A review on the inter-frequency biases of GLONASS carrier-phase data

GLONASS ambiguity resolution (AR) between inhomogeneous stations requires correction of inter-frequency phase biases (IFPBs) (a "station" here is an integral ensemble of a receiver, an antenna, firmware, etc.). It has been elucidated that IFPBs as a linear function of channel numbers are not physical in nature, but actually originate in differential code-phase biases (DCPBs). Although IFPBs have been prevalently recognized, an unanswered question is whether IFPBs and DCPBs are equivalent in enabling GLONASS AR. Besides, general strategies for the DCPB estimation across a large network of heterogeneous stations are still under investigation within the GNSS community, such as whether one DCPB per receiver type (rather than individual stations) suffices, as tentatively suggested by the IGS (International GNSS Service), and what accuracy we are able to and ought to achieve for DCPB products. In this study, we review the concept of DCPBs and point out that IFPBs are only approximate derivations from DCPBs, and are potentially problematic if carrier-phase hardware biases differ by up to several millimeters across frequency channels. We further stress the station and observable specific properties of DCPBs which cannot be thoughtlessly ignored as conducted conventionally. With 212 days of data from 200 European stations, we estimated DCPBs per stations by resolving ionosphere-free ambiguities of 5.3 cm wavelengths, and compared them to the presumed truth benchmarks computed directly with L1 and L2 data on ultra-short baselines. On average, the accuracy of our DCPB products is around 0.7 ns in RMS. According to this uncertainty estimates, we could unambiguously confirm that DCPBs can typically differ substantially by up to 30 ns among receivers of identical types and over 10 ns across different observables. In contrast, a DCPB error of more than 6 ns will decrease the fixing rate of ionosphere-free ambiguities by over 20 %, due to their smallest frequency spacing and highest sensitivity to DCPB errors. Therefore, we suggest that (1) the rigorous DCPB model should be implemented instead of the classic, but inaccurate IFPB model; (2) DCPBs of sub-ns accuracy can be achieved over a large network by efficiently resolving ionosphere-free ambiguities; (3) DCPBs should be estimated and applied on account of their station and observable specific properties, especially for ambiguities of short wavelengths.