A Review of Cross-Scale State Estimation Techniques for Power Batteries in Electric Vehicles: Evolution from Single-State to Multi-State Cooperative Estimation

Abstract

As a critical technological foundation for electric vehicles, power battery state estimation primarily involves estimating the State of Charge (SOC), the State of Health (SOH) and the Remaining Useful Life (RUL). This paper systematically categorizes battery state estimation methods into three distinct generations, tracing the evolutionary progression from single-state to multi-state cooperative estimation approaches. First-generation methods based on equivalent circuit models offer straightforward implementation but accumulate SOC-SOH estimation errors during battery aging, as they fail to account for the evolution of microscopic parameters such as solid electrolyte interphase film growth, lithium inventory loss, and electrode degradation. Second-generation data-driven approaches, which leverage big data and deep learning, can effectively model highly nonlinear relationships between measurements and battery states. However, they often suffer from poor physical interpretability and generalizability due to the “black-box” nature of deep learning. The emerging third-generation technology establishes transmission mechanisms from microscopic electrode interface parameters via electrochemical impedance spectroscopy to macroscopic SOC, SOH, and RUL states, forming a bidirectional closed-loop system integrating estimation, prediction, and optimization that demonstrates potential to enhance both full-operating-condition adaptability and estimation accuracy. This progress supports the development of high-reliability, long-lifetime electric vehicles.

1. Introduction

In response to carbon emission reduction and net-zero targets, the electric vehicle industry chain is accelerating its transition toward deep electrification [1,2]. With their advantage of high energy density, power batteries continue to drive electrification in passenger vehicles, commercial vehicles, and special-purpose vehicles. As a technological advancement of industry growth [3], lithium-ion battery systems are now widely used in battery electric vehicles (BEVs) and plug-in hybrid electric vehicles (PHEVs) through modular design. Battery state estimation is a key part of battery management, including battery modeling, State of Charge (SOC) estimation [4], State of Health (SOH) estimation [5], and Remaining Useful Life (RUL) prediction [6]. Cooperative estimation and prediction of SOC, SOH, and RUL not only enhance optimal control for vehicle energy management systems but also establish a comprehensive battery health management framework and an early safety warning system across the entire battery lifecycle.

Battery state estimation methods have evolved through three generations. Each transition between generations has been driven by new measurement techniques and new theories. Among them, the most prominent are the rapid development of electrochemical impedance spectroscopy measurement techniques and artificial intelligence theories.

The first-generation method employs external time-domain signals such as voltage, current, and temperature as inputs, utilizing coulomb counting [7,8] or Kalman filtering based on equivalent circuit models for SOC estimation. On this basis, internal resistance and capacity variations are indirectly derived through charge accumulation during full cycles [9] or extended Ohm’s law approaches to estimate battery SOH. While computationally efficient and easy to implement, these methods focus solely on macroscopic battery states. They neither characterize electrochemical reactions at electrode/interface scales nor account for cross-scale parameter evolution such as solid electrolyte interphase film growth and active material loss induced by aging. This results in significant cumulative SOC/SOH estimation errors during long-term dynamic operations, severely limiting engineering applicability in complex scenarios such as fast-charging and varying-temperature environments.

The second-generation method is based on deep learning, employing data-driven models like Convolutional Neural Networks (CNNs), Long Short-Term Memory networks (LSTMs), and Gated Recurrent Unit (GRUs) to construct end-to-end nonlinear mappings between battery states and operational data [10,11,12]. Since 2019, this approach has seen widespread adoption in SOC, SOH, and RUL estimation. While enabling easy integration into cloud platforms and effectively capturing high-order nonlinearities, these methods suffer from a lack of physical interpretability due to their “black-box” nature. Simultaneously, the need for manually labeled data, domain adaptation problems across material systems/battery types/operating conditions, and data privacy concerns limit their applicability. Poor generalization and lack of interpretability make it hard to adapt to challenging battery operating conditions, which in turn restricts the practical use of deep learning-based state estimation in onboard battery management systems.

The third-generation method overcomes long-term accuracy degradation in single-state estimation by integrating electrochemical mechanisms with a multi-state cooperative estimation framework, and is characterized by two pathways: a forward path and an inverse feedback path. In the forward path, during battery aging, electrochemical impedance spectroscopy (EIS) is employed to monitor internal microscopic parameters, such as ohmic resistance, SEI layer resistance, and lithium inventory loss. These microscopic parameters are then used to calibrate and constrain the macroscopic state estimation models. In the reverse feedback path, early warnings from the estimated macroscopic states are fed back into the system to adjust the battery’s operating conditions. This feedback helps mitigate the rate of microscopic degradation, thereby extending battery lifespan. Through this integration, these bidirectional interactions bridge micro-scale mechanisms with macro-scale estimations, forming a closed-loop intelligent battery management strategy. This approach achieves not only joint SOC, SOH, and RUL estimation [13] but also tracks multidimensional parameters such as internal resistance [14], degradation modes [15], and electrode aging state [16]. By establishing cross-scale correlation mechanisms that bridge short-timescale dynamic responses and long-timescale battery aging evolution, this methodology significantly enhances state estimation accuracy and operational robustness. A key future challenge will be integrating sub-second SOC dynamics with weekly-to-monthly SOH and RUL degradation processes, which depends on complex onboard electrochemical testing equipment. This integration inevitably introduces computational cost increases for battery management systems (BMS) and worsens the challenges for real-time onboard applications.

This review summarizes methodological advances in cross-scale traction battery state estimation systems and traces the technical evolution from single-state to multi-state cooperative approaches. This paper first reviews battery modeling methods and then analyzes the three core states: SOC, SOH, and RUL. The analysis highlights how estimation has evolved from individual, isolated predictions to integrated, model-based approaches that incorporate additional battery parameters.

2. Battery Modeling

2.1. Equivalent Circuit Model

Equivalent circuit models (ECMs) for lithium-ion batteries characterize internal electrochemical reaction processes and terminal charge/discharge behavior using components such as resistors, capacitors, and ideal voltage sources. Standard ECMs such as the first-order Resistor-Capacitor (RC) model [17], second-order RC model [18], and Partnership for a New Generation of Vehicles (PNGV) model [19] utilize RC parallel networks to simulate dynamic responses, capturing voltage-current relationships during operation. The most commonly used second-order RC equivalent circuit model is shown in Figure 1, and its state-space equation can be described by Equation (1).

$$\begin{array}{l}\left\{\begin{array}{l}{\displaystyle \frac{\mathrm{d}{V}_1(t)}{\mathrm{d}t}}=-{\displaystyle \frac{1}{R_1{C}_1}}{V}_1(t)+{\displaystyle \frac{1}{C_1}}I(t)\hfill \\ {\displaystyle \frac{\mathrm{d}{V}_2(t)}{\mathrm{d}t}}=-{\displaystyle \frac{1}{R_2{C}_2}}{V}_2(t)+{\displaystyle \frac{1}{C_2}}I(t)\hfill \\ {\displaystyle \frac{\mathrm{d}SOC(t)}{\mathrm{d}t}}=-{\displaystyle \frac{{\eta }_c}{Q_n}}I(t)\hfill \end{array}\right.\\ V_L(t)=-R_{0}I(t)-V_1(t)-V_2(t)+V_{oc}(SOC(t))\end{array}$$

(1)

where $V_{oc}(SOC(t))$ is the open-circuit voltage, which can be described by the fitted equation of the OCV-SOC curve to represent the mapping relationship between $V_{oc}$ and $SOC$. $V_L(t)$ denotes the terminal voltage, $I(t)$ denotes the battery current, $R_0$ is the ohmic internal resistance, $R_1$ and $R_2$ denote two polarization resistors, respectively. $C_1$ and $C_2$ denote two capacitors, respectively. $V_1(t)$ and $V_2(t)$ represent the voltage of $C_1$ and $C_2$. ${\eta }_c$ is coulombic efficiency and $Q_n$ is the rated capacity.

