CN104715154A - Nuclear K-mean value track correlation method based on KMDL criteria - Google Patents

Abstract

The invention discloses a nuclear K-mean value track correlation method based on KMDL criteria. The method comprises the following steps that firstly, a typical track correlation scene is established; secondly, the number of target tracks is determined based on the KMDL criteria; thirdly, the nuclear K-mean value algorithm is used for conducting correlation on the track observation scene. According to the nuclear K-mean value track correlation method based on the KMDL criteria, the KMDL criteria and the nuclear K-mean value algorithm are combined to solve the multi-target track correlation problem under the complex environment where clutters are dense, targets are near and the number of the targets is not known. According to the method, the movement state information of the targets is fully utilized, the correlation accuracy rate is effectively increased, the correlation criteria are simple and practicable, the calculated amount is small, the correlation accuracy rate is high, it is not sensitive for target intersection, and the method is suitable for track correlation under the environment where the targets are dense and intersect and applicable to engineering realization.

Description

Based on the kernel c-means Data Association of KMDL criterion criterion

Technical field

The invention belongs to multi-sensor multi-target tracking technical field, be specifically related to a kind of kernel c-means Data Association based on KMDL criterion criterion.

Background technology

Multi-sensor multi-target tracking system receives mainly through Data-Link the local tracks information that each sensing system transmits, then these local tracks information are associated, the calculating of registration, the key problem such as fusion, formed collaborative detection merge after targetpath.

Multi-sensor cooperation target following can realize the accurate tracking to target, and in practical application, target to be tracked exists multiple, now needs correctly to determine the measurement information received by sensor and the corresponding relation between interested target.But the clutter that the radiation source due to falseness produces, the reason such as interference noise and decoy, can cause the uncertainty measuring origin, i.e. the corresponding relation of target and measurement is uncertain, and eliminating this probabilistic method is application track association technology.In distributed system architecture, fusion center receives the local tracks information that single-sensor process obtains, and then carries out fusion formation to these local tracks and estimates more accurately dbjective state, first need the corresponding relation known between local tracks and target.Whether track association problem is exactly from same target in the local tracks that will judge that each sensor obtains.

True Research on Target has intensive, complexity high, influencing each other between multiple goal, the high maneuverability of target flight, the interference of clutter, the existence of sensor error in measurement, all makes track association problem become very difficult.

Summary of the invention

In order to overcome the defect that above-mentioned prior art exists, the object of the present invention is to provide a kind of kernel c-means Data Association based on KMDL criterion criterion, the method can solve the multi-target traces related question under complex environment fast and accurately.

The present invention is achieved through the following technical solutions:

Based on the kernel c-means Data Association of KMDL criterion criterion, comprise the following steps:

Step one: build typical track association scene

First, select the typical model close to target true motion pattern, generate target and measure; Secondly, Poisson distribution is adopted to generate clutter; Then, generate the motor-driven cross flying of target complex height, and the track association scene that heavy dense targets degree is high;

Step 2: use KMDL criterion criterion determination targetpath number

The flight path observation scene in a certain moment in any extraction track association scene, choose this time data as track association sample data, kernel function is incorporated in minimum description length MDL criterion, Minimum description length criterion KMDL criterion under kernel function is utilized to set up the model of accurate description object, carry out KMDL value to calculate, the difference that the value of KMDL is chosen with K value changes, when KMDL is minimum, reach optimum between model complexity and model data matching degree, the K value choosing this moment is flight path optimization number;

Step 3: flight path observation scene kernel c-means algorithm is associated

Adopt the association of kernel c-means algorithm to flight path observation scene, the number K of clustering cluster is the flight path optimization number that step 2 obtains, and then in nuclear space, carry out K-mean cluster, Kernel-based K-means clustering result is respectively K the flight path in a certain moment.

