# Online SoC Estimation of Lithium-Ion Batteries Using a New Sigma Points Kalman Filter
## 1 Introduction
However, in this model there are more model parameters, and their identification is difficult, which makes the electrochemical model too difficult for online SoC estimation. In recent years, artificial intelligence has received more and more attention. Machine learning is an important method to realize artificial intelligence. The machine learning method is applied to the field of battery technology. The machine learning method is based on battery measurement and operating data and realizes battery SoC estimation through algorithms such as neural networks. [PERSON] et al. [24; 25] combined neural networks and the Kalman filter for SoC estimation. [PERSON] et al. [26] applied the adaptive fuzzy neural network to estimate the battery SoC and used 10 driving conditions to analyze and evaluate the proposed algorithm. [PERSON] et al. [27] divided the battery working modes into three states, i.e., idle, charging and discharging. Three neural network models have been designed for battery SoC estimation. However, this method of preprocessing the battery load current can lead to some difficulties in estimating the SoC in real-time. In addition, the SoC estimation accuracy was affected by the state of health (SoH) [28]. [PERSON] et al. [29] proposed a fusion-type SoH estimation method by combining model and data-based to enhance the SoC estimation accuracy and robustness. The main challenge of the machine learning method is obtaining a variety of data of actual working conditions of EVs for training. The machine learning method has high requirements on the processing capacity of automotive chips, which limits its practical application. Significant efforts have been made to study novel methods that can balance the model complexity and calculation efficiency. The equivalent circuit model (ECM) is an ideal candidate. The ECM uses circuit components such as resistors, capacitors and voltage sources to reflect the electrochemical characteristics of the battery. The voltage source in the model represents the thermodynamic equilibrium potential of the battery, and the resistance and capacitance represent the dynamic characteristics of the battery. [PERSON] et al. [30] used a first-order hysteresis model, and [PERSON] et al. [31] used a fractional-order model to further improve the accuracy of the terminal voltage simulation of the battery. The battery SoC estimation method based on the ECM can better balance the model complexity and calculation efficiency [32]. [PERSON] et al. [33] optimized the parameters of ECM through the particle swarm optimization algorithm, which effectively improved the estimation accuracy of SoC. In order to further reduce the influence of process noise on the model and improve SoC estimation accuracy, modern control theory has been applied to SoC estimation. The Kalman filter family algorithms solve the filter gain, covariance and SoC estimation value by comparing the measured voltage and the model voltage. [PERSON] et al. [34] used the Extended Kalman filter (EKF) method for SoC estimation. The extended Kalman filter locally linearizes the non-linear state function and measurement function of the battery through the first-order Taylor series expansion and then performs the Kalman filter. Thus, it is a sub-optimal filter. EKF needs to calculate the Jacobian matrix of the non-linear function and requires the state function and the measurement function to be continuously differentiable. For Gaussian systems, the Jacobian matrix solution process is cumbersome and easily leads to poor numerical stability of EKF and even calculation divergence. In order to overcome these problems, [PERSON] explored a new technique called the Sigma Point Kalman Filter (SPKF) [35; 36], which uses approximate conditional probability density functions instead of non-linear models. The results showed that SPKF is better than EKF in terms of battery SoC estimation accuracy and error range. [PERSON] et al. [37] first proposed the use of central difference to improve the EKF algorithm.