Particle filter method based on adaptive clustering m-h resampling

Abstract

The application discloses a particle filtering method based on adaptive clustering M-H resampling, firstly, a set of random samples with weights, i.e., particles, are used to give a probability distribution estimation of system state, the particles are capacity values of lithium ion batteries, and initialization is performed; then, particles are extracted from an importance probability density function q(x k |x k‑1 ,y k ), particle weights are calculated, the weights are normalized, a particle set is divided into a high-weight particle set X T and a low-weight particle set X H according to a weight threshold W L , the high-weight particle set X H is reserved, the low-weight particle set X L is resampled, the reserved high-weight particle set X H and a new particle set X S are combined, and a new particle set is obtained, and finally, a final state estimation value, i.e., a final capacity estimation value of the lithium ion battery, is calculated. The application solves the problem of low state estimation accuracy in the prior art under the condition that the posterior probability distribution is multi-peak.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear filtering technology, specifically relating to a particle filtering method based on adaptive clustering MH resampling. Background Technology

[0002] In practical applications, every system contains noise to some extent. Sensors are affected by parameters with complex noise detected by the actual environment, which can influence the estimation results. Filtering is needed to reduce errors. Particle filtering (PF) algorithms are advantageous in filtering problems because they are not constrained by the linearity of the system model or the characteristics of noise and are easy to implement, making them widely applicable. Therefore, particle filtering can best represent the true distribution of the state when estimating the state of nonlinear and non-Gaussian systems, effectively improving the estimation accuracy. Traditional resampling often leads to the excessive duplication of high-weight particles and the discarding of low-weight particles as the number of iterations increases. Excessive duplication of high-weight particles leads to over-concentration, resulting in an increasing number of particles with the same weight. This causes a loss of diversity and may ultimately lead to a large error between the state estimation result and the true value. The MH resampling particle filtering method (MHPF) uses crossover and Gaussian mutation to move particles towards the high-probability region, replacing the traditional resampling method. For multi-peak distribution scenarios, an intelligent algorithm is adopted to resample particles. The clustering concept is introduced into MH resampling, and a particle filtering algorithm based on clustering MH resampling (K-means clustering MHPF, KMHPF) is proposed to improve particle distribution, enhance the filtering accuracy and precision of MHPF, and thus improve the accuracy of lithium-ion remaining lifetime estimation. Summary of the Invention

[0003] The purpose of this invention is to provide a particle filtering method based on adaptive clustering MH resampling, which solves the problem of low state estimation accuracy in the case of multi-peaked posterior probability distribution in the prior art.

[0004] The technical solution adopted in this invention is a particle filtering method based on adaptive clustering MH resampling, which is implemented according to the following steps:

[0005] Step 1: Estimate the probability distribution of the system state using a set of weighted random samples, i.e., particles. The particles represent the capacity values ​​of the lithium-ion battery. Let time k = 0, and randomly draw state samples from the prior distribution p(x) to obtain the initial particles. Where k is a time series, k = 1, 2, ..., T, This represents a random estimate of the system state. The initial weights of the particles are represented by i = 1, 2, ..., N, where N is the number of samples for the random estimate of the system state.

[0006] Step 2: From the importance probability density function q(x) k |x k-1 ,y k Particles are extracted from the sample, their weights are calculated, and then the weights are normalized to obtain the particle set. in, This represents the state of the i-th particle at time k. This represents the normalized weight of the i-th particle at time k;

[0007] Step 3: Assemble the particle set Based on the weight threshold W T Divided into a high-weight particle set X H and low-weight particle set X L For the high-weight particle set X H To be retained;

[0008] Step 4: For the low-weight particle set X L Resampling is performed, and the two strategies are controlled by adaptively adjusting the value of the selection probability λ to generate a new particle set X. S An adaptive Gaussian mutation strategy is selected with probability λ, and a crossover strategy is selected with probability 1-λ.

[0009] Step 5: Select the set of high-weight particles X that are retained. H and the new particle set X S Merging them yields a new set of particles.

[0010] Step 6: Calculate the final state estimate, which is the final capacity estimate of the lithium-ion battery.

