Non-linear non-Gaussian system-oriented lithium ion battery SOC state estimation method based on MPR and IGS-SRCPF

Abstract

The invention discloses a non-linear non-Gaussian system-oriented lithium ion battery SOC state estimation method based on MPR and IGS-SRCPF, and the method comprises the steps: combining particle filtering with Gaussian sum filtering, and forming a Gaussian sum particle filtering algorithm; a Gaussian component fusion strategy idea is utilized to improve an existing unsupervised EM algorithm, and an IGS-SRCPF algorithm is obtained; the MPR of a nonlinear non-Gaussian system is defined in the IGS-SRCPF algorithm by referring to a linear Gaussian MPR definition mode, and the MPR-based IGS-SRCPF algorithm is obtained by combining a multi-target HPO-DOA optimization algorithm with a model adjustment coefficient and conditions capable of better designing a high-performance nonlinear non-Gaussian filter according to the particularity of the model adjustment coefficient in the nonlinear non-Gaussian system. Estimating the SOC state of the lithium ion battery by using an MPR-based IGS-SRCPF algorithm to obtain a state estimation result; and correcting the state estimation result by using the deep width learning fusion network to obtain the final SOC state estimation of the lithium ion battery.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of lithium battery SOC state estimation, and particularly relates to a lithium ion battery SOC state estimation method based on MPR and IGS-SRCPF for a nonlinear non-Gaussian system. BACKGROUND

[0002] In the field of battery management systems, the state of charge (SOC) estimation method based on Kalman filtering has been well developed in linear Gaussian systems, which can achieve optimal state estimation and obtain good tracking results. However, lithium ion batteries exhibit significant nonlinear and non-Gaussian characteristics in actual operation, which poses a serious challenge to traditional filtering methods. This complexity is mainly reflected in the multi-modal characteristics of process noise and observation noise. In terms of process noise, its multi-modal characteristics are due to the complex coupling between the nonlinear dynamics inside the battery system and the external working conditions: first, the nonlinear dependence between SOC and parameters leads to significant differentiation of polarization process noise statistical characteristics in different state of charge intervals, forming a typical bimodal distribution. Second, the thermal parameter spatial heterogeneity between cells in the battery pack caused by the temperature gradient effect makes the process noise in the high temperature zone and the low temperature zone show obvious differences; finally, the inconsistent aging leads to the formation of a mixed distribution of healthy cells and degraded cells in the series battery pack. The non-Gaussian characteristics of observation noise cannot be ignored: on the one hand, the sensor range switching will cause the voltage sampling to have a stepwise modal transition between the low range and the high range. On the other hand, electromagnetic compatibility problems make the observation noise form a compound distribution in steady state and transient state. In addition, the intermittent outliers caused by the fluctuation of contact resistance introduced by mechanical vibration coupling also form a multi-modal distribution together with the conventional measurement errors. In view of the complex nonlinear and non-Gaussian characteristics exhibited by lithium battery systems, developing improved Kalman filtering algorithms with stronger robustness and environmental adaptability has important theoretical value and engineering significance for improving the accuracy of SOC estimation.

[0003] The nonlinear Gaussian filter algorithms include the Extended Kalman Filter (EKF) [8-10], the Unscented Kalman Filter (UKF) [11-14] and the Cubature Kalman Filter (CKF) [15-18], etc. The CKF can obtain better filtering effect, so the CKF and its improved algorithms have attracted more attention [19, 20]. The filtering algorithms for non-Gaussian systems usually include the Particle Filter (PF) [21-23] and the Gaussian Sum Filter (GSF) [24-26], etc. The GSF is based on the Gaussian sum theory, uses different linear / nonlinear Gaussian filter algorithms as the sub-filter of the GSF, and derives different non-Gaussian filter algorithms [27, 28]. Many nonlinear non-Gaussian filter algorithms are proposed by using the EKF, the Gaussian-Hermite Filter (GHF), the UKF, the CKF and the Square-Root Cubature Kalman Filter (SRCKF) as the sub-filter [27-31]. The above filtering algorithms, whether for nonlinear or non-Gaussian, are used in different ways to approximate the nonlinear or non-Gaussian system, and cannot completely represent the state of the two systems, so there is a large gap between the system calculation model and the real model. In order to shorten the gap and improve the filtering accuracy, a condition for designing a high-performance filter for nonlinear non-Gaussian systems is urgently needed.

[0004] The document

[32] proposes a prediction-fifth-order cubature Kalman filter method, which can adjust the process noise and its variance matrix of the system model in real time through the prediction filter method, and is suitable for strong nonlinear process noise systems. However, in the recursive process, the square root of the state estimation covariance matrix and the one-step prediction covariance matrix still needs to be calculated at each step, which has the disadvantages of large amount of calculation and numerical instability, cannot guarantee the non-negativity of the covariance matrix, and is easy to cause the divergence of the filter. The document

[33] studies the model parameter ratio theory of Kalman filter in linear Gaussian systems, gives two error covariances of inaccurate systems, proposes the parameter optimization criterion and the concept of model parameter ratio, converts the model noise mismatch problem into a constrained optimization problem, and finds the condition for better designing a high-performance Kalman filter in linear Gaussian systems. However, this model parameter ratio theory is only applicable to linear Gaussian systems, and is not applicable to nonlinear non-Gaussian systems, while the actual situation is more of nonlinear non-Gaussian systems. SUMMARY

[0005] The application aims to solve the problem that the existing Kalman filtering algorithm cannot be applied to the lithium battery system due to the complex nonlinear non-Gaussian characteristics of the lithium battery system, and the SOC state estimation accuracy of the lithium battery is poor, and proposes a lithium ion battery SOC state estimation method based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems, which greatly improves the estimation accuracy of the lithium battery SOC by using a model noise ratio constraint based on a more robust and environmentally adaptable Gaussian and square root volume particle filtering design method.

[0006] Technical scheme: A lithium ion battery SOC state estimation method based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems comprises the following steps:

[0007] The particle filtering and Gaussian filtering are combined to form a Gaussian and particle filtering algorithm; the existing unsupervised EM algorithm is improved by using the Gaussian component fusion strategy idea to obtain the IGS-SRCPF algorithm;

[0008] The SRCKF sub-filter is introduced as the particle Gaussian and sub-filter, and the pseudo matrix of the SRCKF sub-filter is constructed, which is approximately linearized to simplify the definition method of the MPR of the nonlinear non-Gaussian system; the MPR of the nonlinear non-Gaussian system is defined in the IGS-SRCPF algorithm by referring to the definition method of the linear Gaussian MPR, and the model adjustment coefficient and a condition for better designing a high-performance nonlinear non-Gaussian filter are obtained by combining the MPR existence theorem;

[0009] The HPO optimization algorithm and the DOA optimization algorithm are combined to obtain a multi-objective HPO-DOA optimization algorithm; according to the particularity of the model adjustment coefficient in the nonlinear non-Gaussian system, the multi-objective HPO-DOA optimization algorithm is used in combination with the model adjustment coefficient and the condition for better designing a high-performance nonlinear non-Gaussian filter to obtain the IGS-SRCPF algorithm based on MPR;

[0010] The IGS-SRCPF algorithm based on MPR is used to estimate the SOC state of the lithium ion battery to obtain the state estimation result; the state estimation result is corrected by using a deep width learning fusion network to obtain the final lithium ion battery SOC state estimation.

[0011] Advantages: Compared with the prior art, the application has the following advantages:

[0012] (1) The noise performance characteristic of the state of charge (SOC) of a lithium ion battery in the actual estimation process is more non-Gaussian problem, and the method of the present application proposes a Gaussian and square root cubature particle filtering method based on model noise ratio constraint, which fuses Gaussian and SRCKF and particle filtering, improves the unsupervised robust EM algorithm and Gaussian and square root cubature particle filtering algorithm by using reduction control strategy, completes the definition of model parameter ratio under the improved Gaussian and square root cubature particle filtering framework, and according to the existence theorem of model parameter ratio, obtains a model adjustment coefficient and a condition capable of designing a high-performance filter, and combines the coefficient and the condition with the multi-objective hunter prey and dog fusion algorithm, realizes the design of a high-performance nonlinear non-Gaussian SOC state estimation filter based on model feature constraint.

[0013] (2) The filtering method proposed by the method of the present application can adaptively estimate the number of noise covariance sub-terms, extend the linear Gaussian model parameter ratio theory to the nonlinear non-Gaussian model parameter ratio theory, reflect the phenomenon that one optimal estimation can correspond to multiple parameter sets satisfying the constraint, and convert the adaptive filtering problem into a constrained optimization problem, and has strong nonlinear non-Gaussian processing capability. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 The flowchart of the research idea is shown in the figure.

[0015] Figure 2 The SRCKF filtering process is shown in the figure.

[0016] Figure 3 The iteration flowchart of the unsupervised robust EM algorithm is shown in the figure.

[0017] Figure 4 The iteration flowchart of the improved unsupervised robust EM algorithm is shown in the figure.

[0018] Figure 5 The IGS-SRCKF algorithm flowchart is shown in the figure.

[0019] Figure 6 The IGS-SRCPF algorithm flowchart is shown in the figure.

[0020] Figure 7 The multi-objective HPO-DOA algorithm flowchart is shown in the figure.

[0021] Figure 8 The GANs-BLS system logic diagram is shown in the figure.

[0022] Figure 9 The IGS-SRCPF algorithm based on GANs-BLS and MPR is shown in the figure.

[0023] Figure 10Estimation error for process noise covariance component 1

[0024] Figure 11 Estimation error for process noise covariance component 2

[0025] Figure 12 Estimation error for observation noise covariance components 1 and 2

[0026] Figure 13 Estimation error for state

[0027] Figure 14 Estimation error for actual data state DETAILED DESCRIPTION

[0028] The technical solutions of the present application will be further described in combination with the drawings and examples.

