Multi-target tracking method based on BP-PMBM filtering algorithm
1. A multi-target tracking method based on a BP-PMBM filtering algorithm is characterized by comprising the following steps:
(1) initializing an algorithm;
(2) predicting a target state;
(21) predicting the Poisson component in the target state to obtain the prediction intensity of the Poisson component and expressing the prediction intensity by a box particle set;
(22) predicting the MBM component in the target state to obtain a prediction parameter set of the MBM component;
(3) updating the target state;
(31) updating the Poisson component, and obtaining the posterior intensity of the Poisson component according to the predicted intensity of the Poisson component;
(32) updating the MBM component, and obtaining an updated MBM component parameter set according to the prediction parameter set and the measurement information of the MBM component;
(4) pruning the Poisson component and the MBM component;
(5) bin resampling the Poisson component and the MBM component;
(6) and estimating the target state to obtain a global target state estimation value.
2. The multi-target tracking method according to claim 1, wherein step (21) comprises:
(21-1) let the intensity of the Poisson component at the k-1 time be represented by the bin particle setWherein the content of the first and second substances,indicating the state of the ith bin particle at time k-1,represents the importance weight of the ith bin particle at time k-1,represents the number of all bin particles at time k-1;
(21-2) the set of predicted intensity bins for the Poisson component at time k is, accordinglyWherein the content of the first and second substances,representing the number of predicted bin particles.
3. The multi-target tracking method of claim 2, wherein the predicted intensity bin particle sets of Poisson components include a predicted bin particle set of surviving targets and a new target bin particle set, wherein,
the prediction box particle of the survival target is expressed asWherein the content of the first and second substances,the status of the predicted bin particle representing the ith survival target,represents the importance weight of the prediction box particle of the ith survival target, an
In the formula, psIndicates the survival probability of the target, [ omega ]]Represents the process noise interval, [ f ]k|k-1]An inclusion function representing a state transition function;
the new generation target bin particle set is represented asWherein, BkIndicates the number of new-box particles,indicating the status of the ith new target box particle,represents the importance weight of the ith new target bin particle.
4. The multi-target tracking method of claim 3, wherein the predicted intensity bin particle set for the Poisson component is expressed as:
5. the multi-target tracking method according to claim 4, wherein step (22) comprises:
(22-1) let the k-1 time MBM component be represented by a parameter setWhere H denotes the index of the Bernoulli component, Hk-1Representing the number of all Bernoulli components,a label representing the Bernoulli component,andrespectively representing the probability of existence and the weight of the Bernoulli component,representing the probability density of the Bernoulli component;
(22-2) the MBM component prediction parameter set at the k-time is, accordingly, set ofWherein the content of the first and second substances,Hk|k-1＝Hk-1，the probability density of the prediction is represented,representing the number of predicted bin particles.
6. The multi-target tracking method of claim 5, wherein the predicted probability densityRepresented by a set of weighted bin particle sets asWherein the content of the first and second substances,
7. the multi-target tracking method according to claim 6, wherein in step (31), the posterior intensity of the Poisson component isWherein the content of the first and second substances,
8. the multi-target tracking method according to claim 1, wherein step (32) comprises:
(32-1) setting the k time measurement random set as Z { [ Z ]1],…,[zm]}; representing the updated parameter set of MBM components asWherein the updated MBM component comprises three single-target hypotheses, namely a hypothesis that a potential target is detected for the first time, a missed detection hypothesis of a surviving target, and a hypothesis that the surviving target is matched with each measurement;
(32-2) obtaining a parameter set of Bernoulli components formed by the potential targets detected for the first time according to the measurement random set;
(32-3) establishing a missing detection hypothesis and calculating a set of parameters of the missing detection hypothesis for the surviving target;
(32-4) obtaining a parameter set of hypotheses formed by matching the survival target with each measurement according to the measurement random set.
