## 1 Introduction  
Numerous studies have been conducted on SOC estimation. [PERSON] et al. analyzed the application of deep learning in electric vehicle power battery SOC estimation, summarizing the technical process of the deep learning method for lithium battery SOC estimation on commonly used public datasets and the characteristics, advantages, and disadvantages of neural network structures [1]. [PERSON] et al. discussed the latest classification and mathematical models for SOC estimation and envisaged development trends for SOC estimation methods [2]. [PERSON] et al. proposed an online SOC estimation method for lithium-ion batteries based on a simplified electrochemical model (EM), demonstrating the high accuracy of the method in experiments [3]. [PERSON] et al. proposed an online measurement method for battery parameters and SOC estimation using a multi scale, multi-innovation unscented Kalman filter and extended Kalman filter (MIUKF-EKF) to improve the accuracy of SOC real-time estimation [4]. [PERSON] et al. proposed a battery SOC estimation method based on an extended Kalman filter (EKF) and a neural network (NN), improving the accuracy of SOC estimation under low-battery capacity [5]. [PERSON] et al. proposed an SOC estimation method based on a deep neural network (DNN) and Kalman filters. Their experimental results show that this method can improve the robustness of the SOC estimation [6]. [PERSON] et al. proposed an online battery SOC estimation modeling method based on EKF and a back propagation (BP) neural network, which was verified to be practical and reasonable [7]. [PERSON] et al. proposed a model based on combining the double-extended Kalman filter algorithm (DEKF) and BP to estimate and correct SOC in lithium-ion batteries. This method demonstrated good versatility and robustness in experiments [8]. [PERSON] et al. proposed a robust and efficient combined SOC estimation method based on a gated recurrent unit and an adaptive Kalman filter (GRU-AKF), which combines a GRU with a recurrent neural network (RNN) and an AKF. The method showed superior SOC estimation performance and computational efficiency [9]. [PERSON] et al. proposed a long short-term memory (LSTM) neural network combined with an adaptive unscented Kalman filter (AUKF) method to simultaneously estimate SOC and state of energy. The results showed that the method has excellent performance, reduces computational complexity, and improves estimation accuracy [10]. [PERSON] et al. used an LSTM recursive neural network to build a battery performance characterization model and a rolling learning method to update the parameters. They then used an improved square-root Kalman filter (SRCKF) to estimate the SOC of the batteries. In experiments, the SOC estimation error was less than 2% [11]. [PERSON] et al. proposed an improved ampere-hour integration method based on an LSTM network model, and the experimental results showed that the error of the improved ampere-hour integration method for SOC estimation was less than 10% [12]. [PERSON] et al. proposed a joint state of health and state of charge (SOH-SOC) estimation model based on the grey wolf optimizer and back propagation (GWO-BP) neural network-optimized ampere-hour (Ah) integration method, which combines SOH and SOC estimation. The experimental results showed that the estimation error could be stabilized within 5% [13]. [PERSON] et al. proposed a model for SOC estimation based on a deep and wide one-dimensional CNN (1 DCNN) and a transfer learning mechanism. The method displayed good estimation accuracy, learning speed, and generalization ability [14] in experiments. [PERSON] et al. proposed a CNN based on the Laplace distribution, combining spatial feature extraction and an integrated attention mechanism to capture the complex time degradation characteristics of batteries. By introducing uncertainty estimation, the reliability and accuracy of SOC estimation were improved [15]. [PERSON] et al.