Estimation of code observation-specific biases (OSBs) for the modernized multi-frequency and multi-GNSS signals: an undifferenced and uncombined approach

For a long time, code biases of global navigation satellite system (GNSSs) have been parameterized and presented in the differential mode, namely the commonly-known differential code biases (DCB). However, with the continuous modernization of the existing constellations and rapid developments of the new systems, various new frequencies and types of GNSS signals are emerging, which makes the traditional DCB mode less flexible and efficient to handle the new situations and challenges. Recently, code biases in observation-specific representation, which finally provides observation-specific biases (OSBs), turns out to be a good solution and is gradually accepted by the GNSS community, though existing products are generated based on routine procedures and few studies concentrate on the new methods. In view of it, this study aims to propose a rigorous, flexible and efficient approach of OSB estimation for the modernized multi-frequency and, multi-GNSS signals. To achieve this, instead of being-based on linear combinations of raw observations in the existing literature, an extended multi-frequency geometry-free model is first established based on undifferenced and uncombined observations, which can adapt to observations of arbitrary frequencies and types in a compatible and flexible way and is used to extract the various types of linear combinations of the interested OSBs. Then, regarding the previously-obtained linear combinations as virtual observables after station-based ionosphere modeling, all OSB parameters are setup and estimated in a single normal equation, during which a clear identification and elimination of the rank deficiencies in the linear system is carefully conducted by introducing different types of constraints. The proposed new method is validated with one month of real data to generate totally 32 types of OSBs for GPS, GLONASS, Galileo, BeiDou, and QZSS. The estimated OSBs are compared with existing OSB and DCB products from other agencies. Results indicate that the proposed method can be used as a flexible and precise method for full-constellation and full-type OSB estimation.