CN104794735A - Extended target tracking method based on variational Bayesian expectation maximization - Google Patents

Abstract

The invention discloses an extended target tracking method based on variational Bayesian expectation maximization (VBEM) and mainly solves the problem that tracking performance of a target is weakened dramatically under the condition that measurement noise covariance is unknown in the conventional extended target tracking field. The extended target tracking method includes firstly predicting relevant parameters of Gaussian inverse gamma components in joint probability hypothesis density of a target state and the measurement noise covariance; updating the parameters of the Gaussian inverse gamma components; finally acquiring the extended target state and the number by construction and combination. It is proved by simulation experiment that multiple extended targets can be well tracked under the unknown number and the unknown measurement noise covariance, and the extended target tracking method is high in tracking accuracy and can be used for tracking aircrafts and submarine targets.

Description

Based on the Extended target tracking of variation Bayes expectation maximization

Technical field

The invention belongs to technical field of information processing, particularly a kind of method for tracking target, can be used for following the tracks of many Extended target.

Background technology

In traditional target tracking domain, due to the limited resolution of radar, therefore regard target as point target under normal circumstances, namely moment each target can only produce a measurement.In recent years, along with the development of the radar exploration technique and the needs of practical application, more target is considered as Extended target, namely each target can produce multiple measurement in each moment.

In actual target following scene, the number of target cannot be predicted in advance, and therefore the proposition of random set theory meets the needs of target following theory greatly.In the model hypothesis of all multipair targets, the needs following the tracks of theory are at present pressed close in the proposition especially belonging to Extended target theory more, and are widely used in real life, nearly ten years, become the study hotspot in target tracking domain.2003, stochastic finite collection theory was applied to multiple target tracking problem by Mahler, proposed probability hypothesis density PHD filtering.2005, Gilholm and Salmond proposed the Extended target model that a kind of space distribution obeys Poisson distribution.2009, Mahler was deduced Extended target PHD filtering, namely predicted with the measurement random set in each moment target random set, upgraded, then accurately can extract the motion state of target and the number of estimating target.2010, etc. the Gaussian Mixture way of realization giving Extended target PHD.2011, Orguner etc. also been proposed Extended target PHD (ET-CPHD) filtering of band gesture distribution, well solve defect during ET-PHD estimating target number.But, traditional Extended target track algorithm process be all measurement noise covariance be known situation, in reality when measuring noise covariance and being unknown, the tracking performance of Extended target will sharply decline.

Summary of the invention

The object of the invention is to for the problems referred to above, propose a kind of Extended target tracking based on variation Bayes expectation maximization, to improve the tracking performance under measurement noise covariance unknown condition.

Realizing key problem in technology of the present invention is: under gesture probability hypothesis density filter frame, introduce variation Bayes expectation maximization VBEM technology, the joint probability assumed density of estimating target state and measurement noise covariance, realizes the Target Tracking Problem under unknown measurement noise covariance.

VB is the method for a class for the complicated integration of approximate treatment in Bayesian Estimation and machine learning field, VB is used in approximately linear Gaussian Systems herein, the joint probability assumed density of Extended target state and measurement noise covariance, the main thought of this algorithm carries out parametrization to the joint probability assumed density of Extended target state and measurement noise covariance to be similar to, and provide its Parameter Expression form.In process that the joint probability assumed density of Extended target state and measurement noise covariance be similar to theoretical with VB, in order to judge the performance of estimated Gauss against gamma component correlation parameter, the basis of VB in turn introduces expectation maximization EM algorithm.In expectation E step, estimate the expectation value of unknown parameter, provide current parameter estimation; In maximization M step, reappraise distribution parameter, reach maximum to make this likelihood function.The estimates of parameters that M step obtains is used to next E and walks calculating, and this process constantly hockets.This method can be widely used in the situation that data have defect, and has the advantage such as simplicity and stability.

The technical step that the present invention utilizes above-mentioned VBEM technology to carry out Extended target tracking comprises as follows:

(1) when moment k=0, the joint probability assumed density of initialization Extended target state and measurement noise covariance is v ₀(x, R);

(2) when k>=1, to the joint probability assumed density v of Extended target state and measurement noise covariance _k-1|k-1(x, R) and the gesture distribution P for calculating Extended target number _k-1|k-1(num) predict, obtain the Extended target joint probability assumed density v predicted _k|k-1(x, R) and prediction gesture distribution P _k|k-1(num);

(3) to the Extended target state of prediction and the joint probability assumed density v of measurement noise covariance _k|k-1(x, R) and the gesture distribution P for calculating Extended target number _k|k-1(num) upgrade:

(3a) utilize variation Bayes VB method to associating probability hypothesis density v _k|k-1(x, R) is similar to, and obtains the probability hypothesis density Q of the Extended target state represented by the summation form of Gaussian distribution _{x, k|k-1}(x) and the probability hypothesis density Q of measurement noise covariance represented by the summation form of inverse Gamma distribution _{r, k|k-1}(R);

(3b) utilize variation Bayes expectation maximization VBEM method to the probability hypothesis density Q of Extended target state _{x, k|k-1}the probability hypothesis density Q of the gaussian component in (x) and measurement noise covariance _{r, k|k-1}(R) the inverse gamma component in carries out iteration renewal, obtains representing the gaussian component of Extended target motion state x and representing the inverse gamma component of measurement noise covariance R;

(3c) step (2) is predicted to the gesture distribution P obtained _k|k-1(num) upgrade, obtain the gesture distribution P after upgrading _k|k(num);

(4) gaussian component after upgrading and inverse gamma component are carried out pruning and merged, and the gaussian component extracted after merging and against state as Extended target of the position of gamma component and speed;

(5) step (3) is upgraded to the gesture distribution P obtained _k|k(num) be weighted on average, the number of the target that is expanded: ${\mathrm{num}}_{k|k}=\underset{\mathrm{num}=1}{\overset{\∞}{\mathrm{\Σ}}}\mathrm{num}\×p_{k|k}\left(\mathrm{num}\right);$

(6) repeat step (2)-(5), continue to follow the tracks of Extended target.

The present invention has the following advantages:

First, invention introduces variation Bayes EM technology, by estimating the joint probability assumed density of Extended target state and measurement noise covariance, effectively have estimated each target at not actual measurements noise in the same time, the analysis following the tracks of scene for Extended target many under complex environment provides help, ensure that CPHD filtering algorithm can realize following the tracks of Extended target under the unknown measurement noise covariance environment effectively.

Second, the present invention first predicts the correlation parameter of Gauss against gamma component owing to adopting, again Gauss is upgraded against gamma component parameters, finally by pruning the process with the tracking Extended target merging be expanded dbjective state and number, compared with traditional GM-CPHD filtering algorithm, improve tracking accuracy.

Accompanying drawing explanation

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

Fig. 2 is under single experiment condition, follows the tracks of the simulation result figure of Extended target by the inventive method;

Fig. 3 is under 100 experiment conditions, with the simulation result comparison diagram of the inventive method and Traditional GM-CPHD method estimating target number;

Fig. 4 is under 100 experiment conditions, judges the simulation result comparison diagram of target tracking accuracy by the inventive method and Traditional GM-CPHD method by OSPA distance.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described.

