CN104794735B

CN104794735B - Extension method for tracking target based on variation Bayes's expectation maximization

Info

Publication number: CN104794735B
Application number: CN201510152626.9A
Authority: CN
Inventors: 李翠芸; 王晋斌; 姬红兵; 王荣
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2015-04-02
Filing date: 2015-04-02
Publication date: 2017-08-25
Anticipated expiration: 2035-04-02
Also published as: CN104794735A

Abstract

The invention discloses a kind of extension method for tracking target based on variation Bayes's expectation maximization VBEM, mainly solve in traditional extension target tracking domain, in the case where measurement noise covariance is unknown, the problem of tracking performance of target will drastically decline.This method predicts relevant parameter of the Gauss against gamma component in dbjective state and the joint probability hypothesis density for measuring noise covariance first；Gauss is updated against gamma component parameters again；Finally by building and merge be expanded dbjective state and number.Emulation experiment shows that the present invention can track many extension targets under unknown number and unknown measurement noise covariance well, and with higher tracking accuracy, available for the tracking to aircraft and Submarine Target.

Description

Extension method for tracking target based on variation Bayes's expectation maximization

Technical field

The invention belongs to technical field of information processing, more particularly to a kind of method for tracking target, available for many extensions of tracking Target.

Background technology

In traditional target tracking domain, due to the limited resolution of radar, therefore target is regarded as under normal circumstances It is point target, i.e., one moment each target can only produce a measurement.In recent years, the development with the radar exploration technique and reality The need for border is applied, target is more considered as extension target, i.e., each target can produce multiple amounts at each moment Survey.

In actual target following scene, the number of target can not be predicted in advance, therefore the theoretical proposition of random set The need for greatly meeting target following theory.In the model hypothesis of all multipair targets, especially category extends goal theory The need for tracking theory at present is more pressed close in proposition, and it is widely used, nearly ten years, turns into real life Study hotspot in target tracking domain.2003, stochastic finite collection theory was applied to multiple target tracking problem by Mahler, Propose probability hypothesis density PHD filtering.2005, Gilholm and Salmond proposed that a kind of spatial distribution obeys Poisson distribution Extension object module.2009, Mahler was deduced the PHD filtering of extension target, i.e., with the measurement random set at each moment Target random set is predicted, updated, the motion state of target and the number of estimation target then can be accurately extracted.2010 Year,Etc. the Gaussian Mixture way of realization for giving extension target PHD.2011, Orguner etc. had also been proposed band Extension target PHD (ET-CPHD) filtering of gesture distribution, solves defect during ET-PHD estimation target numbers well.However, Traditional extension target tracking algorism processing is all that measurement noise covariance is known situation, in practice when measurement noise association During Unknown Variance, the tracking performance of extension target will drastically decline.

The content of the invention

It is an object of the invention in view of the above-mentioned problems, proposing a kind of extension mesh based on variation Bayes's expectation maximization Tracking is marked, to improve the tracking performance in the case where measuring noise covariance unknown condition.

Realizing the key problem in technology of the present invention is：Under gesture probability hypothesis density filter frame, introduce variation Bayes and expect VBEM technologies, estimation dbjective state and the joint probability hypothesis density for measuring noise covariance are maximized, realizes that unknown measurement is made an uproar Target Tracking Problem under sound covariance.

VB is that a class is used for the method for approximate calculation complexity integration in Bayesian Estimation and machine learning field, VB herein It is used in approximately linear Gaussian Systems, extension dbjective state and the joint probability hypothesis density for measuring noise covariance, the calculation The main thought of method is to assume that density parameterize approximately to extending dbjective state and measuring the joint probability of noise covariance, And provide its Parameter Expression form.Assume with the theoretical joint probabilities to extension dbjective state and measurement noise covariance of VB During density is carried out approximately, in order to judge estimated Gauss against the performance of gamma component relevant parameter, on VB basis It is upper to introduce expectation maximization EM algorithms again.Expecting E steps, estimating the desired value of unknown parameter, provide current parameter Estimation； M steps are being maximized, distributed constant are being reevaluated, so that the likelihood function reaches maximum.The estimates of parameters obtained in M steps by with Walk and calculate in next E, this process is constantly alternately.This method, which can be widely used in data, the feelings of defect Condition, and there is simplicity and stability.

The technical step that the present invention is extended target following using above-mentioned VBEM technologies includes as follows：

(1) in moment k=0, initialization extension dbjective state and the joint probability hypothesis density for measuring noise covariance For v₀(x,R)；

(2) in k >=1, density v is assumed to extension dbjective state and the joint probability for measuring noise covariance_k-1|k-1(x, R) and for the gesture for calculating extension target numbers it is distributed P_k-1|k-1(num) it is predicted, the extension target joint predicted is general Rate assumes density v_k|k-1(x, R) and prediction gesture distribution P_k|k-1(num)；

(3) extension dbjective state and the joint probability of measurement noise covariance to prediction assumes density v_k|k-1(x, R) and Gesture for calculating extension target numbers is distributed P_k|k-1(num) it is updated：

(3a) is using variation Bayes VB methods to joint probability hypothesis density v_k|k-1(x, R) approximately, obtain with height The probability hypothesis density Q for the extension dbjective state that the summation form of this distribution is represented_x,k|k-1(x) and with the summation of inverse Gamma distribution The probability hypothesis density Q for the measurement noise covariance that form is represented_R,k|k-1(R)；