9. The multi-target tracking method according to claim 8, wherein step (6) comprises:
(61) taking the product of the weights of the single-target hypothesis as the weight of the global hypothesis, and finding out the global hypothesis with the maximum weight in all the global hypotheses;
(62) screening out a single target hypothesis with existence probability larger than a certain preset threshold from the global hypothesis with the maximum weight to obtain a state estimation interval of the target;
(63) and obtaining a target state estimation value according to the state estimation interval of the target.
10. The multi-target tracking method according to claim 9, wherein the target state estimation values are:
wherein the content of the first and second substances,represents a state estimation interval of the target, and mid (-) represents a center point of the interval.
Background
The target tracking technology is one of the hot spots in the field of computer vision research, and has wide application prospects in various aspects such as military reconnaissance, accurate guidance, fire fighting, battlefield evaluation, security monitoring and the like. The multi-target tracking refers to simultaneously estimating unknown time-varying target states and target numbers from a series of measurements, and is one of important research directions in the field of target tracking.
The first method is to firstly associate the target and the measurement one by one, and then convert the multi-target tracking problem into a single-target tracking problem by using a Bayesian filtering method, and is a traditional multi-target tracking method. The other method is a multi-target tracking method under a Random Finite Set (RFS) framework, the method models the state and the measurement of the target into two Random Finite sets, and then the number and the state of the target are estimated simultaneously by using a multi-target Bayesian filtering technology, so that the complex data association process between the target and the measurement can be effectively avoided.
However, the traditional multi-target tracking method has low tracking efficiency and poor real-time performance because the data association process is processed; although the multi-target tracking method under the RFS framework can avoid the data association process, the method can only estimate the state and the number of the targets and cannot track the tracks of the targets because the elements in the set are unordered.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a multi-target tracking method based on a BP-PMBM filtering algorithm. The technical problem to be solved by the invention is realized by the following technical scheme:
a multi-target tracking method based on a BP-PMBM filtering algorithm comprises the following steps:
(1) initializing an algorithm;
(2) predicting a target state;
(21) predicting the Poisson component in the target state to obtain the prediction intensity of the Poisson component and expressing the prediction intensity by a box particle set;
(22) predicting the MBM component in the target state to obtain a prediction parameter set of the MBM component;
(3) updating the target state;
(31) updating the Poisson component, and obtaining the posterior intensity of the Poisson component according to the predicted intensity of the Poisson component;
(32) updating the MBM component, and obtaining an updated MBM component parameter set according to the prediction parameter set and the measurement information of the MBM component;
(4) pruning the Poisson component and the MBM component;
(5) bin resampling is carried out on the Poisson component and the MBM component;
(6) and estimating the target state to obtain a global target state estimation value.
In one embodiment of the invention, step (21) comprises:
(21-1) let the intensity of the Poisson component at the k-1 time be represented by the bin particle setWherein the content of the first and second substances,indicating the state of the ith bin particle at time k-1,represents the importance weight of the ith bin particle at time k-1,represents the number of all bin particles at time k-1;
(21-2) the set of predicted intensity bins for the Poisson component at time k is, accordinglyWherein the content of the first and second substances,representing the number of predicted bin particles.
In one embodiment of the invention, the predicted intensity bin particle set of the Poisson component includes a predicted bin particle set of surviving targets and a new target bin particle set, wherein,
the prediction box particle of the survival target is expressed asWherein the content of the first and second substances,the status of the predicted bin particle representing the ith survival target,represents the importance weight of the prediction box particle of the ith survival target, an
In the formula, psIndicates the survival probability of the target, [ omega ]]Represents the process noise interval, [ f ]k|k-1]An inclusion function representing a state transition function;
the new generation target bin particle set is represented asWherein, BkIndicates the number of new-box particles,indicating the status of the ith new target box particle,represents the importance weight of the ith new target bin particle.
In one embodiment of the present invention, the predicted intensity bin particle set for the Poisson component is represented as:
in one embodiment of the invention, step (22) comprises:
(22-1) let the k-1 time MBM component be represented by a parameter setWhere H denotes the index of the Bernoulli component, Hk-1Representing the number of all Bernoulli components,a label representing the Bernoulli component,andrespectively representing the probability of existence and the weight of the Bernoulli component,representing the probability density of the Bernoulli component;
(22-2) the MBM component prediction parameter set at the k-time is, accordingly, set ofWherein the content of the first and second substances,Hk|k-1＝Hk-1，the probability density of the prediction is represented,representing the number of predicted bin particles.
