## 3 Distributed Drive Vehicles Based on MCSRCKF
### Experimental Results and Analysis
#### 4.2.1 Double-Lane Change Condition  
Simulations are performed at an initial vehicle velocity of 90 km/h on a structured pavement, and the adhesion coefficient is set to 0.85. Equations (58) to (59) denote the initial values for the system noise, and the equations shown below express the initial state vector values with their corresponding covariance matrices:  
\[x_{0}=[90/3.6,0,0,90/3.6/R_{0},90/3.6/R_{0},90/3.6/R_{0},90/3.6/R_{0}] \tag{62}\]  
\[P=diag([0.01,0.01,0.01,0.01,0.01,0.01,0.01]) \tag{63}\]  
The driving trajectory, input signals, and observed signals for the estimator are given in Figure 3, and Figure 4 compares the simulation data of the CKF, SCKF, and MCSRCKF in estimating the vehicle state.  
From Figure 4a, it can be observed that the longitudinal speed estimation of the SCKF is better than that of the CKF for this condition, which is because the QR decomposition used by the SCKF replaces the Cholesky decomposition and suppresses the filtering divergence problem arising from the non-positive timing of the covariance matrix. From Table 3, it can be seen that the RMSE of the SCKF is to some extent reduced compared to the CKF, and the RMSE of the MCSRCKF is further reduced compared with the former two. Comparing with the SCKF, the vehicle speed in the longitudinal and lateral directions,respectively, decreased 40.8% and 20.2%, the yaw rate decreased 34%, and the estimated curve of the MCSRCKF is closest to the true value. The reason is that the algorithm uses the discrepancy between the sensor measurements and the true values to construct the MCC's cost function and calculate the matrix of measurement error when the measured value has the strongest correlation with the real value, achieving a real-time update of measurement noise. Therefore, compared with CKF and SCKF, which set the noise to a constant value, MCSRCKF is more adapted to estimate the driving state of distributed drive vehicles in a strongly nonlinear non-Gaussian noise environment by estimating the current measurement noise in real time.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index** & **Parameters** & **CKF** & **SCKF** & **MCSCKF** \\ \hline \multirow{3}{*}{MAE} & \(v_{\mathrm{x}}(\mathrm{m/s})\) & 0.2911 & 0.2128 & 0.1247 \\  & \(v_{\mathrm{y}}(\mathrm{m/s})\) & 0.0396 & 0.0327 & 0.0262 \\  & \(r(\mathrm{rad/s})\) & 0.0075 & 0.0063 & 0.0041 \\ \hline \multirow{3}{*}{RMSE} & \(v_{\mathrm{x}}(\mathrm{m/s})\) & 0.3371 & 0.2375 & 0.1407 \\  & \(v_{\mathrm{y}}(\mathrm{m/s})\) & 0.0572 & 0.0486 & 0.0388 \\ \cline{1-1}  & \(r(\mathrm{rad/s})\) & 0.0113 & 0.0094 & 0.0062 \\ \hline \hline \end{tabular}
\end{table}
Table 3: MAE and RMSE of various algorithms under the Double-lane change condition.  
Figure 3: Double-lane change condition: (**a**) Driving trajectory of vehicle; (**b**) front wheel angle; (**c**) longitudinal acceleration; (**d**) lateral acceleration.  
Figure 4: Simulated vehicle state results in case of the Double-lane change condition: (**a**) longitudinal speed; (**b**) lateral speed; (**c**) yaw rate; (**d**) Rotation speed of left front wheel; (**e**) Rotation speed of right front wheel; (**f**) Rotation speed of left rear wheel; (**g**) Rotation speed of right rear wheel.  
From Figure 4b lateral speed, Figure 4c yaw rate, and Figure 4d-g four wheel rotational angular speed, it can also be seen that the yaw rate changes sharply when the vehicle turns and changes lanes at high speed, and there is a high risk of outliers in the measured data. The noise near the outliers presents a heavy-tailed characteristic, which leads to large errors in the CKF and SCKF at the peak. At this time, MCSRCKF can deal with the influence of discrete points on the estimator and make the results more convergent to the true value, which has strong robustness.