(3b) utilizes probability hypothesis density of the variation Bayes expectation maximization VBEM methods to extension dbjective state Q_x,k|k-1(x) the probability hypothesis density Q of Gaussian component and measurement noise covariance in_R,k|k-1(R) the inverse gamma component in is carried out Iteration updates, and obtains representing extension target state x Gaussian component and represents to measure noise covariance R inverse gamma point Amount；

(3c) predicts that step (2) obtained gesture is distributed P_k|k-1(num) it is updated, the gesture distribution P after being updated_k|k (num)；

(4) Gaussian component after renewal and inverse gamma component are trimmed with being merged, and extracts the Gauss point after merging The position and speed of amount and inverse gamma component are used as the state for extending target；

(5) obtained gesture is updated to step (3) and is distributed P_k|k(num) it is weighted average, the number for the target that is expanded：

(6) repeat step (2)-(5), continue to track extension target.

The present invention has advantages below：

First, invention introduces variation Bayes's EM technologies, by estimating extension dbjective state and measuring noise association side The joint probability of difference assumes density, effectively have estimated each target in actual measurements noise not in the same time, under being complex environment The analysis of many extension target following scenes provides help, it is ensured that CPHD filtering algorithms can be effectively realized to be measured to unknown Target following is extended under noise covariance environment.

Second, the present invention due to using first prediction Gauss against gamma component relevant parameter, then to Gauss against gamma component Parameter is updated, and extends the process of target with merging the dbjective state sum purpose tracking that is expanded finally by trimming, with Traditional GM-CPHD filtering algorithms are compared, and improve tracking accuracy.

Brief description of the drawings

Fig. 1 is the general flow chart of the present invention；

Under the conditions of Fig. 2 is single experiment, the simulation result figure for extending target is tracked with the inventive method；

Fig. 3 is that under 100 experiment conditions, the imitative of target numbers is estimated with the inventive method and Traditional GM-CPHD methods True comparative result figure；

Fig. 4 is under 100 experiment conditions, to be sentenced with the inventive method with Traditional GM-CPHD methods by OSPA distances The simulation result comparison diagram of disconnected target tracking accuracy.

Embodiment

The present invention will be further described below in conjunction with the accompanying drawings.

Reference picture 1, of the invention implements step including as follows：

Step 1, in moment k=0, initialized target state and the joint probability hypothesis density for measuring noise covariance：

Wherein, J₀The number of Gaussian component is represented,The weights of i-th of Gaussian component are represented, N () represents Gauss point Cloth,The average of i-th of Gaussian component is represented,Represent the covariance of i-th of Gaussian component；IG () represents inverse gamma Distribution,I-th of covariance against gamma component is represented,For i-th of constant factor against gamma component,For I-th of iteration factor against gamma component, l represents that the l for measuring noise covariance is tieed up, and d represents to measure the dimension of noise covariance Number.

Step 2, in k >=1, density v is assumed to extension dbjective state and the joint probability for measuring noise covariance_k-1|k-1 (x, R) is predicted, and the extension target joint probability predicted assumes density v_k|k-1(x,R)。

2a) joint probability to survival dbjective state and measurement noise covariance assumes density v_S,k|k-1Gauss in (x, R) The average of componentAnd covarianceIt is predicted, the average for the survival target Gaussian component predictedWith Covariance

Wherein,Represent survival dbjective state transfer matrix, Q_k-1Represent survival object procedure noise covariance, ()^T Represent transposition；

2b) joint probability to survival dbjective state and measurement noise covariance assumes density v_S,k|k-1Inverse gal in (x, R) The constant factor of agate componentAnd iteration factorIt is predicted, the survival target predicted is against gamma component Constant factorWith the iteration factor of inverse gamma component

Wherein ρ_lRepresent forgetting factor, and ρ_l∈(0,1]；

2c) under Gaussian Mixture framework, the average of the survival target Gaussian component of prediction is utilizedCovarianceWith the constant factor of inverse gamma componentIteration factorCalculate survival dbjective state and measure noise The joint probability of covariance assumes density v_S,k|k-1(x,R)：

Wherein, P_S,kRepresent extension target survival probability, J_k-1The Gaussian component number at k-1 moment is represented,When representing k-1 The weights of i-th of Gaussian component are carved, N () represents Gaussian Profile,The survival dbjective state and measurement for representing prediction are made an uproar The joint probability of sound covariance assumes density v_S,k|k-1The average of i-th of Gaussian component in (x, R),Represent depositing for prediction Dbjective state living and the joint probability hypothesis density v for measuring noise covariance_S,k|k-1The association side of i-th of Gaussian component in (x, R) Difference；IG () represents inverse Gamma distribution, and d represents to measure the dimension of noise covariance,Represent the survival target-like of prediction State and the joint probability hypothesis density v for measuring noise covariance_S,k|k-1I-th of constant factor against gamma component in (x, R),The survival dbjective state for representing prediction and the joint probability for measuring noise covariance assume density v_S,k|k-1In (x, R) The iteration factor of i inverse gamma components；

2d) joint probability to derivative goal state and measurement noise covariance assumes density b_k|k-1Gauss point in (x, R) The average of amountAnd covarianceIt is predicted, the average for the derivative goal Gaussian component predictedWith association side Difference

