CN105373805A - A multi-sensor maneuvering target tracking method based on the principle of maximum entropy - Google Patents

Abstract

The invention provides a multi-sensor maneuvering target tracking method based on the principle of maximum entropy. The method comprises the steps of establishing a multi-sensor measurement data set from the same target; calculating the degree of membership between data in the multi-sensor measurement data set, obtaining the class center of the measurement data set through clustering processing to complete the data merging of the multi-sensor measurement data set; performing filtering tracking treatment on the merged data by using the interactive multiple model to update the target; output target track data after update and processing. The method performs data clustering processing based on the principle of fuzzy maximum entropy when merging data of the same target from multiple sensors, and proposes the vector analysis method for decoupled solution of the degree of membership to solve the problems of conventional clustering algorithms that errors are caused because the calculation of the degree of membership is coupled with a clustering center and the initialization of a class center is improper. Thus, the method guarantees full utilization of data of multiple sensors and can realize accurate tracking of a maneuvering target based on the data and the interactive multiple model.

Description

A kind of multisensor maneuvering target tracking method based on maximum entropy criterion

Technical field

The invention belongs to multi-sensor target tracking field, relate to a kind of multisensor maneuvering target tracking method based on maximum entropy criterion.

Background technology

In recent years, fuzzy theory there has been use widely in target following, identification field, the present invention is based on maximum entropy criterion and fuzzy clustering algorithm is applied to multisensor maneuvering target tracking.In the clustering algorithm of classics, usually make degree of membership and cluster centre enter into setting thresholding through several times iteration and realize solving, this just faces iteration threshold and selects and successive ignition computing.In real-time system, be the method avoiding interative computation to adopt direct initialization class center, but this can cause larger cluster error because cluster centre initial selected is improper; The present invention proposes the method for vector analysis, neither needs interative computation, also can avoid because class center initial selected is improper and cause larger cluster error, and the degree of membership decoupling zero realizing participating in without the need to class center solves.

Summary of the invention

Goal of the invention: the present invention is based on maximum entropy criterion and realize maneuvering target state fusion estimation, calculate for degree of membership in clustering algorithm and to be coupled with cluster centre and the initialization of class center introduces error problem improperly, propose the multisensor maneuvering target tracking method based on maximum entropy criterion.

Technical scheme: the present invention proposes a kind of multisensor maneuvering target tracking method based on maximum entropy criterion.The present invention regards the same target data from multisensor as a fuzzy set, data clusters process is carried out based on the criterion of fuzzy maximum entropy to adopting when data merge in set, calculate for degree of membership in traditional clustering algorithm simultaneously and to be coupled with cluster centre and the initialization of class center introduces error problem improperly, the decoupling zero of proposition vector analysis method solves degree of membership.To after in set, data carry out Cluster merging, interacting multiple model algorithm is adopted to carry out filter tracking to target, fuzzy theory is incorporated into multi-sensor data process by the present invention, can making full use of multi-sensor data be realized, and by the accurate tracking realized highly maneuvering target that combines with interactive multi-model.

This method comprises the following steps:

Step 1, sets up the Multisensor Measurement data set deriving from same target; Described multisensor is the sensor of more than three;

Step 2, calculates the degree of membership between Multisensor Measurement data centralization data;

Step 3, asks for class center by clustering processing, completes and merges the data of Multisensor Measurement data set;

Step 4, utilizes interactive multi-model to be combined data and carries out filter tracking process, realize the renewal to target;

Step 5, exports the targetpath data after update process.

