Lithium battery SOC (state of charge) and SOH (state of health) joint estimation method based on dual-high-order volume Kalman filtering

Abstract

The invention discloses a lithium battery SOC (State of Charge) and SOH (State of Health) joint estimation method based on dual-high-order volume Kalman filtering. The method comprises the following steps: firstly, based on a second-order RC equivalent circuit model of a lithium battery; equivalent circuit parameters are identified through a pulse power characteristic experiment, and an OCV-SOC relation curve is fitted through an open-circuit voltage experiment; constructing a dual-high-order volume Kalman filter, wherein the dual-high-order volume Kalman filter comprises an SOC estimation filter and an SOH estimation filter which are parallel to each other; the SOC filter operates in real time according to a sampling period; and finally, taking the SOC estimation value as an observed quantity of an SOH filter, using the SOH estimation value to correct a battery capacity parameter in the SOC filter, and introducing a time scale transformation factor. The method can effectively improve the precision and the real-time performance of battery state estimation, the operation efficiency is remarkably improved compared with an existing method, and the method is suitable for application scenes such as electric automobiles and energy storage power stations with high requirements for the battery state monitoring precision and the real-time performance.

Description

Technical Field

[0001] This invention relates to the field of battery management systems, specifically a joint estimation method for SOC and SOH of lithium batteries based on dual high-order volumetric Kalman filtering. Background Technology

[0002] Lithium-ion batteries are widely used in electric vehicles, energy storage power stations, drones, and portable electronic devices due to their advantages such as high energy density, long cycle life, no memory effect, and environmental friendliness. The Battery Management System (BMS), as the core of the safe and reliable operation of lithium-ion batteries, has one of its main functions being the accurate estimation of the battery's State of Charge (SOC) and State of Health (SOH).

[0003] State of Charge (SOC) reflects the remaining usable capacity of a battery, while State of Harm (SOH) reflects the degree of performance degradation and remaining lifespan. Both are not only important parameters characterizing battery operating status but also crucial for energy optimization management, charge / discharge control, fault diagnosis, and lifespan prediction. A strong coupling exists between SOC and SOH: a decrease in SOH leads to changes in the battery's effective capacity, thus affecting the accuracy of SOC estimation; simultaneously, the trajectory of SOC changes provides a basis for long-term SOH estimation. Therefore, achieving joint estimation of SOC and SOH has become an important issue in BMS research and application.

[0004] Existing methods for State of Charge (SOC) estimation include the ampere-hour integration method, the open-circuit voltage method, the extended Kalman filter (EKF) based on the equivalent circuit model, the unscented Kalman filter (UKF), and the particle filter (PF). Among these, the ampere-hour integration method is significantly affected by accumulated errors, and the open-circuit voltage method requires long periods of inactivity, making it unsuitable for real-time applications. While EKF and UKF can improve the estimation accuracy of nonlinear systems to some extent, their stability is insufficient under strongly nonlinear or highly dynamic conditions. Although the particle filter offers high accuracy, its computational complexity is too high, hindering real-time implementation in embedded BMS. SOH estimation methods mainly include those based on internal resistance measurement, capacity decay modeling, and data-driven prediction. Traditional methods often require long-term cyclic testing or additional experimental data, making them difficult to meet the needs of practical online estimation. Furthermore, SOH changes relatively slowly; direct coupling estimation with SOC often increases the computational load of filtering, potentially impacting real-time performance.

[0005] In recent years, some studies have proposed joint estimation methods for State of Occurrence (SOC) and State of Hypothesis (SOH), such as Dual Extended Kalman Filter (DEKF), Dual Unscented Kalman Filter (DUKF), and Dual Capacitive Kalman Filter (DCKF). However, these methods still have the following shortcomings in practical applications: as the state dimension increases, the computational burden of the filter increases significantly, which is not conducive to the embedded implementation of BMS; under complex operating conditions (such as Dynamic Stress Condition (DST) or Urban Driving Condition (FUDS), the accuracy of joint estimation of SOC and SOH is still difficult to guarantee; most existing algorithms fail to effectively distinguish the time scale differences between SOC and SOH, resulting in low estimation efficiency.

[0006] In summary, existing SOC and SOH estimation methods have trade-offs in terms of accuracy, real-time performance, and computational complexity. There is still a lack of a joint SOC and SOH estimation method that can balance nonlinear processing capability, computational efficiency, and estimation accuracy. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and propose a joint estimation method for SOC and SOH of lithium batteries based on dual high-order capacitive Kalman filtering. This method can reduce the computational burden while ensuring estimation accuracy, and fully consider the time scale difference between SOC and SOH to achieve efficient joint estimation of the two.

