一种综合考虑采样点水平和高程误差的DEM建模算法

为了降低采样点水平和高程误差对数字高程模型（digital elevation model,DEM）建模精度的影响,受总体最小二乘算法启发,以较高精度的多面函数（multiquadric function,MQ）为基函数,发展了整体最小二乘MQ算法（MQ-T）,并分别借助数值实验和实例分析验证模型计算精度。数值实验中,以高斯合成曲面为研究对象,设计了受不同误差分量影响的采样数据,借助MQ-T曲面建模,并将计算结果与传统MQ进行比较。结果表明,当采样点仅受高程误差分量影响时,MQ-T计算结果精度与MQ相当;当采样数据受水平误差分量影响时,MQ-T计算结果中误差小于MQ中误差。实例分析中,以全站仪获取的采样数据为研究对象,借助MQ-T构建测区DEM,并将计算结果与传统插值算法进行比较,如反距离加权（inverse distance weighted,IDW）法、克里金（Kriging）法和澳大利亚国立大学DEM专用插值软件（（Australian National University DEM,ANUDEM）法。精度分析表明,随着采样点密度降低,各种插值算法精度逐步降低;不管采样密度多少,MQ-T计算精度始终高于传统插值算法;对山体阴影图分析表明,MQ-T相比Kriging法有一定峰值削平现象。     

基于高斯过程回归的SRTM数据空洞填补方法

针对现有插值方法对复杂地表模拟能力不足的问题,发展了一种基于非平稳(神经网络)核的高斯过程回归(GPR)方法,并将其应用于SRTM DEM空缺数据填补。以山区SRTM DEM的模拟数据空洞为研究对象,将GPR模拟结果与传统插值方法(TIN、SPLINE和IDW)比较表明:GPR填补精度高于传统插值方法,且空缺区域模拟曲面较好的保持了地形特征。     

基于多点的规则格网DEM的传递误差分析

论述了利用数量不同的格网数据构建的样条函数DEM模型和Coons曲面DEM模型的传递误差不同,指出同一插值方法的DEM模型随着构建模型所用的格网数据数目的增多,传递误差增大;当格网数据数目同样多时,减弱相邻格网单元上格网数据权重比例,传递误差就会相应地减少。     

Noisy Data Smoothing in DEM Construction Using Least Squares Support Vector Machines

Since spatial datasets are subject to sampling errors, a smoothing interpolation method should be employed to remove noise during DEM construction. Although least squares support vector machines (LSSVM) have been widely accepted as a classifier, their effect on smoothing noisy data is almost unknown. In this article, the smoothness of LSSVM was explored, and its effect on smoothing noisy data in DEM construction was tested. In order to improve the ability to deal with large datasets, a local method of LSSVM has been developed, where only the neighboring sampling points around the one to be estimated are used for computation. A numerical test indicated that LSSVM is more accurate than the classical smoothing methods including TPS and kriging, and its error surfaces are more evenly distributed. The real‐world example of smoothing noise inherent in lidar‐derived DEMs also showed that LSSVM has a positive smoothing effect, which is approximately as accurate as TPS. In short, LSSVM with a high efficiency can be considered as an alternative smoothing method for smoothing noisy data in DEM construction.     

Crustal movement patterns of china continent measured by GPS

This paper uses multiquadric equations interpolation to establish a widely covered and valuable speed field model of China, with which the horizontal crustal movement patterns are obtained. The present-day vertical crustal movement velocity image of China is also expressed by GPS observation, from which we can know the vertical crustal movement patterns.     