Wherein, step 2 comprises: (fusion center system is a generic concept in C4ISR architecture and domain of data fusion to establish moment k fusion center system, refer to the disposal system that multi-sensor data is focused on, also can be understood as the integrated numerous sensor of data fusion system, the data processing of all the sensors all focuses in this system, so usually this system is become fusion center system.) receive m about certain target T _kindividual effective measurement cluster analysis is the similarity based on sample characteristics in sample space, and sample is divided into some classes, make sample in class have very large similarity, and between class, sample has very large diversity, and in class, finds maximum common feature; To the m of certain moment same target T _kindividual measurement sample, all comes from same target, and therefore its maximum general character is the common reflection to dbjective state, and this dbjective state general character is the required problem of separating of the present invention just.In order to accurately estimating target state, according to information theory principle of maximum entropy, due to m in reality _kindividual measurement sample be retrieved as independently random occurrence, should make as much as possible close to the true random probability distribution measured, address this problem by entropy maximization.According to Shannon entropy i value 1 ~ m _k, wherein μ _irepresent i-th effective dose measured value z _ibelong to the possible degree of class center c, i.e. degree of membership, application method of Lagrange multipliers is by cost function $E=\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i\left|\right|z_i-c|{|}^2$ With maximization entropy $H=-\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i{\mathrm{ln\μ}}_i$ Be converted into single optimization object function J:

$J=-\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i{\mathrm{ln\μ}}_i-\mathrm{\β}\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i\left|\right|z_i-c|{|}^2,$

Degree of membership μ can be obtained by maximizing target function type _i:

${\mathrm{\μ}}_i=\frac{e^{-\mathrm{\β}\left|\right|z_i-c|{|}^2}}{\underset{j=1}{\overset{m_k}{\Σ}}{e}^{-\mathrm{\β}\left|\right|z_j-c|{|}^2}},\∀i=1,2,...,m_k,$ J value 1 ~ m _k,

Wherein, β is Lagrange multiplier, and c is metric data Ji Lei center, and e is the exponential function of standard.

Step 3 comprises: by minimizing cost function E in the hope of the Ji Lei center c that fetches data:

$E=\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_{i}d(z_i,c)=\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i\left|\right|z_i-c|{|}^2,$

Wherein, d (z _i, c) for effectively to measure z _iabout the Euclidean distance of class center c; μ _imeet

At μ _iunder known condition, can try to achieve class center is under multisensor background, be class center according to a certain up-to-date measurement, so will the weights of selected observed value caused will to be 1, other weights vanishing measured, obviously unreasonable.If select the predicted value of dbjective state to be that class center will cause two kinds of undesirable situations: one, if prediction deviation is greatly and just in time near a certain measurement, now by causing these measurement weights bigger than normal, other measure weights situation less than normal; Its two, if when target fast reserve, predicted value often departs from more greatly all measuring values, because Euclidean distance reacts on degree of membership μ with exponential relationship _i, when its value exceedes to a certain degree, each measurement weights of appearance are tending towards equal situation, thus lose accurate cluster effect.In view of above reason, the present invention proposes the method for vector analysis, not only can avoid loaded down with trivial details interative computation, can also avoid the problem arranging class center, directly realize degree of membership μ _idecoupling zero solve.

Beneficial effect:

This method effectively can avoid the difficult select permeability of cluster centre, has good estimated accuracy.The present invention adopts the method for vector analysis, neither needs interative computation, also can avoid because class center initial selected is improper and cause larger cluster error, and the degree of membership decoupling zero realizing participating in without the need to class center solves.Solve in classical clustering algorithm, usually make degree of membership and cluster centre enter into setting thresholding through several times iteration to solve, face iteration threshold and select and the difficulty of successive ignition computing, solve because cluster centre initial selected is improper and cause larger cluster error; Proved by engineering practice, the present invention can solve maneuvering target track question well, improves tracking and the real-time of maneuvering target.

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Accompanying drawing explanation

Fig. 1 a is measurement vector relations figure of the present invention.

Fig. 1 b is vector synthesis schematic diagram of the present invention.

Fig. 2 a is simulation scenario figure of the present invention.

Fig. 2 b is that enlarged drawing is followed the tracks of in local of the present invention.

Fig. 3 is process flow diagram of the present invention.