[0008] To achieve the above objectives, the technical solution specifically adopted by the present invention is as follows:

[0009] A joint estimation method for SOC and SOH of lithium batteries based on dual high-order capacitive Kalman filtering includes the following steps:

[0010] S1. Based on the second-order RC equivalent circuit model, a state-space equation is constructed that includes the relationship between polarization voltage, current, open-circuit voltage (OCV), and terminal voltage. SOC is used as a rapidly changing state variable, while SOH, characterized by effective capacity, is introduced into the model as a slowly changing state variable. The relationship between OCV and SOC is obtained through polynomial fitting.

[0011] S2. The equivalent circuit parameters (R0, R1, R2, C1, C2) are identified by the pulse power characteristic experiment (HPPC), and the OCV-SOC curve is fitted by the open circuit voltage experiment to obtain the model parameters required for SOC estimation and SOH estimation.

[0012] S3. Design two parallel high-order capacitive Kalman filters. The first filter is used for State of Response (SOC) estimation, employing larger process noise to enhance dynamic response. The second filter is used for State of Response (SOH) estimation, using smaller process noise to ensure long-term estimation stability. Both filters are based on high-order capacitive sampling rules for state propagation to improve the estimation accuracy for nonlinear systems.

[0013] S4. The SOC estimation filter runs in real time according to the sampling period; a time scale transformation factor L is introduced into the SOH filter, and an SOH update is triggered after every L SOC estimation, thereby reducing the computational burden and improving the real-time performance of the system.

[0014] S5. In each estimation loop, the SOC estimation result is used as the observation input to the SOH filter, and the SOH estimation result is used to correct the capacity parameter in the SOC estimation filter, realizing closed-loop interaction and joint update between SOC and SOH.

[0015] This invention has the following characteristics and beneficial effects:

[0016] Compared with existing technologies, this invention has the following advantages: High estimation accuracy. Employing a high-order capacitive Kalman filter, it can better handle the nonlinear characteristics of lithium battery systems. Compared with extended Kalman filter (EKF), unscented Kalman filter (UKF), and dual capacitive Kalman filter (DCKF) methods, the estimation accuracy of SOC and SOH is significantly improved. High computational efficiency. By introducing a multi-timescale mechanism, SOC estimation runs at high frequency, while SOH estimation runs at low frequency, effectively reducing the overall computational complexity and significantly improving the real-time performance and feasibility of embedded systems.

[0017] The system exhibits strong robustness. The SOC estimation filter, configured with relatively large process noise, enables rapid response to dynamic operating conditions; the SOH filter, configured with relatively small process noise, ensures long-term stability. The complementary nature of these two filters enhances the overall robustness of the system. Furthermore, the joint estimation feature, through an information exchange mechanism, allows SOC estimation to provide rapid observations for SOH estimation, while SOH estimation corrects the SOC model parameters. This achieves synergistic optimization of SOC and SOH, improving the stability and reliability of the system estimation.

[0018] Experimental verification has been thorough, demonstrating that this method can control the mean absolute error of SOC to within 0.6% and the SOH estimation error to within 0.3%, far superior to existing methods. The proposed method and system for joint estimation of lithium battery SOC and SOH based on dual high-order capacitive Kalman filtering balances estimation accuracy, computational efficiency, and real-time performance. It is suitable for electric vehicles, energy storage power stations, and other scenarios with high requirements for battery state monitoring, and has broad application prospects. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the second-order RC equivalent circuit model of a lithium battery.

[0020] Figure 2 This is a schematic diagram of the battery terminal voltage response curve under a single pulse discharge, used for model parameter identification.

[0021] Figure 3 This is a block diagram of the overall structure for jointly estimating battery state using the DHCKF algorithm proposed in this invention.

[0022] Figure 4 This is the battery terminal voltage change curve during the HPPC experiment.

[0023] Figure 5 This is the discharge current variation curve of the battery in the HPPC experiment.

[0024] Figure 6 The OCV-SOC relationship curve is obtained by fitting experimental data.

[0025] Figure 7 This is a segment of the terminal voltage response curve used for parameter calculation.

[0026] Figure 8 This is a comparison chart of the SOC estimation results of the method of this invention and other comparison algorithms under FUDS conditions.

[0027] Figure 9 This is a comparison chart of the SOC estimation errors of various algorithms under the FUDS condition.

