發(fā)布時(shí)間：2018-11-29 13:02

【摘要】：隨著空間大地測(cè)量技術(shù)的發(fā)展,數(shù)據(jù)種類(lèi)的豐富,如何有效的融合各類(lèi)觀(guān)測(cè)數(shù)據(jù)進(jìn)行聯(lián)合平差,以獲取不同類(lèi)觀(guān)測(cè)數(shù)據(jù)的有用信息、獲得可靠的平差結(jié)果,成為研究的熱點(diǎn)。然而,大部分聯(lián)合平差成果是基于Gauss-Markov模型展開(kāi)(認(rèn)為僅觀(guān)測(cè)向量包含隨機(jī)誤差)。在許多情況下,系數(shù)矩陣同樣受到隨機(jī)誤差的影響,因此,更為合理的方法應(yīng)當(dāng)考慮變量含誤差模型(errors-in-variables,EIV)。現(xiàn)有的聯(lián)合平差方法存在以下不足之處:(1)聯(lián)合平差方法是在最小二乘平差準(zhǔn)則下求解得出,實(shí)際情況下,系數(shù)矩陣同樣是由含隨機(jī)誤差的觀(guān)測(cè)數(shù)據(jù)組成;(2)大多數(shù)文獻(xiàn)在求解聯(lián)合平差時(shí)視各類(lèi)數(shù)據(jù)等權(quán)比,即人為認(rèn)為各類(lèi)數(shù)據(jù)在聯(lián)合平差中所占的比重相同。針對(duì)上述問(wèn)題,本文將總體最小二乘方法應(yīng)用于聯(lián)合平差問(wèn)題,采用相對(duì)權(quán)比(權(quán)比因子)來(lái)平衡兩類(lèi)或多類(lèi)數(shù)據(jù)之間的比重;推導(dǎo)總體最小二乘聯(lián)合平差準(zhǔn)則下模型參數(shù)估計(jì)公式;探究聯(lián)合平差中相對(duì)權(quán)比的確定方法;將聯(lián)合平差方法應(yīng)用于Mogi模型火山形變等問(wèn)題,驗(yàn)證推導(dǎo)方法在實(shí)際問(wèn)題中的應(yīng)用。具體研究?jī)?nèi)容如下:1.不同類(lèi)數(shù)據(jù)的融合是大地測(cè)量數(shù)據(jù)處理的基本問(wèn)題。推導(dǎo)了多類(lèi)觀(guān)測(cè)數(shù)據(jù)的加權(quán)總體最小二乘平差方法,在相對(duì)權(quán)比的確定方面,設(shè)計(jì)多種方案,結(jié)合驗(yàn)前單位權(quán)方差法和判別函數(shù)最小化方法確定權(quán)比。研究結(jié)果表明:驗(yàn)前單位權(quán)方差法適用于數(shù)據(jù)驗(yàn)前信息相對(duì)準(zhǔn)確的情況,當(dāng)驗(yàn)前信息不準(zhǔn)確時(shí),采用判別函數(shù)最小化法能取得較優(yōu)的參數(shù)估值結(jié)果。2.針對(duì)判別函數(shù)不唯一,實(shí)際應(yīng)用中采用經(jīng)驗(yàn)的判別函數(shù)確定權(quán)比的問(wèn)題。推導(dǎo)了一種附加自適應(yīng)權(quán)比因子的加權(quán)總體最小二乘聯(lián)合平差方法,給出了適用于加權(quán)總體最小二乘聯(lián)合平差的Helmert方差分量估計(jì)公式,自適應(yīng)求解不同類(lèi)觀(guān)測(cè)數(shù)據(jù)參與聯(lián)合平差所占比重,求得模型參數(shù)。模擬算例結(jié)果表明:推導(dǎo)的附加自適應(yīng)權(quán)比因子的加權(quán)總體最小二乘聯(lián)合平差方法能夠取得與已有的總體最小二乘方差分量估計(jì)法相同的平差結(jié)果,且優(yōu)于最小二乘聯(lián)合平差及不顧及權(quán)比因子的加權(quán)總體最小二乘聯(lián)合平差結(jié)果。與已有的總體最小二乘方差分量估計(jì)法相比,推導(dǎo)方法具有較高的計(jì)算效率。通過(guò)聯(lián)合In SAR與GPS數(shù)據(jù),將推導(dǎo)的方法應(yīng)用于L’Aquila地震滑動(dòng)分布反演實(shí)例,對(duì)比了附加自適應(yīng)權(quán)比因子的加權(quán)總體最小二乘聯(lián)合平差方法與最小二乘聯(lián)合平差方法。3.基于本文聯(lián)合平差研究,結(jié)合判別函數(shù)最小化法確定權(quán)比,系統(tǒng)的研究了總體最小二乘聯(lián)合平差方法在長(zhǎng)白山天池火山Mogi模型反演中的應(yīng)用。針對(duì)該模型非線(xiàn)性的特點(diǎn),對(duì)其線(xiàn)性化,給出了觀(guān)測(cè)向量與系數(shù)矩陣協(xié)因數(shù)陣的計(jì)算方法。研究結(jié)果表明:本文方法能獲得合理的壓力源參數(shù)估值結(jié)果,具有一定的實(shí)際應(yīng)用價(jià)值。
[Abstract]:With the development of spatial geodetic technology and the abundance of data types, how to effectively fuse all kinds of observation data for joint adjustment to obtain useful information of different types of observation data and obtain reliable adjustment results has become a hot research topic. However, most of the joint adjustment results are based on Gauss-Markov model expansion (it is considered that only observation vectors contain random errors). In many cases, the coefficient matrix is also affected by random errors. Therefore, a more reasonable method should consider the variable containing error model (errors-in-variables,EIV). The existing joint adjustment methods have the following shortcomings: (1) the joint adjustment method is solved under the least square adjustment criterion. In practice, the coefficient matrix is also composed of observation data with random errors; (2) in solving the joint adjustment, the majority of literatures regard all kinds of data as equal weight ratio, that is to say, the proportion of all kinds of data in the joint adjustment is assumed to be the same. In view of the above problems, this paper applies the total least