Estimation and analysis of GNSS specific-observation biases using constrained rank-deficient virtual observation algorithm

This paper initially introduces two algorithms for the constrained rank-deficient indirect adjustment model and validates their equivalence. Subsequently, using DCBs provided by the Chinese Academy of Sciences (CAS) and the German Aerospace Center (DLR) as observed values, and CAS-provided OSBs as reference values, the accuracy of the virtual observation algorithm is verified. The results indicate that the average Root Mean Square (RMS) values between the estimated OSB value obtained based on CAS's DCB and the reference value is mostly below 0.1 ns. The average RMS values between the OSB estimates derived from DLR's DCBs for GPS, GLONASS, BDS, and Galileo compared to the reference values are 0.31 ns, 0.37 ns, 0.55 ns, and 0.24 ns, respectively, demonstrating a good level of consistency. This further validates the accuracy of the algorithm.