CN101975575B

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

Info

Publication number: CN101975575B
Application number: CN2010105072258A
Authority: CN
Inventors: 姬红兵; 蔡绍晓; 张俊根
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2010-10-15
Filing date: 2010-10-15
Publication date: 2012-03-28
Anticipated expiration: 2030-10-15
Also published as: CN101975575A

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-target tracking method based on particle filtering

Technical Field

The invention belongs to the technical field of guidance and relates to target tracking. In particular to a passive sensor multi-target tracking method based on particle swarm optimization and sequential Monte Carlo, which can be used for systems such as infrared guidance and the like.

Background

In multi-target tracking, due to the influence of target missing detection and clutter, uncertainty exists in association between measurement obtained by a sensor and a target, and angle information measured under a passive condition is a nonlinear function of a target state, so that two problems of data association and nonlinear filtering of measurement and the target need to be solved for accurately estimating the target state to realize target tracking.

The traditional multi-target tracking method comprises a nearest neighbor method NN, a joint probability data association JPDA and a multi-hypothesis tracking MHT algorithm, wherein the nearest neighbor method is to directly associate the nearest measurement of an off-target state with a target, when the measurement precision is higher, the tracking performance is better, and when the measurement precision is reduced, the tracking performance is also seriously reduced; multi-hypothesis tracking is exhaustive of all possible correlation events between the target and the measurements, and gradually extends over time, with the disadvantage that the computation time will grow exponentially with the number of targets and measurements; JPDA is one of the most effective methods for solving data association so far, and assigns a certain probability to each pair of target and measured association, and then completes estimation of the posterior probability and state of the target by predicting and updating two steps in combination with Bayesian criterion.

An algorithm SMC based on sequential Monte Carlo is a nonlinear filtering method developed in recent years, a learner combines JPDA with SMC to solve the problem of multi-target tracking, posterior probability distribution of a moving target is fitted by utilizing a certain number of samples and corresponding weights, and the SMC can fit any probability distribution theoretically when the number of sampled samples tends to be infinite. However, in practical applications, considering the comprehensive requirements of tracking accuracy and real-time performance, the number of samples is usually limited, and a sample depletion phenomenon occurs during sampling and resampling, so that the samples lose diversity, and the state estimation is unstable, resulting in tracking divergence.

Disclosure of Invention

Aiming at the problems, the invention provides a passive sensor multi-target tracking method based on particle filtering, so as to keep the diversity of samples and improve the tracking precision of a target.

The key technology for realizing the invention is as follows: the particle swarm optimization algorithm is utilized to optimize the distribution of the multi-target combined samples, so that the multi-target combined samples are gathered to a high-likelihood region of each target state, namely a region with high occurrence probability of a real target, thus the samples for filtering have rich diversity and the importance of each sample is improved; the joint samples are used for calculating the association probability and the target filtering distribution between a target and measurement, in the resampling process, sampling is not carried out according to the weight values of the joint samples generated by multi-target series connection, but the weight values of the joint samples are decomposed into corresponding target samples according to the likelihood of each target sample, the distribution of the target samples is further optimized, and the target tracking precision is improved, and the specific implementation steps comprise the following steps:

(1) extracting target samples according to the initial distribution of each target, and constructing a combined sample:

{x_{0}^{n}}_{n = 1}^{N} = {x_{0}^{n, 1}, L, x_{0}^{n, i}, L, x_{0}^{n, c}}_{n = 1}^{N};

wherein N represents the combined sample number, i represents the target number, N represents the number of combined samples, c represents the number of targets,

the sample of the target i in the nth joint sample at the time point 0 is represented, and the initial weight of each joint sample is taken as

(2) Calculating a prediction joint sample at the time t:

i∈[1，c]，n∈[1，N]t is more than or equal to 1, wherein,is the sample of target i in the nth joint sample at time t;

(3) optimizing the particle swarm as follows:

(3a) taking each target sample in the prediction combined sample at the time t as an initial sample for particle swarm optimizationIs a target sample

Giving an initial velocity:

(3b) calculating a target sample at time tThe likelihood of the sensor measurement is expressed as

Wherein k is 1, L, m is a particle swarm optimization iteration number, and m is more than or equal to 5, which is the set total particle swarm optimization iteration number;

(3c) finding out individual optimal solution of each sample in the target i according to the likelihood of each target sample in the 1 st iteration to the k th iteration

(3d) According to the likelihood of all samples in the ith target, finding out the global optimum solution in all samples of the target

