CN115390560A - Ground target track tracking method based on mixed grid multi-model - Google Patents
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Abstract
The invention relates to the field of target tracks, in particular to a ground target track tracking method based on a mixed grid multi-model. Step 1: dividing a model set M of the ground target into a coarse model subset and a fine model subset; and 2, step: processing the coarse model subset according to the classification in the step 1 to obtain a coarse model subset with updated probability and carrying out estimation fusion on the coarse model subset; and step 3: step 1, the classified fine model subset is adaptively adjusted according to online data and priori knowledge; and 4, step 4: respectively carrying out probability updating on the rough model subset in the step 2 and the fine model subset in the step 3; and 5: and (4) performing global estimation fusion again on the coarse model subset and the fine model subset which are updated in the step (4). The method is used for solving the problem that the prior technical scheme can not carry out accurate state estimation on the ground target track.
Description
Technical Field
The invention relates to the field of target tracks, in particular to a ground target track tracking method based on a mixed grid multi-model and a readable storage medium.
Background
Since the last 70 s, a variety of fixed structure multi-model algorithms have been applied to state estimation of ground target trajectories. It features that the model set used in the whole state estimation processFixed and time invariant, and assuming a set of modelsAnd the real mode spaceThe same is true. However, when a multi-model algorithm is used to estimate the state of an object with multiple motion patterns, all possible motion patterns cannot be listed, and the model set isAnd the real mode spaceThe same assumption is no longer true.
Disclosure of Invention
The invention provides a ground target track tracking method based on a mixed grid multi-model, which can not accurately estimate the state of a ground target track by utilizing the existing fixed structure multi-model algorithm when the ground target moves in various forms.
The invention is realized by the following technical scheme:
a ground target track tracking method based on a mixed grid multi-model comprises the following steps:
step 1: model set of ground targetInto coarse model subsets M (i =1, \8230;, n) M ) And a fine model subset A (r =1, \8230;, n) A );
Step 2: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) The processing results in a coarse model subset M (i =1, \ 8230;, n) with probability update M ) And carrying out estimation fusion on the two;
and step 3: step 1 classified fine model subset a (r =1, \8230;, n) A ) Self-adaptive adjustment is carried out according to online data and priori knowledge;
and 4, step 4: for the coarse model subset M of step 2 (i =1, \ 8230;, n) M ) And the fine model subset a of step 3 (r =1, \8230;, n) A ) Respectively updating the probability;
and 5: coarse model subset M (i =1, \ 8230;, n) for step 4 probabilistic update M ) And a fine model subset A (r =1, \8230;, n) A ) And carrying out global state estimation fusion again to realize ground target track tracking.
A ground target track tracking method based on a mixed grid multi-model is disclosed, wherein in the step 2, a coarse model subset M (i =1, \ 8230;, n) is subjected to M ) The treatment specifically comprises the following steps:
step 2.1: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) Performing input interaction;
step 2.2: coarse model subset M (i =1, \ 8230;, n) after input interaction for step 2 M ) And carrying out parallel filtering.
A ground target track tracking method based on a mixed grid multi-model is disclosed, wherein in the step 3, a fine model subset A (r =1, \8230; n) A ) The self-adaptive adjustment according to the online data and the prior knowledge specifically comprises the following steps:
step 3.1: classifying according to step 1 on a fine model subset A (r =1, \8230;, n) A ) Designing;
step 3.2: for the fine model subset A (r =1, \8230;, n) designed in step 3.1 A ) And carrying out parallel filtering.
A ground target track tracking method based on a mixed grid multi-model includes the following steps:
where k denotes the time, x denotes the state quantity, f (-) denotes the state equation, h (-) denotes the measurement equation, w denotes process noise, v denotes measurement noise,represents an event m k =m (j) I.e. model m (j) Acting at time k;
in a hybrid mesh multi-model algorithm, a set of modelsThe method comprises two parts, namely a coarse model subset M represented by a coarse grid and a fine model subset A represented by a fine grid; model set for time kIs provided with
Wherein, the coarse model set M is kept unchanged in the whole state estimation process, and the fine model set A is adaptively adjusted according to online data and priori knowledge;
the optimal state estimate based on the minimum mean square error criterion is expressed as
In the formula (I), the compound is shown in the specification,in order to be a global state estimate,representing the sequence of measurements from the initial time to time k,andrespectively a coarse model subset M and a fine model subset A k The posterior probability at time k,andbased on a coarse model subset M and a fine model subset A, respectively k The state estimate obtained at time k.
