CN110297221B - Data association method based on Gaussian mixture model - Google Patents
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The invention discloses a data association method based on a Gaussian mixture model, which comprises the following steps: obtaining a multi-target tracking state model according to the initial states of the multiple targets and a first preset matrix; obtaining an observation model of the target according to the state model and the second preset matrix, and calculating a predicted position and innovation covariance of the target according to the observation model; obtaining a plurality of target effective measurements according to the observation model and a preset wave gate, and constructing a Gaussian mixture model by the plurality of target effective measurements; constructing a posterior probability model according to the Gaussian mixture model, updating parameters in the posterior probability model by using a maximum expectation method, and obtaining a target posterior probability according to the parameters; and constructing an incidence matrix according to the posterior probability of the target, and searching the incidence matrix to obtain the target and the effective target measurement. The method uses the Gaussian mixture model for multi-target tracking, avoids complex matrix splitting of a joint probability data correlation method, reduces the calculated amount, has high tracking precision, and is suitable for real-time multi-target tracking.
Description
Technical Field
The invention belongs to the technical field of multi-target tracking, and particularly relates to a data association method based on a Gaussian mixture model.
Background
With the development of radar technology, the application of multi-target tracking in the military and civil fields is more and more extensive, data association is a core part of the multi-target tracking, and the essence of the data association is to associate measurement with the existing track.
In recent years, many data correlations have been proposed, such as a nearest neighbor data correlation method, a probability data correlation method, a joint probability data correlation method, in which the nearest neighbor data correlation method selects a measurement closest to a target predicted position for state update; the probability data association method considers that all measurements in the tracking gate are probably from the target, and only the probability that the measurements come from the target is different; the joint probability data association method considers the measurement in the cross wave gate, can realize the tracking of multiple targets, but with the increase of the number of the targets, the method has explosive calculated amount, in order to reduce the calculated amount, some improved joint probability data association methods are provided, for example, a clustering probability matrix is calculated approximately, a new confirmation matrix is redefined according to the size of elements in the clustering probability matrix, so that the number of feasible joint events is obviously reduced, and the calculated amount is reduced.
However, in the above method, there is a contradiction between tracking accuracy and calculation amount when tracking multiple targets, that is, the calculation amount is reduced, the tracking effect is poor, the tracking effect is good, and the calculation amount is explosive.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a data association method based on a gaussian mixture model, which includes:
step 1, inputting initial states of a plurality of targets, and predicting the states of the targets according to the initial states of the plurality of targets and a first preset matrix to obtain a multi-target tracking state model, wherein the initial states of the targets comprise initial positions and initial speeds of the targets;
step 2, observing the target according to the state model and a second preset matrix to obtain an observation model of the target, and calculating a predicted position and an innovation covariance of the target according to the observation model;
step 3, obtaining a plurality of target effective measurements according to the observation model and a preset wave gate, equating each target effective measurement to be a Gaussian model to obtain a plurality of Gaussian models, and weighting and summing the Gaussian models to obtain a Gaussian mixture model;
step 4, constructing a posterior probability model according to the Gaussian mixture model, continuously iteratively updating parameters in the posterior probability model by using a maximum expectation method, and obtaining a target posterior probability according to the parameters;
and 5, constructing an incidence matrix according to the target posterior probability, searching the incidence matrix, and finding out the maximum target posterior probability of each column of the incidence matrix, wherein the column of the maximum target posterior probability corresponds to the target, and the row of the maximum target posterior probability corresponds to the target effective measurement.
In an embodiment of the present invention, the state model obtained in step 1 is:
xt(k+1)＝Ft(k)xt(k)+Gt(k)wt(k)；
wherein x ist(k) And xt(k +1) are all target states, Ft(k) For the first predetermined matrix, Gt(k) Is a noise matrix, wt(k) Is the first white gaussian noise.
In an embodiment of the present invention, the observation model obtained in step 2 is:
zt(k)＝H(k)xt(k)+v(k)；
wherein z ist(k) H (k) is the second predetermined matrix, and v (k) is a second white Gaussian noise.
