通用EIV平差模型及其加权整体最小二乘估计

以平差基本理论为基础,提出了EIV(errors-in-variables)平差模型的通用形式,涵盖了间接平差、条件平差、附有参数的条件平差及附有限制条件的间接平差等基本EIV模型形式。基于整体最小二乘估计准则,研究了通用EIV模型的加权整体最小二乘算法,并推导了估计结果的近似精度公式。通用EIV模型及其整体最小二乘算法是对EIV模型估计理论的进一步完善,统一的整体最小二乘算法有利于软件的编程实现,有助于推动EIV模型估计理论的应用。     

TLS估计性质的进一步讨论

通过对整体最小二乘估计进行分析,给出了未知参数估计及残差的统计性质。理论上得出它们均是有偏的,并且它们之间存在一定的线性关系。受系数矩阵误差影响,导致与传统最小二乘的相关结论有所区别。通过与最小二乘估计进行比较,证明了整体最小二乘估计为膨胀型有偏估计;同时得到了整体最小二乘估计的方差和均方误差的计算公式,严格论证了其值均大于最小二乘估计的方差和均方误差,因此当设计矩阵病态时整体最小二乘估计更易受病态性的影响。最后,对整体最小二乘估计与最小二乘估计之间的不同距离进行了比较,给出了选择的判定定理。     

非线性整体最小平差迭代算法

整体最小二乘法不仅考虑观测向量的误差而且还考虑系数矩阵的误差,平差理论相对更为严密。在研究经典整体最小二乘法的基础之上,对系数矩阵元素是表达式或函数情况的非线性整体最小二乘模型进行了描述,用拉格朗日极值条件式推导了基于牛顿型解法的非线性整体最小二乘平差计算公式,并设计了一种对应的迭代算法。最后设计了两组模拟试验分析在观测向量和系数矩阵的输入向量等精度观测和非等精度观测两种情况下参数和验后方差的估计特点。试验结果表明,非线性整体最小二乘平差法获得的参数估计值比最小二乘平差法获得的估计结果更接近参数的实际值,方差分量(或中误差)估计结果也更接近先验值,本文给出的迭代算法是有效的。     

总体最小二乘在沉降监测数据中的应用研究

总体最小二乘估计方法顾及系数矩阵和观测向量误差,具有最小二乘估计方法无法对系数矩阵进行改正的独特优势,在数据处理中具有广泛的应用.基于此,对目前总体最小二乘估计中的参数求解方法和精度提升方法进行了阐述,之后采用路基沉降工程实例,对最小二乘和总体最小二乘预测精度进行比较分析.实验结果表明,总体最小二乘算法的精度更高.     

利用整体最小二乘法建立线性回归模型

对于在实际应用中的直线回归问题,存在着因自变量和因变量选取不同拟合结果存在差异的情况,文中采用了一种线性拟合参数估计的新方法,即整体最小二乘法。文章在描述普通最小二乘和整体最小二乘原理的基础上,并对比其异同,并采用奇异值分解的方法来求解整体最小二乘问题。算例结果表明,采用整体最小二乘方法估计线性回归参数的精度明显高于常规最小二乘法,是一种值得借鉴的算法。     

一种三维激光扫描点云拟合的抗差加权整体最小二乘法

针对三维激光扫描中点云不等精度且易受粗差影响的问题,提出了一种基于入射角定权的抗差加权总体最小二乘的拟合方法。该方法在采用入射角定权的基础上,进行基于标准化残差和中位数的抗差加权整体最小二乘估计,获得待定参数估值,并通过Gauss-Newton迭代算法,推导了模型的迭代计算方法。以平面拟合和球面拟合为例,分别通过仿真数据和实测数据对算法进行验证,结果表明,对于含有粗差的点云,新方法可以获得更为理想的参数估值,其性能优于抗差整体最小二乘和加权整体最小二乘,可以更好地进行三维激光扫描的点云拟合。     