(3e) Obtaining a target sample by utilizing an update equation in a particle swarm optimization algorithm

Position in the (k + 1) th iteration

And velocity

(3f) Repeating the steps (3b) to (3e) m times to obtain a combined sample after particle swarm optimization:

{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,

the optimized target sample is obtained;

(4) updating and normalizing the combined sample weight according to the following steps:

(4a) calculating the average value of the target i measured at the time t according to the measurement value corresponding to the optimized target sample

Sum variance

Select out of the satisfaction

All effective measurements of

j∈[1，M_t]Wherein, y_tFor the measurements obtained by the passive sensor, ∈ 9.21 is the set threshold, M_tThe number of all effective measurements at the time t;

(4b) enumerating the effective measurementCorrelation event phi with target i_i，j；

(4c) Computing effective metrics

Sample form based association likelihood with target i

Calculating an edge correlation event phi in the nth combined sample according to Markov and Bayesian rules of target motion_i，jProbability of (c): p (phi)_i，j|Y^t)ⁿWherein Y is^tRepresents the set of all valid measurements from time 1 to time t;

(4d) the probability of all the associated events of the nth joint sample is summed to obtain the weight of the nth joint sample

And normalizing the weight value to obtain a normalized weight value

(5) From the combined samples and their corresponding weights

Estimating each target state by weighting and summing the combined samples, outputting the result, and simultaneously executing the step (6);

(6) decomposing and resampling the combined sample weight according to the following steps:

(6a) normalizing weight of the nth combined sample

Writing a form of c target sample weight summation:

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wherein the weight of the ith target sample

Obtaining the likelihood of the ith target sample through likelihood calculation;

(6b) the weight of the ith target sample is taken from the N combined sample weights

Based on these weights, N new samples are sampledWherein the sample

The corresponding weight is

Respectively obtaining the first sample before resampling of a target i at the moment t and a weight value corresponding to the first sample;

(7) and (5) repeating the step (2) and continuing to track the target.

The invention has the following advantages:

(1) according to the sampling particle swarm optimization algorithm, the distribution condition of the target samples is improved, so that the target samples are gathered to a high-likelihood region with high probability of occurrence of the target, the importance of each sample is improved, and higher tracking accuracy can be achieved under the condition of fewer target samples;

(2) the invention considers the mutual influence and coupling condition of the similar targets, and performs mixed sampling on the multi-target samples, namely, in the resampling stage of the target samples, the combined sample weight is decomposed into the corresponding target samples according to the likelihood of each target, and then each target is independently resampled according to the decomposed weight, so that the large weight value sample in each target is copied, the small weight value sample is suppressed, the target sample distribution is further optimized, and the tracking precision is improved.

Drawings

FIG. 1 is an overall flow diagram of the present invention;

FIG. 2 is a schematic diagram of particle swarm optimization particle velocity and position updates used in the present invention;

FIG. 3 is a diagram of the effect of one target tracking with the present invention;

figure 4 is a root mean square error plot for position tracking using the present invention.

Detailed Description

Introduction of basic theory

1. System equation

In a Cartesian coordinate system, the position and the speed of the system state in the x and y directions are taken, and the following nonlinear dynamic system model can be established:

x_{t + 1}^{i} = {Fx}_{t}^{i} + {Gv}_{t}^{i} - - - 1)

y_{t} = h (x_{t}^{i}) {+ e}_{t} - - - 2)

where i is 1, L, c denotes the number of objects, c denotes the total number of objects,

respectively representing the coordinates of the object i in the x-direction and the y-direction,

respectively representing the speed of the target i in the x-direction and the y-direction, the subscript te N representing the time, the state noise

Obey variance of

Zero mean gaussian distribution, F, G being the state transition matrix and the input matrix, h being the nonlinear function, and the measurement noise e_tComplianceThe variance is a zero mean gaussian distribution of R,and e_tIndependently of each other, y_tIs the measured value of the sensor.

In the invention, it is assumed that the passive sensor can only observe the azimuth information of the target, so h is defined as follows:

h (x_{t}^{i}) a \tan \frac{y_{t}^{i} - y_{o}}{x_{t}^{i} - x_{o}} - - - 3)

wherein x is_o，y_oIs the position of the sensor.

