State of Charge Estimation for Lithium-Ion Batteries Using a Generalized Mixture Maximum Correlation-Entropy Criterion-Based Extended Kalman Filter Algorithm

WU Chunling; ZHAO Yubing; GENG Limin; XU Xianfeng; WANG Yibo; CHEN Hao

doi:10.7652/xjtuxb202507016

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State of Charge Estimation for Lithium-Ion Batteries Using a Generalized Mixture Maximum Correlation-Entropy Criterion-Based Extended Kalman Filter Algorithm

更新时间：2025-07-09

- State of Charge Estimation for Lithium-Ion Batteries Using a Generalized Mixture Maximum Correlation-Entropy Criterion-Based Extended Kalman Filter Algorithm
- Journal of Xi’an Jiaotong University Vol. 59, Issue 7, Pages: 159-169(2025)
- 作者机构：
  
  1.长安大学能源与电气工程学院， 710064，西安
  2.长安大学陕西省交通新能源开发、应用与汽车节能重点实验室， 710064，西安
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202507016
  CLC： TM912
- Received：26 October 2024，
  
  Online First：27 March 2025，
  
  Published：10 July 2025
- 稿件说明：
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WU Chunling, ZHAO Yubing, GENG Limin, et al. State of Charge Estimation for Lithium-Ion Batteries Using a Generalized Mixture Maximum Correlation-Entropy Criterion-Based Extended Kalman Filter Algorithm[J]. Journal of Xi’an Jiaotong University, 2025, 59(7): 159-169.
DOI：

WU Chunling, ZHAO Yubing, GENG Limin, et al. State of Charge Estimation for Lithium-Ion Batteries Using a Generalized Mixture Maximum Correlation-Entropy Criterion-Based Extended Kalman Filter Algorithm[J]. Journal of Xi’an Jiaotong University, 2025, 59(7): 159-169. DOI： 10.7652/xjtuxb202507016.

摘要

为了解决非高斯噪声环境下荷电状态（SOC）估计不准确以及鲁棒性差等问题，提出一种基于广义混合最大相关熵准则的扩展卡尔曼滤波（GMMCC-EKF）算法。该算法利用两个广义高斯函数构成的核函数得到广义混合熵，继承了广义高斯核的灵活性，并通过统计线性化技术将状态误差和测量误差统一纳入代价函数，进而通过固定点迭代法获得非线性方程的最优估计，然后将广义混合最大相关熵准则与扩展卡尔曼滤波相结合，增强在非高斯噪声环境下的稳定性，提高对复杂数据处理的准确性。为了验证算法有效性，分别选用两种不同类型的锂离子电池，在动态应力测试（DST）工况及多种环境温度（10、25和40 ℃）的新欧洲驾驶循环（NEDC）工况下对电池进行SOC估计。实验结果表明，在25 ℃且均匀混合噪声环境下，对于1号电池，GMMCC-EKF算法的估计精度相对于扩展卡尔曼滤波算法（EKF）和传统最大相关熵扩展卡尔曼滤波算法（MCC-EKF）分别提高了90.1%和83.9%；对于2号电池，估计精度分别提高了72.4%和47.4%，并且在10、40 ℃环境下该算法仍展现出最优性能。对1号、2号电池在25 ℃且拉普拉斯混合噪声环境下进行SOC估计，GMMCC-EKF算法相对于其他两种算法的估计精度也有显著提高。在给定初始值错误的情况下，GMMCC-EKF算法能够快速地收敛到真实值。所提算法具有较高的估计精度、良好的适应性和鲁棒性，可为非高斯噪声环境下的SOC估计提供有效解决方案。

Abstract

To address the challenges of inaccurate state of charge (SOC) estimation and poor robustness in non-Gaussian noise environments

an extended Kalman filter algorithm based on the generalized mixed maximum correntropy criterion (GMMCC-EKF) is proposed. The algorithm employs a kernel function composed of two generalized Gaussian functions to derive the generalized mixed correntropy

inheriting the flexibility of generalized Gaussian kernels. Through statistical linearization techniques

both state errors and measurement errors are incorporated into a unified cost function

and the optimal estimation of nonlinear equations is obtained via fixed-point iteration. By integrating the generalized mixed maximum correntropy criterion with the extended Kalman filter

the algorithm enhances stability in non-Gaussian noise environments and improves accuracy in processing complex data. To validate the algorithm's effectiveness

two different types of lithium-ion batteries are tested under dynamic stress test (DST) conditions and new European driving cycle (NEDC) conditions at various ambient temperatures (10 ℃

25 ℃

and 40 ℃). Experimental results demonstrate that at 25 ℃ under uniform mixed noise conditions

the GMMCC-EKF algorithm improves estimation accuracy by 90.1% and 83.9% compared to the conventional extended Kalman filter (EKF) and maximum correntropy criterion EKF (MCC-EKF)

respectively

for No.1 battery 1. Similarly

for No.2 battery

accuracy improves by 72.4% and 47.4%. The algorithm also maintains superior performance at 10 ℃ and 40 ℃. Under Laplacian mixed noise conditions at 25 ℃

the GMMCC-EKF algorithm exhibits significant accuracy improvements for both No.1 battery and No.2 battery compared to the other two algorithms. Additionally

with erroneous initial values

the GMMCC-EKF algorithm rapidly converges to the true SOC. The proposed algorithm demonstrates high estimation accuracy

strong adaptability

and superior robust performance

providing an effective solution for SOC estimation in non-Gaussian noise environments.

关键词

Keywords

references

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