In step 2, if the model that model set is M, MDL criterion to be selected is M _mdl, model M _mdlstandard be minimize following two sums:

| L _m(M _i) |: descriptive model M _irequired figure place;

| L _c(D|M _i) |: setting models M _i, the figure place needed for description object D, | L _c(D|M _i) | be the language based on model M i description object D;

Then MDL is expressed as follows: $M_{\mathrm{mdl}}=\arg \underset{M_i\∈M}{\min }\left\{L_m\left(M_i\right)\right|+\left|L_c(D\right|M_i\left|\right\};$

MDL form under expansion nuclear function, MDL only with the covariance matrix of descriptive model error | Σ _j| relevant, error changed by former space and consideration convey after transformed space determine, the form of MDL is:

$-\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{n}_j\log \left(\frac{n_j^2}{\mathrm{Dist}(X_k,X_l|k,l\⊆j)}\right)+P(J,D,I)$

N _jbe the number of samples of jth bunch, Dist is by sample X _kbe included into the error of jth bunch, P (J, D, I) is penalty, and D is the dimension of sample, the number that I is bunch;

Error function is the Euclidean distance using kernel formulae discovery, in a jth clustering cluster each point to its center square distance and be the majorized function of kernel c-means:

$S_j=\frac{1}{n_{j}D}\underset{k\⊆j}{\mathrm{\Σ}}K(X_k,X_k)-\frac{1}{n_j}\underset{l\⊆j}{\mathrm{\Σ}}K(X_k,X_l)$

Suppose that K is linear kernel, S equals variance in luv space X, i.e. K (X _k, X _l)=X _kx _l;

Obtain complete MDL formula, suppose that the variance of each dimension bunch is equal, replace covariance matrix determinant Σ _jfor:

$\left|{\mathrm{\Σ}}_j\right|=S_j^D$

Assuming that cluster respectively ties up indifference, then s _jobtain in arbitrary kernel function, then have:

$\mathrm{KMDL}=-\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{n}_j\log \left(\frac{n_j^2}{S_j^D}\right)+J(D^2+3D+2)\log \left(I\right)/2.$

Kernel c-means algorithm described in step 3, comprises the following steps:

1) K sample in nuclear space in any selection flight path scene is as initial cluster center $(m_1^{\mathrm{\φ}},m_2^{\mathrm{\φ}},...m_k^{\mathrm{\φ}});$

2) in nuclear space, by each sample φ (x _i) be assigned in each classification according to nearest neighbouring rule, logical distance calculates, φ (x _i) nearest from which cluster centre, just belong to this classification;

3) cluster centre is recalculated and J ^φvalue;

4) step 2 is repeated) and 3), until continuous n iteration J ^φbe worth constant till.

Step 3) middle J ^φthe computing method of value are:

First, according to step 2) classification of gained, find the center of a sample as such in each category; Then, in each category, respectively with each sample for class center, other each sample point is to the distance at class center in compute classes, and calculates distance sum, and the class center minimum apart from sum is exactly such center; Finally, minor increment sum is exactly such error sum of squares by all kinds of addition obtains J ^φvalue.

K-mean cluster described in step 3 is through non-linearity mapping phi: R by the flight path sample to be sorted of nuclear space ⁿ→ F, x → φ (x), original sample (x ₁, x ₂... x _n) be mapped as (φ (x ₁) ..., φ (x _n)), in the division of nuclear space based on distance, large for similarity measure between sample is classified as a class, until bunch central point convergence.

The concrete operations of K-mean cluster are:

First, the objective function in following formula is minimized:

$J^{\mathrm{\φ}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}{\left|\right|\mathrm{\φ}\left(x_i\right)-m_k^{\mathrm{\φ}}\left|\right|}^2$

Wherein, average: i=1 ..., N, k=1 ..., K, N _kit is the number of samples of kth class;

Then, in nuclear space, any one sample φ (x) and certain class average between distance following formula calculate:

${\left|\right|\mathrm{\φ}\left(x_i\right)-m_k^{\mathrm{\φ}}\left|\right|}^2={\left|\right|\mathrm{\φ}\left(x\right)-\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}\mathrm{\φ}\left(x_i\right)\left|\right|}^2=k(x,x)-2\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}k(x,x_j)+\underset{i,j=1}{\overset{N_k}{\mathrm{\Σ}}}k(x_i,x_j)$

Wherein, k () is exactly kernel function, uses radial kernel function gaussian kernel function:

Compared with prior art, the present invention has following useful technique effect:

The disclosed kernel c-means Data Association based on KMDL criterion criterion of the present invention, based target status information, KMDL criterion criterion and kernel c-means algorithm are combined under solving complex environment that (clutter is intensive, gtoal setting, target numbers is unknown) multi-target traces related question.First, build typical track association scene, select the typical model close to target true motion pattern, generate target and measure, can preferably close to the real motion pattern of target; Generate clutter, real goal is carried out correct coupling, be that association scene is more true to nature, effectively investigate algorithm interrelating effect; In track association Scenario Design, generate the motor-driven cross flying of target complex height, the simulating scenes that heavy dense targets degree is higher.Secondly, kernel function is incorporated in minimum description length MDL criterion, utilizes Minimum description length criterion KMDL criterion under kernel function to set up the mathematical model of accurate description object, by KMDL criterion criterion process a certain moment flight path observation scene data point.Finally, to the kernel c-means algorithm association of flight path observation scene, expand based on the K-means clustering algorithm divided traditional, in clustering algorithm association process, introduce kernel function, then in nuclear space, carry out K-mean cluster.The inventive method makes full use of the movement state information of target, effectively improves association accuracy rate, and association criterion is simple, calculated amount is little, association accuracy is high, intersect insensitive to target, be adapted at carrying out track association in heavy dense targets and Cross-environment, be applicable to Project Realization.

Accompanying drawing explanation

Fig. 1 is the true flight path panorama sketch of target under CT model;

Fig. 2 is the flight path observation figures of 30 sensors to 5 targets;

Fig. 3 is flight path a certain moment observation figure;

Fig. 4 is schematic diagram after a certain moment denoising of flight path;

Fig. 5 is KMDL curve synoptic diagram;

Fig. 6 is that flight path observation scene is based on kernel c-means algorithm associated diagram.

Embodiment

Below in conjunction with specific embodiment, the present invention is described in further detail, and the explanation of the invention is not limited.

Kernel c-means Data Association based on KMDL criterion criterion of the present invention, comprises the following steps:

Step one, build typical track association scene

1, target measures and generates

For maneuvering target, target travel pattern is uncertain, and kinetic characteristic is unforeseen, is difficult to maneuvering target and sets up single model accurately.From three kinds of conventional target movement models: choose conventional typical model uniform motion model (CV), uniformly accelerated motion model (CA), at the uniform velocity turning motion model (CT), generation target measures, preferably close to the real motion pattern of target.

2, clutter generates

In actual applications under truly operation scene, often can be subject to clutter and false-alarm during the sensor detection of a target to the interference of target detection.The existence of clutter and false-alarm may cause gauge point more than real goal number, also may have influence on the effect that sensor detects real goal.Generate clutter, whether validate association algorithm can effectively be got rid of clutter and noise spot, real goal is carried out correct coupling, makes association scene more true to nature, effectively investigate algorithm interrelating effect.

3, between target group, architectural characteristic generates

Under normal conditions, between target group, often there is special architectural characteristic.There is high maneuverability in the motion of target group, target may exist parallel flight or cross flying, and extraterrestrial target closeness exists the several scenes such as height difference.In track association Scenario Design, generate the motor-driven cross flying of target complex height, the simulating scenes that heavy dense targets degree is higher; In plot-track Association Algorithm application, utilize its architectural characteristic fully, investigate the validity of association algorithm.

Here choose at the uniform velocity turning motion model and typically associate scene as one.Suppose 5 targets in 30 sensors observe clutters.Before emulation starts, have 5 targets to obey being evenly distributed on coordinate is [-3km, 3km] × [-3km, 3km] region in, the motion model of all targets obeys approximate at the uniform velocity turning motion model, and initial velocity direction is [-2 π, 2 π] interior stochastic distribution, speed is 20m/s.Sampling time interval is 1s, and the flight path cumulative time is 60s.

