## 4 Experimental Analysis
### Experimental Results of IMMFGO
According to the changes in transition probability for different road sections, it is clear that when sensor accuracy decreases, the corresponding model probabilities also decre  
Figure 7: Trajectory diagram of four algorithms and three sections (unit. meters). interference on positioning results and improving positioning accuracy. To quantitatively evaluate the performance of our algorithm, we calculated the RMSE of each method. Table 2 shows the quantitative results of four algorithms. Figure 8: Schematic diagram of position error results of four algorithms. (**a–c**) are east, north, and vertical position error results, respectively. Table 2 shows that the 3D RMSE of EKF in global accuracy is 14.14 m. At the same time, FGO, optimized by combining historical measurement information, has a 3D RMSE of 10.18 m, which improved by 28% compared to EKF. AFGO and IMMFGO, with a weight adjustment trajectory based on FGO, have achieved certain improvements in positioning accuracy. The 3D RMSE of AFGO is 6.4 m, which improved by 37.1% compared to FGO. The 3D RMSE of IMMFGO is 4.88 m, which improved by 23.7% compared to AFGO, and the positioning results in the east, north and vertical directions have better performances. The experiment shows that compared to the AFGO algorithm, which can adjust weights through preset thresholds, IMMFGO has better performance in complex urban environments. On the basis of the traditional FGO algorithm, IMMFGO can better achieve precise positioning results for vehicles. The proposed system is based on the sensor with the lowest frequency for information fusion. In this experiment, the signal output frequency is 1 Hz, which can meet the positioning and robustness requirements of actual vehicle navigation systems. The comparison results with existing algorithms are shown in Table 3.  
Table 3 shows the performance of proposed algorithm and the previous IMU/GNSS/LiDAR integrated navigation algorithm [43]. In complex urban environments, GNSS or LiDAR alone for navigation tends to have poor performance. IMMFGO achieves better performance than traditional LIO-SAM algorithm because of poor GNSS performance and similar performance of optimal adaptive Integrated GNSS-RTK/LIO algorithm in complex urban canyons. Contrary to adaptive integrated GNSS-RTK/LIO which can only have good performance by testing different thresholds, IMMFGO algorithm evaluates the models \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Types of Error** & **EKF** & **FGO** & **AFGO** & **IMMFGO** & **Improvement** \\ \hline East & 8.07 & 8.16 & 3.66 & 2.85 & 22.1\% \\ North & 10.05 & 3.96 & 3.95 & 2.90 & 26.5\% \\ Vertical & 5.87 & 4.62 & 3.46 & 2.72 & 21.3\% \\
3D & 14.14 & 10.18 & 6.4 & 4.88 & 23.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMSE of the four algorithms and the improvement of IMMFGO to AGO (unit: meters). \begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **3D RMSE (m)** \\ \hline Alone GNSS & 42.02 \\ LIO-SAM & 19.89 \\ Adaptive Integrated GNSS-RTK/LIO \\ (\(el_{th}=90^{\circ},35^{\circ},15^{\circ}\)) & 25.33, 18.88, 4.12 \\ IMMFGO & 4.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: 3D RMSE of proposed algorithm and previous works. Figure 9: Results of the IMMFGO model transition possibility. based on the output of sub-models which does not rely on auxiliary information and has better environmental adaptability.