基于Coons曲面的规则格网DEM表面模型

内插是数字高程模型的核心问题。目前的内插模型主要是由离散的格网数据构建的连续曲面,直接以点推面,可能存在较大的地形误差。本文建立的Coons曲面DEM表面模型,首先利用离散的格网数据构造与格网边界相对应的地形剖面曲线的拟合曲线,再基于拟合曲线构建DEM表面模型。实验表明：Coons曲面DEM表面模型是一种高精度的DEM表面模型,其地形模拟误差比直接基于格网数据建立的双线性内插、样条函数内插和移动曲面拟合法的误差都小,实际地形模拟误差与双线性模型相比减少15％-28％,且精度随着构建边界拟合曲线所用格网点的增多而逐渐提高。     

干热河谷冲沟DEM插值误差的空间分布研究

为了分析云南元谋干热河谷典型冲沟插值误差的空间分布特征,采用反距离加权（inverse distance weighting,IDW）、局部多项式（local polynomial interpolation,LPI）、张力样条（spline with tension,ST）、析取克里格（disjunctive Kriging,DK）以及不规则三角网（triangulated irregular network,TIN）模型方法对高程采样点进行插值,用交叉验证法、相对差系数及沟谷线差异衡量其插值精度。遴选高程误差大于1 m的误差点,用变异系数（coefficient of variation,CV）、全局Moran指数和Getis-Ord G_i*指数分析其空间格局特征。结果表明:TIN和DK精度较高,IDW精度最低;高程误差均呈聚集分布,聚集程度TIN > LPI > DK > ST > IDW;高程误差均呈空间正自相关,TIN模型插值误差的自相关程度最高;误差热点位于坡度大的区域。     

基于高精度曲面模型的DEM构建与误差分析

引入地形表达误差(terrain representation error,Etr),选择标准曲面和甘肃省董志塬地区作为研究对象,利用窗口分析法实现Etr的提取;用统计分析法得出Etr随网格分辨率变化的回归方程;根据误差传播定律计算DEM中误差。数值结果表明,该方法能更准确的计算HASM生成的DEM精度;相同的采样数下,HASM较传统方法(IDW,Spline和Kriging)能生成更高精度和分辨率的DEM。在难以获取已知数据的地区,HASM提供了生成相对准确DEM的高效工具。     

嫦娥三号导航相机测图能力分析及地形重建

基于立体相机成像模型并结合相机参数对嫦娥三号导航相机3维测图能力进行分析,利用摄影测量原理和误差传播定律对巡视器30 m范围内的DEM精度进行了理论分析,推导出导航相机立体影像获得的采样点精度公式,并绘制了DEM的平面精度图和高程精度图;同时使用多线程技术开发了基于导航相机立体影像的地形快速重建算法,利用多线程技术完成影像的特征匹配和密集匹配,并通过分块内插生成DEM。该技术应用于嫦娥三号任务中,有力地支持了嫦娥三号遥操作路径规划相关任务。     

DEM内插算法与精度评定研究

本文分析了DEM数据产品的误差源、内插算法的误差模型,简要介绍了目前DEM数据产品精度评定的指标与方法途径.通过介绍DEM引出了数字高程模型内插方法,比较了各种DEM内插方法,并且分析了模型精度.     

Measuring the accuracy of contour interpolated digital elevation models

Digital elevation models (DEM) are becoming increasingly important as tools in hydrological research and water resources management. Since error and uncertainty are inherently associated with spatial data, a complete evaluation of a DEM is of utmost importance before it is put into subsequent analysis. The present paper offers an innovative approach for quality assessment of contour interpolated DEMs of different resolutions. Five most frequently cited interpolation methods viz., TIN with linear interpolation, Inverse Distance Weighing, Thin Plate Spline, Ordinary Kriging and TOPOGRID were selected for gridding of contours at five different resolutions i.e., 30m, 45m, 60m, 75m and 90m. In order to compare the quality of interpolated DEMs, a qualitative and quantitative evaluation of inter-polated DEMs for their vertical, horizontal and shape accuracy were carried out. It was found that different interpolation methods produced DEMs with different levels of artifacts. The analyses of vertical accuracy suggested that the variations were not pronounced in nature. However, the quantitative comparisons for horizontal and shape accuracy showed that there was a high level of disparity with significant differences among the interpolated DEMs.     