With reference to Fig. 1, specific implementation step of the present invention comprises as follows:

Step 1, when moment k=0, the joint probability assumed density of initialized target state and measurement noise covariance:

$v_0(x,R)=\underset{i=1}{\overset{J_0}{\mathrm{\Σ}}}\left[w_0^{\left(i\right)}N(x;m_0^{\left(i\right)},P_0^{\left(i\right)})\underset{l=1}{\overset{d}{\mathrm{\Π}}}\mathrm{IG}({\left({\mathrm{\σ}}_{0,l}^{\left(i\right)}\right)}^2;{\mathrm{\α}}_{0,l}^{\left(i\right)},{\mathrm{\β}}_{0,l}^{\left(i\right)})\right]$

Wherein, J ₀represent the number of gaussian component, represent the weights of i-th gaussian component, N () represents Gaussian distribution, represent the average of i-th gaussian component, represent the covariance of i-th gaussian component; IG () represents inverse Gamma distribution, represent the covariance of i-th inverse gamma component, be the constant factor of i-th inverse gamma component, be the iteration factor of i-th inverse gamma component, l represents the l dimension of measurement noise covariance, and d represents the dimension of measurement noise covariance.

Step 2, when k>=1, to the joint probability assumed density v of Extended target state and measurement noise covariance _k-1|k-1(x, R) predicts, obtains the Extended target joint probability assumed density v predicted _k|k-1(x, R).

2a) to the joint probability assumed density v of survive dbjective state and measurement noise covariance _{s, k|k-1}the average of gaussian component in (x, R) and covariance predict, obtain the average of the survival target gaussian component predicted and covariance

$m_{S,k|k-1}^{\left(i\right)}=F_{S,k-1}^{\left(i\right)}{m}_{S,k-1}^{\left(i\right)}$

$P_{S,k|k-1}^{\left(i\right)}=Q_{k-1}+F_{S,k-1}^{\left(i\right)}{P}_{S,k-1}^{\left(i\right)}{\left(F_{S,k-1}^{\left(i\right)}\right)}^T$

Wherein, represent survival dbjective state transition matrix, Q _k-1represent survival object procedure noise covariance, () ^trepresent transposition;

2b) to the joint probability assumed density v of survive dbjective state and measurement noise covariance _{s, k|k-1}the constant factor of inverse gamma component in (x, R) and iteration factor predict, obtain the constant factor of survival target against gamma component of prediction with the iteration factor of inverse gamma component

${\mathrm{\α}}_{S,k|k-1,l}^{\left(i\right)}={\mathrm{\ρ}}_l{\mathrm{\α}}_{S,k-1,l}^{\left(i\right)}$

${\mathrm{\β}}_{S,k|k-1,l}^{\left(i\right)}={\mathrm{\ρ}}_l{\mathrm{\β}}_{S,k-1,l}^{\left(i\right)}$

Wherein ρ _lrepresent forgetting factor, and ρ _l∈ (0,1];

2c) under Gaussian Mixture framework, utilize the average of the survival target gaussian component of prediction covariance with the constant factor of inverse gamma component iteration factor calculate the joint probability assumed density v of survival dbjective state and measurement noise covariance _{s, k|k-1}(x, R):

$v_{S,k|k-1}(x,R)=P_{S,k}\underset{i=1}{\overset{J_{k-1}}{\mathrm{\Σ}}}\left[w_{k-1}^{\left(i\right)}N(x;m_{S,k|k-1}^{\left(i\right)},P_{S,k|k-1}^{\left(i\right)})\underset{l=1}{\overset{d}{\mathrm{\Π}}}\mathrm{IG}({\left({\mathrm{\σ}}_{S,k|k-1}^{\left(i\right)}\right)}^2;{\mathrm{\α}}_{S,k|k-1,l}^{\left(i\right)},{\mathrm{\β}}_{S,k|k-1.l}^{\left(i\right)})\right]$

Wherein, P _s,krepresent Extended target survival probability, J _k-1represent the gaussian component number in k-1 moment, represent the weights of k-1 moment i-th gaussian component, N () represents Gaussian distribution, represent the survival dbjective state of prediction and the joint probability assumed density v of measurement noise covariance _{s, k|k-1}the average of i-th gaussian component in (x, R), represent the survival dbjective state of prediction and the joint probability assumed density v of measurement noise covariance _{s, k|k-1}the covariance of i-th gaussian component in (x, R); IG () represents inverse Gamma distribution, and d represents the dimension of measurement noise covariance, represent the survival dbjective state of prediction and the joint probability assumed density v of measurement noise covariance _{s, k|k-1}the constant factor of i-th inverse gamma component in (x, R), represent the survival dbjective state of prediction and the joint probability assumed density v of measurement noise covariance _{s, k|k-1}the iteration factor of i-th inverse gamma component in (x, R);

2d) to the joint probability assumed density b of derivative goal state and measurement noise covariance _k|k-1the average of gaussian component in (x, R) and covariance predict, obtain the average of the derivative goal gaussian component predicted and covariance

$m_{b,k|k-1}^{(i,j)}=F_{b,k-1}^{\left(j\right)}{m}_{b,k-1}^{(i,j)}+d_{b,k-1}^{\left(j\right)}$

$P_{b,k|k-1}^{(i,j)}=Q_{b,k-1}^{\left(j\right)}+F_{b,k-1}^{\left(j\right)}{P}_{b,k-1}^{\left(i\right)}{\left(F_{b,k-1}^{\left(j\right)}\right)}^T$

Wherein, i represents that k-1 moment Gauss is against i-th of gamma component, and j represents the Gauss that derived by k-1 moment to the k moment jth against gamma component, represent the state-transition matrix of derivative goal, represent the status maintenance positive quantity of derivative goal, represent derivative goal process noise covariance;

2e) to the joint probability assumed density b of derivative goal state and measurement noise covariance _k|k-1the constant factor of inverse gamma component in (x, R) and iteration factor predict, obtain the constant factor of derivative goal against gamma component of prediction and iteration factor

${\mathrm{\α}}_{b,k|k-1,l}^{(i,j)}={\mathrm{\ρ}}_l{\mathrm{\α}}_{b,k-1,l}^{\left(i\right)}$

${\mathrm{\β}}_{b,k|k-1,l}^{(i,j)}={\mathrm{\ρ}}_l{\mathrm{\β}}_{b,k-1,l}^{\left(i\right)};$

2f) under Gaussian Mixture framework, utilize the average of the derivative goal gaussian component of prediction covariance with the constant factor of inverse gamma component iteration factor calculate the joint probability assumed density b of derivative goal state and measurement noise covariance _k|k-1(x, R):