2. Particle swarm optimization

Setting a group X of N particles in a D-dimension search space as X ═ X₁，L x_n L，x_NIn which the N ∈ [1, N ]]The position and velocity of each particle being x_n＝(x_n1，x_n2，L x_nD) And v_n＝(v_n1，v_n2，L，v_nD) And the optimal solution of its position is s_n＝(s_n1，s_n2，L，s_nD) And the whole populationThe optimal solution for the position is g ═ g₁，g₂，L g_D) Then, the nth particle position and velocity in the kth particle swarm optimization iteration are updated as follows:

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

wherein k is 1, L, m is the number of the particle swarm optimization iteration, m is the preset total number of the particle swarm optimization iteration, D is 1, L, D is the number of the particle dimension,

d-th dimension data indicating a position of the n-th particle,d-th dimension data representing the velocity of the nth particle,represents an optimal solution of the d-th dimensional data in the position of the n-th particle,representing the optimal solution of the d-th dimension data in the positions of all particles in the whole population, c₁And c₂The learning factor is a classical number between (0, 2), and zeta and eta are uniformly distributed pseudo-random numbers between (0, 1); due to the fact thatIndicates the difference vector between the current position of the nth particle and its optimal position, so c₁The capability of searching the nth particle to the optimal position of the nth particle is characterized; while

Then the difference vector representing the current position of the nth particle and the optimal position of the particle in the whole population, so c₂The capability of searching the optimal position of the particle to the whole population is represented; formula 4) includes

The update representing the nth particle velocity is also dependent on its pre-iteration velocity. Updating of particle position and velocity in basic particle swarm optimization algorithmAs shown in fig. 2.

Secondly, the invention relates to a passive sensor multi-target tracking method based on particle filtering

Referring to fig. 1, the specific implementation steps of the present invention include the following:

step 1. initialize the target sample

Let initial time t equal to 0, according to the initial distribution of target i

Extracting a target sample

Parallel-serial configuration of combined samples

i∈[1，c]，n∈[1，N]N is the number of samples extracted, c is the number of targets, wherein,

and

respectively representing the coordinates of the ith target sample in the nth combined sample in the x direction and the y direction,

and

respectively representing the speeds of the ith target sample in the nth combined sample in the x direction and the y direction, and taking the initial weight of the nth combined sample as

Step 2, calculating prediction combined sample at time t

Target sample according to time t-1

And equation of state 1) calculating the predicted sample at time t

These prediction samples are used to construct the joint sample at time t:t is more than or equal to 1, wherein,

representing the ith target sample in the nth joint sample at time t.

Step 3, performing particle swarm optimization on the predicted combined sample

(3.1) taking each target sample in the prediction combined samples at the time t as initial samples for particle swarm optimization

Sample(s)

The initial speeds of (a) are:

(3.2) calculating samplesMeasure y for the sensor_tLikelihood of

Is shown as

Wherein k is 1, L, m is the particle swarm optimization iteration number, m is more than or equal to 5, y is the set total particle swarm optimization iteration number, y_tR is a measurement covariance matrix for the measurement values obtained by the sensor,

is composed of a target sample

Calculating a measurement value according to the measurement update equation 2);

(3.3) finding the ith target sample in the nth joint sample in the 1 st to kth iterations

Minimum value of (2) by

Representing that the corresponding sample is taken as the individual optimal solution of the ith target sample in the nth joint sample

(3.4) finding all samples in the ith target

Minimum value of (2) by

To show that the corresponding sample is taken as the ith sampleGlobal optimal solution for all samples in a target

(3.5) bonding

And a sample

Speed in the k-th iteration

Updating equation 4) according to the particle swarm optimization speed

Speed in the k +1 th iteration

(3.6) bondingAnd

updating samples according to position update equation 5) for particle swarm optimization

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

(3.7) repeating the steps (3.2) - (3.6) m times to obtain an optimized combined sample

{x_{t}^{n}}_{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, updating and normalizing the combined sample weight

(4.1) according to the sampleCalculating the mean value of the target i measured at the time t

Sum covariance

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<math> <mrow> <msubsup> <mi>σ</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>Σ</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>′</mo> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo></mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein,

is a target sampleCorresponding measurement values;

(4.2) use of the mean valueSum covariance

Selecting a set of valid measurements satisfying the condition of equation 11)

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Wherein j is 1, L M_t，M_tThe total number of effective measurement is shown, and epsilon is 9.21 which is a set threshold value;

(4.3) measurement of examples

Correlation event phi with target i_i，j；

(4.4) calculating the effective measurement

Sample form based association likelihood with target i

(4.5) calculating the edge correlation event phi in the nth combined sample according to Markov property and Bayesian rule of target motion_i，jProbability of p (phi)_i，j|Y^t)ⁿ，