However, RC parallel networks exhibit only simple exponential characteristics, which oversimplify complex electrochemistry. This simplification creates voltage prediction errors compared to experimental measurements. Researchers have therefore developed higher-order ECMs including third-order [20] and multi-order RC models [21] by adding RC networks, achieving better approximation of nonlinear charge/discharge dynamics. Although these models improve voltage prediction accuracy, they also increase computational complexity and make parameter identification more difficult, as demonstrated in several studies.

To better capture the dynamic behavior of electrochemical reactions within the battery, researchers have developed the fractional-order equivalent circuit model. Fractional-order equivalent circuit models require EIS measurements from lithium-ion batteries. As a nondestructive characterization technique, EIS applies variable-frequency small-amplitude Alternating Current (AC) excitation to measure frequency-dependent impedance, forming spectra from multi-frequency data. Offline EIS typically requires electrochemical workstations [22,23], yet faces practical constraints including high cost, operational complexity, and bulky equipment that hinder real-time battery monitoring. Developing online EIS technology is therefore essential. Abareshi et al. [24] introduced a multifunction controllable EIS device using a synchronous buck converter with low-cost input filtering for bidirectional operation. They subsequently applied H∞ control and quantitative feedback theory to develop a robust controller ensuring stable reference tracking under modeling uncertainties. However, inherent load-induced ripple (e.g., from motor controllers) increases voltage and current measurement noise in Direct Current to Direct Current (DC-DC) based EIS acquisition [25]. Zhao et al. [26] established a correlation detection-based method that injects excitation signals via reference-synchronized electronic switches at battery terminals. This approach exploits the uncorrelated nature of noise, DC components, and harmonics with the reference signal to obtain the impedance’s real and imaginary components as shown in Figure 2b. By achieving high noise rejection, it significantly improves the robustness of online EIS in noisy operating conditions compared to the DC-DC-based method in Figure 2a. Regarding distortion points in EIS measurements, [26] proposes an improved Levenberg–Marquardt algorithm to correct the measured EIS by optimizing battery model parameters corresponding to the measured EIS within the trust region.

Fractional-order equivalent circuit models fit measured EIS using electrical components including resistors, inductors, capacitors, constant phase elements (CPEs), and Warburg elements. The first-order [27] and second-order [28] fractional models represent the most prevalent configurations where the former contains a single R//CPE network and the latter incorporates two such networks. The second-order equivalent circuit model accounts for different electrochemical processes across frequency bands. At high frequencies, inductive impedance from internal current collectors is represented by inductors; at mid-frequencies, the charge-transfer process and double-layer capacitance are modeled using two parallel resistor–constant phase element (R//CPE) networks; and at low frequencies, diffusion dynamics are described by Warburg elements. Once the model structure is established, optimization methods including recursive least squares [29], state transition algorithms [30], and differential evolution [31] determine component parameters. Crucially, time-domain memory effect of the CPE enables precise modeling of voltage dynamics over extended durations, thus granting fractional models significantly superior voltage fitting accuracy compared to integer-order equivalent circuit models throughout complete charge–discharge cycles.

2.2. Electrochemical Model

Unlike equivalent circuit models, electrochemical models employ mathematical partial differential equations to describe internal electrode processes across liquid-phase and solid-phase domains. The representative pseudo-two-dimensional (P2D) model [32] comprehensively simulates liquid-phase ion diffusion, solid-phase diffusion, and interfacial reactions, enabling high-precision characterization of internal/external battery behavior. However, extracting voltage, current, and parametric variations from the P2D model requires solving computationally expensive partial differential equations. For practical state estimation algorithm development, the P2D model is further simplified by neglecting ion conduction, electron conduction, and liquid-phase ion diffusion processes, thereby reducing to the Single Particle (SP) model [33]. This simplified approach considers only interfacial reactions and solid-phase diffusion, achieving accelerated computation while maintaining broad applicability in SOC estimation [34], SOH assessment [35], and thermal simulations [36].

2.3. Comparison and Summary of Battery Models

Battery modeling connects measurable external signals such as voltage and current to internal electrochemical processes through simplified assumptions. It uses equivalent circuit elements or physical equations to represent realistic charge and discharge behavior. Integer-order equivalent circuit models, shown in Figure 3a–c, achieve a balance between accuracy and complexity and have been successfully implemented in various embedded systems. Fractional-order equivalent circuit models, illustrated in Figure 3d, improve accuracy in characterizing battery dynamic behavior with multiple relaxation time constants despite increased complexity. When microscopic-level variable descriptions such as electrode states are required, both integer-order and fractional-order equivalent circuit models are insufficient. Therefore, electrochemical models are necessary, as illustrated in Figure 3e, which provides improved accuracy in simulation and thermal behavior analysis.

Due to the complexity of electrochemical models, EIS technology is more frequently employed in practical applications for direct measurement of internal battery impedance, enabling precise analysis of battery aging conditions. Consequently, EIS technology serves as the critical bridge transitioning from second-generation to third-generation techniques. The regular acquisition of fractional-order equivalent circuit model parameters through EIS, followed by their application as constraints for subsequent SOC, SOH, and RUL estimation, has emerged as a pivotal technical direction for future development.

3. State Estimation

3.1. SOC Estimation

3.1.1. Single-State SOC Estimation Using Time-Domain Features

Accurate estimation of lithium-ion battery SOC is critical for enhancing energy utilization efficiency and extending service life of lithium-ion batteries [37]. SOC represents the ratio of residual capacity to rated capacity, mathematically expressed as Equation (2):

$$SOC={\displaystyle \frac{Q_t}{Q_n}}\times 100\%$$

(2)

where $Q_n$ is the rated capacity and $Q_t$ is the residual capacity. Since SOC cannot be measured directly [38], its estimation has become a major focus of research in the energy field, promoting extensive studies conducted worldwide.