In one embodiment of the present invention, said step 2 calculates a predicted position and an innovation covariance of the target based on said observation model, wherein,
the predicted position of the target is:
the innovation covariance of the target is:
S(k+1)＝H(k+1)Pt(k+1|k)H(k+1)T+R(k)；
wherein the content of the first and second substances,
for state prediction of said target, Pt(k +1| k) is a variance prediction of the target, (. C)TFor transposition, R (k) is the variance of the second white Gaussian noise.
In an embodiment of the present invention, the gaussian mixture model obtained in the step 3 is:
wherein I is the number of the Gaussian models, alpha is a mixing coefficient, mu is a mean value, and Σ is a variance.
In an embodiment of the present invention, the constructing a posterior probability model according to the gaussian mixture model in step 4, continuously iteratively updating parameters in the posterior probability model by using a maximum expectation method, and obtaining a target posterior probability according to the parameters includes:
calculating to obtain the initial posterior probability of the target according to the posterior probability model, the number of the targets, the predicted position of the target and the target innovation covariance;
and continuously and iteratively updating parameters in the posterior probability model by using a maximum expectation method according to the posterior probability model and the initial posterior probability of the target, and obtaining the posterior probability of the target according to the parameters.
In an embodiment of the present invention, the posterior probability model constructed according to the gaussian mixture model in the step 4 is:
wherein, betajE {1,2, … I } as target, yjFor the target effective measurement, the posterior probability model pM(βj＝i|yj) Is recorded as gammaji。
In one embodiment of the present invention, parameters in the posterior probability model are continuously updated iteratively by using a maximum expectation method according to the posterior probability model and the initial posterior probability of the target, and the target posterior probability is obtained according to the parameters, wherein the parameters in the posterior probability model include the mean μ, the variance Σ, and the mixing coefficient α, wherein,
the mean μ is:
the variance Σ is:
the mixing coefficient alpha is:
wherein J is a constant representing the number of target valid measurements.
In an embodiment of the present invention, the incidence matrix constructed in the step 5 according to the target posterior probability is:
in an embodiment of the present invention, the searching the correlation matrix in step 5 to find the maximum target posterior probability of each column of the correlation matrix includes:
and searching the incidence matrix by using a clustering method to find the maximum target posterior probability of each column of the incidence matrix.
Compared with the prior art, the invention has the beneficial effects that:
the invention uses the Gaussian mixture model for multi-target tracking, avoids complex matrix splitting of a joint probability data association method, reduces the calculated amount, has higher tracking precision, and is suitable for a real-time multi-target tracking environment.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flowchart of a data association method based on a gaussian mixture model according to an embodiment of the present invention;
fig. 2 is a tracking trajectory diagram of a data association method based on a gaussian mixture model according to an embodiment of the present invention;
FIG. 3 is a trace diagram of a conventional simplified joint probability data association method according to an embodiment of the present invention;
FIG. 4 is a tracking trace diagram of a conventional joint probability data association method according to an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating error comparison of a target 1 in three data association methods according to an embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating error comparison of a target 2 in three data association methods according to an embodiment of the present invention;
FIG. 7 is a schematic diagram illustrating error comparison of a target 3 in three data association methods according to an embodiment of the present invention;
fig. 8 is a schematic diagram illustrating error comparison of a target 4 in three data association methods according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
The data association is a core part of multi-target tracking, and the current common data association methods comprise a nearest neighbor data association method, a probability data association method and a joint probability data association method, and the methods only study the latest valid measurement set of the confirmed targets, so that the method is a suboptimal Bayes method. The nearest neighbor data association method is simple in calculation, but is not high in precision; the probability data association method is only suitable for single target tracking in a clutter environment; the joint probability data association method can well track multiple targets, but with the increase of the number of the targets, the calculated amount is exploded, and in order to reduce the calculated amount, some improved joint probability data association methods are proposed, but the improved joint probability data association method reduces the calculated amount by sacrificing the tracking precision, and the tracking effect is not good.
Based on the above existing problems, please refer to fig. 1, and fig. 1 is a schematic flow chart of a data association method based on a gaussian mixture model according to an embodiment of the present invention. The embodiment provides a data association method based on a Gaussian mixture model, which comprises the following steps:
step 1, inputting initial states of a plurality of targets, and predicting the states of the targets according to the initial states of the plurality of targets and a first preset matrix to obtain a multi-target tracking state model, wherein the initial states of the targets comprise initial positions and initial speeds of the targets.
