A general framework for error analysis in measurement-based GIS Part 1: The basic measurement-error model and related concepts

This is the first of a four-part series of papers which proposes a general framework for error analysis in measurement-based geographical information systems (MBGIS). The purpose of the series is to investigate the fundamental issues involved in measurement error (ME) analysis in MBGIS, and to provide a unified and effective treatment of errors and their propagation in various interrelated GIS and spatial operations. Part 1 deals with the formulation of the basic ME model together with the law of error propagation. Part 2 investigates the classic point-in-polygon problem under ME. Continuing to Part 3 is the analysis of ME in intersections and polygon overlays. In Part 4, error analyses in length and area measurements are made. In this present part, a simple but general model for ME in MBGIS is introduced. An approximate law of error propagation is then formulated. A simple, unified, and effective treatment of error bands for a line segment is made under the name of covariance-based error band. A new concept, called maximal allowable limit, which guarantees invariance in topology or geometric-property of a polygon under ME is also advanced. To handle errors in indirect measurements, a geodetic model for MBGIS is proposed and its error propagation problem is studied on the basis of the basic ME model as well as the approximate law of error propagation. Simulation experiments all substantiate the effectiveness of the proposed theoretical construct.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grants Council.     

A general framework for error analysis in measurement-based GIS Part 3: Error analysis in intersections and overlays

This is the third of a four-part series on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we study the characteristics of error structures in intersections and polygon overlays. When locations of the endpoints of two line segments are in error, we analyze errors of the intersection point and obtain its error covariance matrix through the propagation of the error covariance matrices of the endpoints. An approximate law of error propagation for the intersection point is formulated within the MBGIS framework. From simulation experiments, it appears that both the relative positioning of two line segments and the error characteristics of the endpoints can affect the error characteristics of the intersection. Nevertheless, the approximate law of error propagation captures nicely the error characteristics under various situations. Based on the derived results, error analysis in polygon-on-polygon overlay operation is also performed. The relationship between the error covariance matrices of the original polygons and the overlaid polygons is approximately established.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grants Council.     

A general framework for error analysis in measurement-based GIS Part 2: The algebra-based probability model for point-in-polygon analysis

This is the second paper of a four-part series of papers on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we discuss the problem of point-in-polygon analysis under randomness, i.e., with random measurement error (ME). It is well known that overlay is one of the most important operations in GIS, and point-in-polygon analysis is a basic class of overlay and query problems. Though it is a classic problem, it has, however, not been addressed appropriately. With ME in the location of the vertices of a polygon, the resulting random polygons may undergo complex changes, so that the point-in-polygon problem may become theoretically and practically ill-defined. That is, there is a possibility that we cannot answer whether a random point is inside a random polygon if the polygon is not simple and cannot form a region. For the point-in-triangle problem, however, such a case need not be considered since any triangle always forms an interior or region. To formulate the general point-in-polygon problem in a suitable way, a conditional probability mechanism is first introduced in order to accurately characterize the nature of the problem and establish the basis for further analysis. For the point-in-triangle problem, four quadratic forms in the joint coordinate vectors of a point and the vertices of the triangle are constructed. The probability model for the point-in-triangle problem is then established by the identification of signs of these quadratic form variables. Our basic idea for solving a general point-in-polygon (concave or convex) problem is to convert it into several point-in-triangle problems under a certain condition. By solving each point-in-triangle problem and summing the solutions, the probability model for a general point-in-polygon analysis is constructed. The simplicity of the algebra-based approach is that from using these quadratic forms, we can circumvent the complex geometrical relations between a random point and a random polygon (convex or concave) that one has to deal with in any geometric method when probability is computed. The theoretical arguments are substantiated by simulation experiments.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grants Council.     

An Application of Close Range Photogrammetry In Dolphin Studies

Dolphins are agile animals and are very difficult to measure at sea. However, for the conservation of threatened or endangered species, measurement may be vital because it allows a demographic analysis of the population. Hector's dolphin (Cephalorhynchus hectori) is a rare species living only in coastal waters around New Zealand where it is studied from small boats. This paper describes a stereophotogrammetric technique developed to measure body length accurately at sea without having to capture the individual. Constant calibration with the use of a control frame allowed accurate body length measurements of dolphins to be made with this low cost system, with a measurement error of 4 per cent to 6 per cent of actual length.     

