For realizing real-time GNSS PPP with smartphones, we developed a software based on the Android platform. In real-time processing, the software collects the raw GNSS measurement data from the embedded GNSS chip according to the Android Location API and also receives the real-time streams of the multi-GNSS broadcast ephemerides, the satellite orbit and clock correction products, and the ionospheric VTEC products from the Networked Transport of RTCM via Internet Protocol (NTRIP) Caster via NTRIP, and RTCM represents Radio Technical Commission for Maritime Services. After obtaining the required raw GNSS data, the code pseudoranges, carrier phases, and Doppler measurements are generated, and the received correction messages are decoded according to the RTCM standards. Then, the user’s precise positions can be estimated based on the above approaches. The used GNSS constellations and frequencies in our smartphone PPP processing software are GPS L1 + L5, Galileo E1 + E5a, GLONASS L1, and BDS B1I.

Based on this software, the two kinematic experiments presented in the datasets section were carried out in a real-time mode. The precise satellite orbit/clock corrections and the ionospheric VTEC product used were the real-time SSRA00CAS0 and IONO05CAS0 streams both provided by the Chinese Academy of Sciences (CAS). The reference trajectories of the experimental smartphones for the two vehicle-based kinematic tests were computed by post-processing the RTK data collected with the geodetic receivers, and only the fixed RTK solutions were used. Besides, the PVT (Position, Velocity, and Time) solutions of the experimental smartphones provided by the manufacturer were also collected for comparison. In this section, the positioning results of the two experiments obtained in the vehicle-roof and dashboard modes are compared and analyzed.

### Vehicle-roof mode experiment

For the vehicle-roof mode experiment, taking the Mate30_A and P40_A smartphones as the example, the positioning errors of real-time PPP and PVT results in the East (*E*), North (*N*), and Up (*U*) components are presented in Fig. 10 for Mate30_A and Fig. 11 for P40_A. The horizontal (*H*) and vertical (*V*) positioning errors of PPP and PVT results are also presented. To evaluate the positioning accuracy, the Root Mean Square (RMS) and the 95th percentile values of the positioning errors in horizontal and vertical components are calculated for the PPP and PVT results, as shown in Table 6. And the corresponding improvements of PPP solutions relative to PVT results are also computed and presented in the table. The symbol of the arrow “↑” in the table represents the improvement in the positioning accuracy of the PPP results relative to that of smartphones’ PVT solutions (the same below).

As shown in Fig. 10, the mean values of positioning errors of PVT solutions for the Mate30_A smartphone are 1.16, 1.15, and − 5.63 m in *E*, *N*, and *U* components respectively, and the corresponding RMS values are 1.95, 2.10, and 6.01 m. For the PVT results, the positioning errors fluctuate within 3–6 m in the horizontal component for most of the epochs, while in the vertical component the positioning errors are not only significantly large but also with a bias of about − 5.6 m. For the PPP solutions, the positioning errors in E and N components vary within ± 2.0 m, and in the U component within ± 4.0 m. The average positioning errors of PPP solutions in *E*, *N*, and *U* components are 0.08, 0.43, and 0 m, respectively, and the corresponding RMS values are 1.00, 0.94, and 1.30 m.

As shown in Fig. 11, for the PVT solutions of the P40_A smartphone, the RMS values of the positioning errors are 1.88 m in the E component, 2.16 m in the N component, and 4.59 m in the U component with the mean values of 0.28, 0.06, and − 3.92 m in the corresponding components. In addition, the horizontal positioning errors of PVT results fluctuate within 4 m for most of the epochs and the vertical positioning errors have a bias of about − 4 m, which is like the situation of the Mate30_A smartphone. For the PPP solutions, the absolute positioning errors are below 1.0 m in E and N components and within 3.0 m in the U component for most of the time. The average positioning errors in *E*, *N* and *U* directions are − 0.13, 0.06, and 0.47 m, and the corresponding error RMS values are 0.39, 0.57, and 1.22 m. Therefore, the PPP solution is not only obviously better than the PVT solution, but also without significant biases.

According to the statistical results summarized in Table 6, the positioning accuracy of PPP is around 1.0 m in the horizontal component and 1.5 m in the vertical component with the best being 0.69 m in the horizontal component with the P40_A smartphone. Compared with the horizontal and vertical RMS values of the PVT results, the improvement of PPP results with the Mate30_A smartphone is 52% in the horizontal component and 78% in the vertical component, and 52% and 63% in the corresponding components for the Mate30_B smartphone. For the two P40 smartphones, the improvement of PPP results is 46% in the horizontal component and 57% in the vertical component relative to the PVT results for the P40_B smartphone, while it reaches about 74% both in the horizontal and vertical components for the P40_A smartphone.

In addition, to compare the PVT and PPP results in terms of the 95th percentile, Table 6 shows that the positioning accuracy at the 95th percentile for the PPP results of the Mate30_A smartphone is 2.3 m horizontally and 2.7 m vertically with the improvement of 49% and 80%, respectively, relative to its PVT solutions. Similar to the Mate30_A smartphone, the horizontal and vertical positioning accuracy of PPP results of the Mate30_B smartphone is 2.0 and 3.1 m at the 95th percentile, respectively, and the corresponding improvement relative to its PVT solutions is 63% and 54% respectively. For the P40_B smartphone, the 95th percentile values of the horizontal and vertical errors of PPP results are 2.0 and 3.6 m, respectively, which are also similar to that of the Mate30_B smartphone, particularly in the horizontal component. As for the P40_A smartphone, its positioning accuracy in terms of the 95th percentile is 1.2 and 2.7 m in horizontal and vertical components with an improvement of 61% for both components, which is the best one among the four experimental smartphones. The above analysis tells that the real-time PPP results can achieve the horizontal accuracy of about 1 m level in terms of RMS and 1–2 m level at the 95th percentile for the vehicle-based kinematic positioning with a smartphone mounted outside the vehicle.

### Dashboard mode experiment

Like the analysis for the vehicle-roof mode experiment, the Mate30_A and P40_A smartphones are also taken as examples for illustration here. Figure 12 illustrates the error sequences of the real-time PPP solutions and the PVT results with the Mate30_A smartphone in the directions of *E*, *N*, and *U* components, and compares the PPP and PVT results in horizontal and vertical directions. Figure 13 shows the error sequences of the PPP and PVT results of the P40_A smartphone in *E*, *N*, and *U* directions, and compares the PPP and PVT results in horizontal and vertical directions. To evaluate the positioning performance, the values of RMS and the 95th percentile, and the corresponding improvements of PPP solutions relative to the PVT results in horizontal and vertical directions are summarized in Table 7.

As shown in Fig. 12, The absolute positioning errors of the PVT solutions of the Mate30_A smartphone mainly fluctuate within 2 and 4 m in the *E* and *N* components, respectively, however, the positioning error in the *U* component fluctuates greatly in the range of − 8 to 0 m. According to statistics, the mean values of the positioning errors in *E*, *N*, and *U* directions of the PVT solutions for Mate30_A smartphone are − 0.02, − 0.29, and − 2.69 m and the corresponding RMS values are 1.27, 1.56, and 3.96 m respectively. For the PPP solutions, the positioning errors generally vary within ± 2 m in the *E* and *N* components and within ± 3 m in the *U* component with the mean values of − 0.19, − 0.03, and − 0.62 m in *E*, *N*, and *U* directions, and the corresponding RMS values are 0.83, 1.06, and 1.70 m, respectively.

As can be seen from Fig. 13, the horizontal positioning errors of the PVT solutions for the P40_A smartphone vary within 6 m in the start period and then within 3 m, while the positioning error in the vertical direction fluctuates from − 8 to 2 m generally. According to statistics, the RMS values of the positioning errors of PVT solutions for the P40 smartphone are 1.88, 1.71, and 3.90 m in *E*, *N*, and *U* directions, respectively, and the average positioning errors in *E*, *N*, and *U* directions are − 1.42, − 0.57, and − 3.20 m, respectively. In contrast, the fluctuation of the positioning errors for the PPP solutions of P40_A smartphone is smoother within ± 2 m in the E and N components and within ± 3 m in the U component. The average PPP positioning errors in *E*, *N*, and *U* directions are − 0.05, 0.35, and − 0.50 m, and the corresponding RMS values are 0.54, 0.92, and 1.24 m, respectively. Therefore, the PPP solution is obviously better than the PVT solution, and there is no obvious systematic deviation.

According to the statistics given in Table 7, the RMSs of positioning results obtained based on real-time PPP are about 1.0–1.5 m in the horizontal direction and 1–2 m in the vertical direction, especially for the two P40 smartphones the RMS errors in horizontal and vertical directions are around 1.2 m. Compared with the horizontal and vertical RMS values of the PVT results, the corresponding improvements are 33% and 57% for the experimental Mate30_A smartphone, 34% and 44% for the Mate30_B smartphone, and 36% and 72% for the P40_B smartphone, respectively, while the P40_A smartphone gives a highest improvement of 58% and 68% in horizontal and vertical directions, respectively. The 95th percentile values are 2.3 and 3.4 m in horizontal and vertical directions for the PPP results of the Mate30_A smartphone, and the improvement is 31% and 52%, respectively, compared with the PVT solutions. The positioning accuracy of the PPP results of the Mate30_B smartphone is almost the same as that of the Mate30_A smartphone in terms of the 95th percentile. For the P40_B smartphone, the positioning accuracy at the 95th percentile is 2.6 m in the horizontal direction and 2.3 m in the vertical direction with the corresponding improvement of 35% and 69% relative to the PVT results. P40_A smartphone can achieve the highest positioning accuracy in terms of the 95th percentile among the four experimental smartphones with 1.9 m in the horizontal direction and 2.4 m in the vertical direction, improving by around 65% relative to its PVT results. In conclusion, the real-time PPP results can achieve a horizontal positioning accuracy of about 1–1.5 m in terms of RMS and better than 2.7 m at the 95th percentile for the vehicle-based kinematic positioning with the smartphone installed on the dashboard inside the vehicle, which is the practical application scenario in vehicle navigation.

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