3.2, designing a detailed model subset comprises calculating mode moments;
definition ofi =1,2, \ 8230, n is the ith model m (i) First two orders of moment, mu i Is a model m (i) When designing the fine model subset, the desired pattern of the fine model subset at time kAnd probabilityNot yet acquired, and therefore often utilize the expected pattern at time k-1And probabilityCarrying out replacement; thus, the desired modeCan be obtained by the following calculation
In the formula (I), the compound is shown in the specification,a desired pattern that is a subset of the coarse patterns;
from the equation, the desired mode covariance can be obtained as ∑ k Comprises the following steps:
the expected pattern at time k is given by equations (5) and (6)And covariance ∑ k Next, a set of detailed model subsets is designed by using the method of moment matchingRespectively matching the first two moments of the model subset with the expected patternsSum covariance Σ k Equal;
for a ground moving target, designing a model set by considering a constant-speed model and cooperative turning models with different parameters, and adaptively refining the model setIs designed as follows
In the formula, p is more than or equal to 0 0 < 1 is a predetermined parameter, and subscript n is a vectorDimension of (2), number of models n A = n +2, number of models n for cooperative turning model A =3;
In-process model setAfter the design of (2), further utilizeComputing a subset of the fine modelsWhere B may be represented by ρ Σ k Obtained by Cholseky decomposition and meets rho sigma k =BB T (ii) a Thereby completing the design of the fine model set.
A ground target track tracking method based on mixed grid multi-model is used for tracking coarse model subset M (i =1, \8230;, n) M ) Performing input interactions includes model probability prediction
Hybrid weights
Hybrid state estimation and covariance
The coarse model subset M is filtered in parallel into
Wherein KF (·) denotes Kalman filtering;
the probability update of the subset M of the coarse model comprises a likelihood function
Normalized constant
Model probability update
Estimating and fusing the rough model subset M;
where EF (-) denotes the estimated fusion.
A ground target track tracking method based on mixed grid multi-model is obtained by designing a fine model subset A
Wherein FMD (-) represents a fine model subset design;
carrying out parallel filtering on the fine model subset A;
wherein KF (·) represents Kalman filtering;
the probability update of the fine model subset A comprises a likelihood function
Probability of model
Normalized constant
Model probability update
The state estimation fusion of the fine model subset A is specifically
Where EF (-) denotes the estimated fusion.
A ground target track tracking method based on mixed grid multi-model for estimation fusionThe combined coarse model subset M (i =1, \8230;, n) M ) The probability updating is carried out specifically as
For the estimated fused fine model subset A (r =1, \8230;, n) A ) The probability updating is carried out specifically as
A ground target track tracking method based on mixed grid multi-model is used for updating the probability of a coarse model subset M (i =1, \ 8230;, n) M ) And a probability updated fine model subset a (r =1, \8230;, n) A ) The global estimation fusion is performed again specifically in that,
a computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the above-mentioned method steps.
The invention has the beneficial effects that:
the method adaptively designs the fine model set by using a moment matching method based on the estimation result, and completes the state estimation of the ground target by performing weighted fusion on the estimation result of the fine model set, so that the method has higher estimation precision than a single model algorithm and an interactive multi-model algorithm.
Drawings
Fig. 1 is a schematic diagram of the principle of the present invention.
Fig. 2 is a schematic diagram of the filter structure of the present invention.
FIG. 3 is a graph of the initial moment model distribution and corresponding probability of the present invention.
FIG. 4 is a diagram of the first two moments of the initial time model of the present invention.
Fig. 5 is a diagram of the target motion trajectory of the present invention.
Fig. 6 is a schematic diagram of the target speed profile of the present invention.
FIG. 7 is a schematic diagram of a position estimation error curve of the present invention.
