Theory & Application Of Data Processing In Space Of Nonlinear Models

With the rapid development of science & technology in surveying and mapping, Adjustment and data processing in linear model space is the bottleneck for further improving the data quality . For more than twenty years, scholars in the fields of statistics and surveying & mapping do good researches about nonlinear data processing, and make great advance in so many problems as nonlinear adjustment, change-point analysis non-parameter statistics diagnosis, nerve network, nonlinear regression analysis etc, but remaining many problems to be solved. In this thesis, aimed at some questions in adjustment and data analysis of deformation, by connected, comprehensive and systematic way to investigate, and make some useful conclusions, doubtlessly, it will do great help to the advance of theory on nonlinear data processing.In this thesis, firstly discussing the definition and classifications of error and precision, sort the gross error into the random error, meantime treat the general precision as a standard of assessment the parameter's quality. Secondly do research on the mathematic features. Based on Cook distance, putting forward a judgment criterion on stress and weak nonlinear models; based on definition of real error, establishing a poly-robust estimation criterion function ?SMSE=minE(X-X):,applying AR(1) model to describe real error, under strict of SMSE criterion, with help of iteration working out the adjustment function in nonlinear space, and applying Monte-Carlo method to estimate the variance of nonlinear function; on the background of MLE.deducing estimation way of random parameters in the space of nonlinear variance models, on the back of poly-robust. putting forward the assessment formula of adjustment general precision; in this paper, proposed some way of decomposing and synthesizing on index, factor and model about nonlinear time-serial analysis, Giving the detail proof on non-parameter estimation of the nonlinear time-serial model, elaborating the dropping dimension way of high dimension data.Applying some way and theory to solution of nonlinear GPS baseline , GPS elevation regression by nonlinear Gauss function , and nonlinear time-serials model analysis on deformation of bridge tower, and got meaningful conclusion and results. Those examples have proved the nonlinear theory and method of data processing to be correct from the viewpoint of practice.