$b_{k|k-1}(x,R)=\underset{i=1}{\overset{J_{k-1}}{\mathrm{\Σ}}}\underset{j=1}{\overset{J_{b,k}}{\mathrm{\Σ}}}\left[w_{k-1}^{\left(i\right)}{w}_{b,k}^{\left(j\right)}N(x;m_{b,k|k-1}^{(i,j)},P_{b,k|k-1}^{(i,j)})\underset{l=1}{\overset{d}{\mathrm{\Π}}}\mathrm{IG}({\left({\mathrm{\σ}}_{b,k|k-1,l}^{(i,j)}\right)}^2;{\mathrm{\α}}_{b,k|k-1,l}^{(i,j)},{\mathrm{\β}}_{b,k|k-1,l}^{(i,j)})\right]$

Wherein, J _b,krepresent the derivative goal gaussian component number in k-1 moment to k moment, represent the weights of a k moment jth derivative goal gaussian component, represent that k-1 moment to the k moment derives by i-th gaussian component the average obtaining a jth gaussian component, represent that k-1 moment to the k moment derives by i-th gaussian component the covariance obtaining a jth gaussian component; represent that k-1 moment to the k moment is derived the constant factor obtaining a jth inverse gamma component by i-th inverse gamma component, represent that k-1 moment to the k moment is derived the iteration factor obtaining a jth inverse gamma component by i-th inverse gamma component;

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

${\mathrm{\γ}}_k(x,R)=\underset{i=1}{\overset{J_{\mathrm{\γ},k}}{\mathrm{\Σ}}}\left[w_{\mathrm{\γ}.k}^{\left(i\right)}N(x;m_{\mathrm{\γ},k}^{\left(i\right)},P_{\mathrm{\γ},k}^{\left(i\right)})\underset{l=1}{\overset{d}{\mathrm{\Π}}}\mathrm{IG}({\left({\mathrm{\σ}}_{\mathrm{\γ},k,l}^{\left(i\right)}\right)}^2;{\mathrm{\α}}_{\mathrm{\γ},k,l}^{\left(i\right)},{\mathrm{\β}}_{\mathrm{\γ},k,l}^{\left(i\right)})\right]$

Wherein, J _{γ, k}for k moment newborn target gaussian component number, for the weights for k moment newborn target i-th gaussian component, for the state average of newborn target i-th gaussian component, for the motion state covariance of newborn target i-th gaussian component; for the constant factor of the inverse gamma component of newborn target i-th, for the iteration factor of the inverse gamma component of newborn target i-th.

2h) utilize step 2a) to step 2g) parameter that obtains, calculate the joint probability assumed density v of Extended target state and measurement noise covariance _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, when k>=1, pair potential distribution P _k-1|k-1(num) predict, obtain prediction gesture distribution P _k|k-1(num):

$P_{k|k-1}\left(\mathrm{num}\right)=\underset{j=0}{\overset{\mathrm{num}}{\mathrm{\Σ}}}{P}_{\mathrm{birth},k}(\mathrm{num}-j)\underset{h=j}{\overset{\∞}{\mathrm{\Σ}}}\frac{h!}{j!(h-j)!}{P}_{k-1|k-1}\left(h\right)p_{S,k}^j{\left({1-p}_{S,k}\right)}^{h-j}$

Wherein, P _{birth, k}(num-j) probability of k-1 moment to k moment newborn num-j Extended target is represented, p _s,krepresent the survival probability of k moment Extended target, P _k-1|k-1the probability of h Extended target is carved with when () represents k-1 h,! Represent factorial, represent that the k-1 moment is to the probability being carved with j Extended target survival during k, (1-p _s,k) ^h-jrepresent that the k-1 moment is to the probability being carved with h-j Extended target extinction during k.

The joint probability assumed density v of step 4. pair Extended target state and measurement noise covariance _k|k-1(x, R) and prediction gesture distribution P _k|k-1(num) upgrade:

4a) utilize variation Bayes VB method by joint probability assumed density v _k|k-1(x, R) is approximately:

In formula, Q _{x, k|k-1}x summation form that () is Gaussian distribution,

Q _{r, k|k-1}(R) be the summation form of inverse Gamma distribution,

$Q_{R,k|k-1}\left(R\right)=\underset{i=1}{\overset{J_k}{\mathrm{\Σ}}}\left[\underset{l=1}{\overset{d}{\mathrm{\Π}}}\mathrm{IG}({\left({\mathrm{\σ}}_{k|k-1,l}^{\left(i\right)}\right)}^2;{\mathrm{\α}}_{k|k-1,l}^{\left(i\right)},{\mathrm{\β}}_{k|k-1,l}^{\left(i\right)})\right];$

Wherein, represent the forecast power of i-th gaussian component in a kth moment, i=1 ..., J _k, J _krepresent the number of a kth moment Extended target gaussian component, N () represents Gaussian distribution, for a kth moment predicts the average of i-th gaussian component obtained, for a kth moment predicts the covariance of i-th gaussian component obtained; IG () represents inverse Gamma distribution, for a kth moment predicts the constant factor of i-th the inverse gamma component obtained, for a kth moment predicts the iteration factor of i-th the inverse gamma component obtained, l=1 ..., d, d represent the dimension of measurement noise covariance;

4b) utilize variation Bayes expectation maximization VBEM method to the probability hypothesis density Q of Extended target state _{x, k|k-1}the probability hypothesis density Q of the gaussian component in (x) and measurement noise covariance _{r, k|k-1}(R) the inverse gamma component in carries out iteration renewal:

(4b1) constant factor of the inverse gamma component of setting and iteration factor wherein l=1 ..., d, d are the dimension of measurement noise covariance R;

(4b2) according to two factors of the inverse gamma component of setting, calculate and measure noise covariance:

wherein n=1 ..., N, N are maximum iteration time, and diag [...] represents diagonalization element wherein;

(4b3) measurement noise covariance is utilized calculate and upgrade the factor

$S_W^{\left(n\right)}=H_W{P}_{k|k-1}^{\left(i\right)}{H_W}^T+R_W^{\left(n\right)}$

Wherein, represent measurement noise covariance matrix carry out the matrix after the measurement number of diagonal line connection active cell W, blkdiag () expression carries out diagonal line connection to element wherein, | W| represents the measurement number of active cell W; H _wrepresent observing matrix H _kmatrix after the measurement number of vertical connection active cell W, represent the observing matrix H in k moment _ktransposition; represent the Extended target gaussian component motion state covariance that k-1 to the k moment is predicted, representing matrix H _wtransposition;

(4b4) the renewal factor is utilized calculated gains matrix

$K_k^{\left(i\right)\left(n\right)}=P_{k|k-1}^{\left(i\right)}{H}_W^T{\left[S_W^{\left(n\right)}\right]}^{-1}$

Wherein [] ^-1represent matrix inversion;

(4b5) gain matrix is utilized calculate Extended target gaussian component motion state with Extended target gaussian component motion state covariance

$m_{k|k}^{\left(i\right)\left(n\right)}=m_{k|k-1}^{\left(i\right)}+K_k^{\left(i\right)\left(n\right)}(z_W-H_W{m}_{k|k-1}^{\left(i\right)})$

$P_{k|k}^{\left(i\right)\left(n\right)}=[I-K_k^{\left(i\right)\left(n\right)}{H}_W]P_{k|k-1}^{\left(i\right)}$