FIG. 8 is a schematic diagram of the velocity estimation error curve of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A hybrid mesh multi-model algorithm is applied to track tracking of ground maneuvering targets. The hybrid grid is formed by mixing a coarse grid representing a coarse model and a fine grid representing a fine model (as shown in fig. 1), each grid point corresponds to one target motion model, coordinates of the grid points are relevant parameters in the target motion model, and different grid points represent different models.
A ground target track tracking method based on a mixed grid multi-model comprises the following steps:
step 1: model set of ground targetInto coarse model subsets M (i =1, \8230;, n) M ) And a fine model subset A (r =1, \8230;, n) A );
The coarse model set M is kept unchanged in the whole state estimation process, and the fine model set A is adaptively adjusted according to online data and priori knowledge;
step 2: classifying the coarse model subset M (i =1, \ 8230;, n) according to step 1 M ) The processing results in a coarse model subset M (i =1, \ 8230;, n) with probability update M ) And carrying out estimation fusion on the two;
and step 3: step 1 classified fine model subset a (r =1, \8230;, n) A ) Self-adaptive adjustment is carried out according to online data and priori knowledge;
and 4, step 4: for the coarse model subset M of step 2 (i =1, \ 8230;, n) M ) And the fine model subset a of step 3 (r =1, \8230;, n) A ) Respectively updating the probability;
and 5: coarse model subset M (i =1, \ 8230;, n) for step 4 probabilistic update M ) And a fine model subset A (r =1, \8230;, n) A ) And carrying out global state estimation fusion again to realize ground target track tracking.
A ground target track tracking method based on mixed grid multi-model is disclosed, in the step 2, a coarse model subset M (i =1, \8230; n) M ) The treatment specifically comprises the following steps:
step 2.1: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) Performing input interaction;
step 2.2: coarse model subset M (i =1, \ 8230;, n) after input interaction for step 2 M ) And carrying out parallel filtering.
A ground target track tracking method based on a mixed grid multi-model is disclosed, wherein in the step 3, a fine model subset A (r =1, \8230; n) A ) The self-adaptive adjustment according to the online data and the prior knowledge specifically comprises the following steps:
step 3.1: classifying according to step 1 on a fine model subset A (r =1, \8230;, n) A ) Designing;
step 3.2: for the fine model subset A (r =1, \8230;, n) designed in step 3.2 A ) And carrying out parallel filtering.
A ground target track tracking method based on a mixed grid multi-model includes the following steps:
where k denotes the time, x denotes the state quantity, f (-) denotes the state equation, h (-) denotes the measurement equation, w denotes process noise, v denotes measurement noise,represents an event m k =m (j) I.e. model m (j) Acting at time k;
in a hybrid mesh multi-model algorithm, a set of modelsThe method comprises two parts, namely a coarse model subset M represented by a coarse grid and a fine model subset A represented by a fine grid; model set for time kIs provided with
Wherein, the coarse model set M is kept unchanged in the whole state estimation process, and the fine model set A is adaptively adjusted according to online data and priori knowledge;
the optimal state estimate based on the minimum mean square error criterion is expressed as
In the formula (I), the compound is shown in the specification,in order to be a global state estimate,representing the sequence of measurements from the initial time to time k,andrespectively a coarse model subset M and a fine model subset A k The posterior probability at time k,andbased on a coarse model subset M and a fine model subset A, respectively k The state estimate obtained at time k.
