# State of Charge Estimation for Lithium-Ion Power Battery Based on H-Infinity Filter Algorithm
The ampere-hour integration [9], also known as the coulomb counting method, incurs a low calculation cost, as well as enables fast calculation. It is the estimation method of the SOC currently adopted by most electric vehicles. However, the estimation method based on ampere-hour integration requires high accuracy requirements from the initial parameters of the battery model. It is difficult to meet the sampling accuracy and frequency requirements of the sensor during the actual application of the battery. Data-driven estimation methods can be divided into three categories according to different algorithms: support vector machine (SVM) [10], neural network (NN) [11], and the fuzzy control method [12]. These methods are similar to the black box model in the battery modeling process. In order to achieve high estimation accuracy and strong adaptability, a large amount of data is usually required for training. Moreover, the selection of training data is very strict, while requiring high precision in data fitting, as well as meeting the applicability of non-linear models. The data that does not meet the requirements will make it difficult to train the model, which will affect the accuracy and, consequently, the SOC estimation to a great extent. The model-based SOC estimation method is self-adjusted by the difference between the battery's measured voltage and the model's output voltage. This is done to overcome the error caused due to uncertainty, and achieve the purpose of improving the estimation accuracy of the SOC. It is a robust closed-loop estimation algorithm. Common methods include the impedance method [13], particle filter (PF) [14], Kalman filter (KF) [15], and improved algorithm [16; 17; 18]. Among them, the PF algorithm can provide better results in a non-Gaussian white noise system, but its operation intensity is higher than that of the KF algorithm. The KF algorithm is widely used, because it can find the optimal solution for a linear Gaussian system. A simple linear system can use the ordinary KF algorithm [19], whereas for complex nonlinear models, the extended Kalman filter (EKF) algorithm has been studied and applied extensively [20; 21; 22]. Based on the equivalent circuit model, [PERSON] [23; 24] used Kalman filter series algorithms (KF, EKF, unscented Kalman filter (UKF)) to achieve the identification of model parameters and SOC estimation at the same time. [PERSON] et al. [25] improved the traditional EKF algorithm, and realized that when the input and output of the system changed, the noise covariance matrix in the algorithm responded accordingly to self-correct the noise. Thus, the influence of noise on the accuracy of the traditional EKF algorithm is overcome; however, the EKF algorithm requires that the input noise of the model be white noise with known statistical characteristics. It is greatly affected by the measurement accuracy of the sensor during vehicle operation, and has not been applied in real vehicles. To solve the above problems, the H-infinity filter (HIF) algorithm based on the minimum-maximum criterion is adopted in this study instead of the traditional EKF algorithm. This algorithm takes into account the time-varying element of battery parameters, and does not require the details of process noise and measurement noise. Therefore, the HIF can expand the scope of application of the SOC estimation algorithm and improve the robustness of the algorithm under real vehicle operating conditions. [PERSON] et al. [26] used the HIF algorithm to estimate the SOC of lithium-ion batteries, and the method was tested by real-time experimental data of batteries. However, it ignores the measurement noises and random disturbances. [PERSON] et al. [27] proposed an adaptive H-infinity filter (AHIF) algorithm to predict the SOC of lithium-ion batteries. The proposed algorithm is comprehensively validated within a full operational temperature range of battery, and with different aging status. Even so, it ignores the effects of application conditions on SOC estimation.