Early SOC estimation research primarily focused on single-state SOC estimation. As a fundamental approach, coulomb counting achieves dynamic SOC tracking through current integration, though cumulative current measurement errors cause SOC estimation deviations. Jeong et al. [39] proposed an enhanced coulomb counting algorithm that constructs an error prediction model using open-circuit voltage (OCV) observations during brief rest periods. By incorporating reset time optimization and error compensation mechanisms, this method limits SOC estimation errors to within 2.07% under Urban Dynamometer Driving Schedule (UDDS) conditions, providing a reliable solution for dynamic scenarios. To further improve dynamic adaptability, Kalman filter algorithms have been widely implemented. Xia et al. [40] applied extended Kalman filtering (EKF) with linearized equivalent circuit models for recursive SOC estimation, experimentally demonstrating errors below 3%. Zheng et al. [41] used unscented Kalman filtering (UKF) with fractional-order equivalent circuit models to keep estimation errors below 1.04% under dynamic operating conditions. Addressing OCV-SOC curve uncertainties, Zhao et al. [42] developed an electrochemical impedance model containing controlled sources. They employed radial basis function (RBF) neural networks to approximate OCV-SOC curve uncertainties in battery models, further designing an RBF-based nonlinear SOC observer. Lyapunov stability analysis proved that the estimation error of the observer remains bounded, while experimental results confirmed the high accuracy and robustness of the proposed method under complex operating conditions. This integration of equivalent circuit models with intelligent algorithms provides novel approaches for resolving model uncertainty challenges.

With advancements in big data and machine learning technologies, data-driven approaches have gained increasing adoption for SOC estimation. Early data-driven methods primarily relied on traditional machine learning models. Deng et al. [43] proposed a data-driven method based on Gaussian process regression (GPR). Experimental results validated that its estimation root mean square error (RMSE) remained below 3.9% across various dynamic operating conditions, temperature variations, aging conditions, and even extreme scenarios. As deep learning advanced, Ahn et al. [44] proposed a LSTM-based temporal feature extraction framework that integrates mainstream m-LSTM and gradient g-LSTM in parallel to capture long-term dependencies in current-voltage sequences. The dual-LSTM approach achieved an average 12.02% improvement in accuracy compared to the conventional LSTM model. It also showed faster convergence during training and maintained high-precision SOC estimation, even when faced with unexpected or noisy data. Zhang et al. [45] enhanced the LSTM architecture by integrating a self-attention mechanism to improve temporal feature learning. Experimental results across datasets with varying temperatures and initial charge levels demonstrate high accuracy in SOC estimation. The MAE was 0.84% at 50 °C, compared to 1.06% at 0 °C. When starting from a fully charged state, the MAE was 1.09%, decreasing to 1.15% at 60% initial charge.

To address the inherent interpretability limitations of data-driven approaches, Tao et al. [46] proposed a physics-informed neural network (PINN) based multi-task learning framework, embedding equivalent circuit model constraints into LSTMs via online learning strategies to dynamically update physical parameters, as shown in Figure 4. Multi-condition aging experiments show that the proposed method improves SOC estimation accuracy by an average of 59.73% compared to the baseline model. This data-mechanism dual-driven paradigm provides a feasible solution for overcoming pure data-driven methods’ interpretability constraints. Through a multi-task learning approach, a deep neural network is first used to simultaneously predict the parameters of the second-order RC equivalent circuit model and the SOC under different temperatures. Then, the model generates voltage curves, and both the voltage error and SOC error are jointly used as the loss function to train the neural network. In this way, when the temperature changes, the model can adapt by predicting the model parameters and SOC at corresponding temperatures, thereby achieving SOC estimation results with better physical interpretability.

As research advances in model-based and data-driven approaches, studies increasingly focus on hybrid architecture design. Zhao et al. [47] developed a novel high-accuracy SOC estimation method using dual polarization (DP) model parameters as random forest input features. Through maximal information coefficient analysis and random forest feature importance scoring, they identified seven critical features. An innovative extract segment fusion method was then created to combine EKF advantages with feature-enhanced random forest for SOC estimation. Testing across five driving cycles demonstrated MAE below 0.080% and RMSE below 0.107%, showing significant potential for electric vehicle implementation.

3.1.2. SOC and Multi-State Cooperative Estimation

As research deepens, researchers have increasingly recognized that during lithium-ion battery operation, SOC exhibits strong coupling characteristics with parameters such as internal resistance, capacity, and SOH. This renders single-state SOC estimation inadequate for complex scenarios, positioning multi-state co-estimation as a new research direction.

Zhao et al. [48] proposed a variable-structure fractional-order equivalent circuit model. As the battery ages, the number of R//CPE networks in the fractional-order model change. As the SOC changes, the ohmic resistance also changes. The variable-structure model can be described by Equation (3).

$$\begin{array}{l}\left\{\begin{array}{l}\begin{array}{l}{D}^{{\alpha }_1}{V}_1(t)=-{\displaystyle \frac{1}{R_1{C}_1}}{V}_1(t)+{\displaystyle \frac{1}{C_1}}I(t)\hfill \\ D^{{\alpha }_2}{V}_2(t)=-{\displaystyle \frac{1}{R_2{C}_2}}{V}_2(t)+{\displaystyle \frac{1}{C_2}}I(t)\hfill \\ {\displaystyle \frac{\mathrm{d}SOC(t)}{\mathrm{d}t}}=-{\displaystyle \frac{{\eta }_c}{Q_n}}I(t)\hfill \end{array}\\ {\displaystyle \frac{\mathrm{d}{R}_0(t)}{\mathrm{d}t}}=h(SOC)\end{array}\right.\\ V_L(t)=-R_{0}I(t)-V_1(t)-V_2(t)+V_{oc}\end{array}$$

(3)

where $0<{\alpha }_1,{\alpha }_2<1$ is the order of two CPE, $D^{\alpha }$ is the fractional-order differential operator. Based on the proposed battery model, a fractional-order extended state observer treating internal resistance as an augmented state, enabling real-time tracking of internal resistance uncertainty. The extended state observer is expressed as shown in Equation (4).

$$\left\{\begin{array}{l}\begin{array}{ll}\widehat{x}(k+1)& =[T_h^{r}A+diag(\alpha )]\widehat{x}(k)-{\displaystyle \sum _{q=2}^{N+1}{(-1)}^q{\omega }_{\alpha }^q\widehat{x}(k+1-1)}\\ & +T_h^{r}Bu(k)+T_h^{r}L(y(k)-\widehat{y}(k))\hfill \end{array}\hfill \\ \widehat{y}(k)=C\widehat{x}(k)\hfill \end{array}\right.$$

(4)

where ${\omega }_{\alpha }^q$ is the Newtonian binomial coefficients and $T_h^r=diag[{\omega }_q^{{\alpha }_1},{\omega }_q^{{\alpha }_2},{\omega }_q^1,{\omega }_q^1]$.Lyapunov stability analysis confirmed its uniformly bounded estimation error, with experimental simulations achieving a mean MAE as low as 0.73% as shown in Figure 5a.