3.2, designing a detailed model subset comprises calculating mode moments;
in the mixed grid multi-model method, the models in the adaptive fine model subset are not fixed, and are correspondingly adjusted according to the output results of the filters corresponding to other models, so that the accuracy of describing the target motion mode can be improved in the limited number of models. The design of the detailed model subset mainly comprises two parts, namely the calculation of mode moments, namely the calculation of first moment and second moment of grid point coordinates, and the generation of the detailed model subset. Definition ofi =1,2, \ 8230, n is the ith model m (i) First two orders of moment, mu i Is a model m (i) When designing the fine model subset, the desired pattern of the fine model subset at time kAnd probabilityNot yet acquired, and therefore often utilize the expected pattern at time k-1And probabilityCarrying out replacement; thus, the desired modeCan be obtained by the following calculation
In the formula (I), the compound is shown in the specification,a desired pattern that is a subset of the coarse patterns;
from the equation, the covariance of the desired pattern is ∑ k Comprises the following steps:
the expected pattern at time k is given by equations (5) and (6)And covariance ∑ k Next, a set of detailed model subsets is designed by using the method of moment matchingRespectively connecting the first two moments of the model subset with the expected modeSum covariance Σ k Equal;
for a ground moving target, designing a model set by considering a constant-speed model and cooperative turning models with different parameters, and adaptively refining the model setIs designed as follows
In the formula, p is more than or equal to 0 0 < 1 is a predetermined parameter, and subscript n is a vectorDimension of (2), number of models n A = n +2, number of models n for cooperative turning model A =3;
In-process model setAfter the design of (2), further utilizeComputing a subset of the fine modelsWhere B may be represented by ρ Σ k Obtained by Cholseky decomposition and meets rho sigma k =BB T (ii) a Thereby completing the design of the fine model set.
A ground target track tracking method based on mixed grid multi-model is used for tracking coarse model subset M (i =1, \8230;, n) M ) Performing input interactions includes model probability prediction
Mixing weights
Hybrid state estimation and covariance
Parallel filtering the coarse model subset M into
Wherein KF (·) denotes Kalman filtering;
the probability update of the subset M of the coarse model comprises a likelihood function
Normalized constant
Model probability update
Estimating and fusing the rough model subset M;
where EF (-) denotes the estimated fusion.
A ground target track tracking method based on mixed grid multi-model is obtained by designing a fine model subset A
Wherein FMD (-) represents a fine model subset design;
performing parallel filtering on the fine model subset A;
wherein KF (·) represents Kalman filtering;
the probability update of the fine model subset A comprises a likelihood function
Probability of model
Normalized constant
Model probability update
The estimation fusion of the fine model subset A is specifically
Where EF (-) represents the estimated fusion.
A ground target track tracking method based on mixed grid multi-model is used for estimating a fused coarse model subset M (i =1, \8230; n) M ) The probability updating is carried out specifically as
For the estimated fused fine model subset A (r =1, \8230;, n) A ) The probability updating is carried out specifically as
A ground target track tracking method based on mixed grid multi-model is used for updating the probability of a coarse model subset M (i =1, \ 8230;, n) M ) And a probability updated fine model subset a (r =1, \8230;, n) A ) The global estimation fusion is performed again specifically in that,
a computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the above-mentioned method steps.
To obtain global state estimatesNeed to calculateAndfour variables. Since the coarse model subset M remains unchanged throughout the state estimation process, the state estimation can be performed using an interactive multi-model algorithmAnd its covarianceCalculating and outputting a coarse modelProbabilities in the coarse model subset MAnd the like.
After the state estimation based on the coarse model subset is completed, the state estimation result based on the fine model subset is calculated. First, a fine model subset A at time k is defined k Is composed of
In the formula, m (r) Representing models in a subset of fine models, n A The number of models in the subset of fine models.
In the formula (I), the compound is shown in the specification,for a fine model m at time k (r) The probability in the fine-model subset a,andbased on a thin modelState estimation and covariance of
In the formula (I), the compound is shown in the specification,is a thin modelA priori probabilities in the fine model subset A, the probabilities being associated with the fine modelA likelihood function generated according to a certain criterion in the design of the self-adaptive fine model setAnd a normalization constant c 2 Are respectively as
In the formula (I), the compound is shown in the specification,andwhich are the measured residual and residual covariance at time k output by the sub-filter r.
Fine model subset A k The posterior probability at time k can be expanded to
In the traditional multi-model algorithm, jump between models is usually represented by a first-order Markov chain, and then the models are refined in the formulaIs predicted with probability ofCan be rewritten as
In the formula (I), the compound is shown in the specification,π jr representation modelTo modelThe transition probability of (2).
However, in the mixed grid multi-model algorithm, the model in the fine model set changes in real time according to the output result of each sub-filter, and it is difficult to give a suitable transition probability matrix [ pi ] jr ]。
Therefore, the invention utilizes another way to calculate the model prediction probabilityNamely, it is
In the formula (I), the compound is shown in the specification,is a thin modelIn the fine model subset A k A prior probability of (2).