整体最小二乘法在非量测型相机检校中的应用

目前,非量测数码相机已广泛应用于摄影测量等领域,相机内外方位元素始终是摄影测量计算的基本数据,关系着后续生产成果的质量。针对传统的相机检校中,采用最小二乘平差估计对直接线性变换算法进行求解,进而求解相机内方位元素和畸变参数等相机内部参数,未顾及物方控制点坐标误差的问题,文章引入以变量误差模型为基础的整体最小二乘平差方法计算单应性参数,求解畸变参数、内方位元素等参数。其同时顾及了观测向量和系数矩阵的偶然误差,建立的模型更加严密、更加合理。实验结果表明,在计算焦距、主点偏移量等参数时,采用整体最小二乘平差方法比最小二乘平差方法计算精度更加提高。     

基于部分最小二乘岭估计的粗差定值定位

在利用部分最小二乘原理进行粗差定值定位时,模型的法方程矩阵可能存在病态性,使得到的粗差定值定位结果不可靠。文中针对观测数据包含多个粗差且法方程病态问题,利用岭估计处理病态问题,建立部分最小二乘岭估计的粗差定值定位方法,给出粗差搜索步骤,利用迭代算法实现多个粗差的定值和定位。通过模拟算例分析部分最小二乘法、部分最小二乘岭估计在粗差搜索方面的效果,从另一个角度探讨粗差处理方法,推广现有的误差理论,证明文中方法的有效性。     

病态加权总体最小二乘平差的岭估计解法

采用岭估计法处理加权总体最小二乘平差的病态性问题,推导了相应的求解公式及均方误差评定精度的方法,定义了病态加权总体最小二乘平差中的模型参数分辨矩阵,并讨论了岭参数的含义及其作用,给出了确定病态加权总体最小二乘岭估计中岭参数的岭迹法、广义交叉核实法和L曲线法。算例计算了普通最小二乘、普通总体最小二乘的结果,并比较了三种确定岭参数的方法在处理病态加权最小二乘岭估计和病态加权总体最小二乘岭估计中的优缺点。     

最小体积约束的线性光谱解混算法

提出了最小体积单体约束的线性光谱解混算法。该算法不需要假设数据中存在纯像元,采用二次规划方法计算降维后的端元矩阵,利用最小二乘方法实现丰度估计和端元提取。实验结果表明,此算法解混的结果整体上优于MVC-NMF算法。     

整体最小二乘法平面坐标转换在基坑水平位移监测中的应用

在参数求解过程中,经常遇到参数估计模型的观测向量和系数矩阵都可能存在误差的情况,于是人们在20世纪80年代提出了整体最小二乘方法。近几年,整体最小二乘才被引入测量领域。本文详细阐述了整体最小二乘法平面坐标转换基于奇异值分解原理的解算过程。在此基础上,把整体最小二乘法平面直角坐标转换应用到基坑水平位移监测中,改进了传统的变形监测数据处理方法,并运用工程实例验证了该方法的可行性。     

一种由粗到精的边坡形变检测方法

现代化工程建设的过程会形成很多边坡,而这些边坡一旦遭到意外破坏,会对人民的生命财产安全造成巨大威胁.因此,对边坡进行持续的形变检测至关重要.地面激光扫描技术(TLS)是一种现代化的边坡检测手段.基于此,本文提出了一种由粗到精的边坡形变检测方法.对于经过良好配准的两期边坡点云,该方法首先计算两期点云的最近匹配点距离,并进...     

Airborne LiDAR and Terrestrial Laser Scanning Derived Vegetation Obstruction Factors for Visibility Models

Research presented here explores the feasibility of leveraging vegetation data derived from airborne light detection and ranging (LiDAR) and terrestrial laser scanning (TLS) for visibility modeling. Using LiDAR and TLS datasets of a lodgepole pine (Pinus contorta) dominant ecosystem, tree canopy and trunk obstructions were isolated relevant to a discrete visibility beam in a short‐range line‐of‐sight model. Cumulative obstruction factors from vegetation were compared with reference visibility values from digital photographs along sightline paths. LiDAR‐derived tree factors were augmented with single‐scan TLS data for obstruction prediction. Good correlation between datasets was found up to 10 m from the terrestrial scanner, but fine scale visibility modeling was problematic at longer distances. Analysis of correlation and regression results reveal the influence of obstruction shadowing inherent to discrete LiDAR and TLS, potentially limiting the feasibility of modeling visibility over large areas with similar technology. However, the results support the potential for TLS‐derived subcanopy metrics for augmenting large amounts of aerial LiDAR data to significantly improve models of forest structure. Subtle LiDAR processing improvements, including more accurate tree delineation through higher point density aerial data, combined with better vegetation quantification processes for TLS data, will advance the feasibility and accuracy of data integration.     