Method of reducing HASM boundary error

High accuracy surface modeling (HASM) constructed based on the fundamental theorem of surface is more accurate than the classical methods. However, because of boundary error, location error, etc, HASM has a big accuracy loss in real-world examples. In former researches we solved the location error with Taylor expansion. In order to reduce the HASM boundary error and improve its accuracy further, this paper presents a new method of Laplace interpolation to compute the region boundary value. Gaussian synthetic surface and the real world test region are employed to validate the efficiency of this method. Results show that the boundary value computed with Laplace interpolation is more accurate than the classical methods, which can be regarded as an alternative for boundary value computation.     

地基GPS网层析水汽三维分布数值积分新方法

针对传统层析方法的缺点,本文结合数值积分参数化方法,设计并实现了一种顾及地球曲率的水平与垂直方向分开插值的地基GPS网层析湿折射率三维分布方法,明显简化了垂直插值的运算,减少了层析实际观测方程中零系数参数的比例。利用美国Dallas地区CORS网实测GPS数据与气象数据,结合位于该区域的FWD探空站探空数据提供的湿折射率垂直轮廓线,验证分析了该方法用于实测数据的可行性及其精度。结果表明：相对于传统层析方法,新方法能够明显提高层析湿折射率垂直轮廓线的精度,与探空结果相比,新方法的RMS、误差分布均优于传统方法,而且垂直内插方法的精度也略高于复杂的三次样条垂直内插方法。     

基于随机过程的格网DEM精度场模型

针对目前DEM格网精度从理论上难于统一量化描述问题,提出一种基于随机过程的格网DEM（grid digital elevation model, grid DEM）精度场模型,该模型从随机过程理论入手,借助DEM的统一插值模型,建立了DEM两类误差（噪声误差和逼近误差）的数学表达,并分析了构成DEM误差的各个分量的数学意义。与已有的模型相比,该模型实现了传统DEM两类误差的统一描述,此外,该模型适用任意插值方式生成的格网DEM的精度评价。     

Accuracy assessment of GDEM,SRTM, and DLR-SRTM in Northeastern China

This paper compares the accuracy of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM), Shuttle Radar Topography Mission (SRTM) C-band and German Aerospace Centre (DLR)-SRTM X-band digital elevation models (DEMs) with the Ziyuan 3 (ZY-3) stereoscopic DEM and ground control points (GCPs). To date, the horizontal error of these DEMs has received little attention in accuracy assessments. Using the ZY-3 DEM as reference, this study examines (1) the horizontal offset between the three DEMs and the reference DEM using the normalised cross-correlation method, (2) the vertical accuracy of those DEMs using kinematic GPS data and (3) the relationship between the three DEMs and the reference ZY-3 DEM. The results show that the SRTM and DLR-SRTM have greater vertical accuracy after applying horizontal offset correction, whereas the vertical accuracy of the ASTER GDEM is less than the other two DEMs. These methods and results can be useful for researchers who use DEMs for various applications.     

Accuracy assessment of lidar-derived digital elevation models

Despite the relatively high cost of airborne lidar-derived digital elevation models (DEMs), such products are usually presented without a satisfactory associated estimate of accuracy. For the most part, DEM accuracy estimates are typically provided by comparing lidar heights against a finite sample of check point coordinates from an independent source of higher accuracy, supposing a normal distribution of the derived height differences or errors. This paper proposes a new methodology to assess the vertical accuracy of lidar DEMs using confidence intervals constructed from a finite sample of errors computed at check points. A non-parametric approach has been tested where no particular error distribution is assumed, making the proposed methodology especially applicable to non-normal error distributions of the type usually found in DEMs derived from lidar. The performance of the proposed model was experimentally validated using Monte Carlo simulation on 18 vertical error data-sets. Fifteen of these data-sets were computed from original lidar data provided by the International Society for Photogrammetry and Remote Sensing Working Group III/3, using their respective filtered reference data as ground truth. The three remaining data-sets were provided by the Natural Environment Research Council's Airborne Research and Survey Facility lidar system, together with check points acquired using high precision kinematic GPS. The results proved promising, the proposed models reproducing the statistical behaviour of vertical errors of lidar using a favourable number of check points, even in the cases of data-sets with non-normally distributed residuals. This research can therefore be considered as a potentially important step towards improving the quality control of lidar-derived DEMs.     