Neglecting the jumps between the subset of fine models and the set of coarse models, have
Substitution of formula (17) into formula (16) gives
In combination of formulae (12), (13) and (18), formula (14) can be further derived as
In the formula (I), the compound is shown in the specification,is the probability of the coarse model subset M at time k-1.
According to the relation between the probability of the coarse model subset and the probability of the fine model subset, the probability of the coarse model subset M at the time k can be obtainedIs composed of
Therefore, global state estimation of ground target track tracking can be carried out according to the formula.
TABLE 1 hybrid grid Multi-model Algorithm flow
In the above table, KF (·) represents kalman filtering, EF (·) represents estimated fusion, and FMD (·) represents fine model subset design.
And (3) performing track tracking mathematical simulation by respectively using an IMM (inertial measurement model) algorithm and a mixed grid multi-model algorithm by using the ground moving target model as a model set template and angular velocity in the cooperative turning model as a grid point coordinate parameter.
(1) Model set parameters
In addition to the constant velocity model, the coarse model set is defined to include two cooperative turning model components, the turning rate of which is [ 2 ]-15°15°]. Transition probability matrix pi between coarse models HG Is composed of
Initial coarse model probability of
In the fine model design, n A =3 is the number of models in the subset of fine models, and the other preset parameters ρ =0.2 0 =0.4。
For the interactive multi-model, a constant-speed model and two cooperative turning models are selected from the model set, and the turning speed of the model is [ -15 degrees and 15 degrees ].
(2) Parameters of object motion
The motion trail of the ground target is shown in fig. 5, and a speed change curve of the target is shown in fig. 6;
the interactive multi-model tracking filter and the hybrid grid multi-model tracking filter are respectively utilized to perform 100 Monte Carlo mathematical simulations, and the obtained simulation results are summarized as shown in FIGS. 7-8:
TABLE 2 root mean square error
The method establishes a coarse model set based on prior information, adaptively designs a fine model set based on an estimation result by using a moment matching method, and completes state estimation of a target by performing weighted fusion on the estimation result of the coarse model set, so that the method has higher estimation precision than an interactive multi-model algorithm.
Claims (10)
1. A ground target track tracking method based on a mixed grid multi-model is characterized by comprising the following steps:
step 1: model set of ground targetInto coarse model subsets M (i =1, \8230;, n) M ) And a fine model subset A (r =1, \8230;, n) A );
And 2, step: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) The processing results in a coarse model subset M (i =1, \ 8230;, n) with probability update M ) And carrying out estimation fusion on the two;
and step 3: step 1 classified fine model subset a (r =1, \8230;, n) A ) Self-adaptive adjustment is carried out according to online data and priori knowledge;
and 4, step 4: for the coarse model subset M of step 2 (i =1, \ 8230;, n) M ) And the fine model subset a of step 3 (r =1, \8230;, n) A ) Respectively updating the probability;
and 5: coarse model subset M (i =1, \ 8230;, n) for step 4 probabilistic update M ) And a fine model subset A (r =1, \8230;, n) A ) And carrying out global state estimation fusion again to realize ground target track tracking.
2. The method for tracking the ground target trajectory based on the mixed grid multi-model as claimed in claim 1, wherein in the step 2, the coarse model subset M (i =1, \8230;, n) is selected M ) The treatment specifically comprises the following steps:
step 2.1: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) Performing input interaction;
step 2.2: coarse model subset M (i =1, \ 8230;, n) after input interaction for step 2 M ) And performing parallel filtering.
3. The method for tracking the ground target trajectory based on the mixed grid multi-model as claimed in claim 1, wherein the step 3 is performed on a subset A of fine models (r =1, \8230;, n) A ) The self-adaptive adjustment according to the online data and the prior knowledge specifically comprises the following steps:
step 3.1: classifying according to step 1 on a fine model subset A (r =1, \8230;, n) A ) Designing;
step 3.2: for the fine model subset A (r =1, \8230;, n) designed in step 3.1 A ) And carrying out parallel filtering.