Dbjective state $x_k=\left[\begin{array}{ccccc}{p}_{x,k}& {\stackrel{\·}{p}}_{x,k}& p_{y,k}& {\stackrel{\·}{p}}_{y,k}& {\mathrm{\ω}}_k\end{array}\right],$ Motion model:

x _k＝Fx _k-1+w _k-1

$F=\left[\begin{array}{ccccc}1& \frac{\sin {\mathrm{\ω}}_{k-1}T}{{\mathrm{\ω}}_{k-1}}& 0& -\frac{1-\cos {\mathrm{\ω}}_{k-1}T}{{\mathrm{\ω}}_{k-1}}& 0\\ 0& \cos \mathrm{\ωT}& 0& -\sin {\mathrm{\ω}}_{k-1}T& 0\\ 0& \frac{1-\cos {\mathrm{\ω}}_{k-1}T}{{\mathrm{\ω}}_{k-1}}& 1& \frac{\sin {\mathrm{\ω}}_{k-1}T}{{\mathrm{\ω}}_{k-1}}& 0\\ 0& \sin {\mathrm{\ω}}_{k-1}T& 0& \cos {\mathrm{\ω}}_{k-1}T& 0\\ 0& 0& 0& 0& 1\end{array}\right]$

Wherein x _kthe state value of k moment target, p _x,kthe position of k moment x, the speed of k moment x, p _y,kthe position of k moment y, the speed of k moment y, w _kbe k moment corresponding process noise, F is state-transition matrix, and ω is turning rate, and T is the sampling time.

Process noise is white Gaussian noise, and average is 0, and variance is:

$Q_{k-1}=\mathrm{diag}\left({\left[\begin{array}{ccccc}{0.1}^2& {0.001}^2& {0.1}^2& {0.001}^2& {\mathrm{\δ}}_u^2\end{array}\right]}^T\right)$

δ _u＝0.005(π/180)rad/s。

Measurement model is nonlinear equation:

$z_k=\left[\begin{array}{c}\arctan (p_{x,k}/p_{y,k})\\ \sqrt{p_{x,k}^2+p_{y,k}^2}\end{array}\right]+v_k$

Measurement noise is white Gaussian noise, and average is 0, and variance is:

v _k～N(·；[0.001,0] ^T,R _k)；

$R_k=\mathrm{diag}\left({[{\mathrm{\σ}}_{\mathrm{\θ}}^2,{\mathrm{\σ}}_r^2]}^T\right);$

σ _θ＝0.1(π/180)rad；σ _r＝5m。

Fig. 1 illustrates at the uniform velocity in turning motion model, the flight path of target within all sampling times.In this scene, detection of a target number is 5, and sensor is 30.

Step 2, calculating flight path are observed scene KMDL value and choose best targetpath number

Between flight path, shared data message needs the correct coupling between target, and transmitting terminal sends the observation information of series of complex, and receiving end uses a kind of matching algorithm it to be mated with local observation data.Sensor is when associating by observation data, consider the existence of the situation such as system deviation, stochastic error, false-alarm, leakage detection, and be subject to the constraint of sensing system self-condition, in order to solve complicated related question, in CT motion model, extract the observation scene of multiple goal within a certain sampling time, choose 30 sensors to 5 a certain moment gauge points of target as track association sample point.

Kernel function is incorporated in minimum description length MDL criterion, utilizes Minimum description length criterion KMDL criterion under kernel function to set up the mathematical model of accurate description object.Scene data point is observed: when descriptive model curve undermatching flight path observation contextual data with KMDL criterion criterion process a certain moment flight path, model is not enough to the regularity of catching the reflection of multi-target traces data, though at this moment model complexity is low, but model and track data matching degree poor, describe length bigger than normal; When model curve overmatching data point, capture the fluctuation that noise causes simultaneously, can not the rule of capture-data reflection, though high at this situation model and Data Matching degree, but model complexity is high, causes that to describe length bigger than normal; When reaching optimum between model complexity and model data matching degree, model captures the regularity that data reflect, model complexity is lower, model and Data Matching degree higher, now corresponding KMDL value is minimum, and the K value of correspondence is flight path optimization number.

Any extraction a certain moment point flight path observation scene, chooses this time data as track association sample data.Fig. 2 is the flight path observation figures of 30 sensors to 5 targets.Fig. 3 is flight path a certain moment observation figure.Fig. 4 is schematic diagram after a certain moment denoising of flight path.

