The frequency division multiple access (FDMA) strategy used in GLONASS causes inter-frequency phase bias (IFPB) and inter-frequency code bias (IFCB) between receivers from different manufacturers. The existence of IFPB and IFCB significantly increases the difficulties of fixing GLONASS ambiguity and limits the accuracy and reliability of GLONASS positioning. Moreover, the initial value of IFPB and IFCB may be unavailable or unreliable with the increasing number of receivers from different manufacturers in recent years. In this study, a real-time and reliable calibration algorithm of IFPB and IFCB based on multi-GNSS assistance is proposed by providing a fixed solution. Real-time IFPB rate and IFCB can be obtained using this algorithm without the initial IFPB and IFCB. The IFPB rate for all GLONASS satellites and IFCB for each GLONASS satellite are estimated due to different characteristics of IFPB and IFCB. IFPB calibration can be divided into constant and real-time IFPB calibrations to meet the different positioning requirements. Results show that constant IFPB rate has only 2 mm difference from the mean value of real-time IFPB rate. The IFPB rate and IFCB estimated by this algorithm have excellent stability, and the change in reference satellite cannot affect the results of IFPB rate and the stability of IFCB. The centimetre-level positioning results can be obtained using two calibration methods, and the positioning results with real-time calibration method are 10%–20% better than those with the constant calibration method. Under satellite-deprived environments, the improvements of multi-GNSS positioning accuracy with constant inter-frequency bias calibration gradually increase as the satellite cut-off elevation angle increases compared with GPS/BDS, which can reach up to 0·9 cm in the vertical direction.
Correction to: A Digital Adaptive Calibration Method of Timing Mismatch in TIADC Based on Adjacent Channels Lagrange Mean Value Difference
