本文選題：EIV模型　切入點(diǎn)：總體最小二乘　出處：《東華理工大學(xué)》2017年碩士論文

【摘要】：系數(shù)矩陣含有誤差(error-in-variables,EIV)的模型是常見的數(shù)學(xué)模型,廣泛的應(yīng)用于信號處理、通信工程、計(jì)算機(jī)視覺等領(lǐng)域。解決EIV模型的參數(shù)估計(jì)的最簡單的辦法是采用只考慮觀測向量有隨機(jī)誤差的最小二乘(Least Square,LS)求解,理論上不再是最優(yōu)解�？紤]系數(shù)矩陣和觀測向量隨機(jī)誤差的總體最小二乘算法(Total Least Squares,TLS)陸續(xù)被提出,其平差理論和應(yīng)用研究成為研究的熱點(diǎn)。本文研究現(xiàn)有EIV模型的解法,結(jié)合常見的數(shù)據(jù)擬合問題研究如何合理運(yùn)用TLS算法;利用資源三號影像數(shù)據(jù),研究EIV模型平差方法在光學(xué)遙感中的應(yīng)用,提出了基于TLS的在軌調(diào)制解調(diào)函數(shù)(Modulation Transfer Function,MTF)監(jiān)測和利用TLS求解基于有理函數(shù)模型(Rational Function Model,RFM)區(qū)域網(wǎng)平差補(bǔ)償系數(shù)的方法。本文的主要研究工作具體總結(jié)如下:針對系數(shù)矩陣和觀測量中各元素的相關(guān)性、系數(shù)矩陣的結(jié)構(gòu)性特點(diǎn),總結(jié)了一般的TLS、LS-TLS、MSTLS、WTLS、NTLS等算法的推導(dǎo)過程,著重分析了各算法的適用性,給出了各種算法的程序?qū)崿F(xiàn)步驟。選取空間直線、多項(xiàng)式曲線、圓曲線三類曲線的擬合為例,采取“數(shù)學(xué)表達(dá)形式-模型構(gòu)建-算法選取-精度評價(jià)-實(shí)例分析”研究思路,選取合理TLS算法,通過模擬數(shù)據(jù)和實(shí)例數(shù)據(jù),驗(yàn)證了各自算法的有效性。空間直接擬合上,建立了空間直線的通用EIV模型,提出了采用混合結(jié)構(gòu)總體最小二乘算法求解模型參數(shù),實(shí)例結(jié)果表明,MSTLS算法擬合空間直線理論更嚴(yán)謹(jǐn),精度有一定的提高;多項(xiàng)式曲線合上,根據(jù)其一般表達(dá)形式,建立EIV模型,采用NTLS求解未知參數(shù),模擬實(shí)驗(yàn)結(jié)果表明,NTLS算法擬合多項(xiàng)式曲線,效果較好;圓曲線擬合上,以圓曲線參數(shù)形式為基礎(chǔ)構(gòu)建的EIV模型,采用總體最小二乘求解待定參數(shù),通過模擬數(shù)據(jù)和實(shí)例發(fā)現(xiàn),對這種方法對圓曲線擬合的解算效率、解算精度方面有優(yōu)勢。在應(yīng)用研究上提出了基于TLS的在軌MTF監(jiān)測的方法。采用基于TLS的刃邊法獲取亞像素刃邊位置,最終得到其各頻率處的MTF值。結(jié)合資源三號01星的后視相機(jī)影像數(shù)據(jù)展開精度驗(yàn)證,實(shí)驗(yàn)結(jié)果表明,基于TLS的在軌MTF監(jiān)測辦法是可行的,相比常規(guī)的不考慮系數(shù)矩陣誤差的刃邊法理論上更加嚴(yán)謹(jǐn),垂軌方向上奈奎斯特頻率(即0.5頻率)處的MTF提高了1.56%;同時(shí)把EIV模型平差方法應(yīng)用到求解基于的RFM區(qū)域網(wǎng)平差補(bǔ)償系數(shù)上,選取平移縮放補(bǔ)償模型和仿射變換補(bǔ)償模型,采用TLS和TS求解RFM系統(tǒng)誤差補(bǔ)償系數(shù),結(jié)合資源三號衛(wèi)星01星2015年06月12日019013軌的湖北咸寧地區(qū)前后影像,布設(shè)實(shí)驗(yàn)方案,給出實(shí)驗(yàn)流程圖,實(shí)驗(yàn)結(jié)果表明,不管是采用平移縮放模型還是仿射變換模型,總體最小二乘求解補(bǔ)償模型參數(shù)相比最小二乘求解補(bǔ)償系數(shù),再立體交會(huì)得到地面點(diǎn)大地坐標(biāo),幾何定位精度可以達(dá)到相當(dāng)甚至更好的精度。例如在采用平移縮放補(bǔ)償模型時(shí),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.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：P237;P207.2

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