[0028] Figure 10 This is a comparison chart of the SOH estimation results of the method of this invention and other comparative algorithms under FUDS conditions.

[0029] Figure 11 This is a comparison chart of the SOH estimation errors of various algorithms under the FUDS condition. Detailed Implementation

[0030] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0031] Example 1

[0032] This embodiment provides a joint estimation method for SOC and SOH of lithium batteries based on dual high-order capacitive Kalman filtering, such as... Figure 1 As shown, it includes the following steps:

[0033] S1. Based on the second-order RC equivalent circuit model of lithium battery, state-space equations with SOC as the core state variable and state-space equations with battery capacity as the SOH characterization quantity are established respectively.

[0034] In this embodiment, the battery model is the foundation for state estimation. Establishing the battery model is the first step in Kalman filtering to estimate SOC and SOH, and a highly reliable battery model is the basis for SOC and SOH estimation.

[0035] In this embodiment, SOC is defined as the ratio of remaining battery capacity to nominal battery capacity under the same environmental conditions and a specific discharge rate:

[0036]

[0037] Among them, Q res Q represents the remaining battery capacity after partial discharge. new This refers to the nominal battery capacity.

[0038] State of Balance (SOH) is typically reflected by capacity decay rate and internal resistance change. The SOH of a lithium battery is defined by its maximum capacity and can be expressed by the following formula:

[0039]

[0040] In the formula, Q cap This indicates the amount of electricity the battery can release when fully charged at the current moment. For brand new lithium batteries, the initial State of Charge (SOH) is typically greater than or equal to 1. However, as the battery is used more times, it gradually ages, leading to an increase in Q. cap The value gradually decreases, which in turn reduces the SOH value of the lithium battery.

[0041] Equivalent models of lithium batteries are mathematical models used to simulate and describe the dynamic behavior and characteristics of lithium batteries under different operating conditions. These models are crucial for system design, control algorithm development, and battery performance evaluation. Among them, the second-order RC circuit equivalent model is one of the common and suitable models, which can accurately describe the dynamic response and polarization effect of the battery.

[0042] By using a second-order RC circuit equivalent model, the effects of the battery's internal resistance, capacitance, and polarization capacitance on the charging and discharging process can be considered. This model structure allows us to better understand the voltage changes, internal resistance effects, and polarization effects during the battery's charging and discharging process, providing an important reference for system design.

[0043] like Figure 1 The second-order RC equivalent circuit model shown includes an ohmic resistor R0, two polarization resistors R1 and R2, and two polarization capacitors C1 and C2. The state variables are SOC, U1, and U2, where U1 and U2 are polarization voltages. The equivalent circuit parameters include R0, R1, R2, C1, and C2.

[0044] This second-order RC equivalent circuit model can accurately describe the dynamic response and polarization effect of the battery. OCU represents the battery open-circuit voltage, I represents the load current, and R0 represents the ohmic resistance. The second-order RC equivalent circuit contains two components consisting of concentration polarization resistors R1 and R2 and concentration polarization capacitors C1 and C2.

[0045] Based on the equivalent circuit model of the battery, the state equation and observation equation of the battery's SOC can be derived as follows.

[0046] Equations of state:

[0047]

[0048] Observation equation:

[0049]

[0050] Where T represents the current sampling period, η represents the charge / discharge efficiency of the lithium battery, and Q... n This represents the charge capacity of the lithium battery. The state variable is x. k =[SOC k U 1,k U 2,k The control variable is u. k =I k The observed variable is y k =U k The system noise is w k Its covariance is Q, and its observation noise is v. k Its covariance is R. h(SOC) k ) is the nonlinear relationship function between OCV and SOC.

[0051] The above matrix form can be further abstracted into a more general SOC state-space equation, which is expressed as:

[0052]

[0053] Wherein, the state variable is x k =[SOC k U 1,k U 2,k SOC k Let U be the state of charge of the battery at time k. 1,k The first-order RC branch voltage reflects the battery's polarization effect, U 2,k The second-order RC branch voltage reflects the diffusion effect of the battery, i k Let be the operating current of the battery at time k. A and B are the state transition matrix and input matrix, respectively, determined by the parameters of the battery equivalent circuit model. w k Let y be the process noise, representing the uncertainty of the system model. k For observation purposes, specifically the battery's terminal voltage, U oc(SOC k The open-circuit voltage is a nonlinear function of the state of charge (SOC), R0 is the ohmic internal resistance, and v k The observation noise represents the measurement error;

[0054] This paper defines SOH as capacity. Since the battery capacity does not change significantly in a short period of time, this means that the battery capacity at two adjacent moments can be considered a constant value. Therefore, the state equation and observation equation used to estimate the capacity can be expressed as follows.

