Unbiased estimation formula of unit weight standard deviation in regularization solution

Regularization method is an effective method for solving ill-posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula is verified with numerical case of 1 000 sample data by use of the typical ill-posed equation, i. e. the Fredholm integration equation of the first kind.     

Unbiased estimation formula of unit weight standard deviation in regularization solution

Regularization method is an effective method for solving ill-posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula is verified with numerical case of 1000 sample data by use of the typical ill-posed equation, i.e. the Fredholm integration equation of the first kind.     

基于标准差方法的地缘环境单元划分研究

地缘环境是由地理位置相互联系并产生关系的环境.文中提出将地缘环境指标分为本底、关联及位势3大类,其中本底指标又被分为社会经济、政治军事、战略资源和生态环境4类,各类又被细分为4个子类,各指标之间可以通过加权叠加方法进行综合生成指标体系.标准差反映数据与其平均值之间的离散程度.文中以标准差法为划分方法,以地缘环境指标体系及其加权叠加为划分依据,对我国周边地缘环境中的敏感地区之一——南亚进行了地缘环境单元划分实验.实验结果表明标准差方法在地缘环境单元划分中表现有效且准确.     

线性模型的泛最小二乘法

本文首先针对线性模型提出了泛最小二乘法,在设计矩阵不加限制的情形下,得到了参数的泛最小二乘估计量。该方法既发扬了最小二乘法的优点,又克服了它的一些不足,它包含了常见的岭估计和最小二乘估计法;其次讨论了泛最小二乘法的理论依据;接着研究了泛最小二乘估计量的一些统计性质,并与最小二乘估计进行比较,在一定意义上前者优于后者;然后讨论了平衡参数的选取问题;最后,给出一个应用,说明了泛最小二乘法的有效性和可行性。     

地形标准差聚类多面函数拟合高程异常方法

针对多面函数拟合高程异常时,难以确定中心点的问题,该文利用地形标准差确定高程异常点的分类个数,进行聚类分析,并以地形标准差与距离的比值作为指标,从高程异常点中选择了中心点,同时利用多面函数拟合了高程异常曲面,较好地解决了多面函数拟合中心点难以选择且拟合精度不高的问题。在两个地区应用结果显示,利用地形标准差聚类拟合的高程异常,比单独采用聚类分析和地形标准差的方法在外符合精度上分别平均提高了27%和48%。提出了利用地形标准差选择多面函数中心点的方法,有效地降低了多面函数选择中心点的随机性,提高了多面函数拟合的精度。     

A Bayesian estimator for linear calibration error effects in thermal remote sensing

The Bayesian land surface temperature estimator previously developed has been extended to include the effects of imperfectly known gain and offset calibration errors. It is possible to treat both gain and offset as nuisance parameters and, by integrating over an uninformative range for their magnitudes, eliminate the dependence of surface temperature and emissivity estimates upon the exact calibration error.     

线状要素多尺度表达不确定性的综合分析与评价研究

空间数据的多尺度表达和GIS数据的精度分析及质量控制问题是当今地理信息科学和国际GIS界十分关注的两大前沿课题。本文首先确立线状要素多尺度表达的实现方式;然后紧紧围绕线状要素多尺度表达的实现流程,分析线状要素多尺度表达不确定性的来源,并利用误差传播规律建立线状要素多尺度表达误差传播规律;最后通过实验得出线状要素在尺度扩展中不确定性的变化规律。     

地图线状要素眼动识别的朴素贝叶斯方法

眼动追踪技术在人机交互、用户行为识别、预测等方面得到了广泛应用,但是如何自动识别用户的地图阅读行为,眼动行为仍具有一定的挑战性.本文提出了一种基于朴素贝叶斯分类模型的方法识别用户阅读地图线状要素时的眼动行为.本试验首先通过25名被试者阅读地图过程中的眼动行为进行数据采集,然后提取了250个眼动特征并对其进行离散化处理,...     

引入模型误差的线性回归模型

在线性回归模型中,经常出现病态问题,严重影响计算结果的精度.文中提出一种引入模型误差求解部分参数的方法,此方法可以改变病态问题,提高部分参数的求解精度,且通过算例检验这种方法的可行性,并探讨它的使用范围.     

Selection criteria for linear regression models to estimate individual tree biomasses in the Atlantic Rain Forest,Brazil

Background

Biomass models are useful for several purposes, especially for quantifying carbon stocks and dynamics in forests. Selecting appropriate equations from a fitted model is a process which can involves several criteria, some widely used and others used to a lesser extent. This study analyzes six selection criteria for models fitted to six sets of individual biomass collected from woody indigenous species of the Tropical Atlantic Rain Forest in Brazil. Six models were examined and the respective fitted equations evaluated by the residual sum of squares, adjusted coefficient of determination, absolute and relative estimates of the standard error of estimate, and Akaike and Schwartz (Bayesian) information criteria. The aim of this study was to analyze the numeric behavior of these model selection criteria and discuss the ease of interpretation of them. The importance of residual analysis in model selection is stressed.

