Study On The Total Least Squares Method Of Partial EIV Model And Its Application

A classic model of adjustment usually takes the random error of observation vector into consideration but assumes that the coefficient matrix is deterministic. For this type of models, we can adopt the least squares(LS) method to estimate the parameters. A errors-in-variables model considers both the random error of observation vector and the random error in coefficient matrix. For this type of models, we can use the total least squares(TLS) method to estimate the unknown parameters. However, in the practical application of geodetic and engineering surveying, we often have to deal with a model in which the coefficient matrix only contains random error partly. For this kind of situation, a partial-EIV(PEIV) should be used to estimate the model parameters.Whether in EIV models or in PEIV models, a large part of researches have assumed that(1) there is no correlation between the observation vector and the elements of the coefficient matrix;(2) the observation vector and coefficient matrix has the same unit weight variance. In other words, data constituting the observation and the coefficient matrix are from the same kind of observation data. Obviously, the above two assumptions often cannot be guaranteed in the actual problems, and it also limits the application of the existing research in the practical production. How to solve these problems is one of the important topics in geodetic data processing field. The major contributions of this dissertation can be summarized as follows:1)The construction method of PEIV model are studied systematically and some conclusion has been made about advantage and the existing problems of the model. On the base of PEIV model, three kinds of weighted total least squares(WTLS)algorithms are derived when the observations and elements in coefficient matrix are heteroscedastic and correlated. The feasibility and correctness of these algorithms above is shown through examples. Research shows that these algorithms has good effect, especially for the situation that coefficient matrix consists of constant elements and repeating elements.2)The properties of the total least squares adjustment model with weight scaling factor is studied systematically. Concerning the issue that the observation vector and coefficient matrix may has the different unit weight variance, which leads to inaccurate weight. On the base of observation vector and coefficient matrix’s stochastic model, the new adjustment criterion is built. By adding weight scaling factor into adjustment criterion, the contribution of observation and coefficient matrix to parameter estimation is adaptively adjusted. The application of variance component estimation(VCE)in EIV model is studied systematically. On the base of PEIV model, the method of Helmert VCE in EIV model is derived, and this method is used to determine the weight scaling factor in the total least squares adjustment model with weight scaling factor. At last, the feasibility and effective of this method is verified through examples.3)The prior unite weight variance method and minimum discriminate function method is deduced. The direct computational formal of the prior unite weight variance method is derived in detail and new discriminant functions are introduced to determine the weight scaling factor. Research shows that when the prior unit weight variances of observation and coefficient matrix are known and accurate, the prior unite weight variance method is better, and if the priori information is unknown, the minimum discriminate function method is better.4)On the basis of PEIV model, combining with the adjustment criterion with weight scaling factor, the effect of the random errors of the design matrix in the crust strain inversion process is investigated systematically.