In one embodiment of the invention, the predicted probability densityRepresented by a set of weighted bin particle sets asWherein the content of the first and second substances,
in one embodiment of the present invention, in step (31), the posterior intensity of the Poisson component isWherein the content of the first and second substances,
in one embodiment of the invention, step (32) comprises:
(32-1) setting the k time measurement random set as Z { [ Z ]1],…,[zm]}; representing the updated parameter set of MBM components asWherein the updated MBM component comprises three single-target hypotheses, namely a hypothesis that a potential target is detected for the first time, a missed detection hypothesis of a surviving target, and a hypothesis that the surviving target is matched with each measurement;
(32-2) obtaining a parameter set of Bernoulli components formed by the potential targets detected for the first time according to the measurement random set;
(32-3) establishing a missing detection hypothesis and calculating a set of parameters of the missing detection hypothesis for the surviving target;
(32-4) obtaining a parameter set of hypotheses formed by matching the survival target with each measurement according to the measurement random set.
In one embodiment of the present invention, step (6) comprises:
(61) taking the product of the weights of the single-target hypothesis as the weight of the global hypothesis, and finding out the global hypothesis with the maximum weight in all the global hypotheses;
(62) screening out a single target hypothesis with existence probability larger than a certain preset threshold from the global hypothesis with the maximum weight to obtain a state estimation interval of the target;
(63) and obtaining a target state estimation value according to the state estimation interval of the target.
In one embodiment of the present invention, the target state estimation value is:
wherein the content of the first and second substances,represents a state estimation interval of the target, and mid (-) represents a center point of the interval.
The invention has the beneficial effects that:
the multi-target tracking method based on the BP-PMBM filtering algorithm is popularized to a Label Random Finite Set (LRFS) on the basis of the PMBM filtering algorithm to realize the tracking of a target track, and the box particle implementation mode of the algorithm is provided, so that the method has the advantages of high tracking precision, high operation speed, capability of distinguishing the track and the like.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 1 is a schematic flow chart of a multi-target tracking method based on a BP-PMBM filtering algorithm according to an embodiment of the present invention;
FIG. 2 is a graph illustrating a motion trajectory and a measurement of an object under a linear scene according to an embodiment of the present invention;
FIG. 3 is a graph of the tracking effect of a one-time Monte Carlo BP-PMBM filter in a linear scenario according to an embodiment of the present invention;
FIG. 4 is an average target number estimate for 100 Monte Carlo simulations in a linear scenario, provided by an embodiment of the present invention;
FIG. 5 is an average OSPA distance of 100 Monte Carlo simulations in a linear scenario provided by an embodiment of the present invention;
fig. 6 shows the real motion trajectories and the measured distribution of clutter of 6 targets in the observation area in the non-linear scene according to the embodiment of the present invention;
FIG. 7 shows a Monte Carlo tracking performance of the BP-PMBM filtering algorithm in the non-linear scenario provided by the embodiment of the present invention;
fig. 8 is an average target number estimation of 100 monte carlo simulations of a BP-PMBM filtering algorithm under a nonlinear scenario when an average noise number r is 10 according to an embodiment of the present invention;
fig. 9 is an average OSPA distance of 100 monte carlo simulations when the average noise number r is 10 by the BP-PMBM filtering algorithm in the nonlinear scenario provided by the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
First, a Box Particle (BP) filtering and a Poisson Multi-Bernoulli mixing (PMBM) filtering method are introduced.
BP filtering is a generalized particle filter algorithm that combines interval analysis with a sequential monte carlo method, using a bin of particles of controllable size and known maximum error instead of point particles used in particle filtering and using an error bound model to describe the random uncertainty of the system.