Embodiment

The present invention adopts the maneuvering target tracking method based on fuzzy maximum entropy, and as shown in Figure 3, the present invention realizes carrying out tracking process to maneuvering target from following step:

Step 1, sets up the Multisensor Measurement data set deriving from same target;

Step 2, calculates the degree of membership between Multisensor Measurement data centralization data;

Step 3, asks for class center by clustering processing, completes and merges the data of Multisensor Measurement data set;

Step 4, utilizes interactive multi-model to be combined data and carries out filter tracking process, realize the renewal to target;

Step 5, exports the targetpath data after update process.

Wherein, the fuzzy clustering formulation process based on maximum entropy is as follows:

(1) based on the fuzzy clustering of maximum entropy

If moment k fusion center receives the m about certain target T _kindividual effective measurement Z _k={ z ₁, z ₂..., z _mk, interested is how by this m _kthe current state of individual measurement estimating target.According to fuzzy clustering, this problem can be regarded as the cluster process of optimal programming, corresponding cost function is such as formula shown in (1).

$E=\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_{i}d(z_i,c)=\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i\left|\right|z_i-c|{|}^2---\left(1\right)$

Wherein, d (z _i, c) for measuring z _iabout the Euclidean distance of class center c; Wherein μ _irepresent i-th effective dose measured value z _ibelong to the possible degree of class center c, i.e. degree of membership, and meet

At μ _iunder known condition, can try to achieve class center c is:

$c=\frac{\underset{i}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i{z}_i}{\underset{i}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i}---\left(2\right)$

Cluster analysis is the similarity based on sample characteristics in sample space, and sample is divided into some classes, make sample in class have very large similarity, and between class, sample has very large diversity, and in class, finds maximum common feature; To the m of certain moment same target T _kindividual measurement sample, all comes from same target, and therefore its maximum general character is the common reflection to dbjective state, and this dbjective state general character is the required problem of separating of the present invention just.In order to accurately estimating target state, according to information theory principle of maximum entropy, due to m in reality _kindividual measurement sample be retrieved as independently random occurrence, should make in formula (1) as much as possible close to the true random probability distribution measured, address this problem by entropy maximization.Shannon entropy expression formula is,

$H=-\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i{\mathrm{ln\μ}}_i---\left(3\right)$

Cost function (1) and maximization entropy are converted into single optimization object function by application method of Lagrange multipliers:

$J=-\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i{\mathrm{ln\μ}}_i-\mathrm{\β}\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i\left|\right|z_i-c|{|}^2---\left(4\right)$

Wherein β is Lagrange multiplier, can obtain by maximizing target function type (4):

${\mathrm{\μ}}_i=\frac{e^{-\mathrm{\β}\left|\right|z_i-c|{|}^2}}{\underset{j=1}{\overset{m_k}{\Σ}}{e}^{-\mathrm{\β}\left|\right|z_j-c|{|}^2}},\∀i=1,2,...,m_k---\left(5\right)$

Wherein, class center c selection course is as follows:

(2) class center c selects

Observation type (2) and formula (5), formula (2) Zhong Lei center c is the state parameter of target T that will estimate of the present invention just.Due to μ _ibe coupled with class center c, in common clustering algorithm, adopt default precision thresholding to carry out successive ignition and solve.But this alternative manner exists and is difficult to determine that suitable thresholding, loop iteration are consuming time and may be absorbed in the risk of Local Minimum; Therefore, usually choose suitable class center c in actual applications and directly bring formula (5) calculating degree of membership μ into _i, then by μ _i(2) formula of substitution asks for final class center c.

In existing treatment technology, usually adopting up-to-date measurement to be class center or predicted value is class center.Under multisensor background, be class center according to a certain up-to-date measurement, so will the weights of selected observed value caused will to be 1, other weights vanishing measured, obviously unreasonable.If select the predicted value of dbjective state to be that class center will cause two kinds of undesirable situations: one, if prediction deviation is greatly and just in time near a certain measurement, now by causing these measurement weights bigger than normal, other measure weights situation less than normal; Its two, if when target fast reserve, predicted value often departs from more greatly all measuring values, because Euclidean distance in formula (4) reacts on degree of membership μ with exponential relationship _i, when its value exceedes to a certain degree, each measurement weights of appearance are tending towards equal situation, thus lose accurate cluster effect.In view of above reason, the present invention proposes the method for vector analysis, not only can avoid loaded down with trivial details interative computation, can also avoid the problem arranging class center, directly realize degree of membership μ _idecoupling zero solve.As shown in Figure 2 b, for enlarged drawing is followed the tracks of in local of the present invention.Can see that the present invention has great progress compared to existing technology.

