Research On The Total Least Squares Joint Adjustment And Its Application

With the development of space geodetic technique, we can acquire more kinds of space geodetic data. How to fuse those kinds of datasets, so as to assimilate useful information and achieve dependent results has become a hot spot of research. The majority of the existing researches are based on the classical Gauss-Markov model(i.e.only the errors in the observation vector are considered). However, the coefficient matrix is also contaminated by random errors in many cases. Therefore, a more reasonable method should consider the errors-in-variables(EIV) model. Existing joint adjustment methods have the following shortcomings:(1) Most joint adjustment methods are based on least squares theory. Actually, the coefficient matrix is also consisted with random errors;(2) While using joint adjustment, the majority of papers take the weight scaling factor as identical, which means that each dataset holds the same proportion.Regarding the issues above, in this paper, the total least squares method is applied to joint adjustment theory. Weight scaling factor is considered to balance the weight in two or more kinds of datasets. Model parameter estimation formula is derived in accordance to the objective function of total least squares joint adjustment. The method for determine the weight scaling factor is investigated. While applied to the model of the deformation of volcano etc., the efficacy of the proposed method is verified. The main researches and innovations of this paper are as follows:1. It is a basic problem for geodetic data processing of integrating different kinds of dataset. An iterative method of WTLS joint adjustment is derived. In terms of determining the weight scaling factor, some schemes are designed, which are the prior unit weight variance method and the minimum discriminate function method. Research shows that: we can fix the weight scaling factor while using the prior unit weight variance method when prior information is accurate. However, when the priorinformation is inaccurate, the minimum discriminate function method can achieve effective results.2. Because of the minimum discriminate function is not unique, we should use empirical formula to determine the weight scaling factor. In this part, an iterative method of weighted total least squares joint adjustment with auto-match weight scaling factor is proposed. Variance factors of different types of geodetic data are estimated according to Helmert estimation method, so as to determine the weight scaling factor automatically. In the end, the model parameters can be obtained simultaneously.Research shows that: the proposed method can achieve the same estimated results with the existing method of total least squares variance component estimation. It is also better than the results of least squares joint adjustment and weighted total least squares without considering the weight scaling factor. Compared with the method of total least squares variance component estimation, our method is computationally more efficient.The proposed method is also applied to fault slip inversion, while joint the In SAR and GPS data to obtain the slip parameters in L’Aquila(central Italy) earthquake. The results of the proposed method and least squares joint adjustment are compared.3. Based on the research of this paper, the proposed method of this paper is applied to the inversion of the Mogi model of Changbai Tianchi volcano. The minimum discriminate function is used to determine the weight scaling factor. Considering the nonlinear characteristic of the Mogi model, the linearized form is derived. Formulae of the calculation of the cofactor matrices of the observation vector and the coefficient matrix are also derived. Research shows that: the proposed method can achieve the reasonable pressure source parameters and has a certain practical application value.