The PMBM filtering method is a multi-target tracking method under an RFS framework, and models the state of multiple targets into a mixture of a Poisson random set and a multi-Bernoulli random set, namely a Poisson part and an MBM part, wherein the Poisson part is used for representing all undetected targets, and the MBM part is used for processing all data association hypotheses.
The multi-target tracking method based on the BP-PMBM filter algorithm provided by this embodiment is based on the PMBM filter algorithm, and is generalized to a Labeled Random Finite Set (LRFS) to realize tracking of a target track, and a box particle implementation manner of the algorithm is proposed, that is, the BP-PMBM filter algorithm, the filter structure of which is as follows:
the algorithm can be divided into Poisson and MBM parts, wherein the Poisson part can be described by the intensity of the Poisson part and can be represented as a group of weighted box particle setsIndicates the state interval (bin),for its weight, N is the number of bin particles. The MBM part is a mixture of a plurality of labeled Bernoulli components, each of which represents a target-measurement association hypothesis and can be described by a parameter set { l, r, w, p }, wherein l represents a label, r and w are respectively the existence probability and weight of the Bernoulli component, and p represents the probability density of the Bernoulli component, and can be represented by a set of weighted box particle setsAnd (4) showing.
Specifically, referring to fig. 1, fig. 1 is a schematic flow chart of a multi-target tracking method based on a BP-PMBM filtering algorithm according to an embodiment of the present invention, including:
(1) initializing an algorithm;
specifically, the PMBM probability density includes Poisson and MBM parts, and the initial intensity of the Poisson part can be determined by a set of weighted box particlesIt is shown that,for a set of bin particles sampled from an initial state, N0The initial weight of each box particle is 1/N for the number of the box particles at the initial moment0。
Since the initial time instants have not yet produced Bernoulli components, the initial probability density of MBM is an empty set.
(2) Predicting a target state;
(21) predicting the Poisson component in the target state to obtain the prediction intensity of the Poisson component and expressing the prediction intensity by a box particle set;
further, the step (21) includes:
(21-1) let the intensity of the Poisson component at the k-1 time be represented by the bin particle setWherein the content of the first and second substances,indicating the state of the ith bin particle at time k-1,represents the importance weight of the ith bin particle at time k-1,represents the number of all bin particles at time k-1;
(21-2) the set of predicted intensity bins for the Poisson component at time k is, accordinglyWherein the content of the first and second substances,representing the number of predicted bin particles.
Further, the predicted intensity bin particle set of the Poisson component includes a predicted bin particle set of surviving targets and a nascent target bin particle set, wherein,
the prediction box particle of the survival target is expressed asWherein the content of the first and second substances,the status of the predicted bin particle representing the ith survival target,represents the importance weight of the prediction box particle of the ith survival target, an
In the formula, psIndicates the survival probability of the target, [ omega ]]Represents the process noise interval, [ f ]k|k-1]An inclusion function representing a state transition function;
the new generation target bin particle set is represented asWherein, BkIndicates the number of new-box particles,indicating the status of the ith new target box particle,represents the importance weight of the ith new target bin particle.
The predicted intensity bin particle set for the Poisson component is expressed as:
(22) predicting the MBM component in the target state to obtain a prediction parameter set of the MBM component;
further, the step (22) includes:
(22-1) let the k-1 time MBM component be represented by a parameter setWhere H denotes the index of the Bernoulli component, Hk-1Representing the number of all Bernoulli components,a label representing the Bernoulli component,andrespectively representing the probability of existence and the weight of the Bernoulli component,representing the probability density of the Bernoulli component;
in particular, the amount of the solvent to be used,can be set by a set of weighted box particlesA description is given.
