## 4 Experimental Analysis
### Experimental Results of IMMFGO  
To evaluate the performance of IMMFGO, we compare four algorithms, namely EKF, FGO, AFGO [41], and IMMFGO, and all apply the IMU/GNSS/LiDAR loose-coupled navigation system as the same sensors. During the experiment, the GNSS signal may be interrupted in special road sections, and LiDAR may be affected by the outside environments. Additionally, AFGO and IMMFGO have additional parameters for adaptive \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sources** & **Parameter Types** & **Parameter Values** \\ \hline \multirow{3}{*}{Xsens-Mti-10 IMU} & Frequency & 100 Hz \\  & Gyroscope random drift error & 18 \({}^{\circ}\)/h \\  & Accelerometer random drift error & 15 \(\upmu\)g \\ \hline U-blox M8T & Frequency & 1 Hz \\ GNSS receiver & Positioning accuracy & 2.5 m \\ \hline \multirow{3}{*}{HDL-32E Velodyne LiDAR} & Frequency & 10 Hz \\  & Measurement Range & 80 m \\ \cline{1-1}  & Range Accuracy & 2 cm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vehicle navigation platforms and sensors information. Figure 6: The platform and trajectory of vehicle experiment collected in the urban canyon. (**a**) The vehicle navigation platform and distribution of sensors; (**b**) the trajectory of the vehicle experiment and division of different road sections based on environmental characteristics. optimization. The GNSS threshold is set as 2 m and the LiDAR threshold as 1.5 m for the AFGO algorithm, while the number of sub-models of the IMMFGO algorithm is 2, namely the GNSS navigation sub-model and the LiDAR navigation sub-model. The initial transition probability from GNSS to LiDAR is set as 0.9. The trajectory results of the four algorithms are shown in Figure 7.  
As shown in Figure 7, the black solid line represents the reference trajectory. The purple, blue, and green dashed lines represent the trajectory results of EKF, FGO, and AFGO, respectively. The solid red line represents the proposed IMMFGO algorithm. In case of gradually increasing interference in section (1), the positioning results of the proposed IMMFGO algorithm and the traditional FGO algorithm are better. The AFGO algorithm may produce specific errors in the positioning results due to the fixed threshold. In case of stable errors during section (2), the AFGO and IMMFGO algorithms can adaptively adjust sensor weights and achieve good global estimation performance, while the trajectory of the traditional FGO algorithm will be smoothed through global optimization with lower positioning accuracy. In case of sudden interference during section (3), the IMMFGO algorithm can adjust the weights of sensors, thus obtaining better positioning results than the AFGO algorithm, since the threshold set by the AFGO algorithm is unsuitable for unknown sudden faults. Then, east, north, and vertical position errors of different road sections are shown in Figure 8.  
From the trajectory positioning results in Figure 7 and the position errors in Figure 8, it can be seen that both EKF and FGO are strongly affected by external interference, leading to decreased positioning accuracy. However, the trajectory of the FGO algorithm can be optimized through historical information, thereby improving specific performance. Compared to other algorithms, AFGO and IMMFGO have the ability to adaptively optimize the weights in case of interference. While the AFGO algorithm is based on a fixed detection threshold according to personal experience, and its performance is poor in dynamic or sudden interference situations, the proposed IMMFGO algorithm changes sensor weights based on sensor performance and environmental changes, of which the threshold is adaptively adjusted, resulting in good performance under different interference conditions. The probability transition results of the IMMFGO algorithm are shown in Figure 9.  
Figure 9 shows the transition probability of the IMMFGO sub-models. IMMFGO can reduce the impact of environmental interference on positioning accuracy by switching model probabilities, which has good results in global positioning.