WO2020087362A1

WO2020087362A1 - Particle filtering method, system, and computer readable storage medium

Info

Publication number: WO2020087362A1
Application number: PCT/CN2018/113079
Authority: WO
Inventors: 李良群; 王小梨; 谢维信
Original assignee: 深圳大学
Priority date: 2018-10-31
Filing date: 2018-10-31
Publication date: 2020-05-07

Abstract

A particle filtering method, used for target tracking. The method solves the technical problem that the tracking effect of a target has a large error in the prior art, and comprises: initializing a time table, and setting the number of T-S fuzzy models (S1); extracting a particle state from a prior probability to obtain an antecedent parameter and a consequent parameter of the T-S fuzzy model (S2); identifying the consequent parameter of the T-S fuzzy model (S3); identifying the antecedent parameter of the T-S fuzzy model, and calculating a weight of the T-S fuzzy model (S4); fusing the state of each T-S fuzzy model, and updating the model weight (S5); sampling particles (S6); calculating and standardizing a particle weight (S7); resampling the particles, and calculating and standardizing the resampled particle weight (S8); calculating a particle state and a covariance estimation result according to the identified consequent parameter, the identified antecedent parameter, the model weight, and the resampled particle weight (S9); and outputting a particle state and a covariance estimation result at a non-zero moment in the time table (S10). Therefore, a target can be accurately tracked.

Description

Particle filtering method, system and computer readable storage medium

Technical field

The invention relates to the technical field of target tracking.

Background technique

The TS (full name Takagi–Sugeno) model is a fuzzy inference model proposed by Takagi and Sugeno. It can introduce fuzzy semantic information that can critically determine the motion model in a simple manner, and this model can approximate a nonlinear system of any shape . Target tracking is to estimate the future movement state of the target based on the estimated state at the previous moment and the effective observation at the current moment, so as to obtain the target's movement trajectory; in order to obtain the state information of the target's movement trajectory, such as the target's position and speed And acceleration, most scholars use the popular Kalman filter algorithm, but the algorithm has many uncertainties in the tracking effect when the target is maneuvering.

technical problem

At present, the multi-model algorithm is mainly used to solve the uncertainty modeling problem. In such methods, the interactive multi-model algorithm of the model switching mechanism is superior; however, the model switching mechanism makes the algorithm easy to cause large The estimation error makes the tracking effect have a larger error.

Technical solution

A first aspect of the present invention provides a basic particle filtering method, including: initializing a timetable and setting the number of TS fuzzy models; extracting particle states from a priori probabilities, and obtaining the TS fuzzy based on the extracted particle states The anterior and posterior parameters of the model; the identification of the posterior parameters of the TS fuzzy model; the observation and calculation of the fuzzy membership of each TS fuzzy model; the identification of the antecedent parameters of the TS fuzzy model, and according to the fuzzy The degree of membership calculates the model weights of the TS fuzzy model; fuse the state of each TS fuzzy model and update the model weights; sample the particles; calculate and normalize the particle weights; resample the particles and calculate And standardized re-sampled particle weights; calculate particle state and covariance estimation results based on the identified post-ware parameters, the identified pre-ware parameters, the model weights, and the re-sampled particle weights ; Output particle state and covariance estimation results at non-zero time in the timetable.

Beneficial effect

By calculating the fuzzy membership of each TS fuzzy model and fusing the state of each TS fuzzy model, multiple semantic fuzzy sets can be used to fuzzyly represent the target feature information, and a universal TS fuzzy model semantic framework can be constructed. Therefore, the spatial feature information is introduced into the particle filter to achieve accurate sampling of the particles, so that when the tracked target suddenly changes direction or the target's dynamic a priori information is inaccurate, it can effectively track the target accurately.

BRIEF DESCRIPTION

1 is a schematic block diagram of a flow of a particle filtering method according to an embodiment of the invention;

2 is a schematic block diagram of a structure of an electronic device according to an embodiment of the present invention.