Wherein, degree of membership μ _isolution procedure is as follows:

(3) degree of membership μ _isolve

Suppose the m of certain moment acquisition about target T _kindividual measurement, c is the class center expected, so arbitrary z _imeasure with other and class center c forms vector distribution plan as Fig. 1 a, its vector correlation is:

Can obtain according to formula (6),

Obviously, because each measurement obtains as independent random event, according to Probability Statistics Theory, m is worked as _kthe m of certain moment same target T can be thought time enough large _kindividual measurement has with expectation class center c characteristic, its vectorial building-up process as shown in Figure 1 b,

Namely m is worked as in theory _kduring > > 1, its final vector sum to go to zero.So, formula (7) can be reduced to:

And then have:

Make function for:

Due to the class center that c is global optimum, then with z _ithe dull increase away from class center c, with it is close, dullness reduces, and works as z _iwith class center c _jglobal minimum is obtained, i.e. function when overlapping completely in Monotone Bounded, then with G there is proportional relation:

Therefore, can by function collection is measured as portraying with the public factor of class center c degree of membership.Thus, can by d (z in cost function formula (1) _i, c) be heavily expressed as:

And then, can obtain under maximum entropy criterion:

${\mathrm{\μ}}_i=\frac{e^{-\mathrm{\β}{\left(G\right(\left|\right|\stackrel{\→}{z_{i}c}\left|\right|\left)\right)}^2}}{\underset{j=1}{\overset{m_k}{\Σ}}{e}^{-\mathrm{\β}{\left(G\right(\left|\right|\stackrel{\→}{z_{j}c}\left|\right|\left)\right)}^2}}---\left(13\right)$

At μ _iunder known condition, obtaining class center is:

So far, through type (12), (13) and (14) can not need to select cluster centre and loop iteration computing, thus the decoupling zero realizing degree of membership and class center solves.System just can use formula (13) gained carry out the filtering process of respective objects, the present invention adopts and is formed multi-model (IMM) algorithm be for further processing to c by constant speed (CV), normal (CA) and normal Jerk (CJ) model of accelerating in emulation experiment.As shown in Figure 2 a, be simulation scenario figure of the present invention.

It is as follows that factor-beta chooses process:

(4) factor-beta is chosen

In theory, maximization formula (3) is made to obtain optimum solution, then need β → ∞, but the reduction of the middle cost function exponentially with the increase of β of formula (1), after β reaches a certain value, the optimization object function of formula (3) is without marked change.The suitable β factor should be chosen as the case may be in actual applications, adopt the optimal value β of formula (15) _opt:

β _opt＝-ln(ε)/d _min(15)

Wherein ε is an enough little normal number, d _min=min{d (z _i, c) }.Clutter density is introduced, shown in (16) in β:

β＝η/λ(16)

η (η ∈ [0,1]) is a suitable normal number, and λ is clutter density.

In invention, choose such as formula the β value shown in (17):

$\mathrm{\β}=\mathrm{\α}/{\mathrm{\σ}}_d^2---\left(17\right)$

Wherein, get α=0.5, thus make the membership function in formula (13) meet Gaussian characteristics, this more can guarantee required by be subordinate to angle value close to practical situations.