Wherein, I represents a unit matrix, z _wrepresent all measurements in certain division unit W;

(4b6) Extended target gaussian component motion state is extracted positional information, this positional information is used represent;

(4b7) this gaussian component positional information is utilized with measurement noise covariance calculate and measure Y _{n '}by position the probability γ of the gaussian component generation at place _{n ' i}:

${\mathrm{\γ}}_{n^{\′}i}=\frac{{\mathrm{\π}}_{i}N\left(Y_{n^{\′}}\right|m_{k|k}^{\′\left(i\right)\left(n\right)},R_k^{\left(i\right)\left(n\right)})}{\underset{i=1}{\overset{J_k}{\mathrm{\Σ}}}{\mathrm{\π}}_{i}N\left(Y_{n^{\′}}\right|m_{k|k}^{\′\left(i\right)\left(n\right)},R_k^{\left(i\right)\left(n\right)})},$

Wherein, J _krepresent Extended target gaussian component number, Y _{n '}represent the n-th ' individual measurement of active cell W, n '=1 ..., | W|; N () represents Gaussian distribution; π _irepresent mixing constant, n _irepresent by position the effective dose detecting number of the gaussian component generation at place,

(4b8) measurement Y is utilized _{n '}by position the probability γ of the gaussian component generation at place _{n ' i}, iteration upgrades the positional information of the target gaussian component motion state that is expanded

$m_{k|k}^{\′\′\left(i\right)\left(n\right)}=\frac{1}{N_i}\underset{n^{\′}=1}{\overset{\left|W\right|}{\mathrm{\Σ}}}{\mathrm{\γ}}_{n^{\′}i}{Y}_{n^{\′}};$

(4b9) positional information of Extended target gaussian component motion state is utilized mixing constant π _i, measurement noise covariance calculate maximum likelihood function L ^{(i) (n)}:

$L^{\left(i\right)\left(n\right)}=\underset{n^{\′}=1}{\overset{\left|W\right|}{\mathrm{\Σ}}}\ln \underset{i=1}{\overset{J_k}{\mathrm{\Σ}}}{\mathrm{\π}}_{i}N\left(Y_{n^{\′}}\right|m_{k|k}^{\′\′\left(i\right)\left(n\right)},R_k^{\left(i\right)\left(n\right)}),$ Wherein J _krepresent Extended target gaussian component number;

(4b10) judge | L ^{(i) (n)}-L ^{(i) (n-1)}| whether be less than constant ε=0.01, judge whether current iteration frequency n is less than maximum iteration time N=100 simultaneously, if so, then stop iteration; Otherwise, return step (4b2), upgrade inverse gamma component iteration factor: ${\mathrm{\β}}_{k,1}^{\left(i\right)(n+1)}=\frac{\mathrm{\Σ}{\mathrm{\β}}_W^{(n+1)}}{d\left|W\right|},$

Wherein, represent vector middle all elements is added,

${\mathrm{\β}}_W^{(n+1)}={\mathrm{\β}}_W^{\left(n\right)}+\frac{1}{2}{(z_W-H_W{m}_{k|k}^{\left(i\right)\left(n\right)})}_j^2+\frac{1}{2}{\left(H_W{P}_{k|k}^{\left(i\right)\left(n\right)}{H}_W^T\right)}_{\mathrm{jj}},{(\·)}_j^2$ Represent to the jth of vector dimension element square, () _jjrepresent the diagonal entry getting matrix, represent iteration factor vector after the measurement number of vertical connection active cell W, z _wrepresent the measurement of active cell;

(4b11) Extended target state component is extracted extended target motion state covariance iteration factor that is, $m_{k|k}^{\left(i\right)}=m_{k|k}^{\left(i\right)\left(n\right)},P_{k|k}^{\left(i\right)}=P_{k|k}^{\left(i\right)\left(n\right)},{\mathrm{\β}}_{k,l}^{\left(i\right)}={\mathrm{\β}}_{k,l}^{\left(i\right)\left(n\right)},$ Wherein Extended target state component in positional information be the positional information that iteration upgrades the Extended target component motion state obtained in step (4b8)

4c) pair potential distribution P _k|k-1(num) upgrade, obtain the gesture distribution P after upgrading _k|k(num) be expressed as follows:

$P_{k|k}\left(\mathrm{num}\right)=\left\{\begin{array}{cc}\frac{{\mathrm{\Σ}}_{p\∠Z}{\mathrm{\Σ}}_{W\∈p}{\mathrm{\ψ}}_{p,W}{G}_{k|k-1}^{\left(\mathrm{num}\right)}\left(0\right)\left(\begin{array}{c}{G}_{\mathrm{FA}}\left(0\right)\frac{\mathrm{\ηW}}{\left|p\right|}\frac{{\mathrm{\ρ}}^{\mathrm{num}-\left|P\right|}}{(\mathrm{num}-|p\left|\right)!}{\mathrm{\δ}}_{\mathrm{num}\≥\left|p\right|}\\ +G_{\mathrm{FA}}^{\left(\right|W\left|\right)}\left(0\right)\frac{{\mathrm{\ρ}}^{\mathrm{num}-p+1}}{(\mathrm{num}-|p|+1)!}{\mathrm{\δ}}_{\mathrm{num}\≥\left|p\right|-1}\end{array}\right)}{{\mathrm{\Σ}}_{p\∠Z}{\mathrm{\Σ}}_{W\∈p}{\mathrm{\Ψ}}_{p,W}{l}_{p,W}},& \left|Z\right|\≠0\\ \frac{{\mathrm{\ρ}}^{\mathrm{num}}{G}_{k|k-1}^{\left(\mathrm{num}\right)}\left(0\right)}{G_{k|k-1}\left(\mathrm{\ρ}\right)}& \left|Z\right|=0\end{array}\right.$

Wherein, p ∠ Z represents that measurement is collected Z is divided into p nonvoid subset, and W ∈ p represents the some unit under p nonvoid subset, G _k|k-1(ρ) status predication probability generating function is represented, represent the num rank local derviation of status predication probability generating function, G _fA(0) represent false-alarm probability generating function when not measuring, η W represents that Extended target produces measurement probability, | p| represents all non-NULL number of unit under p division, expression false-alarm probability generating function | W| rank local derviation, δ _{num>=| p|}representing when target numbers num is greater than division unit | during p|, value is 1, otherwise is 0, | Z|=0 represents that Extended target does not produce measurement, | W| represents the measurement number in each non-dummy cell W, l _p,Wrepresent that measuring division unit is | false-alarm constant coefficient during p|-1, ψ _p,Wrepresent that target produces the product of measurement probability, ρ represents the probability that Extended target component is not detected:

$\mathrm{\ρ}=\mathrm{\Σ}{\stackrel{\‾}{\mathrm{\ω}}}_{k|k-1}^j[1-P_D(\·)+P_D(\·)G_z\left(0\right|\·)]$