插值条件下格网DEM坡度计算模型的噪声误差分析

针对目前DEM（Digital Elevation Model, DEM）数字地形分析的精度评价多数不考虑DEM误差的空间自相关性或仅仅采用经验的自相关性模型问题,本文从DEM插值入手,从理论上推导了插值条件下格网DEM邻域窗口内坡度噪声误差的空间自相关性模型以及坡度精度模型,并选取典型的插值方法和坡度差分算法,从实验角度分析了在顾及和不顾及空间自相关性两种情况下的格网DEM坡度计算模型的噪声精度,实验结果表明：坡度精度受DEM噪声误差的空间自相关性影响较大,并与DEM插值方法和坡度计算模型中的差分算法有关。     

考虑基线去相关的编队InSAR测高精度分析

针对主星带辅星群编队InSAR的双站、斜视、空间基线等特点，首先建立绝对测高误差与相对测高误差模型；重点分析了基线去相关对干涉相位误差的影响；对干涉车轮和钟摆编队的测高性能、对测高精度与基线矢量的关系进行仿真分析；其次与两种经典近似几何关系下的测高精度分析进行对比。仿真结果表明：干涉测高精度必须考虑基线去相关的影响；相对测高精度明显优于绝对测高精度；经典近似几何给分析测高精度带来很大误差。     

Improving the Elevation Accuracy of Digital Elevation Models: A Comparison of Some Error Detection Procedures

The widespread availability of powerful desktop computers, easy‐to‐use software tools and geographic datasets have raised the quality problem of input data to be a crucial one. Even though accuracy has been a concern in every serious application, there are no general tools for its improvement. Some particular ones exist, however, and some results are presented here for a particular case of quantitative raster data: Digital Elevation Models (DEM). Two procedures designed to detect anomalous values (also named gross errors, outliers or blunders) in DEMs, but valid also for other quantitative raster datasets, were tested. A DEM with elevations varying from 181 to 1044 m derived from SPOT data has been used as a contaminated sample, while a manually derived DEM obtained from aerial photogrammetry was regarded as the ground truth to allow a direct performance comparison for the methods with real errors. It is assumed that a “better” value can be measured or obtained through some methodology once an outlier location is suggested. The options are different depending upon the user (DEM producers might go to the original data and make another reading, while end users might use interpolation). Both choices were considered in this experiment. Preliminary results show that for the available dataset, the accuracy might be improved to some extent with very little effort. Effort is defined here as the percentage of points suggested by the methodology in relation with its total number: thus 100 per cent effort implies that all points have been checked. The method proposed by López (1997) gave poor results, because it has been designed for errors with low spatial autocorrelation (which is not the case here). A modified version was then designed and compared with the method proposed by Felicísimo (1994). The three procedures can be applied both for error detection during DEM generation and by end users, and they might be of use for other quantitative raster data. The choice of the best methodology is different depending on the effort involved. The conclusions have been derived for a photogrammetrically obtained DEM; other production procedures might lead to different results.     

RTS系列全站仪轴系误差调校方法

阐述了全站仪视准轴、垂直轴和水准轴的几何关系及对测角误差的影响,详细说明了RTS系列全站仪三轴误差的检验和调整方法,使全站仪用户对仪器的轴系误差有初步的了解,有利于用户在使用全站仪过程中有效控制测量误差,保证工程测量精度。