Nonlinear Least Squares Surveying And Mapping Adjustment By Parameters And Spatial Data Error Analying

With the fast development of science and technology, especially the progress in digital engineering such as digital city, digital mine and so on, nonlinear data in multi-sources, different-types, multi-dimension, multi-period and so on are obtained in surveying and mapping. Due to the breakthrough of techniques and means and wider application of surveying and mapping, traditional theories and methods of it is being severely challenged. Classical method of processing data of surveying and mapping is that generally the nonlinear functions are generally expanded into linear ones in the place of the approximate values of unknown parameters by Taylor, then the linear models obtained are used to replace the nonlinear ones and data are processed in linear space. Obviously, the linearization of nonlinear model not only requires the approximation of unknown parameters which are close to the real values, but also nonlinear degrees of nonlinear models are weak. Otherwise, the precision of adjustment is not easy to meet to requirement of high precision, and the adjusted data can not reflect the nonlinear nature of objectives, and can not meet the demand of theories and applied fields of modern surveying and mapping. Therefore, great attention and interest is paid on the study of nonlinear surveying and mapping data processing. Luckily, the advance in nonlinear science and computer science provides basis to the study in the last 20 years. And excellent progresses in measurement of nonlinear degree of nonlinear models, new adjustment algorithms to estimate parameters of nonlinear functions models, error propagation and precision analysis on nonlinear least-square parameters adjustment and so on are made. But nonlinear science is more complicate than the linear one, and it is unpractical to apply the theories and methods of linear space into nonlinear space. Then new methods and technologies to process nonlinear data in nonlinear space by nonlinear science are needed, and then the results of adjustment can reflect the nature of the questions.Study is made under the support of CNSF (Code: 40174003). Fist, comprehensive analysis on the current study on data processing is made, and characters of Newton methods about nonlinear surveying and mapping data processing are discussed, and then new solutions to parameters estimate with multi-sources, multi-types, multi-dimension, multi-precision bynonlinear least square are presented such as PSB algorithm, digital continuation and generalized digital continuation algorithm, cone model method, tensor analysis method, GCMA(mixed algorithm of gradient method and conjugate gradient method), combining algorithm based on Newton method and gradient method and confidence region and so on, and a new fast difference iterative algorithm is proposed towards parameters estimation containing random parameters in nonlinear models, and a new solutions to nonlinear least squares surveying and mapping adjustment by parameters estimation both considering the random and nonrandom parameters is presented after studying on nonlinear data processing in deformation monitoring, and at last primary analysis on error propagation of spatial data is made and approximate error propagation formula and error analysis formula to length and area are proposed. At the meantime, a new method of estimating parameters of generalized nonlinear model on considering random parameters.