GIS中折线元及面元置信水平的随机模拟

置信水平是描述GIS中线元素与面元素的位置不确定性的重要指标之一.文中应用Monte Carlo方法,利用C 中的rand()函数,经过转换,首先产生符合对点误差分布的节点坐标,再按照置信域的构建规则生成大量的随机区域,通过数值判断,算出区域覆盖要素真值的频率,以此频率作为置信水平的近似值,克服了用解析证明方法研究置信水平时结果往往过于保守这一缺陷.本模拟方法有较大的适用范围,为类似的置信水平研究提供了一般方法.     

GIS中线元的误差熵带研究

基于现有的线元位置不确定性模型大多与置信水平的选取有关,而置信水平的选取带有一定程度的主观性,因而不能惟一确定,引入信息熵理论,提出了线元的误差熵带模型,并将它与“E－带”进行了比较,计算了落入其内的概率。该模型根据联合熵惟一确定,与置信水平的选取无关。     

对偶四元数GPS辅助光束法区域网平差

针对GPS辅助光束法区域网平差中线元素和角元素分而治之引起转动和平移的耦合误差问题,该文提出了一种基于对偶四元数的GPS辅助光束法区域网平差方法。利用对偶四元数统一描述像空间坐标系与WGS84坐标系之间的旋转和平移关系,建立对偶四元数GPS辅助光束法区域网平差模型,实现了区域网影像外方位元素以及待定点WGS84坐标的平差解算。实验结果表明,本算法具有对迭代初值无依赖性、迭代次数少和精度高的优点,为姿态稳定较差的轻小无人机影像的GPS辅助光束法区域网平差提供了一种新的思路。     

对偶四元数近景影像空中三角测量法

提出了一种对偶四元数近景影像空中三角测量方法,利用对偶四元数统一表示光线束在空间中的螺旋运动,近景区域网内所有光线束的角元素用对偶四元数的实部表示,所有线元素以对偶四元数的实部和对偶部分共同表示,最终建立对偶四元数空中三角测量平差模型,实现内、外方位元素和模型点物方坐标的解算。选用真实影像和大姿态角模拟影像开展了空中三角测量试验,试验结果证明对偶四元数近景影像空中三角测量方法能获得较高的精度。     

选主元矩阵原位替换解算方法

矩阵行列式、矩阵方程未知数和矩阵逆阵元素,可采用矩阵原位替换解算方法,利用矩阵元素约化值进行解算,但矩阵元素约化值计算过程中要求矩阵主元约化值不能等于零,在没有确认矩阵是否满秩的情况下,其值等于零有可能由矩阵元素排列结构引起,也有可能由矩阵秩亏引起,如何判别矩阵主元约化值为零的成因,在排除矩阵秩亏的情况下,如何利用选主元矩阵原位替换解算方法继续完成相应矩阵解算,是本文研究的内容。该研究可使矩阵原位替换解算方法得到更加广泛的应用。     

未知分布误差的熵不确定度

分析现有估计方法的不足，提出基于最大熵的不确定度估计。所得的指标不受置信水平选取时的主观性影响，适合于GIS中未知分布误差的不确定性度量。     

GIS 中基本几何要素的置信区域问题研究

以概率论为工具解析地研究了误差椭圆的2个重要性质，在此基础上分别为点、线及多边形建立了由椭圆和线段组成的置信域，并给出了所建置信域与其置信水平的关系。最后通过算例讨论了置信域的可视化表示问题。     

POS数据用于立体模型恢复时的上下视差分析

从连续法相对定向原理出发，推导了直接由像片外方位元素恢复立体模型时模型点上下视差的计算公式，用模拟数据验证了计算方法的正确性，并对两组不同摄影比例尺的实际航摄像片进行了试验。通过比较利用GPS辅助光束法区域网平差获得的像片外方位元素和POS提供的像片外方位元素重建立体模型所产生的模型上下视差，分析了POS系统误差对模型上下视差的影响。结果表明，直接利用POS提供的像片外方位元素进行安置元素测图会出现作业员难以忍受的模型上下视差，不能满足地形测图的规范要求。     