Specifically, in the embodiment, the states of a plurality of targets are predicted through the initial states of the plurality of targets and the first preset matrix, so that the state model x for multi-target tracking is determinedt(k +1) is:
xt(k+1)＝Ft(k)xt(k)+Gt(k)wt(k) (1)
wherein, Ft(k) For a first predetermined matrix, for limiting the state of multiple targets, Gt(k) Is a noise matrix for noise driving, wt(k) Is the first white gaussian noise with variance Q.
According to the above formula (1), a plurality of target tracking states can be obtained.
And 2, observing the target according to the state model and the second preset matrix to obtain an observation model of the target, and calculating the predicted position and the innovation covariance of the target according to the observation model.
Specifically, in this embodiment, a plurality of targets are observed through the state model obtained in step 1 and the second preset matrix, so as to determine the observation model z for multi-target trackingt(k) Comprises the following steps:
zt(k)＝H(k)xt(k)+v(k) (2)
wherein H (k) is a second predetermined matrix for limiting the observation of the target, and v (k) is a second white Gaussian noise with variance R.
According to the above formula (2), observations of a plurality of targets can be obtained.
Meanwhile, in the present embodiment, the predicted position and the innovation covariance of the target are calculated according to the state model of formula (1) and the observation model of formula (2), specifically, the predicted position of the target is designed as follows:
wherein H (k) is the second predetermined matrix,
for the purpose of state prediction of the object, the present embodiment
The design of (1) is as follows:
wherein, Ft(k) For the first predetermined matrix mentioned above, the first predetermined matrix,
is a state differential prediction of the target.
For the innovation covariance of the target, the embodiment is specifically designed as follows:
S(k+1)＝H(k+1)Pt(k+1|k)H(k+1)T+R(k) (5)
wherein H (k +1) is the second predetermined matrix, H (k +1)TIs the transpose of H (k +1), R (k) is the variance matrix of the second white Gaussian noise v (k), Pt(k +1| k) as the target variance prediction matrix, this example PtThe design of (k +1| k) is:
Pt(k+1|k)＝Ft(k)Pt(k|k)Ft(k)T (6)
wherein, Ft(k) For the first predetermined matrix, Ft(k)TIs Ft(k) Transpose of (P)t(k | k) is the covariance prediction matrix of the target.
And 3, obtaining a plurality of target effective measurements according to the observation model and the preset wave gate, equating each target effective measurement to be a Gaussian model to obtain a plurality of Gaussian models, and weighting and summing the Gaussian models to obtain a Gaussian mixture model.
Specifically, in this embodiment, a preset wave gate is provided, the observation obtained by the observation model in step 2 is processed, the observation falling into the preset wave gate is determined as the target effective measurement, a plurality of target effective measurements are obtained, each target effective measurement is equivalent to a gaussian model, a plurality of gaussian models exist in the plurality of effective measurements, and a gaussian mixture model is obtained through the plurality of gaussian models. Specifically, a gaussian mixture model is obtained by weighting and summing a plurality of gaussian models, and the gaussian mixture model of this embodiment is designed as follows:
wherein I is the number of Gaussian models, α is the mixing coefficient, μ is the mean, and Σ is the variance.
The Gaussian mixture model designed by the embodiment has a simple structure, is low in calculated amount in the target tracking process, and is easy to realize.
And 4, constructing a posterior probability model according to the Gaussian mixture model, continuously iteratively updating parameters in the posterior probability model by using a maximum expectation method, and obtaining the target posterior probability according to the parameters.
In this embodiment, a posterior probability model is constructed according to the gaussian mixture model obtained in the step 3, where the posterior probability model includes a target and a target effective measurement, and specifically, the posterior probability model is designed as follows:
wherein, betajE {1,2, … I } as target, yjFor effective measurement of the target, the embodiment uses the posterior probability model p for the convenience of subsequent writingM(βj＝i|yj) Is recorded as gammaji。
The step 4 of this embodiment is specifically implemented by the following steps 4.1 and 4.2:
and 4.1, calculating to obtain the initial posterior probability of the target according to the posterior probability model, the number of the targets, the predicted positions of the targets and the covariance of the target innovation.