To address capacity attenuation interference on SOC estimation caused by aging, Sharma et al. [49] introduced a CNN framework incorporating attention mechanisms. This achieves cooperative SOC and capacity estimation through adaptive feature weighting allocation, with multi-condition and aging tests demonstrating its high accuracy and computational efficiency in dual-parameter cooperative estimation as shown in Figure 5b. However, when electric vehicles are driving under conditions of significant temperature fluctuations and strong electromagnetic interference, voltage and current sensors within the BMS introduce time-variant noise characteristics. This compromises the effectiveness of conventional Kalman filtering algorithms. To address this issue, Xie et al. [50] developed a variational Bayesian algorithm, as shown in Figure 5c. This method achieves accurate cooperative estimation of SOC, model parameters, and noise parameters by minimizing the Kullback–Leibler (KL) divergence between the variational distributions and the true posterior distributions, which can be described by Equations (5) and (6):

$$\{q(x_k),q(P_k^{x-}),q(R_k^{x-})\}=\arg \min KLD(q(x_k)q(P_k^{x-})q(R_k^{x-})||p(x_k,P_k^{x-},R_k^{x-}|z_{1:k}))$$

(5)

$$\{q({\theta }_k),q({\xi }_k),q({\Sigma }_k)\}=\arg \min KLD(q({\theta }_k)q({\xi }_k)q({\Sigma }_k)||p({\theta }_k,{\xi }_k,{\Sigma }_k|z_{1:k}))$$

(6)

where $x_k={[U_{1,k},U_{2,k},SO{C}_k]}^{\mathrm{T}}$ is the state vector, $z_k=U_{L,k}$ is measurement vector, $P_k^{x-}$ and $R_k^{x-}$ are covariance matrix of state and measurement noise. ${\theta }_k$ is the battery model parameter vector, ${\xi }_k$ is the auxiliary mean vector related to ${\theta }_k$, ${\Sigma }_k$ is the auxiliary variance vector related to ${\theta }_k$. By solving the optimization problems in Equations (5) and (6) using coordinate ascent variational inference, a variational Bayesian FEKF is constructed, which maintains the RMSE consistently below 1.3% during HPPC and FUDS tests across temperature cycles ranging from −15 °C to 45 °C, as well as under time-varying noise conditions.

The methods in references [48,50] are improved from traditional state observers and the extended Kalman filter, respectively. Although these methods increase computational complexity and computational overhead, they can improve the accuracy of the SOC algorithm at different aging stages and under different temperature conditions by actively and adaptively adjusting the parameters of the battery model. Reference [49] utilizes a data-driven approach, using deep neural networks to learn the complex mapping relationship between input data and SOC under multi-condition and aging conditions, which often requires more sufficient labeled data.

Wang et al. [51] proposed a SOC-SOH co-estimation method integrating temperature and aging factors. They employed Sage-Husa adaptive unscented Kalman filtering for dynamic SOC and capacity estimation while establishing mappings between SOH, capacity, and temperature using backpropagation neural networks (BPNNs). Validation across multiple temperatures and aging states showed RMSE below 1.2% for SOC and 2.5% for SOH. Bao et al. [52] introduced a dual-task learning framework for joint SOC and state of energy (SOE) estimation in battery packs. This approach captures task-relevant temporal features through GRU encoding enhanced by feature attention mechanisms while improving both model efficiency and accuracy via data preprocessing operations including correlation analysis and sliding windows. Validation on real-world operational data from six electric vehicles with cumulative mileage exceeding 80,000 km achieved SOC and SOE errors below 3%, demonstrating high precision and strong robustness under complex variable vehicle operating conditions.

Routh et al. [53] presented an online joint estimation method for SOC, SOH, and RUL that utilizes particle filtering (PF) with the DCL model to estimate capacity fade for SOH determination, dynamically updates capacity parameters during aging using estimated values, integrates updated capacity with ECM parameters for EKF-based SOC estimation, and characterizes capacity fade via ampere-hour throughput (AhT) to enable RUL prediction through the DCL model; experimental results demonstrated SOH relative error bands of ±0.05% and SOC error bands of 0% to −0.3% for new batteries versus 0% to −0.35% for aged batteries, outperforming existing joint estimation approaches.

3.1.3. Comparison and Summary of SOC Estimation

Despite significant progress in dynamic accuracy for SOC estimation, the sensitivity of model parameters to aging processes has become a major challenge in practical applications. As batteries undergo hundreds of cycles, active material loss at electrodes and electrolyte decomposition cause increased internal resistance and capacity fade. Without real-time capacity fade correction, conventional independent SOC estimation methods lacking aging state feedback may generate substantial errors during mid-to-late battery life stages.

A cross-scale coupling effect exists between rapid-timescale SOC dynamics and long-timescale aging evolution, driving development of cooperative estimation techniques for SOC, SOH, and model parameters. Precise identification of the dynamic evolution of these states is necessary for real-time updating of SOC model parameters. while multi-state estimation accuracy critically depends on accurate acquisition of SOH and model parameters. EIS captures electrode interface kinetics accurately in the frequency domain, providing essential parameter support for multi-state cooperative estimation. Consequently, when SOC estimation errors increase significantly due to accumulated aging, developing online EIS-based updating strategies will emerge as the core direction for overcoming multi-state estimation bottlenecks. Table 1 presents a comparison of SOC estimation methods along with their advantages and disadvantages.

Table 1. Comparison of SOC estimation methods.

SOC Estimation Paradigm	Method Example	Core Advantages	Limitations	Future Development Direction
Single-state estimation	[39,40,41,43]	High real-time performance	Ignores parameter aging drift	Requires SOH feedback for calibration
Multi-state cooperative estimation	[48,49,50,52]	Adapts to model parameter variations induced by aging	Dependent on SOH and model parameter estimation accuracy	Design of online EIS recalibration mechanisms

Table 1. Comparison of SOC estimation methods.

SOC Estimation Paradigm	Method Example	Core Advantages	Limitations	Future Development Direction
Single-state estimation	[39,40,41,43]	High real-time performance	Ignores parameter aging drift	Requires SOH feedback for calibration
Multi-state cooperative estimation	[48,49,50,52]	Adapts to model parameter variations induced by aging	Dependent on SOH and model parameter estimation accuracy	Design of online EIS recalibration mechanisms

3.2. SOH Estimation

3.2.1. Single-State SOH Estimation Using Time-Domain Features

SOH is an indicator that describes the degree of battery aging, characterizing the degradation of its current performance relative to its initial performance. It can be defined in two ways: based on capacity or based on internal resistance, with the capacity-based definition being the most widely used. The capacity-based SOH is expressed as shown in Equation (7) according to [54,55].

$$SOH={\displaystyle \frac{C_t}{C_n}}\times 100\%$$

(7)

where $C_n$ is the initial rated capacity and $C_t$ is the maximum available capacity.

SOH estimation includes two primary paradigms: single-state SOH estimation and cooperative SOH estimation integrated with other states. Single-state SOH estimation method fundamentally constructs health indicators manually from charge–discharge data based on aging mechanisms or extracts features through deep neural networks before designing prediction algorithms for SOH estimation. Hou et al. [56] extracted charging health indicators including time to peak temperature, constant voltage phase duration for equal current drop, and constant current phase duration for equal voltage rise. After analyzing health factor correlations with SOH using Spearman and Pearson coefficients, they proposed a Beetle Antennae Search optimized extreme learning machine method for SOH estimation. Zhu et al. [57] extracted six statistical features from relaxation voltage curves—variance, skewness, maximum, minimum, mean, and kurtosis—achieving minimum RMSE of 1.1% for SOH estimation through XGBoost and support vector regression (SVR) methods. Their transfer model constructed via feature linear transformation further reduced validation dataset RMSE below 1.7%. Additionally, laboratory conditions enable stable extraction of diverse time-domain health indicators from constant voltage charging [58] and discharge curves [59].

