# Vehicle Pose Estimation Method Based on Maximum Correntropy Square Root Unscented Kalman Filter
## 5 Results
### Simulation Results and Analysis
#### 5.1.2 The Stability Analysis of Different Algorithms  
In the fields of target tracking, navigation, and autonomous driving, the stability of filtering algorithms directly affects the accuracy and reliability of state estimation. Due to variations in motion speed, the system nonlinearity significantly increases, which may lead to substantial errors or even divergence in SLAM algorithms. Therefore, analyzing the stability of different algorithms under varying speeds holds significant theoretical and practical value.  
We conducted 100 Monte Carlo simulation experiments in low-speed (8 m/s), medium-speed (15 m/s), and high-speed (30 m/s) scenarios. The measurement noise was set as Gaussian mixture noise, while the state noise followed a Gaussian distribution. The Average Root Mean Square Error (ARMSE) and divergence count per 100 runs were used as evaluation metrics for algorithm stability. The experimental results are presented in Tables 4 and 5.  
As shown in Tables 4 and 5, the EKF-SLAM algorithm exhibits significant limitations in high-speed scenarios (30 m/s), with an error of 3.1131 m, an error growth rate of 216%, and a divergence rate of 25%. These empirical results conclusively validate the inherent shortcomings of linearization approximations when applied to highly nonlinear systems operating at elevated velocities. The UKF-SLAM algorithm demonstrates notable  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **ARMSE (8 m/s)** & **ARMSE (15 m/s)** & **ARMSE (30 m/s)** &
\begin{tabular}{c} **Error growth rate** \\ **(8\(\rightarrow\)30 m/s)** \\ \end{tabular} \\ \hline EKF-SLAM [13] & 0.9858 & 1.8040 & 3.1131 & 216\% \\ UKF-SLAM [20] & 0.8607 & 1.3159 & 2.3353 & 171\% \\ SRUKF-SLAM [23] & 0.8208 & 1.0231 & 1.4518 & 77\% \\ MCUKF-SLAM [39] & 0.7891 & 1.1233 & 1.8623 & 136\% \\ The proposed MCSRUKF-SLAM & **0.4655** & **0.5633** & **0.8039** & **73\%** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of average RMSE for various algorithms at different speeds (Unit: m).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **ARMSE (m)** & **Aerror\({}_{x}\) (m)** & **Aerror\({}_{y}\) (m)** & **Aerror\({}_{\phi}\) (rad)** \\ \hline EKF-SLAM [13] & 1.3783 & 0.6039 & 0.8841 & 0.0171 \\ UKF-SLAM [20] & 1.1340 & 0.4336 & 0.6119 & 0.0138 \\ SRUKF-SLAM [23] & 1.1091 & 0.4257 & 0.6005 & 0.0137 \\ MCUKF-SLAM [39] & 1.0767 & 0.4018 & 0.5903 & 0.0135 \\ The proposed MCSRUKF-SLAM & **0.6851** & **0.2734** & **0.3849** & **0.0123** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of average RMAE and average state estimation error for some SLAM algorithms in colored noise.  
improvements through unscented transformation, reducing the error by 25% compared to EKF at 30 m/s. However, its 171% error growth rate and 13% divergence rate still indicate insufficient adaptability to high-speed conditions. In contrast, SRUKF-SLAM exhibits excellent error control capabilities, achieving zero divergence across all speed ranges and maintaining a low error growth rate of 77%. The square-root decomposition effectively enhances its numerical stability. The MCUKF-SLAM algorithm demonstrates notable limitations in high-speed scenarios (30 m/s), where maintaining positive definiteness of the covariance matrix becomes challenging. This instability leads to significant estimation errors, reflected in a 136% error growth rate and an 8% divergence rate. The proposed MCSRUKF-SLAM algorithm achieves zero divergence across all speed ranges and delivers the best error growth rate (73%). These results confirm its superior numerical stability, as the square-root decomposition effectively addresses numerical ill-conditioning issues.