[0011] The invention is further characterized in that,

[0012] Step 2 is as follows:

[0013] Calculate the particle weights according to equation (1):

[0014]

[0015] According to equation (2), the weights are normalized to obtain the particle set.

[0016]

[0017] In formulas (1) and (2), For the i-th particle at time k Weights before normalization To observe the likelihood probability density, Let the state transition probability density be... This is the importance probability density function.

[0018] Step 3 is as follows:

[0019] Step 3.1: Assemble the particle set The particles are arranged in descending order of importance based on their weights, resulting in a set W.

[0020] Step 3.2: First, set the weight threshold W. T Then, for each particle in the particle set W, and the weight threshold W... T Comparisons were made, and the particles were divided into a high-weight set X. H and low-weight particle set X L If the particle's weight is greater than the weight threshold W T Then it is stored in X H If the particle's weight is less than the weight threshold W T Then it is stored in X L Low-weight particle set X L These are invalid particles, specifically the low-weight particle set X. L Resampling was performed using a clustering MH resampling strategy, and the particle set was... The specific division method is as follows:

[0021]

[0022] W T Defined as:

[0023]

[0024] N eff Defined as:

[0025]

[0026] In formulas (3), (4), and (5), X L For a set of low-weight particles, X H For a high-weighted particle set, W T For the weight threshold, Indicates rounding up, N eff The effective number of particles;

[0027] Step 3.3: Set the high-weight particle set X H particles As the input matrix to the k-means algorithm, the particle set X is solved iteratively using k-means. H Divided into two categories, namely X H1 and X H2This prepares for the crossover and Gaussian mutation in the two resampling selection strategies, causing particles to move towards the maximum likelihood region.

[0028]

[0029] In the formula, X H1 For the particles contained in the first cluster, X H2 The particles contained in the second cluster.

[0030] Step 4 is as follows:

[0031] Step 4.1: According to the adaptive selection strategy, perform Gaussian mutation or crossover operations on all low-weight particles. Select the first proposed distribution (Gaussian mutation method proposed in Step 4.3) with a probability of λ (0 < λ < 1); otherwise, select the second proposed distribution (crossover method proposed in Step 4.2) with a probability of 1-λ. The adaptive selection strategy is as follows:

[0032]

[0033] In the formula, λ is the selection probability;

[0034] Step 4.2: Use an adaptive crossover strategy to generate a set of particles X with high weights. H1 and low-weight particle set X L Intermediate weight particles The specific operation is as follows: From X H1 Randomly select a high-weight particle and X L Particles to be sampled in Crossing helps increase the number of effective particles. The number of particles after the adaptive cross-resampling strategy is calculated according to the following formula:

[0035]

[0036] In the formula, The j-th particle after the crossover at time k Where, j∈{1,2,…N} L},N L The number of particles in the low-weight particle set. For high-weight particles after clustering, l∈{1,2,…N} H1},N H1 The number of particles in the high-weight particle set after clustering, a random number. The crossover rate is calculated using the following formula.

[0037]

[0038] In the formula, For random number αj The upper bound;

[0039] Combining formulas (8) and (9), we know that Represents low-weight particles Transferred to The amount of information determines the newly generated particles. It contains information on high and low weight particles;

[0040] Step 4.3: Apply an adaptive Gaussian mutation operation to the low-weight particles based on the selection probability λ, and then extract the high-weight particles from the clustered set X. H1 A particle is randomly selected from the sample and subjected to Gaussian mutation according to the following formula:

[0041]

[0042] In the formula, Let j be the Gaussian-mutated particle, where j∈{1,2,…N} L},N L The number of particles in the low-weight particle set. For the unmutated particle, l∈{1,2,…N} H1},N H1 Let μ be the number of particles in the high-weight particle set after clustering, and μ be the mean. For variance;

[0043] An adaptive variance function is established by minimizing the Euclidean distance between each pair of particles; the calculation formula is as follows:

[0044]

[0045] Where m is the extracted particle number.

