总体最小二乘联合平差方法及其应用研究

发布时间：2018-11-29 13:02

【摘要】：随着空间大地测量技术的发展,数据种类的丰富,如何有效的融合各类观测数据进行联合平差,以获取不同类观测数据的有用信息、获得可靠的平差结果,成为研究的热点。然而,大部分联合平差成果是基于Gauss-Markov模型展开(认为仅观测向量包含随机误差)。在许多情况下,系数矩阵同样受到随机误差的影响,因此,更为合理的方法应当考虑变量含误差模型(errors-in-variables,EIV)。现有的联合平差方法存在以下不足之处:(1)联合平差方法是在最小二乘平差准则下求解得出,实际情况下,系数矩阵同样是由含随机误差的观测数据组成;(2)大多数文献在求解联合平差时视各类数据等权比,即人为认为各类数据在联合平差中所占的比重相同。针对上述问题,本文将总体最小二乘方法应用于联合平差问题,采用相对权比(权比因子)来平衡两类或多类数据之间的比重;推导总体最小二乘联合平差准则下模型参数估计公式;探究联合平差中相对权比的确定方法;将联合平差方法应用于Mogi模型火山形变等问题,验证推导方法在实际问题中的应用。具体研究内容如下:1.不同类数据的融合是大地测量数据处理的基本问题。推导了多类观测数据的加权总体最小二乘平差方法,在相对权比的确定方面,设计多种方案,结合验前单位权方差法和判别函数最小化方法确定权比。研究结果表明:验前单位权方差法适用于数据验前信息相对准确的情况,当验前信息不准确时,采用判别函数最小化法能取得较优的参数估值结果。2.针对判别函数不唯一,实际应用中采用经验的判别函数确定权比的问题。推导了一种附加自适应权比因子的加权总体最小二乘联合平差方法,给出了适用于加权总体最小二乘联合平差的Helmert方差分量估计公式,自适应求解不同类观测数据参与联合平差所占比重,求得模型参数。模拟算例结果表明:推导的附加自适应权比因子的加权总体最小二乘联合平差方法能够取得与已有的总体最小二乘方差分量估计法相同的平差结果,且优于最小二乘联合平差及不顾及权比因子的加权总体最小二乘联合平差结果。与已有的总体最小二乘方差分量估计法相比,推导方法具有较高的计算效率。通过联合In SAR与GPS数据,将推导的方法应用于L’Aquila地震滑动分布反演实例,对比了附加自适应权比因子的加权总体最小二乘联合平差方法与最小二乘联合平差方法。3.基于本文联合平差研究,结合判别函数最小化法确定权比,系统的研究了总体最小二乘联合平差方法在长白山天池火山Mogi模型反演中的应用。针对该模型非线性的特点,对其线性化,给出了观测向量与系数矩阵协因数阵的计算方法。研究结果表明:本文方法能获得合理的压力源参数估值结果,具有一定的实际应用价值。
[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.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P207

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