Wherein, i represents k-1 moment Gauss against i-th of gamma component, and j represents what is derived by the k-1 moment to k moment Gauss against j-th of gamma component,The state-transition matrix of derivative goal is represented,Represent the state of derivative goal Correction,Represent derivative goal process noise covariance；

2e) joint probability to derivative goal state and measurement noise covariance assumes density b_k|k-1Inverse gamma in (x, R) The constant factor of componentAnd iteration factorIt is predicted, the derivative goal predicted is normal against gamma component Measure the factorAnd iteration factor

2f) under Gaussian Mixture framework, the average of the derivative goal Gaussian component of prediction is utilizedCovarianceWith the constant factor of inverse gamma componentIteration factorCalculate derivative goal state and measure noise The joint probability of covariance assumes density b_k|k-1(x,R)：

Wherein, J_b,kThe derivative goal Gaussian component number at k-1 moment to k moment is represented,Represent that the k moment derives for j-th The weights of target Gaussian component,Represent that k-1 moment to the k moment is derived by i-th of Gaussian component and obtain j-th of Gauss point The average of amount,Represent that k-1 moment to the k moment is derived the covariance for obtaining j-th of Gaussian component by i-th of Gaussian component；Represent that k-1 moment to the k moment is derived by i-th against gamma component and obtain j-th of constant factor against gamma component,Represent that k-1 moment to the k moment is derived by i-th against gamma component and obtain j-th of iteration factor against gamma component；

2g) calculate newborn dbjective state and measure the joint probability density γ of noise covariance_k(x,R)：

Wherein, J_γ,kFor k moment newborn target Gaussian component number,For for k moment newborn i-th of Gaussian component of target Weights,For the state average of newborn i-th of Gaussian component of target,For the motion of newborn i-th of Gaussian component of target State covariance；For newborn i-th of constant factor against gamma component of target,It is i-th of newborn target against gamma The iteration factor of component.

2h) using step 2a) arrive step 2g) obtained parameter, calculate extension dbjective state and measurement noise covariance Joint probability assumes density v_k|k-1(x,R)：

v_k|k-1(x, R)=v_S,k|k-1(x,R)+b_k|k-1(x,R)+γ_k(x,R)。

Step 3, in k >=1, pair potential distribution P_k-1|k-1(num) it is predicted, obtains prediction gesture distribution P_k|k-1(num)：

Wherein, P_birth,k(num-j) probability of k-1 moment to k moment newborn num-j extension target, p are represented_S,kRepresent The k moment extends the survival probability of target, P_k-1|k-1(h) represent to be carved with the h probability for extending target during k-1,！Represent factorial, Represent to be carved with the probability that j extension target is survived when the k-1 moment is to k, (1-p_S,k)^h-jRepresent to be carved with h-j when the k-1 moment is to k Extend the probability that target is withered away.

Step 4. pair extends dbjective state and measures the joint probability hypothesis density v of noise covariance_k|k-1(x, R) and prediction Gesture is distributed P_k|k-1(num) it is updated：

Joint probability 4a) is assumed into density v using variation Bayes VB methods_k|k-1(x, R) is approximately：

In formula, Q_x,k|k-1(x) it is the summation form of Gaussian Profile,

Q_R,k|k-1(R) it is the summation form of inverse Gamma distribution,

Wherein,Represent forecast power of i-th of Gaussian component k-th of moment, i=1 ..., J_k, J_kRepresent kth The individual moment extends the number of target Gaussian component, and N () represents Gaussian Profile,I-th obtained for k-th of moment prediction The average of individual Gaussian component,The covariance of i-th of the Gaussian component obtained for k-th of moment prediction；IG () represents inverse Gamma distribution,I-th of the constant factor against gamma component obtained for k-th of moment prediction,For k-th when I-th of iteration factor against gamma component that prediction is obtained is carved, l=1 ..., d, d represent to measure the dimension of noise covariance；

4b) utilize probability hypothesis density Q of the variation Bayes expectation maximization VBEM methods to extension dbjective state_x,k|k-1 (x) the probability hypothesis density Q of Gaussian component and measurement noise covariance in_R,k|k-1(R) the inverse gamma component in is iterated Update：

The constant factor of the inverse gamma component of (4b1) settingAnd iteration factor Wherein l=1 ..., d, d are the dimension for measuring noise covariance R；

(4b2) is calculated according to two factors of the inverse gamma component of setting and is measured noise covariance：

Wherein n=1 ..., N, N are maximum iteration, diag [...] table Show diagonalization element therein；

(4b3) is utilized and is measured noise covarianceCalculate updating factor

Wherein,Represent to measuring noise covariance matrixCarry out diagonal connection active cell W measurement number Matrix afterwards, blkdiag () expressions carry out diagonal connection to element therein, | W | represent active cell W measurement number Mesh；H_WRepresent to observing matrix H_kMatrix after vertical connection active cell W measurement number, Represent the observing matrix H at k moment_kTransposition；The extension target Gaussian component motion state that expression k-1 to the k moment is predicted Covariance,Representing matrix H_WTransposition；

(4b4) utilizes updating factorCalculate gain matrix

Wherein []^-1Represent to matrix inversion；

(4b5) utilizes gain matrixCalculate extension target Gaussian component motion stateIt is high with extension target This component motion state covariance