[0046] Step 4.4: Update the particle set X according to the acceptance / rejection criterion function. S Determine whether to accept the newly generated particle. With acceptance rate The probability of new particles generated after resampling by The probability of retaining the original particles The acceptance / rejection criterion function is shown below:

[0047]

[0048] In the formula, For acceptance rate, These are the new particles generated after resampling. For particles Weights before normalization For particles Weights before normalization.

[0049] Step 5 is as follows:

[0050] The set of high-weight particles X retained in step 3.2 H and the new particle set X generated after resampling S Merging them yields a new set of particles. And calculate the particle according to equation (2) Corresponding normalized weights

[0051] Step 6 is as follows:

[0052] After renormalizing all particle weights in step 5 The optimal estimate of the system state at time k is obtained, and the state estimation formula is as follows:

[0053]

[0054] In formula (8), This is the optimal estimate of the system state at time k, which is also the capacity value of the lithium-ion battery that needs to be obtained during the entire filtering process. Let k be a random estimate of the system state at time k. For random estimates The corresponding weights are k = 1, 2, ..., T.

[0055] The beneficial effects of this invention are that the particle filtering method based on adaptive clustering MH resampling resamples the low-weight particle set through clustering MH sampling using crossover or Gaussian mutation, causing particles to move towards the high-probability region. Specifically, Gaussian mutation involves randomly selecting a particle from the clustered particle set and performing Gaussian mutation. The particle distribution is optimized based on particle similarity, and the variance in Gaussian mutation is used by utilizing the minimum Euclidean distance between pairs of particles within the same cluster, avoiding particle deviation from the high-probability region in multi-modal distributions. Crossover involves crossing the low-weight particle with the clustered high-weight particles to generate intermediate-weight particles between the high-weight and low-weight particle sets. The particle set is updated after acceptance / rejection criterion function, and finally, the system is filtered. This invention, through clustering MH resampling, keeps newly extracted particles in the high-probability region, improving the overall quality of the particles and increasing particle diversity. This improves the accuracy and precision of filtering, resulting in better system filtering performance, thereby improving the accuracy of lithium battery capacity estimation and promoting the development of new energy vehicles and other fields. Attached Figure Description

[0056] Figure 1 This is a data distribution diagram of battery capacity degradation in an embodiment of the present invention;

[0057] Figure 2 This is a comparison chart of the filtering results of the present invention and MHPF;

[0058] Figure 3 This is a comparison chart of the absolute deviation between the present invention and MHPF;

[0059] Figure 4 This is a comparison diagram of the MAPE of the present invention and MHPF. Detailed Implementation

[0060] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0061] When dealing with multimodal posterior distributions, the particle filtering method based on clustering-MH resampling optimizes the particle distribution using the particle similarity principle, effectively preventing newly extracted particles from straying far from high-probability regions. Based on the aforementioned crossover or Gaussian mutation operations, the overall quality of the particles is effectively improved, while also enhancing particle diversity and filtering accuracy. First, N initial particles are extracted from the prior distribution p(x). Then, from the importance probability density function q(x) k |x k-1 ,y k Particles are extracted from the sample, their weights are calculated using the weighting formula, and then the weights are normalized to obtain the particle set. Next, the particle set Based on the weight threshold, it is divided into a high-weight particle set X. H and low-weight particle set X L The set of high-weight particles is retained, while the set of low-weight particles X is retained. L Each particle is clustered and resampled using the MH method, and the particle set X is updated by accepting the rejection criterion function. S The high-weight particle set X H and the new particle set X S Merging them yields a new set of particles. To achieve the final system filtering, the particles are defined as follows: Specifically, clustering MH resampling involves generating a random number r∈[0,1]. If this random number is less than the selection probability, a Gaussian mutation operation is performed to generate particles. New particles are extracted from the vicinity of high-weight particles to replace low-weight particles, driving low-weight particles to move towards these high-probability regions. Otherwise, a crossover operation is performed to generate particles, sampling in the region between high-weight and low-weight particle regions. The specific steps of Gaussian mutation are as follows: For the set of high-weight particles X… H These particles are clustered according to the k-means algorithm. The input matrix for the k-means algorithm is used to group particles with similar characteristics based on Euclidean distance. The resulting clustered particle set X... H1A particle is randomly selected from the dataset, and a Gaussian mutation operation is performed on this high-weight particle. The variance of the Gaussian mutation is calculated using the minimum Euclidean distance between pairs of particles after k-means clustering. Particles are then selected within a certain walking range to avoid invalid particle updates. The specific steps of crossover are as follows: a high-weight particle after clustering is randomly selected from the dataset. With low-weight particles to be sampled A crossover operation is performed to generate intermediate-weight particles that fall between the high-weight particle set and the low-weight particle set. After the particle update operation is completed, the weights of the resulting particles are calculated to obtain the optimal estimate of the system state at each time step, thus completing the system's filtering process.