$\mathrm{\ηW}=p_{k|k-1}\left[P_D(\·)G_z^{\left(\right|W\left|\right)}\left(0\right|\·)\underset{z^{\′}\∈W}{\mathrm{\Π}}\frac{p_z\left(z^{\′}\right|\·)}{p_{\mathrm{FA}}\left(z^{\′}\right)}\right]$

$l_{p,W}=G_{\mathrm{FA}}\left(0\right)G_{k|k-1}^{\left(\right|p\left|\right)}\left(\mathrm{\ρ}\right)\frac{\mathrm{\ηW}}{\left|p\right|}+G_{\mathrm{FA}}^{\left(\right|W\left|\right)}\left(0\right)G_{k|k-1}^{\left(\right|p|-1)}\left(\mathrm{\ρ}\right)$

${\mathrm{\ψ}}_{p,W}=\underset{W^{\′}\∈p-W}{\mathrm{\Π}}{\mathrm{\ηW}}^{\′}$

Wherein, Π takes advantage of symbol for connecting, represent a jth Gauss against gamma component at the proportion shared by current all Gausses are in gamma component, p _k|k-1represent single Extended target state transition probability density function, p _z(z ' |) represent that Extended target measures likelihood, p _fA(z ') represents that false-alarm measures likelihood, G _z(0|) measurement probability generating function is represented, expression measurement probability generating function | W| rank local derviation, z ' ∈ W represents that measuring z ' belongs to unit W, P _d() represents detection probability, and W ' ∈ p-W represents that p divides unit remaining after removing unit W in lower all unit, and η W ' expression Extended target false-alarm measures and produces probability, expression status predication probability generating function | p| rank local derviation, expression status predication probability generating function | p|-1 rank local derviation.

Step 5. is carried out pruning to the gaussian component after renewal and inverse gamma component and merges, and its step is as follows:

(5a) arrange two and prune thresholding T1 and T2, one merges thresholding U:T1=10 ^-5, T2=120, U=10; Largest Gaussian one is set against gamma component number: J _max=100;

(5b) measurement noise covariance corresponding to each Extended target component is calculated:

(5c) establish variable l '=0, prune the Extended target component after upgrading, the sequence number set I obtaining the Extended target component after pruning corresponding is: $I=\{i=1,...,J_k|w_k^{\left(i\right)}>T1,{\left|\right|R_k^{\left(i\right)}\left|\right|}_2<T2\};$

(5d) make l '=l '+1, get represent and get maximum weights element i ' in corresponding set I, extracts meeting the component merging thresholding U in the Extended target component after pruning, the sequence number set that the Extended target component obtaining being applicable to merging is corresponding for: $\stackrel{\&OverBar;}{Q}=\{i\&Element;I|{(m_k^{\left(i\right)}-m_k^{\left(i^{\&prime;}\right)})}^T{\left(P_k^{\left(i\right)}\right)}^{-1}(m_k^{\left(i\right)}-m_k^{\left(i^{\&prime;}\right)})\&le;U\};$

(5e) respectively to sequence number set the weights of the Extended target component of middle correspondence motion state constant factor iteration factor covariance merge, obtain the weights of the Extended target component after merging motion state constant factor iteration factor covariance as follows:

${\tilde{w}}_k^{\left(l^{\&prime;}\right)}=\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)},$

${\tilde{m}}_k^{\left(l^{\&prime;}\right)}=\frac{1}{{\tilde{w}}_k^{\left(l^{\&prime;}\right)}}\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)}{m}_k^{\left(i\right)},$

${\widetilde{\mathrm{\&alpha;}}}_k^{\left(l^{\&prime;}\right)}=\frac{1}{{\tilde{w}}_k^{\left(l^{\&prime;}\right)}}\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)}{\mathrm{\&alpha;}}_k^{\left(i\right)},$

${\widetilde{\mathrm{\&beta;}}}_k^{\left(l^{\&prime;}\right)}=\frac{1}{{\tilde{w}}_k^{\left(l^{\&prime;}\right)}}\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)}{\mathrm{\&beta;}}_k^{\left(i\right)},$

${\tilde{P}}_k^{\left(l^{\&prime;}\right)}=\frac{1}{{\tilde{w}}_k^{\left(l^{\&prime;}\right)}}\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)}(P_k^{\left(i\right)}+({\tilde{m}}_k^{\left(l^{\&prime;}\right)}-m_k^{\left(i\right)}){({\tilde{m}}_k^{\left(l^{\&prime;}\right)}-m_k^{\left(i\right)})}^T);$

(5f) sequence number set corresponding with the Extended target component of the applicable merging that step (5d) obtains in the sequence number set I that the Extended target component after pruning step (5c) obtained is corresponding in identical element get rid of, then judge whether sequence number set I corresponding to Extended target component after pruning is empty set, if be empty set, then returns step (5d), otherwise execution (5g);

(5g) whether judgment variable l ' is greater than largest Gaussian one against gamma component number J _maxif, l ' > J _max, then by weights corresponding Gauss by arranging from big to small, and gets front J against gamma component _maxindividual weights the Gauss being greater than 0.5 is against state as Extended target of the position of gamma component and speed; If l ' < is J _max, then by all weights the Gauss being greater than 0.5 correspondence is against state as Extended target of the position of gamma component and speed.

Step 6. is according to step 4c) upgrade the gesture distribution P obtained _k|k(num) be weighted on average, the number of the target that is expanded: ${\mathrm{num}}_{k|k}=\underset{\mathrm{num}=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{num}\&times;p}_{k|k}\left(\mathrm{num}\right);$

The state of the target that is expanded and number can complete the tracking to Extended target later.

The present invention further illustrates by following emulation experiment for the effect of following the tracks of Extended target:

1. simulated conditions

Consider to do linear uniform motion 4 targets in two dimensional surface, and occur that two positions the situation that movement locus intersects, sampling period are whole observation process continues 40 moment, and the equation of motion and the 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.Extended target state-transition matrix F, input matrix G, Gaussian noise w _k, observing matrix H is set to:

$F=\left[\begin{array}{cccc}1& 0& T& 0\\ 0& 1& 0& T\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right],G=\left[\begin{array}{cc}1/2& 0\\ 0& 1/2\\ 1& 0\\ 0& 1\end{array}\right],w_k~N\left(\begin{array}{cc}0,& \left[\begin{array}{cc}{\mathrm{\&sigma;}}_w^2& 0\\ 0& {\mathrm{\&sigma;}}_w^2\end{array}\right]\end{array}\right),H=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$

Realistic objective follows the tracks of measurement noise v in scene _kcovariance be unknown, this experiment in establish real measurement noise standard deviation sigma _v=1;

If three the measurement noise standard deviations adopted in Traditional GM-CPHD algorithm are respectively σ=0.05,1,50;

If target generation detecting number obeys Poisson distribution, Parameter for Poisson Distribution β=20, target produces adjustment location Gaussian distributed;

If target survival probability p _s,k=0.99, detection probability p _d,k=0.98;

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

The state arranging newborn target is $m_{\mathrm{\&gamma;}}^{\left(1\right)}={[-\mathrm{100,200,0,0}]}^T,m_{\mathrm{\&gamma;}}^{\left(2\right)}={[0,-\mathrm{100,0,0}]}^T,$ The covariance of newborn target is P _γ=diag [10,10,10,10];

Arrange and prune thresholding T1=10 ^-5, prune thresholding T2=120, merge 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. emulate content and result

Emulation 1, adopt the inventive method to follow the tracks of the single experiment of Extended target movement locus under the unknown measurement noise covariance, result as shown in Figure 2.As can be seen from Figure 2, the inventive method can well follow the tracks of Extended target movement locus.

