CN109492769A - A kind of particle filter method, system and computer readable storage medium - Google Patents

Abstract

The invention discloses a particle filtering method, which is used for target tracking, and solves the technical problem that the tracking effect of the target has a large error in the prior art. number; extract the particle state from the prior probability, and obtain the antecedent parameters and consequent parameters of the T-S fuzzy model; identify the consequent parameters of the T-S fuzzy model; identify the antecedent parameters of the T-S fuzzy model Identify and calculate the weights of the T-S fuzzy models; fuse the states of each T-S fuzzy model to update the model weights; sample the particles; calculate and standardize the particle weights; resample the particles and calculate and standardized resampled particle weights; calculate particle state and covariance estimation results according to the identified consequent parameters, identified antecedent parameters, model weights and resampled particle weights; output non-zero time in the schedule The particle state and covariance estimation results are obtained, so that the target can be accurately tracked.

Description

A particle filtering method, system and computer-readable storage medium

technical field

The present invention relates to the technical field of target tracking, and in particular, to a particle filtering method, system and computer-readable storage medium.

Background technique

The T-S (full name is 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 way, and this model can approximate any shape nonlinear system. .

Target tracking is to estimate the future motion state of the target on the basis of the estimated state of the previous moment and the effective observation at the current moment, so as to obtain the motion trajectory of the target; in order to obtain the state information of the target motion trajectory, such as the position and speed of the target And acceleration, most scholars use the popular Kalman filter algorithm, but this algorithm has many uncertainties in the tracking effect when the target is maneuvering.

At present, the multi-model algorithm is mainly used to solve the uncertainty modeling problem. Among such methods, the interactive multi-model algorithm of the model switching mechanism is superior; however, the use of the model switching mechanism makes the algorithm easy to cause large problems at the time of model switching. The estimation error of , so that there is a large error in the tracking effect.

SUMMARY OF THE INVENTION

The main purpose of the present invention is to provide a particle filtering method, a system and a computer-readable storage medium, aiming at solving the technical problem that the tracking effect of the target has a large error in the prior art.

In order to achieve the above object, a first aspect of the present invention provides a basic particle filtering method, including: initializing a timetable, and setting the number of T-S fuzzy models; Obtain the antecedent parameters and consequent parameters of the T-S fuzzy model; identify the consequent parameters of the T-S fuzzy model; observe and calculate the fuzzy membership degree of each T-S fuzzy model; identify the antecedent parameters of the T-S fuzzy model, Calculate the model weights of the T-S fuzzy model according to the fuzzy membership; fuse the states of each T-S fuzzy model, and update the model weights; sample the particles; calculate and standardize the particle weights; Resampling, and calculating and normalizing the resampled particle weights; calculating the particle state according to the identified consequent parameters, the identified antecedent parameters, the model weights, and the resampled particle weights and covariance estimation results; output the particle states and covariance estimation results at non-zero moments in the schedule.

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

Further, the observation and calculation of the fuzzy membership degree of each T-S fuzzy model include: identifying the similarity function between the T-S fuzzy semantic model estimation result and the measurement matrix according to the relevant entropy standard; defining the fuzzy C regression clustering according to the relevant entropy standard 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, obtain the partial derivative of the corresponding weight of each particle, and obtain the membership expression between the T-S fuzzy model and the data ; Apply the membership matrix to the optimized objective function after the similarity function is calculated.

Further, identifying the antecedent parameters of the T-S fuzzy model includes: setting the fuzzy membership function of the antecedent parameters as a Gaussian function; calculating the mean value and the root mean square of the antecedent parameter membership function of the Gaussian function. Error; a function to derive the state and covariance estimates of the T-S fuzzy semantic model.

Further, calculating the model weights of the T-S fuzzy model according to the fuzzy membership degree includes: defining the state of the target at a non-zero time in the timetable, and defining the at least two target features of the non-zero time target consisting of: vector; define the fuzzy membership function, indicating the degree of determination of the vector on the state; define the posterior probability distribution and the state and weight of the particle at the previous moment; on the basis of the particle set existing at the previous moment Fusing the particles extracted from the posterior probability distribution to obtain a sample set; and calculating the weights of the T-S fuzzy model according to the sample set.

Further, the defining a posteriori probability distribution includes: establishing the state function of the particle at the moment in the timetable according to the known nonlinear function, and establishing the measurement matrix function of the particle at the moment in the timetable; according to the known non-linear function 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, and the posterior probability density distribution is obtained.

