Multi-GNSS and multi-type observable-specific code bias calibration method: a generalized model across diverse satellite clock datums

With the emergence of new frequencies and observable types of Global Navigation Satellite Systems (GNSS), code bias represented as observable-specific code bias (OSB) has proven to be an effective solution for flexibly achieving consistency across different signals. Since code bias products and precise clock products should be used consistently, satellite clock datums must be taken into account when generating or applying OSB products. An effective approach is to align code bias products with the clock datums of the corresponding precise clock products prior to precision point positioning (PPP). However, the cross-datum calibration model for OSB has not yet been studied. This study proposes a generalized OSB calibration method applicable across diverse satellite clock datums, accommodating multiple frequencies and diverse observable types. To achieve this, multi-GNSS OSBs are estimated using the derived uncombined model, leveraging precise products from four International GNSS Service Analysis Centers. Experiments demonstrate that OSB estimates derived from different clock products exhibit a systematic bias of up to 2 ns, which is related to clock datums originating from the initial satellite clock bias. For each frequency and observable type, differences in OSB estimates exhibit a strong negative correlation with differences in initial satellite clock bias. The slope of this linear correlation is determined via regression analysis, and serves as the core coefficient for formulating the OSB calibration model. Kinematic PPP experiments are performed under various constellation configurations to verify the efficacy of the proposed model. After calibration, the average three-dimensional root-mean-squares of positioning errors are reduced by approximately 14.9%, 2.0%, and 2.6% for BDS-3, BDS-3 + GPS, and BDS-3 + GPS + Galileo solutions, respectively, due to different OSB variations related to the clock datum. It is therefore recommended users apply this OSB calibration method prior to PPP, especially for BDS-3.