Emulation 2, adopt the inventive method to estimate to contrast from traditional target numbers adopting three GM-CPHD methods of different measurement noise covariance to carry out testing for 100 times respectively, result as shown in Figure 3.As can be seen from Figure 3, the inventive method is equally good to the estimation effect of target numbers with the GM-CPHD method under traditional given actual measurements noise covariance.But, traditional GM-CPHD method, when measuring noise covariance and being unknown, and use measurement noise covariance and actual value deviation ratio larger time, very large deviation can be there is in the target numbers estimated, occur intersecting the moment at these two target trajectories of k=20, k=35, target numbers occurs undetected simultaneously;

Emulation 3, adopt the inventive method to contrast from traditional tracking accuracy adopting three GM-CPHD methods of different measurement noise covariance to be undertaken testing for 100 times by OSPA distance respectively, result as shown in Figure 4.As can be seen from Figure 4, the inventive method is equally good with the tracking accuracy of the GM-CPHD algorithm under traditional given actual measurements noise covariance.But, traditional GM-CPHD method, when use measurement noise covariance and real measurement noise covariance deviation ratio larger time, tracking accuracy can become very poor.

Experiment shows, when the Extended target of the inventive method under process measurement noise covariance is unknown condition follows the tracks of scene, its tracking effect is better than traditional GM-CPHD Extended target tracking.

Claims (5)

1., based on an Extended target tracking for variation Bayes expectation maximization, comprise the steps:

(1) when moment k=0, the joint probability assumed density of initialization Extended target state and measurement noise covariance is v ₀(x, R);

(2) when k>=1, to the joint probability assumed density v of Extended target state and measurement noise covariance _k-1|k-1(x, R) and the gesture distribution P for calculating Extended target number _k-1|k-1(num) predict, obtain the Extended target joint probability assumed density v predicted _k|k-1(x, R) and prediction gesture distribution P _k|k-1(num);

(3) to the Extended target state of prediction and the joint probability assumed density v of measurement noise covariance _k|k-1(x, R) and the gesture distribution P for calculating Extended target number _k|k-1(num) upgrade:

(3a) utilize variation Bayes VB method to associating probability hypothesis density v _k|k-1(x, R) is similar to, and obtains the probability hypothesis density Q of the Extended target state represented by the summation form of Gaussian distribution _{x, k|k-1}(x) and the probability hypothesis density Q of measurement noise covariance represented by the summation form of inverse Gamma distribution _{r, k|k-1}(R);

(3b) utilize variation Bayes expectation maximization VBEM method to the probability hypothesis density Q of Extended target state _{x, k|k-1}the probability hypothesis density Q of the gaussian component in (x) and measurement noise covariance _{r, k|k-1}(R) the inverse gamma component in carries out iteration renewal, obtains representing the gaussian component of Extended target motion state x and representing the inverse gamma component of measurement noise covariance R;

(3c) step (2) is predicted to the gesture distribution P obtained _k|k-1(num) upgrade, obtain the gesture distribution P after upgrading _k|k(num);

(4) gaussian component after upgrading and inverse gamma component are carried out pruning and merged, and the gaussian component extracted after merging and against state as Extended target of the position of gamma component and speed;

(5) step (3) is upgraded to the gesture distribution P obtained _k|k(num) be weighted on average, the number of the target that is expanded: ${\mathrm{num}}_{k|k}=\underset{\mathrm{num}=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\mathrm{num}\&times;p_{k|k}\left(\mathrm{num}\right);$

(6) repeat step (2)-(5), continue to follow the tracks of Extended target.

2. the Extended target tracking based on variation Bayes expectation maximization according to claim 1, wherein, utilizes variation Bayes VB method to associating probability hypothesis density v described in step (3a) _k|k-1(x, R) is similar to, and is undertaken by following formula:

$Q_{x,k|k-1}\left(x\right)=\underset{i=1}{\overset{J_k}{\mathrm{\&Sigma;}}}\left[w_{k|k-1}^{\left(i\right)}N(x;m_{k|k-1}^{\left(i\right)},P_{k|k-1}^{\left(i\right)})\right]$

$Q_{R,k|k-1}\left(R\right)=\underset{l=1}{\overset{J_k}{\mathrm{\&Sigma;}}}\left[\underset{l=1}{\overset{d}{\mathrm{\&Pi;}}}\mathrm{IG}({\left({\mathrm{\&sigma;}}_{k|k-1,l}^{\left(i\right)}\right)}^2;{\mathrm{\&alpha;}}_{k|k-1,l}^{\left(i\right)},{\mathrm{\&beta;}}_{k|k-1,l}^{\left(i\right)})\right]$

Wherein, Q _{x, k|k-1}x summation form that () is Gaussian distribution, is expressed as

Q _{r, k|k-1}(R) be the summation form of inverse Gamma distribution, be expressed as

$Q_{R,k|k-1}\left(R\right)=\underset{l=1}{\overset{J_k}{\mathrm{\&Sigma;}}}\left[\underset{l=1}{\overset{d}{\mathrm{\&Pi;}}}\mathrm{IG}({\left({\mathrm{\&sigma;}}_{k|k-1,l}^{\left(i\right)}\right)}^2;{\mathrm{\&alpha;}}_{k|k-1,l}^{\left(i\right)},{\mathrm{\&beta;}}_{k|k-1,l}^{\left(i\right)})\right];$

represent the weights of i-th gaussian component in a kth moment, i=1 ..., J _k, J _krepresent the number of a kth moment Extended target gaussian component, N () represents Gaussian distribution, for a kth moment predicts the average of i-th gaussian component obtained, for a kth moment predicts the covariance of i-th gaussian component obtained; IG () represents inverse Gamma distribution, for a kth moment predicts the constant factor of i-th the inverse gamma component obtained, for a kth moment predicts the iteration factor of i-th the inverse gamma component obtained, l=1 ..., d, d represent the dimension of measurement noise covariance.