Wherein, I represents a unit matrix, z_WRepresent all measurements in some division unit W；

(4b6) extracts extension target Gaussian component motion statePositional information, the positional information is used Represent；

(4b7) utilizes the Gaussian component positional informationWith measurement noise covarianceCalculate and measure Y_n′By position PutThe probability γ of the Gaussian component generation at place_n′i：

Wherein, J_kRepresent extension target Gaussian component number, Y_n′Expression active cell W the n-th ' individual measurement, n '= 1,...,|W|；N () represents Gaussian Profile；π_iRepresent mixed coefficint,N_iRepresent by positionThe Gauss at place The effective dose detecting number that component is produced,

(4b8) is utilized and is measured Y_n′By positionThe probability γ of the Gaussian component generation at place_n′i, iteration, which updates, to be expanded Open up the positional information of target Gaussian component motion state

(4b9) utilizes the positional information for extending target Gaussian component motion stateMixed coefficint π_i, measure noise CovarianceCalculate maximum likelihood function L⁽ⁱ⁾⁽ⁿ⁾：

Wherein J_kRepresent extension target Gaussian component number；

(4b10) judges | L⁽ⁱ⁾⁽ⁿ⁾-L^(i)(n-1)| whether less than constant ε=0.01, while whether judging current iteration frequency n Less than maximum iteration N=100, if it is, stopping iteration；Otherwise, return to step (4b2), updates inverse gamma component and changes For the factor：

Wherein,Represent to vectorMiddle all elements are added,

Represent to tie up element to the jth of vector Square, ()_jjExpression takes the diagonal entry of matrix,Represent to iteration factorVertical connection active cell W's The vector after number is measured,z_WRepresent the measurement of active cell；

(4b11) extracts extension dbjective state componentExtend target state covarianceIteration factor That is,Wherein extend dbjective state componentIn positional information use Be iteration updates obtained extension target component motion state in step (4b8) positional information

4c) pair potential distribution P_k|k-1(num) it is updated, the gesture distribution P after being updated_k|k(num) it is expressed as follows：

Wherein, p ∠ Z represent to be divided into p nonvoid subset collection Z is measured, and W ∈ p represent a certain under p-th of nonvoid subset Individual unit, G_k|k-1(ρ) represents status predication probability generating function,Represent the num of status predication probability generating function Rank local derviation, G_FA(0) false-alarm probability generating function when representing not measure, η W represent that extension target produces measurement probability, | p | table Show all non-NULL number of unit under p-th of division,Represent false-alarm probability generating function | W | rank local derviation, δ_num≥|p| Represent when target numbers num be more than division unit | p | when value be 1, be otherwise 0, | Z |=0 represent extend target do not produce Measure, | W | represent the measurement number in each non-dummy cell W, l_p,WRepresent that measuring division unit is | p | false-alarm constant coefficient when -1, ψ_p,WRepresent that target produces the product of measurement probability, ρ represents to extend the probability that target component is not detected：

Wherein, Π multiplies symbol to connect,Represent that j-th of Gauss divides against gamma component in current all Gausses against gamma Shared proportion, p in amount_k|k-1Represent single extension dbjective state probability density function, p_z(z ' |) represents extension aim parameter Survey likelihood, p_FA(z ') represents that false-alarm measures likelihood, G_z(0 |) represents measurement probability generating function,Represent to measure Probability generating function | W | rank local derviation, z ' ∈ W represent that measuring z ' belongs to unit W, P_D() represents detection probability, W ' ∈ p-W tables Show p divide under remaining unit after removing unit W in all units, η W ' expressions extension target false-alarm, which is measured, produces probability,Represent status predication probability generating function | p | rank local derviation,Represent status predication probability generating function | p | -1 rank local derviation.

Gaussian component and inverse gamma component after step 5. pair renewal are trimmed with being merged, and its step is as follows：

(5a) sets two trimming thresholdings T1 and T2, and one merges thresholding U：T1=10^-5, T2=120, U=10；Set most Big Gauss is against gamma component number：J_max=100；

(5b) calculates the corresponding measurement noise covariance of each extension target component:

(5c) sets variable l '=0, and the extension target component after renewal is trimmed, the extension target point after being trimmed Measuring corresponding sequence number set I is：

(5d) makes l '=l '+1, takesExpression takes maximum weightsCorresponding collection Element i ' in I is closed, the component that thresholding U is merged to being met in the extension target component after trimming is extracted, obtain being adapted to merging The corresponding sequence number set of extension target componentFor：

(5e) is respectively to sequence number setIn it is corresponding extension target component weightsMotion stateConstant because SonIteration factorCovarianceMerge, the weights of the extension target component after being mergedMove shape StateConstant factorIteration factorCovarianceIt is as follows：

Obtained in the corresponding sequence number set I of extension target component after the trimming that (5f) obtains step (5c) with step (5d) The corresponding sequence number set of extension target component for the suitable merging arrivedMiddle identical element is got rid of, and is then judged after trimming Extend whether the corresponding sequence number set I of target component is empty set, if not being empty set, return to step (5d) is otherwise performed (5g)；

Whether (5g) judgment variable l ' is more than largest Gaussian one against gamma component number J_maxIf, l ' ＞ J_max, then by weightsCorresponding Gauss by arranging from big to small, and takes preceding J against gamma component_maxIndividual weightsGauss more than 0.5 is against gamma The position of component and speed are used as the state for extending target；If l ' ＜ J_max, then by all weightsIt is corresponding more than 0.5 Gauss is used as the state for extending target against the position of gamma component and speed.

