Combined BeiDou-2 and BeiDou-3 instantaneous RTK positioning: stochastic modeling and positioning performance assessment

The global BeiDou navigation satellite system (BDS-3) has been in operation recently and many related applications have been already compatible with BDS-3 satellites. Most applications still use the empirical stochastic models for combined regional BeiDou navigation satellite system (BDS-2) and BDS-3 positioning. However, BDS-3 has different satellite design, and the empirical stochastic models may not describe the observation precisions and the correlation characteristics of BDS-3 signals well and finally degrade the positioning performance. Hence, in this contribution, the variance-covariance component estimation is applied to calculate the precisions of observations and their spatiotemporal correlations as well as the cross-correlations for BDS-2 and BDS-3 multi-frequency signals. With the retrieved stochastic model, the performance of integer ambiguity resolution and positioning are then numerically demonstrated on short baseline. The results show that the observation precisions are in general elevation-dependent for both BDS-2 and BDS-3 except for BDS-2 geostationary earth orbit (GEO) satellites. For both BDS-2 and BDS-3, the spatial correlations are adequately small to be ignored in practical data processing. For the receivers we used, the cross-correlations are found significantly amongst the BDS-2 multi-frequency phase signals. Moreover, the temporal correlations differ between different frequencies and observations. The combined BDS-2 and BDS-3 can improve the ambiguity resolution success rate and positioning accuracy.