A Bayesian method of GNSS cycle slips detection based on ARMA model

Based on the time series analysis method, this article develops a Bayesian method of detecting and repairing the cycle slips in the GNSS carrier-phase data. Firstly, this article analyses the characteristics of the cycle slips in the GNSS carrier-phase observations and establishes the relationships between the cycle slips and the additive outliers (AOs) in the stationary time series. When the ARMA (autoregressive moving-average) model is used to fit the stationary time series obtained by differencing the GNSS carrier-phase observations, the detection of cycle slips in the GNSS carrier-phase observations can be transformed to the detection of AOs in the ARMA model. Then, this article proposes a Bayesian method of detecting the AOs in the ARMA model, and the implementation of detecting the cycle slips in the GNSS carrier-phase observations is also developed. Finally, the new Bayesian method of detecting the cycle slips is used to the real GNSS carrier-phase data. From the comparison among the Bayesian method, the high-order differences method and ionospheric residual method, we can find that the Bayesian method has a better detection efficiency for several kinds of cycle slips in the GNSS carrier-phase observations than other methods.