[0055] Equations of state:

[0056] Q k+1 =Q k +r k

[0057] Observation equation:

[0058]

[0059] Wherein, the state variable is Q k The remaining capacity at time k is represented by the observed variable y. k =U k r is the predicted terminal voltage of the battery. k For system noise, v k To observe noise.

[0060] The more general state-space equation for SOH is expressed as:

[0061]

[0062] Where, θ k =Q k Let θ be the available capacity of the battery at time k. k r represents the state quantity of SOH. k This represents the noise during capacity decay, reflecting the uncertainty of capacity gradually decreasing with cycling. k To observe noise.

[0063] S2. Identify the equivalent circuit parameters through pulse power characteristic experiments, and fit the OCV-SOC relationship curve through open-circuit voltage experiments.

[0064] In this embodiment, the experimental subject is an 18650 ternary lithium battery (rated capacity 3.35Ah). An HPPC discharge experiment was conducted at a standard room temperature of 25°C. The experimental procedure was as follows: first, the battery was fully charged to 100% SOC, then pulsed discharged with a constant current. For every 10% decrease in SOC, the battery was allowed to stand for a period of time, and the stable open-circuit voltage was recorded until the discharge was stopped. The voltage and current curves obtained from the experiment are shown below. Figure 4 and Figure 5 As shown.

[0065] Specifically, the identification process is as follows:

[0066] OCV-SOC curve acquisition: The OCV value and corresponding SOC value were recorded after each period of battery rest. The battery OCV-SOC curve was plotted using the curve fitting toolbox in MATLAB. This article takes 7th-order polynomial fitting as an example to obtain the expressions for OCV and SOC:

[0067] U oc = a0 + a1 × SOC + a2 × SOC 2 +a3×SOC 3 +a4×SOC 4 +a5×SOC 5 +a6×SOC 6 +a7×SOC 7

[0068] Among them, a i (i = 0, 1, ... 7) are the parameters to be identified.

[0069] RC parameter identification and analysis Figure 7 The voltage rebound curve for a single pulse discharge is shown. According to the formula:

[0070]

[0071] Calculate R0 using the abrupt change in voltage at the instant the current is switched on and off (segments AB and CD), where U A U B U C U D ,yes Figure 7 The voltages at points A, B, C, and D, and I, the battery operating current, are given by the following two formulas:

[0072]

[0073] Calculate R1, R2, C1, and C2 using the subsequent slow voltage changes (segments BC and DE). Where U is the battery terminal voltage, R1 and R2 are the polarization resistances in the equivalent circuit, Δt is the time interval, and U... oc The open-circuit voltage (OCV) of the battery is determined by the state of charge (SOC). U1 and U2 represent the voltage drops in the first-order and second-order RC branches, respectively, reflecting the polarization effect of the battery. τ1 and τ2 correspond to the time constants of the first-order and second-order RC branches. This process is repeated for all SOC points to obtain the parameter identification results shown in Table 1.

[0074] Table 1. Parameter Identification Results

[0075]

[0076] S3. Construct a dual high-order capacitive Kalman filter, which includes a parallel SOC estimation filter and a SOH estimation filter, both of which use high-order capacitive sampling rules for state prediction and updating.

[0077] In this embodiment, the overall structure of the algorithm is as follows: Figure 3 As shown, this structure contains two parallel HCKF filters that estimate the SOC and SOH respectively and work together at different time scales.

[0078] SOC-HCKF Filter: This filter operates based on a simplified SOC state-space equation. It employs a high-order capacitive Kalman filter algorithm with a 5th-order capacitive rule, specifically including filter initialization, time update, and measurement update. This filter is responsible for updating the SOC value at a micro-timescale (each sampling period). In general, a nonlinear discrete system can be represented by the following state-space model:

[0079]

[0080] Where f corresponds to the SOC state equation function, and g corresponds to the SOC nonlinear observation equation function. Process noise w k With covariance matrix Q and observation noise v k Given a covariance matrix R, a high-order capacitive Kalman filter algorithm using a 5th-order capacitive rule is given, comprising three parts: filter initialization, time update, and measurement update. The steps are as follows:

[0081] (1) Filter initialization

[0082]

[0083] (2) Time update

[0084] Calculate the volume point x k,i (i = 0, 1, ..., 2n) 2 ).