3. the Extended target tracking based on variation Bayes expectation maximization according to claim 1, wherein, utilizes variation Bayes expectation maximization VBEM method to the probability hypothesis density Q of Extended target state described in step (3b) _{x, k|k-1}the probability hypothesis density Q of the gaussian component in (x) and measurement noise covariance _{r, k|k-1}(R) the inverse gamma component in carries out iteration renewal, carries out as follows:

(3b1) constant factor of the inverse gamma component of setting and iteration factor wherein l=1 ..., d, d are the dimension of measurement noise covariance R;

(3b2) according to inverse gamma component two factors of setting, calculate and measure noise covariance: wherein n=1 ..., N, N are maximum iteration time, and diag [...] represents diagonalization element wherein;

(3b3) measurement noise covariance is utilized calculate and upgrade the factor

$S_W^{\left(n\right)}=H_W{P}_{k|k-1}^{\left(i\right)}{H_W}^T+R_W^{\left(n\right)}$

Wherein, represent measurement noise covariance matrix carry out the matrix after diagonal line connection active cell W measurement number, blkdiag () expression carries out diagonal line connection to element wherein, | W| represents the measurement number of active cell W; H _wrepresent observing matrix H _kmatrix after the measurement number of vertical connection active cell W, represent the observing matrix H in k moment _ktransposition; represent the Extended target gaussian component motion state covariance that k-1 to the k moment is predicted, representing matrix H _wtransposition;

(3b4) the renewal factor is utilized calculated gains matrix

$K_k^{\left(i\right)\left(n\right)}=P_{k|k-1}^{\left(i\right)}{H}_W^T{\left[S_W^{\left(n\right)}\right]}^{-1},$

Wherein [] ^-1represent matrix inversion;

(3b5) gain matrix is utilized calculate Extended target gaussian component motion state with Extended target gaussian component motion state covariance

$m_{k|k}^{\left(i\right)\left(n\right)}=m_{k|k-1}^{\left(i\right)}+K_k^{\left(i\right)\left(n\right)}(z_w-H_w{m}_{k|k-1}^{\left(i\right)})$

$P_{k|k}^{\left(i\right)\left(n\right)}=[I-K_k^{\left(i\right)\left(n\right)}{H}_W]P_{k|k-1}^{\left(i\right)}$

Wherein, I represents a unit matrix, z _wrepresent all measurements in certain division unit W;

(3b6) Extended target gaussian component motion state is extracted positional information, this positional information is used represent;

(3b7) this gaussian component positional information is utilized with measurement noise covariance calculate and measure Y _{n '}by position the probability γ of the gaussian component generation at place _{n ' i}:

${\mathrm{\&gamma;}}_{n^{\&prime;}i}=\frac{{\mathrm{\&pi;}}_{i}N\left(Y_{n^{\&prime;}}\right|m_{k|k}^{\&prime;\left(i\right)\left(n\right)},R_k^{\left(i\right)\left(n\right)})}{\underset{i=1}{\overset{J_k}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}_{i}N\left(Y_{n^{\&prime;}}\right|m_{k|k}^{\&prime;\left(i\right)\left(n\right)},R_k^{\left(i\right)\left(n\right)})}$

Wherein, J _krepresent Extended target gaussian component number, Y _{n '}represent the n-th ' individual measurement of active cell W, n '=1 ..., | W|; N () represents Gaussian distribution; π _irepresent mixing constant, n _irepresent by position the effective dose detecting number of the gaussian component generation at place,

(3b8) measurement Y is utilized _{n '}by position the probability γ of the gaussian component generation at place _{n ' i}, iteration upgrades the positional information of the target gaussian component motion state that is expanded

$m_{k|k}^{\&prime;\&prime;\left(i\right)\left(n\right)}=\frac{1}{N_i}\underset{n^{\&prime;}=1}{\overset{\left|W\right|}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_{n^{\&prime;}i}{Y}_{n^{\&prime;}};$

(3b9) positional information of Extended target gaussian component motion state is utilized mixing constant π _i, measurement noise covariance calculate maximum likelihood function L ^{(i) (n)}:

$L^{\left(i\right)\left(n\right)}=\underset{n^{\&prime;}=1}{\overset{\left|W\right|}{\mathrm{\&Sigma;}}}1n\underset{i=1}{\overset{J_k}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}_{i}N\left(Y_{n^{\&prime;}}\right|m_{k|k}^{\&prime;\&prime;\left(i\right)\left(n\right)},R_k^{\left(i\right)\left(n\right)}),$ Wherein J _krepresent Extended target gaussian component number;

(3b10) judge | L ^{(i) (n)}-L ^{(i) (n-1)}| whether be less than constant ε=0.01, judge whether current iteration frequency n is less than maximum iteration time N=100 simultaneously, if so, then stop iteration, otherwise return step (3b2), upgrade inverse gamma component iteration factor:

Wherein, represent vector middle all elements is added,

${\mathrm{\&beta;}}_W^{(n+1)}={\mathrm{\&beta;}}_W^{\left(n\right)}+\frac{1}{2}{(z_W-H_W{m}_{k|k}^{\left(i\right)\left(n\right)})}_j^2+\frac{1}{2}{\left(H_W{P}_{k|k}^{\left(i\right)\left(n\right)}{H}_W^T\right)}_{\mathrm{jj}},$ represent to the jth of vector dimension element square, () _jjrepresent the diagonal entry getting matrix, represent iteration factor vertical connection active cell W measures the vector after number, z _wrepresent the measurement of active cell;

(3b11) Extended target state component is extracted extended target motion state covariance iteration factor that is, $m_{k|k}^{\left(i\right)}=m_{k|k}^{\left(i\right)\left(n\right)},P_{k|k}^{\left(i\right)}=P_{k|k}^{\left(i\right)\left(n\right)},{\mathrm{\&beta;}}_{k.l}^{\left(i\right)}={\mathrm{\&beta;}}_{k,l}^{\left(i\right)\left(n\right)},$ Wherein Extended target state component in positional information be the positional information that iteration upgrades the Extended target component motion state obtained in step (3b8)

4. the Extended target tracking based on variation Bayes expectation maximization according to claim 1, wherein, described step (3c) pair potential distribution P _k|k-1(num) upgrade, obtain the gesture distribution P after upgrading _k|k(num) be expressed as follows:

$P_{k|k}\left(\mathrm{num}\right)=\left\{\begin{array}{cc}\frac{{\mathrm{\&Sigma;}}_{p\&angle;Z}{\mathrm{\&Sigma;}}_{W\&Element;p}{\mathrm{\&psi;}}_{p,W}{G}_{k|k-1}^{\left(\mathrm{num}\right)}\left(0\right)\left(\begin{array}{cc}{G}_{\mathrm{FA}}\left(0\right)\frac{\mathrm{\&eta;W}}{\left|p\right|}\frac{{\mathrm{\&rho;}}^{\mathrm{num}-\left|P\right|}}{(\mathrm{num}-|p\left|\right)!}& {\mathrm{\&delta;}}_{\mathrm{num}\&GreaterEqual;\left|p\right|}\\ +G_{\mathrm{FA}}^{\left(\right|W\left|\right)}\left(0\right)\frac{{\mathrm{\&rho;}}^{\mathrm{num}-p+1}}{(\mathrm{num}-|p|+1)!}& {\mathrm{\&delta;}}_{\mathrm{num}\&GreaterEqual;\left|p\right|-1}\end{array}\right)}{{\mathrm{\&Sigma;}}_{p\&angle;Z}{\mathrm{\&Sigma;}}_{W\&Element;p}{\mathrm{\&psi;}}_{p,W}{l}_{p,W}},& \left|Z\right|\&NotEqual;0\\ \frac{{\mathrm{\&rho;}}^{\mathrm{num}}{G}_{k|k-1}^{\left(\mathrm{num}\right)}\left(0\right)}{G_{k|k-1}\left(\mathrm{\&rho;}\right)}& \left|Z\right|=0\end{array}\right.$