Step 6. is according to step 4c) update obtained gesture distribution P_k|k(num) it is weighted averagely, be expanded target Number：

The tracking to extending target can be completed after the state and number of the target that is expanded.

The effect that the present invention is used to track extension target can be further illustrated by following emulation experiment：

1. simulated conditions

Consider to do 4 targets of linear uniform motion in two dimensional surface, and occur what movement locus intersected two positions Situation, the sampling period isWhole observation process continues 40 moment, and the equation of motion and measurement equation of target are respectively：

x_k=Fx_k-1+Gw_k

y_k=Hx_k+v_k

Wherein, Gaussian noise w_kStandard deviation sigma_w=2.Extend dbjective state transfer matrix F, input matrix G, Gaussian noise w_k, observing matrix H is set to：

Noise v is measured in realistic objective tracking scene_kCovariance be unknown, real measure is set in this experiment and is made an uproar Sound standard deviation sigma_v=1；

If it is respectively σ=0.05,1,50 that three used in Traditional GM-CPHD algorithms, which measure noise criteria difference,；

If target yield detecting number obeys Poisson distribution, Parameter for Poisson Distribution β=20, target produces adjustment location and obeyed Gaussian Profile；

If target survival probability p_S,k=0.99, detection probability p_D,k=0.98；

If clutter number obeys the Poisson distribution that average is 5, clutter is obeyed in whole observation area and is uniformly distributed.

The state for setting newborn target isNewborn target Covariance is P_γ=diag [10,10,10,10]；

Trimming thresholding T1=10 is set^-5, thresholding T2=120 is trimmed, merges thresholding U=10, largest Gaussian one is against gamma component Number J_max=100, forgetting factor ρ=0.9, experiment simulation number of times is 100 times.

2. emulation content and result

Emulation 1, using single experiment of the inventive method to extension target trajectory under unknown measurement noise covariance It is tracked, as a result as shown in Figure 2.Figure it is seen that the inventive method can be very good tracking extension target motion rail Mark.

Emulation 2, using the inventive method and traditional three GM-CPHD sides that different measurement noise covariances are respectively adopted Method carries out the target numbers estimation contrast of 100 experiments, as a result as shown in Figure 3.From figure 3, it can be seen that the inventive method and biography GM-CPHD methods under the given actual measurements noise covariance of system are equally good to the estimation effect of target numbers.But, pass The GM-CPHD methods of system, when measure noise covariance it is unknown when, and the measurement noise covariance used and actual value deviation ratio compared with When big, very big deviation can occur for the target numbers of estimation, while in k=20, the two target trajectories of k=35 are handed over The moment is pitched, missing inspection occur in target numbers；

Emulation 3, using the inventive method and traditional three GM-CPHD sides that different measurement noise covariances are respectively adopted The tracking accuracy that method carries out 100 experiments by OSPA distances is contrasted, as a result as shown in Figure 4.From fig. 4, it can be seen that of the invention Method is good as the tracking accuracy of the GM-CPHD algorithms under traditional given actual measurements noise covariance.But, tradition GM-CPHD methods, when the measurement noise covariance that uses with it is real measure noise covariance deviation ratio it is larger when, tracking essence Degree can become very poor.

Experiment shows that the inventive method measures the extension target following scene under noise covariance is unknown condition in processing When, its tracking effect is better than traditional GM-CPHD extension method for tracking target.

Claims

1. a kind of extension method for tracking target based on variation Bayes's expectation maximization, comprises the following steps：

(1) in moment k=0, initialization extension dbjective state and the joint probability hypothesis density for measuring noise covariance are v₀ (x,R)；

(2) in k >=1, density v is assumed to extension dbjective state and the joint probability for measuring noise covariance_k-1|k-1(x, R) and Gesture for calculating extension target numbers is distributed P_k-1|k-1(num) it is predicted, the extension target joint probability predicted is false If density v_k|k-1(x, R) and prediction gesture distribution P_k|k-1(num)；

(3) extension dbjective state and the joint probability of measurement noise covariance to prediction assumes density v_k|k-1(x, R) and it is used for Calculate the gesture distribution P of extension target numbers_k|k-1(num) it is updated：

(3a) is using variation Bayes VB methods to joint probability hypothesis density v_k|k-1(x, R) approximately, obtain with Gauss point The probability hypothesis density Q for the extension dbjective state that the summation form of cloth is represented_x,k|k-1(x) and with the summation form of inverse Gamma distribution The probability hypothesis density Q of the measurement noise covariance of expression_R,k|k-1(R)；

(3b) utilizes probability hypothesis density Q of the variation Bayes expectation maximization VBEM methods to extension dbjective state_x,k|k-1(x) In Gaussian component and measure noise covariance probability hypothesis density Q_R,k|k-1(R) the inverse gamma component in is iterated more Newly, obtain representing extension target state x Gaussian component and represent to measure noise covariance R inverse gamma component：

The constant factor of the inverse gamma component of (3b1) settingAnd iteration factor Wherein l=1 ..., d, d are the dimension for measuring noise covariance R；

