Bayesian Methods For Time Series Outliers Detection And Applications In Gps Data Processing

The observation of time series may be influenced by outliers. If we forecasts directly, neglecting the influence, will lead to false result. So, in dynamic surveying data analysis and data processing practice, the seeking for approaches to dealing with time series outliers becomes very important.On the basis of reviewing and summarizing the actual researching state of time series outliers detection systemically, this paper will mainly discuss the approaches to outliers detection in time series utilizing the modern Bayesian theories and methods. And syncretizing prior information with observing information, Bayesian method for outliers detection in stationary time series is put forward. Furthermore, the method is applied in the research on the data processing of GPS; also optimize the modeling and predicting methods of clock error and VTEC series.The main conclusions are as follows:1. Firstly, we summarized and analyzed the outliers detecting methods in the present. This paper divided the stationary time series into three classes, then pointed out the influence on modeling and predicting,when there are outliers in time series. Furthermore, reviewed and summarized traditional outliers detecting method. Finally, suggested the limitation of traditional methods.2. Bayesian method for outliers positioning were given secondly. Given some special restrictions, we can change time series outliers positioning into outliers positioning in linear regression model. Based on the theory of Bayesian Statistical diagnostics, we put forward Bayesian method of outliers positioning. And then, under the condition of both the non-informative priors and normal-gamma prior information, Bayesian method for posterior probability calculating were given respectively.3. Bayesian methods for outliers estimating were given thirdly. Applying Bayesian statistical estimating theory, under the condition of both the non-informative priors and normal-gamma prior information, Bayesian estimations for outliers are given respectively to perfect outliers estimations as one important aspect of outliers detecting.4. Box-Jenkins modeling method on GPS time series and Bayesian method for outliers detecting were put forward. Then modeling the GPS clock error series and ionospheric VTEC series with Box-Jenkins method, At last, modify the outliers with the new method, improving the predicting accuracy of the GPS clock error series and ionospheric VTEC series. Theoretical analysis and mass numerical examples demonstrate that the new method is useful and efficient.