[0085]

[0086] In the formula It is the state estimate at time k; P k S is the covariance matrix of the state variables at time k. k It is P k The Cholesky decomposition, i.e., P k =S k S T k .

[0087] Point set ξ i for

[0088]

[0089] Where, ξ i For the i-th volume point, e i Let i be the element in the i-th column of the n-dimensional identity matrix, i.e., the i-th basis vector. and They are respectively:

[0090]

[0091] The parameter j is the index or The number is determined by the following formula:

[0092]

[0093] State prediction in one step, calculation of the transfer volume point χ k+1 / k,i .

[0094] χ k+1 / k,i =f(x) k,i )

[0095] Calculate the predicted state value at time k+1

[0096] ω i The weights corresponding to the i-th volume point are used for weighted averaging:

[0097]

[0098] Estimate the prior state error covariance matrix P at time k+1. k+1 / k

[0099]

[0100] Among them, Q k For system noise covariance

[0101] (3) Measurement update

[0102] Calculate the volume points used for measurement updates:

[0103]

[0104]

[0105] Calculate the volume point y passed through the measurement equation. k+1,i .

[0106] y k+1,i =h(χ k+1 / k,i )

[0107] Calculate the predicted measurement value at time k+1

[0108]

[0109] Calculate the filter gain matrix K at time k+1. k+1

[0110]

[0111] Calculate the state estimate at time k+1

[0112]

[0113] SOH-HCKF Filter: This filter operates based on the SOH state-space equation. Its algorithm is the same as the SOC-HCKF, but the state variable is the battery capacity Q. n .

[0114] In this embodiment, the SOC filter is configured with a large process noise covariance, where the process noise variance configured in the filter is comparable to or even larger than the observation noise variance, to enhance the filter's adaptability to rapid changes in operating conditions. The SOH filter is configured with a small process noise covariance, where the process noise variance configured in the filter is much smaller than the observation noise variance, to characterize the slow decay of battery capacity.

[0115] S4, the SOC estimation filter runs in real time according to the sampling period, and the SOH filter is updated once after every L SOC estimations, where L is the time scale transformation factor.

[0116] In this embodiment, the time scale transformation factor L is set to 400. SOC-HCKF runs once per second, while SOH-HCKF runs only once after 400 SOC calculations. The new capacity value calculated by SOH-HCKF is immediately provided to SOC-HCKF to update its subsequent calculation model. As shown in Table 2, this multi-time scale method significantly reduces the algorithm runtime from 11.42 seconds to 0.028 seconds.

[0117] Table 2. Multi-timescale algorithm schedule

[0118]

[0119] S5. The algorithm performance is verified through experiments. The SOC estimate is used as the observation of the SOH filter. The SOH estimate is used to correct the battery capacity parameter in the SOC estimation filter. At the same time, a time scale transformation factor is introduced so that the estimation frequency of SOH is lower than the estimation frequency of SOC, thus realizing closed-loop interaction.

[0120] In this embodiment, to comprehensively evaluate the performance of the DHCKF algorithm, the FUDS working condition was selected for simulation experiments, and the results were compared with the DEKF, DUKF, and DCKF algorithms.

[0121] SOC performance estimation: From Figure 8 and Figure 9 The comparison results show that the DHCKF estimation curve is closest to the true value, with the smallest error. Table 3 shows that the DHCKF's mean absolute error (MAE) is 0.0059 and its root mean square error (RMSE) is 0.0074, both significantly better than the other three algorithms.

[0122] Table 3. SOC estimates MAE and RMSE

[0123]

[0124] SOH performance estimation: From Figure 10 and Figure 11 The comparison results show that DHCKF's SOH estimation result is closest to the true value of 1, and has the smallest fluctuation, demonstrating the best stability. Table 4 shows that DHCKF's MAE is 0.00071 and RMSE is 0.00086, with errors also significantly smaller than the comparison algorithms.

[0125] Table 4. SOH estimates MAE and RMSE

[0126]

[0127] Based on the simulation results above, the DHCKF-based joint estimation method provided in this embodiment exhibits excellent performance in both dynamic and steady-state conditions, verifying the effectiveness of the model and the rationality of the filter design. It can provide reliable SOC and SOH information support for practical BMS.

[0128] Example 2

[0129] This embodiment provides a battery management system, including a processor and a memory. The memory stores a computer program, and when the processor executes the program, it implements the lithium battery SOC and SOH joint estimation method based on dual high-order capacitive Kalman filtering disclosed in this embodiment.