利用PICS导航数据进行独立模型法区域网联合平差的研究

用PICS导航系统所记录的摄站坐标作控制点，进行独立模型法区域网联合平差，用二次多项式作摄站坐标控制方程式中的附加参数，以消除导航定位数据中的系统误差。研究分三个阶段进行。首先，用带有各种误差的模拟数据进行平差方法试验；然后，用真区域网进行稠密地面控制加密并分析PICS记录坐标的精度；最后，用PICS导航数据和稀疏布设的地面控制点进行了区域网联合平差。本文介绍的研究结果表明，摄站坐标随机误差对区域网加密精度的影响，平面元素存在跳跃而失去其使用价值，而PICS的摄站高程坐标可减少大量的高程控制点，加密精度能满足中、小比例尺加密的要求。     

全部像元参加的影像几何匹配算法

影像几何匹配之目的是从确定对应的影像中提取其间的几何转换参数,在摄影测量测图、变形物面监测和飞行平台动态性能分析等方面有许多实用需求。不同于普遍悉知的特征点影像匹配算法,本文研究的算法是把对应影像内的全部像元素参加匹配运算,从而按最小二乘准则求解对应影像间的几何转换参数值。文中阐述了算法原理,包括灰度对应方程、信息量不等式及最小二乘求解方法,尤其是详细探讨了灰度信息的小波分析及由信噪比计算信息量的方法。为验证本文的理论和方法,采用了直升机载视频相机的序列影像进行了试验,给出了相对定向元素和视差格网的两种解算结果。最后给出了本文方法与传统特征点匹配方法可利用信息量不等式进行对比分析的结论。     

非线性平差精度评定的自适应蒙特卡罗法

针对现有的非线性平差精度评定理论中,蒙特卡罗法模拟次数的选择不具有客观性,无法对结果进行直接控制,以及没有同时考虑到平差参数估值、随机量改正数和单位权方差估值的有偏性等问题,把自适应蒙特卡罗法融入到非线性平差精度评定理论中。通过基于自适应蒙特卡罗法的估值偏差计算和参数估值协方差阵计算,设计了非线性平差精度评定一套理论完整的算法流程。基于对偶变量的思想,提出了参数估值偏差计算的对偶自适应蒙特卡罗法。直线拟合模型和椭圆拟合模型两个算例结果表明,非线性平差精度评定的自适应蒙特卡罗法能获得稳定且合理的精度评定结果,具有更强的适用性;对偶自适应蒙特卡罗法计算估值偏差的收敛速度更快,效率更高。     

Confidence regions for GPS baselines by Bayesian statistics

 The global positioning system (GPS) model is distinctive in the way that the unknown parameters are not only real-valued, the baseline coordinates, but also integers, the phase ambiguities. The GPS model therefore leads to a mixed integer–real-valued estimation problem. Common solutions are the float solution, which ignores the ambiguities being integers, or the fixed solution, where the ambiguities are estimated as integers and then are fixed. Confidence regions, so-called HPD (highest posterior density) regions, for the GPS baselines are derived by Bayesian statistics. They take care of the integer character of the phase ambiguities but still consider them as unknown parameters. Estimating these confidence regions leads to a numerical integration problem which is solved by Monte Carlo methods. This is computationally expensive so that approximations of the confidence regions are also developed. In an example it is shown that for a high confidence level the confidence region consists of more than one region. Received: 1 February 2001 / Accepted: 18 July 2001     

相关估计显著水平的Monte Carlo模拟检验

相关分析技术是多种研究领域常用的数值处理工具,本文应用蒙特 罗方法,通过大量的数值计算,获得一个容量大,稳定性好的相关系数临界值表。对于数字滤波的情形,蒙特卡罗模拟结果表明,样本自由度降低到滤波前的ｘ分之一。其中,ｘ为奈魁斯特频率与滤波器通频带宽度的比值。文中还给出两个资料分析的应用实便。     

大地测量反演中的量子退火法初探

本文第一次将量子退火法引入到大地测量反演中,介绍了基本原理,给出了算法流程图,并通过与蒙特卡罗法、模拟退火法的算例比较,表明其收敛速度快等优点,显示了在实际大地测量非线性反演中的应用潜力。     