全站仪构建全局测量空间的精度仿真分析

针对在大尺寸测量空间内进行全局测量时,存在测量范围大、精度较难控制等一系列问题,文章对全站仪构建全局测量空间的方法进行了研究。基于误差传播定律和精度匹配的原则,通过Matlab编程对全站仪构建全局测量空间的精度进行了仿真分析,分别从平面精度与高程精度的匹配、点位总精度的分布规律以及边角精度的匹配三个方面,定量分析了精度受各观测要素影响的规律,并设计了简单可行的测量方案,对Matlab仿真分析的结论进行了验证。     

测量机器人系统构成与精度研究

对测量机器人的特点进行了详细分析 ,对其自动化的工作原理进行了研究 ,其核心技术是用CCD摄像机获取目标图像 ,用计算机软件对数字图像进行分析和匹配 ,提取所需要的特征点 ,再配以精密马达伺服机构控制经纬仪系统的水平和垂直旋转 ,从而实现观测自动化。同时还简要介绍了与测量机器人配套使用的软件 ,并给出了试验结果。     

无人机倾斜摄影测量在房屋建筑面积测算中的应用

针对目前房屋建筑面积测量外业工作强度大、测量精度低、成图效率低等主要问题,本文提出了基于无人机倾斜摄影测量的房屋建筑面积测算方法。首先从无人机倾斜摄影、实景三维建模、数字正射影像制作、三维数字化测图、图件制作和面积指标计算等方面进行了研究,然后对试验结果进行了精度评定。结果表明,地形图平面位置中误差为4.6 cm,高程中误差为4.2 cm,房角点点位中误差为4.6 cm,建筑物边长中误差为4.5 cm,房屋建筑物面积较差小于城市商品房二级精度面积限差,各项精度均符合国家标准规范要求,该方法用于房屋建筑面积测算是可行的。     

How large is Aroostook County? Exploring the historical mutability of US county area measurements

Area measurements play a prominent role in many types of geographical and historical analyses. The accuracy and precision of such measurements, however, are dependent on a host of input factors, including the type of instrumentation used as well as the scale and projection of the source map and its level of cartographic generalization. As a consequence of variability in these inputs, published area measures change over time. This paper reviews the record of land area measurements for counties published by the US Census Bureau between 1880 and 2000, documents the major changes in measurement instrumentation and procedures employed, and analyzes patterns of the greatest variability in reported values. Two states are used as case studies (Iowa and Maine). The results suggest that the greatest variability occurs in those areas with irregular borders, thus reflecting the interaction of the source maps with human measurement error and the encoding capabilities of the area measurement instruments. The observations also indicate that variability in area measurements for counties has decreased over time.     

Performance analysis of a stand-alone high-sensitivity receiver

The use of GPS for personal location using wireless devices requires satellite signal measurements both outdoors and indoors. In the outdoor environment propagation paths may range from line-of-sight to shaded or blocked. The indoor environment may range from single-floor wooden constructions to high-rise buildings and underground facilities. In this paper, a high-sensitivity receiver which operates in unaided stand-alone mode is tested under a range of shaded and blocked signal environments, ranging from residential outdoor areas to urban canyons and residential houses. The measurement analysis is performed in both the observation and position domains. The results show that the receiver tested is able to yield measurements with C/N₀ degradations in excess of 20 dB-Hz, as compared to line-of-sight measurements. Position results are a function of the geometry of the remaining satellites, which in turn is a function of the environment. Electronic Publication     

图斑形状特征对原面积中误差公式的修正——一个面积中误差估算模型

本文考虑到多边形图斑形状特征对面积量算误差的显著影响，用一“特征参数”T，将图斑形状特征量化。经参数T修正的面积中误差估算公式有较低的“偏离度”，且数学形式简单，采用修正模型可设定新的面积量算容许误差，并可改进图斑面积平差的传统方法。     

Impacts of Positional Error on Spatial Regression Analysis: A Case Study of Address Locations in Syracuse, New York

Positional error is the error produced by the discrepancy between reference and recorded locations. In urban landscapes, locations typically are obtained from global positioning systems or geocoding software. Although these technologies have improved the locational accuracy of georeferenced data, they are not error free. This error affects results of any spatial statistical analysis performed with a georeferenced dataset. In this paper we discuss the properties of positional error in an address matching exercise and the allocation of point locations to census geography units. We focus on the error's spatial structure, and more particularly on impacts of error propagation in spatial regression analysis. For this purpose we use two geocoding sources, we briefly describe the magnitude and the nature of their discrepancies, and we evaluate the consequences that this type of locational error has on a spatial regression analysis of pediatric blood lead data for Syracuse, NY. Our findings include: (1) the confirmation of the recurrence of spatial clustering in positional error at various geographic resolutions; and, (2) the identification of a noticeable but not shockingly large impact from positional error propagation in spatial auto‐binomial regression analysis results for the dataset analyzed.     

