###### Abstract
This means that the positioning performance using dual-frequency ionosphere-free PPP is difficult to maintain at a high accuracy. This fact results in it being the case that single-frequency PPP is still the most available precise positioning mode for most smartphones. In addition, the inconsistent clocks in the carrier phase and pseudo-range in smartphones resulted in inconsistent pseudo-ranges and carrier phase observations [3]. Such inconsistencies have been resolved by [PERSON] et al. (2021) and [PERSON] et al. (2019) by setting independent receiver clock biases for the pseudo-range and carrier phase in [2; 17]. [PERSON] et al. (2023) demonstrated that such inconsistencies can also be recovered by adjusting the phase or using only the first value of the FullBiasNanos while generating a pseudo-range [18]. Currently, many studies have been performed to improve the accuracy of smartphones through post-processing models. For example, by using a Hatch-filtering-based carrier-phase-smoothed pseudo-range, the positioning accuracy based on the double-differenced pseudo-range with this carrier phase smoothing technique is less than 5 m [19]. According to the work in [20], the positioning accuracy based on smartphones' pseudo-ranges can be improved by more than 50% after introducing the velocity-aided constraint. While using the PPP mode, positioning accuracies in the horizontal and vertical components are approximately 0.37 m and 0.51 m [21]. While employing a C/N\({}_{0}\) weight function method in the positioning mode based on the fusion of the pseudo-range, carrier phase, and Doppler observations, a higher positioning accuracy can be achieved. Specifically, such an approach can obtain positioning accuracies of 0.6 m and 1.4 m in the horizontal direction and vertical direction, respectively [22]. Meanwhile, it has also been indicated that the C/N\({}_{0}\)-dependent weight function model is more effective than the satellite elevation-dependent weight function for a smartphone positioning system [23]. However, smartphones need high-accuracy positioning services in real time rather than in post-processing. Theoretically, two GNSS data processing schemes can fulfil this purpose. The first one is to receive the real-time orbit/clock products from one of the IGS centers via the internet, and the other one is to use the BDS PPP-B2b service from satellites. Significantly, the satellite-based PPP-B2b service provided by BDS will not rely on the internet and is much more useful for smartphone-based positioning applications. At present, the BDS PPP-B2b service only provides precision orbit/clock corrections for BDS-3 and GPS satellites, and introductions on the system design, signal structure, data format, and encoding method of BDS PPP-B2b products can be found in [24]. The update interval of the BDS PPP-B2b clock correction is normally 6 s, while the update interval for other information (i.e., orbit) is 48 s [25]. [PERSON] et al. (2018) evaluated the performance of the static PPP based on the BDS PPP-B2b service using four IGS stations' data, providing positioning accuracies of 0.3 m and 0.6 m in the horizontal and vertical directions, respectively [26]. Similarly, [PERSON] et al. (2024) analyzed the accuracy of the real-time orbit/clock products from the BDS PPP-B2b service and an IGS center (CNES), and also evaluated the impacts of these products on the PPP accuracy [27]. The results illustrated that the PPP-B2b service can provide centimeter-level and decimeter-level positioning accuracy in China and its surrounding areas. [PERSON] and [PERSON] (2025) also analyzed the positioning accuracy of a PPP-B2b-based PPP in vehicle applications [28], and positioning accuracies of about 0.5 m and 3.0 m in the horizontal and vertical components were obtained. Accordingly, it is possible to obtain a decimeter-level positioning accuracy by using the BDS PPP-B2b service.