## 2 Remaining Useful Life (RUL) Prognostics Methodologies
### RUL Prognostics Methodologies Based on Filtering Techniques  
The methods of RUL prediction based on filtering techniques have also been studied. [PERSON] _et al._[39] proposed a state estimation method of lithium-ion batteries based on Kalman filtering (KF), but the method did not consider the influence of actual road conditions. Besides, the KF algorithm aims at linear Gauss, and its accuracy is not high when it comes to the strong nonlinear degradation process of the lithium-ion battery. Given that the extended Kalman filter (EKF) can better deal with the nonlinear Gauss problem, [PERSON] _et al._[40] presented an inline SOH and SOC estimation method for Li-ion battery packs, which used the coulomb counting method to calculate SOC and an extended Kalman filter (EKF) technique to estimate SOH. The advantages of algorithm are less estimation error and fast response time. However, the EKF is a nonlinear part for the first-order Taylor expansion, which ignores the high order, so the errors become larger. Unscented Kalman filter (UKF) is similar to the EKF, which uses Gauss distribution to approximate state distribution to only a few data points called Sigma. Through the nonlinear model, the mean and variance can be accurate to the nonlinear term of second-order Taylor expansion, so the accuracy of nonlinear filtering is higher. Thus, [PERSON] _et al._[41] not only built a joint coulomb counting method and battery voltage model but also introduced the UKF to adjust model parameters, estimated the battery status, and predicted the RUL, which was better than the EKF. [PERSON] _et al._[42] built a nonlinear time series prediction model to predict the battery life and adopted the UKF to predict residual. The accuracy of estimation was obviously higher than the EKF. In order to improve prediction accuracy, PF based on the Bayesian filter and the Monte Carlo method has also been used in RUL prediction in recent years and achieves the prediction values of posterior probability density through the update of time and measurement. [PERSON] _et al._[43] constructed a state-space model based on logistic regression and PF to predict RUL with NASA's lithium battery degradation experiment data. [PERSON] _et al._[44] used a PF algorithm to calculate RUL based on the statistical data of lithium-ion battery life and compared it with the calculation method in the EKF. The results show that the PF shows more accuracy and can predict the actual failure time better than the EKF. [PERSON] _et al._[45] proposed a model fused with an empirical exponential and a polynomial regression model to describe the battery's degradation trend. Model parameters are adjusted by the PF method. [PERSON] _et al._[50] proposed a methodology for the prediction of RUL using the PF framework. [PERSON] _et al._'s[51] research has found that PF is more accurate than the method (nonlinear least squares and an unscented Kalman filter (UKF)) for predicting RUL. [PERSON] _et al._[52] presented the implementation of a PF prognostic framework that uses statistical characterization to estimate the state of charge of a battery. The results show that the proposed framework can prognosticate the discharge time in terms of conditional expectations. [PERSON] _et al._[53] proposed a spherical cubature particle filter (SCPF) to solve the degradation state-space model of lithium-ion batteries. The analytical results show that it is more effective compared to the existing PF-based prognostic method. At the same time, [PERSON] _et al._[54] proposed a battery RUL prediction algorithm based on the UKF, and the result shows that it is better than the PF. These algorithms based on artificial intelligence or filtering techniques contribute to the improvement of prediction accuracy. The experimental result shows that these approaches can efficiently estimate the RUL of lithium batteries. However, in the actual operation process, this is not the case. Temperature and currents are time-varying. The methods mentioned above mainly consider discharging at a constant temperature and current.