CN101975575B - Multi-target tracking method for passive sensor based on particle filtering - Google Patents

Abstract

The invention discloses a multi-target tracking method for a passive sensor based on particle filtering, which belongs to the technical field of guidance and mainly solves the problems of easy divergent tracking and inaccurate target state estimation in the traditional multi-target tracking method. The method optimizes distribution of multi-target samples through particle swarm optimization and sample mixing sampling algorithms and tracks the multi-target combined with a joint probability data association algorithm. The method comprises the following steps of: firstly, optimizing the distribution of multi-target joint samples by utilizing the particle swarm optimization algorithm so that the multi-target joint samples are gathered in a high likelihood region with a bigger probability of occurrence of a real target; secondly, calculating an associated probability between the targets and observation and the posterior probability distribution of the targets by utilizing the samples; and finally, decomposing a joint sample weight into the corresponding target sample in a likelihood way according to each target sample in the re-sampling process, and independently re-sampling each target according to the decomposed weight, and further optimizing the distribution of the target sample so as to improve the precision of target tracking.

Description

Passive sensor multi-object tracking method based on particle filter

Technical field

The invention belongs to the guidance technology field, relate to target following.Specifically a kind of passive sensor multi-object tracking method based on particle group optimizing and sequential Monte Carlo can be used for systems such as infrared guidance.

Background technology

In the multiple target tracking; Because the influence of target omission and clutter; Association between measurement of sensor gained and the target exists uncertain; And the angle information of under passive condition, being surveyed is the nonlinear function of dbjective state, therefore wants accurate estimating target state to realize target following, solves data association and two problems of nonlinear filtering of measurement and target with regard to needs.

Traditional multi-object tracking method comprises nearest neighbor method NN; JPDA JPDA, many hypothesis are followed the tracks of the MHT algorithm, and wherein nearest neighbor method is with directly being associated with target from the nearest measurement of dbjective state; When measuring accuracy is higher; Tracking performance is better, and when measuring accuracy descends, its tracking performance also will seriously descend; Many hypothesis tracking then are all possible correlating events between exhaustive target and the measurement, and progressively by the time expansion, its shortcoming is that computing time will be with number of targets and the growth of measurement number exponentially; JPDA solves one of effective method of data association till now, and it gives every pair of target and measurement relatedly gives certain probability, combines bayesian criterion through predicting and upgrade the estimation of two steps completion target posterior probability and state then.

Algorithm SMC based on sequential Monte Carlo is the non-linear filtering method that developed recently gets up; There is the scholar that JPDA is combined with SMC; In order to solve the multiple target tracking problem, utilize the sample of some and corresponding weights to come the posterior probability of match moving target to distribute, theoretically; When the sampling given figure is tending towards for a long time infinite, SMC can any probability distribution of match.But owing in the practical application, consider the composite request of tracking accuracy and real-time, sample number is limited usually; It the phenomenon of sample dilution can occur in the process of sampling and resampling; Make sample lose diversity, state estimation is unstable, causes following the tracks of dispersing.

Summary of the invention

To the problems referred to above, the present invention proposes a kind of passive sensor multi-object tracking method based on particle filter, to keep the diversity of sample, improves target tracking accuracy.

Realize that key problem in technology of the present invention is: utilize particle swarm optimization algorithm to optimize the distribution of multiple goal associating sample; Make it gather the high likelihood region of each dbjective state; Be the bigger zone of real goal probability of occurrence, will have rich diversity in order to the sample of filtering like this and each sample importance is improved; Utilize association probability and target filtering between these associating sample calculation targets and the measurement to distribute; And in the resampling process; The weights sampling of the associating sample that no longer produces according to multiple goal series connection decomposes in the corresponding target sample by each target sample likelihood and goes the distribution of further optimization aim sample but will unite sample weights; Improve the precision of target following, concrete performing step comprises as follows:

(1) according to the initial distribution extracting objects sample of each target, the tectonic syntaxis sample:

${\left\{x_0^n\right\}}_{n=1}^N={\{x_0^{n,1},L,x_0^{n,i},L,x_0^{n,c}\}}_{n=1}^N;$

Wherein, N representes associating sample sequence number; I representes target sequence number; N representes the associating number of samples; C representes the target number;

expression 0 is n sample of uniting target i in the sample constantly, and initial weight of each associating sample is taken as

(2) calculate t prediction associating sample constantly:

i ∈ [1; C]; N ∈ [1; N]; T>=1, wherein, is t n sample of uniting target i in the sample constantly;

(3) optimize population as follows:

(3a) The joint prediction time t in the sample as the target sample PSO initial sample as the target sample

given initial velocity:

(3b) calculate the likelihood that t moment target sample measures sensor; Be expressed as

wherein; K=1; L; M is a particle group optimizing iteration sequence number, the total particle group optimizing iterations of m>=5 for setting;

(3c) according to the likelihood of each target sample in the 1st to the k time iteration, find out the individual optimum solution

of each sample among the target i

(3d) according to the likelihood of all samples in i the target, find out the globally optimal solution

in all samples of this target

(3e) using particle swarm optimization algorithm update equations obtained in the target sample

(k +1) th iteration in the position

and speed

(3f) repeating step (3b)～(3e) m time obtains the associating sample behind the particle group optimizing:

${\{x_t^{n,1},L,x_t^{n,i},L,x_t^{n,c}\}}_{n=1}^N={\{x_{n,t}^{m,1},L{x}_{n,t}^{m,i}L,x_{n,t}^{m,c}\}}_{n=1}^N,$

Wherein,

is the target sample after optimizing;

(4) as follows the associating sample weights is upgraded and normalization:

(4a), calculate the average that target i measures at t constantly according to the pairing measuring value of target sample after optimizing

And variance

Select satisfied

All effective measurements

J ∈ [1, M _t], wherein, y _tBe the measurement that passive sensor obtains, the threshold value of ε=9.21 for setting, M _tBe all numbers that effectively measure of the t moment;

(4b) enumerate out effective measurement Correlating event φ with target i _{I, j}

(4c) calculate effectively measurement

With the related likelihood of target i based on sample form

By the Markov property and the bayesian criterion of target travel, calculate edge correlating event φ in n the associating sample _{I, j}Probability: p (φ _{I, j}| Y ^t) ⁿ, wherein, Y ^tExpression is from the 1st to t all set that effectively measure constantly;

(4d) ask n the associating sample all correlating events probability with; Obtain the weights

of n associating sample and, obtain normalization weights

its normalization

(5) through being sued for peace, the associating sample weighting estimates each dbjective state by associating sample and corresponding weights

thereof; Output as a result of, and while execution in step (6);

(6) as follows the associating sample weights is decomposed and resampling:

(6a) write the normalization weights

of n associating sample as form that c target sample weights are sued for peace:

${\stackrel{\‾}{w}}_t^n={\stackrel{\‾}{w}}_t^{n,1}+L{\stackrel{\‾}{w}}_t^{n,i}L+{\stackrel{\‾}{w}}_t^{n,c},$

Wherein the weights of i target sample

calculate through the likelihood of i target sample and obtain;

(6b) from N associating sample weights; Each takes out the weights formations

of i target sample according to these weights; Sample N new sample wherein, and its corresponding weights of sample

are respectively preceding l sample and corresponding weights thereof of t target i resampling constantly for

;

(7) repeating step (2) continues tracking target.

The present invention has the following advantages:

(1) the present invention's particle swarm optimization algorithm of sampling has improved the distribution situation of target sample; Make target sample assemble to the big high likelihood region of target probability of occurrence; And the importance of each sample is improved, and under the less condition of target sample, can reach higher tracking accuracy;

(2) the present invention has considered the situation that the close existence of target influences each other and is coupled, to multiple goal sample mixing sampling, promptly in resampling stage of target sample; To unite sample weights earlier decomposes in the corresponding target sample by each target likelihood and goes; Each target independently is resampled by the weights after decomposing again, make in each target greatly that the weights sample is able to duplicate, little weights sample is able to inhibition; Further optimize the target sample distribution, improved tracking accuracy.

