Bayesian Methods For Gross Errors Detection Of Correlated Observations And Its Application In Gps Network Adjustment

With development of surveying theory and observation technology, there will be more and more correlated observations appearing in the field of measuring data processing. However, in practice, most current methods for analyzing gross errors are only limited to independent observation, thus for detecting gross errors of correlated observations they are not ideal, especially in GPS network adjustment. Meanwhile, those methods cannot take account of and make full use of prior information of unknown parameters, leading to not only a waste of information but also unreasonable conclusions sometimes.According to systemically reviewing and evaluating the research process of gross errors of correlated observations, as well as through strongly connecting modern state of GPS measuring data processing, this paper could apply modern Bayesian statistic theories to discuss questions of gross errors detection under correlated states. Furthermore, on the basis of integration of prior information and observing information, we put forward Bayesian methods for gross errors detection of correlated observations, and finally apply it in GPS network adjustment.Major research achievement and innovation as follows:1. Bayesian methods for gross errors positioning of correlated observations. With Bayesian statistic theory of hypothesis testing, we introduce a classification variable for each observation, therefore, the problem of gross errors positioning is transformed to another one to calculate the posterior probabilities of classification variables. Furthermore, basing on Gibbs sampling, an algorithm for computing the posterior probability of classification variables is designed. Thus finally, we build the Bayesian methods for gross errors positioning of correlated observations basing on the posterior probability of classification variables.2. Bayesian methods for gross errors estimation of correlated observations. With Bayesian statistical estimating theory, we deduce and build Bayesian estimating formulas for parameters of gross errors in condition of normal-gamma prior information and non- prior information after gross errors positioning is finished. And then we could readjust to eliminate influence from gross errors so as to perfect Bayesian methods for gross errors estimating of correlated observations.3. Bayesian methods for gross errors detection of correlated observations in GPS network adjustment.In view of characteristics of GPS network, we have built a mathematical model for gross errors detection in the paper, and also designed corresponding algorithm and implementing procedures. In conclusion, both theoretical analysis and numerical examples have demonstrated that, Bayesian methods for gross errors detection of correlated observations are effective, especially in GPS network adjustment. They can syncretize prior information with observing information perfectly, detect gross errors of correlated observations successfully and diminish negative influence of gross errors effectively. Comparing to other relevant methods, ours seems more feasible and effective.