Best Mode of the Invention

A first aspect of the present invention provides a basic particle filtering method, including: initializing a timetable and setting the number of TS fuzzy models; extracting particle states from a priori probabilities, and obtaining the TS fuzzy based on the extracted particle states The anterior and posterior parameters of the model; the identification of the posterior parameters of the TS fuzzy model; the observation and calculation of the fuzzy membership of each TS fuzzy model; the identification of the antecedent parameters of the TS fuzzy model, and according to the fuzzy The membership degree calculates the model weights of the TS fuzzy model; fuse the state of each TS fuzzy model and update the model weights; sample the particles; calculate and normalize the particle weights; resample the particles and calculate And standardized re-sampled particle weights; calculate particle state and covariance estimation results based on the identified post-ware parameters, the identified pre-ware parameters, the model weights, and the re-sampled particle weights ; Output particle state and covariance estimation results at non-zero time in the timetable.

Further, the identification of the posterior parameters of the T-S fuzzy model includes: constructing a Kalman filter equation for each T-S fuzzy rule; and identifying posterior parameters according to the Kalman equation.

Further, the observing and calculating the fuzzy membership of each TS fuzzy model includes: identifying the similarity function between the estimation result of the TS fuzzy semantic model and the measurement matrix according to the relevant entropy criterion; defining the fuzzy C regression clustering according to the relevant entropy criterion The objective function of the algorithm; maximize the relevant entropy standard, and combine the constraints to optimize the objective function; according to the objective function to derivate the corresponding weight of each particle, get the membership expression between the TS fuzzy model and the data After the membership matrix is calculated by the similarity function, it is applied to the optimized objective function.

Further, the identification of the antecedent parameters of the TS fuzzy model includes: setting the fuzzy membership function of the antecedent parameter to a Gaussian function; calculating the mean value and root mean square of the antecedent parameter membership function of the Gaussian function Error; derive the state of the TS fuzzy semantic model and the function of covariance estimation.

Further, the calculation of the model weight of the TS fuzzy model according to the fuzzy membership includes: defining the state of the target at non-zero time in the timetable, and defining at least two target features of the non-zero time target Vector; define the fuzzy membership function, which represents the degree to which the vector determines the state; define the posterior probability distribution and the state and weight of the particles at the previous moment; on the basis of the set of particles that existed at the previous moment A sample set is obtained by fusing particles extracted from the posterior probability distribution; the weight of the TS fuzzy model is calculated according to the sample set.

Further, the defining the posterior probability distribution includes: establishing a state function of the particle at the time in the timetable according to a known nonlinear function, and establishing a measurement matrix function of the particle at the time in the timetable; according to known The initial value of the probability density of predicts the measured value of the matrix function; the prior value is updated according to the measured value and the Bayesian formula to obtain the posterior probability density distribution.

Further, the calculating and normalizing the particle weights include: constructing the importance density function update particle of the particle filter according to the state of the TS fuzzy semantic model and the function of covariance estimation; calculating according to the density function and the weight update formula And standardized particle weights.

A second aspect of the present invention provides a target tracking system, including any of the particle filtering methods described above.

A third aspect of the present invention provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that the processor executes the computer program , Any of the particle filtering methods mentioned above is implemented.

A fourth aspect of the present invention provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, any of the particle filtering methods described above is implemented.

Embodiments of the invention

Please refer to FIG. 1 for a particle filtering method, including: S1, initializing the timetable, and setting the number of TS fuzzy models; S2, extracting the particle state from the prior probability, and obtaining the TS fuzzy model according to the extracted particle state Anterior and posterior parameters of S; S3, identify the posterior parameters of the TS fuzzy model; S4, identify the anterior parameters of the TS fuzzy model, and calculate the model weight of the TS fuzzy model; S5, each The state of the TS fuzzy model is fused and the model weights are updated; S6, the particles are sampled; S7, the particle weights are calculated and normalized; S8, the particles are resampled, and the particle weights are calculated and normalized; S9 ， Calculate the particle state and covariance estimation results based on the identified afterward parameters, the identified beforehand parameters, model weights and resampled particle weights; S10, output the particle state and covariance at non-zero time in the timetable Estimate the results.

The identification of the posterior parameters of the T-S fuzzy model includes: constructing a Kalman filter equation for each T-S fuzzy rule; identifying the posterior parameters according to the Kalman equation.