Results

The adjusted coefficient of determination (\( R^{2}_{adj.} \)) and the standard error of estimate in percentage (Syx%) are relative model selection criteria and are not affected by sample size and scale of the response variable. The sum of squared residuals (SSR), the absolute standard error of estimate (Syx), the Akaike information criterion and the Schwartz information criterion, in turn, depend on these quantities. The best fit model was always the same within a given data set regardless the model selection criteria considered (except for SSR in two cases), indicating they tend to converge to a common result. However, such criteria are not always closely related across different data sets. General model selection criteria are indicative of the average goodness of fit, but do not capture bias and outlier effects. Graphical residual analysis is a useful tool to this detection and must always be used in model selection.

Conclusions

It is concluded that the criteria for model selection tend to lead to a common result, regardless their mathematical formulation and statistical significance. Relative measures of goodness of fitting are easier to interpret than the absolute ones. Careful graphical residual analysis must always be used to confirm the performance of the models.

     

线性参照模型在铁路空间数据库中的应用

线性参照模型是以线性参考系统为基础,以动态分段技术为核心的一维空间数据模型。本文针对铁路空间数据的一维线性分布特征与铁路部门以一维线路为主体的运维管理模式,探讨了铁路空间数据的线性建模方法,利用空间数据库技术实现铁路空间数据、属性数据及业务数据的一维线性存储与管理,并提出了基于一套多尺度线性参照模型的铁路空间数据库的设计方案。试验表明,该方案能够为全路提供一套统一的一维管理基准,在动态数据管理、数据更新和共享等方面具有较大优势。     

Epipolar resampling of linear pushbroom satellite imagery by a new epipolarity model

This paper presents a practical epipolarity model for high-resolution linear pushbroom satellite images acquired in either along-track or cross-track mode, based on the projection reference plane in object space. A new method for epipolar resampling of satellite stereo imagery based on this model is then developed. In this method, the pixel-to-pixel relationship between the original image and the generated epipolar image is established directly by the geometric sensor model. The approximate epipolar images are generated in a manner similar to digital image rectification. In addition, by arranging the approximate epipolar lines on the defined projection reference plane, a stereoscopic model with consistent ground sampling distance and parallel to the object space is thus available, which is more convenient for three-dimensional measurement and interpretation. The results obtained from SPOT5, IKONOS, IRS-P5, and QuickBird stereo images indicate that the generated epipolar images all achieve high accuracy. Moreover, the vertical parallaxes at check points are at sub-pixel level, thus proving the feasibility, correctness, and applicability of the method.     

A framework for creating and validating a non-linear spectrum-biomass model to estimate the secondary succession biomass in moist tropical forests

Uncertainties remain in the use of remote sensing technologies to provide validated model-derived estimates of the biomass of the secondary succession (SS) forests in the Amazon Basin. The objectives of this study were to develop a modeling framework for creating a valid spectrum-biomass model to estimate the SS biomass, to assess the utility of the framework and the accuracy and validity of the model, and to identify the model’s determinants. Data sources for this study include 1992–1993 vegetation inventory data and 1991 Landsat Thematic Mapper (TM) data on the Altamira region of Para, Brazil, and 1994–1995 vegetation inventory data and 1994 Landsat TM data on the nearby Bragantina region. The allometric approach was used to estimate the biomass of the sampled sites based on the vegetation inventory data. A framework for the spectrum-biomass regression model was developed based on the estimated biomass of the sampled sites and the Landsat data. The framework includes (1) the pooling of data from Bragantina and the use of ANCOVA to justify this approach; (2) image calibration; (3) biomass data age-adjustment, (4) selection of independent variables, (5) regression model development, and (6) model assessment and validation. The cubic regression model with TM Band5-related predictors was found to best fit the data as evidenced by an adjusted R-squared value of 0.865, mean square error (MSE) of the model, and the analysis of residuals. Residual analysis showed that the model might yield a better estimation on a lower biomass values than on higher biomass values. In addition, further analyses identified several determinants that can impact the accuracy of the spectrum-biomass model. ANCOVA confirmed that the relationship between the biomass and the spectrum is independent of the Altamira and Bragantina regions, and that it was appropriate to pool sampled data from both regions in the proposed model. The model development methodology and the model produced from this research will be of value to researchers using the spectrum-biomass modeling approaches to estimate the biomass and study the SS rates in moist tropical forests.     