Practical electric vehicle operation involves complex charge–discharge conditions that typically yield incomplete and stochastic charging data with inherently nonlinear mappings to SOH. Consequently, researchers increasingly utilize deep neural networks to establish direct mappings between health features and SOH, enabling accurate prediction under complex real-world operating conditions. Deng et al. [60] extracted statistical features from battery charging data, determining optimal feature sets through correlation analysis and feature selection. Their sequence-to-sequence deep neural network model predicted future capacity trajectories while two Gaussian process regression-based residual models compensated prediction errors caused by local capacity variations. This framework achieved capacity prediction errors below 1.6% on real-world electric vehicle data as depicted in Figure 6a. Lu et al. [61] developed a robust data-driven framework incorporating gated convolutional neural networks (GCNN) for battery SOH estimation, enhancing model performance on new datasets and limited training data through fine-tuning techniques. Validation using 1.2 million charging segments from 464 electric vehicles demonstrated algorithm efficacy.

Zhang et al. [62] extracted twelve health indicators from multi-stage fast charging curve data, including peak voltage, valley voltage, and voltage gradients at current transition points for each charging phase. Their radial basis function neural network approach achieved MAE and RMSE below 0.90% and 1.10%, respectively, for SOH prediction across diverse battery types under various fast charging modes. Wang et al. [63] identified the first peak, valley, and corresponding voltages in incremental capacity curves as health indicators, establishing nonlinear mappings between health features and SOH through deep belief networks. This method demonstrated SOH prediction errors as low as 2% when validated on three lithium iron phosphate battery datasets with different discharge depths. It should be noted that precise IC curve acquisition remains challenging under real-world operating conditions due to measurement noise and sensor resolution limitations. Bilfinger et al. [64] demonstrated that data collection at 10 s intervals typically proves sufficient for practical IC curve analysis applications.

3.2.2. Single-State SOH Estimation Using Frequency-Domain Features

Traditional SOH estimation methods primarily rely on external parameters such as current, voltage, and temperature, which can be easily affected by noise and operating condition variations. EIS captures rich internal electrochemical dynamics, providing reliable SOH estimation references. With advancements in EIS theory, correlations between EIS characteristics and SOH have been increasingly investigated. EIS-derived features constitute frequency-domain indicators offering mechanism-level reflection of lithium-ion battery degradation across frequency bands. Principal EIS-extracted features include: broadband characteristics [65,66,67], equivalent fractional-order model parameters [68,69], and specific-frequency attributes [70,71,72,73,74].

Xia et al. [75] employed sequential forward selection with multi-objective optimization to extract EIS health indicators, developing a sine sparrow search-optimized support vector regression model that achieves SOH estimation errors below 2.58%. Zhang et al. [76] leveraged prior knowledge of battery dynamics to extract geometric health indicators from EIS that exhibit approximately linear correlation with SOH, subsequently developing a deep sigma-point process model with cyclic architecture for SOH estimation. Zhang et al. [77] employed variational autoencoders to learn latent space distributions in EIS data, subsequently applying variational mode decomposition to isolate capacity-correlated components from the extracted features. These processed features were then mapped to SOH via a bidirectional gated recurrent unit model, with the algorithm framework shown in Figure 6b. While frequency-domain SOH estimation methods are immune to time-domain noise interference and complex charging behaviors, but require higher measurement costs and must incorporate precise offline or online EIS measurement results to achieve accurate SOH estimates.

3.2.3. SOH and Multi-State Cooperative Estimation

The paradigm of cooperative estimation integrating SOH with other parameters not only focuses on SOH estimation itself but also enables simultaneous identification of correlated states including degradation modes, electrode degradation status, and internal battery impedance. Sun et al. [78] obtained internal resistance data from 9.4 Ah prismatic cells under varied SOH, SOC conditions, temperatures, and charge/discharge rates through modified reference performance characterization testing, developing a health-state-incorporated dynamic resistance model via least squares support vector machines. He et al. [79] introduced frequency-domain degradation mode estimation, employing Pearson correlation analysis to select maximally correlated time-domain features, and achieved precise SOH prediction using sparse spectrum Gaussian process regression, as shown in Figure 6c. In contrast to the single-state estimation methods presented in references [60,77], the method in reference [79] focuses more on utilizing the aging pattern quantification indicators obtained in the frequency domain to select the time-domain features most relevant to SOH. This approach helps eliminate redundancy in the time-domain features and achieve more interpretable SOH estimation results.

At a more microscopic scale, Reference [16] links battery SOH degradation to electrode aging states by proposing stoichiometric states for quantifying degradation modes, further enabling online estimation of both capacity and power degradation indicators alongside real-time degradation mode identification. Three main degradation modes, i.e., loss of the lithium inventory (LLI), loss of active material in the positive electrode (LAM_PE), and loss of active material in the negative electrode (LAM_NE), are quantified using Equations (8)–(10):

$$LLI=1-{\displaystyle \frac{C_{PE,t}{\theta }_{EOC,t}^{+}+C_{NE,t}{\theta }_{EOC,t}^{-}}{C_{PE,0}{\theta }_{EOC,0}^{+}+C_{NE,0}{\theta }_{EOC,0}^{-}}}$$

(8)

$$LA{M}_{PE}=1-{\displaystyle \frac{C_{PE,t}}{C_{PE,0}}}$$

(9)

$$LA{M}_{NE}=1-{\displaystyle \frac{C_{NE,t}}{C_{NE,0}}}$$

(10)

where ${\theta }_{EOC}^{+}$ and ${\theta }_{EOC}^{-}$ are the stoichiometric states of positive electrode (PE) and negative electrode (NE), respectively. $C_{PE}$ and $C_{NE}$ are the capacity of the positive electrode and negative electrode. The subscripts 0 and t represent the fresh battery and the aged battery, respectively. Zhang et al. [80] implemented physics-informed neural networks to reconstruct internal electrode states, subsequently generating incremental capacity and differential voltage curves for health feature extraction and accurate SOH estimation. This integrated paradigm simultaneously expands the functions of battery management system, enhances SOH estimation accuracy, and strengthens physical interpretability.

Figure 6. SOH estimation methods: (a) single-state SOH Estimation using time-domain data [60]; (b) single-state SOH estimation using frequency-domain data [77]; (c) time-frequency fusion for aging mode characterization and SOH cooperative estimation [80].

Figure 6. SOH estimation methods: (a) single-state SOH Estimation using time-domain data [60]; (b) single-state SOH estimation using frequency-domain data [77]; (c) time-frequency fusion for aging mode characterization and SOH cooperative estimation [80].

3.2.4. Comparison and Summary of SOH Estimation

The core value of SOH estimation extends beyond quantifying current aging status to providing constraints for capacity fade trajectory modeling, which forms the foundation for high-confidence RUL prediction.

