (SVM) classifier. Choosing and constructing appropriate kernel function models has been a hot topic in SVM studies. But so far, its implementation can only rely on the experience and the specific sample characteristics without a unified pattern. Thus, this article explored the related theories and research findings of kernel functions, analyzed the classification characteristics of EO-1 Hyperion hyperspectral imagery, and combined a polynomial kernel function with a radial basis kernel function to form a new kernel function model (PRBF). Then, a hyperspectral remote sensing imagery classifier was constructed based on the PRBF model, and a genetic algorithm (GA) was used to optimize the SVM parameters. On the basis of theoretical analysis, this article completed object classification experiments on the Hyperion hyperspectral imagery of experimental areas and verified the high classification accuracy of the model. The experimental results show that the effect of hyperspectral image classification based on this PRBF model is apparently better than the model established by a single global or local kernel function and thus can greatly improve the accuracy of object identification and classification. The highest overall classification accuracy and kappa coefficient reached 93.246% and 0.907, respectively, in all experiments.     

Helmert扰动位及其积分核函数的椭球实用公式

借助以地心参考椭球面为边界面的第二大地边值问题的理论,基于Helmert空间的Neumann边值条件,给定Helmert扰动位的椭球解表达式,并详细推导第二类勒让德函数及其导数的递推关系、Helmert扰动位函数的椭球积分解以及类椭球Hotine积分核函数的实用计算公式,便于后续椭球域第二大地边值问题的实际研究。     

Construction of spherical harmonic series for the potential derivatives of arbitrary orders in the geocentric Earth-fixed reference frame

The derivatives of the Earth gravitational potential are considered in the global Cartesian Earth-fixed reference frame. Spherical harmonic series are constructed for the potential derivatives of the first and second orders on the basis of a general expression of Cunningham (Celest Mech 2:207–216, 1970) for arbitrary order derivatives of a spherical harmonic. A common structure of the series for the potential and its first- and second-order derivatives allows to develop a general procedure for constructing similar series for the potential derivatives of arbitrary orders. The coefficients of the derivatives are defined by means of recurrence relations in which a coefficient of a certain order derivative is a linear function of two coefficients of a preceding order derivative. The coefficients of the second-order derivatives are also presented as explicit functions of three coefficients of the potential. On the basis of the geopotential model EGM2008, the spherical harmonic coefficients are calculated for the first-, second-, and some third-order derivatives of the disturbing potential T, representing the full potential V, after eliminating from it the zero- and first-degree harmonics. The coefficients of two lowest degrees in the series for the derivatives of T are presented. The corresponding degree variances are estimated. The obtained results can be applied for solving various problems of satellite geodesy and celestial mechanics.     

Meissel-Stokes核函数应用于区域大地水准面分析

为提高区域大地水准面计算精度,基于EGM2008地球重力场位系数模型分析Meissel-Stokes核函数、截断误差系数以及截断误差。选取实验区,采用移去-恢复法评价Meissel-Stokes核函数计算大地水准面的精度。结果表明:Meissel-Stokes核函数及其截断误差系数收敛速度快;截断误差小且稳定。在积分半径不易扩展的情况下,应用Meissel-Stokes核函数计算区域大地水准面,比标准Stokes计算大地水准面精度略高。     

Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution

Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same degree as that of the original spherical Poisson kernel. Received: 4 June 1996 / Accepted: 7 April 1997     

一种基于核回归的SAR图像自适应相干斑抑制方法

为了在抑制相干斑噪声的同时更好地保持SAR图像中的点目标和边缘目标,在经典核回归方法的基础上,本文提出了基于核回归的SAR图像自适应相干斑抑制方法。通过分析SAR图像的幅度分布特性,在构建模型时,以图像的幅度值为判别条件,使核函数在幅值较小的背景区域具有较大的光滑作用以抑制噪声,而在幅值较大的目标区域光滑作用较小以保护目标特征;同时考虑对边缘的保护作用,基于散布矩阵修正了自适应核回归方法,建立了基于核回归的SAR图像自适应相干斑抑制方法。试验结果表明,该算法通过将幅度值和散布矩阵引入核函数,更好地抑制了噪声,同时也保持了图像中的点目标和边缘。     

基于高斯过程回归的变形智能预测模型及应用

岩体或建构筑物的变形通常具有复杂性和非线性等特性,一般的回归模型难以精确地进行回归预测,应用高斯过程回归理论对变形监测数据呈现出的非线性特征进行时间序列分析。考虑到监测数据的不断更新和累积,以及超参数与样本集的适应性,首先研究了“递进-截尾式”超参数自动更新模式和训练样本集的选择方法;在此基础上构建了以时间作为输入项的高斯过程回归变形智能预测模型（GPR-TIPM）;将该模型应用于矿山边坡监测点非线性时间序列分析中,通过分析变形趋势,最终采用Matérn 32和平方指数协方差函数相加的方式进行核函数组合。实验结果表明,采用组合核函数的预测性能较单一核函数有所改善,该方法提高了模型的泛化能力,GPR-TIPM模型在短期内的预测效果较理想。     

基于Allan方差和SVR的MEMS陀螺仪随机误差分析与预测

为了使低成本MEMS陀螺仪数据的精度更高,本文提出了一种混合核函数支持向量回归（SVR）的MEMS陀螺仪随机误差预测模型,并通过粒子群优化（PSO）算法对模型参数和核函数参数进行优化;同时通过Allan方差法对SVR预测前后的MEMS陀螺仪随机误差数据进行分析。试验结果表明：混合核函数SVR对MEMS陀螺仪随机误差的预测准确度可达99.99%;当MEMS陀螺仪所处状态不同,但噪声特性相同时,可采用统一的SVR预测模型预测随机误差,研究结果为进一步用于MEMS陀螺仪的实时误差补偿中提供依据。     

特征维数对支持向量机分类器性能影响的研究——以高光谱遥感影像为例

本文为验证SVM对高维特征的适应性和可靠性,针对不同特征提取方法与特征组合,以国产OMISⅡ传感器获得的北京昌平地区高光谱遥感据为例,对SVM分类器中特征维数对分类准确率的影响进行了试验,通过对主成分分析、最小噪声分离算法、相关系数分组后特征提取、导数光谱等的分析,表明SVM分类器的分类精度随着特征维数波动,其中主成分分析降维后提取的特征具有用于分类能够获得最高的准确率。通过与最大似然法和光谱角制图分类算法的比较,说明在同样的特征输入情况下SVM分类算法分类的准确率高于最大似然法和光谱角制图分类器。