(22-2) the MBM component prediction parameter set at the k-time is, accordingly, set ofWherein, each parameter is calculated as follows:
Hk|k-1＝Hk-1 (8)
further, the probability density is predictedCan be set by a set of weighted box particlesIs shown in whichTo predict the number of box particles, its value andthe same is true. The weight and the state of the box particles are respectively as follows:
(3) updating the target state;
(31) updating the Poisson component, and obtaining the posterior intensity of the Poisson component according to the predicted intensity of the Poisson component;
specifically, the predicted intensity of the Poisson component at time k is determined from the bin particle set obtained in step (21)Expressed, the posterior intensity of the Poisson component at time k can be expressed as a bin particle setWherein the content of the first and second substances,
(32) updating the MBM component, and obtaining an updated MBM component parameter set according to the prediction parameter set and the measurement information of the MBM component;
in this embodiment, the predicted MBM component at time k, obtained in step (22), can be expressed as a parameter setOf the form (1), wherein the probability density of the Bernoulli componentCan be set by a set of weighted box particlesIt is shown that,is the number of bin particles.
Further, the step (32) includes:
(32-1) setting the k time measurement random set as Z { [ Z ]1],…,[zm]}; representing the updated parameter set of MBM components asWherein the updated MBM component comprises three single-target hypotheses, namely a hypothesis that a potential target is detected for the first time, a missed detection hypothesis of a surviving target, and a hypothesis that the surviving target is matched with each measurement;
specifically, each measurement can be considered to originate from a potential target detected for the first time, the number of such hypotheses is the same as the number m of measurements, each surviving target is likely to be missed at the current time, and the number of missed hypotheses is the same as the number H of predicted single target hypothesesk|k-1Similarly, each surviving target may match any of the measurements at the current time, and the number of such hypotheses is the product H of the number of predicted hypotheses and the number of measurementsk|k-1X m, number of updated hypotheses Hk＝m+Hk|k-1+Hk|k-1×m，Can be collected by weighting the binsAnd (4) showing.
(32-2) obtaining a parameter set of Bernoulli components formed by the potential targets detected for the first time according to the measurement random set;
specifically, for any measurement, which can be considered as a potential target to be detected for the first time, a Bernoulli component is formed, and the component is set as (l)n,rn,wn,pn)，pnCan be collected by weighting the binsA description is given.
In this embodiment, for the Bernoulli component formed when the potential target is first detected, if the predicted strength of the Poisson componentAll box particles in relation to a certain measurement [ z ]]Likelihood of (1) andabove a certain predetermined threshold, thenIs composed ofAll likelihood of not 0The weight of each bin of particles is:
where N is the number of bin particles for which the likelihood is not 0.
The existence probability and the weight of the Bernoulli component are respectively as follows:
the label is lnAnd k is the current time, and j is the index of the measurement.
If it is about measurement [ z]Likelihood of (1) andif the preset threshold is not reached, thenrn＝0，wn＝c(z)，ln＝0。
(32-3) establishing a missing detection hypothesis and calculating a set of parameters of the missing detection hypothesis for the surviving target;
in particular, a single target hypothesis for each surviving targetFirst, a false negative assumption is made (l)mis,rmis,wmis,pmis) The probability density of the hypothesis may be represented by a set of weighted box particle sets, where the state of each box particle is associated with the weighted box particle set that predicted the Bernoulli probability densityThe box particle states in the box are the same, and the weight is:
the assumed existence probability and weight are respectively:
the label is as follows:
(32-4) obtaining a parameter set of hypotheses formed by matching the survival target with each measurement according to the measurement random set.
In particular, all measurements are traversed, for each measurement [ z ]]All are combined withMatching is performed to form a new hypothesis (l)det,rdet,wdet,pdet) The state and predicted Bernoulli probability density of each bin in the set of bin particles describing the hypothesized probability densityThe box particle states in the box are the same, and the weight is:
the assumed existence probability and weight are respectively:
rdet＝1 (22)
the label is as follows:
(4) pruning the Poisson component and the MBM component;
since the number of bin populations in the Poisson component and the number of hypotheses in the MBM component increase and decrease with time, the filter operation rate decreases, and therefore, the Poisson component and the MBM component need to be clipped.
In particular, it is possible to set two thresholds TPAnd TBAnd respectively corresponding to a Poisson component and an MBM component, for the Poisson component, cutting off box particles with the box particle weight value lower than a preset threshold value, and for the MBM component, cutting off Bernoulli items with the Bernoulli weight value lower than the threshold value.