Table 2. Comparison of SOH estimation methods.

SOH Estimation Paradigm	Method Example	Core Advantages	Limitations	Future Development Direction
Time-domain-based method	[54,55,60,61]	Large data availability with rich aging characteristics	Affected by SOC operating range	High Robustness and Strong Generalization Capability
Frequency-domain-based method	[65,66,76,77]	Direct acquisition of electrode-level aging features with intuitive degradation trends	Dependent on accurate online EIS measurements	Driving physics-informed RUL prediction
Multi-state cooperative estimation	[78,79,80]	Macro-micro integration	Multi-scale coordination	Bridging SOC and RUL

systematically compares performance differences among time-domain feature methods, frequency-domain feature methods, and multi-state cooperative estimation approaches. Fundamentally, microscopic aging mechanisms including SEI layer growth kinetics, lithium inventory loss, and electrode structural damage serve as the fundamental drivers of battery lifespan degradation, while SOH merely represents their macroscopic manifestation. This necessitates cooperative estimation of SOH with parameters such as electrode aging status and interface impedance to accurately capture battery aging progression. Building upon this foundation, RUL prediction should go beyond traditional statistical models by using historical SOC and SOH data to build lifetime trajectory models informed by electrochemical mechanisms. This shift moves the approach from empirical prediction toward physics-driven estimation.

3.3. RUL Prediction

3.3.1. RUL Prediction Using Degradation Empirical Models

RUL is defined as the number of remaining operational cycles until end-of-life, requiring accurate prediction through modeling of battery degradation trends, with its mathematical expression given in Equation (11):

$$RU{L}_i=N_{EOL}-N_i$$

(11)

where $RU{L}_i$ denotes RUL in the i-th cycle, $N_{EOL}$ denotes the cycle number at which a battery is considered to have reached its end of life, $N_i$ denotes the cycle number of the i-th cycle.

Typical single-state RUL prediction methods rely on historical capacity fade data to establish mapping relationships between capacity degradation and cycle count using semi-empirical models or deep learning techniques.

Empirical models effectively characterize comprehensive capacity degradation behaviors across diverse operating conditions due to their structural simplicity. Han et al. [81] developed a semi-empirical framework integrating Arrhenius kinetics with power-law functions, utilizing genetic algorithms for parameter identification and implementing cumulative degradation theory to predict capacity fade under dynamic cycling conditions. For grid-scale energy storage applications, Xu et al. [82] developed a dual-exponential model for grid-scale energy storage that integrates internal degradation mechanisms, such as SEI layer growth, with external operating factors including cycle count, SOC, temperature, and depth of discharge (DOD). The model’s effectiveness was validated under PJM regulation cycles. Due to the limited capability of empirical models in capturing high-order nonlinear degradation behaviors, researchers have turned to hybrid approaches that combine them with nonlinear filtering or deep learning for real-time trajectory identification and correction. Shi et al. [83] introduced a time-varying nonparametric kernel density estimator integrated with adaptive kernel auxiliary particle filters, significantly enhancing remaining useful life prediction accuracy. Meng et al. [84] used important points from local charging curves to generate pseudo-degradation trajectories that guide long short-term memory network training, enabling end-to-end early prediction of battery degradation patterns as illustrated in Figure 7. The advantage of this method is that it does not require complete charging curves as input data, making it applicable to most passenger and commercial vehicle use cases. Moreover, the introduction of empirical models provides additional supervisory information for neural network learning. However, the challenge of this method lies in how to trade off data-driven losses and empirical model losses during training to achieve convergence of prediction errors.

Meng et al. [85] implemented model-free Kalman filtering for state tracking to process partial battery degradation data, transforming the raw time-series prediction problem into forecasts of virtual degradation rates and accelerations. This was executed through an iterative Gaussian process regression strategy with sliding windows for multi-step capacity fade prediction. Zhang et al. [86] addressed unpredictable phenomena such as capacity recovery or sudden capacity drops caused by unknown switching points between stable and rapid degradation states, proposing a RUL prediction method based on nonlinear drift-driven Wiener processes and Markov chain switching models to enhance RUL prediction accuracy and adaptability. While these approaches achieve high-precision degradation trajectory identification through explicit capacity modeling, their inability to incorporate multi-state physical coupling mechanisms constrains generalization capability under complex operating conditions.

3.3.2. Data-Driven RUL Prediction

Data-driven models are increasingly employed for remaining useful life prediction owing to their superior nonlinear fitting capabilities. Zhao et al. [87] selected 16 critical features from 79 candidates including direct, evolutionary, and statistical characteristics using a discretization and feature-importance fusion strategy, subsequently developing a sparse autoencoder-Transformer ensemble model for RUL prediction. Their approach constrained prediction error below 7.43% using merely 30 charge–discharge cycles, achieving a maximum error of only 2.6% in early-stage prediction with the first 100 cycles, as shown in Figure 8. With its large set of manually constructed features, this method can identify the most suitable features for different operating conditions, showing significant advantages in RUL prediction tasks with limited cycle data samples.

Capacity degradation curves of lithium-ion batteries are not strictly monotonic due to uncontrolled internal chemical reactions, which can occasionally lead to small capacity recoveries. Such non-monotonic behavior introduces noise that can significantly interfere with the model’s ability to capture the overall degradation trend. To address this issue, Liu et al. [88] extracted global degradation trends while simultaneously eliminating oscillatory noise components via empirical mode decomposition of capacity fade curves, subsequently inferring complete degradation trajectories and remaining useful life through a GRU-FC hybrid network. Yao et al. [89] derived statistical features by fitting Gaussian mixture distributions to incremental capacity curve probability densities, concurrently extracting physical features from discharge cycles. Following preprocessing and integration, these multimodal features were processed by a feature-encoding LSTM-CNN architecture, achieving a 29.4% reduction in prediction mean square error.

Xia et al. [90] extracted high-indirect-correlation health indicators from charge/discharge characteristics, applying a novel trend segmentation strategy to generate fuzzy-granulated upper and lower bound subsequences. These subsequences were denoised through variational mode decomposition, then modeled and predicted using gated recurrent units. By integrating the dual prediction sequences, they ultimately constructed an interval prediction model for RUL. To explicitly quantify the impact of degradation knee points on residual lifespan, researchers have established joint modeling frameworks for simultaneous RUL and knee point prediction [91,92,93]. This reliably ensures precise tracking of degradation trajectories while preventing substantial prediction errors at knee points.