If the model that model set is M, MDL criterion to be selected is M _mdl, model M _mdlstandard be minimize following two (namely describing length) sums: | L _m(M _i) |: descriptive model M _irequired figure place (can be regarded as the code length summation needed by all parameter codings, also referred to as description length).| L _c(D|M _i) |: setting models M _i, the figure place needed for description object D.Here | L _c(D|M _i) | be the language based on model M i description object D.MDL is expressed as follows: $M_{\mathrm{mdl}}=\arg \underset{M_i\∈M}{\min }\left\{L_m\left(M_i\right)\right|+\left|L_c(D\right|M_i\left|\right\}.$

MDL form under expansion nuclear function, MDL only and the covariance matrix of descriptive model error | Σ _j| relevant.Error changed by former space and consideration convey after transformed space determine, the more general form of MDL is:

$-\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{n}_j\log \left(\frac{n_j^2}{\mathrm{Dist}(X_k,X_l|k,l\⊆j)}\right)+P(J,D,I)$

N _jbe the number of samples of jth bunch, Dist is by sample X _kbe included into the error of jth bunch, P (J, D, I) is penalty, and D is the dimension of sample, the number that I is bunch.

The simplest error function is the Euclidean distance using kernel formulae discovery, in a jth clustering cluster each point to its center square distance and be the majorized function of kernel c-means

$S_j=\frac{1}{n_{j}D}\underset{k\⊆j}{\mathrm{\Σ}}K(X_k,X_k)-\frac{1}{n_j}\underset{l\⊆j}{\mathrm{\Σ}}K(X_k,X_l)$

Suppose that K is linear kernel, S equals variance in luv space X, i.e. K (X _k, X _l)=X _kx _l.Obtain complete MDL formula, suppose that the variance of each dimension bunch is equal, covariance matrix determinant Σ can be replaced _jfor:

$\left|{\mathrm{\Σ}}_j\right|=S_j^D$

Do not have difference so assuming that cluster is respectively tieed up consider S _jcan obtain in arbitrary kernel function, can obtain

$\mathrm{KMDL}=-\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{n}_j\log \left(\frac{n_j^2}{S_j^D}\right)+J(D^2+3D+2)\log \left(I\right)/2$

To a certain moment point flight path observation scene, choose the value of this time data calculating K MDL, the difference that the value of KMDL is chosen with K value changes, and reaches optimum when KMDL is minimum between model complexity and model data matching degree, and the K chosen now is that best cluster number is target number.Fig. 5 is KMDL curve synoptic diagram, and KMDL minimum value is-732.2927, and now K value is 5.

Step 3, with kernel c-means algorithm, scene clustering is observed to flight path

The association of kernel c-means algorithm is adopted to flight path observation scene, wherein the number K of clustering cluster is the target number of KMDL criterion gained, expand based on the K-means clustering algorithm divided traditional, kernel function is introduced in clustering algorithm association process, then in nuclear space, K-mean cluster is carried out, carry out K-mean cluster new feature space (nuclear space) the inside, the flight path sample to be sorted of nuclear space is through non-linearity mapping phi: R ⁿ→ F, x → φ (x) is original sample (x ₁, x ₂... x _n) be mapped as (φ (x ₁) ..., φ (x _n)), in the division of nuclear space based on distance, large for similarity measure between sample is classified as a class, until bunch central point close to convergence.Kernel-based K-means clustering result is respectively K the flight path in a certain moment.

Particularly, use Kernel-based K-means clustering algorithm to observe scene clustering to flight path, first utilize one Nonlinear Mapping φ: R ⁿ→ F, x → φ (x), by original space R _nsample x to be sorted be mapped in a high-dimensional feature space F (nuclear space), object to give prominence to the feature difference between different classes of sample, make sample become linear separability (or approximately linear can divide), then carry out K-mean cluster at higher-dimension nuclear space.In nuclear space, sample to be sorted becomes (φ (x ₁) ..., φ (x _n)), carrying out Kernel-based K-means clustering is exactly the objective function that will minimize in following formula:

$J^{\mathrm{\φ}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}{\left|\right|\mathrm{\φ}\left(x_i\right)-m_k^{\mathrm{\φ}}\left|\right|}^2$

Wherein, average: i=1 ..., N, k=1 ..., K, N _kit is the number of samples of kth class.