Further, the calculation and standardization of particle weights include: constructing the importance density function update particles of particle filtering according to the state of the T-S fuzzy semantic model and the function of covariance estimation; calculating according to the density function and the weight update formula. and normalized particle weights.

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

A third aspect of the present invention provides an electronic device, comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program , implement any of the above particle filtering methods.

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

The present invention provides a particle filtering method, which has the beneficial effects that: by calculating and observing the fuzzy membership degree of each T-S fuzzy model, and merging the progress state of each T-S fuzzy model, the target feature information can be processed by multiple semantic fuzzy sets. Fuzzy representation, to build a general T-S fuzzy model semantic framework, so as to introduce spatial feature information into particle filtering to achieve accurate sampling of particles, so that when the tracked target suddenly changes direction or the dynamic prior information of the target is inaccurate and other complex The target can be accurately tracked effectively.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained according to these drawings without creative efforts.

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

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

Detailed ways

In order to make the purpose, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. The embodiments described above are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts shall fall within the protection scope of the present invention.

Please refer to Figure 1, which is a particle filtering method, including: S1, initializing the timetable, and setting the number of T-S fuzzy models; S2, extracting particle states from the prior probability, and obtaining T-S fuzzy models according to the extracted particle states S3, identify the consequent parameters of the T-S fuzzy model; S4, identify the antecedent parameters of the T-S fuzzy model, and calculate the model weights of the T-S fuzzy model; S5, identify each The state of the T-S 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 resampled particle weights are calculated and normalized; S9 , calculate the particle state and covariance estimation results according to the identified consequent parameters, the identified antecedent parameters, the model weights and the resampled particle weights; S10, output the particle state and covariance of the non-zero time in the timetable estimated results.

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

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

in, represents the g features of the target at time k, represents the fuzzy membership function of the g-th target feature, is the target state equation of the ith model at time k, is the observation equation of the ith model at time k, are the ith model process noise and observation noise, respectively, is the state estimation result of the ith model at time k.

In the modeling of the T-S fuzzy model, for the identification of the consequent parameters, in this embodiment, Kalman filtering is used to realize the identification of the consequent parameters. In other embodiments, the least squares or the weighted least squares can also be used method, for each T-S 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:

Formula 6:

Identifying the antecedent parameters of the T-S fuzzy model includes: observing and calculating the fuzzy membership degree of each T-S fuzzy model; setting the fuzzy membership function of the antecedent parameters as a Gaussian function; calculating the antecedent parameter membership function of the Gaussian function The mean and root mean square error of ; derive the function of the state and covariance estimates of the T-S fuzzy semantic model.

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

in, is the mean of the membership functions of the antecedent parameters of the Gaussian model, is the root mean square error, then Equation 8 can be obtained, and Equation 8 is expressed as follows:

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

Formula 10:

in, Represents the state of the ith linear model rule Kalman filtering at time k.

Observing and calculating the fuzzy membership degree of each T-S fuzzy model includes: identifying the similarity function between the T-S fuzzy semantic model estimation result 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, the partial derivative of the corresponding weight of each particle is obtained, and the membership degree expression between the T-S fuzzy model and the data is obtained; the membership degree matrix is similar to After the degree function is calculated, it is applied to the optimized objective function.

Calculating the model weights of the T-S fuzzy model includes: defining the state of the target at a non-zero time in the timetable, and defining a vector composed of at least two target features of the target at the non-zero time; defining a fuzzy membership function, which represents the relationship between the vector and the state. Determine the degree; define the posterior probability distribution and the state and weight of the particles at the previous moment; fuse the 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 T-S according to the sample set The weights of the fuzzy model.

set up is an observation set, is a predicted observation set, z _k,l represents the l ^th observation, while Represents the predicted observation based on the fuzzy rule i ^th at time k. The objective function of the fuzzy C-regression clustering algorithm is as shown in Equation 11. Equation 11 is as follows:

where m is the weight index, generally m=2, represents the metric function between the observation and the output of the fuzzy rule l ^th , the membership function satisfies Equation 12, and Equation 12 is as follows:

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

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

where β,λ _k are the Lagrange multiplier vectors, and (D _ik ) ² is the distance measurement function, then formula 15 and formula 16 can be obtained, and formula 15 is expressed as follows:

Equation 16 is expressed as follows:

in, for a given target state The observed z _k,l likelihood function. is the innovation covariance matrix obtained by Equation 2; according to the objective function Find the partial derivative to get the degree of membership Update expression Equation 17, Equation 17 is expressed as follows:

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

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

Defining the posterior probability distribution includes: establishing the state function of the particle at the time of the timetable according to the known nonlinear function, and establishing the measurement matrix function of the particle at the time of 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 are the particles, 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 aspect of particle filtering is importance sampling. Suppose that the distribution p(x) is approximated by a discrete random measure. If particles are drawn from p(x), then each particle is given an equal weight 1/M. When it is troublesome to directly sample from p(x), you can extract particles x _j from a distribution q(x), set it as the importance density function, and assign weights according to these distributions, then there is Equation 21, Equation 21 represents as follows:

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

And considering the problems of particle degradation and particle diversity, spatial motion feature information is introduced into PF. set up is a vector composed of g target feature information of the target at time k, and G is the number of features. using discrete random measures Approximate the posterior distribution p(x _0:k-1 |z _1:k-1 ,θ _1:k- ). Given discrete random measurements χ _{k 1} and observations z _k , the goal is to use χ _{k 1} to obtain χ _k . Sequential importance sampling methods do this by sampling particles x _k,j and appending them to x _0:k-1,j , forming x _0:k,j , and updating the weights μ _k,j .

According to the sequential importance sampling filtering idea of Bayesian estimation, in order to calculate a sequential estimation of a posterior probability density function, a posterior probability distribution formula is set.

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 , Equation 24 can be obtained, and Equation 24 is expressed as follows:

x _k,j ~q(x _k |x _0:k-1,j ,z _1:k ,θ _1:k );

Thus, the weights are updated according to the weight update formula, the weight update formula is formula 25, and formula 25 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 the important density function.

Calculating and normalizing particle weights includes: constructing the importance density function of particle filtering according to the state of the T-S fuzzy semantic model and the function of covariance estimation to update particles; calculating and normalizing particle weights according to the density function and weight update formula.

Obtain TS fuzzy model state estimation according to Equation 9 and Equation 10 and covariance estimation The importance density function of the particle filter is constructed to update the particles. The importance density function is shown in Equation 26. Equation 26 is expressed as follows:

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

In addition, a nonlinear discrete dynamic system 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 ); Equation 28 29 is represented as follows:

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

f _k : and h _k : are some known nonlinear functions, is the state of the system at time k, is the measurement matrix at time k, and 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 the probability density p(x ₀ |z ₀ )=p(x ₀ ) is known, then 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 obtaining the measured value _zk , the prior value is updated through the Bayesian formula to obtain the posterior probability density. The posterior probability density function is shown in Equation 31, and Equation 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 solution formula of p(z _k |z _{1:k 1} ) is as shown in Equation 32, and Equation 32 is as follows:

p(z _k |z _1:k-1 )=∫p(z _k |x _k )p(x _k |z _1:k-1 )dx _k ;

Equation 30 and Equation 31 are the basic principles of Bayesian filtering, but the integrals in Equation 30 can be analyzed for some dynamic systems, 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 noises with known covariances. Monte Carlo based on random sampling operations can transform the integral operation into the summation operation of finite sample points, and the equation 30 can be converted into The operation is transformed into a probability transition accumulation process of finite sample points.

The working process or principle of the particle filtering method provided by the present invention is as follows: initialize the timetable, set k=0, set the model number as Nf, and extract the particle state from the prior probability p(x ₀ ). M is the number of particles; for each moment in the timetable, that is, when k represents different moments, let j=1,2...,M, and then use T-is the fuzzy model to update the particles, and use formula 2 to formula 6 to estimate during the period Consequence parameters and use Equation 19 to identify the antecedent parameter And the model weights are calculated by formula 8 And use the deformation formulas of Equation 9 and Equation 10, that is, Equation 33 and Equation 34 to update the state of particle j and state covariance Equation 33 is expressed as follows:

Equation 34 is expressed as follows:

Then for the deformation formula using Equation 23, that is, using Equation 35 to sample the particles, Equation 35 is expressed as follows:

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

Equation 36 is expressed as follows:

In Equation 35 and Equation 36, is the predicted observation, calculated using formula 1; then the particles are resampled, and the resampled particle state and covariance estimation results are estimated according to the above steps; finally, the state and state covariance estimation at time k is output according to formula 37 and formula 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-mentioned 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 in the memory 601 and running on the processor 602, and the processor 602 executes the computer During the program, the particle filtering method described in the foregoing embodiment is implemented.

