Study On Total Least Squares Model And Its Application For Data Processing Of Mine Area

With the development of data processing theory and observation technology, the methods of mine survey have been changed. At present, one important work of mine survey is to reform the previous reference systems, because reference systems have influence on the accuracy of mine survey data processing. The survey data of mine has obvious characters because of the special geomorphological features and work environment, such as poor accuracy, easy to be interfered, reference systems are inconsistent and hard to maintain. Total least squares has been drawing attention of survey researchers, it has been widely applied in the fields of survey in recent years. On base of discussion coordinate systems transformation, adjustment of underground traverse survey, and height anomaly fitting problems which exist in processing of mine survey data, the dissertation talks about the traditional factors which have influence on accuracy of survey data processing. At the same time, problems such as model parameters estimation, regularization of ill-posed model, robust estimation, and algorithm for adjustment of model with constrained parameters which exist widely in least squares estimation are discussed under total least squares estimation. The main conclusions of the dissertation are drawn as:(1) Combined with the characters of survey data in China, mathematical model for space coordinate transformation and model for plane coordinate transformation are discussed, besides, when the transformation models are applied to transform reference-ellipsoid-centric coordinate to geocentric coordinate, which model is more suitable for transformation has been investigated. A linearization model for plane coordinate transformation is presented. Coordinate transformation of mine area is taken for example to analyze whether total least squares model is suitable for processing data of mine area. The solution for adjustment of observed peg-top azimuths at underground traverse is discussed, and the indirect adjustment model of underground traverse is presented in the dissertation. The quadric surface polynomial model is taken as an example to talk about the topics that significance test of model, influence that error of random model has on significance test, when height anomaly of mine area is fitted. Algorithm for collocation the residual of fitting is proposed, and the feasibility of the algorithm are demonstrated by an instance that height anomaly fitting of mine area.(2) Geometric meaning of total least squares model is analyzed. Compared with least squares model, conclusion can be drawn that residual of fittng model based on total least squares must be less than least squares model from the geometric meaning of mathematical model. Three typical solutions for total least squres model are discussed: algorithm based on singular value decomposition, algorithm based on extremal function, algorithm based on Largrange function. Based on the Largrange algorithm, solution for unbiased estimation of mean square error of unit weight is proposed. Algorithms based on singular value decomposition and Largrange function are applied to realize height anomaly fitting of mine area through an instance, and the results of the instance demonstrate that compared with the current accuracy of observation data, the effective of application total least squres theory for realization height anomaly fitting is not obvious.(3) Solution for regularization of rank-deficient total least squares model is proposed. An iterative algorithm of total least squares robust estimation based on Largrange function is also presented. Because the data processing models are easy to have gross error and ill-posed models are easy to exist under the work environment of mine area, in order to get over the deficient mine data processing model, the dissertation focuses on solutions for regularization and robust estimation of total least squares based on discussion of traditional least squares estimation, and the application of total least squares estimation in fields of mine data processing has also been solved. To verify the feasibility of solution for rand-deficient total least squares model, the three-dimensional coordinate transformation model which is adapted to big rotation angle is taken for an example. Besides, plane coordinate transformation and computation exterior orientation elements are applied to discuss the algorithm for robust estimation of total least squares based on IGG(institute of geodesy & geophysics, Chinese academy of sciences) weight function, and conclusions are drawn based on discussion.(4) Solutions for total least squares model with inequality constraints and its parameters estimation are proposed in the dissertation. The geometric meaning of inequality constraint model is discussed. Total least squares model can be considered as the category of least squares model based on Tikhonov regularization theory, total least squares model can also be considered as expansion of least squares model. Exhaustive method is applied to establish iterative algorithm for total least squares model with inequality constraints based on the theory of zero weight and infinite weight. Two instances that deformation monitoring data processing of mine area and adjustment of underground traverse are applied to verify the models with inequality constraints, and the results of the instances clearly demonstrate that data processing based on inequality constraints is satisfied with the true fact, however, from the instances, inequality model can also make the results of data processing be twisted at the same time.At last of the dissertation, the problems existing in total least squares model and its application in data processing of survey have been analyzed and concluded, besides, development and investigation directions of total least squares theory have been expected.