(3b2) is calculated according to two factors of inverse gamma component of setting and is measured noise covariance：Wherein n=1 ..., N, N are maximum iteration, and diag [...] represents diagonalization Element therein；

(3b3) is utilized and is measured noise covarianceCalculate updating factor

Wherein,Represent to measuring noise covariance matrixCarry out diagonal connection active cell W and measure the square after number Battle array, blkdiag () expressions carry out diagonal connection to element therein, | W | represent active cell W measurement number；H_WTable Show to observing matrix H_kMatrix after vertical connection active cell W measurement number, Represent The observing matrix H at k moment_kTransposition；The extension target Gaussian component motion state association side that expression k-1 to the k moment is predicted Difference,Representing matrix H_WTransposition；

(3b4) utilizes updating factorCalculate gain matrix

Wherein []^-1Represent to matrix inversion；

(3b5) utilizes gain matrixCalculate extension target Gaussian component motion stateWith extension target Gaussian component Motion state covariance

(3b6) extracts extension target Gaussian component motion statePositional information, the positional information is usedRepresent；

(3b7) utilizes the Gaussian component positional informationWith measurement noise covarianceCalculate and measure Y_n′It is by positionThe probability γ of the Gaussian component generation at place_n′i：

<mrow> <msub> <mi>&gamma;</mi> <mrow> <msup> <mi>n</mi> <mo>&prime;</mo> </msup> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&pi;</mi> <mi>i</mi> </msub> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>Y</mi> <msup> <mi>n</mi> <mo>&prime;</mo> </msup> </msub> <mo>|</mo> <msubsup> <mi>m</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> </mrow> <mrow> <mo>&prime;</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>R</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>J</mi> <mi>k</mi> </msub> </munderover> <msub> <mi>&pi;</mi> <mi>i</mi> </msub> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>Y</mi> <msup> <mi>n</mi> <mo>&prime;</mo> </msup> </msub> <mo>|</mo> <msubsup> <mi>m</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> </mrow> <mrow> <mo>&prime;</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>R</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>

Wherein, J_kRepresent extension target Gaussian component number, Y_n′Represent active cell W the n-th ' it is individual measure, n '=1 ..., | W |；N () represents Gaussian Profile；π_iRepresent mixed coefficint,N_iRepresent by positionThe Gaussian component at place is produced Effective dose detecting number,

(3b8) is utilized and is measured Y_n′By positionThe probability γ of the Gaussian component generation at place_n′i, iteration, which updates, to be expanded target The positional information of Gaussian component motion state

<mrow> <msubsup> <mi>m</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> </mrow> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>N</mi> <mi>i</mi> </msub> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <msup> <mi>n</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mo>|</mo> <mi>W</mi> <mo>|</mo> </mrow> </munderover> <msub> <mi>&gamma;</mi> <mrow> <msup> <mi>n</mi> <mo>&prime;</mo> </msup> <mi>i</mi> </mrow> </msub> <msub> <mi>Y</mi> <msup> <mi>n</mi> <mo>&prime;</mo> </msup> </msub> <mo>;</mo> </mrow>

(3b9) utilizes the positional information for extending target Gaussian component motion stateMixed coefficint π_i, measure noise covarianceCalculate maximum likelihood function L⁽ⁱ⁾⁽ⁿ⁾：

Wherein J_kRepresent extension target Gaussian component number；

(3b10) judges whether current iteration frequency n is less than maximum iteration N=100, and current iteration frequency n is not less than maximum Iterations N=100, then stop iteration, and current iteration frequency n is less than maximum iteration N=100, and | L⁽ⁱ⁾⁽ⁿ⁾-L^(i)(n-1) | less than constant ε=0.01, then stop iteration, otherwise return to step (3b2), update inverse gamma component iteration factor：

Wherein,Represent to vectorMiddle all elements are added, Represent square to the jth dimension element of vector, ()_jjExpression takes the diagonal entry of matrix,Represent to iteration factorVertical connection active cell W measures the vector after number,

(3b11) extracts extension dbjective state componentExtend target state covarianceIteration factorThat is,Wherein extend dbjective state componentIn positional information be Iteration updates the positional information of obtained extension target component motion state in step (3b8)

(4) Gaussian component after renewal and inverse gamma component are trimmed with being merged, and extract the Gaussian component after merging with The position of inverse gamma component and speed are used as the state for extending target；

(6) repeat step (2)-(5), continue to track extension target.

2. the extension method for tracking target according to claim 1 based on variation Bayes's expectation maximization, wherein, step Utilization variation Bayes VB methods described in (3a) are to joint probability hypothesis density v_k|k-1(x, R) is carried out approximately, as follows Carry out：

<mrow> <msub> <mi>Q</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>J</mi> <mi>k</mi> </msub> </munderover> <mo>&lsqb;</mo> <msubsup> <mi>w</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mi>N</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>;</mo> <msubsup> <mi>m</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>P</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow>

<mrow> <msub> <mi>Q</mi> <mrow> <mi>R</mi> <mo>,</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>J</mi> <mi>k</mi> </msub> </munderover> <mo>&lsqb;</mo> <munderover> <mo>&Pi;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>d</mi> </munderover> <mi>I</mi> <mi>G</mi> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>l</mi> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>;</mo> <msubsup> <mi>&alpha;</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>l</mi> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>&beta;</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>l</mi> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow>

Wherein, Q_x,k|k-1(x) it is the summation form of Gaussian Profile, is expressed as