[0062] The particle filtering method based on adaptive clustering MH resampling is characterized by the following steps:

[0063] Step 1: Estimate the probability distribution of the system state using a set of weighted random samples, i.e., particles. The particles represent the capacity values ​​of the lithium-ion battery. Let time k = 0, and randomly draw state samples from the prior distribution p(x) to obtain the initial particles. Where k is a time series, k = 1, 2, ..., T, This represents a random estimate of the system state. The initial weights of the particles are represented by i = 1, 2, ..., N, where N is the number of samples for the random estimate of the system state.

[0064] Step 2: From the importance probability density function q(x) k |x k-1 ,y k Particles are extracted from the sample, their weights are calculated, and then the weights are normalized to obtain the particle set. in, This represents the state of the i-th particle at time k. This represents the normalized weight of the i-th particle at time k;

[0065] Step 2 is as follows:

[0066] Calculate the particle weights according to equation (1):

[0067]

[0068] According to equation (2), the weights are normalized to obtain the particle set.

[0069]

[0070] In formulas (1) and (2), For the i-th particle at time k Weights before normalization To observe the likelihood probability density, Let the state transition probability density be... This is the importance probability density function.

[0071] Step 3: Assemble the particle set Based on the weight threshold W T Divided into a high-weight particle set X H and low-weight particle set X L For the high-weight particle set X H To be retained;

[0072] Step 3 is as follows:

[0073] Step 3.1: Assemble the particle set The particles are arranged in descending order of importance based on their weights, resulting in a set W.

[0074] Step 3.2: First, set the weight threshold W. T Then, for each particle in the particle set W, and the weight threshold W... T Comparisons were made, and the particles were divided into a high-weight set X. H and low-weight particle set X L If the particle's weight is greater than the weight threshold W T Then it is stored in X H If the particle's weight is less than the weight threshold W T Then it is stored in X L Low-weight particle set X L These are invalid particles, specifically the low-weight particle set X. L Resampling is performed using a clustering-based MH resampling strategy to improve particle distribution. Particle set The specific division method is as follows:

[0075]

[0076] W T Defined as:

[0077]

[0078] N eff Defined as:

[0079]

[0080] In formulas (3), (4), and (5), X L For a set of low-weight particles, X H For a high-weighted particle set, W T For the weight threshold, Indicates rounding up, N eff The effective number of particles;

[0081] Step 3.3: Set the high-weight particle set X H particles As the input matrix to the k-means algorithm, the particle set X is solved iteratively using k-means. H Divided into two categories, namely X H1 and X H2 This prepares for the crossover and Gaussian mutation in the two resampling selection strategies, causing particles to move towards the maximum likelihood region.

[0082]

[0083] In the formula, X H1 For the particles contained in the first cluster, X H2 The particles contained in the second cluster.

[0084] Step 4: For the low-weight particle set X L Resampling is performed, and the two strategies are controlled by adaptively adjusting the value of the selection probability λ to generate a new particle set X. S An adaptive Gaussian mutation strategy is selected with probability λ, and 1 - The probability selection of λ uses a crossover strategy;

[0085] Step 4 is as follows:

[0086] Step 4.1: According to the adaptive selection strategy, perform Gaussian mutation or crossover operations on all low-weight particles. Select the first proposed distribution (Gaussian mutation method proposed in Step 4.3) with a probability of λ (0 < λ < 1); otherwise, select the second proposed distribution (crossover method proposed in Step 4.2) with a probability of 1-λ. The adaptive selection strategy is as follows:

[0087]