3.3.3. SOH-RUL Cooperative Prediction

SOH reflects the current maximum available capacity of a battery, and the degradation curve derived from this state serves as a key input for remaining useful life prediction. Fundamentally, both processes require accurate full-lifecycle prediction of maximum remaining capacity. Consequently, researchers increasingly integrate SOH estimation with RUL prediction. Zhou et al. [94] extracted critical health features including constant-current charge time and constant-voltage charge time from lithium-ion battery cycling data, enhancing SOH and residual capacity prediction through bilinear CNN and fractional-order PSO–ACO-optimized categorical boosting. Pang et al. [95] formulated capacity estimation and RUL prediction as dynamic nonlinear filtering problems, achieving precise recursive forecasting via improved particle swarm optimization integrated with particle filtering. Guo et al. [96] extracted 11 health features from multi-stage charging profiles including time-to-3.4 V during charging, time-to-2 V-cutoff during discharging, and charging temperature drop, then applied Savitzky–Golay filtering before feeding smoothed features into gated recurrent units for simultaneous SOH-RUL prediction, maintaining prediction errors below 1.00% across the full lifecycle. Feng et al. [97] employed charging-voltage differentiation and multi-strategy attention regression to comprehensively extract temporal features, attaining determination coefficients of 0.99 for SOH and 0.94 for RUL in joint estimation.

3.3.4. Comparison and Summary of RUL Prediction

RUL prediction not only provides decision-making basis for maintenance and replacement of EV power batteries but also guides whole-vehicle energy management strategy optimization through dynamic reconstruction of safety margins.

Table 3. Comparison of RUL prediction methods.

SOH Estimation Paradigm	Method Example	Core Advantages	Challenges	Future Development Direction
Empirical Model-Based Methods	[81,82,83,84]	Low computational complexity and high efficiency	Poor adaptability to operational condition variations	Empirical models constrain data-driven models
Data-Driven Methods	[87,88,89,90]	Adaptability to complex operating conditions	Requires accurate historical SOH as input	Integration with data generation methods to enhance cross-condition adaptability
SOH-RUL Cooperative Estimation	[94,95,96,97]	Suitable for real-time recursive estimation	Requires correction of recursive cumulative errors	Feedback correction of SOH and RUL prediction accuracy

systematically compares empirical models-based methods, data-driven-based methods, and SOH-RUL cooperative estimation methods. Empirical models demonstrate significant advantages in grid-scale energy storage applications with stable operating conditions due to mathematical simplicity and physical interpretability. However, data-driven methods, while adaptable to dynamic characteristics under random loads and complex conditions in electric vehicles, face limitations from historical data dependency and cross-scenario generalization capability. When historical data is limited, cooperative estimation strategies combining SOH recursive prediction with deep learning offer greater advantages than traditional methods. Electrochemical mechanism-constrained lifetime trajectory modeling circumvents the “black-box” limitations of pure data-driven approaches while resolving the adaptability bottleneck of empirical models in dynamic scenarios, delivering high-confidence RUL prediction solutions for battery management systems.

3.4. Summary of the Generational Transition

In this section, we summarize the representative methods, lab tests, and datasets for the generational transition, as shown in

Table 4. Summary of the generational transition from the perspectives of methods, lab tests, and datasets.

State	Generation	Methods	Lab Tests	Datasets
SOC	First	Coulomb counting [8], Kalman filtering [40,41]	Capacity test, HPPC test, and OCV-SOC test	New European driving cycle, Federal test procedure [41]
	Second	Neural networks [44], filtering and neural network hybrid methods [46]	First generation tests under various temperatures and C-rates	DST, BBDST and DST test datasets under different temperature [44,46]
	Third	Joint estimation of SOC and battery parameters [48,50]	The EIS test is added to the second-generation tests	RPT and EIS tests datasets [48] FUDS tests datasets [50]
SOH	First	Ampere-hour throughput during the charging process [9]	Capacity test and cycling test	Laboratory cycling test datasets [9]
	Second	Neural networks [60,77],	Cycling test and real-world electric vehicle data	Real-world commercial electric vehicle data [60,61], EIS datasets [77]. MIT tests datasets [59]
	Third	Time-frequency fusion methods [80] Physics-informed neural network [80]	Cycling test, EIS test, and real-world electric vehicle data	NCA and NCM battery datasets with EIS [77]
RUL	First	Empirical models [81], Wiener processes and Markov chain switching models [86]	Cycling test under various temperatures and C-rates	NASA tests datasets [83]
	Second	Neural networks [6,89], hybrid model [12,88]	Cycling test and random real-world electric vehicle data	CALCE tests datasets [84] MIT tests datasets [87]
	Third	Dual time-scale state-coupled co-estimation [13], Physics-informed neural network [98]	Cycling test, EIS test, and random real-world electric vehicle data	NCA and NCM battery datasets with EIS [77]

. This overview illustrates the evolution of theoretical algorithms and the growing use of diverse datasets across the generational transition in SOC estimation, SOH estimation, and RUL prediction.

For the first-generation battery state estimation systems, Kalman filtering-based SOC estimation methods typically require lithium-ion battery models constructed from OCV-SOC tests, HPPC tests, and capacity tests. These models are then validated under dynamic operating conditions such as DST and BBDST tests. For SOH estimation and RUL prediction, cycle life tests involving multiple full charge–discharge cycles are required to develop Ampere-hour throughput-based methods or empirical capacity fade models. the first-generation methods are limited in their ability to capture the nonlinear relationships present in these datasets.

For the second-generation battery state estimation systems, the introduction of artificial neural networks has led to increasing attention on uncovering latent features and patterns within data. Many battery datasets now include variations in temperature, discharge rate, and depth of discharge, enabling researchers to rapidly evaluate the estimation accuracy of neural network-based methods under diverse operating conditions. Moreover, researchers have begun applying artificial neural networks to real-world electric vehicle data to meet the practical demand for accurate state estimation from highly stochastic and complex operational data.

For third-generation battery state estimation systems and their future development, the rapid advancement of EIS measurement technology enables researchers to extract microscopic aging parameters from battery internals, increasingly integrating them with artificial neural network-based methods to enhance joint estimation accuracy of SOC, SOH, and RUL. Consequently, EIS test data are incorporated into cycling aging experiments to quantify the evolution characteristics of microscopic aging parameters across the aging timeline. After that, the design of closed-loop systems has evolved gradually. When the battery’s remaining useful life falls short of expectations or its aging rate increases, the operational strategy needs to be adjusted to extend its remaining useful life.

4. Future Evolution: Closed-Loop System for Multi-State Cooperative Estimation

4.1. Development of Multi-State Cooperative Estimation Methods

Future advancements in battery state estimation will focus on multi-state cooperative estimation of SOC, SOH, and RUL, establishing micro-macro scale parameter transfer mechanisms to achieve precise mapping between electrode aging status and system-level performance, thereby overcoming accuracy limitations of single-state estimation. Such approaches have demonstrated promising progress [53,98,99]. Liu et al. [99] designed a novel end-to-end multi-time-resolution attention-based interaction network that intelligently extracts multi-scale temporal features from battery cycling data through a multi-resolution patching module, interactive learning module, and multi-head self-attention mechanism, achieving MAE below 0.45% for SOC, 0.45% for SOH, and 63 cycles for RUL prediction.

When RUL predictions show a declining remaining life, operational strategies such as charging protocols, discharging protocols, and maintenance schedules can be adjusted to extend the battery’s lifespan, thus realizing closed-loop regulation of battery’s multiple-states [100,101,102]. Zhu et al. [103] propose a method for extending the cycle lifetime of lithium-ion batteries by raising the lower cutoff voltage to 3 V when the capacity degradation threshold is reached, as shown in Figure 9. The method is applied to three different types of lithium-ion batteries and results in a 16.7% to 38.1% increase in cycle life at 70% of their beginning-of-life capacity. It offers significant benefits in terms of cost savings, environmental impact reduction, and enhanced suitability for second-life applications.

