EIV模型平差方法及其在光学卫星遥感中的应用研究

发布时间：2018-04-01 23:14

本文选题：EIV模型　切入点：总体最小二乘　出处：《东华理工大学》2017年硕士论文

【摘要】：系数矩阵含有误差(error-in-variables,EIV)的模型是常见的数学模型,广泛的应用于信号处理、通信工程、计算机视觉等领域。解决EIV模型的参数估计的最简单的办法是采用只考虑观测向量有随机误差的最小二乘(Least Square,LS)求解,理论上不再是最优解。考虑系数矩阵和观测向量随机误差的总体最小二乘算法(Total Least Squares,TLS)陆续被提出,其平差理论和应用研究成为研究的热点。本文研究现有EIV模型的解法,结合常见的数据拟合问题研究如何合理运用TLS算法;利用资源三号影像数据,研究EIV模型平差方法在光学遥感中的应用,提出了基于TLS的在轨调制解调函数(Modulation Transfer Function,MTF)监测和利用TLS求解基于有理函数模型(Rational Function Model,RFM)区域网平差补偿系数的方法。本文的主要研究工作具体总结如下:针对系数矩阵和观测量中各元素的相关性、系数矩阵的结构性特点,总结了一般的TLS、LS-TLS、MSTLS、WTLS、NTLS等算法的推导过程,着重分析了各算法的适用性,给出了各种算法的程序实现步骤。选取空间直线、多项式曲线、圆曲线三类曲线的拟合为例,采取“数学表达形式-模型构建-算法选取-精度评价-实例分析”研究思路,选取合理TLS算法,通过模拟数据和实例数据,验证了各自算法的有效性。空间直接拟合上,建立了空间直线的通用EIV模型,提出了采用混合结构总体最小二乘算法求解模型参数,实例结果表明,MSTLS算法拟合空间直线理论更严谨,精度有一定的提高;多项式曲线合上,根据其一般表达形式,建立EIV模型,采用NTLS求解未知参数,模拟实验结果表明,NTLS算法拟合多项式曲线,效果较好;圆曲线拟合上,以圆曲线参数形式为基础构建的EIV模型,采用总体最小二乘求解待定参数,通过模拟数据和实例发现,对这种方法对圆曲线拟合的解算效率、解算精度方面有优势。在应用研究上提出了基于TLS的在轨MTF监测的方法。采用基于TLS的刃边法获取亚像素刃边位置,最终得到其各频率处的MTF值。结合资源三号01星的后视相机影像数据展开精度验证,实验结果表明,基于TLS的在轨MTF监测办法是可行的,相比常规的不考虑系数矩阵误差的刃边法理论上更加严谨,垂轨方向上奈奎斯特频率(即0.5频率)处的MTF提高了1.56%;同时把EIV模型平差方法应用到求解基于的RFM区域网平差补偿系数上,选取平移缩放补偿模型和仿射变换补偿模型,采用TLS和TS求解RFM系统误差补偿系数,结合资源三号卫星01星2015年06月12日019013轨的湖北咸宁地区前后影像,布设实验方案,给出实验流程图,实验结果表明,不管是采用平移缩放模型还是仿射变换模型,总体最小二乘求解补偿模型参数相比最小二乘求解补偿系数,再立体交会得到地面点大地坐标,几何定位精度可以达到相当甚至更好的精度。例如在采用平移缩放补偿模型时,平面精度提高了0.037652m,高程精度提高了0.021388m。
[Abstract]:The model of coefficient matrix with error error is a common mathematical model, which is widely used in signal processing, communication engineering, computer vision and so on.The simplest way to solve the parameter estimation of EIV model is to use the least squares least square method (LSs), which only considers the random error of the observation vector, which is no longer the optimal solution in theory.Total Least Squares TLS (Total Least Squares TLS), which considers the random error of coefficient matrix and observation vector, has been proposed one after another, and its adjustment theory and application have become a hot research topic.In this paper, we study the solution of existing EIV model, combining with common data fitting problems, study how to use TLS algorithm reasonably, and study the application of EIV model adjustment method in optical remote sensing using the data of resource 3 image.This paper presents a method for monitoring modulation and demodulation Transfer function MTF based on TLS and using TLS to solve the adjustment compensation coefficient of regional network based on rational Function model.The main research work of this paper is summarized as follows: according to the correlation between the coefficient matrix and the elements in the observational quantity and the structural characteristics of the coefficient matrix, the derivation process of the general algorithms such as TLS- TLS-TLS/ MSTLS/ WTLS- NTLS is summarized, and the applicability of the algorithms is emphatically analyzed.The implementation steps of various algorithms are given.The fitting of three kinds of curves, spatial straight line, polynomial curve and circular curve, is taken as an example, and the reasonable TLS algorithm is chosen by the research idea of "mathematical expression form-model building-algorithm selection-precision evaluation-case analysis".The validity of each algorithm is verified by simulating data and instance data.In the direct fitting of space, the general EIV model of spatial straight line is established, and the model parameters are solved by using the hybrid structure total least square algorithm. The example shows that the theory of fitting spatial straight line is more rigorous and the precision is improved to a certain extent.According to the general expression of polynomial curve, the EIV model is established, and the unknown parameters are solved by NTLS. The simulation results show that the polynomial curve is fitted well by NTLS algorithm.The EIV model is constructed on the basis of circular curve parameters, and the undetermined parameters are solved by using the total least squares. Through the simulation data and examples, it is found that this method has advantages in solving the efficiency and accuracy of the circular curve fitting.In the application research, the method of monitoring on orbit MTF based on TLS is put forward.The edge position of sub-pixel is obtained by edge method based on TLS, and the MTF value of each frequency is obtained.The experimental results show that the in-orbit MTF monitoring method based on TLS is feasible and is more rigorous than the conventional edge method which does not consider the error of coefficient matrix.In the vertical orbit, the MTF at Nyquist frequency (i.e. 0.5 frequency) is increased by 1.56.The adjustment method of EIV model is applied to solve the adjustment compensation coefficient of RFM area network based on, and the translation scaling compensation model and affine transformation compensation model are selected.TLS and TS are used to solve the error compensation coefficient of RFM system. Combined with the image before and after the 019013 orbit of Resource-3 Satellite 01 on June 12, 2015 in Xianning, Hubei Province, the experimental scheme is set up, and the flow chart of the experiment is given. The experimental results show that,Whether by using the translation scaling model or the affine transformation model, the parameters of the compensation model are solved by the total least square method, and the compensation coefficients are solved by the least square method, and the geodetic coordinates of the ground point are obtained by stereo rendezvous.Geometric positioning accuracy can reach considerable or better accuracy.For example, the plane accuracy is increased by 0.037652m and the elevation accuracy by 0.021388m by using the translation scaling compensation model.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P237;P207.2

【参考文献】