State of health (SOH) estimation and remaining useful life (RUL) prediction can ensure reliable and safe system operation and reduce unnecessary maintenance costs. In this paper, to improve the accuracy and reliability of SOH estimation and RUL prediction, a novel method based on second-order central difference particle filter (SCDPF) is proposed. By optimizing the importance probability density function, the particle degeneracy phenomenon of particle filter (PF) can be solved. Experiments from the National Aeronautics and Space Administration (NASA) and the Center for Advanced Life Cycle Engineering (CALCE) of the University of Maryland are conducted to demonstrate the effectiveness and satisfactory performance of the proposed SCDPF approach. The maximum error and the root mean square error (RMSE) of the SCDPF fitting approach are quite small, the minimum values of those are 0.006102 Ah and 0.001599, which are lower than those of the unscented particle filter (UPF) and particle filter (PF). The average RUL errors and average PDF width of SCDPF method are also smaller, which validates the accuracy and stability of the proposed method.

To meet practical usage requirements, lithium-ion batteries usually need to form a battery pack. However, due to production deviations and different usage environments, there are inconsistencies between batteries within the battery pack. This makes it challenging to estimate the state of charge (SOC) of the battery pack accurately. This article proposes a battery pack SOC estimation approach based on discharge stage division and fusion modeling. According to the battery discharge characteristics and SOC inconsistency, three stages are divided in the battery pack discharge process. In the first stage, the second-order RC model and Extended Kalman Filter (EKF) algorithm are employed for SOC estimation as the consistency between batteries is good. In the second stage, the representative battery and Long Short-Term Memory (LSTM) recurrent neural network will be used to consider the impact of battery inconsistency on battery SOC estimation. An ampere-hour integration with constraint factor for smoothing is applied to enhance the estimation accuracy of the LSTM network. In the third stage, EKF is utilized to estimate the SOC of all batteries as the inconsistency between batteries increases significantly and reaches a maximum at the end of discharge. Finally, experiments and actual vehicle tests under the Worldwide Harmonized Light Vehicles Test Cycle (WLTC) working condition are conducted to verify the effectiveness of proposed methods on the ternary lithium battery pack at 0°C, 25°C, and 45°C. Compared with other algorithms, the proposed method has good estimation performance, with a maximum RMSE of only 0.8%. The maximum prediction error under actual vehicle operating conditions is less than 1.2%.