The T-S fuzzy model can use multiple linear systems to represent a nonlinear system of arbitrary precision. For the T-S fuzzy model with target feature information, each linear model rule is defined as Equation 1, and Equation 1 is expressed as follows:

among them,

Represents the g features of the target at time k,

The fuzzy membership function representing the g-th target feature,

Is the target state equation of the i-th model at time k,

Is the observation equation of the i-th model at time k,

Are the process noise and observation noise of the i-th model,

Is the state estimation result of the i-th model at time k.

In TS fuzzy model modeling, for the identification of the posterior parameters, in this embodiment, Kalman filtering is used to identify the posterior parameters. In other embodiments, least squares or weighted least squares can also be used Method, for each TS fuzzy rule, the Kalman filter equation is as follows from formula 2 to formula 6, and formula 2 to formula 6 are expressed as follows:

Formula 2:

Formula 3:

Formula 4:

Formula 5:

Equation 6:

Identification of the antecedent parameters of the TS fuzzy model includes: observing and calculating the fuzzy membership of each TS fuzzy model; setting the fuzzy membership function of the antecedent parameter to a Gaussian function; calculating the antecedent parameter membership function of the Gaussian function The mean value and root mean square error of the; the function of the state and covariance estimation of the TS fuzzy semantic model.

In order to realize the adaptive identification of the antecedent parameters, the fuzzy membership function of the antecedent parameters is defined as a Gaussian function such as Equation 7, which is expressed as follows:

among them,

Is the mean value of the membership function of the Gaussian model anterior

For the root-mean-square error, Equation 8 can be obtained.

Finally, the state and covariance estimation formula 9 and formula 10 based on the T-S fuzzy semantic model are expressed as follows: Formula 9:

Equation 10:

among them,

Represents the state after the Kalman filtering of the i-th linear model at time k.

Observing and calculating the fuzzy membership of each TS fuzzy model includes: identifying the similarity function between the estimation result of the TS fuzzy semantic model and the measurement matrix according to the relevant entropy standard; defining the objective function of the fuzzy C regression clustering algorithm according to the relevant entropy standard; Maximize the relevant entropy standard, and combine the constraints to optimize the objective function; according to the objective function to derivate the corresponding weight of each particle, get the membership expression between the TS fuzzy model and the data; pass the membership matrix through similarity After the degree function is calculated, it is applied to the optimized objective function.

Calculating the model weights of the TS fuzzy model includes: defining the state of the target at non-zero time in the timetable, and defining a vector of at least two target features of the target at non-zero time; defining the fuzzy membership function, which represents the vector's Determine the degree; define the posterior probability distribution and the state and weight of the particles at the previous time; fuse the particles extracted from the posterior probability distribution on the basis of the particle set existing at the previous time to obtain the sample set; calculate the TS based on the sample set The weight of the fuzzy model.

set up

Is an observation set,

Is a set of prediction observations, z _{k, l} means l ^th observations, and

Represents the prediction observation based on fuzzy rule i ^th at time k. The objective function of fuzzy C-regression clustering algorithm is shown in formula 11, which is as follows:

Where m is the weight index, which is generally

Represents the metric function between the observation and output of the fuzzy rule l ^th . The membership function satisfies Equation 12, which is as follows:

At the same time, in order to discriminate the similarity between the estimation result of TS fuzzy semantic model and the observation z _{k, l} , the relevant entropy criterion is introduced as formula 13, which is expressed as follows:

among them,

Is a Gaussian kernel function,

It is the fuzzy membership of i ^th observation and i ^th rule at time k. In order to maximize the correlation entropy standard formula 11, combined with the constraint conditions of formula 10, the objective function is defined as formula 14, which is expressed as follows:

Where β, λ _k is the Lagrangian multiplier vector, and (D _ik ) ² is the distance measurement function, then Equation 15 and Equation 16 can be obtained, and Equation 15 is expressed as follows:

Equation 16 is expressed as follows:

among them,

For a given target state

The observed z _{k, l} likelihood function.

