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.

State of charge (SOC) and state of energy (SOE) of lithium-ion batteries (LIBs) are fundamental parameters in the battery management system (BMS). However, the simultaneous estimation of the two states is challenging since the SOC and SOE are highly affected by the battery uncertain operating conditions. In this paper, a joint SOC and SOE estimation method is proposed based on a bidirectional gated recurrent neural network (BiGRU) with an improved pigeon-inspired genetic (PG) optimization algorithm. The BiGRU network is first used to capture bidirectional information embedded in the battery data and to make up for the loss of information in general recurrent neural networks (RNNs) learning. Then, the hyper-parameters of the BiGRU are optimized by the PG algorithm to make the data features of LIBs match the network topology. In two dynamic driven cycles, the average root mean square errors (RMSEs) of SOC and SOE estimations with the proposed PG-BiGRU method reach 1.3%. Furthermore, compared with the long short-term memory (LSTM) network, GRU, BiGRU, and pigeon-inspired optimized BiGRU (PIO-BiGRU), the PG-BiGRU algorithm yields the best SOC and SOE joint prediction accuracy, with RMSE values of 0.83% and 0.94%, respectively, which means that the proposed method can effectively reduce the complexity of parameters’ adjustment and improve the prediction accuracy.