On non-combinatorial weighted total least squares with inequality constraints

Observation systems known as errors-in-variables (EIV) models with model parameters estimated by total least squares (TLS) have been discussed for more than a century, though the terms EIV and TLS were coined much more recently. So far, it has only been shown that the inequality-constrained TLS (ICTLS) solution can be obtained by the combinatorial methods, assuming that the weight matrices of observations involved in the data vector and the data matrix are identity matrices. Although the previous works test all combinations of active sets or solution schemes in a clear way, some aspects have received little or no attention such as admissible weights, solution characteristics and numerical efficiency. Therefore, the aim of this study was to adjust the EIV model, subject to linear inequality constraints. In particular, (1) This work deals with a symmetrical positive-definite cofactor matrix that could otherwise be quite arbitrary. It also considers cross-correlations between cofactor matrices for the random coefficient matrix and the random observation vector. (2) From a theoretical perspective, we present first-order Karush–Kuhn–Tucker (KKT) necessary conditions and the second-order sufficient conditions of the inequality-constrained weighted TLS (ICWTLS) solution by analytical formulation. (3) From a numerical perspective, an active set method without combinatorial tests as well as a method based on sequential quadratic programming (SQP) is established. By way of applications, computational costs of the proposed algorithms are shown to be significantly lower than the currently existing ICTLS methods. It is also shown that the proposed methods can treat the ICWTLS problem in the case of more general weight matrices. Finally, we study the ICWTLS solution in terms of non-convex weighted TLS contours from a geometrical perspective.     

Comparative Analyses of the Point Cloud Produced by Using Close-Range Photogrammetry and Terrestrial Laser Scanning for Rock Surface

Point cloud produced by using theoretically and practically different techniques is one of the most preferred data types in various engineering applications and projects. The advanced methods to obtain point cloud data in terrestrial studies are close range photogrammetry (CRP) and terrestrial laser scanning (TLS). In the TLS technique, separated from the CRP in terms of system structure, denser point cloud at certain intervals can be produced. However, point clouds can be produced with the help of photographs taken at appropriate conditions depending on the hardware and software technologies. Adequate quality photographs can be obtained by consumer grade digital cameras, and photogrammetric software widely used nowadays provides the generation of point cloud support. The tendency and the desire for the TLS are higher since it constitutes a new area of research. Moreover, it is believed that TLS takes the place of CRP, reviewed as antiquated. In this study that is conducted on rock surfaces located at Istanbul Technical University Ayazaga Campus, whether point cloud produced by means photographs can be used instead of point cloud obtained by laser scanner device is investigated. Study is worked on covers approximately area of 30 m?×?10 m. In order to compare the methods, 2D and 3D analyses as well as accuracy assessment were conducted. 2D analysis is areal-based whereas 3D analysis is volume-based. Analyses results showed that point clouds in both cases are similar to each other and can be used for similar other studies. Also, because the factors affecting the accuracy of the basic data and derived product for both methods are quite variable, it was concluded that it is not appropriate to make a choice regardless of the object of interest and the working conditions.     

Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis

The weighted total least squares (TLS) method has been developed to deal with observation equations, which are functions of both unknown parameters of interest and other measured data contaminated with random errors. Such an observation model is well known as an errors-in-variables (EIV) model and almost always solved as a nonlinear equality-constrained adjustment problem. We reformulate it as a nonlinear adjustment model without constraints and further extend it to a partial EIV model, in which not all the elements of the design matrix are random. As a result, the total number of unknowns in the normal equations has been significantly reduced. We derive a set of formulae for algorithmic implementation to numerically estimate the unknown model parameters. Since little statistical results about the TLS estimator in the case of finite samples are available, we investigate the statistical consequences of nonlinearity on the nonlinear TLS estimate, including the first order approximation of accuracy, nonlinear confidence region and bias of the nonlinear TLS estimate, and use the bias-corrected residuals to estimate the variance of unit weight.     

