# Intelligent Environment-Adaptive GNSS/INS Integrated Positioning with Factor Graph Optimization
## 4 Performance Assessment and Validation
### Experiment Results
#### 4.2.4 Integration Validation Using NovAtel Data  
Among the three receivers, NovAtel misses the most GNSS epochs. With only 622 remaining epochs available, integration methods using NovAtel data cost the shortest computational time as well. Among the three discussed receivers, although NovAtel with the lowest GNSS availability of 67.6% (i.e., 622/920) generates the highest RMSE and STD shown in Table 7, this receiver provides the closest fit trajectory to the ground truth as depicted in Figure 11 and the lowest 2D error according to Figure 12 when GNSS information becomes available. Likewise, the large positioning drifts of KF-based methods shown in Figure 11 are mitigated by the more robust FGO algorithm, and this significantly improves the accuracy and smoothness. This is reflected in Table 7, where the RMSE and STD levels of FGO and AFGO are approximately 10% of those in AKF and AKF, respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Metrics** & **GNSS** & **KF** & **AKF** & **FGO** & **AFGO** \\ \hline
2D RMSE[m] & 84.30 & 140.61 & 108.47 & 42.85 & 23.89 \\ \hline
2D STD[m] & 79.32 & 128.99 & 98.47 & 33.49 & 14.88 \\ \hline Number of epochs with available solutions & 795 & 920 & 920 & 920 & 920 \\ \hline Average computational time [s] & – & \(6.92\times 10^{-3}\) & \(7.01\times 10^{-3}\) & \(5.97\times 10^{-1}\) & \(6.33\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Overall evaluations on GNSS solutions and GNSS/INS integration, including KF, AKF, FGO, and AFGO, for the Xiaomi data.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Metrics** & **GNSS** & **KF** & **AKF** & **FGO** & **AFGO** \\ \hline
2D RMSE[m] & 10.36 & 424.52 & 358.47 & 40.26 & 38.20 \\ \hline
2D STD[m] & 8.24 & 374.62 & 320.72 & 33.61 & 31.00 \\ \hline Number of epochs with available solutions & 622 & 920 & 920 & 920 & 920 \\ \hline Average computational time [s] & – & \(6.54\times 10^{-3}\) & \(6.76\times 10^{-3}\) & \(5.65\times 10^{-1}\) & \(5.76\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Overall evaluations of GNSS solutions and GNSS/INS integration, including KF, AKF, FGO, and AFGO, for NovAtel data.  
For a more detailed analysis of the two existing drifts, at junction A (roughly second 110-130), neither a significant trajectory drift nor large 2D error occur, but these appear at junctions B (roughly second 290-350) and C (roughly second 630-730) given that many epochs with GNSS positioning are missing. Available GNSS epochs are particularly sparse around junction B, and the positioning performance of the NovAtel receiver is even negatively impacted after passing the crossroad (i.e., shaded area of Junction B in Figure 12). This even results in a larger error accumulated using the INS transition only, thus causing a large error in the position of the two-dimensional space.  
Figure 11: Trajectories of different positioning solutions using NovAtel data, with the large drift at junctions B and C being pointed out by the magenta arrow.  
Figure 12: 2D positioning errors of different positioning solutions using NovAtel data throughout 920 epochs, with the periods at junctions A, B, and C 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.  
more extreme positioning drift than those at the subsequent junction C. This comparison is reflected in the two large drifts in Figure 11 and the two peaks around roughly second 500 and 730 of Figure 12.