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1. INTRODUCTION
Multi-GNSS navigation and positioning is an inevitable trend caused by the modernisation programme of GPS and GLONASS and the rapid development of the BDS and Galileo programmes. The participation of the GLONASS system can increase the number of visible satellites as appropriate and improve the positioning performance of GNSS. Unlike GPS/BDS/Galileo, GLONASS employs a frequency division multiple access (FDMA) strategy and transmits signals on 14 frequencies (frequency number from −7 to 6). Given the difference in signal wavelength between GLONASS satellites, however, receiver hardware delay cannot be eliminated in double-difference (DD) observation for an inhomogeneous baseline that consists of receivers from different manufacturers, thereby bringing in inter-frequency bias (IFB) issues in GLONASS phase and pseudorange observations (Wanninger and Wallstab-Freitag, 2007; Takac, 2009; Yamada et al., 2010; Reussner and Wanninger, 2011; Wanninger, 2012). The existence of IFPB and IFCB significantly increases the difficulties of fixing GLONASS ambiguity and limits the accuracy and reliability of GLONASS positioning (Shi et al., 2013; Yao et al., 2017; Tian et al., 2018).
The Russian Federation has planned to add code division multiple access (CDMA) signal to the GLONASS signal structure as part of its modernisation programme since 2008 (Revnivykh, 2011). However, Russian Space Agency officials have indicated that FDMA signals will be retained in Glonass-K2 and Glonass-KM satellites in the future to ensure the compatibility of FDMA receivers. Therefore, the issues of GLONASS IFPB and IFCB will continue in the next few years (Takac, 2009; Karutin and Inst, 2015).
There have been many attempts by researchers to investigate the characteristics of GLONASS IFPB and IFCB and to calibrate these biases. Pratt et al. (1998) suggested that GLONASS IFPB has a linear relationship with the frequency number. Wanninger and Wallstab-Freitag (2007) confirmed this finding in several baselines of various GPS/GLONASS receivers, which can be utilised to model IFPB, so that they can be estimated by one IFPB rate parameter. Reussner and Wanninger (2011) verified that IFCB is mainly a frequency function, but simple linear modelling is insufficient, which even show large difference between receivers from the same manufacturer. Wanninger (2012) employed single-difference (SD) GPS and GLONASS observations to determine the GLONASS IFPB rates and proved that the IFPB rates are similar for L1 and L2 and also...