Bayesian Detection For Outliers Based On Autoregressive Model And Applications In GNSS Cycle Slips Detection

Outlier detection in time series is an important part of time series analysis. This article ismainly concerned with the problem of detecting outliers with different types, the problem ofmasking and swamping for detecting additive outlier patches, and applications in cycle slipsdetection based on Bayesian statistical theory in statisary time series. The main conclusions areas follows:1. Bayes method for outlier detection based on different types of classification variables. Anew model is proposed to detect different types of outliers simultaneously based on theconception of introducing different types of classification variables to the corresponding types ofoutliers; the threshold for outlier detection is given explicitly according to Bayesian hypothesistheory; Gibbs sampler is used to compute the posterior probabilities of classification variables inthe proposed detection method for outlier detecton.2. Unmasking Bayes method for detecting additive outlier patches. We intensively look intothe reasons of masking and swamping about detecting patches of additive outliers; the reason isthat the existence of additive outlier patches causes serious bias in estimating their magnitudes,which makes initial conditions of Gibbs sampling unreasonable, and then makes Gibbs samplingdivergent. According to the reasons above and making full use of the correlations of time series,we obtain an accurate estimate of the magnitudes of additive outlier patches by generalized leastsquares estimation, so as to design an adaptive Gibbs sampling, and ultimately to propose aBayesian unmasking method for detecting additive outlier patches.3. Applications of the Bayes methods for outlier detection in time series to cycle slipsdetection in GNSS. Considering the character of cycle slips in phase data and the relationsbetween cycle slips and outliers, this paper proposes a Bayesian method for cycle slips detectionbased on the posterior probabilities of classification variables in the respective of Bayesianhypothesis. Besides, this paper deals with the problem of masking and swamping about cycleslips detection in a thorough new conception. An adaptive Gibbs sampling algorithm is designedthrough analyzing the reasons of masking and swamping about cycle slips detection.Then anunmasking Bayesian method for cycle slips detection is proposed. Furthermore, accurateestimation of cycle slips is given based on Bayesian point estimation.Examples illustrate that the simultaneous detection model proposed by this article canappropriately handle different types of outliers that occur at the same time point or at differenttime points in the data of time series, which efficiently avoid the problems that caused by dealingwith different types of outliers separately, such as the confusion of outlier types; Bayesiandetection method for additive outlier patches can efficiently prevent the occurrence of masking and swamping. Applications illustrate that these theories and methods can be successfully usedto process the data of satellite clock errors and to detect cycle slips in phase data.