4. The method for tracking the ground target trajectory based on the hybrid grid multi-model as claimed in claim 1, wherein the step 1 is specifically a discrete hybrid system as follows:
where k denotes the time, x denotes the state quantity, f (-) denotes the state equation, h (-) denotes the measurement equation, w denotes process noise, v denotes measurement noise,represents an event m k =m (j) I.e. model m (j) Acting at time k;
in the mixed grid multi-model algorithm, a model setThe method comprises two parts, namely a coarse model subset M represented by a coarse grid and a fine model subset A represented by a fine grid; model set for time kIs provided with
Wherein, the coarse model set M is kept unchanged in the whole state estimation process, and the fine model set A is adaptively adjusted according to online data and priori knowledge;
the optimal state estimate based on the minimum mean square error criterion is expressed as
In the formula (I), the compound is shown in the specification,in order to be a global state estimate,representing the sequence of measurements from the initial time to time k,andrespectively a coarse model subset M and a fine model subset A k The posterior probability at time k is,andbased on a coarse model subset M and a fine model subset A, respectively k The state estimate obtained at time k.
5. The method for tracking the ground target track based on the hybrid grid multi-model as claimed in claim 3, wherein the step 3.2 of designing the subset of the detailed models comprises calculating mode moments;
definition ofn is the ith model m (i) First two orders of moment, mu i Is a model m (i) When designing the fine model subset, the desired pattern of the fine model subset at time kAnd probabilityNot yet acquired, and therefore often utilize the expected pattern at time k-1And probabilityCarrying out replacement; thus, the desired modeCan be obtained by the following calculation
In the formula (I), the compound is shown in the specification,a desired pattern that is a subset of the coarse patterns;
from the equation, the covariance of the desired pattern is ∑ k Comprises the following steps:
the expected pattern at time k is given by equations (5) and (6)And covariance ∑ k Below, ofDesigning a group of fine model subsets by using a method of moment matchingRespectively matching the first two moments of the model subset with the expected patternsSum covariance Σ k Equal;
for a ground moving target, the design of a model set is carried out by considering a constant-speed model and cooperative turning models with different parameters, and the model set is adaptive to a fine model setIs designed as follows
In the formula, p is not less than 0 0 < 1 is a predetermined parameter, and subscript n is a vectorDimension of (2), number of models n A = n +2, number of models n for cooperative turning model A =3;
6. The method for tracking the ground target trajectory based on the hybrid grid multi-model as claimed in claim 2, wherein the coarse model subset M (i =1, \8230;, n) is selected M ) Performing input interactions includes model probability prediction
Hybrid weights
Hybrid state estimation and covariance
The coarse model subset M is filtered in parallel into
Wherein KF (·) denotes Kalman filtering;
the probability update of the subset M of the coarse model comprises a likelihood function
Normalized constant
Model probability update
Estimating and fusing the rough model subset M;
where EF (-) denotes the estimated fusion.
7. The ground target track tracking method based on the hybrid grid multi-model as claimed in claim 3, characterized in that the fine model subset A is designed to obtain
Wherein FMD (-) represents a fine model subset design;
performing parallel filtering on the fine model subset A;
wherein KF (·) represents kalman filtering;
the probability update of the fine model subset A comprises a likelihood function
Probability of model
Normalized constant
Model probability update
The estimation fusion of the fine model subset A is specifically
Where EF (-) represents the estimated fusion.
8. The method for tracking the ground target trajectory based on the hybrid grid multi-model as claimed in claim 1, wherein the subset M (i =1, \8230;, n) of the coarse models after the estimation fusion is performed M ) The probability updating is carried out specifically as
For the estimation of the fused fine model subset A (r =1, \8230;, n) A ) The probability updating is carried out specifically as
9. The method for tracking the ground target trajectory based on the hybrid grid multi-model as claimed in claim 1, wherein the probability-updated coarse model subset M (i =1, \8230;, n) is selected from M ) And a probability updated fine model subset a (r =1, \8230;, n) A ) The global estimation fusion is performed again specifically in that,
10. a computer-readable storage medium, characterized in that a computer program is stored in the computer-readable storage medium, which computer program, when being executed by a processor, carries out the method steps of any one of the claims 1-9.
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