In nuclear space, any one sample φ (x) and certain class average between distance following formula calculate:

${\left|\right|\mathrm{\φ}\left(x_i\right)-m_k^{\mathrm{\φ}}\left|\right|}^2={\left|\right|\mathrm{\φ}\left(x\right)-\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}\mathrm{\φ}\left(x_i\right)\left|\right|}^2=k(x,x)-2\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}k(x,x_j)+\underset{i,j=1}{\overset{N_k}{\mathrm{\Σ}}}k(x_i,x_j)$

Wherein, k () is exactly kernel function, uses radial kernel function gaussian kernel function here gaussian kernel function characteristic of correspondence space is infinite dimensional, the higher dimensional space of data-mapping can not be limited by dimension.

Kernel-based K-means clustering algorithm is used to have following steps:

(1) initial cluster center is determined that is: K sample in nuclear space in any selection flight path scene is as initial cluster center.

(2) in nuclear space, by each sample φ (x _i) be assigned in each classification according to nearest neighbouring rule.Calculated by above formula distance, φ (x _i) nearest from which cluster centre, just belong to this classification.

(3) cluster centre is recalculated and J ^φvalue.Due at nuclear space, can not computing center clearly, therefore a sample can only be selected in each category to replace class center, and concrete grammar is: according to the classification of step (2) gained, finds the center of a sample as such in each category.In each category, respectively with each sample for class center, other each sample point is to the distance at class center in compute classes, and calculates distance sum, and the class center minimum apart from sum is exactly such center.Minor increment sum is exactly such error sum of squares by all kinds of add up and just obtain J ^φvalue.

(4) step (2) and (3) is repeated, until continuous n iteration J ^φtill being worth constant (or change is very little).

Simulation result is as Fig. 6.By above-mentioned steps, adopt KMDL criterion criterion determination targetpath number K to a certain moment flight path scene extracted in CT motion model, utilize kernel c-means algorithm to carry out track association cluster, each class of result is the local tracks coming from same target.

Claims (6)

1., based on the kernel c-means Data Association of KMDL criterion criterion, it is characterized in that, comprise the following steps:

Step one: build typical track association scene

First, select the typical model close to target true motion pattern, generate target and measure; Secondly, Poisson distribution is adopted to generate clutter; Then, generate the motor-driven cross flying of target complex height, and the track association scene that heavy dense targets degree is high;

Step 2: use KMDL criterion criterion determination targetpath number

The flight path observation scene in a certain moment in any extraction track association scene, choose this time data as track association sample data, kernel function is incorporated in minimum description length MDL criterion, Minimum description length criterion KMDL criterion under kernel function is utilized to set up the model of accurate description object, carry out KMDL value to calculate, the difference that the value of KMDL is chosen with K value changes, when KMDL is minimum, reach optimum between model complexity and model data matching degree, the K value choosing this moment is flight path optimization number;

Step 3: flight path observation scene kernel c-means algorithm is associated

Adopt the association of kernel c-means algorithm to flight path observation scene, the number K of clustering cluster is the flight path optimization number that step 2 obtains, and then in nuclear space, carry out K-mean cluster, Kernel-based K-means clustering result is respectively K the flight path in a certain moment.

2. the kernel c-means Data Association based on KMDL criterion criterion according to claim 1, is characterized in that, in step 2, if the model that model set is M, MDL criterion to be selected is M _mdl, model M _mdlstandard be minimize following two sums:

| L _m(M _i) |: descriptive model M _irequired figure place;

| L _c(D|M _i) |: setting models M _i, the figure place needed for description object D, | L _c(D|M _i) | be the language based on model M i description object D;

Then MDL is expressed as follows: $M_{\mathrm{mdl}}=\arg \underset{M_i\∈M}{\min }\left\{L_m\left(M_i\right)\right|+\left|L_c\left(D\right|M_i|\right\};$