[0088] In the formula, λ is the selection probability;

[0089] Step 4.2: Use an adaptive crossover strategy to generate a set of particles X with high weights. H1 and low-weight particle set X L Intermediate weight particles The specific operation is as follows: From X H1 Randomly select a high-weight particle and X L Particles to be sampled in Crossing helps increase the number of effective particles. The number of particles after the adaptive cross-resampling strategy is calculated according to the following formula:

[0090]

[0091] In the formula, The j-th particle after the crossover at time k Where, j∈{1,2,…N} L},N L The number of particles in the low-weight particle set. For high-weight particles after clustering, l∈{1,2,…N} H1},N H1 The number of particles in the high-weight particle set after clustering, a random number. The crossover rate is calculated using the following formula.

[0092]

[0093] In the formula, For random number α j The upper bound;

[0094] Combining formulas (8) and (9), we know that Represents low-weight particles Transferred to The amount of information determines the newly generated particles. It contains information on high and low weight particles;

[0095] Step 4.3: Apply an adaptive Gaussian mutation operation to the low-weight particles based on the selection probability λ, and then extract the high-weight particles from the clustered set X. H1 A particle is randomly selected from the sample and subjected to Gaussian mutation according to the following formula:

[0096]

[0097] In the formula, Let j be the Gaussian-mutated particle, where j∈{1,2,…N} L},N L The number of particles in the low-weight particle set. For the unmutated particle, l∈{1,2,…N} H1},N H1 Let μ be the number of particles in the high-weight particle set after clustering, and μ be the mean. For variance;

[0098] Due to variance This determines the mass of the particle after Gaussian mutation. The larger the value, the farther the new particle is from the original high-weight particles. Especially when the posterior probability distribution is multimodal, an excessively large random sampling region can cause particles to jump out of the high-probability region of the posterior probability distribution, rendering the Gaussian mutation ineffective. Therefore, an adaptive variance function is established by minimizing the Euclidean distance between each pair of particles. The calculation formula is as follows:

[0099]

[0100] Where m is the extracted particle number.

[0101] Step 4.4: Update the particle set X according to the acceptance / rejection criterion function. S Determine whether to accept the newly generated particle. With acceptance rate The probability of new particles generated after resampling by The probability of retaining the original particles The acceptance / rejection criterion function is shown below:

[0102]

[0103] In the formula, For acceptance rate, These are the new particles generated after resampling. For particles Weights before normalization For particles Weights before normalization.

[0104] Step 5: Select the set of high-weight particles X that are retained. H and the new particle set X S Merging them yields a new set of particles.

[0105] Step 5 is as follows:

[0106] The set of high-weight particles X retained in step 3.2 H and the new particle set X generated after resampling S Merging them yields a new set of particles. And calculate the particle according to equation (2) Corresponding normalized weights

[0107] Step 6: Calculate the final state estimate, which is the final capacity estimate of the lithium-ion battery.

[0108] Step 6 is as follows:

[0109] After renormalizing all particle weights in step 5 The optimal estimate of the system state at time k is obtained, and the state estimation formula is as follows:

[0110]

[0111] In formula (8), This is the optimal estimate of the system state at time k, which is also the capacity value of the lithium-ion battery that needs to be obtained during the entire filtering process. Let k be a random estimate of the system state at time k. For random estimates The corresponding weights, k = 1, 2, ..., T;

[0112] The filtering results of the system can provide necessary data support and basic assurance for the subsequent analysis and control of the system.

[0113] This invention discloses a filtering method based on clustering-based MH resampling. When dealing with multi-peaked posterior distributions, it employs Gaussian mutation and crossover resampling strategies to update the particle set, improving the overall quality and diversity of the particles to obtain the particles required for system filtering. This particle set is updated after acceptance of a rejection criterion function. Finally, the weights of the particles in the updated set are calculated and weighted averaged to obtain the optimal estimate of the system state, which is the final system filtering result. This enables filtering of sensor-collected observation data. This invention can perform filtering even with multi-peaked posterior distributions without considering the posterior distribution itself, improving the accuracy and precision of the filtering results, reducing system filtering bias, and enhancing the filtering effect, thus facilitating further system analysis and control. This invention solves the problem of low state estimation accuracy in existing technologies when the posterior distribution is multi-peaked.