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

The above-mentioned memory 601 , processor 602 , input device 603 and output device 604 are connected through 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. Memory 601 is used to store a set of executable program codes, and processor 602 is coupled to 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 above-mentioned embodiments, and the computer-readable storage medium may be one of the above-mentioned embodiments. memory 601. A computer program is stored on the computer-readable storage medium, and when the program is executed by the processor 602, the particle filtering method described in the foregoing method embodiments is implemented.

Further, the computer-storable medium may also be a USB flash drive, a removable hard disk, a read-only memory 601 (ROM, Read-Only Memory), a RAM, a magnetic disk or an optical disk and other media that can store program codes.

In the several embodiments provided in this application, it should be understood that if the system is implemented in the form of software function modules and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium , including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes: U disk, removable 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 codes.

It should be noted that, for the convenience of description, the foregoing method embodiments are all expressed as a series of action combinations, but those skilled in the art should know that the present invention is not limited by the described action sequence, because Certain steps may be performed in other orders or simultaneously in accordance with the present invention. 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 all necessary for 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 idea of the embodiment of the present invention, there will be changes in the specific implementation and application scope. In conclusion, the contents of this specification should not be construed as limiting the present invention.

Claims (10)

1. A method of particle filtering, comprising:

initializing a timetable and setting the number of T-S fuzzy models;

extracting a particle state from the prior probability, and obtaining a front piece parameter and a back piece parameter of the T-S fuzzy model according to the extracted particle state;

identifying the back part parameters of the T-S fuzzy model;

identifying the former parameters of the T-S fuzzy model, and calculating the model weight of the T-S fuzzy model;

fusing the state of each T-S fuzzy model and updating the model weight;

sampling the particles;

calculating and standardizing the weight value of the particles;

resampling the particles, and calculating and standardizing the weight values of the resampled particles;

calculating a particle state and covariance estimation result according to the identified back piece parameter, the identified front piece parameter, the model weight and the resampled particle weight;

and outputting the particle state and covariance estimation result at the non-zero time in the timetable.

2. The particle filtering method according to claim 1,

the identification of the back part parameters of the T-S fuzzy model comprises the following steps:

constructing a Kalman filtering equation for each T-S fuzzy rule;

and identifying the parameters of the back part according to the Kalman equation.

3. The particle filtering method according to claim 1,

the identification of the front piece parameters of the T-S fuzzy model comprises the following steps:

observing and calculating the fuzzy membership of each T-S fuzzy model;

setting the fuzzy membership function of the front part parameters as a Gaussian function;

calculating the mean value and the root mean square error of the membership function of the front part parameters of the Gaussian function;

and obtaining a function of the state and covariance estimation of the T-S fuzzy semantic model.

4. The particle filtering method according to claim 3,

the observing and calculating the fuzzy membership of each T-S fuzzy model comprises the following steps:

distinguishing a similarity function between the T-S fuzzy semantic model estimation result and the measurement matrix according to the correlation entropy standard;

defining a target function of a fuzzy C regression clustering algorithm according to a correlation entropy standard;

maximizing a correlation entropy standard, and optimizing the objective function by combining constraint conditions;

calculating partial derivatives of the weights corresponding to the particles according to the objective function to obtain a membership expression between the T-S fuzzy model and the data;

and calculating a membership matrix through the similarity function, and then applying the membership matrix to the optimized objective function.

5. The particle filtering method according to claim 1,

the calculating the model weight of the T-S fuzzy model comprises the following steps:

defining the state of a target at a non-zero moment in a timetable, and defining a vector formed by at least two target characteristics of the target at the non-zero moment;

defining a fuzzy membership function which represents the degree of decision of the vector on the state;

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

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

and calculating the weight of the T-S fuzzy model according to the sample set.

6. The particle filtering method according to claim 5,

the defining a posterior probability distribution includes:

establishing a state function of the particles at the moment in the timetable according to a known nonlinear function, and establishing a measurement matrix function of the particles at the moment in the timetable;

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

and updating the prior value according to the measured value and a Bayesian formula to obtain posterior probability density distribution.

7. The method of claim 3, wherein the calculating and normalizing the particle weight values comprises:

establishing an importance density function updating particle of particle filtering according to the state of the T-S fuzzy semantic model and a covariance estimation function;

and calculating and standardizing the particle weight according to the density function and the weight updating formula.

8. An object tracking system comprising a method as claimed in any one of claims 1 to 7.

9. An electronic device, comprising: memory, processor and computer program stored on the memory and executable on the processor, characterized in that the processor implements the method of any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the method of any one of claims 1 to 7.