# Estimating BDS-3 Satellite Differential Code Biases with the Single-Frequency Uncombined PPP Model
###### Abstract  
Differential Code Bias (DCB) is a crucially systematic error in satellite positioning and ionospheric modeling. This study aims to estimate the BeiDou-3 global navigation satellite system (BDS-3) satellite DCBs by using the single-frequency (SF) uncombined Precise Point Positioning (PPP) model. The experiment utilized BDS-3 B1 observations collected from 25 International GNSS Service (IGS) stations located at various latitudes during March 2023. The results reveal that the accuracy of estimating B1I-B3I DCBs derived from single receiver exhibits latitude dependence. Stations in low-latitude regions show considerable variability in the root mean square (RMS) of absolute offsets for satellite DCBs estimation, covering a wide range of values. In contrast, mid- to high-latitude stations demonstrate a more consistent pattern with relatively stable RMS values. Moreover, it has been observed that the stations situated in the Northern Hemisphere display a higher level of consistency in the RMS values when compared to those in the Southern Hemisphere. When incorporating estimates from all 25 stations, the RMS of the absolute offsets in satellite DCBs estimation consistently remained below 0.8 ns. Notably, after excluding 8 low-latitude stations and utilizing data from the remaining 17 stations, the RMS of absolute offsets in satellite DCBs estimation decreased to below 0.63 ns. These enhancements underscore the importance of incorporating a sufficient number of mid- and high-latitude stations to mitigate the effects of ionospheric variability when utilizing SF observations for satellite DCBs estimation. differential code bias; BeiDou-3 global navigation satellite system; single-frequency; precise point positioning; zero-mean condition 20232379  
parameters are closely lumped [6; 7], and their estimation is often performed simultaneously [8; 9; 10]. Hence, any inaccuracies in the ionospheric modeling may propagate into errors in the estimation of satellite DCBs using this approach. The second approach involves utilizing external high-precision ionospheric products, such as the Global Ionospheric Map (GIM), to constrain the Vertical Total Electron Content (VTEC) parameters [11; 12]. The satellite DCBs are then estimated based on the fixed VTEC values. However, the accuracy of this method heavily relies on the quality of the external ionospheric products [13; 14]. Typically, GIM products offer an overall accuracy of only 2-8 TECU [8]. Therefore, this study will focus on estimating both the satellite DCBs and the ionospheric model parameters. Securing highly precise ionospheric observables from BDS observation data is of utmost importance, serving as a crucial prerequisite to achieve accurate and reliable estimations of satellite DCB parameters [15]. The substantial increase in the number of BDS-3 satellites compared to BDS-2 provides a greater abundance of observations for conducting ionospheric inversion. This enhanced satellite constellation facilitates the attainment of high-precision estimates of VTEC and satellite DCBs through the utilization of BDS-3 signals. The increased spatial and temporal coverage afforded by BDS-3 enables more accurate and reliable ionospheric modeling, leading to improved VTEC and satellite DCBs estimation capabilities [16]. However, this advanced level of ionospheric modeling is heavily dependent on the utilization of datasets collected from a dense network of ground-based receivers, which provides a large volume of data for precise analysis and reconstruction of the ionospheric electron density distribution. The globally distributed IGS reference stations equipped with dual-frequency (DF) receivers were primarily established for geodetic applications. The current number of GNSS reference stations is insufficient to adequately support space-atmosphere studies, particularly for tropospheric and ionospheric sensing applications [17; 18]. To achieve high-precision ionospheric modeling, a denser network of reference stations is required, which can lead to increased hardware costs.