<math> <mrow> <mi>p</mi> <msup> <mrow> <mo>(</mo> <msub> <mi>φ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>|</mo> <msup> <mi>Y</mi> <mi>t</mi> </msup> <mo>)</mo> </mrow> <mi>n</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>c</mi> </mfrac> <msubsup> <mi>P</mi> <mi>d</mi> <mrow> <mi>c</mi> <mo>-</mo> <msup> <mi>c</mi> <mn>0</mn> </msup> </mrow> </msubsup> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>c</mi> <mn>0</mn> </msup> </msup> <msubsup> <mi>P</mi> <mi>f</mi> <mrow> <msub> <mi>M</mi> <mi>t</mi> </msub> <mo>-</mo> <mrow> <mo>(</mo> <mi>c</mi> <mo>-</mo> <msup> <mi>c</mi> <mn>0</mn> </msup> <mo>)</mo> </mrow> </mrow> </msubsup> <munder> <mi>Π</mi> <mrow> <mrow> <mo>(</mo> <mi>j</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&Element;</mo> <mi>φ</mi> </mrow> </munder> <mi>p</mi> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>t</mi> <mi>j</mi> </msubsup> <mo>|</mo> <msubsup> <mi>x</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo></mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein, P_fAnd P_dRespectively representing false alarm probability and target detection probability, c⁰Is a correlation event phi_i，jNumber of undetected targets in, Y^tRepresents the set of all valid measurements from time 1 to time t;

(4.6) summing the probabilities of all the associated events of the n-th joint sample to obtain the weight of the n-th joint sampleAnd normalizing the weight value to obtain a normalized weight value

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Step 5, estimating the target state

Using the coupling obtained in step 3Composite sample

And the combined sample weight obtained in step 4

As in equation 16) to estimate the target state, output as a result, and simultaneously performs step 6,

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step 6, decomposing and resampling the combined sample weight

(6.1) calculating the likelihood of the ith target sample in the nth joint sample at the time t:

(6.2) calculating the weight of the ith target sample in the nth joint sample according to the likelihood of the ith target sample in the nth joint sample:

<math> <mrow> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>l</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>/</mo> <munderover> <mi>Σ</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>c</mi> </munderover> <msubsup> <mi>l</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>n</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo></mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>

the normalized weight of the nth combined sample

The form of summation of the weights of c target samples can be written:

<math> <mrow> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>n</mi> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <mi>L</mi> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mi>L</mi> <mo>+</mo> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>c</mi> </mrow> </msubsup> <mo>;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo></mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow> </math>

(6.3) from the N combined sample weights, each weight of the ith target sample is taken out to formBased on these weights, N new samples are sampled

Wherein the sample

The corresponding weight is

The first sample before target i resampling at time t and the corresponding weight value are respectively.

And 7, repeating the step 2 and continuously tracking the target.

The effect of the invention can be further illustrated by the following experimental simulation:

1. simulation conditions and parameters

Simulation scenario as shown in fig. 3, the real state of each target appearing in the simulation scenario is x ═ x, v_x，y，v_y]', x, y are the coordinates of each object in the x and y directions of the Cartesian coordinate system, v_x，v_yRespectively for the speed of each target in the x-direction and the y-direction. The state equation and the measurement equation of the target are respectively shown in the formulas 1) and 2), and each target is subject to a constant speed model:

F = [\begin{matrix} 1 & T & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & T \\ 0 & 0 & 0 & 1 \end{matrix}],

G = [\begin{matrix} T^{2} / 2 & 0 \\ T & 0 \\ 0 & T^{2} / 2 \\ 0 & T \end{matrix}]

where T is the sampling time interval, the sensor provides azimuthal information,

the simulation parameters are shown in table 1 below,

TABLE 1 Experimental simulation parameters

2. Simulation content and result analysis

In a pure azimuth tracking simulation experiment of three targets under the condition of three sensors, the root mean square error RMSE and the tracking loss rate of the positions of the tracking method of the invention and two multi-target tracking methods of the existing iMC-JPDA and jMC-JPDA are compared in the simulation experiment, and simulation results are respectively shown in FIG. 4 and Table 2, wherein:

FIG. 4(a) is a graph comparing the root mean square error of the positions of the method of the present invention with iMC-JPDA and jMC-JPDA for the sample number N equal to 30;

FIG. 4(b) is a graph comparing the root mean square error of the positions of the method of the present invention with iMC-JPDA and jMC-JPDA at a sample number of N-50;

FIG. 4(c) is a graph comparing the root mean square error of the positions of the method of the present invention with iMC-JPDA and jMC-JPDA at 80 samples N;

FIG. 4(d) is a graph comparing the root mean square error of the positions of the method of the present invention with iMC-JPDA and jMC-JPDA for a sample number of N-100;

as can be seen from FIGS. 4(a) -4 (d), the RMSE for all three tracking methods decreased as the number of samples increased, but the RMSE for the present invention was consistently lower than that for the iMC-JPDA and jMC-JPDA methods.

