# An Analysis of Satellite Multichannel Differential Code Bias for BeiDou SPP and PPP
## 1 Introduction  
Since 31 July 2020, the third generation of BDS-3 independently developed by China has been providing all-weather, all-day, high-precision positioning, speed measurement and timing services for free to global users. GNSS hardware and physical limitations cause hardware delays in code and phase measurements during the signal's transmission from a satellite or reception in a GNSS receiver [1]. The transmitter links of navigation signals are different from frequency to frequency, and the parameter used to describe the difference in hardware delays between two different frequencies is called DCB [2]. Due to the difference in the signal structure, signal regime, signal modulation method, and frequency of different navigation systems, the observables are affected by DCBs at both the satellite and receiver terminals. Satellite DCB is usually called timing group delay (TGD), while receiver DCB iscalled inter-frequency bias (IFB) [3; 4]. The TGD parameters are broadcast in the navigation message. The IFB parameters are usually absorbed by the receiver clock or ambiguity parameters because the DCB at a certain signal at the receiver is the same for all satellites and is not considered when the receiver clock is an unknown parameter. The broadcast TGDs in navigation messages agree well (within about 2 ns) with the MGEX DCBs after zero-mean normalization, and these parameters have the equivalent beneficial effect on positioning [5]. The position accuracy of triple-frequency SPP with the BDS only was improved by 74.6% after DCB correction [6]. The positioning accuracy of dual-frequency SPP with B1I/B3I and B1C/B2a showed that the improvement range for horizontal components is 60.2% to 74.4%, and the vertical components improved by about 50% after the modification of TGD and DCB [7]. The DCB correction resulted in millimeter- to centimeter-scale improvements in static PPP and centimeter- to decimeter-scale improvements in dynamic PPP for both GPS and BDS [8]. Static PPP accuracy exhibited a millimeter-level improvement and accuracy was improved by about 10% after DCB correction [9]. The uncorrected code biases can pollute the receiver clock and carrier phase ambiguities and impede the rapid convergence of PPP [5]. The convergence of PPP with B1I/B3I and B1C/B2a can be accelerated by up to 50% when the DCBs are corrected [7]. With DCB products, the convergence time of single-frequency PPP with BDS-2 can also be shortened significantly [10]. Although the DCB had no influence on the accuracy of PPP with any ionosphere-free combinations, the convergence speeds were greatly improved by the TGD/DCB correction [11]. [PERSON] et al. demonstrated DCB slightly better than TGD and could also speed up the convergence of PPP with B1I/B3I [12]. These analyses of positioning accuracy and the convergence of PPP under different combinations of DCB and TGD are far from comprehensive and are worthy of further study. With the completion of BDS-3 and the upgrade to BDS ground receivers, more comprehensive observation data, navigation messages, and DCB products can be obtained, which provide a good basis for DCB research. In order to directly apply kinds of code bias to GNSS original observation data [13], directly describe the bias of individual pseudo-range measurements without difference, and reduce the associated redundant code bias, the Bias and Calibration Working Group (BCWG) established by the IGS advocates for the expansion of traditional DCB to the absolute parameter of OSB to adapt to multi-mode and multi-frequency GNSS applications and developments [14; 15]. Nevertheless, a comprehensive study of each signal channel of DCBs and OSBs is lacking in the existing literature. Furthermore, the stability, correlation, and influence of TGD and multichannel DCBs on BDS positioning are still unclear. There are few studies on the stability of the multichannel DCB of BDS-3 and its comparative analysis with OSB.