MDL form under expansion nuclear function, MDL only with the covariance matrix of descriptive model error | ∑ _j| relevant, error changed by former space and consideration convey after transformed space determine, the form of MDL is:

$-\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{n}_j\log \left(\frac{n_j^2}{\mathrm{Dist}(X_k,X_l|k,l\⊆j)}\right)+P(J,D,I)$

N _jbe the number of samples of jth bunch, Dist is by sample X _kbe included into the error of jth bunch, P (J, D, I) is penalty, and D is the dimension of sample, the number that I is bunch;

Error function is the Euclidean distance using kernel formulae discovery, in a jth clustering cluster each point to its center square distance and be the majorized function of kernel c-means:

$S_j=-\frac{1}{n_{j}D}\underset{k\⊆j}{\mathrm{\Σ}}K(X_k,X_k)-\frac{1}{n_j}\underset{l\⊆j}{\mathrm{\Σ}}K(X_k,X_l)$

Suppose that K is linear kernel, S equals variance in luv space X, i.e. K (X _k, X _l)=X _kx _l;

Obtain complete MDL formula, suppose that the variance of each dimension bunch is equal, replace covariance matrix determinant ∑ _jfor:

$\left|{\mathrm{\Σ}}_j\right|=S_j^D$

Assuming that cluster respectively ties up indifference, then s _jobtain in arbitrary kernel function, then have:

$\mathrm{KMDL}=-\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{n}_j\log \left(\frac{n_j^2}{S_j^D}\right)+J(D^2+3D+2)\log \left(I\right)/2.$

3. the kernel c-means Data Association based on KMDL criterion criterion according to claim 1, is characterized in that, the kernel c-means algorithm described in step 3, comprises the following steps:

1) K sample in nuclear space in any selection flight path scene is as initial cluster center

2) in nuclear space, by each sample φ (x _i) be assigned in each classification according to nearest neighbouring rule, logical distance calculates, φ (x _i) nearest from which cluster centre, just belong to this classification;

3) cluster centre is recalculated and J ^φvalue;

4) step 2 is repeated) and 3), until continuous n iteration J ^φbe worth constant till.

4. the kernel c-means Data Association based on KMDL criterion criterion according to claim 3, is characterized in that, step 3) middle J ^φthe computing method of value are:

First, according to step 2) classification of gained, find the center of a sample as such in each category; Then, in each category, respectively with each sample for class center, other each sample point is to the distance at class center in compute classes, and calculates distance sum, and the class center minimum apart from sum is exactly such center; Finally, minor increment sum is exactly such error sum of squares by all kinds of addition obtains J ^φvalue.

5. the kernel c-means Data Association based on KMDL criterion criterion according to claim 1, is characterized in that, the K-mean cluster described in step 3, is through non-linearity mapping phi: R by the flight path sample to be sorted of nuclear space ⁿ→ F, x → φ (x), original sample (x ₁, x ₂... x _n) be mapped as (φ (x ₁) ..., φ (x _n)), in the division of nuclear space based on distance, large for similarity measure between sample is classified as a class, until bunch central point convergence.

6. the kernel c-means Data Association based on KMDL criterion criterion according to claim 5, is characterized in that, the concrete operations of K-mean cluster are:

First, the objective function in following formula is minimized:

$J^{\mathrm{\φ}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}{\left|\right|\mathrm{\φ}\left(x_i\right)-m_k^{\mathrm{\φ}}\left|\right|}^2$

Wherein, average: i=1 ..., N, k=1 ..., K, N _kit is the number of samples of kth class;

Then, in nuclear space, any one sample φ (x) and certain class average between distance following formula calculate:

${\left|\right|\mathrm{\φ}\left(x_i\right)-m_k^{\mathrm{\φ}}\left|\right|}^2={\left|\right|\mathrm{\φ}\left(x\right)-\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}\mathrm{\φ}\left(x_i\right)\left|\right|}^2=k(x,x)-2\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}k(x,x_j)+\underset{i,j=1}{\overset{N_k}{\mathrm{\Σ}}}k(x_i,x_j)$

Wherein, k () is exactly kernel function, uses radial kernel function gaussian kernel function: