# Native Smartphone Single- and Dual-Frequency GNSS-PPP/IMU Solution in Real-World Driving Scenarios
## 4 Results Analysis
### Kinematic Performance Assessment with Different Processing Strategies
#### 4.2.1 Single-Frequency PPP-IC/IMU Processing  
Figure 7a illustrates the horizontal error (with respect to the reference solution) comparison for SF-PPP (GREC) processing. To better appreciate the impact of the IMU measurements, the positioning solutions processed with PPP-only, tightly-coupled PPP/MIS IMU, and PPP/Xsens IMU integration are represented as red, blue, and green lines, respectively, and the EKF horizontal position precision estimates are included in comparison to the real horizontal position errors with the same time series. The two black rectangles mark the two aforementioned outages (A and B). As expected, the horizontal errors relying on GNSS alone for GNSS PPP (red line) increase sharply when the vehicle passes through these sky obstructions. Correspondingly, it can be observed from Figure 7b that the horizontal precision estimated by the EKF increases significantly at elapsed times 5.5 and 15.4 min, proving that the EKF estimated precision is sensitive to the GNSS outages. However, the magnitude of the precision level from the outages was significantly higher compared to the actual errors, reflecting that the estimated precision cannot serve as the representative of actual position error.  
In contrast, the tightly-coupled PPP/IMU processing approach significantly mitigates the positioning errors during the outages, especially with the aid of Xsens IMU and to a lesser extent with the smartphone IMU. In addition, 4% improvements from estimated precision can be observed as well when integrating IMUs. Table 3 provides the horizontal error summary statistics from the different sensor fusion combinations. The horizontal position standard deviation (about the mean) error statistics shows the repeatability of the estimates, which are reduced from 6.0 m with just GNSS PPP measurements to under 1 m when either IMU's measurements are incorporated. Importantly, the rms (i.e., the accuracy) of SF-PPP solution is improved from 6.3 m to 1.7 m and 1.6 m by integrating the smartphone and Xsens IMU, respectively. The IMU provides little gain for 95 th percentile error as the tightly-coupled PPP/IMU solutions depend heavily on GNSS in open-sky  
Figure 7: Horizontal error with respect to the reference trajectory and filter estimated precision comparison for single-frequency PPP processing using smartphone GNSS measurements, GNSS + IMU measurements, and GNSS and Xsens IMU measurements. (**a**) Horizontal position error. (**b**) Horizontal precision estimate.  
environments, implying the fusion strategy did no harm to the PPP solutions when visible satellites are sufficient. However, the IMU significantly constrains the maximum error (100 percentile) when GNSS measurement limitations are most sensitivity to position estimation. In addition, Table 4 quantifies the error growth with respect to the outage time during Outage B. Owing to insufficient satellites, the horizontal positioning performance of traditional SF-PPP degrades significantly and the error exceeds 100 m when the elapsed time is 925 s. In contrast, maximum horizontal errors of 5.8 m and 2.4 m can be observed when the vehicle passed through Outage B with the aid of smartphone and Xsens IMUs, respectively. Refs. [25; 26] show similar smartphone SF-PPP positioning performance through kinematic vehicle experiments, but solutions are improved significantly by integrating IMUs in this study.