基于Membrane MRF模型的SAR图像贝叶斯去斑

SAR图像可以看作是真实反映地物后向散射特性的无噪图像与相干斑噪声的乘积,通过贝叶斯估计从图像观测值估计出图像真值即可去除相干斑.而贝叶斯去斑的关键在于建立能与SAR图像特性相匹配的先验信息模型.用MembraneMRF模型对先验信息建模,克服了以往所用GMRF模型对参数估计十分敏感的问题,并通过对该模型邻域结构的自适应调整来分类处理处于匀质区域和含结构特征区域的像元,在有效抑制相干斑的同时较好地保持图像的结构特征.仿真和实际SAR图像数据的实验结果,验证了所提方法的有效性.     

利用Minkowski距离逼近道路网络距离算法研究

道路网络背景下的距离度量（如道路网络距离、旅行时间）是在空间分析或空间统计过程中常用的距离度量,但在科研过程中由于道路数据的可获得性和精度等方面的限制,该类距离的计算可能较为困难。Minkowski距离函数是欧氏空间中的广义距离函数,其参数p值的不同代表着对空间不同的度量。利用Minkowski的通用性和灵活性（参数p不同的取值）,研究如何更好地逼近道路网络距离。同时,探索不同道路网络的部分计量特征（如密度、弯曲度等）与最优p值之间的关系。实验证明,相对于最常用的欧氏距离度量,优选p值后的Minkowski距离函数能够更大程度上逼近道路距离。而通过对道路网络计量特征与最优p值之间的关系的分析,指出了弯曲度与最优p值之间的对应关系,它对于p值的选择具有重要的指导意义。此外,为了验证Minkowski距离逼近算法的可行性,以地理加权回归分析为例,通过对比传统的欧氏距离度量、最优Minkowski距离度量和道路网络距离（旅行时间）对模型解算结果的影响,指出优选后Minkowski距离一定程度上更接近于采用旅行时间对模型解算的结果。     

有限元法逼近高程异常曲面的应用研究

GPS水准的纯几何方法在逼近高程异常曲面时,由于没有顾及到似大地水准面的物理特性,因此其拟合结果往往不稳定.试图从地壳均衡理论出发,构造数学物理模型并采用有限元法来逼近高程异常曲面.     

利用标准单点定位技术评价电离层模型

针对电离层模型的评价问题,提出了标准单点定位的方法,验证了该方法的可行性,并深入分析了GIM模型/Klobuchar模型在空域、时域上对SPP定位精度的影响。实验结果表明:选择GIM模型或Klobuchar模型,中纬地区SPP定位精度最高,低纬地区最差。与Klobuchar模型相比,高、中、低纬地区选择GIM模型的三维定位精度均有较大幅度提升,最大改进达34.20%;在太阳活跃期、低谷期,GIM模型的三维定位精度也明显高于Klobuchar模型,且活跃期GIM模型相对Klobuchar模型的改进率达20.14%,比低谷期高12.25%。从定位精度看,SPP解算选择GIM模型整体优于采用Klobuchar模型。     

线性参照系统下的嵌套金字塔模型构建

针对线性参照虚拟场景构建中缺乏有效的空间数据模型的问题,本文以金字塔模型、空间索引结构和动态分段等相关研究为基础,提出了线性参照系统下的嵌套金字塔模型构建方法.首先,结合线性场景数据特征,对动态分段技术进行拓展,增加垂直方向结构化金字塔模型;然后,将线性参照在多尺度下进行静态分段,对相互独立的弧段分别进行存储,构建静态...     

基于线性模型的二维直角坐标变换

二维直角坐标变换模型在工程领域中应用非常广泛,该模型是一个非线性模型,对于多公共点的二维直角坐标变换需要进行模型的线性化,计算待求参数的近似值,再利用间接平差原理计算各待求参数最或然值。本文在非线性模型基础上推导出一个线性模型,利用该模型进行二维直角坐标变换,无需计算待求参数近似值,对于涉及到二维直角坐标变换的问题,可以简化其解算过程。     

基于高光谱Hyperion数据的线性光谱混合模型与神经网络模型的比较

混合像元问题是定量遥感中的热点问题之一,为了改进从遥感数据中提取定量信息,人们建立了各种混合光谱分解技术,其中线性光谱混合模型和神经网络模型就是两种比较成熟的方法。以陕西省横山地区的高光谱Hyperion数据为研究基础,通过最小噪声变换(MNF)、像元纯度指数(PPI)转换和RMS误差分析的迭代方法相结合提取影像中的纯净像元作为终端端元。分别运用神经网络模型和线性光谱混合模型对影像进行光谱分解,得到各个组分的分解图像。以标准植被指数(NDVI)影像为衡量标准,选取训练样本点,分别对两种模型进行回归分析,结果显示NDVI影像与线性光谱混合模型植被分解图像的判定系数(R2=0.91)要大于其与神经网络模型的判定系数(R2=0.81)。进一步分析表明在一般情况下,线性光谱混合模型具有比神经网络模型略高的分离精度,但是神经网络模型对细部信息的提取的效果要好于线性光谱混合模型,最后提出了端元均方根误差(EAR)指数,一种新的混合像元分解的思路。