# Estimating BDS-3 Satellite Differential Code Biases with the Single-Frequency Uncombined PPP Model
###### Abstract
To address this issue, replacing expensive high-precision multi-frequency and multi-GNSS receivers with more affordable low-cost SF receivers can be advantageous in future planning. Leveraging the capabilities of cost-effective SF receivers makes it an attractive option to strike a balance between the need for dense station networks and the associated hardware costs. Nevertheless, the present dearth of relevant algorithms poses a challenge, creating an urgent demand for a cost-effective solution that can fulfill accuracy requirements. The development of such a low-cost solution would significantly enhance the feasibility of high-precision ionospheric modeling without incurring prohibitive hardware expenditures. Several publications have demonstrated the potential of SF receivers for retrieving VTEC and satellite DCBs. The code-minus-carrier (CMC) combination method, utilizing SF pseudorange and carrier phase observations, has been employed to model the VTEC for high- and mid-latitude stations. However, it is noteworthy that the precision of VTEC estimation is significantly impacted by multipath and pseudorange noises [19]. Alternatively, the SF uncombined PPP model demonstrates its efficacy in simultaneously estimating satellite DCBs and VTEC parameters using SF receivers. Remarkably, when applied to GPS L1 data collected by a single receiver, this model achieves daily estimates of satellite DCBs with absolute deviations of less than 1 ns from their ground truth values [8]. In addition, VTEC parameters retrieved from the SF uncombined PPP model exhibit comparable accuracy to those achieved through the commonly used DF method [18] and carrier-to-code leveling (CCL) method [20]. Previous studies on the SF uncombined PPP model have primarily focused on its application for VTEC estimation, while research on satellite DCBs has been limited to the GPS system. The primary contribution of this study is the estimation of BDS-3 satellite DCBs using SF receivers, taking advantage of the sufficient number of observable BDS-3 satellites. Throughout the process, special attention is paid to address the conversion of zero-mean conditions, particularly when the availability of observable satellites for receivers exhibits non-stationary behavior. Furthermore, this study thoroughly investigates the influence of station latitude on the accuracy and stability of the estimated BDS-3 satellite DCBs. Additionally, it examines the significant benefits and advantages of utilizing multiple SF receivers for the precise estimation of BDS-3 satellite DCBs. The paper is structured as follows: Section 1 is the Introduction, followed by Section 2 which introduces the methods and relevant theories for satellite DCBs estimation using the SF uncombined PPP model. Section 3 provides details about the experimental data used and the processing strategies employed. In Section 4, experimental evaluations are conducted using BDS-3 SF data from 25 IGS stations in March 2023. The BDS-3 satellite DCBs are estimated using both single receiver and multiple receivers based on the SF uncombined PPP. The accuracy of the estimated results is assessed by comparing them with the satellite DCB products provided by the Chinese Academy of Sciences (CAS). Section 5 summarizes the conclusions drawn from the experimental analysis.