square method to the joint adjustment problem, and uses the relative weight ratio (the weight ratio factor) to balance the proportion between two or more kinds of data. The estimation formula of model parameters under the general least square combined adjustment criterion is derived, and the determination method of relative weight ratio in joint adjustment is explored. The combined adjustment method is applied to the volcanic deformation of the Mogi model, and the application of the derivation method to the practical problems is verified. The specific research contents are as follows: 1. The fusion of different types of data is the basic problem of geodetic data processing. The weighted global least square adjustment method for multiple observation data is derived. In the determination of relative weight ratio, several schemes are designed, and the weight ratio is determined by combining the prior unit weight variance method and the discriminant function minimization method. The results show that the prior unit weight variance method is suitable for the case where the prior information of the data is relatively accurate. When the prior information is not accurate, the discriminant function minimization method can obtain better parameter estimation results. 2. In view of the fact that the discriminant function is not unique, the empirical discriminant function is used to determine the weight ratio. In this paper, a weighted population least squares combined adjustment method with adaptive weight ratio factor is derived, and the Helmert variance component estimation formula suitable for weighted population least squares combined adjustment is given. The model parameters are obtained by adaptively solving the proportion of different kinds of observation data participating in the joint adjustment. The simulation results show that the proposed weighted population least squares combined adjustment method with adaptive weight ratio factor can obtain the same adjustment results as the existing least square variance component estimation method. It is better than the least square combined adjustment and the weighted total least squares combined adjustment without weight ratio factor. Compared with the existing least square variance component estimation method, the derivation method has higher computational efficiency. By combining In SAR and GPS data, the derivation method is applied to the inversion of L'Aquila seismic slip distribution, and the weighted total least squares combined adjustment method with the least square combined adjustment method is compared with the least squares combined adjustment method. Based on the study of joint adjustment and the determination of weight ratio by minimization of discriminant function, the application of total least squares combined adjustment method in inversion of Mogi model of Tianchi volcano in Changbai Mountain is systematically studied. According to the nonlinear characteristics of the model, the method of calculating the cofactor matrix between the observation vector and the coefficient matrix is given for the linearization of the model. The results show that the proposed method can obtain reasonable estimation results of pressure source parameters and has certain practical application value.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：P207

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