Specifically, in the present embodiment, the initial posterior probability of the target is first calculated according to the posterior probability model of equation (8), and at this time, initial values are assigned to the three parameters of the mixing coefficient α, the mean μ, and the variance Σ in equation (8), where the initial value assigned to the mixing coefficient α in the present embodiment is 1/Q, Q is the number of targets, and the initial value assigned to the mean μ is the predicted position of the target obtained by equation (3)
The initial value of the variance Σ is the target innovation covariance S (k +1) obtained by equation (5). The initial posterior probability of the target is obtained through the assignment of the three parameters of the mixing coefficient alpha, the mean value mu and the variance sigma and the computation of the posterior probability model of the formula (8), and the initial posterior probability of the target is used as the initial value for updating the posterior probability of the subsequent target, so that the target tracking effect can be improved.
And 4.2, continuously and iteratively updating parameters in the posterior probability model by using a maximum expectation method according to the posterior probability model and the initial posterior probability of the target, and obtaining the posterior probability of the target according to the parameters.
Specifically, in this embodiment, on the basis that the initial posterior probability of the target is obtained in step 4.1, the maximum Expectation method (EM for short) is used to continuously and iteratively update the three parameters, i.e., the mixing coefficient α, the mean μ, and the variance Σ, in the posterior probability model, and the updated target posterior probability is obtained according to the updated three parameters, i.e., the mixing coefficient α, the mean μ, and the variance Σ. Specifically, in the present embodiment, in the process of updating the three parameters, i.e., the mixing coefficient α, the mean μ, and the variance Σ, the mixing coefficient α is designed as:
wherein J is a constant representing the number of target valid measurements of the target.
The mean μ is designed as:
the variance Σ is designed to:
the present embodiment iteratively updates the mixing coefficient α of equation (9), the mean μ of equation (10), and the variance Σ of equation (11) according to the maximum expectation method until the convergence condition is satisfied, and then updates the target posterior probability γ corresponding to the parameterji. Wherein, the meeting the convergence condition comprises reaching the maximum iteration number or converging the function.
And 5, constructing an incidence matrix according to the target posterior probability, searching the incidence matrix, and finding out the maximum target posterior probability of each row of incidence matrix, wherein the row where the maximum target posterior probability is located corresponds to the target, and the row where the maximum target posterior probability is located corresponds to the target effective measurement.
Specifically, in this embodiment, the incidence matrix is constructed by updating the target posterior probability obtained by the three parameters of the mixing coefficient α, the mean μ, and the variance Σ in step 4, and specifically, the constructed incidence matrix is:
wherein, in the formula (12) < gamma >jiThe posterior probability of the target corresponding to the target.
The incidence matrix U constructed in this embodiment is a corresponding relationship between the target and the target effective measurement, and its row corresponds to the target effective measurement and its column corresponds to the target. And searching the incidence matrix U to find out the maximum target posterior probability in each row of the incidence matrix, wherein the row of the maximum target posterior probability corresponds to the target, and the row of the maximum target posterior probability is the target effective measurement corresponding to the row of the target. And (3) repeatedly searching each column of the incidence matrix U of the formula (12) until each target finds the corresponding target effective measurement, so as to complete the tracking of multiple targets.
Further, in this embodiment, the incidence matrix is searched to find the maximum target posterior probability of each column of the incidence matrix, and specifically, each column of the incidence matrix is searched by using a clustering method to find the maximum target posterior probability of each column of the incidence matrix.
Preferably, the clustering method comprises a density clustering method and a K-means clustering method.
Specifically, in this embodiment, the association matrix obtained by the above formula (12) is not directly searched, but the clustering idea is used for reference, the clustering method is used to perform clustering processing on the posterior probability of the target in each column in the association matrix to obtain the classified posterior probability of the target, and the maximum posterior probability of the target in the column of the association matrix is found from the classified posterior probability of the target, so as to find the target and the target effective measurement. In the embodiment, the clustering method is used for classifying the posterior probability of the target in each row of incidence matrix, so that the target data can be accurately quantized, the given target data can be accurately classified, and the target and the corresponding target effective measurement can be obtained.