Is the new interest covariance matrix obtained by formula 2; according to the objective function

Find the partial derivative to get the degree of membership

The expression formula 17 is updated, and the formula 17 is expressed as follows:

Therefore, the fuzzy membership of the i ^th fuzzy rule at time k is calculated as Equation 18, which is expressed as follows:

After the membership matrix U is calculated by Equation 16, it can be used in Equation 19 of the antecedent parameter identification of the T-S fuzzy model. Equation 19 is expressed as follows:

Defining the posterior probability distribution includes: establishing the state function of the particle at the time in the timetable according to the known nonlinear function, and establishing the measurement matrix function of the particle at the time in the timetable; according to the known initial value of the probability density Predict the measured value of the matrix function; update the prior value according to the measured value and the Bayesian formula to obtain the posterior probability density distribution.

definition

Is a set of particles, where x _j is a particle, M is the number of particles used in the approximation, μ _j is the corresponding weight of each particle, and

The χ approximate distribution p (x) is Equation 20, which is expressed as follows:

Where δ (xx _j ) is the Dirichlet function.

The next important content of particle filtering is importance sampling. Suppose the distribution p (x) is approximated by discrete random measures. If particles are extracted from p (x), then each particle will be given an equal weight 1 / M. When direct sampling from p (x) is more troublesome, you can extract particles x _j from a distribution q (x), set it as an importance density function, and assign according to these distributions

For the weight, there is Formula 21, which is expressed as follows:

Among them, the normalized weight of the particles can be expressed by formula 22, which is expressed as follows:

And considering the problems of particle degradation and particle diversity, the spatial motion feature information is introduced into PF. set up

It is a vector composed of g target feature information of the target at time k, and G is the feature number. Discrete stochastic measure

Approximating the posterior distribution p (x _{0: k-1} | z _{1: k-1} , θ _{1: k-} ). Given discrete random measurements χ _k ₁ and observation z _k , the purpose is to use χ _k _{1 to} obtain χ _k . The sequence importance sampling method achieves this by extracting particles x _{k, j} and appending them to x _{0: k-1, j} to form x _{0: k, j} and updating the weight μ _{k, j} .

According to the sequential importance sampling filtering idea of Bayesian estimation, in order to calculate a sequential estimate of the posterior probability density function, the posterior probability distribution formula is set. The posterior probability distribution formula is as formula 23, and formula 23 is expressed as follows:

q (x _{0: k} | z _{1: k} , θ _{1: k} ) = q (x _k | x _{0: k-1} , z _{1: k} , θ _{1: k} ) q (x _{0: k-1} | z _{1: k} ₁ , θ _{1: k-1} );

Based on the trajectories x _{0: k} _{1, j} and x _{k, j} , formula 24 can be obtained, which is expressed as follows:

x _{k, j} ～ q (x _k | x _{0: k-1, j} , z _{1: k} , θ _{1: k} );

Therefore, the weight value is updated according to the weight value update formula, and the weight value update formula is formula 25, which is expressed as follows:

Among them, p (z _k | x _k ) represents the likelihood function, p (x _{k, j} | x _{0: k-1, j} , θ _k ) is the state transition function,

Is an important density function.

The calculation and normalization of particle weights include: building the importance density function of the particle filter according to the state of the T-S fuzzy semantic model and the function of covariance estimation to update the particles; calculating and normalizing the particle weights according to the density function and the weight update formula.

Obtain the TS fuzzy model state estimation according to Equation 9 and Equation 10

And covariance estimates

The particle density is constructed by the importance density function to update the particles. The importance density function is shown in Equation 26, which is expressed as follows:

According to formula 24 and formula 23, the particle weight calculation formula 27 is obtained. Formula 27 is expressed as follows:

In addition, the nonlinear discrete dynamic system also needs to be considered. The functions of the nonlinear discrete dynamic system are shown in Equation 28 and Equation 29. Equation 28 is expressed as follows: x _k = f _k (x _k-1 , v _k-1 ) 29 means as follows:

z _k = h _k (x _k , e _k );

with

Are some known nonlinear functions,

Is the state of the system at time k,

Is the measurement matrix at time k,

with

Represents process noise and measurement noise. The essence of the Bayesian filtering principle is to use all known information to obtain the posterior probability density function of the system state variables, including two steps of prediction and update, the initial value of probability density p (x ₀ | z ₀ ) = p (x ₀ ) Known, the prediction is made by formula 30, which is expressed as follows:

p (x _k | z _{1: k-1} ) = ∫p (x _k | x _k-1 ) p (x _k-1 | z _{1: k-1} ) dx _k-1 ;