(5) Bin resampling is carried out on the Poisson component and the MBM component;
specifically, a random subdivision strategy is adopted, the sampling frequency is determined according to the weight of each box particle, and if the resampling frequency of a certain box particle is n, the box particle is divided into n subintervals after resampling, and finally the subintervals are used as the box particle after resampling.
(6) And estimating the target state to obtain a global target state estimation value.
(61) Taking the product of the weights of the single-target hypothesis as the weight of the global hypothesis, and finding out the global hypothesis with the maximum weight in all the global hypotheses;
specifically, the product of the weights of all the single target hypotheses in the global hypothesis j isAs the weight of the global hypothesis j, find out the global hypothesis with the largest weight, and let it be j*I.e. by
(62) Screening out a single target hypothesis with existence probability larger than a certain preset threshold from the global hypothesis with the maximum weight to obtain a state estimation interval of the target;
in particular, traverse global hypothesis j*All the single target hypotheses are screened out, the single target hypotheses with the existing probability larger than a certain preset threshold T are screened out, and the probability density of the single target hypotheses can be determined by the particle setExpressed, the state estimation interval of the target can be represented by the weighted particle sum of each hypothesis, i.e.
(63) And obtaining a target state estimation value according to the state estimation interval of the target.
Specifically, the state estimate for the target may be expressed as:
where mid (-) denotes the center point of the interval.
The multi-target tracking method based on the BP-PMBM filtering algorithm provided by this embodiment is based on the PMBM filtering algorithm, and is popularized to a Labeled Random Finite Set (LRFS) to realize tracking of a target track, and a box particle implementation manner of the algorithm is provided.
Example two
The invention is further illustrated below in connection with MATLAB simulations.
Simulation experiment I: filtering performance representation of BP-PMBM in linear scene
Assume that the area size is [ -250m,250m]×[-250m,250]m two-dimensional simulation monitoring area with random noise has 6 targets which do uniform turning motion within 50 observation moments in sequence, and the target state isWherein (x, y) represents the position of the target,for the speed of the target in the x-direction and y-direction,representing the angular velocity of the target. Table 1 shows the initial state and survival time of 6 targets.
TABLE 1 target initial State and survival time
Target serial number
Target initial state/(m, m/s, m, m/s, rad/s)
Starting time/s
End time/s
1
[150,-2,100,-8,-2π/180]T
1
50
2
[150,-10,100,0,3π/180]T
5
24
3
[-100,8,0,-8,π/180]T
8
30
4
[-100,8,0,8,-π/180]T
12
27
5
[-50,8,150,1,π/180]T
18
35
6
[-50,8,150,-8,π/180]T
22
37
Assuming that the probability density of the nascent object follows a Gaussian distribution, i.e. pb＝N(x；mb,Pb) The new probability of the object is rb0.01, the new target initial state is Variance is PB＝diag([10,10,10,10,3π/180])2. Assuming that the sampling period T is 1s, the state equation and the measurement equation of the target are:
xk＝Fxk-1+Gvk (27)
zk＝Hxk+wk (28)
wherein the content of the first and second substances,
setting the length of the measuring interval as [15m,15m]TThe noise covariance and the process covariance are R ═ diag ([ 1.5)2,1.52])m2Andwherein sigmaω＝3m/s2，σuPi/180 rad/s. The number of clutter follows a Poisson distribution with an average value r 10, which is uniformly distributed within the monitored area. The target survival probability and the detection probability are respectively ps＝0.99，pd0.98, OSPA parameter p 1, c 300. The actual motion trajectories and measurement and tracking results of the 6 targets are shown in fig. 2-3.
Fig. 2 is a graph of a target motion trajectory and a measurement graph in a linear scene according to an embodiment of the present invention, a solid line in fig. 2 shows a real motion trajectory of 6 targets, and a square area represents interval measurement. Fig. 3 is a graph of the tracking effect of the one-time monte carlo of the BP-PMBM filter in the linear scene provided by the embodiment of the present invention, and the tracks of different targets in fig. 3 are marked with different symbols, as can be seen from fig. 3, the proposed algorithm can accurately track the states and tracks of multiple targets.