[0029] The SOC state estimation system of a lithium ion battery is taken as an object in the embodiment, and a lithium battery SOC state estimation method based on a model parameter ratio (MPR) and an improved Gaussian sum square-root cubature particle filter (IGS-SRCPF) is proposed. First, a Gaussian sum particle filter algorithm is generated by combining a particle filter algorithm and a Gaussian sum algorithm, the unsupervised expectation maximization algorithm (EM) algorithm and the Gaussian sum algorithm are improved by using the Gaussian component fusion strategy idea in document

[34] , and non-Gaussian decomposition is performed on the initial state of a single particle to fit and generate multiple nonlinear particle Gaussian sub-terms, thereby simplifying the MPR research of the particle Gaussian sub-terms. Second, the SRCKF is introduced as a particle Gaussian sum sub-filter, which reduces the computational burden and obtains higher computational efficiency compared with the CKF, while ensuring the non-negativity of the covariance matrix and avoiding the divergence of the filter. Then, a pseudo-matrix of the SRCKF sub-filter is constructed, which is approximately linearized, thereby further simplifying the problem to the MPR research of the linear Gaussian sub-terms. Next, the MPR of the nonlinear non-Gaussian system is defined in the IGS-SRCPF framework by referring to the definition method of the linear Gaussian MPR, and the model adjustment coefficient and the condition for better designing a high-performance filter in the nonlinear non-Gaussian system are obtained by combining the MPR existence theorem. Finally, the SOC state estimation result is obtained by using the new multi-objective hunter prey-dingo optimization algorithm (HPO-DOA) combined with the model adjustment coefficient and the condition for designing a high-performance filter, and a deep-width learning fusion network.

[0030] The above process is further described.

[0031] The model of the discrete nonlinear non-Gaussian system is as follows:

[0032] x k+1 = f k (x k )+ w k+1，k (1)

[0033] z k = h k (x k )+ v k (2)

[0034] wherein k represents a time, x k ∈R n represents a system state vector, f k :R n →R n , h k :R n →R p respectively represent a system state matrix and a measurement matrix, w k+1,k ∈R n represents a non-Gaussian process noise, z k ∈R p is an observation vector, v k ∈R p represents a non-Gaussian observation noise, and the state noise and the measurement noise are independent of each other.

[0035] In practical applications, the filters for the nonlinear non-Gaussian system model are all used in different ways to approximate the nonlinear or non-Gaussian system. How to approximate the two systems as much as possible is a great difficulty in the current research. Since these filters cannot completely capture the state characteristics of the nonlinear and non-Gaussian system, the conventional nonlinear non-Gaussian filtering method often cannot achieve the best estimation.

[0036] The existing nonlinear non-Gaussian filtering algorithm, whether it is for nonlinear systems or non-Gaussian systems, is to approximate nonlinearity or non-Gaussian in different ways, and cannot completely represent the state of the two systems, so the conventional nonlinear non-Gaussian filter cannot obtain optimal estimation. The existing MPR theory research is only applicable to linear Gaussian systems, not to nonlinear non-Gaussian systems, while the actual situation is more of a nonlinear non-Gaussian system, such as the complex non-Gaussian battery SOC state estimation system involved in the embodiment. Therefore, the nonlinear non-Gaussian MPR theory is studied based on the IGS-SRCPF framework. First, in order to increase the non-Gaussian processing capability of the algorithm, the embodiment combines particle filtering and Gaussian sum filtering to propose a Gaussian sum particle filtering method. Compared with the existing Gaussian sum particle filtering, the embodiment considers the reduction control in the importance sampling part (GS-SRCKF), effectively reducing the computational complexity, and at the same time, the Gaussian sum particle filtering algorithm of the embodiment considers the decomposition step of the non-Gaussian term on the initial state of a single particle when performing importance sampling on each particle, thereby improving the filtering accuracy. Second, the unsupervised robust EM algorithm in the Gaussian sum particle filtering and the reduction control method used in the Gaussian sum algorithm are only to limit the number of maximum Gaussian sub-terms, thereby causing the waste of part of the effective Gaussian sub-terms, so the unsupervised EM algorithm and the Gaussian sum algorithm are improved by using the Gaussian component fusion strategy in the literature

[34] to generate multiple nonlinear particle Gaussian sub-terms, thereby simplifying the MPR research of the particle Gaussian sub-term. Then, in view of the fact that the existing GS-CPF uses CKF as a particle Gaussian sub-filter, which has the disadvantages of large computational load and numerical instability, cannot guarantee the non-negativity of the covariance matrix, and is prone to cause the divergence of the filter, the SRCKF is introduced as a particle Gaussian sum sub-filter, which reduces the computational burden and obtains higher computational efficiency compared with CKF, while guaranteeing the non-negativity of the covariance matrix and avoiding the divergence of the filter. Next, in order to simplify the definition method of the nonlinear non-Gaussian system MPR and facilitate the analysis of the mismatch process noise covariance and the mismatch observation noise covariance in the Gaussian sub-term, the pseudo matrix of the SRCKF sub-filter is constructed, which is approximately linearized, thereby further simplifying the problem to the MPR research of the linear Gaussian sub-term. Referring to the definition method of the linear Gaussian MPR, the MPR of the nonlinear non-Gaussian system is defined in the IGS-SRCPF framework, and combined with the MPR existence theorem, the model adjustment coefficient and a condition for better designing a high-performance nonlinear non-Gaussian filter are obtained. Finally, the HPO optimization algorithm and the DOA optimization algorithm are combined, the model adjustment coefficient is used according to the particularity of the model adjustment coefficient in the nonlinear non-Gaussian system, and the multi-objective HPO-DOA optimization algorithm is combined with the condition for designing a high-performance filter to estimate the SOC state of the lithium ion battery, and the state estimation result is obtained. The state estimation result is corrected by using the deep-width learning fusion network. The research thought diagram of the embodiment is as follows:Figure 1 shown.

[0037] In order to simplify the theoretical research of nonlinear non-Gaussian MPR, a pseudo-matrix of SRCKF sub-filter is constructed in the IGS-SRCPF framework to solve the definition problem of nonlinear non-Gaussian MPR by using the definition idea of ​​linear Gaussian MPR.

[0038] The CKF filtering process is similar to the UKF, but its theoretical derivation is more rigorous. However, in the recursive process of CKF, each step needs to calculate the square root of the state estimation covariance matrix and the one-step prediction covariance matrix, which brings the disadvantages of large computational complexity and numerical instability. In contrast, SRCKF directly propagates and updates the square root of the state variance matrix in the form of Cholesky decomposition based on CKF, thereby reducing the computational burden and improving computational efficiency. At the same time, SRCKF can ensure the non-negative definiteness of the covariance matrix, avoid the divergence of the filter, and thus improve the convergence speed and numerical stability of the filter. Therefore, SRCKF is selected as the sub-filter of the Gaussian sum. The filtering process of the initialized SRCKF is as follows Figure 2 shown.

[0039] By using Gaussian and particle filter algorithms, the complex non-Gaussian MPR theory can be simplified to the MPR theory of multi-particle Gaussian sub-items. PF approximates the probability density function of any random variable by random sampling points, and replaces the integral operation with the sample mean to achieve the state estimation of the target. The estimation effect of PF is very dependent on the importance function. (k is a discrete time point). Sampling a set of sample points from a reasonable importance function is very important for improving the accuracy of target state estimation. Reference

[39] uses GS-CKF as the importance function of PF and combines the advantages of the two algorithms to improve the state estimation accuracy of the filter.

[0040]

[0041] It is known that SRCKF has higher computational efficiency and filtering accuracy than CKF. Therefore, this embodiment uses IGS-SRCKF as the importance function of PF. At the same time, on this basis, non-Gaussian decomposition is performed on the initial state of each particle and a reduction fusion strategy is added to improve the algorithm performance. Based on the above conclusions, formula (3) is modified as follows:

[0042]

[0043] On this basis, the IGS-SRCPF algorithm of the embodiment also uses the improved EM algorithm in document

[27] (which is referred to as an unsupervised robust EM algorithm in the embodiment), which can adaptively estimate the number of optimal Gaussian components compared with the traditional EM algorithm, but the algorithm is prone to waste of finite Gaussian sub-terms, so an improved unsupervised robust EM algorithm is proposed according to the fusion strategy idea in document

[34] . The specific steps of the IGS-SRCPF algorithm are as follows:

[0044] Step 1 initialization. First assume x0 as an initial state quantity, generate H particles from the prior distribution p(x0) Calculate the initial state and the estimation error covariance P0.

[0045]

[0046] The improved EM algorithm in document

[27] is adopted, and the process noise probability density function p(w k,k-1 ) and the measurement noise probability density function p(v k ) are expressed in the form of Gaussian sum:

[0047]

[0048] wherein, and are the weights of the corresponding Gaussian sub-terms, and have:

[0049]

[0050] wherein, the unsupervised robust EM algorithm process is as follows:

[0051] Taking the measurement noise data as an example, it is assumed that there is a group of measurement noise data V k =(v1,v2,…,v n ), wherein v k is a p-dimensional vector generated by a Gaussian mixture model:

[0052]

[0053] wherein, are the weight, mean and covariance of the i-th Gaussian term of the Gaussian mixture model respectively, and r k represents the number of components of the mixture model.

[0054] Step 1: initialize parameters. Let r k =n, β=1. Take any value, i.e. θ value, and set a small enough ε>0 as the condition to judge the end of the loop. Wherein β is:

[0055]

[0056] Step 2: E-step: Calculate the implicit parameter z ki :

[0057]

[0058] Step 3: M-step: Update weights by equations (13), (14) and (11) respectively. and β, and let β = 1 for the first iteration.

[0059]

[0060]

[0061] Step 4: When When , invalidate the i-th Gaussian component and remove the mixing coefficient at this time At the same time, the Gaussian component parameters When the number of iterations is greater than 60, set β = 0.

[0062] Step 5: Update from equations (15) and (16) to obtain and z ki′ , and updated by equations (14) and (17) and

[0063]

[0064] Step 6: Update z according to formula (12) ki .

[0065] Step 7: If The iteration stops, otherwise go to step 3 to continue.

[0066] The iterative flow chart of the unsupervised robust EM algorithm is as follows Figure 3 shown.

[0067] Although the above algorithm can adaptively estimate the number of Gaussian subterms, there is a problem of wasting valid Gaussian subterms. Therefore, this embodiment proposes a fusion strategy to improve step 4 of the algorithm.

[0068] First, remove the weight less than The Gaussian component of is used to perform the Gaussian component fusion strategy on the interval of formula (18).

[0069]

[0070] Among the Gaussian components in this interval, find the one with the largest weight.

[0071]

[0072] And find the qualified Gaussian components according to the following criteria.

[0073]

[0074] where,

[0075] Combine these Gaussian components into one Gaussian distribution by weighted average, whose mean and covariance are:

[0076]

[0077] where,

[0078] Delete all Gaussian components that have been fused, repeat the above steps until all Gaussian components are completed, and finally only keep the first S Gaussian distributions with relatively large weights. The improved unsupervised EM algorithm flow chart is shown in Figure 4

[0079] Step 2 importance sampling.

[0080] Step 2.1 Gaussian fitting.

[0081] The initial probability density function of H particles is approximated by the improved unsupervised robust EM algorithm In the form of Gaussian sum (or approximate Gaussian sum form) as follows:

[0082]

[0083] where, is the weight of its corresponding Gaussian sub-item, and has:

[0084]

[0085] Step 2.2 distributed filtering.

[0086] The filtering probability density function is approximated by the Gaussian sum form of formula (25) for H particles respectively:

[0087]

[0088] where, the measurement And:

[0089] N k|k = N k|k-1 ·r k (26) ​

[0090] In addition, based on the predicted state mean Prediction covariance matrix Measurement noise mean and the measurement variance matrix Calculate the Gaussian subterm of the hth particle using the SRCKF filtering algorithm The filtered mean and the covariance matrix

[0091] At this time, the measurement likelihood function of the state estimation of the i-th Gaussian sub-term of the h-th particle can be expressed as:

[0092]

[0093] The indicators j and l are calculated as follows:

[0094]

[0095] Where i = 1, 2, ..., N k|k , j = 1, 2, ..., N k|k-1 , l=1,2,…,r k ;symbol Indicates a floor operation.

[0096] Filter weights It is necessary to integrate three pieces of information, namely the prediction filter weights The weight of the probability density function of measurement noise And the likelihood function of the state estimate Therefore The adaptive calculation method is:

[0097] Step 2.3 Global point estimation. After the Gaussian sub-items of each particle obtain the filtering state at time k, the global filtering mean at time k can be calculated using equations (30) and (31): and covariance matrix

[0098]

[0099] Similarly, the state estimates at other time points can also be calculated using equations (30) to (31).

[0100] Step 2.4 Simplified Control. Generally, the process and measurement noise distributed in the form of Gaussian sum will accumulate over time and lead to the continuous increase of the number of Gaussian sub-terms, such as N in Equation (26). k|k and N given later k+1|kThis will inevitably increase the computational overhead and reduce the filtering practicability. Therefore, in order to improve the real-time performance of the algorithm while ensuring the filtering accuracy, the Gaussian component fusion strategy described in document

[34] is adopted in the embodiment. After the estimated mean and covariance of each sub-term are calculated at time k, the Gaussian components with weights greater than G' are retained and the other components are deleted.

[0101]

[0102] where G' is the weight of the Gth Gaussian component in descending order of weight.

[0103] In the remaining Gaussian components, find the one with the largest weight:

[0104]

[0105] And find the Gaussian components that meet the conditions according to the following criteria:

[0106]

[0107] where,

[0108] Combine these Gaussian components by weighted averaging into a Gaussian distribution, whose mean and covariance are:

[0109]

[0110] where,

[0111] Delete all Gaussian components that have performed fusion operations, and then repeat the above steps until all Gaussian components are completed. Finally, only the first S Gaussian distributions with relatively large weights are retained, and the corresponding weights are re-normalized to reduce the computational complexity.

[0112] Step 2.5 prediction update. The predicted state probability density function can be represented by the following formula:

[0113]

[0114]

[0115]

[0116] It can be seen that the calculation of the prediction weight integrates two pieces of information, namely the filtering weight and the weight of the process noise probability density function

[0117] In addition, based on the estimated state mean and the estimated variance matrix Process noise mean and process noise covariance matrix Using SRCKF to calculate predicted mean and covariance matrix In addition, c and d are respectively

[25] :

[0118]

[0119] where i = 1, 2, …, N k+1|k , c = 1, 2, …, N k|k , d = 1, 2, …, q k .

[0120] Step 3 particle update.

[0121] Based on the importance function of IGS-SRCKF and Generate new particles

[0122]

[0123] Step 4 Calculate particle weights and normalize.

[0124] Other H-1 particles repeat step2-step3 steps to get all particle state estimation, calculate particle weight and normalize:

[0125]

[0126] In the formula, the particle and weight one-to-one correspondence.

[0127] Step 5 Random resampling.

[0128] Random resampling of particles, that is, using roulette algorithm to copy particles. This algorithm needs to generate a random number that obeys uniform distribution in [0, 1] in advance. For particles with large weights, the probability of the random number falling into the weight corresponding interval of the particle is higher, and the particle is more likely to be copied, while the particles with small weights are more likely to be discarded. Repeat the above particle copying process (the number of particle copying is equal to the total number of particles H).

[0129] Step 6 Calculate state estimation and estimation error covariance matrix.

[0130] According to the resampled particles, the final target posterior state estimation and estimation error covariance matrix at time k are calculated.

[0131]

[0132] At this point, the state filtering process at time k is completed, and then the above steps are repeated to complete the estimation of the state quantity and error covariance matrix at the next time. The schematic diagrams of the IGS-SRCKF filtering algorithm and the IGS-SRCPF filtering algorithm are shown in FIGS. 8 and 9, respectively. Figure 5 、 Figure 6

[0133] The above algorithm uses SRCKF as a sub-filter to estimate the system state corresponding to each particle Gaussian sub-item, and then realizes global estimation by combining each particle Gaussian sub-item. Next, the definition of MPR in the sub-filter will be further studied in the case of mismatched noise covariance of the system.

[0134] 1.3.3 Constructing a pseudo matrix

[0135] The filter can be split into HxN k|k sub-filters by the IGS-SRCPF filtering algorithm. Next, the pseudo matrix of the SRCKF sub-filter is further constructed, which can simplify the complex nonlinear MPR theory research into the MPR theory research of multiple linear Gaussian sub-items. Referring to the method of constructing a pseudo matrix of the CKF filter in reference

[40] , the pseudo observation matrix of the SRCPF sub-filter is:

[0136]

[0137] The pseudo state transition matrix is:

[0138]

[0139] wherein,

[0140]

[0141] Thus, the iteration process of the sub-filter is simplified as:

[0142]

[0143] wherein, the calculation of i, j, l, c and d is shown in equations (28) and (39).

[0144] Define the model parameter ratio

[0145] Similarly to the linear Gaussian Kalman filtering algorithm, for IGS-SRCPF filtering, if accurate noise covariance can be obtained in each particle Gaussian sub-item, the accuracy of the IGS-SRCPF filtering result can be effectively improved.

[0146] There is mismatched noise covariance in the particle Gaussian sub-item ​

[0147] It is known that the accuracy of the noise covariance in each particle Gaussian sub-filter is usually poor. That is, when the sub-filter has a mismatched noise covariance, for each particle Gaussian sub-filter, we have

[41]

[0148]

[0149] where, denotes the true observation noise covariance of the i-th Gaussian sub-filter of each particle, denotes the true process noise covariance of the i-th Gaussian sub-filter of each particle. denotes the assumed observation noise covariance of the i-th Gaussian sub-filter of each particle in practical applications, denotes the assumed process noise covariance of the i-th Gaussian sub-filter of each particle in practical applications, and are denoted by the superscript u. and denote the bias of the particle Gaussian sub-filter.

[0150] It is known that the Kalman filter with a mismatched noise covariance in each particle Gaussian sub-filter

[42]

[0151]

[0152] where the superscript f denotes the actual computed value of the sub-filter. However, according to

[43] , we have is not the TMSE of the particle Gaussian sub-filter estimate at time k Because:

[0153]

[0154] From equations (53) and (54), we have the TMSE of is [41, 43]

[0155]

[0156] where,

[0157]

[0158] where the superscript m denotes the true value of the filter. In addition, the indices e and g are computed as

[25]

[0159]

[0160] The model parameter ratio of the improved Gaussian sum SRCPF filter

[0161] The MPR theory method for linear Gaussian is described in

[33] , so for a linear Gaussian sub-system, let

[0162]

[0163] where, is the process noise parameter ratio of the i-th Gaussian subterm of each particle, is the process noise parameter ratio of the i-th Gaussian subterm of each particle, is the model parameter ratio of the i-th Gaussian subsystem of each particle.

[0164] This embodiment is to study the MPR theory in nonlinear non-Gaussian systems, using the IGS-SRCPF filter framework, under which there are H x N k|k linear particle Gaussian subterms. For the noise covariance Gaussian subterm, there are q k process noise covariance Gaussian subterms, which are respectively: There are r k observation noise covariance Gaussian subterms, which are respectively: Therefore, there are q k x r k combinations, which are respectively:

[0165]

[0166] Thus, in the Gaussian and SRCPF filter framework,

[0167]

[0168] is called the process noise parameter ratio, and

[0169]

[0170] is called the observation noise parameter ratio, and

[0171]

[0172] is called the MPR of the system. If the MPR of another model is:

[0173]

[0174] then the two models are said to have the same model parameter ratio.

[0175] Noise estimation based on parameter estimation criteria

[0176] Model adjustment coefficient estimation

[0177] Novelty of the known sub-filter is

[0178]

[0179] The covariance matrix of [33, 41, 43] is:

[0180]

[0181] The superscript f denotes the computed value. But The true value of the covariance matrix of [33, 41, 43] is not

[0182] The superscript m denotes the true value.

[0183] In each particle Gaussian subsystem, there is a model parameter ratio existence theorem, that is, if the estimated value of the process noise covariance sub-item

[0184] satisfies the process noise sub-item parameter ratio of the system, the estimated value of the observation noise covariance sub-item satisfies the observation noise sub-item parameter ratio of the system, and the minimum value of can be obtained, then they must satisfy the model parameter ratio of the particle Gaussian subsystem [33, 41]. According to the model parameter ratio existence theorem of the linear Gaussian system, this embodiment rises to the nonlinear non-Gaussian system model parameter ratio existence theorem. In the IGS-SRCPF filter framework, if the estimated value of the process noise covariance sub-item

[0185] satisfies the process noise parameter ratio shown in equation (68), the estimated value of the observation noise covariance sub-item satisfies the observation noise parameter ratio shown in equation (69), and the minimum value of in each Gaussian sub-item can be obtained, then they must satisfy the system model parameter ratio shown in equation (70). Thus, under the condition that the parameter ratio of each noise covariance sub-item is known, the estimated value of the noise covariance sub-item obtained by solving the minimum value of can be obtained. b h，i is a scalar greater than 0. When , the noise covariance deviation of the sub-filter is:

[0186]

[0187]

[0188] According to (58) and (62), we have:

[0189]

[0190] Again, according to the simplified filter parameter linear multiple theorem, that is, in a linear Gaussian subsystem, for a constant system, if holds, when and are multiplied by the same scalar K, at the system reaches a steady state, [33, 41, 43]. It can be shown that, Substituting this into the above equation (77) gives:

[0191]

[0192] From the above equation (78) we know Since in the estimation process, is not accurate, we stretch and into vectors X h，i , Y h，i respectively. Using the least squares method to estimate b h，i [33, 41, 43]:

[0193] b h，i = ((X h，i ) T X h，i ) -1 (X h，i ) T Y H,i (79)

[0194] Substitute b h,i into equations (75), (76) to get:

[0195]

[0196] In summary, we can get the parameter estimation criterion under the improved Gaussian and SRCPF framework:

[0197] For each Gaussian sub-term, the necessary and sufficient condition for is:

[0198]

[0199] s.t. satisfy the process and observation noise parameter ratio.

[0200] HPO-DOA algorithm

[0201] The combination of HPO optimization algorithm

[44] and DOA optimization algorithm

[45] is used to realize the simultaneous estimation of multiple noise covariance sub-terms, so as to obtain the required and The detailed steps of HPO-DOA algorithm are shown in Step1-Step5, where in Step1, after the initial population is generated, the individuals estimated by the improved unsupervised robust EM algorithm in the foregoing are also put into the randomly generated initial population.

[0202] Algorithm flow

[0203] Since there are different model adjustment coefficients for each particle Gaussian subterm, the algorithm uses a multi-objective function optimization method to solve it. The specific multi-objective HPO-DOA algorithm flow is as follows:

[0204] (1) Randomly generate population individuals in the interval [x min , x max ], and retain the weight calculated by the improved robust EM algorithm, the number of process noise Gaussian subterms c q , and the number of observation noise Gaussian subterms c r . The individuals should satisfy the parameter ratio of each process noise subterm and the parameter ratio of each measurement process noise (for the individuals estimated by the improved unsupervised robust EM algorithm and put into the randomly generated initial population, take the first element on the diagonal of each noise covariance of the individual, and also make the individual satisfy the parameter ratio condition according to the parameter ratio value). The estimation method steps of the noise covariance subterm parameter ratio are as follows:

[0205] 1) Estimate the parameter ratio of A times of noise covariance subterms by the improved unsupervised robust EM algorithm.

[0206] 2) Retain the first c q process noise subterms and the first c r observation noise subterms obtained each time, and supplement 0 for the insufficient.

[0207] 3) Take the average of the parameter ratios of A noise covariance subterms.

[0208] 4) Repeat steps 1)-3) A times to obtain A new results.

[0209] 5) Take the average of the A results.

[0210] 6) Repeat steps 1)-5) A times to obtain A new results.

[0211] 7) Take the average of the A new results.

[0212] And so on... It can be found that the more the number of cycles is, the closer the estimated noise subterm parameter ratio value is to the true value.

[0213] (2) Construct HxN k|k fitness functions Substitute the population individuals as the noise covariance corresponding to each particle Gaussian subterm into the filtering algorithm, and obtain the corresponding by formula (73), formula (74), and calculate the fitness value of the population individual corresponding to each fitness function.

[0214] (3) Find the global optimal position in the population corresponding to each fitness function according to the fitness value.

[0215] (4) Divide each hunter and prey in HxN k|k populations.

[0216] (5) Update the individuals in the population.

[0217] (6) Calculate the fitness value of each individual corresponding to each fitness function after updating, and find the global optimal position in the population corresponding to each fitness function.

[0218] (7) Determine whether the number of iterations reaches the upper limit. If yes, output the optimal individual corresponding to each fitness function as the noise covariance estimation value of each Gaussian subterm Otherwise, go to step (4).

[0219] (8) Calculate the adjustment coefficient b h,i according to formula (79).

[0220] (9) Substitute the adjustment coefficient, and calculate

[0221] (10) Sum multiple to obtain the final and

[0222] (11) Substitute and into the IGS-SRCPF filtering algorithm proposed in this embodiment.

[0223] The flowchart of the algorithm is shown in Figure 7 .

[0224] GANs-BLS optimization of MPR-based IGS-SRCPF

[0225] GANs-BLS system

[0226] This embodiment proposes an innovative deep learning and broad learning (Broad Learning System, BLS) fusion method, which uses generative adversarial networks (Generative Adversarial Networks, GANs) for feature extraction, and then inputs these deep features into the broad learning system for prediction. This method combines the advantages of GANs in generating high-quality features and the fast training ability of broad learning, so that the model significantly improves the training efficiency while maintaining high accuracy.

[0227] Generative Adversarial Networks (GANs) consist of a generator and a discriminator. This example uses a trained GANs model to first generate realistic data features through the generator, and then extract high-level feature representations of these data through the discriminator. Given an input dataset X = {x1, x2, ..., x n}, where x i is the original input sample, the generator G(z) accepts the random noise vector z as input and generates pseudo data The discriminator D(x) is used to distinguish between real data and generated data, and extract their high-level feature representations. The specific process is as follows:

[0228] (1) Generator G(z) accepts random noise z to generate pseudo data

[0229]

[0230] where z is typically sampled from a normal distribution.

[0231] (2) Discriminator D(x) for real data x i and generate data Perform classification and extract high-level feature representation:

[0232]

[0233] Among them, D f (·) represents the feature representation extracted by the intermediate layer of the discriminator.

[0234] (3) High-level feature representation H of real data real ={h1,h2…,h n} and high-level feature representation of generated data It can be further merged to obtain the complete feature set H:

[0235] H=[H real ;H gen ] (85)

[0236] By combining high-level feature representations of real data with those of generated data, we can fully leverage the strengths of generative adversarial networks (GANs) and broad learning systems (BLS), enhancing both the expressive power of features and improving the model's generalization and prediction accuracy. Here, H is the feature matrix input to the BLS system for subsequent prediction tasks.

[0237] BLS System Predictor

[0238] Extracted and merged feature sets are input into the BLS system. The BLS quickly trains the prediction model by the pseudo-inverse method. Assuming that the dimension of the feature vector H is m, the BLS will perform linear regression by constructing an enhanced node matrix Z, and finally output the prediction result.

[0239] The calculation steps of the BLS are as follows:

[0240] (1) Construct the input weight matrix W and the bias vector b to generate the enhanced feature matrix Z:

[0241] Z = σ(HW + b) (86)

[0242] where σ(·) is an activation function, usually ReLU or sigmoid function.

[0243] (2) Calculate the pseudo-inverse matrix Z + , which is used to solve the case that Z may not be full rank or irreversible, and its calculation formula is:

[0244] Z + = (Z T Z) -1 Z T (87)

[0245] In the case of high-dimensional data or insufficient rank of the matrix, methods such as singular value decomposition (SVD) can be used for solution.

[0246] (3) Calculate the output weight matrix B by the least square method:

[0247] B = (Z T Z + λI) -1 Z T Y (88)

[0248] where Y is the real label matrix, and λ is the regularization parameter.

[0249] (4) Prediction output:

[0250]

[0251] where is the output of the GANs-BLS system.

[0252] The logic diagram of the GANs-BLS system is shown in Figure 8 .

[0253] Error compensation method of GANs-BLS

[0254] This embodiment uses GANs-BLS to optimize the IGS-SRCPF algorithm based on MPR, and the parameters affecting the pose estimation error (the difference between the state prediction value and the state estimation value ) As the input of GANs-BLS network, the results of IGS-SRCPF algorithm based on MPR are corrected from the compensation angle by using the nonlinear mapping ability and adaptive ability of GANs-BLS network, so as to improve the filtering accuracy. The specific training method is:

[0255] 1) The difference between the state one-step prediction of IGS-SRCPF algorithm based on MPR and the state estimation value is taken as the input sample of GANs-BLS.

[0256] 2) The difference between the real value and the state estimation value is taken as the output sample of the network.

[0257] 3) GANs-BLS learns the mapping relationship between the prediction error and the actual error of IGS-SRCPF algorithm based on MPR.

[0258] 4) The error between the filtering estimation value and the actual value is output. The flow of IGS-SRCPF algorithm based on GANs-BLS and MPR is shown in Figure 9

[0259] It can be seen from Figure 9 that the measurement information of the sensor is input into the IGS-SRCPF algorithm based on MPR to obtain the filtering result, and the difference between the filtering state estimation value and the state one-step prediction is input into the trained GANs-BLS. Then, the GANs-BLS network gives the error between the filtering result and the actual value. Finally, the optimal estimation of IGS-SRCPF based on MPR and the output of GANs-BLS are summed, that is, the optimal estimation value of IGS-SRCPF algorithm based on GANs-BLS and MPR:

[0260]

[0261] wherein, is the output value of IGS-SRCPF algorithm based on GANs-BLS and MPR, B perr is the output value based on GANs-BLS network, is the state estimation value based on IGS-SRCPF algorithm based on MPR.

[0262] ​High-precision SOC estimation enables the battery management system to adjust the charging and discharging strategy and other control parameters in real time and accurately under complex working conditions, so as to ensure the safety and reliability of the battery operation. In order to improve the SOC estimation accuracy of lithium batteries, this chapter proposes a lithium-ion battery SOC state estimation method based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems. This embodiment mainly includes 5 new works. The first new work is to combine GS-SRCKF with particle filtering to form GS-SRCPF filtering algorithm. Compared with the existing Gaussian and particle volume filtering algorithm (GS-CPF), the algorithm performs Gaussian decomposition on the initial state of a single particle in the importance sampling part while considering the reduction control. The Gaussian decomposition on the initial state of a single particle can improve the filtering accuracy, and the consideration of the reduction control can reduce the calculation amount. And the existing GS-CPF uses CKF algorithm as the particle Gaussian sub-filter, while this embodiment uses SRCKF. SRCKF has lower calculation amount and stronger filtering ability than CKF. The second new work is to propose an improved unsupervised EM algorithm and IGS-SRCPF algorithm. Both algorithms improve the existing unsupervised EM algorithm and the reduction control strategy of GS-SRCPF by using the Gaussian component fusion strategy of the robust Gaussian and set Kalman filter algorithm in document

[34] , effectively realizing the reduction of calculation complexity while ensuring the accuracy of the algorithm. The third new work is to define MPR under the IGS-SRCPF framework. In the nonlinear Gaussian sub-item, the pseudo matrix of the SRCKF sub-filter is constructed by referring to the construction method of the CKF pseudo matrix, so as to analyze the mismatched process noise covariance and mismatched observation noise covariance in the Gaussian particle sub-item, and thus define the MPR under the IGS-SRCPF framework. The MPR theory is upgraded from the existing linear Gaussian system to the nonlinear non-Gaussian system. The fourth new work is to obtain a condition for better designing high-performance nonlinear non-Gaussian filters. According to the MPR existence theorem, the model noise mismatch problem in each linear Gaussian particle sub-item is converted into a constrained optimization question, so as to obtain a condition for designing high-performance filters for nonlinear non-Gaussian systems for the IGS-SRCPF filter studied in this embodiment. The fifth new work is to propose a multi-objective HPO-DOA algorithm. The HPO-DOA algorithm replaces the single predation method in the original HPO algorithm with the predation strategy of the DOA algorithm, and the "prey" of the DOA algorithm is changed from the optimal value of the last iteration to the individual found by the "predator-prey discrimination strategy" to serve as the "prey", so as to obtain an optimization algorithm with better optimization performance. Since the model adjustment coefficients corresponding to each particle Gaussian sub-item are inconsistent in the MPR theory calculation in this embodiment, a multi-objective HPO-DOA algorithm is designed.

[0263] Simulation experiment

[0264] Parameter setting

[0265] The state equation and the observation equation of the battery system are:

[0266]

[0267] U b，k = U b0 - R b I b，k - U bv，k - U bl，k + v k (92)

[0268] where SOC b，k is the state of charge of the battery system at time k, U bs，k is the short-term polarization voltage, U bl，k is the long-term polarization voltage, Δt is the sampling time interval, R bs is the short-term polarization resistance, C bs is the short-term polarization capacitance, R bl is the long-term polarization resistance, C bl is the long-term polarization capacitance, τ1 = R bs C bs is the time constant reflecting the fast dynamic polarization effect, τ2 = R bl C bl is the time constant reflecting the slow dynamic polarization effect, η is the coulombic efficiency, C b0 is the nominal capacity of the battery system, I b，k is the battery system current, w k is the non-Gaussian process noise. U b，k is the battery system terminal voltage, U b0 is the open-circuit voltage, R b is the ohmic internal resistance, v k is the non-Gaussian observation noise.

[0269] The initial state x0 and the covariance matrix P0 of the battery system are:

[0270] x0 = [0.5 0 0] T (93)

[0271] P0 = diag{0.01, 10 -4 , 25 × 10 -4} (94)

[0272] where diag denotes a diagonal matrix.

[0273] Both the process and the measurement noise are represented by Gaussian mixture models as follows:

[0274]

[0275]

[0276] where each weight parameter is set as: β k = 0.3, γ k = 0.4, and the rest of the parameters are set as:

[0277]

[0278] According to Q 1 and its corresponding weight β k , β k x n process noise data are generated. According to Q 2 and its corresponding weight (1-β k ), (1-β k ) x n process noise data are generated. The combination of the two generates n process noise data, which is the real noise data set in this embodiment. Similarly, n real measurement noise data are generated. The expression for generating noise data can be obtained from the literature

[47] as shown in equation (98).

[0279]

[0280] In the above formula, n = 50, sqrtm() represents the square root of the matrix, and rand(a, b) represents generating a random number of a rows and b columns.

[0281] In order to verify the advancement and effectiveness of the MPR and IGS-SRCPF algorithm (HPO-DOA-MPR) based on the multi-objective HPO-DOA algorithm as the optimization algorithm proposed in this embodiment, it is compared with the improved GS-CKF filter algorithm (IGSCKF) in the reference

[27] , the credibility-based IGSCKF algorithm (C-IGSCKF) in the reference [], and the MPR and IGS-SRCPF algorithm (EM-PSO-MPR) based on the multi-objective EM-PSO algorithm

[43] as the optimization algorithm. For both the multi-objective HPO-DOA and multi-objective EM-PSO optimization algorithms, the population size is set to 20 and the maximum number of iterations is set to 50. Since the estimated value of the noise covariance sub-item in the simulation part needs to be compared with the set true value, in order to verify the accuracy of the algorithm's estimation of the noise covariance sub-item when satisfying the MPR theory, and when the improved unsupervised robust EM algorithm is used to adaptively estimate the number of noise covariance sub-items and their parameter ratios, the number of noise covariance sub-items will not be equal to the set actual true noise covariance number. Therefore, the traditional EM algorithm is used here, that is, the number of noise covariance sub-items and the parameter ratio of each noise covariance sub-item are set in advance. In the later actual data processing, the improved unsupervised robust EM algorithm designed in this embodiment will be used. First, 50 Monte Carlo experiments are used to verify its ability to estimate process noise and observation noise covariance sub-items. The error curves of the noise covariance sub-items estimated by the four algorithms and the true noise covariance sub-items are as shown below. Figure 10- Figure 12 The root mean square error results of the noise covariance sub-items estimated by the four algorithms are shown in Tables 1 to 3.

[0282] Table 1 Estimation error of process noise covariance component 1

[0283]

[0284] Table 2 Estimation error of process noise covariance component 2

[0285]

[0286] Table 3 Estimation error of observation noise covariance component 1

[0287]

[0288] Depend on Figure 10- Figure 12, it can be seen from Table 1-Table 3 that the MPR and IGS-SRCPF algorithm proposed in the embodiment can more accurately estimate each noise covariance subterm compared with the IGSCKF algorithm and the IGSCKF algorithm based on credibility, and in the selection of optimization algorithm, the error result obtained when the multi-objective HPO-DOA algorithm is used is smaller than that when the multi-objective EM-PSO is used, so the optimization performance of the multi-objective HPO-DOA algorithm proposed in the embodiment is better. The state estimation error results of the battery system of the three algorithms are as shown in Figure 13 , and the root mean square error results are as shown in Table 4. Figure 13 , it can be seen from Table 4 that the MPR and IGS-SRCPF algorithm proposed in the embodiment can more accurately estimate the state of the battery system compared with the IGSCKF filter algorithm and the IGSCKF algorithm based on credibility, and in the selection of optimization algorithm, the state error result obtained when the multi-objective HPO-DOA algorithm is used is smaller than that when the multi-objective EM-PSO is used, so the optimization performance is better when the multi-objective HPO-DOA algorithm proposed in the embodiment is used.

[0289] Table 4 Root mean square error of estimation effect of different algorithms

[0290]

[0291] To verify the effectiveness of the new algorithm in actual engineering application, this section uses the battery system measurement data provided by Shenzhen Juema Energy Co., Ltd. to verify and compare the algorithm. The state and observation equations are as shown in equations (91) and (92). The initial state x0 and the initial covariance matrix P0 of the battery system are as shown in equations (93) and (94). The comparison results of different algorithms for processing actual data are as shown in Figure 14 and Tables 5 and 6.

[0292] Table 5 Root mean square error of estimation effect of different algorithms

[0293]

[0294] Table 6 Comparison of running time of different optimization algorithms

[0295]

[0296] By observing Figure 14 and Tables 5 and 6, it can be seen that in terms of actual data processing performance, the algorithm proposed in this chapter is obviously better than the IGSCKF filter algorithm and the IGSCKF algorithm based on credibility. At the same time, in the selection of optimization algorithm, the performance of the multi-objective HPO-DOA optimization algorithm is better than that of the multi-objective EM-PSO optimization algorithm, and the running time is shorter.

[0297] For the SOC estimation problem of lithium-ion batteries in nonlinear non-Gaussian environments, the embodiment proposes an IGS-SRCKF state estimation method based on MPR suitable for nonlinear non-Gaussian complex battery systems after in-depth analysis of the existing MPR filtering algorithm applicable to linear Gaussian systems. The main innovations of this method include improving the design of the GS-SRCPF filtering algorithm, defining MPR in the IGS-SRCPF filtering framework, proposing a condition that can design high-performance nonlinear non-Gaussian filters, and completing the application of multi-objective HPO-DOA optimization algorithm. Experiments show that compared with existing algorithms, the algorithm proposed in this embodiment has significant advantages in model parameter solving and filtering accuracy. In the future, from the perspective of credibility and MPR theory fusion, a multi-mode fusion lithium-ion battery SOC estimation method will be studied.

[0298] References:

[0299] [1]Cheng J H,Yu P P,Huang Y R.Application of Improved Kalman Filterin UnderGround Positioning System of Coal Mine[J].IEEE Transactions onApplied Superconductivity,2021,31(8):30-33.

[0300] [2]Raffaello C,Nascimento V H.On the Tracking Performance of AdaptiveFilters and Their Combinations[J].IEEE Transactions on Signal Processing,2021,69(11):3104-3116.

[0301] [3]Zhou Y,Hu J N,Zhao Y,et al.Vehicle target tracking based on improved compressive sensing algorithm of Kalman filter[J].Journal of Hunan University(Natural Science),2023,50(01):11-21.

[0302] [4]Wang YY, Zhang Y, Xu DJ, Miao W Q.ADeformation MeasurementAlgorithm Based on Adaptive Variable Parameter Multiple Model for Large Ships[J]. IEEE Transactions on Instrumentation and Measurement, 2021,70(5):25-34.

[0303] [5]Kevin RF, Anton J HA Study of Endpoint-Constrained NonlinearTracking Filters[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(6): 3952-3961.

[0304] [6]Lyu

[0305] [7] Yang Jiaxuan, Chen Boguo, Ma Lingqi. Ship trajectory tracking based on interactive multi-model square root cubature Kalman filter[J]. Chinese Journal of Ship Research, 2022, 17(04): 12-23.

[0306] [8] Guihal J M, Auger F, Bernard N, Schaeffer E. Efficient Implementation of Continuous Discrete Extended Kalman Filters for State and Parameter Estimation of Nonlinear Dynamic Systems[J]. IEEE Transactions on Industrial Informatics, 2022, 18(5): 3077-3085.

[0307] [9] Liu X, Ren Z, Lyu H, Jiang Z, Ren P, Chen B. Linear and Nonlinear Regression-Based Maximum Correntropy Extended Kalman Filtering[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(5): 3093-3102.

[0308]

[10] Wu C L, Zheng K J, Xu X F, et al. Research on Dynamic State Estimation of Power System Based on Adaptive Interpolation Strong Tracking Extended Kalman Filter[J]. Power System Technology, 2023, 2(07): 1-13.

[0309]

[11] Kuti J, Rudas I J, Lyu H, Gao H J, Galambos P. Computationally Relaxed Unscented Kalman Filter[J]. IEEE Transactions on Cybernetics, 2023, 53(3): 1557-1565.

[0310]

[12] Cui X B, Xu B W. State of Charge Estimation of Lithium-Ion Battery Using Robust Kernel Fuzzy Model and Multi-Innovation UKF Algorithm Under Noise[J]. IEEE Transactions on Industrial Electronics, 2022, 69(11): 11121-11131.

[0311]

[13] Zheng X,Zhang H,Wang Z,Zhang C.Nonlinear State Estimation with Multisensor Stochastic Scheduling[J].IEEE Transactions on Systems,Man,and Cybernetics:Systems,2022,52(05):3349-3359.

[0312]

[14] Ma W T,Kou X,Guo Y S,et al.Constrained dynamic state estimation based on extended KRSL unscented Kalman filter[J].Power System Automation,2023,6(08):1-15.

[0313]

[15] Wang Z,Huang M S,Wang M S,Wu J,Zhang Y G.A ComputationallyEfffcient Outlier-Robust Cubature Kalman Filter for Underwater GravityMatching Navigation[J].IEEE Transactions on Instrumentation and Measurement,2022,71(05):18-23.

[0314]

[16] Sadr M A M,Champagne B.Joint Channel Estimation and RobustBeamforming Design for AF Relaying Using IMM Kalman Filters[J].IEEETransactions on Vehicular Technology,2023,72(02):1775-1790.

[0315]

[17] Li S, Li Z, Fernando T, Lu H H, Wang Q L. Application of Event-Triggered Cubature Kalman Filter for Remote Nonlinear State Estimation in Wireless Sensor Network[J]. IEEE Transactions on Industrial Electronics, 2020, 68(06): 5133-5145.

[0316]

[18] Luo Y, Liao Y R, Li Z M, et al. Adaptive Interacting Multiple Model Tracking Algorithm Based on CKF for High-Speed Target Tracking[J]. Journal of Beijing University of Aeronautics and Astronautics, 2023, 7(05): 1-20.

[0317]

[19] Liu W S, Hu Y H, Wang T H. An Improved GNSS / INS Navigation Method Based on Cubature Kalman Filter for Occluded Environment[J]. Measurement Science and Technology, 2023, 34(03): 16-27.

[0318]

[20] Zhu J, Liu B C, Wang H X, et al. Research on Sensorless Control of PMLSM Based on Improved Cubature Kalman Filter[J]. Control Engineering, 2021, 28(03): 471-477.

[0319]

[21] Silva I, Pendo C, Torres-Sospedra J, Moreira A. TrackInFactory: A Tight Coupling Particle Filter for Industrial Vehicle Tracking in Indoor Environments[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(07): 4151-4162.

[0320]

[22] Li W, Guo L. Robust Particle Filtering with Time-Varying Model Uncertainty and Inaccurate Noise Covariance Matrix[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(11): 7099-7108.

[0321]

[23] Jiang T, Fan B, Qin W T. Trajectory Tracking Method Based on Genetic Resampling Particle Filter[J]. Modern Radar, 2022, 44(02): 58-63.

[0322]

[24] Xu H, Yuan H D, Duan K Q, Xie W C, Wang Y L. An Adaptive Gaussian Sum Kalman Filter Based on a Partial Variational Bayesian Method[J]. IEEE Transactions on Automatic Control, 2019, 65(11): 4793-4799.

[0323]

[25] Liu Y, Dong K, Liu J, et al. Adaptive Gaussian Sum Kalman Filter Algorithm Based on SRCKF[J]. Control and Decision, 2014, 29(12): 2158-2164.

[0324]

[26] Dai Q, Feng W, Xu H X. Gaussian Sum Filter Considering Time-Varying Non-Gaussian Noise and Its Navigation Application[J]. Geomatics and Geodynamics, 2021, 41(3): 274-278.

[0325]

[27] Ge Q B, Wang H B, Yang Q M, et al. Robot Motion State Estimation Based on Improved Gaussian Mixture Model[J]. Acta Automatica Sinica, 2022, 48(8): 1972-1983.

[0326]

[28] Wu H, Chen S X, Yang B F, et al. Robust Gaussian Sum Volume Kalman Filter Algorithm for Infrared Target Tracking[J]. Journal of Infrared and Millimeter Waves, 2016, 35(1): 123-128.

[0327]

[29] Wang Y H. Filtering and Smoothing Method for Complex Nonlinear Dynamic System[D]. University of Electronic Science and Technology of China, 2019.

[0328]

[30] Xu H, Xie W C, Wang Y L. Gaussian and cubature Kalman filtering algorithms under angular flicker noise[J]. Systems Engineering and Electronics, 2019, 41(02): 229-235.

[0329]

[31] Chen Y, Sheng A D, Qi G Q, Li Y Y. Diffusion Self-Triggered Square-Root Cubature Information Filter for Nonlinear Non-Gaussian Systems and Its Application to The Optic-Electric Sensor Network[J]. Information Fusion, 2020, 55(03): 260-268.

[0330]

[32] Zhao X D, Wang B, Wang Z S. Predictive-fifth-order cubature Kalman filter method[J]. Acta Aeronautica Et Astronautica Sinica, 2023, 2(03): 14-26.

[0331]

[33] Ge Q B, Li Y Y, Wang Y L, Hu X M, Sun C Y. Adaptive Kalman Filtering Based on Model Parameter Ratios[J]. IEEE Transactions on Automatic Control, 2024.

[0332]

[34] Jiang H N, Cai Y L. Robust Gaussian sum cubature Kalman filter and its application to bearing-only tracking[J]. Control Theory and Applications, 2018, 35(02): 129-136.

[0333]

[35] Chong S, Zhang Y, Guo X T, Chen X Y, Cao H L, Tang J, Li J, Liu J. Seamless GPS / Inertial Navigation System Based on Self-Learning Square-Root Cubature Kalman Filter[J]. IEEE Transactions on Industrial Electronics, 2021, 68(01): 499-508.

[0334]

[36] YANG Y J,GAN Y,LI C H,et al.A Modified SRCKF Algorithm Based on Minimizing Innovation Covariance[J].Journal of Beijing University of Aeronautics and Astronautics,2023,49(01):138-144.

[0335]

[37] LI C H,MA J,YANG Y J,et al.A Multi-Sensor Fusion Adaptive Robust Algorithm Based on SRCKF[J].Journal of Beijing University of Aeronautics and Astronautics,2023,49(01):220-228.

[0336]

[38] Bai J G,Ge Q B,Li H,Xiao J M,Wang Y L.Aircraft Trajectory Filtering Method Based on Maximum Correntropy and Gaussian-Sum SRCKF[J].Cognitive Computation and Systems,2022,4(03):205-217.

[0337]

[39] CHENG Y,GE Q B. An Unmanned Ship Pose Estimation Algorithm Based on Non-Gaussian Feature Recognition and GSCPF[J].Control Engineering,2024.

[0338]

[40] TANG S S. Observability Analysis Method for Noise-Dependent Nonlinear Systems[D]. Hangzhou University of Electronic Science and Technology,2020.

[0339]

[41] LI Y Y. Engineering Intelligent Kalman Filtering Method[D]. Hangzhou University of Electronic Science and Technology,2020.

[0340]

[42] Ge Q B,Shao T,Duan Z S,Wen C L.Performance Analysis of the Kalman Filter with Mismatched Noise Covariances[J].IEEE Transactions on Automatic Control,2016,61(12):4014-4019.

[0341]

[43] Ge Q B,Hu X M,Li Y Y,He H L,Song Z H.A Novel Adaptive Kalman Filter Based on Credibility Measure[J].IEEE / CAA Journal of Automatica Sinica,2023,10(01):103-120.

[0342]

[44] Narue I,Keynia F,Molahosseini A S.Hunter-Prey Optimization:Algorithm and Applications[J].Soft Computing,2022,26(03):1279-1314.

[0343]

[45] Hernán P V,Adrián F.A Bio-Inspired Method for Engineering DesignOptimization Inspired by Dingoes Hunting Strategies[J].MathematicalProblemsin Engineering,2021,20(06):1135-1153.

[0344]

[46] Zhang Xingguo,Li Jing,He Hongli.Application of IMM-UKF in Real-Time Data Processing of Photoelectric Theodolite[J].Electronics Optics & Control,2012,19(04):81-84.

[0345]

[47] Huang Xiaoping.Kalman Filter Principle and Application[M].Electronic Industry Press,2015.

Claims

1. A lithium-ion battery SOC state estimation method based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems, characterized by: The following steps are involved: Combine particle filtering and Gaussian filtering to form a Gaussian particle filtering algorithm; By using the Gaussian component fusion strategy, the existing unsupervised EM algorithm is improved to obtain the IGS-SRCPF algorithm. The SRCKF sub-filter is introduced as a sub-filter of the particle Gaussian sum, and a pseudo-matrix of the SRCKF sub-filter is constructed to approximately linearize it, simplifying the definition of the MPR of nonlinear non-Gaussian systems. Referring to the definition of linear Gaussian MPR, the MPR of nonlinear non-Gaussian systems is defined in the IGS-SRCPF algorithm. Combined with the MPR existence theorem, the model adjustment coefficient and a condition for better designing high-performance nonlinear non-Gaussian filters are obtained. The HPO optimization algorithm and the DOA optimization algorithm are combined to obtain the multi-objective HPO-DOA optimization algorithm. Based on the particularity of the model adjustment coefficient in nonlinear non-Gaussian systems, the multi-objective HPO-DOA optimization algorithm is combined with the model adjustment coefficient and the conditions that can better design high-performance nonlinear non-Gaussian filters to obtain the MPR-based IGS-SRCPF algorithm. The MPR-based IGS-SRCPF algorithm is used to estimate the SOC state of the lithium-ion battery to obtain the state estimation result; the deep-width learning fusion network is used to correct the state estimation result to obtain the final lithium-ion battery SOC state estimation.

2. The method for lithium-ion battery SOC estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 1, characterized in that: The particle filter and the Gaussian filter are combined to form a Gaussian particle filter algorithm; By using the Gaussian component fusion strategy, the existing unsupervised EM algorithm is improved to obtain the IGS-SRCPF algorithm. The specific steps include: The model of discrete nonlinear non-Gaussian system is expressed as: x k+1 =f k (x k )+w k+1,k (1) z k =h k (x k )+v k (2) Among them, k represents the time, x k ∈R n represents the system state vector, f k :R n →R n 、h k :R n →R p Represent the system state matrix and measurement matrix respectively, w k+1，k ∈R n represents non-Gaussian process noise, z k ∈R p is the observation vector, v k ∈R p represents non-Gaussian observation noise, and the state noise and measurement noise are independent of each other; Use GS-CKF as the importance function of particle filtering, combine particle filtering with Gaussian sum filtering to form Gaussian sum particle filtering algorithm; Step 1: Assume x0 is the initial state variable and generate H particles from the prior distribution p(x0) Recalculate the initial state and the estimated error covariance P0; The process noise probability density function p(w k，k-1 ) and the measurement noise probability density function p(v k ) are expressed in the form of Gaussian sum: in, and is the weight of the corresponding Gaussian sub-item, and: Step 2 Importance sampling; Step 3: Particle update; Step 4: Calculate particle weights and normalize them; Step 5: Random resampling; Step 6 Calculate the state estimate and the estimation error covariance matrix; At this point, the state filtering process at time k has been completed, and the above steps are repeated to complete the estimation of the state quantity and error covariance matrix at the next moment; The above algorithm uses SRCKF as a sub-filter to estimate the system state corresponding to each particle Gaussian sub-term separately, and then realizes the global estimation by combining the Gaussian sub-terms of each particle.

3. The method for lithium-ion battery SOC estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 2, characterized in that: The importance sampling comprises the following steps: Step 2.1 Gaussian fitting: The improved unsupervised EM algorithm is used to transform the initial probability density function of H particles into It can be expressed in the form of Gaussian sum: in, is the weight of the corresponding Gaussian sub-item, and: Step 2.2 Distributed filtering: For each of the H particles, the Gaussian sum form of formula (25) is used to approximate the filtering probability density function: Among them, measurement and: N k|k =N k|k-1 ·r k (26) In addition, based on the predicted state mean Prediction covariance matrix Measurement noise mean and the measurement variance matrix Calculate the Gaussian subterm of the hth particle using the SRCKF filtering algorithm The filtered mean and the covariance matrix At this time, the measurement likelihood function of the state estimation of the i-th Gaussian sub-term of the h-th particle is expressed as: The indicators j and l are calculated as follows: Where i = 1, 2, ..., N k|k , j = 1, 2, ..., N k|k-1 , l=1,2,…,r k ;symbol Indicates floor operation; Filter weights It is necessary to integrate three pieces of information, namely the prediction filter weights The weight of the probability density function of measurement noise And the likelihood function of the state estimate Therefore The adaptive calculation method is: Step 2.3 Global point estimation: After the Gaussian sub-items of each particle obtain the filtering state at time k, the global filtering mean at time k is calculated using equations (30) and (31): and covariance matrix Similarly, the state estimates at other time points can also be calculated using equations (30) to (31); Step 2.4 Simplify control: Using the Gaussian component fusion strategy, after calculating the estimated mean and covariance of each sub-item at time k, the Gaussian components with weights greater than G′ are first retained and the other components are deleted: Among them, G′ is the weight of the Gth Gaussian component after the weights are sorted from large to small; Among the remaining Gaussian components, find the one with the largest weight: And find the Gaussian components that meet the conditions according to the following criteria: in, These Gaussian components are combined into a Gaussian distribution by weighted averaging, whose mean and covariance are: in, Delete all Gaussian components that have been fused, and then repeat the above steps until all Gaussian components have completed the operation; finally, only the first S sub-Gaussian distributions with large weights are retained, and the corresponding weights are normalized again; Step 2.5 Prediction Update: The predicted state probability density function is expressed as follows: in, It can be seen that the prediction weight The calculation of the two pieces of information, namely the filter weight and the weight of the process noise probability density function In addition, based on the estimated state mean Estimated variance matrix Process noise mean and the process noise covariance matrix Calculated using SRCKF The predicted mean and the covariance matrix In addition, c and d are expressed as: Where i = 1, 2, ..., N k+1|k , c=1,2,…,N k|k , d=1,2,…,q k ; The existing unsupervised EM algorithm process is as follows: Assume that there is a set of measurement noise data V k =(v1, v2, ..., v n ), where v k is a p-dimensional vector generated by the Gaussian mixture model: Where, are the weight, mean and covariance of the i-th Gaussian term in the Gaussian mixture model, r k Indicates the number of components of the mixture model; Step 1: Let r k =n, β=1, Take any value, that is, the value of θ, and set ε>0 as the condition for judging the end of the loop; where β is: Step 2: Calculate the implicit parameter z ki : Step 3: Update the weights by equations (13), (14) and (11) respectively. and β, in the first iteration, let β = 1; Step 4: When When , invalidate the i-th Gaussian component and remove the mixing coefficient at this time At the same time, the Gaussian component parameters When the number of iterations is greater than 60, let β = 0; Step 5: Update from equations (15) and (16) to obtain and z ki′ , and updated by equations (14) and (17) and Step 6: Update z according to formula (12) ki ; Step 7: If Then the iteration stops, otherwise go to step 3 to continue; The method of improving the existing unsupervised EM algorithm by using the Gaussian component fusion strategy includes: improving step 4 of the existing unsupervised EM algorithm by using the Gaussian component fusion strategy, including: Delete weight less than The Gaussian component of , the Gaussian component fusion strategy is performed on the interval of formula (18); Among the Gaussian components in this interval, find the one with the largest weight: And find the Gaussian components that meet the conditions according to the following criteria: in, These Gaussian components are combined into a Gaussian distribution by weighted averaging, whose mean and covariance are: in, Delete all Gaussian components that have been fused, repeat the above steps until all Gaussian components have completed the operation, and finally retain only the first S sub-Gaussian distributions with large weights.

4. The method for lithium-ion battery SOC state estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 3, characterized in that: The particle update comprises the following steps: Based on the IGS-SRCKF importance function and Generate new particles The calculation and normalization of particle weights include the following steps: Repeat step 2-step 3 for the other H-1 particles to obtain the state estimates of all particles, calculate the particle weights and normalize them: In the formula, the particle and weights One-to-one correspondence; The calculation of the state estimation quantity and the estimation error covariance matrix comprises the following steps: Calculate the final target posterior state estimator and estimation error covariance matrix at time k based on the resampled particles:

5. The method for lithium-ion battery SOC state estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 4, characterized in that: The SRCKF sub-filter is introduced as a sub-filter of the particle Gaussian sum, and a pseudo-matrix of the SRCKF sub-filter is constructed to approximately linearize it, thereby simplifying the definition of the MPR of the nonlinear non-Gaussian system; the specific operations include: By using the IGS-SRCPF algorithm, the filter is split into H×N k|k is a sub-filter; The pseudo observation matrix of the SRCPF sub-filter is: The pseudo-state transfer matrix is: in, Thus the iterative process of the sub-filter is simplified to: Wherein, the calculations of i, j, l, c and d are shown in equations (28) and (39); It is known that in each particle Gaussian subterm, when there is mismatched noise covariance in the subsystem, for each particle Gaussian subterm, there is: Where, represents the true observation noise covariance of the i-th Gaussian sub-item of each particle, represents the true process noise covariance of the i-th Gaussian sub-item of each particle, represents the observed noise covariance of the Gaussian sub-term assumption for each particle in practical applications, In practical applications, the noise covariance of the Gaussian sub-term of each particle i is represented by the superscript u. and represents the deviation of the particle Gaussian subterm; It is known that there is a Kalman filter with mismatched noise covariance in the Gaussian subterms of each particle: Wherein, the superscript f represents the actual calculated value of the sub-filter; but It is not the Gaussian sub-item filter estimate of the particle at time k TMSE, because: From equations (53) and (54), we can get The TMSE is: in, Wherein, the superscript m represents the true value of the filter; In addition, the indicators e and g are calculated as follows:

6. The method for lithium-ion battery SOC state estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 5, characterized in that: The reference linear Gaussian MPR definition method defines the MPR of a nonlinear non-Gaussian system in the IGS-SRCPF framework, and combines the MPR existence theorem to obtain the model adjustment coefficient and a condition for better designing a high-performance nonlinear non-Gaussian filter. The specific operations include: Referring to the definition of linear Gaussian MPR, for the linear Gaussian subsystem, let: in, is the process noise parameter ratio of the i-th Gaussian sub-item of each particle, is the process noise parameter ratio of the i-th Gaussian sub-item of each particle, is the model parameter ratio of the i-th Gaussian subsystem of each particle; In the nonlinear non-Gaussian system, the MPR theory is studied using the IGS-SRCPF algorithm. Under this algorithm, there are H×N k|k linear particle Gaussian subterms; for the noise covariance Gaussian subterm, there exists q k The process noise covariance Gaussian sub-terms are: Existence k The observation noise covariance Gaussian sub-terms are: Therefore, there are q k ×r k The combinations are: Therefore, in the Gaussian and SRCPF filter framework, is called the process noise parameter ratio, is called the observation noise parameter ratio, is called the MPR of the system; if the MPR of another model is: Then the two models are said to conform to the same model parameter ratio; Innovation of known sub-filters for The covariance matrix of is: The superscript f indicates the calculated value; but Not really The true value of the covariance matrix is: The superscript m indicates the true value; In each particle Gaussian subsystem, there is an existence theorem for the model parameter ratio, that is, if the estimated value of the process noise covariance subterm is Satisfy the system's process noise sub-item parameter ratio, and the estimated value of the observation noise covariance sub-item Satisfy the system's observation noise sub-item parameter ratio, and can be obtained The minimum value of , then they must satisfy the model parameter ratio of the Gaussian subsystem of the particle; According to the existence theorem of the model parameter ratio of the linear Gaussian system, in the IGS-SRCPF algorithm framework, if the estimated value of the process noise covariance sub-term is The process noise parameter ratio shown in equation (68) satisfies the estimated value of the observation noise covariance sub-term The observation noise parameter ratio shown in formula (69) is satisfied, and the value of each Gaussian sub-item can be obtained. The minimum value of , then they must satisfy the system model parameter ratio shown in formula (70); Therefore, when the parameter ratio of each noise covariance sub-item is known, by finding The estimated value of the noise covariance sub-term obtained by the minimum value of b h,i is a scalar greater than 0; when When , the noise covariance deviation of the sub-filter is: According to (58) and (62), we can get: Then, according to the simplified linear multiple theorem of filter parameters, in the linear Gaussian subsystem, for the steady-state system, if Established, when and Multiply by the same scalar K, when the system reaches a steady state, It can be seen that Substituting it into the above formula (77) we can get: From the above formula (78), we can know that Since in the estimation process, is not accurate, so and Stretch them into vector X h，i , Y h,i ; Use the least squares method to estimate b h,i : b h，i =((X h，i ) T X h,i ) -1 (X h,i ) T Y h,i (79) b h，i Substituting into equations (75) and (76), we can obtain: In summary, the parameter estimation criteria under the improved Gaussian and SRCPF framework are obtained: For each Gaussian subterm, The necessary and sufficient conditions are: st satisfies the ratio of process and observation noise parameters.

7. The method for lithium-ion battery SOC state estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 6, characterized in that: The HPO optimization algorithm and the DOA optimization algorithm are combined to obtain a multi-objective HPO-DOA optimization algorithm; According to the particularity of the model adjustment coefficient in the nonlinear non-Gaussian system, the multi-objective HPO-DOA optimization algorithm is combined with the model adjustment coefficient and the conditions for better design of high-performance nonlinear non-Gaussian filters to obtain the MPR-based IGS-SRCPF algorithm, which specifically includes the following steps: (1) In the defined interval [x min , x max ] Randomly generate population individuals, retain the weights calculated by the improved unsupervised EM algorithm, and the number of Gaussian sub-items of process noise c q , the number of Gaussian subterms of observation noise c r ;individual The parameter ratio of each process noise sub-item and the parameter ratio of each measurement process noise should be satisfied. For an individual estimated using the improved unsupervised EM algorithm in a randomly generated initial population, the first diagonal element of each noise covariance of the individual should be taken, and the individual should satisfy the parameter ratio condition. (2) Construct H×N k|k Fitness function Substitute the noise covariance corresponding to the Gaussian sub-item of each particle into the filtering algorithm, and obtain the corresponding Gaussian sub-item of each particle through equations (73) and (74). And calculate the fitness value of the population individuals corresponding to each fitness function; (3) Find the global optimal position of each fitness function in the population individuals according to each fitness value; (4) In H×H k|k Differentiate between hunters and prey within a population; (5) Update individuals in the population; (6) Calculate the fitness values ​​corresponding to the individuals after the fitness function is updated and find the global optimal position of the corresponding individuals in the population; (7) Determine whether the number of iterations reaches the upper limit. If so, output the optimal individual corresponding to each fitness function as the noise covariance estimate of each Gaussian sub-item. Otherwise go to step (4); (8) According to formula (79), calculate the adjustment coefficient b h,i ; (9) Substitute the adjustment coefficient and calculate in each particle Gaussian sub-term according to equations (80) and (81): (10) Multiple Sum and average to obtain the final and (11) and Substitute it into the IGS-SRCPF algorithm to obtain the MPR-based IGS-SRCPF algorithm.

8. The method for lithium-ion battery SOC estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 7, characterized in that: The use of a deep-width learning fusion network includes: using a generative adversarial network to extract features, and inputting these features into a width learning system for prediction; The generative adversarial network consists of a generator and a discriminator; Generator G(z) accepts random noise z to generate pseudo data Discriminator D(x) for real data x i and pseudo data Perform classification and extract high-level feature representation: Among them, D f (·) represents the feature representation extracted by the intermediate layer of the discriminator; High-level feature representation H of real data real ={h1, h2, ..., h n } and high-level feature representation of pseudo data Further merging to obtain the complete feature set H: H=[H real ;H gen ] (85) Feature Set It is input into the width learning system, and the width learning system quickly trains the prediction model through the pseudo-inverse method. Assuming that the dimension of the feature vector H is m, the width learning system performs linear regression by constructing the enhanced feature matrix Z and finally outputs the prediction result.

9. The method for lithium-ion battery SOC estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 8, characterized in that: The width learning system constructs an enhanced feature matrix Z to perform linear regression and finally outputs the prediction results, specifically including: Construct the input weight matrix W and bias vector b to generate the enhanced feature matrix Z: Z=σ(HW+b) (86) Where σ(·) is the activation function; Calculate the pseudo-inverse matrix Z + : WITH + =(Z T WITH) -1 WITH T (87) Calculate the output weight matrix B by the least squares method: B=(Z T Z+λI) -1 Z T Y (88) Where Y is the true label matrix and λ is the regularization parameter; Prediction output: in, is the output of the GANs-BLS system.

10. The method for lithium-ion battery SOC estimation based on MPR and IGS-SRCPF for nonlinear non-Gaussian systems according to claim 9, characterized in that: The IGS-SRCPF algorithm based on MPR is used to estimate the SOC state of the lithium-ion battery to obtain a state estimation result; The state estimation results are corrected using a deep-width learning fusion network to obtain the final lithium-ion battery SOC state estimation. The specific operations include: The sensor's measurement information is input into the MPR-based IGS-SRCPF algorithm to obtain the filtering result; The difference between the state one-step prediction and the state estimation value of the MPR-based IGS-SRCPF algorithm is used as the input sample of the deep and wide learning fusion network; the difference between the true value and the state estimation value is used as the output sample of the deep and wide learning fusion network; The deep and wide learning fusion network learns the mapping relationship between the prediction error and the actual error of the IGS-SRCPF algorithm and outputs the error between the filter estimate and the actual value. The optimal estimate is obtained by summing the state estimate of the MPR-based IGS-SRCPF algorithm and the output of the deep-width learning fusion network: in, is the optimal estimate, R perr is the output of the deep-width learning fusion network, is the state estimation value of the MPR-based IGS-SRCPF algorithm.

Images