# Research on an Energy Recovery Strategy for Fuel Cell Commercial Vehicles Based on Slope Estimation
## 5 Experimental Simulation and Conclusions
### Slope Estimation Algorithm Validation
#### 5.3.2 Identification Results and Error Analysis  
Internationally, road slope classifications mainly include the following categories: normal slope ranging from 0\({}^{\circ}\) to 0.5\({}^{\circ}\), slight slope from 0.5\({}^{\circ}\) to 2\({}^{\circ}\), gentle slope from 2\({}^{\circ}\) to 5\({}^{\circ}\), and moderate slope from 5\({}^{\circ}\) to 15\({}^{\circ}\). In the Cruise2019 simulation software, road conditions  
Figure 10: (**a**) Acceleration filtering effect and (**b**) slope variation in variable slope.  
with gentle slopes and variable slopes were specifically created to verify the accuracy of the strong tracking filtering algorithm. The term \"gentle slope\" refers to slopes with good road conditions and a gradual change in slope. \"Variable slope\" refers to slopes with significant changes in slope, characterized by an unstable rate of change. Figure 11b illustrates the variations in the slope gradient for the variable slope condition.  
Figure 11 presents the performance and error slopes of the Strong Tracking Adaptive Filter (STF) and the Adaptive Filter (AF) algorithms for identifying gentle slopes and variable road slopes. The algorithms were applied to both fixed slope road segments and variable slope road segments for identification. In the case of variable slope roads, as shown in Figure 11a, the fluctuation frequency of the STF algorithm is lower than that of the AF algorithm, indicating that the STF algorithm performs better in slope identification with good tracking performance. From Figure 11c, it can be observed that the identification error of STF is generally controlled within \(1^{\circ}\), while the identification accuracy of AF is significantly lower, with a higher error rate compared to STF. As shown in Figure 11b, for  
Figure 11: Road slope identification results: (**a**) variable slope road, (**b**) gentle slope road, (**c**) error in variable slope road, and (**d**) error in gentle slope road.  
fixed slopes, the identification curve of STF is closer to the reference slope and exhibits smaller fluctuations compared to AF, although the difference between the two is not substantial. From Figure 11d, it can be seen that the identification error range of STF is smaller than that of AF. [PERSON] suggests that when the slope identification error is within 0.2\({}^{\circ}\), it can be considered as reaching a stable state of slope identification [29].  
Based on the estimated road slope from the vehicle's travel analysis, the identified road slope information is analyzed in terms of the mean absolute error (MAE) and the root mean square error (RMSE). The analysis results are presented in Table 3. The calculation formula for the mean absolute error is:  
\[E_{MA}=\frac{1}{N}\underset{i=1}{\overset{N}{\sum}}|a_{i}-\hat{a}_{i}| \tag{55}\]  
The formula for calculating the root mean square error is:  
\[E_{RMS}=\sqrt{\frac{1}{N}\underset{i=1}{\overset{N}{\sum}}(a_{i}-\hat{a}_{i}) ^{2}} \tag{56}\]  
From Table 3, it can be observed that in terms of the MAE, during the fixed slope phase, the STF algorithm has a smaller average absolute error compared to the AF algorithm. This holds true during the variable slope phase as well. For the RMSE, the STF algorithm exhibits a smaller root mean square error than the AF algorithm, both during the fixed slope and variable slope phases. In conclusion, the STF algorithm outperforms the AF algorithm in terms of identification accuracy.