Description of drawings

Fig. 1 is overall flow figure of the present invention;

Fig. 2 is particle group optimizing particle rapidity and the position renewal synoptic diagram that the present invention uses;

Fig. 3 is the design sketch that carries out a target following with the present invention;

Fig. 4 is the root-mean-square error figure that carries out Position Tracking with the present invention.

Embodiment

One, basic theory introduction

1. system equation

Under the cartesian coordinate system, system state is got x, and the position of y direction and speed can be set up following nonlinear dynamic system model:

$x_{t+1}^i={\mathrm{Fx}}_t^i+{\mathrm{Gv}}_t^i---1)$

$y_t=h\left(x_t^i\right){+e}_t---2)$

Wherein, i=1, L, c represent the sequence number of target, c representes total target numbers,

Represent the coordinate of target i on x direction and y direction respectively,

Represent the speed of target i on x direction and y direction respectively, subscript t ∈ N express time, state-noise

The obedience variance does

The zero-mean Gaussian distribution, F, G are respectively state-transition matrix and input matrix, h is a nonlinear function, measurement noise e _tObeying variance is the zero-mean Gaussian distribution of R, With e _tSeparate, y _tMeasuring value for sensor.

The azimuth information that the hypothesis passive sensor can only observed object among the present invention, so the h definition is as follows:

$h\left(x_t^i\right)a\tan \frac{y_t^i-y_o}{x_t^i-x_o}---3)$

Wherein, x _o, y _oPosition for sensor.

2. particle group optimizing

Be located at the population X={x that forms by N particle in the search volume of D dimension ₁, L x _nL, x _N, wherein, n ∈ [1, N] individual particle position and speed are respectively x _n=(x _N1, x _N2, L x _ND) and v _n=(v _N1, v _N2, L, v _ND), and the optimum solution of its position is s _n=(s _N1, s _N2, L, s _ND), and the optimum solution of whole population position is g=(g ₁, g ₂, L g _D), then the renewal of n particle position and speed is following in the k time particle group optimizing iteration:

$v_{\mathrm{nd}}^{k+1}=v_{\mathrm{nd}}^k+c_1\mathrm{\ζ}(s_{\mathrm{nd}}^k-x_{\mathrm{nd}}^k)+c_2\mathrm{\η}(g_d^k-x_{\mathrm{nd}}^k)---4)$

$x_{\mathrm{nd}}^{k+1}=x_{\mathrm{nd}}^k+v_{\mathrm{nd}}^{k+1}---5)$

Wherein, k=1, L, m are the sequence numbers of particle group optimizing iteration, and m is the total degree of predefined particle group optimizing iteration, d=1, and L, D represent the sequence number of particle dimension,

Represent n the d dimension data in the particle position, Represent n the d dimension data in the particle's velocity, The optimum solution of representing d dimension data in n the particle position, Represent in the whole population optimum solution of d dimension data in all particle position, c ₁And c ₂Be the study factor, its classical value is the positive constant between (0,2), and ζ and η are equally distributed pseudo random number between (0,1); Because What represent is the difference vector of n particle current location and itself optimal location, so c ₁Characterized the ability of n particle to himself optimal location search; And

So the difference vector of then representing particle optimal location in n particle current location and the whole population is c ₂Characterized the ability of this particle to whole population optimal location search; Formula 4) comprises in

The renewal of representing n particle rapidity also will be depended on the speed that its iteration is preceding.The renewal of elementary particle colony optimization algorithm particle position and speed is shown in accompanying drawing 2.

Two, the present invention is based on the passive sensor multi-object tracking method of particle filter

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

Step 1. initialization target sample

Make initial time t=0; Initial distribution

extracting objects sample

parallel-series tectonic syntaxis sample

i ∈ [1 according to target i; C]; N ∈ [1; N]; The sample number of N for extracting; C is a number of targets; Wherein,

and

represent the coordinate of i target sample on x direction and y direction in n the associating sample respectively;

and

representes the speed of i target sample on x direction and y direction in n the associating sample respectively, and the initial weight of n associating sample is taken as

Step 2. is calculated t prediction associating sample constantly

According to t-1 target sample

and state equation 1 constantly) calculate t forecast sample

constantly with these forecast samples structure t associating sample constantly: t>=1; Wherein, i target sample in

expression t moment n associating sample.