隧道工程横向贯通误差的影响因素及其误差分析

影响隧道贯通误差的因素主要有洞内起始方位角、测角精度和测边精度,本文分析起始方位角、测边、测角对隧道贯通误差的影响,得到曲线型、直伸型两种隧道的公式,尤其是分析不同长度、不同精度、不同导线边长条件下横向贯通误差的变化,得出一定规律来指导实践。     

多镜头组合型全景相机两种成像模型的定位精度比较

根据多镜头组合型全景相机的严格成像机理,分析了广泛采用的全景理想成像模型系统误差的来源,推导出误差分布规律,并深入比较了严格成像模型和理想成像模型之间的差异.首先,分析了理想模型的单片物方定位误差和像方后方交会误差,理论公式表明其误差分布和物像间距及视角大小相关;其次,分析了全景立体像对的理想核线误差,并证明误差受像对间的旋转角和Z坐标影响.最后,分别采用室内、外数据对两种模型的空间后方交会、核线模型、光束法平差进行比较分析.试验结果表明,室外条件下由于物距接近于全景投影面、立体影像间旋转角较小等因素,两种模型的差异很小,且都达到了相当于1像素左右的测量精度;在狭窄的室内条件下,由于物距小、旋转角大等因素,严格模型在测量精度上明显优于理想模型.     

野外大长度量值传递稳定性与可靠性分析

因瓦基线尺是国家野外大长度量值传递的法定标准器,本文通过对一组因瓦基线尺多年的检定资料、基线场的多次测量成果以及与维塞拉光波干涉仪测量成果的比较分析,论述我国野外大长度量值传递的稳定性与可靠性.     

城市复杂排水管线点埋深的测量精度分析

通过对某市排水设施普查数据进行分析研究,得出当井底状况复杂时,《城市地下管线探测规程》对明显管线点埋深的测量精度要求已很难满足。数据分析显示,当井底状况较为复杂时(少量淤泥或积水)且管线点埋深在3m以下,排水管线点埋深的测量中误差的允许值建议取±10cm;埋深在3m以上时,排水管线点埋深的测量中误差允许值建议取±1/30 H(H为管线点的埋深);当井底状况极为复杂(淤泥较多、积水严重或水流湍急)时,排水管线点埋深测量限差建议按隐蔽管线点处理,建议取值为0.15 H。     

Kalman滤波异常误差检测

为检测动态导航观测异常和动态模型异常误差，本文利用状态方程预测残差二次型构造了整体误差检验法，即观测误差和动力学模型误差整体检验法；讨论了三种观测异常检测法，即以模型为基准的观测异常检验，以当前历元可靠观测为基准的异常检验，以状态Kalman滤波估值为基础的观测异常检验；分析了三种动力模型异常检测法，即状态不符值检验法，以状态参数Kalman滤波估值为基础的动力模型误差检验法，以可靠观测为基础的动力模型误差整体检验法。并对这几种异常检测法进行了简单分析。     

GPS弦距与常规光电测距弦距的比较与分析

比较GPS弦距与常规光电测距弦距的差别，对分析GPS测量误差问题，解决GPS与地面数据联合平差中权的确定问题，以及检核GPS网的解算结果具有重要意义。本文利用一多期复测成果，对其中的一些问题作了初步探讨。     

Error analysis of the 3D similarity coordinate transformation

The 3D similarity coordinate transformation with the Gauss–Helmert error model is investigated. The first-order error analysis of an analytical least-squares solution to this problem is developed in detail. While additive errors are assumed in the translation and scale estimates, a 3 × 1 multiplicative error vector is defined to effectively parameterize the rotation matrix estimation error. The propagation of the errors in the coordinate measurements to the errors in the estimated transformation parameters is derived step-by-step, and the formulae for calculating the variance–covariance matrix of the estimated parameters are presented.     

虚拟参考站技术在管线测量中的应用

针对常规测量技术在管线测量中的局限性,首先介绍了虚拟参考站技术（VRS）原理、组成及误差;探讨了VRS技术用于管线测量的施测方法,然后用一实例对VRS技术和常规测量进行了对比分析,最后得出了一些有益的结论。     

基于Android系统的重力仪数据采集及计算软件开发

针对目前重力测量数据处理软件多是基于Windows系统,而这与携带Android移动设备相比多有不便的问题,该文提出了一种基于Android系统的重力数据采集及计算软件的开发。按照国家重力测量规范,针对CG-5型相对重力仪,设计研发了一款基于Android系统平台的重力数据采集及计算软件,较好地方便了用户野外携带。其具有新建、打开测线、数据采集处理、点之记拍照、导航定位、数据查询、信息标定、CG-5数据文档读取、报表生成等功能。在数据处理模块的传统改正项中,新增了海潮负荷改正和地下水变化改正,减少了误差项。通过将软件用于实地重力测量计算,证实该软件运行流畅、结果正确,提高了相对重力测量内外业一体化效率。