Wherein, p ∠ Z represents that measurement is collected Z is divided into p nonvoid subset, and W ∈ p represents the some unit under p nonvoid subset, G _k|k-1(ρ) status predication probability generating function is represented, represent the num rank local derviation of status predication probability generating function, G _fA(0) represent false-alarm probability generating function when not measuring, η W represents that Extended target produces measurement probability, | p| represents all non-NULL number of unit under p division, expression false-alarm probability generating function | W| rank local derviation, δ _num>=prepresenting when target numbers num is greater than division unit | during p|, value is 1, otherwise is 0, | Z|=0 represents that Extended target does not produce measurement, | W| represents the measurement number in each non-dummy cell W, l _p,Wrepresent that measuring division unit is | false-alarm constant coefficient during p|-1, ψ _p,Wrepresent that target produces the product of measurement probability, ρ represents the probability that Extended target component is not detected:

$\mathrm{\&rho;}=\mathrm{\&Sigma;}{\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_{k|k-1}^j[1-P_D(\&CenterDot;)+P_D(\&CenterDot;)G_z\left(0\right|\&CenterDot;)]$

$\mathrm{\&eta;W}=p_{k|k-1}\left[P_D(\&CenterDot;)G_z^{\left(\right|W\left|\right)}\left(0\right|\&CenterDot;)\underset{z^{\&prime;}\&Element;W}{\mathrm{\&Pi;}}\frac{p_z\left(z^{\&prime;}\right|\&CenterDot;)}{p_{\mathrm{FA}}\left(z^{\&prime;}\right)}\right]$

$l_{p,W}=G_{\mathrm{FA}}\left(0\right)G_{k|k-1}^{\left(\right|p\left|\right)}\left(\mathrm{\&rho;}\right)\frac{\mathrm{\&eta;W}}{\left|p\right|}+G_{\mathrm{FA}}^{\left(\right|W\left|\right)}\left(0\right)G_{k|k-1}^{\left(\right|p|-1)}\left(\mathrm{\&rho;}\right)$

${\mathrm{\&psi;}}_{p,W}=\underset{W^{\&prime;}\&Element;p-W}{\mathrm{\&Pi;}}\mathrm{\&eta;}{W}^{\&prime;}$

Wherein, Π takes advantage of symbol for connecting, represent a jth Gauss against gamma component at the proportion shared by current all Gausses are in gamma component, p _k|k-1represent single Extended target state transition probability density function, p _z(z ' |) represent that Extended target measures likelihood, p _fA(z ') represents that false-alarm measures likelihood, G _z(0|) measurement probability generating function is represented, expression measurement probability generating function | W| rank local derviation, z ' ∈ W represents that measuring z ' belongs to unit W, P _d() represents detection probability, and W ' ∈ p-W represents that p divides unit remaining after removing unit W in lower all unit, and η W ' expression Extended target false-alarm measures and produces probability, expression status predication probability generating function | p| rank local derviation, expression status predication probability generating function | p|-1 rank local derviation.

5. the Extended target tracking based on variation Bayes expectation maximization according to claim 1, wherein, carrying out pruning to the gaussian component after renewal and inverse gamma component and merging described in step (4), carries out as follows:

(5a) arrange two and prune thresholding T1 and T2, one merges thresholding U:T1=10 ^-5, T2=120, U=10; Largest Gaussian one is set against gamma component number: J _max=100;

(5b) measurement noise covariance corresponding to each Extended target component is calculated:

(5c) establish variable l '=0, prune the Extended target component after upgrading, the sequence number set I obtaining the Extended target component after pruning corresponding is: $I=\{i=1,...,J_k|w_k^{\left(i\right)}>T1,{\left|\right|R_k^{\left(i\right)}\left|\right|}_2<T2\};$

(5d) make l '=l '+1, get represent and get maximum weights element i ' in corresponding set I, extracts meeting the component merging thresholding U in the Extended target component after pruning, the sequence number set that the Extended target component obtaining being applicable to merging is corresponding for:

$\stackrel{\&OverBar;}{Q}=\{i\&Element;I|{(m_k^{\left(i\right)}-m_k^{\left(i^{\&prime;}\right)})}^T{\left(P_k^{\left(i\right)}\right)}^{-1}(m_k^{\left(i\right)}-m_k^{\left(i^{\&prime;}\right)})\&le;U\};$

(5e) respectively to sequence number set the weights of the Extended target component of middle correspondence motion state constant factor iteration factor covariance merge, obtain the weights of the Extended target component after merging motion state constant factor iteration factor covariance as follows:

${\tilde{w}}_k^{\left(l^{\&prime;}\right)}=\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right),}$

${\tilde{m}}_k^{\left(l^{\&prime;}\right)}=\frac{1}{{\tilde{w}}_k^{\left(l^{\&prime;}\right)}}\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)}{m}_k^{\left(i\right)},$

${\widetilde{\mathrm{\&alpha;}}}_k^{\left(l^{\&prime;}\right)}=\frac{1}{{\tilde{w}}_k^{\left(l^{\&prime;}\right)}}\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)}{\mathrm{\&alpha;}}_k^{\left(i\right)},$

${\widetilde{\mathrm{\&beta;}}}_k^{\left(l^{\&prime;}\right)}=\frac{1}{{\tilde{w}}_k^{\left(l^{\&prime;}\right)}}\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)}{\mathrm{\&beta;}}_k^{\left(i\right)},$

${\tilde{P}}_k^{\left(l^{\&prime;}\right)}=\frac{1}{{\tilde{w}}_k^{\left(l^{\&prime;}\right)}}\underset{i\&Element;\stackrel{\&OverBar;}{Q}}{\mathrm{\&Sigma;}}{w}_k^{\left(i\right)}(P_k^{\left(i\right)}+({\tilde{m}}_k^{\left(l^{\&prime;}\right)}-m_k^{\left(i\right)}){({\tilde{m}}_k^{\left(l^{\&prime;}\right)}-m_k^{\left(i\right)})}^T);$

(5f) sequence number set corresponding with the Extended target component of the applicable merging that step (5d) obtains in the sequence number set I that the Extended target component after pruning step (5c) obtained is corresponding in identical element get rid of, then judge whether sequence number set I corresponding to Extended target component after pruning is empty set, if be not empty set, return step (5d), otherwise perform (5g);

(5g) whether judgment variable l ' is greater than largest Gaussian one against gamma component number J _maxif, l ' > J _max, then by weights corresponding Gauss by arranging from big to small, and gets front J against gamma component _maxindividual weights the Gauss being greater than 0.5 is against state as Extended target of the position of gamma component and speed; If l ' < is J _max, then by all weights the Gauss being greater than 0.5 correspondence is against state as Extended target of the position of gamma component and speed.