In this study, we develop a Multi-constellation Global Navigation Satellite System (GNSS) Receiver Differential Code Bias (MGR-DCB) model. The model estimates the receiver DCBs for the Global Positioning System (GPS), BeiDou and Galileo signals from the ionosphere-corrected geometry-free linear combinations of the code observations. In order to account for the ionospheric delay, a Regional Ionospheric Model (RIM) over Europe is developed. GPS observations from 60 International GNSS Servoce (IGS) and EUREF reference stations are processed in the Bernese-5·2 Precise Point Positioning (PPP) module to estimate the Vertical Total Electron Content (VTEC). The RIM has spatial and temporal resolutions of 1° × 1° and 15 minutes, respectively. The receiver DCBs for three stations from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) are estimated for three different days. The estimated DCBs are compared with the MGEX published values. The results show agreement with the MGEX values with mean difference and Root Mean Square Error (RMSE) values less than 1 ns. In addition, the combined GPS, BeiDou and Galileo VTEC values are evaluated and compared with the IGS Global Ionospheric Maps (IGS-GIM) counterparts. The results show agreement with the GIM values with mean difference and RMSE values less than 1 Total Electron Content Unit (TECU).

Maintaining good positioning performance has always been a challenging task for Global Navigation Satellite Systems (GNSS) applications in partially obstructed environments. A method that can optimise positioning performance in harsh environments is proposed. Using a carrier double-difference (DD) model, the influence of the satellite-pair geometry on the correlation among different equations has been researched. This addresses the critical relationship between DD equations and its ill-posedness. From analysing the collected multi-constellation observations, a strong correlation between the condition number and the positioning standard deviation is detected as the correlation coefficient is larger than 0·92. Based on this finding, a new method for determining the reference satellites by using the minimum condition number rather than the maximum elevation is proposed. This reduces the ill-posedness of the co-factor matrix, which improves the single-epoch positioning solution with a fixed DD ambiguity. Finally, evaluation trials are carried out by masking some satellites to simulate common satellite obstruction scenarios including azimuth shielding, elevation shielding and strip shielding. Results indicate the proposed approach improves the positioning stability with multi-constellation satellites notably in harsh environments.