A single difference-based multi-GNSS inter-system model with consideration of inter-frequency bias and inter-system bias

By calibrating the inter-system bias (ISB), an inter-system model can be achieved to improve the performance of multi-global navigation satellite system (GNSS) positioning. A number of studies were carried out to compose inter-system models among code division multiple access (CDMA) systems. However, due to the frequency division multiple access (FDMA) technique, GLONASS phase and code observations suffer from inter-frequency phase bias (IFPB) and inter-frequency code bias (IFCB) respectively, which make it difficult to obtain the ISB among GLONASS and CDMA systems. In addition, most of the current inter-system models are unable to handle mixed frequencies. A new single difference-based uniform inter-system model suitable for all of the CDMA and FDMA frequency combinations is proposed in this study. We first utilize a particle filter approach to extract the IFPB rate. Afterwards, the multi-ISB parameters can be estimated by the proposed model simultaneously. Four short baselines containing the signals of GLONASS, GPS, BDS3, BDS2, Galileo, and QZSS are selected to validate the model. The quantitative results indicate that the IFPB rate can be extracted precisely by a particle filter within ten epochs. The inter-system phase bias valuations are sufficiently stable on a daily scale and have standard deviation near 0.01 cycles. After de-weighting the GLONASS code observations to reduce the influence of IFCB, the inter-system code bias is also stable. Furthermore, imposing the stable ISB on the multi-GNSS inter-system model can effectively improve the single-frequency real-time kinematic positioning accuracy and reliability for severely obstructed situations with only a small number of satellites observed.