[0130] Example 3

[0131] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the lithium battery SOC and SOH joint estimation method based on dual high-order capacitive Kalman filtering disclosed in this embodiment.

[0132] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

[0133] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filter, characterized in that, Comprising the following steps: S1, based on the second-order RC equivalent circuit model of lithium battery, the state space equation with SOC as the core state variable and the state space equation with battery capacity as SOH are established respectively; S2, the equivalent circuit parameters are identified through pulse power characteristic experiment, and the OCV-SOC relationship curve is fitted through open circuit voltage experiment; S3, a double high-order cubature Kalman filter is constructed, which includes a SOC estimation filter and a SOH estimation filter in parallel, both of which use high-order cubature sampling rules for state prediction and update; S4, the SOC filter runs in real time according to the sampling period, and the SOH filter triggers an update once every L times of SOC estimation, L being a time scale transformation factor; S5, the SOC estimation value is used as the observation value of the SOH filter, and the SOH estimation value is used to correct the battery capacity parameter in the SOC filter, and at the same time, a time scale transformation factor is introduced to make the estimation frequency of SOH lower than that of SOC, realizing closed-loop interaction.

2. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 1, characterized in that, The second-order RC equivalent circuit model in step S1 includes ohmic resistance R0, two polarization resistances R1 and R2, and two polarization capacitances C1 and C2, and the state variables are SOC, U1 and U2, wherein U1 and U2 are polarization voltages.

3. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 2, characterized in that, In step S2, the equivalent circuit parameters include R0, R1, R2, C1 and C2.

4. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 1, characterized in that, In step S1, the state space equation of SOC is represented as: where x is the state variable k = [SOC k U 1,k U 2,k ] T , SOC k is the state of charge of the battery at the kth time, U 1,k is the first-order RC branch voltage, reflecting the polarization effect of the battery, U 2,k is the second-order RC branch voltage, reflecting the diffusion effect of the battery, i k is the working current of the battery at the kth time, A and B are the state transition matrix and the input matrix, determined by the parameters of the equivalent circuit model of the battery, w k is the process noise, representing the uncertainty of the system model, y k is the observation, i.e., the terminal voltage of the battery, U oc is the open-circuit voltage of (SOC k ), which is a nonlinear function of SOC, R0 is the ohmic resistance, v k is the observation noise, representing the measurement error; The state space equation of SOH is represented as: where θ k = Q n,k is the available capacity of the battery at the kth time, where θ k represents the state quantity of SOH, r k is the capacity attenuation process noise, reflecting the uncertainty of the gradual attenuation of capacity with cycles, v k is the observation noise.

5. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 1, characterized in that, The OCV-SOC relationship in step S2 is obtained by polynomial fitting, and the expression is: U oc = a0 + a1 x SOC + a2 x SOC 2 + a3 x SOC 3 + a4 x SOC 4 + a5 x SOC 5 + a6 x SOC 6 + a7 x SOC 7 wherein a i are parameters to be identified, where i = 0, 1, … 7.

6. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 1, characterized in that, The high-order cubature Kalman filter in step S3 uses 5-order cubature rule for state prediction and measurement update.

7. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 1, characterized in that, The SOC filter is configured with a larger process noise covariance, and the SOH filter is configured with a smaller process noise covariance.

8. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 1, characterized in that, In step S4, a time scale transformation factor L is set, and once every L times of SOC estimation triggers SOH estimation and update, thereby realizing coordinated update under macro and micro time scales, and the value range of the time scale transformation factor L is 100-500.

9. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 8, characterized in that, The value of L is 400.

10. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 1, characterized in that, The high-order cubature Kalman filtering algorithm in step S3 comprises the following steps: Filter initialization; Time update: generate cubature points and perform state prediction; Measurement update: calculate filtering gain, update state estimation value and covariance matrix.

11. The lithium battery SOC and SOH joint estimation method based on double high-order cubature Kalman filtering according to claim 10, characterized in that, The set of cubature points used for one-step state prediction in the time update step is: where ξ i is the i-th volume point, e i is the i-th column element of the n-dimensional identity matrix, i.e. the i-th basis vector, and are respectively: The parameter j is an index or numbered by the following formula: ω i ωi is the weight value corresponding to the i-th volume point, used in the weighted average:

12. A battery management system, characterized by, A processor and a memory, the memory stores a computer program, and the processor implements the method of claim 1-11 when executing the program.

13. A computer readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the method of claim 1-11 based on the double high-order cubature Kalman filter for lithium battery SOC and SOH joint estimation.

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