Using Multi-Antenna Trajectory Constraint to Analyze BeiDou Carrier-Phase Observation Error of Dynamic Receivers

Appropriate cycle-slip and measurement-error models are essential for BeiDou carrier-phase-based integrity risk calculation. To establish the receiver's measurement-error model, an accurate position reference of the GNSS antenna is fundamental for calculating the measurement error. However, it is still a challenge to acquire position references for dynamic BeiDou receivers, resulting in improper GNSS measurement-error models and unreliable integrity monitoring. This paper proposes an improved precise relative positioning scheme by adopting multi-antenna trajectory constraints for dynamic BeiDou receivers. The dynamic experiments show an obvious decline of 78.7%, at most, in the positioning failure rate of the proposed method, as compared with the traditional method. The position solutions obtained from the proposed approach are used as the reference to analyze the cycle-slip and measurement-error characteristics of the dynamic receiver. The field test results indicate that the cycle-slip rate decreases with the increase of signal-to-noise ratio (SNR), and cycle slipping obeys a positively skewed distribution that could be fitted by the Gaussian mixture model (GMM). On the other hand, the standard deviation of the carrier-phase measurement error is inversely proportional to SNR, and its distribution is characteristically fat-tailed, which could be fitted by the bi-normal model.