Q_R,k|k-1(R) it is the summation form of inverse Gamma distribution, is expressed as

<mrow> <msub> <mi>Q</mi> <mrow> <mi>R</mi> <mo>,</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>J</mi> <mi>k</mi> </msub> </munderover> <mo>&lsqb;</mo> <munderover> <mo>&Pi;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>d</mi> </munderover> <mi>I</mi> <mi>G</mi> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>l</mi> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>;</mo> <msubsup> <mi>&alpha;</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>l</mi> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>&beta;</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>l</mi> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>;</mo> </mrow>

Represent weights of i-th of Gaussian component k-th of moment, i=1 ..., J_k, J_kRepresent k-th of moment extension target The number of Gaussian component, N () represents Gaussian Profile,The equal of i-th obtained of Gaussian component is predicted for k-th of moment Value,The covariance of i-th of the Gaussian component obtained for k-th of moment prediction；IG () represents inverse Gamma distribution, I-th of the constant factor against gamma component obtained for k-th of moment prediction,I-th obtained for k-th of moment prediction The iteration factor of individual inverse gamma component, l=1 ..., d, d represent to measure the dimension of noise covariance.

3. the extension method for tracking target according to claim 1 based on variation Bayes's expectation maximization, wherein, it is described Step (3c) pair potential is distributed P_k|k-1(num) it is updated, the gesture distribution P after being updated_k|k(num) it is expressed as follows：

<mrow> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mo>&Sigma;</mo> <mrow> <mi>p</mi> <mo>&angle;</mo> <mi>Z</mi> </mrow> </msub> <msub> <mo>&Sigma;</mo> <mrow> <mi>W</mi> <mo>&Element;</mo> <mi>p</mi> </mrow> </msub> <msub> <mi>&psi;</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>W</mi> </mrow> </msub> <msubsup> <mi>G</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>G</mi> <mrow> <mi>F</mi> <mi>A</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mfrac> <mrow> <mi>&eta;</mi> <mi>W</mi> </mrow> <mrow> <mo>|</mo> <mi>p</mi> <mo>|</mo> </mrow> </mfrac> <mfrac> <msup> <mi>&rho;</mi> <mrow> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>-</mo> <mrow> <mo>|</mo> <mi>P</mi> <mo>|</mo> </mrow> </mrow> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>-</mo> <mo>|</mo> <mi>p</mi> <mo>|</mo> <mo>)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> </mtd> <mtd> <msub> <mi>&delta;</mi> <mrow> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>&GreaterEqual;</mo> <mrow> <mo>|</mo> <mi>p</mi> <mo>|</mo> </mrow> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msubsup> <mi>G</mi> <mrow> <mi>F</mi> <mi>A</mi> </mrow> <mrow> <mo>(</mo> <mo>|</mo> <mi>W</mi> <mo>|</mo> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mfrac> <msup> <mi>&rho;</mi> <mrow> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>-</mo> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>-</mo> <mo>|</mo> <mi>p</mi> <mo>|</mo> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> </mtd> <mtd> <msub> <mi>&delta;</mi> <mrow> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>&GreaterEqual;</mo> <mrow> <mo>|</mo> <mi>p</mi> <mo>|</mo> </mrow> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> <mrow> <msub> <mo>&Sigma;</mo> <mrow> <mi>p</mi> <mo>&angle;</mo> <mi>Z</mi> </mrow> </msub> <msub> <mo>&Sigma;</mo> <mrow> <mi>W</mi> <mo>&Element;</mo> <mi>p</mi> </mrow> </msub> <msub> <mi>&psi;</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>W</mi> </mrow> </msub> <msub> <mi>l</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>W</mi> </mrow> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mrow> <mo>|</mo> <mi>Z</mi> <mo>|</mo> </mrow> <mo>&NotEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msup> <mi>&rho;</mi> <mrow> <mi>n</mi> <mi>u</mi> <mi>m</mi> </mrow> </msup> <msubsup> <mi>G</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>&rho;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> <mtd> <mrow> <mrow> <mo>|</mo> <mi>Z</mi> <mo>|</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

Wherein, p ∠ Z represent to be divided into p nonvoid subset collection Z is measured, and W ∈ p represent some list under p-th of nonvoid subset Member, G_k|k-1(ρ) represents status predication probability generating function,Represent that the num ranks of status predication probability generating function are inclined Lead, G_FA(0) false-alarm probability generating function when not measuring is represented, η W represent that extension target produces measurement probability, | p | represent the All non-NULL number of unit under p division,Represent false-alarm probability generating function | W | rank local derviation, δ_num≥|p|Represent When target numbers num be more than division unit | p | when value be 1, be otherwise 0, | Z |=0 represent extension target do not produce measurement, | W | represent the measurement number in each non-dummy cell W, l_p,WRepresent that measuring division unit is | p | false-alarm constant coefficient when -1, ψ_p,WTable Show that target produces the product of measurement probability, ρ represents to extend the probability that target component is not detected：

<mrow> <mi>&rho;</mi> <mo>=</mo> <mo>&Sigma;</mo> <msubsup> <mover> <mi>&omega;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> <mo>&lsqb;</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mo>&CenterDot;</mo> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>P</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mo>&CenterDot;</mo> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>|</mo> <mo>&CenterDot;</mo> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow>

