The Studies On Nonlinear Data Processing For Multi-source Multi-dimension Multi-type And Multi-precision Surveying Data

This paper is part of the project "Generalized nonlinear dynamic least square theory and it's application in geography filed" (No. 40174003), supported by the National Natural Science Foundation of China. Based on optimal theory, statistic theory and the theory of nonlinear data processing, the theory of combined data processing for multi-source multi-dimension multi-type and multi-precision surveying data is studied systematically, which includes mainly four parts as follows.Firstly, on the basis of the known theory of nonlinear data processing, the function model of nonlinear combined indirect processing, the function model of nonlinear combined conditioned processing, and the function model of nonlinear combined conditioned processing with parameters for multi-source multi-dimension multi-type and multi-precision surveying data are established. Simultaneously, the corresponding nonlinear leastsquare models are put forward. Aiming at the models established, several algorithms are set up.Secondly, aiming at characteristics that there are not only non-random parameters but also random parameters in the function of the data processing models, also the random parameters are usually dynamic, three generalized nonlinear dynamic processing function model and their nonlinear dynamic LS models are proposed. Aiming at the characteristics that the surveying data is obtained by various surveying instruments and is of multi-source multi-dimension multi-type multi- precision and multi-state, and that there are not only non-random parameters but also random parameters in the function of the data processing models, also the random parameters are usually dynamic, a generalized nonlinear dynamic inderect processing model, a generalized nonlinear dynamic conditioned processing model, a generalized nonlinear dynamic conditioned processing model with parameters and according generalized nonlinear dynamic LS models for combined data processing on multi-source multi-dimension multi-type multi- precision and multi-state surveying data are proposed. Considering the large scale and high dimension, algorithms are proposed..Thirdly, considering the characteristic that several data can be gained by GPS simultaneously, a multi-response model for GPS adjustment is given. Two estimations—maximum likelihood estimation and nonlinear leastsquare estimation are givenat two cases. About the leastsquare estimation at a case, combining quasi-Newton method and trust region method, a new hybrid algorithm is proposed.At last, the accuracy evaluation in data processing for multi-source and multi-precisionsurveying data is researched. First of all, the asymptotic %2 -distribution of RSS in nonlineardata processing model is derived by using stochastic expansion and saddlepoints approximations method. Furthermore, the accuracy evaluation method is given in nonlinear data processing model. Based on these results, the accuracy evaluation methods are given in nonlinear combined processing model and generilied nonlinear dynamic combined processing model for multi-source multi-precision surveying data at the case of normal distribution of errors. In addition, a linear data processing model for multi-source surveying data is suggested. Applying saddlepoints approximations method and the results in reference [106], the asymptotic distribution of LS estimation of parameters and asymptotic distribution of RSS in linear data processing model for multi-source surveying data are derived. Then the accuracy evaluation method is given when errors according to general distributions.