The associating sample of step 3. pair prediction carries out particle group optimizing

(3.1) at time t predict the combined sample of each target sample as PSO initial sample

sample

the initial velocity is:

(3.2) calculate sample Sensor is measured y _tLikelihood

Be expressed as

$f_{n,t}^{k,i}=p\left(y_t\right|x_{n,t}^{k,i})=\frac{1}{\sqrt{2\mathrm{\π}\det \left(R\right)}}\exp (-\frac{1}{2}{(y_t-y_{n,t}^{k,i})}^{\′}{\left(R\right)}^{-1}(y_t-y_{n,t}^{k,i}))---6)$

Wherein, k=1, L, m are particle group optimizing iteration sequence number, the total particle group optimizing iterations of m>=5 for setting, y _tBe the measuring value that sensor obtains, R is the measurement covariance matrix,

For by target sample

According to measuring renewal equation 2) measuring value that calculates;

(3.3) find out in the 1st to the k time iteration; N minimum value of uniting

of i target sample in the sample; The individual optimum solution

of its corresponding sample as i target sample in n the associating sample got in the expression with

(3.4) find out the minimum value of

of all samples in i the target; The globally optimal solution

of its corresponding sample as all samples in i the target got in expression with

(3.5) combine

and the speed

of sample

in the k time iteration according to the Velocity Updating equation 4 of particle group optimizing), the speed

of new samples

in the k+1 time iteration more

$v_{n,t}^{k+1,i}=v_{n,t}^{k,i}+c_1\mathrm{\ζ}(s_{n,t}^{k,i}-x_{n,t}^{k,i})+c_2\mathrm{\η}(g_{n,t}^{k,i}-x_{n,t}^{k,i})---7)$

(3.6) combined and

Depending on the location of PSO update equation 5) updates the sample

$x_{n,t}^{k+1,i}=x_{n,t}^{k,i}+v_{n,t}^{k+1,i}---8)$

(3.7) repeating step (3.2)～(3.6) are m time, the associating sample after being optimized ${\left\{x_t^n\right\}}_{n=1}^N={\{x_t^{n,1},L{x}_t^{n,i}L,x_t^{n,c}\}}_{n=1}^N={\{x_{n,t}^{m,1},L{x}_{n,t}^{m,i}L,x_{n,t}^{m,c}\}}_{n=1}^N.$

Step 4. associating sample weights is upgraded and normalization

(4.1) based on a sample calculate the target i at time t measured mean

and covariance

${\stackrel{\‾}{y}}_t^i=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{y}_t^{n,i}---9)$

${\mathrm{\σ}}_t^i=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}(y_t^{n,i}-{\stackrel{\‾}{y}}_t^i){(y_t^{n,i}-{\stackrel{\‾}{y}}_t^i)}^{\′}---10)$

Wherein,

is the corresponding measuring value of target sample ;

(4.2) using the mean value and covariance

elect satisfies 11) conditions measured an effective collection

$y_t^j=\{y_t:{(y_t-{\stackrel{\‾}{y}}_t^i)}^{\′}{\left({\mathrm{\σ}}_t^i\right)}^{-1}(y_t-{\stackrel{\‾}{y}}_t^i)\≤\mathrm{\ϵ}\}---11)$

Wherein, j=1,, L M _t, M _tThe total number that expression effectively measures, the threshold value of ε=9.21 for setting;