[0114] Example

[0115] This embodiment predicts the capacity of a Li-ion 18650 lithium cobalt oxide battery with a rated capacity of 2Ah and a nominal voltage of 3.7V. The battery capacity degradation data is as follows: Figure 3 As shown.

[0116] To better predict the battery capacity degradation process, a system state-space model needs to be determined. The state equation is shown in equation (9), and the observation equation is shown in equation (10). The initial values ​​of the model parameters are set as a1 = 1.942 and b1 = -2.052 × 10⁻⁶. -3 c1 = 1.572 × 10 -7 d1 = 0.07406.

[0117]

[0118]

[0119] In formula (9), k is the number of cycles of the lithium-ion battery (k = 2, 3, ..., 168), a k c kHere are the estimated values ​​of the battery's internal impedance-related parameters at time k, b k d k w represents the estimated value of the battery aging rate-related parameters at time k. a w b w c w d These represent the process noise of the four parameters a, b, c, and d in the state equation, respectively; Q in formula (10) k For the estimated capacity of the battery after k cycles, measure the noise v. k ~N(0,0.001), N(0,0.001) is the standard normal distribution, which is a Gaussian distribution with a mean of 0 and a variance of 0.001.

[0120] The simulation step number T is set to 168, and the number of particles in the particle sets of both the MHPF and KMHPF methods (this invention) is set to N = 150.

[0121] right Figure 1 The battery capacity degradation data of battery B0007 is processed to obtain the system's filtering results, such as... Figure 2 As shown.

[0122] To more accurately analyze the effectiveness of this invention, MAE (mean absolute deviation) and MAPE (mean absolute percentage error) were selected as system indicators for comparative analysis. Figure 3 This is a comparison chart of the deviations between MHPF and the present invention; Figure 4 Table 1 shows a comparison of the MAPE of MHPF and the present invention for each cycle. As can be seen from Table 1, after the improvement, the MAE of the complete filtering process of the present invention is reduced to 29.787% of the RMSE of the MHPF method, and the overall MAPE of the present invention is reduced by 0.0345% compared with the MAPE of the MHPF method.

[0123] Table 1

[0124]

[0125] The experimental results above show that, compared with the standard MHPF, the present invention (i.e., the particle filtering method based on clustering MH resampling) has smaller deviation, better filtering effect, and higher accuracy and precision.

Claims

1. A particle filtering method based on adaptive clustering MH resampling, characterized in that, The specific steps are as follows: Step 1: Estimate the probability distribution of the system state using a set of weighted random samples, i.e., particles. These particles represent the capacity values ​​of the lithium-ion battery. Let time k=0, and estimate the probability distribution from the prior distribution. Initial particles are obtained by randomly sampling state samples. ,in, It is a time series. , This represents a random estimate of the system state. This represents the initial particle weights. , The number of samples for the random estimate of the system state; Step 2: From the importance probability density function Particles are extracted from the sample, their weights are calculated, and then the weights are normalized to obtain the particle set. ,in, express Time of the first The state of each particle express Time of the first Normalized weights of each particle; Step 2 is described in detail below: Calculate the particle weights according to equation (1): (1) According to equation (2), the weights are normalized to obtain the particle set. ; (2) In formulas (1) and (2), for Time of the first Particles Weights before normalization To observe the likelihood probability density, Let the state transition probability density be... It is the importance probability density function; Step 3: Assemble the particle set Based on weight threshold Divided into high-weight particle sets and low-weight particle set For high-weight particle sets To be retained; Step 3 is as follows: Step 3.1: Assemble the particle set The particles are sorted in descending order of importance based on their weights to obtain the particle set. ; Step 3.2: First, set the weight threshold. Then the particle set Each particle and weight threshold in Comparison, divided into high-weight particle sets and low-weight particle set If the particle's weight is greater than the weight threshold Then stored in If the particle's weight is less than the weight threshold Then stored in Low-weight particle set These are invalid particles, specifically low-weight particle sets. Resampling was performed using a clustering MH resampling strategy, and the particle set was... The specific division method is as follows: (3) Defined as: (4) Defined as: (5) In formulas (3), (4), and (5), For a low-weight particle set, For a high-weight particle set, For the weight threshold, Indicates rounding up. The effective number of particles; Step 3.3: Set up the high-weight particles particles As the input matrix for the k-means algorithm, the particle set is solved iteratively using k-means. Divided into two categories and This prepares for the crossover and Gaussian mutation in the two resampling selection strategies, causing particles to move towards the maximum likelihood region. (6) In the formula, The particles contained in the first cluster. For the particles contained in the second cluster; Step 4: For the low-weight particle set Resampling is performed, and the selection probability is adaptively adjusted. The value controls two strategies for generating new particle sets. With probability Choose an adaptive Gaussian mutation strategy, in order to The probability of choosing to use a crossover strategy; Step 5: Retain the set of high-weight particles and new particle set Merging them yields a new set of particles. ; Step 6: Calculate the final state estimate, which is the final capacity estimate of the lithium-ion battery.

