# Intelligent Environment-Adaptive GNSS/INS Integrated Positioning with Factor Graph Optimization
## 4 Performance Assessment and Validation
### Experiment Results
#### 4.2.2 Integration Validation Using U-Blox Data  
The 2D trajectories of ground truth and different navigation solutions (i.e., GNSS, KF, AKF, FGO, and AFGO) are shown in Figure 7, while Figure 8 provides the 2D positioning error of these solutions along the whole path. Based on the results of the 2D solutions, the RMSE throughout 920 s and the standard deviation (STD) of the 2D errors are proposed for evaluation and are shown in Table 5 along with the information of the number of available GNSS epochs and integration time. The smaller the values of RMSE and STD, the more accurate the navigational solutions and the smoother trajectory there could be. Some features in U-Blox outcomes will be analyzed as the following. At all three junctions A, B, and C stated in Figure 5, the 2D trajectories in Figure 7 show observable drifts, and Figure 8 shows that the 2D positioning errors in the shaded junction periods increase compared with the surrounding epochs. Especially at junction C (roughly second 630-730), large drift and a 2D positioning error of over 350 m happens for integration methods when missing multiple GNSS epochs. This could be caused by the INS transition without a GNSS update, and error is thus accumulated with time elapsing. However, FGO and AFGO significantly outperform KF-based methods by avoiding the large drifts shown in the shaded area C in Figure 8. This can be connected with the advantage of FGO, which estimates states more precisely by considering all historical epochs. Additionally, although Figure 8 shows that the performance of the four GNSS/INS integration methods (i.e., KF, AKF, FGO, and AFGO) varies on the time frame, the overall RMSE and STD results in Table 5 proves that accuracy and smoothness improve across the integration methods (from KF to AFGO). Both RMSE and STD using AFGO are reduced to less than 33.3% of those based on KF. It is noted that the RMSE (26.39 m) and STD (22.30 m) of GNSS prove to be smaller than those of KF (70.18 m RMSE and 61.72 m STD) and AKF (66.84 m RMSE and 59.19 m STD). This is acceptable because only 852 epochs with available positioning information are evaluated in the GNSS solution. In contrast, as for integration  
Figure 7: Trajectories of different positioning solutions using U-Blox data, with the large drift at junction C being pointed out by the magenta arrow. methods, all 920 epochs are processed with either GNSS/INS coupling or INS propagation, thus inducing a larger calculated RMSE and STD. Moreover, the average computational time for each of the integration methods has been calculated using the equation:  
\[Average\ computational\ time=\frac{t_{total}}{920} \tag{30}\]  
where \(t_{total}\) refers to the total computational time for the GNSS/INS integration of 920 epochs. This decreasing update rate from KF to AFGO indicates an increasing total computational time. This coincides with our expectation that the FGO algorithm and adaptive uncertainty settings will take extra time. Notably, although the trajectory of this study covers multiple urban environments, it has the constraints of short duration (920 s in total) and a limited number of measured epochs (852 epochs). The evaluation for the other two receivers (i.e., Xiaomi and NovAtel) with similar cases will be discussed in the following paragraphs. Figure 8: 2D positioning errors of different positioning solutions using U-Blox data throughout 920 epochs with the periods at junctions A, B, and C being shaded in gray. The upper subplot depicts the full range of 2D errors, while the lower one shows the zoom-in view from 0 to 100 m.