Table 2 shows the loss of tracking of the inventive method compared to the existing iMC-JPDA and jMC-JPDA,

TABLE 2 comparison of loss of tracking rates of the inventive method with iMC-JPDA and jMC-JPDA

As can be seen from Table 2, the tracking loss rate of the method of the present invention is significantly lower than that of the iMC-JPDA and jMC-JPDA tracking methods under the condition of the same number of samples, and when the number of samples N exceeds 30, the tracking loss of the method of the present invention does not occur.

Claims

1. A passive sensor multi-target tracking method based on particle filtering comprises the following steps:

wherein N represents the combined sample number, i represents the target number, N represents the number of combined samples, c represents the number of targets,the sample of the target i in the nth joint sample at the time point 0 is represented, and the initial weight of each joint sample is taken as

(2) Calculating a prediction joint sample at the time t:

i∈[1，c]，n∈[1，N]t is more than or equal to 1, wherein,

is at time t

Samples of target i from the n joint samples;

(3) optimizing the particle swarm as follows:

(3a) taking each target sample in the prediction combined sample at the time t as an initial sample for particle swarm optimization

Is a target sample

Giving an initial velocity:

(3b) calculating a target sample at time t

The likelihood of the sensor measurement is expressed asWherein k is 1, …, m is the particle swarm optimization iteration number, and m is more than or equal to 5, which is the set total particle swarm optimization iteration number;

Position in the (k + 1) th iteration

And velocity

wherein,

the optimized target sample is obtained;

Sum variance

Select out of the satisfaction

All effective measurements of

j∈[1，M_t]，

Wherein, y_tFor the measurements obtained by the passive sensor, ∈ 9.21 is the set threshold, M_tThe number of all effective measurements at the time t;

(4b) enumerating the effective measurement

Correlation event phi with target i_i，j；

(4c) Computing effective metrics

Sample form based association likelihood with target i

By eyeMarkov property and Bayes criterion of the target motion are used for calculating an edge correlation event phi in the nth combined sample_i，jProbability of (c): p (phi)_i，j|Y^t)ⁿWherein Y is^tRepresents the set of all valid measurements from time 1 to time t;

And normalizing the weight value to obtain a normalized weight value

(5) From the combined samples and their corresponding weights

(6a) normalizing weight of the nth combined sample

Writing a form of c target sample weight summation:

<math> <mrow> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>n</mi> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <mo>·</mo> <mo>·</mo> <mo>·</mo> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>·</mo> <mo>·</mo> <mo>·</mo> <mo>+</mo> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>c</mi> </mrow> </msubsup> <mo>,</mo> </mrow> </math>

wherein, the weight of the ith target sample

The likelihood calculation of the ith target sample is obtained by the following steps:

firstly, the likelihood of the ith target sample in the nth combined sample at the time t is calculated:

wherein, y_tIn order to obtain a measurement value for the sensor,

is a target sample

The corresponding measured value is measured by the corresponding measuring instrument,

the variance measured at time t for target i,

<math> <mrow> <msubsup> <mi>σ</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>Σ</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>′</mo> </msup> </mrow> </math>

wherein,

<math> <mrow> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>Σ</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>y</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> </mrow> </math>

then, according to the likelihood of the ith target sample in the nth joint sample, calculating the weight of the ith target sample in the nth joint sample:

<math> <mrow> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>l</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>/</mo> <munderover> <mi>Σ</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>c</mi> </munderover> <msubsup> <mi>l</mi> <mi>t</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mover> <mi>w</mi> <mo>&OverBar;</mo> </mover> <mi>t</mi> <mi>n</mi> </msubsup> <mo>;</mo> </mrow> </math>

(6b) the weight of the ith target sample is taken from the N combined sample weightsBased on these weights, N new samples are sampled

Wherein the sample

The corresponding weight is

(7) and (5) repeating the step (2) and continuing to track the target.