After the measured value z _k is obtained, the prior value is updated by the Bayesian formula to obtain the posterior probability density. The posterior probability density function is as shown in Formula 31, and Formula 31 is as follows:

p (x _k | z _{1: k} ) = p (z _k | x _k ) p (x _k | z _{1: k-1} ) / p (z _k | z _{1: k-1} ),

Among them, p (z _k | z _{1: k-1} ) is a standardized constant, and the formula for solving p (z _k | z _{1: k} ₁ ) is shown in Equation 32, which is as follows:

p (z _k | z _{1: k-1} ) = ∫p (z _k | x _k ) p (x _k | z _{1: k-1} ) dx _k ;

The basic principles of Bayesian filtering in Equation 30 and Equation 31, but the integration of Equation 30 into some dynamic systems can be resolved, and the most important solution is the Kalman filter; set f _k and h _k is linear, and v _k and e _k are additive Gaussian noise with known covariance. Monte Carlo based on random sampling operation can convert the integral operation into a summation operation of finite sample points, that is, the formula 30 The operation is transformed into a process of cumulative accumulation of finite sample points.

The particle filtering method provided by the present invention has the following working process or principle: initialize the timetable, make k = 0, and set the model number to Nf, and extract the particle state from the prior probability p (x ₀ )

M is the number of particles; for each time in the time table, that is, k represents different times, let j = 1, 2 ..., M, and then use T- to update the particles with the fuzzy model, during which use formulas 2 to 6 to estimate After the parameters

And use equation 19 to identify the antecedent parameters

And calculate the model weights by Equation 8.

And use the modified formulas of formula 9 and formula 10, that is, formula 33 and formula 34 to update the state of particle j

And state covariance

Equation 33 is expressed as follows:

Equation 34 is expressed as follows:

Then, the deformation formula using formula 23, that is, the particle is sampled using formula 35, formula 35 is expressed as follows:

The calculation formula of the particle weight value is calculated using the deformation formula of formula 27, that is, the formula 35 is used to calculate the particle weight value, and the normalization of the particle weight value uses the formula 36, and the formula 35 is expressed as follows:

Equation 36 is expressed as follows:

In Equation 35 and Equation 36,

It is a predictive observation, calculated using Equation 1; then resampling the particles, and estimating the resampled particle state and covariance estimation results according to the above steps; and finally outputting the state and state covariance estimation at time k according to Equation 37 and Equation 38 As a result, Equation 37 is expressed as follows:

Equation 38 is expressed as follows:

The present application also provides a target tracking system, including the above particle filtering method, and tracking the target according to the target tracking system.

An embodiment of the present application provides an electronic device. Please refer to FIG. 2. The electronic device includes: a memory 601, a processor 602, and a computer program stored on the memory 601 and executable on the processor 602. The processor 602 executes the computer When the program is implemented, the generation method of the incremental kernel density estimator described in the foregoing embodiments of FIGS. 1 to 4 is implemented.

Further, the electronic device further includes: at least one input device 603 and at least one output device 604.

The aforementioned memory 601, processor 602, input device 603, and output device 604 are connected via a bus 605.

The input device 603 may specifically be a camera, a touch panel, a physical button, a mouse, or the like. The output device 604 may specifically be a display screen.

The memory 601 may be a high-speed random access memory (RAM, Random Access Memory) memory, or may be a non-volatile memory (non-volatile memory), such as a disk memory. The memory 601 is used to store a set of executable program codes, and the processor 602 is coupled to the memory 601.

Further, an embodiment of the present application further provides a computer-readable storage medium. The computer-readable storage medium may be provided in the electronic device in the foregoing embodiments, and the computer-readable storage medium may be as shown in FIG. 6 described above. The memory 601 in the embodiment is shown. A computer program is stored on the computer-readable storage medium, and when the program is executed by the processor 602, the generation method of the incremental kernel density estimator described in the foregoing method embodiment is implemented.

Further, the computer storable medium may also be various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory 601 (ROM, Read-Only Memory), RAM, magnetic disk, or optical disk.

In the several embodiments provided in this application, it should be understood that if the system is implemented in the form of a software function module and sold or used as an independent product, it may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention essentially or part of the contribution to the existing technology or all or part of the technical solution can be embodied in the form of a software product, the computer software product is stored in a storage medium , Including several instructions to enable a computer device (which may be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program code .

