# State Parameter Fusion Estimation for Intelligent Vehicles Based on IMM-MCCKF
## 4 Simulation Verification  
### Configuration of Simulation Experiment Environment  
A collaborative simulation was conducted using MATLAB/Simulink and the vehicle simulation program CarSim to assess the efficacy and accuracy of the IMM-MCCKF technique in estimating vehicle state parameters. Starting with a C-class car model from CarSim, building an electric vehicle model with distributed drive. Additionally, a drive motor model was constructed using MATLAB/Simulink. The simulation sampling time was configured to 0.001 s, which allowed for the input of sensor signals necessary for estimating the vehicle's state in Simulink. Furthermore, non-Gaussian noise was introduced into the sensor input signals to assess the algorithm's estimation performance under non-Gaussian noise conditions. Table 1 contains the whole set of parameters for the C-class vehicle model, and Figure 3 shows the procedure of the estimate algorithm.  
An IMM-MCCKF vehicle state parameter estimator was developed in MATLAB/Simulink and designed to test two vehicle operating scenarios: double lane-change and sinusoidal steering. While maintaining consistent input parameters, the MCCKF and CKF algorithms were compared in simulation experiments.  
The Markov transition matrix in this paper is configured according to Equation (64):  
\[p=\begin{bmatrix}0.98&0.01&0.01\\ 0.01&0.98&0.01\\ 0.01&0.01&0.98\end{bmatrix} \tag{64}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Abbreviation** & **Parameter Name** & **Value** \\ \hline \(a\) & The distance from the front axle to the center & 1.015 m \\ \(m\) & Mass of vehicle of gravity & 1270 kg \\ \(w\) & Track width & 1.675 m \\ \(b\) & Distance from the front to the rear to the chassis’s & 1.895 m \\ \(h_{cgg}\) & Height of the center of gravity & 0.54 m \\ \(R\) & Effective radius & 0.325 m \\ \(I_{z}\) & Yaw moment of inertia & 1536.7 kg\(\cdot\)m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The simulation parameter table for a C-class vehicle in CarSim.  
Figure 3: IMM-MCCKF workflow diagram.  
During the actual operation of the vehicle, sensor measurements can be affected by outliers, rendering sensor noise typically non-Gaussian. This paper models the sensor signals that occur during the operation of a vehicle. The system's process and measurement noise assumes a non-Gaussian distribution with heavy tails. The model adheres to the specified covariance matrix criteria.  
\[\begin{array}{rcl}Q&\sim&0.20,v_{k}&\sim&0.8N(0,0.001)+0.2N(0,1)\\ Q&\sim&0.20,w_{k}&\sim&0.8N(0,0.001)+0.2N(0,1)\end{array} \tag{65}\]  
Considering the uncertainty in process and measurement noise during actual vehicle operation, different noise levels are empirically assigned to the submodels of the IMM-MCCKF algorithm as follows:  
\[\begin{array}{rcl}Q_{1}&=&diag([0.208,0.208,0.208])\\ R_{1}&=&diag([0.208,0.208,0.208])\\ Q_{2}&=&10Q_{1},R_{2}=10R_{1}\\ Q_{3}&=&100Q_{2},R_{3}=100R_{2}\end{array} \tag{66}\]  
where 1, 2, and 3 represent submodel 1, submodel 2, and submodel 3, respectively.  
Both submodels have process and measurement noise that is ten and a hundred times higher than the original model. This paper compares the MCCKF and CKF algorithms using noise parameters that align with submodel 1 of the IMM-MCCKF. The system state and measurement equations are also consistent with the IMM-MCCKF.