多变量总体最小二乘在点云拼接中的应用

在三维激光扫描仪使用过程中,为了减小点云拼接时的误差问题,本文利用同方差多元变量的EIV(Errors In Variables)模型及总体最小二乘的方法解决三维空间点的相似变换,较传统的迭代算法计算空间坐标转换的方法,具有非迭代性、可靠性和计算过程中的简便性。最后,利用实际工程案例对非迭代算法的有效性进行了验证。     

遥感在河流谷坡工程地质环境评价中的应用

河流谷坡工程地质环境评价是水电工程的前期工作,直接关系到工程的选址、建设规模和水利资源的充分利用。 本文利用现有航空遥感资料,对四川雅砻江中游的鲜水河口至官地河段,约510 km河流谷坡的物理地质现象进行了判读,运用数理统计和工程地质综合分析的方法,对该河流区段的工程地质环境进行了评价,并对其发展趋势进行了预测,为该地区丰富的水利资源的开发利用提供了决策依据;对于区域工程地质环境评价,尤其是基础工作薄弱、自然条件恶劣、地面工作难以开展的高山峡谷地区的河流谷坡工程地质环境评价和发展趋势预测提出了新的方法。     

Moving from plot-based to hillslope-scale assessments of savanna vegetation structure with long-range terrestrial laser scanning (LR-TLS)

Reliable quantification of savanna vegetation structure is critical for accurate carbon accounting and biodiversity assessment under changing climate and land-use conditions. Inventories of fine-scale vegetation structural attributes are typically conducted from field-based plots or transects, while large-area monitoring relies on a combination of airborne and satellite remote sensing. Both of these approaches have their strengths and limitations, but terrestrial laser scanning (TLS) has emerged as the benchmark for vegetation structural parameterization – recording and quantifying 3D structural detail that is not possible from manual field-based or airborne/spaceborne methods. However, traditional TLS approaches suffer from similar spatial constraints as field-based inventories. Given their small areal coverage, standard TLS plots may fail to capture the heterogeneity of landscapes in which they are embedded. Here we test the potential of long-range (>2000 m) terrestrial laser scanning (LR-TLS) to provide rapid and robust assessment of savanna vegetation 3D structure at hillslope scales. We used LR-TLS to sample entire savanna hillslopes from topographic vantage points and collected coincident plot-scale (1 ha) TLS scans at increasing distances from the LR-TLS station. We merged multiple TLS scans at the plot scale to provide the reference structure, and evaluated how 3D metrics derived from LR-TLS deviated from this baseline with increasing distance. Our results show that despite diluted point density and increased beam divergence with distance, LR-TLS can reliably characterize tree height (RMSE = 0.25–1.45 m) and canopy cover (RMSE = 5.67–15.91%) at distances of up to 500 m in open savanna woodlands. When aggregated to the same sampling grain as leading spaceborne vegetation products (10–30 m), our findings show potential for LR-TLS to play a key role in constraining satellite-based structural estimates in savannas over larger areas than traditional TLS sampling can provide.     

Application of multispectral LiDAR to automated virtual outcrop geology

Terrestrial laser scanning (TLS) is a valuable tool for creating virtual 3D models of geological outcrops to enable enhanced modeling and analysis of geologic strata. Application of TLS data is typically limited to the geometric point cloud that is used to create the 3D structure of the outcrop model. Digital photography can then be draped onto the 3D model, allowing visual identification and manual spatial delineation of different rock layers. Automation of the rock type identification and delineation is desirable, and recent work has investigated the use of terrestrial hyperspectral photography for this purpose. However, passive photography, whether visible or hyperspectral, presents several complexities, including accurate spatial registration with the TLS point cloud data, reliance on sunlight for illumination, and radiometric calibration to properly extract spectral signatures of the different rock types. As an active remote sensing method, a radiometrically calibrated TLS system offers the potential to directly provide spectral information for each recorded 3D point, independent of solar illumination. Therefore, the practical application of three radiometrically calibrated TLS systems with differing laser wavelengths, thereby achieving a multispectral dataset in conjunction with 3D point cloud data, is investigated using commercially available hardware and software. The radiometric calibration of the TLS intensity values is investigated and the classification performance of the multispectral TLS intensity and calibrated reflectance datasets evaluated and compared to classification performed with passive visible wavelength imagery. Results indicate that rock types can be successfully identified with radiometrically calibrated multispectral TLS data, with enhanced classification performance when fused with passive visible imagery.