In recent years, researchers have explored methods to extend the remaining useful life of batteries, and constructing a digital twin model [104] of the battery has emerged as one of the primary approaches. Ji et al. [105] propose a digital twin-based charging management framework that provides real-time battery state estimation and adaptive charging adjustments based on reinforcement learning according to user preferences over the lifecycle, improving user satisfaction and extending battery lifespan. In [105], the reward function is designed as shown in Equations (12)–(14):

$$\left\{\begin{array}{c}{r}_t^V=1-{\displaystyle \frac{‖\widehat{V}-V‖}{‖\widehat{V}‖}}\\ r_t^{SOC}=1-{\displaystyle \frac{‖S\widehat{O}C-SOC‖}{‖S\widehat{O}C‖}}\\ r_{cycle}^{SOH}=1-{\displaystyle \frac{‖S\widehat{O}H-SOH‖}{‖S\widehat{O}H‖}}\end{array}\right.$$

(12)

$$\left\{\begin{array}{c}{r}_{cycle}^{time}={\displaystyle \frac{ti\widehat{m}{e}_{ch}-tim{e}_{ch}}{ti\widehat{m}{e}_{ch}}}\\ r_{cycle}^{RUL}={\displaystyle \frac{RUL-R\widehat{U}L}{R\widehat{U}L}}\end{array}\right.$$

(13)

$$R\left(s,a\right)=\left({\omega }_1{r}^{ctrl}+{\omega }_2{r}^{time}+{\omega }_3{r}^{RUL}\right)\left({\omega }_4{r}^V+{\omega }_5{r}^{SOC}+{\omega }_6{r}^{SOH}\right)$$

(14)

where $r_t^V$, $r_t^{SOC}$ and $r_t^{SOH}$ are the evaluations of voltage, $SOC$ and $SOH$, which are used together with data drift monitoring to guide the time of update of digital twin models. $r_{cycle}^{time}$ and $r_{cycle}^{RUL}$ are the reward quantification for improving charging efficiency and extending service life, respectively. $r^{ctrl}$ is the reward quantification for changing the action of digital twins when the battery charging preference changes. Adopting these reward functions can enable the state of the digital twin model to approximate that of the physical battery. Then, based on the current output of the digital twin, control instructions are generated to extend the remaining useful life of the battery.

4.2. Future Evolution of Multi-State Closed-Loop System

Despite these developments, the spatiotemporal mismatch between sub-second scale SOC dynamic responses and weekly-to-monthly scale SOH/RUL aging evolution remains a core bottleneck for multi-state closed-loop estimation systems. To address this, we propose a SOC-SOH-RUL multi-state bidirectional cooperative closed-loop system. In the forward path, battery microscopic aging parameters are obtained by introducing EIS measurements, which guide the SOC, SOH, and RUL estimation algorithms to produce more accurate outputs. In the inverse path, an optimization problem is solved to maximize the remaining battery life and minimize the degradation rate of health states and microscopic aging parameters, yielding optimal charging SOC boundaries and charging rates that extend the battery’s useful life. The system architecture is illustrated in Figure 10.

The forward path of multi-state cooperative estimation operates as follows: When battery aging induces significant SOC estimation errors, EIS measurements are performed on the vehicle-mounted battery to recalibrate the battery model through parameter re-identification. Subsequently, internal microscopic parameters, including ohmic resistance, SEI layer resistance, electrode stoichiometric states, and lithium inventory loss, are extracted and quantified from the measured EIS. Through correlation analysis between microscopic parameters and time-domain features extracted from macroscopic battery data, the time-domain features that contribute most significantly to battery degradation are identified, enabling accurate SOH estimation. These SOH estimates form degradation curves that provide reliable input data for RUL prediction, while the identified microscopic parameters impose physical constraints on RUL prediction, thereby enhancing both prediction accuracy and interpretability.

The inverse feedback path operates as follows: First, we calculate the difference between the predicted RUL and the theoretical RUL in the forward path, as well as the degradation rate of SOH over the most recent interval. When both the remaining life and the SOH degradation rate exceed predefined thresholds, the battery is considered to be undergoing rapid aging and facing potential safety risks. Second, RUL and SOH are described as functional relationships with respect to the upper charging SOC boundary, lower discharging SOC boundary, charging rate, and battery microscopic aging parameters. An optimization problem is formulated to maximize the remaining useful life and minimize the degradation rates of SOH and microscopic aging parameters. A charging capacity constraint is applied to ensure that each charging cycle meets the operational requirements of electric vehicles. Finally, after solving the optimization problem, the battery state estimation system actively optimizes the SOC boundaries for charging and discharging as well as the charging rate. This helps suppress side reaction rates in the high-SOC and low-SOC regions, slow down the aging process of microscopic parameters, reduce SOH degradation, and thereby extend the actual RUL. Consequently, the lifespan boundary derived from RUL prediction feeds back to the SOC control layer, closing the loop to achieve collaborative autonomy through the “estimation–prediction–optimization” framework.

By establishing this bidirectional closed-loop system, the BMS acquires proactive decision-making capability to dynamically reconstruct safety margins based on aging mechanisms. This achieves optimal balance between performance requirements and service life extension, fundamentally overcoming the limitations of traditional BMS passive response architectures.

5. Conclusions and Outlook

This review systematically traces the evolutionary trajectory of three-generation battery state estimation methods: First-generation single-state estimation methods based on equivalent circuit models offer computational simplicity but fail to correlate with internal electrochemical behaviors; second-generation data-driven approaches, while capable of fitting nonlinear characteristics, suffer from weak generalization capability and poor interpretability due to “black-box” limitations; third-generation gray-box models integrating electrochemical mechanisms overcome these constraints through multi-state cooperative estimation, simultaneously estimating sub-second scale dynamic parameters (SOC) and long-term aging states (SOH, RUL) via cross-scale state coordination mechanisms, significantly enhancing estimation accuracy and operational adaptability across diverse conditions.

Future advancements will focus on multi-state cooperative estimation of powertrain SOC, SOH, and RUL across heterogeneous time scales. This review proposes a bidirectional closed-loop system for SOC-SOH-RUL multi-state cooperative estimation that establishes quantitative correlations between microscopic electrode interface reactions and macroscopic system performance degradation through electrochemical impedance spectroscopy and electrochemical kinetic equations. This framework resolves the spatiotemporal mismatch between dynamic responses and aging evolution inherent in conventional methods, improving full-lifecycle estimation accuracy and robustness for SOC, SOH, and RUL. By optimizing SOC operating ranges based on RUL predictions, the system extends remaining service life while ensuring safety. Breakthroughs in state estimation technology will significantly enhance intelligent battery operation and maintenance capabilities, providing core support for electric vehicle range optimization, fault prognosis, and second-life applications, thereby driving the evolution of new energy transportation systems toward higher reliability, extended service life, and reduced costs.