Automatic Determination of Number of Homogenous Regions in SAR Images Utilizing Splitting and Merging Based on a Reversible Jump MCMC Algorithm

This paper presents an algorithm dealing with initial segmentation of speckled Synthetic Aperture Radar (SAR) intensity images in order to automatically determine the number of homogeneous regions. Taking this problem into account, segmentation procedure utilizing splitting and merging is designed, iteratively. The proposed approach is based upon Bayesian inference, a maximum likelihood gamma distribution parameter estimator, and a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. By using of image splitting operation, SAR image is partitioned into finite regions iteratively, until all individual regions are coherent. Then each region is assigned a unique label to indicate the class to which the homogeneous region belongs. The intensities of pixels in each coherent region are assumed to satisfy identical and independent gamma distribution. Then an RJMCMC scheme is designed to simulate the posterior distribution in order to estimate the number of components and delineate an initial segmentation. Thus, the main purpose of this research is to define the number of homogeneous regions rather than a perfect segmentation, i.e. model outputs can be served for unsupervised segmentation methodologies as prior information. The results obtained from Radarsat-1/2 of SAR intensity images show that the proposed algorithm is both capable and reliable in defining the accurate number of homogeneous regions in a wide variety of SAR intensity images, comprising a high level of speckle noise.     

基于Monte Carlo方法的不确定性地理现象可视化

应用Monte Carlo方法伪随机数模拟表达随机过程现象的数学方法，并结合粒子系统模型提出了一种地理现象空间分布不确定性特征的动画可视化方法。通过栅格单元的随机运动，从视觉上表达现象分布在空间定位、属性特征上的不确定性、模糊性，同时由Monte Carlo方法控制随机过程中现象分布的统计规律。     

陆生动物声音遥感：定位与误差分析

声音遥感技术可以极大地提高人们对动物的监测、研究和保护能力。本研究设计了一套廉价的陆生动物声音定位系统。该系统集成了市场上现成的录音笔和无线控制设备,价格明显低于许多动物定位系统。使用自主研发的声音定位软件,在X、Y方向上的绝对定位误差最大为1.69 m,可满足大部分动物定位需求;Z方向的定位误差偏大,结果尚不理想。为了揭示影响声音定位系统精度的各种因素及其影响,采用蒙特卡罗方法进行分析,发现录音站点的位置测量误差、到达时间差的估计误差和声速的估计误差均会影响最终的声音定位精度。此外,该方法还可用于在声音定位系统布设阶段确定系统参数的合理数值,包括录音节点总个数和空间尺度。     

Robust estimation by expectation maximization algorithm

A mixture of normal distributions is assumed for the observations of a linear model. The first component of the mixture represents the measurements without gross errors, while each of the remaining components gives the distribution for an outlier. Missing data are introduced to deliver the information as to which observation belongs to which component. The unknown location parameters and the unknown scale parameter of the linear model are estimated by the EM algorithm, which is iteratively applied. The E (expectation) step of the algorithm determines the expected value of the likelihood function given the observations and the current estimate of the unknown parameters, while the M (maximization) step computes new estimates by maximizing the expectation of the likelihood function. In comparison to Huber’s M-estimation, the EM algorithm does not only identify outliers by introducing small weights for large residuals but also estimates the outliers. They can be corrected by the parameters of the linear model freed from the distortions by gross errors. Monte Carlo methods with random variates from the normal distribution then give expectations, variances, covariances and confidence regions for functions of the parameters estimated by taking care of the outliers. The method is demonstrated by the analysis of measurements with gross errors of a laser scanner.     

Monte Carlo Method of Finding Overlap Area Between Two Image Scenes when Only Corner Coordinates are Known

In the applications of remote-sensing it is a common task of finding out the overlap area of coverage between two images. There are several methods available to find overlap area of varying time complexities. In this paper a method based on Monte Carlo approach is presented along with an algorithm to find common area using only corner coordinate information of the images. This method take less time than compared to the image matching methods via correlations when complete images are given. Further, this algorithm facilitate finding optimal pairs(automatically) that can be mosaicked depending on the overlap area requirement. Another simplest and considerably fast algorithm is also elaborated for evaluation. A comparison of both methods is done with a sample of Cartosat-2 images and the results are presented.