<mrow> <mi>&eta;</mi> <mi>W</mi> <mo>=</mo> <msub> <mi>p</mi> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&lsqb;</mo> <msub> <mi>P</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mo>&CenterDot;</mo> <mo>)</mo> </mrow> <msubsup> <mi>G</mi> <mi>z</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>W</mi> <mo>|</mo> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mn>0</mn> <mo>|</mo> <mo>&CenterDot;</mo> <mo>)</mo> </mrow> <munder> <mo>&Pi;</mo> <mrow> <msup> <mi>z</mi> <mo>&prime;</mo> </msup> <mo>&Element;</mo> <mi>W</mi> </mrow> </munder> <mfrac> <mrow> <msub> <mi>p</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>z</mi> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>&CenterDot;</mo> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>p</mi> <mrow> <mi>F</mi> <mi>A</mi> </mrow> </msub> <mrow> <mo>(</mo> <msup> <mi>z</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&rsqb;</mo> </mrow>

<mrow> <msub> <mi>&psi;</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>W</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>&Pi;</mo> <mrow> <msup> <mi>W</mi> <mo>&prime;</mo> </msup> <mo>&Element;</mo> <mi>p</mi> <mo>-</mo> <mi>W</mi> </mrow> </munder> <msup> <mi>&eta;W</mi> <mo>&prime;</mo> </msup> </mrow>

Wherein, Π multiplies symbol to connect,Represent j-th of Gauss against gamma component in current all Gausses against institute in gamma component The proportion accounted for, p_k|k-1Represent single extension dbjective state probability density function, p_z(z ' |) represents that extension target is measured seemingly So, p_FA(z ') represents that false-alarm measures likelihood, G_z(0 |) represents measurement probability generating function,Represent measurement probability life Into function | W | rank local derviation, z ' ∈ W represent that measuring z ' belongs to unit W, P_D() represents detection probability, and W ' ∈ p-W represent that p is drawn Remaining unit after removing unit W in all units under point, η W ' expressions extension target false-alarm, which is measured, produces probability,Table Show status predication probability generating function | p | rank local derviation,Represent status predication probability generating function | p | -1 rank is inclined Lead.

4. the extension method for tracking target according to claim 1 based on variation Bayes's expectation maximization, wherein, step (4) being trimmed the Gaussian component after renewal and inverse gamma component with being merged described in, is carried out as follows：

(4a) sets two trimming thresholdings T1 and T2, and one merges thresholding U：T1=10^-5, T2=120, U=10；Set maximum high This is against gamma component number：J_max=100；

(4b) calculates the corresponding measurement noise covariance of each extension target component:

(4c) sets variable l '=0, and the extension target component after renewal is trimmed, the extension target component pair after being trimmed The sequence number set I answered is：

(4d) makes l '=l '+1, takesExpression takes maximum weightsIn corresponding set I Element i ', the component that thresholding U is merged to being met in the extension target component after trimming is extracted, and obtains being adapted to the extension of merging The corresponding sequence number set of target componentFor：

(4e) is respectively to sequence number setIn it is corresponding extension target component weightsMotion stateConstant factor Iteration factorCovarianceMerge, the weights of the extension target component after being mergedMotion state Constant factorIteration factorCovarianceIt is as follows：

<mrow> <msubsup> <mover> <mi>w</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>&Element;</mo> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> </mrow> </munder> <msubsup> <mi>w</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> </mrow>

<mrow> <msubsup> <mover> <mi>m</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <msubsup> <mover> <mi>w</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> </mfrac> <munder> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>&Element;</mo> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> </mrow> </munder> <msubsup> <mi>w</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>m</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> </mrow>

<mrow> <msubsup> <mover> <mi>&alpha;</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <msubsup> <mover> <mi>w</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> </mfrac> <munder> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>&Element;</mo> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> </mrow> </munder> <msubsup> <mi>w</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> </mrow>

<mrow> <msubsup> <mover> <mi>&beta;</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <msubsup> <mover> <mi>w</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> </mfrac> <munder> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>&Element;</mo> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> </mrow> </munder> <msubsup> <mi>w</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>&beta;</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> </mrow>

<mrow> <msubsup> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <msubsup> <mover> <mi>w</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> </mfrac> <munder> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>&Element;</mo> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> </mrow> </munder> <msubsup> <mi>w</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <mo>(</mo> <mrow> <msubsup> <mover> <mi>m</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>m</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mover> <mi>m</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mi>l</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>m</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>)</mo> </mrow> <mo>;</mo> </mrow>

Obtained in the corresponding sequence number set I of extension target component after the trimming that (4f) obtains step (4c) with step (4d) It is adapted to the corresponding sequence number set of extension target component mergedMiddle identical element is got rid of, and then judges the extension after trimming Whether the corresponding sequence number set I of target component is empty set, the return to step (4d) if being not empty set, otherwise performs (4g)；

Whether (4g) judgment variable l ' is more than largest Gaussian one against gamma component number J_maxIf, l ' ＞ J_max, then by weightsIt is right The Gauss answered by arranging from big to small, and takes preceding J against gamma component_maxIndividual weightsGauss more than 0.5 is against gamma component Position and speed are used as the state for extending target；If l ' ＜ J_max, then by all weightsMore than 0.5 corresponding Gauss against gal The position of agate component and speed are used as the state for extending target.