2. The particle filtering method based on adaptive clustering MH resampling according to claim 1, characterized in that, Step 4 is as follows: Step 4.1: Perform Gaussian mutation or crossover operations on all low-weight particles according to the adaptive selection strategy, with a selection probability of . The probability is to choose the first suggested distribution, i.e., the Gaussian mutation method proposed in step 4.3; otherwise, use the probability of choosing the first suggested distribution. The probability of choosing the second suggested distribution, i.e., the crossover method proposed in step 4.2, is adopted, with the adaptive selection strategy being... (7) In the formula, For the probability of selection; Step 4.2: Use an adaptive crossover strategy to generate a set of particles with high weights. and low-weight particle set Intermediate weight particles The specific operation is as follows: From Randomly select a high-weight particle and Particles to be sampled in Crossing helps increase the number of effective particles. The number of particles after the adaptive cross-resampling strategy is calculated according to the following formula: (8) In the formula, for The first time after the time crossover Particles ,in, , The number of particles in the low-weight particle set. For high-weight particles after clustering, , The number of particles in the high-weight particle set after clustering, a random number. The crossover rate is calculated using the following formula. (9) In the formula, For random numbers The upper bound; Combining formulas (8) and (9), we know that Represents low-weight particles Transferred to The amount of information determines the newly generated particles. It contains information on high and low weight particles; Step 4.3: Based on the selection probability An adaptive Gaussian mutation operation is applied to low-weight particles to improve the clustered high-weight particle set. A particle is randomly selected from the sample and subjected to Gaussian mutation according to the following formula: (10) In the formula, These are particles resulting from Gaussian mutation, among which... , The number of particles in the low-weight particle set. For the particles before mutation, , This represents the number of particles in the high-weight particle set after clustering. The mean, For variance; An adaptive variance function is established by minimizing the Euclidean distance between each pair of particles; the calculation formula is as follows: (11) in, The extracted particle number. ; Step 4.4: Update the particle set according to the acceptance / rejection criterion function. Determine whether to accept the newly generated particle. With an acceptance rate The probability of new particles generated after resampling ,by The probability of retaining the original particles The acceptance / rejection criterion function is shown below: (12) In the formula, For acceptance rate, These are the new particles generated after resampling. For particles Weights before normalization For particles Weights before normalization.

3. The particle filtering method based on adaptive clustering MH resampling according to claim 2, characterized in that, Step 5 is described in detail below: The set of high-weight particles retained in step 3.2 and the new set of particles generated after resampling Merging them yields a new set of particles. And calculate the particle according to equation (2). Corresponding normalized weights .

4. The particle filtering method based on adaptive clustering MH resampling according to claim 3, characterized in that, Step 6 is as follows: After renormalizing all particle weights in step 5 The optimal estimate of the system state at time k is obtained, and the state estimation formula is as follows: （8） In formula (8), That is, the system The optimal estimate of the system state at any given time is the capacity value of the lithium-ion battery that needs to be obtained during the entire filtering process. for A stochastic estimate of the system state at time t. For random estimates The corresponding weights, .

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