According to the target tracking method, the target data are classified through the clustering method, the target tracking is carried out according to the classified target data, the calculated amount and the tracking time of the target tracking are reduced, the processing precision of effective target measurement is improved through clustering, and the target tracking effect is further improved.
To sum up, in the data association method based on the gaussian mixture model provided in this embodiment, the target effective measurements of all targets are equivalent to a gaussian mixture model, the predicted position of the target is used as the initial value of the mean μ, the innovation covariance of the target is used as the initial value of the variance Σ, the initial posterior probability of the target is obtained through the posterior probability model, then the mean μ, the variance Σ, and the mixing coefficient α in the posterior probability model are updated according to the maximum expectation method, and the updated mean μ, variance Σ, and mixing coefficient α are updated according to the updated posterior probability modelObtaining updated target posterior probability by the mean value mu, the variance sigma and the mixing coefficient alpha, constructing an incidence matrix U by the obtained target posterior probability, wherein the columns of the incidence matrix U correspond to targets, the rows correspond to target effective measurement of the targets, searching the incidence matrix U by using a clustering method to find the maximum target posterior probability gammajmaxi，γjmaxiAnd representing that the target effective measurement j belongs to the target i, and repeatedly searching each column of the association matrix U until each target finds the associated target effective measurement.
The data association method based on the Gaussian mixture model is used for multi-target tracking, the data association means that the target is effectively measured and the existing track is associated to update the state, compared with the traditional data association method, the data association method has the advantages that the calculated amount is less, the calculated amount is reduced, and the target tracking precision is guaranteed; the embodiment is mainly used for solving the problem of computation explosion of the traditional joint probability data association method and is suitable for a real-time multi-target tracking environment.
To illustrate the effect of the present embodiment, the following simulation experiment is further illustrated:
simulation conditions are as follows:
the embodiment is described based on three data association methods, which include a joint probability data association method (JPDA for short), a Simplified joint probability data association method (sjp pda for short), and a Gaussian mixture model based method (Gaussian mixture model for short) provided in the embodiment.
In this embodiment, four targets in cross motion in a clutter environment are tracked, a sampling interval is 1s, a monte carlo simulation frequency is 50 times, and a variance of state noise is Qii＝10-4km2Variance of observed noise is Rii＝0.0225km2The noise wave density is lambda 0.625km-2The threshold value of the preset wave gate is PgInputting initial states of 4 targets, wherein the initial state of each target comprises an initial position of the target and an initial position of the targetThe starting velocity, the initial positions of 4 targets and the initial velocity of the targets are shown in table 1.
TABLE 14 initial states of the targets
And (3) simulation result analysis:
referring to fig. 2, fig. 3, and fig. 4, fig. 2 is a trace graph of a data association method based on a gaussian mixture model according to an embodiment of the present invention, fig. 3 is a trace graph of a conventional simplified joint probability data association method according to an embodiment of the present invention, and fig. 4 is a trace graph of a conventional joint probability data association method according to an embodiment of the present invention. In fig. 2, 3, and 4, the abscissa represents the position of the target on the x-axis, and the ordinate represents the position of the target on the y-axis. As can be seen from fig. 2, 3, and 4, the tracking curve of the data association method and the joint probability data association method designed in this embodiment and the simplified joint probability data association method is consistent with the real curve of the target, and it can be seen that the data association method provided in this embodiment can well track the target.
