## 4 Experimental Results and Analysis  
The experimental results were obtained using MATLAB simulation software ([[https://www2.mathworks.cn/discovery/simulation-software.html](https://www2.mathworks.cn/discovery/simulation-software.html)]([https://www2.mathworks.cn/discovery/simulation-software.html](https://www2.mathworks.cn/discovery/simulation-software.html))). First, the SoC was estimated via the EKF algorithm, which is depicted in Figure 3. The current, voltage, and temperature data used were measured using the experimental equipment. The initial SoC value was set to 90%, the time step was 1 s, and the total simulation time was 2000 s, where \(R_{a}=R_{b}=15\), and \(\tau=R_{b}C_{b}\) are time constants, which are generated by the normrnd function. The normal distribution generated by the randn function was used as the initial value of noise and observation noise, and the identity matrix generated by the eye function was used as the initial value of the covariance matrix. Further, the BBO algorithm was used to optimize the weight and threshold of the BP neural network, and then the SoC estimation compensation value was output. Combined with the estimation value obtained using the EKF method, the SoC estimation value was finally obtained. By using the newff function to establish a forward-type BP neural network, experiments were conducted on 1000 sets of data, and the predicted output of the network was set to \(1\times 10^{-5}\). After 2000 iterations, the network was trained. As a training set, the first 900 collections of data were employed, while the last 100 groups of data served as the test set. The learning rate was 0.01, and the training goal error was \(1\times 10^{-7}\). The main parameter-setting steps of the BBO algorithm include setting the weight and threshold value range to [-3, 3], the maximum quantity of iterations to 100, the quantity of habitats to 50, the habitat retention rate to 0.2, and the maximum mutation rate to 0.01. The following is a comparison of the results regarding the accuracy of the three algorithms for estimating lithium battery SoC value obtained through simulation, as shown in Figure 8.  
As can be seen in Figure 8, with the increase in simulation time, the experimental real value of the SoC of the power battery decreases, and the experimental measured value of the SoC fluctuates in an interval due to the addition of noise perturbation to the experiments, while the SoC value estimated via the BBOBP-EKF method is essentially in the middle of the interval of the experimental value and is very stable and fluctuates with the  
Figure 8: Comparison of SoC accuracy. fluctuation of the real SoC value, which is closer to the actual battery SoC value compared to the SoC value estimated by the BP-EKF algorithm and the EKF algorithm. Compared with the BP-EKF algorithm and the EKF algorithm, the estimated SoC values are closer to the actual battery SoC values, leading to the conclusion that the accuracy of the SoC values obtained via the BBOBP-EKF method has been improved to a certain extent. Meanwhile, after simulation, a comparison of the error curves of the EKF algorithm, BP-EKF algorithm, and BBOBP-EKF algorithm with respect to estimating the battery SoC value is also shown in Figure 9, which shows that the EKF algorithm fluctuates outside the error 0 value, and the BP-EKF algorithm and BBOBP-EKF method essentially fluctuate above and below the error 0 value, but the error float of the BBOBP-EKF method is much higher than that of the BP-EKF algorithm or the EKF algorithm; however, the error fluctuation of the BBOBP-EKF method is lower and more stable than that of the BP-EKF algorithm, so the BBOBP-EKF method is more effective in the estimation of battery SoC.