(4.3) enumerate out measurement

Correlating event φ with target i _{I, j}

(4.4) to calculate the effective measurement

i with the target sample forms-based association likelihood

$p\left(y_t^j\right|x_t^{n,i})=\frac{1}{\sqrt{2\mathrm{\π}\det \left({\mathrm{\σ}}_t^i\right)}}\exp (-\frac{1}{2}{(y_t^j-y_t^{n,i})}^{\′}{\left({\mathrm{\σ}}_t^i\right)}^{-1}(y_t^j-y_t^{n,i}))---12)$

(4.5) Markov property and the bayesian criterion by target travel calculates edge correlating event φ in n the associating sample _{I, j}Probability p (φ _{I, j}| Y ^t) ⁿ,

$p{\left({\mathrm{\φ}}_{i,j}\right|Y^t)}^n=\frac{1}{c}{P}_d^{c-c^0}{(1-P_d)}^{c^0}{P}_f^{M_t-(c-c^0)}\underset{(j,i)\∈\mathrm{\φ}}{\mathrm{\Π}}p\left(y_t^j\right|x_t^{n,i})---13)$

Wherein, P _fAnd P _dRepresent false-alarm probability and target detection probability respectively, c ⁰Be correlating event φ _{I, j}In the number of undetected target, Y ^tExpression is from the 1st to t all set that effectively measure constantly;

(4.6) ask n the associating sample all correlating events probability with; Obtain the weights of n associating sample and, obtain normalization weights

its normalization

$w_t^n=\mathrm{\Σp}{\left({\mathrm{\φ}}_{i,j}\right|Y^t)}^n---14)$

${\stackrel{\‾}{w}}_t^n=w_t^n/\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{w}_t^n.---15)$

Step 5. dbjective state is estimated

Utilize associating sample weights

that associating sample

that step 3 obtains and step 4 obtain by formula 16) the estimating target state; Output as a result of; And while execution in step 6

$x_t^i=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{x}_t^n\·{\stackrel{\‾}{w}}_t^n.---16)$

Step 6. pair associating sample weights is decomposed and is resampled

(6.1) calculate t n likelihood of uniting i target sample in the sample constantly:

$l_t^{n,i}=\frac{1}{\sqrt{2\mathrm{\π}\det \left({\mathrm{\σ}}_t^i\right)}}\exp (-\frac{1}{2}{(y_t-y_t^{n,i})}^{\′}{\left({\mathrm{\σ}}_t^i\right)}^{-1}(y_t-y_t^{n,i}))---17)$

(6.2), calculate the weights of i target sample in n the associating sample according to the likelihood of i target sample in n the associating sample:

${\stackrel{\‾}{w}}_t^{n,i}=(l_t^{n,i}/\underset{n=1}{\overset{c}{\mathrm{\Σ}}}{l}_t^{n,i}){\stackrel{\‾}{w}}_t^n---18)$

Then the normalization weights

of n associating sample can be write as the form of c target sample weights summation:

${\stackrel{\‾}{w}}_t^n={\stackrel{\‾}{w}}_t^{n,1}+L{\stackrel{\‾}{w}}_t^{n,i}L+{\stackrel{\‾}{w}}_t^{n,c};---19)$

(6.3) from N associating sample weights; Each takes out the weights formations of i target sample according to these weights; Sample N new sample

wherein, and its corresponding weights of sample

are respectively preceding l sample and corresponding weights thereof of t target i resampling constantly for

.

Step 7. repeating step 2 continues tracking target.

Effect of the present invention can further specify through following experiment simulation:

1. simulated conditions and parameter

Simulating scenes is as shown in Figure 3, and the time of day that appears at each target in the simulating scenes is x=[x, v _x, y, v _y] ', x, y are respectively the coordinate of each target on cartesian coordinate system x direction and y direction, v _x, v _yBe respectively the speed of each target on x direction and y direction.The state equation of target and measurement equation are respectively suc as formula 1) and 2) shown in, and each target is all obeyed normal fast model:

$F=\left[\begin{array}{cccc}1& \mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000028251140000022.png,HDA0000028251140000031.png"\; state="\{\{state\}\}">T</figure-callout>}& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& \mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000028251140000022.png,HDA0000028251140000031.png"\; state="\{\{state\}\}">T</figure-callout>}\\ 0& 0& 0& 1\end{array}\right],$ $G=\left[\begin{array}{cc}{T}^2/2& 0\\ \mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000028251140000022.png,HDA0000028251140000031.png"\; state="\{\{state\}\}">T</figure-callout>}& 0\\ 0& T^2/2\\ 0& T\end{array}\right]$

Wherein, T is a sampling time interval; Sensor provides azimuth information;

simulation parameter is as shown in table 1

Table 1 experiment simulation parameter

2. emulation content and interpretation of result

Emulation experiment is followed the tracks of at the pure position angle of three targets under three sensor conditions; Rate is followed in the root-mean-square error RMSE and the mistake that have contrasted the position of tracking of the present invention and existing iMC-JPDA and two kinds of multi-object tracking methods of jMC-JPDA in the emulation experiment; Simulation result is respectively shown in Fig. 4 and table 2, wherein:

Fig. 4 (a) is under the sample number N=30 condition, the comparison diagram of the position root-mean-square error of the inventive method and iMC-JPDA and jMC-JPDA;

Fig. 4 (b) is under the sample number N=50 condition, the comparison diagram of the position root-mean-square error of the inventive method and iMC-JPDA and jMC-JPDA;

Fig. 4 (c) is under the sample number N=80 condition, the comparison diagram of the position root-mean-square error of the inventive method and iMC-JPDA and jMC-JPDA;

Fig. 4 (d) is under the sample number N=100 condition, the comparison diagram of the position root-mean-square error of the inventive method and iMC-JPDA and jMC-JPDA;

Can find out that from Fig. 4 (a)～4 (d) along with the increase of sample number, the RMSE of three kinds of trackings all reduces, but RMSE of the present invention is lower than the RMSE of iMC-JPDA and jMC-JPDA method all the time.

Table 2 is that the mistake of the inventive method and existing iMC-JPDA and jMC-JPDA is compared with rate,

The mistake of table 2 the inventive method and iMC-JPDA and jMC-JPDA with rate relatively

Can find out that by table 2 under the condition of same sample number, the inventive method is lost with rate and is starkly lower than iMC-JPDA and jMC-JPDA tracking, and when sample number N surpassed 30, the situation of following no longer appearred losing in the inventive method.

Claims (1)

1. passive sensor multi-object tracking method based on particle filter comprises:

(1) according to the initial distribution extracting objects sample of each target, the tectonic syntaxis sample:

${\left\{x_0^n\right\}}_{n=1}^N={\{x_0^{n,1},\&CenterDot;\&CenterDot;\&CenterDot;,x_0^{n,i},\&CenterDot;\&CenterDot;\&CenterDot;,x_0^{n,c}\}}_{n=1}^N;$

Wherein, N representes associating sample sequence number; I representes target sequence number; N representes the associating number of samples; C representes the target number; expression 0 is n sample of uniting target i in the sample constantly, and initial weight of each associating sample is taken as

(2) calculate t prediction associating sample constantly:

${\left\{x_t^n\right\}}_{n=1}^N={\{x_t^{n,1},\&CenterDot;\&CenterDot;\&CenterDot;,x_t^{n,i},\&CenterDot;\&CenterDot;\&CenterDot;,x_t^{n,c}\}}_{n=1}^N,$ I ∈ [1, c], n ∈ [1, N], t>=1, wherein,

Be t constantly the

N sample of uniting target i in the sample;

(3) optimize population as follows:

(3a) The joint prediction time t in the sample as the target sample PSO initial sample

as the target sample

given initial velocity:

(3b) calculate the likelihood that t moment target sample

measures sensor; Be expressed as wherein; K=1; M is a particle group optimizing iteration sequence number, the total particle group optimizing iterations of m>=5 for setting;

(3c) according to the likelihood of each target sample in the 1st to the k time iteration, find out the individual optimum solution

of each sample among the target i

(3d) according to the likelihood of all samples in i the target, find out the globally optimal solution

in all samples of this target

(3e) using particle swarm optimization algorithm update equations obtained in the target sample