Referring to fig. 4 and 5, fig. 4 is an average target number estimation of 100 monte carlo simulations in a linear scenario according to an embodiment of the present invention; fig. 5 is an average OSPA distance of 100 monte carlo simulations in a linear scenario provided by an embodiment of the present invention. As can be seen from fig. 4, the filter can estimate the number of targets more accurately, and has better tracking accuracy. Since the filters are all based on the multi-hypothesis tracking idea, when the target disappears, the weight change of the vanishing target hypothesis component has a certain delay, so in fig. 4, at the time 24, 27, 30, 35, 37, when the target disappears, the number of real targets decreases, the number of estimated targets decreases with a delay of one time, and the OSPA distance at the corresponding time in fig. 5 has a peak.
The time for a single trace in the experiment was about 35s, the number of box particles was 40, and the number of box particles per nascent target was 5.
And (2) simulation experiment II: filtering performance representation of SMC-PMBM in nonlinear scene
In the experiment, MATLAB simulation is carried out on a BP-PMBM filtering algorithm under a nonlinear radar observation system, and performance are evaluated and tracked. Suppose that the region size is [ -250m, within 50 observation instants]×[-250m,250m]The simulation monitoring area carries out uniform turning motion on 6 new targets in sequence, and the target state isTable 2 shows the initial states and start and end times of the 6 targets.
TABLE 2 target initial State and Start-stop time
Target serial number
Target initial state/(m, m/s, m, m/s, rad/s)
Starting time/s
End time/s
1
[250,-2,100,-8,-π/180]T
1
50
2
[250,-10,100,0,3π/180]T
8
27
3
[-150,6,-200,5,π/180]T
5
30
4
[-150,4,-200,12,3π/180]T
12
27
5
[-170,10,150,-1,-π/180]T
14
31
6
[-170,8,150,-8,-π/180]T
22
37
The state equation and nonlinear measurement equation of the target are:
xk＝Fxk-1+Gvk (29)
wherein the content of the first and second substances,
the sampling period of the sensor is T1 s, and the process noise covariance isWherein sigmaω＝3m/s2，σu4 pi/180 rad/s; measured noise covariance ofWherein sigmaα＝π/(4×180)rad，σρ1m, and a measurement interval of [ Δ α, Δ ρ ]]TWherein Δ α ═ 6 π/180rad, Δ ρ ═ 20 m. The probability of object neogenesis is rb0.01, the initial state of the new target is Variance is Pb＝diag([10,10,10,10,3π/180])2。
The number of clutter is subject to Poisson distribution with mean value r of 10 and the clutter is uniformly distributed in the monitoringWithin the zone. Target survival probability of ps0.99, detection probability pdThe OSPA parameter is set to c 300 and p 1 0.98.
Referring to fig. 6 and 7, fig. 6 is a measurement distribution of real motion trajectories and clutter of 6 targets in an observation area under a non-linear scene according to an embodiment of the present invention, where a solid line in fig. 6 is the real motion trajectory of the target, and a square area represents interval measurement of the target and the clutter. Fig. 7 is a one-time monte carlo tracking representation of the BP-PMBM filtering algorithm in the nonlinear scene provided by the embodiment of the present invention, and as can be seen from fig. 7, the filter can basically and effectively track the states of multiple targets and distinguish tracks of different targets. Referring to fig. 8 and fig. 9, fig. 8 is an average target number estimation of 100 monte carlo simulations when an average noise number r is 10 for the BP-PMBM filtering algorithm under the nonlinear scenario provided by the embodiment of the present invention; fig. 9 is an average OSPA distance of 100 monte carlo simulations when the average noise number r is 10 by the BP-PMBM filtering algorithm in the nonlinear scenario provided by the embodiment of the present invention.
As can be seen from fig. 8 and 9, the number estimation of the BP-PMBM filtering algorithm is more accurate and has better OSPA distance performance.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