Referring to fig. 5, fig. 6, fig. 7, and fig. 8, fig. 5 is a schematic diagram of error comparison based on a target 1 in three data association methods according to an embodiment of the present invention, fig. 6 is a schematic diagram of error comparison based on a target 2 in three data association methods according to an embodiment of the present invention, fig. 7 is a schematic diagram of error comparison based on a target 3 in three data association methods according to an embodiment of the present invention, and fig. 8 is a schematic diagram of error comparison based on a target 4 in three data association methods according to an embodiment of the present invention. In fig. 5, 6, 7, and 8, the abscissa represents time, and the ordinate represents the error of the target, which is specifically the root mean square error in this embodiment. As can be seen from fig. 5, 6, 7, and 8, errors of the data association method designed in this embodiment in the target 1, the target 2, the target 3, and the target 4 are all smaller than those of the other two methods, and the processing and overall tracking performance of the data association method provided in this embodiment when the targets intersect is significantly better than that of the joint probability data association method and that of the simplified joint probability data association method, the target tracking accuracy is higher, and the overall stability of the data association method provided in this embodiment is also better.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (8)
1. A data association method based on a Gaussian mixture model is characterized by comprising the following steps:
step 1, inputting initial states of a plurality of targets, and predicting the states of the targets according to the initial states of the plurality of targets and a first preset matrix to obtain a multi-target tracking state model, wherein the initial states of the targets comprise initial positions and initial speeds of the targets;
step 2, observing the target according to the state model and a second preset matrix to obtain an observation model of the target, and calculating a predicted position and an innovation covariance of the target according to the observation model;
step 3, obtaining a plurality of target effective measurements according to the observation model and a preset wave gate, equating each target effective measurement to be a Gaussian model to obtain a plurality of Gaussian models, and weighting and summing the Gaussian models to obtain a Gaussian mixture model, wherein the Gaussian mixture model is as follows:
wherein I is the number of the Gaussian models, alpha is a mixing coefficient, mu is a mean value, and sigma is a variance;
step 4, constructing a posterior probability model according to the Gaussian mixture model, continuously and iteratively updating parameters in the posterior probability model by using a maximum expectation method, and obtaining a target posterior probability according to the parameters, wherein the posterior probability model constructed according to the Gaussian mixture model is as follows:
wherein, betajE {1,2, … I } as target, yjFor the target effective measurement, the posterior probability pM(βj＝i|yj) Is recorded as gammaji；
And 5, constructing an incidence matrix according to the target posterior probability, searching the incidence matrix, and finding out the maximum target posterior probability of each column of the incidence matrix, wherein the column of the maximum target posterior probability corresponds to the target, and the row of the maximum target posterior probability corresponds to the target effective measurement.
2. The method according to claim 1, wherein the state model obtained in step 1 is:
xt(k+1)＝Ft(k)xt(k)+Gt(k)wt(k)；
wherein x ist(k) And xt(k +1) are all target states, Ft(k) For the first predetermined matrix, Gt(k) Is a noise matrix, wt(k) Is the first white gaussian noise.
3. The method according to claim 2, wherein the observation model obtained in step 2 is:
zt(k)＝H(k)xt(k)+v(k)；
wherein z ist(k) H (k) is the second predetermined matrix, and v (k) is a second white Gaussian noise.
4. The method of claim 3, wherein step 2 calculates a predicted position and an innovation covariance of the target based on the observation model, wherein,
the predicted position of the target is:
the innovation covariance of the target is:
S(k+1)＝H(k+1)Pt(k+1|k)H(k+1)T+R(k)；
wherein the content of the first and second substances,
for state prediction of said target, Pt(k +1| k) is a variance prediction of the target, (. C)TFor transposition, R (k) is the variance of the second white Gaussian noise.
5. The method according to claim 4, wherein the step 4 of constructing a posterior probability model according to the Gaussian mixture model, continuously iteratively updating parameters in the posterior probability model by using a maximum expectation method, and obtaining a target posterior probability according to the parameters comprises:
calculating to obtain the initial posterior probability of the target according to the posterior probability model, the number of the targets, the predicted position of the target and the target innovation covariance;
and continuously and iteratively updating parameters in the posterior probability model by using a maximum expectation method according to the posterior probability model and the initial posterior probability of the target, and obtaining the posterior probability of the target according to the parameters.
6. The method according to claim 5, wherein parameters in the posterior probability model are continuously updated iteratively by using a maximum expectation method according to the posterior probability model and the initial posterior probability of the target, and the target posterior probability is obtained according to the parameters, wherein the parameters in the posterior probability model comprise the mean μ, the variance Σ, and the mixing coefficient α, wherein,
the mean μ is:
the variance Σ is:
the mixing coefficient alpha is:
wherein J is a constant representing the number of target valid measurements.
7. The method according to claim 6, wherein the correlation matrix constructed in step 5 according to the target posterior probability is:
8. the method according to claim 1, wherein the step 5 of searching the correlation matrix to find the maximum target a posteriori probability of each column of the correlation matrix comprises:
and searching the incidence matrix by using a clustering method to find the maximum target posterior probability of each column of the incidence matrix.
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