Ionospheric delay prediction based on online polynomial modeling for real-time cycle slip repair of undifferenced triple-frequency GNSS signals

•An online cycle slip repairing method is proposed for GNSS triple-frequency signal.•An online polynomial modeling method is proposed to predict ionospheric delay.•Model uncertainty is adaptively tuned online.•Numerically efficient emplementation of the proposed method is expoited.•Real BDS data is analyzed to check the performance of the proposed method. In real-time cycle slip repair of undifferenced triple frequency Global Navigation Satellite Systems (GNSS) phase signals, ionospheric delay prediction is crucial in estimating the narrow lane part of the cycle slips. A quadratic model is recursively constructed using estimated ionospheric delays and used to perform one-step prediction. The model errors are distinguished from the data introduced errors and the model error variance is adaptively tuned online. In estimating the float narrow-lane cycle slips, a statistically rigorous error model is followed where the correlations between the predicted ionospheric delays and the epoch-differenced phases are given full considerations. An efficient algorithm for implementing the proposed method is developed where matrix inversion is avoided. A real Beidou System (BDS) data set is employed to check the performance of the proposed method. The manually introduced cycle slips have been all correctly repaired.