(5) interactive multi-model is selected

The present invention adopts and forms multi-model (IMM) algorithm (list of references: NaiduVPS, GirijaG.andShanthaumarN.ThreeModelIMM-EKFforTrackingTarg etsExcutingEvasiveManeuvers [P] .45 by constant speed (CV), normal acceleration (CA) and normal Jerk (CJ) model ^thaIIAAAerospaceSciencesMeetingandExhibit, AIAA2007-1204, January2007) class center c is for further processing.Wherein normal Jerk model is:

${\mathrm{\Φ}}_{CJ}=\left[\begin{array}{cc}{\mathrm{\φ}}_{jr}& 0_{4\×4}\\ 0_{4\×4}& {\mathrm{\φ}}_{jr}\end{array}\right]$

${\mathrm{\φ}}_{jr}=\left[\begin{array}{cccc}1& T& \frac{T^2}{2}& \frac{T^3}{6}\\ 0& 1& T& \frac{T^2}{2}\\ 0& 0& 1& T\\ 0& 0& 0& 1\end{array}\right]$

The probability of model is u=[1/31/31/3], and its Model transfer probability is:

$\mathrm{\π}=\left[\begin{array}{ccc}0.91& 0.045& 0.045\\ 0.085& 0.83& 0.085\\ 0.085& 0.085& 0.83\end{array}\right].$

The method that the present invention proposes has two principal features: one, and do not need initialization class center, the decoupling zero realizing degree of membership solves, and is improve the estimated accuracy of dbjective state; Its two, because cluster result is comprehensively determined by sample set, therefore in multi-sensor environment, to the insensitive characteristic of particular sensor systematic error.In actual applications, the systematic error of sensor exists more or less, and particularly along with the increase of detection range, the performance of its azimuthal error is all the more obvious; Therefore, the method that the present invention proposes has good engineer applied and is worth.

The invention provides a kind of multisensor maneuvering target tracking method based on maximum entropy criterion; the method and access of this technical scheme of specific implementation is a lot; the above is only the preferred embodiment of the present invention; should be understood that; for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.The all available prior art of each ingredient not clear and definite in the present embodiment is realized.

Claims (3)

1., based on a multisensor maneuvering target tracking method for maximum entropy criterion, it is characterized in that, comprise the following steps:

Step 1, sets up the Multisensor Measurement data set deriving from same target;

Step 2, calculates the degree of membership between Multisensor Measurement data centralization data;

Step 3, asks for metric data Ji Lei center by clustering processing, completes and merges the data of Multisensor Measurement data set;

Step 4, utilizes interactive multi-model to be combined data and carries out filter tracking process, realize the renewal to target;

Step 5, exports the targetpath data after update process.

2. a kind of multisensor maneuvering target tracking method based on maximum entropy criterion according to claim 1, it is characterized in that, step 2 comprises: establish moment k fusion center system to receive m about target T _kindividual effective dose measured value Z _k, according to Shannon entropy i value 1 ~ m _k, wherein μ _irepresent i-th effective dose measured value z _ibelong to the possible degree of class center c, i.e. degree of membership, application method of Lagrange multipliers is by cost function with maximization entropy be converted into single optimization object function J:

$J=-\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i{\mathrm{ln\μ}}_i-\mathrm{\β}\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i{||z_i-c||}^2,$

Degree of membership μ is calculated by maximizing objective function J _i:

${\mathrm{\μ}}_i=\frac{e^{-\mathrm{\β}{||z_i-c||}^2}}{\underset{j=1}{\overset{m_k}{\Σ}}{e}^{-\mathrm{\β}{||z_j-c||}^2}},\∀i=1,2,...,m_k,$ J value 1 ~ m _k,

Wherein, β is Lagrange multiplier, and c is metric data Ji Lei center, and e is the exponential function of standard.

3. a kind of multisensor maneuvering target tracking method based on maximum entropy criterion according to claim 2, it is characterized in that, step 3 comprises: by minimizing cost function E in the hope of the Ji Lei center c that fetches data:

$E=\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_{i}d(z_i,c)=\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i{||z_i-c||}^2,$

Wherein, d (z _i, c) be effective dose measured value z _iabout the Euclidean distance of class center c; μ _imeet $\underset{i=1}{\overset{m_k}{\Σ}}{\mathrm{\μ}}_i=1,\∀{\mathrm{\μ}}_i\∈\[0,1\],$

At μ _iunder known condition, obtaining class center is