(k +1) th iteration in the position

and speed

(3f) repeating step (3b)～(3e) m time obtains the associating sample behind the particle group optimizing:

${\{x_t^{n,1},\&CenterDot;\&CenterDot;\&CenterDot;,x_t^{n,i},\&CenterDot;\&CenterDot;\&CenterDot;,x_t^{n,c}\}}_{n=1}^N={\{x_{n,t}^{m,1},\&CenterDot;\&CenterDot;\&CenterDot;x_{n,t}^{m,i}\&CenterDot;\&CenterDot;\&CenterDot;,x_{n,t}^{m,c}\}}_{n=1}^N,$

Wherein,

is the target sample after optimizing;

(4) as follows the associating sample weights is upgraded and normalization:

(4a), calculate the average that target i measures at t constantly according to the pairing measuring value of target sample after optimizing

And variance

Select satisfied

All effective measurements

J ∈ [1, M _t],

Wherein, y _tBe the measurement that passive sensor obtains, the threshold value of ε=9.21 for setting, M _tBe all numbers that effectively measure of the t moment;

(4b) enumerate out effective measurement

Correlating event φ with target i _{I, j}

(4c) calculate effectively measurement

With the related likelihood of target i based on sample form

By the Markov property and the bayesian criterion of target travel, calculate edge correlating event φ in n the associating sample _{I, j}Probability: p (φ _{I, j}| Y ^t) ⁿ, wherein, Y ^tExpression is from the 1st to t all set that effectively measure constantly;

(4d) ask n the associating sample all correlating events probability with; Obtain the weights

of n associating sample and, obtain normalization weights its normalization

(5) through being sued for peace, the associating sample weighting estimates each dbjective state by associating sample and corresponding weights

thereof; Output as a result of, and while execution in step (6);

(6) as follows the associating sample weights is decomposed and resampling:

(6a) write the normalization weights

of n associating sample as form that c target sample weights are sued for peace:

${\stackrel{\&OverBar;}{w}}_t^n={\stackrel{\&OverBar;}{w}}_t^{n,1}+\&CenterDot;\&CenterDot;\&CenterDot;{\stackrel{\&OverBar;}{w}}_t^{n,i}\&CenterDot;\&CenterDot;\&CenterDot;+{\stackrel{\&OverBar;}{w}}_t^{n,c},$

Wherein, the weights of i target sample

calculate the likelihood of i target sample through following steps and obtain:

At first, calculate t n likelihood of uniting i target sample in the sample constantly:

$l_t^{n,i}=\frac{1}{\sqrt{2\mathrm{\&pi;}\det \left({\mathrm{\&sigma;}}_t^i\right)}}\exp (-\frac{1}{2}{(y_t-y_t^{n,i})}^{\&prime;}{\left({\mathrm{\&sigma;}}_t^i\right)}^{-1}(y_t-y_t^{n,i}))$

Wherein, y _tBe the measuring value of sensor acquisition,

Be target sample

Corresponding measuring value,

The variance that measures constantly at t for target i,

${\mathrm{\&sigma;}}_t^i=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}(y_t^{n,i}-{\stackrel{\&OverBar;}{y}}_t^i){(y_t^{n,i}-{\stackrel{\&OverBar;}{y}}_t^i)}^{\&prime;}$

Wherein,

${\stackrel{\&OverBar;}{y}}_t^i=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_t^{n,i}$

Then, according to the likelihood of i target sample in n the associating sample, calculate the weights of i target sample in n the associating sample:

${\stackrel{\&OverBar;}{w}}_t^{n,i}=(l_t^{n,i}/\underset{n=1}{\overset{c}{\mathrm{\&Sigma;}}}{l}_t^{n,i}){\stackrel{\&OverBar;}{w}}_t^n;$

(6b) from N associating sample weights; Each takes out the weights formations of i target sample according to these weights; Sample N new sample

wherein, and its corresponding weights of sample

are respectively preceding l sample and corresponding weights thereof of t target i resampling constantly for

;

(7) repeating step (2) continues tracking target.

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