It should be noted that the foregoing method embodiments are described as a series of action combinations for the sake of simplicity, but those skilled in the art should be aware that the present invention is not limited by the sequence of actions described because According to the invention, certain steps may be performed in other orders or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present invention.

The above is a description of a particle filtering method, system and computer-readable storage medium provided by the present invention. For those skilled in the art, according to the ideas of the embodiments of the present invention, there will be changes in specific implementation and application scope In summary, the content of this specification should not be construed as limiting the present invention.

Industrial applicability

The particle filtering method, system and computer readable storage medium provided by the present invention solve the technical problem that the tracking effect of the target has a large error in the prior art.

Claims

A particle filtering method, characterized in that it includes:

Initialize the timetable and set the number of T-S fuzzy models;

Extract the particle state from the prior probability, and obtain the anterior and posterior parameters of the T-S fuzzy model according to the extracted particle state;

Identify the subsequent parameters of the T-S fuzzy model;

Identify the antecedent parameters of the T-S fuzzy model and calculate the model weights of the T-S fuzzy model;

Fuse the state of each T-S fuzzy model and update the model weights;

Sampling particles;

Calculation and standardization of particle weights;

Resample the particles, and calculate and standardize the weights of the resampled particles;

Calculating the particle state and the covariance estimation result according to the identified posterior parameter, the identified posterior parameter, the model weight and the resampled particle weight;

Output the particle state and covariance estimation results at non-zero time in the timetable.
The particle filtering method according to claim 1, wherein:

The identification of the posterior parameters of the T-S fuzzy model includes:

For each T-S fuzzy rule, construct a Kalman filter equation;

According to the Kalman equation, the following parameters are identified.
The particle filtering method according to claim 1, wherein:

The identification of the antecedent parameters of the T-S fuzzy model includes:

Observe and calculate the fuzzy membership of each T-S fuzzy model;

Set the fuzzy membership functions of the antecedent parameters to Gaussian functions;

Calculating the mean value and root mean square error of the antecedent parameter membership function of the Gaussian function;

The function of state and covariance estimation of T-S fuzzy semantic model is obtained.
The particle filtering method according to claim 3, characterized in that

The observed and calculated fuzzy membership of each T-S fuzzy model includes:

Identify the similarity function between the estimation result of the T-S fuzzy semantic model and the measurement matrix according to the relevant entropy standard;

Define the objective function of fuzzy C regression clustering algorithm according to the relevant entropy standard;

Maximize the relevant entropy standard and combine the constraints to optimize the objective function;

According to the objective function, the partial derivatives of the corresponding weights of the particles are derived, and the membership expression between the T-S fuzzy model and the data is obtained;

After the membership matrix is calculated by the similarity function, it is applied to the optimized objective function.
The particle filtering method according to claim 1, wherein:

The model weights for calculating the T-S fuzzy model include:

Define the state of the target at non-zero time in the timetable, and define a vector composed of at least two target features of the non-zero time target;

Define a fuzzy membership function that indicates how much the vector determines the state;

Define the posterior probability distribution and the state and weight of the particles at the previous moment;

Fuse particles extracted from the posterior probability distribution on the basis of the particle set existing at the previous moment to obtain a sample set;

Calculate the weight of the T-S fuzzy model according to the sample set.
The particle filtering method according to claim 5, wherein:

The defined posterior probability distribution includes:

Establish the state function of the particle at the time in the timetable according to the known nonlinear function, and establish the measurement matrix function of the particle at the time in the timetable;

Predict the measured value of the matrix function according to the known initial value of the probability density;

The prior value is updated according to the measured value and the Bayesian formula to obtain the posterior probability density distribution.
The particle filtering method according to claim 3, wherein the calculation and normalization of particle weights include:

Construct the importance density function update particle of the particle filter according to the state of the T-S fuzzy semantic model and the function of covariance estimation;

Calculate and normalize particle weights according to the density function and weight update formula.
An object tracking system, characterized by comprising the method according to any one of claims 1 to 7.
An electronic device, comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that when the processor executes the computer program, claim 1 is realized The method according to any one of 7.
A computer-readable storage medium on which a computer program is stored, characterized in that, when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.