# Estimation of Skid-Steered Wheeled Vehicle States Using STUKF with Adaptive Noise Adjustment
## 5 Experiment Results and Analysis
### Turning Driving Condition at Low Speed  
In this study, we emphatically discuss the vehicle state estimation in turning conditions. In this experimental condition, the test vehicle turns at a low speed (about 5 km/h) and turns at a 0.2 rad/s. The vehicle moving trace is shown in Figure 8. Figure 8 shows that the turn radius is about 7 m. The vehicle moves in a counterclockwise direction. Figure 9 shows the longitudinal state of the vehicle when it turns. The two estimation algorithms show almost no difference when the longitudinal velocity changes slightly. The longitudinal slip rate of the right side is positive because the right left is the outside wheels which are in the skidding condition. Similarly, the left side is the inside wheels which are in the slipping condition. When a skid-steered wheeled vehicle turns, the speed difference between the wheels on the sides would lead to a large tire slip rate even though the vehicle is moving on the ground with a high adhesion coefficient. Figure 8: The skid-steered wheeled vehicle moving trace when it turns. The lateral velocity, yaw rate, and tire sideslip angle estimation results are shown in Figure 10. The two estimation algorithms perform almost similarly when observing yaw rate, because yaw rate is the measurement value. In this study, the yaw rate calculated by the encoders' data is also compared with the observer result which is the cyan line shown in Figure 10. The calculated result by the encoder is larger than the real values because it ignores the longitudinal slip rate. The result calculated by encodes verifies that simple longitudinal velocity and yaw rate calculating method only using an encoder is not accurate enough when the vehicle driving is in strong nonlinear conditions. The lateral velocity estimation result by AN-STUKF is more accurate than the results estimated by the traditional UKF. The AN-STUKF shows higher accuracy than the traditional UKF when the vehicle drives in strong nonlinear conditions. The sideslip angle of tires is calculated by (6). As shown in Figure 11, all the sideslip angles are negative, which expresses that all the tire cornering directions are negative to the \(y\)-axis. The sideslip angles indicate that the middle and rear axes are obviously in a nonlinear condition. The tires on the rear axis are out of the sideslip limit, which is usually about 30 degrees [47]. A large sideslip angle indicates that the tires are in a severe lateral slip condition. This driving condition should be avoided. One reason is that lateral sideslip of tire would damage the tire. Another reason is that a large sideslip angle would require the tire to work in a severe nonlinear condition, which creates difficulty in control. Figure 11 shows the tire marks of a skid-steered wheeled vehicle driving in turning and straight conditions. The tire is obviously skidid  
Figure 10: The lateral state when a skid-steered wheeled vehicle turns in a small radius. Figure 9: The longitudinal state when a skid-steered wheeled vehicle turns in a small radius. The sideslip angle of vehicle body is calculated by:  
\[\beta=\arctan\biggl{(}\frac{\dot{y}}{\dot{x}}\biggr{)} \tag{40}\]  
The sideslip angles of the vehicle body estimation results are shown in Figure 12. The AN-STUKF performs better than the traditional UKF in sideslip angle observing, especially in nonlinear conditions. The sideslip angle of a skid-steered wheeled vehicle when it turns at a small radius would become quite large, which would cause a negative effect on vehicle stability control. Table 2 shows the error analyses of the small radius turning driving condition for the two estimations. The relative error used the data from 20 to 40 s to avoid the influence of values close to zero. The proposed AN-STUKF performs much better than the traditional UKF in all error evaluation indexes.