###### Abstract  
The global system of BDS (BeiDou Navigation Satellite System), i.e., BDS-3, is characterized with a multi-frequency signal broadcasting capability, which was demonstrated as beneficial for GNSS (Global Navigation Satellite System) data processing. However, research on real-time BDS-3 clock estimation with multi-frequency signals is quite limited, especially for the new BIC and B2a signals. In this study, we developed models for BDS-3 multi-frequency real-time data processing, including the uncombined model for clock estimation and the GFIF (Geometry-Free Ionosphere-Free) combined model for IFCB (Inter-Frequency Clock Bias) determination. Based on the models, simulated real-time numerical experiments with about 80 global IGS (International GNSS Service) network stations are conducted for validation and analysis. The results indicate that: (1) the uncombined model with multi-frequency signals can achieve comparable accuracy with the traditional dual-frequency IF model in terms of clock estimation, and the double-differenced clock STDs (Standard Deviations) are generally less than 0.05 ns with post-processed clocks as a reference; (2) unlike the BIC and B1I/B3I signals, the satellite IFCBs generated from multi-frequency clock estimation show apparent temporal variations for B2a and B1I/B3I signals, further investigation with GFIF models confirm the variations mainly result from the errors of receiver antenna corrections. Therefore, we addressed the feasibility of the uncombined model and the importance of accurate antenna information in the multi-frequency data processing.  
real-time; BDS-3; clock; inter-frequency clock bias; multi-frequency; uncombined model +
Footnote †: journal: remote sensing
However, with more signals involved, the processing complexity increases accordingly since more linear combinations can be formed. Therefore, the UC (Un-Combined) model is preferred over the IF combined model in multi-frequency data processing [12; 13].  
The BDS, as a constellation transmitting multi-frequency signal, has gone through three phases, including the experimental system BDS-1, the regional system BDS-2, and the global system BDS-3. The BDS-3, completed in July 2020, consists of 24 MEO satellites, three IGSO satellites, and three GEO satellites, among which, the MEO and IGSO satellites are broadcasting OS (Open Service) signals on five distinct frequency bands [14; 15]: legacy B1I (1561.098 MHz) and B3I (1268.520 MHz), and new B1C (1575.420 MHz), B2a (1176.450 MHz) and B2b (1207.140 MHz). In [11], the contribution of BDS-3 multi-frequency signals on PPP integer ambiguity resolutions was investigated. In [16], BDS-3 precise orbit determination with B1C and B2a dual-frequency signals was assessed. In [17], the real-time BDS-2/BDS-3 combined clock estimation with overlapping B1I and B3I signals was analyzed. However, the aforementioned research is limited to either IF combination or B1I and B3I signals.  
In this study, we will develop the UC model for real-time BDS-3 clock estimation with multi-frequency signals and assess the consistency of BDS-3 multi-frequency signals with the GFIF (Geometry-Free Ionosphere-Free) combination [18]. Since receivers with the B2b signal track capability are quite limited for the current IGS network, the following models and experiments will be restricted to the other four signals, i.e., B1I/B3I/B1C/B2a. The remainder of this paper is organized as follows. After a detailed derivation of mathematical models for real-time BDS-3 clock estimation with UC multi-frequency signals, simulated real-time numerical experiments with IGS network observation data will be conducted and analyzed. Finally, some conclusions and suggestions will be given.