CN109946694A - Circumference SAR multi-object tracking method based on stochastic finite collection - Google Patents
Circumference SAR multi-object tracking method based on stochastic finite collection Download PDFInfo
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Abstract
Circumference SAR multi-object tracking method based on stochastic finite collection, the present invention relates to circumference SAR multi-object tracking methods.The purpose of the present invention is to solve tradition to calculate complicated problem based on the multi-object tracking method of data correlation.Process are as follows: one: Preliminary detection is carried out to moving target based on DPCA-CFAR method, obtains the measuring value of moving target；Two: according to moving target measuring value, establishing the state vector set of multiple mobile object and measure vector set；Three: obtained measurement vector being modified, measures vector after being compensated；Four: according to vector is measured after compensation, establishing dbjective state model and measurement model；Five: the target following based on GMPHD filter is carried out according to the dbjective state model and measurement model that provide.The present invention is for microwave remote sensing technique and radar data process field.
Description
Technical field
The present invention relates to microwave remote sensing techniques and radar data process field more particularly to multiple target tracking algorithm field.
Background technique
Circumference SAR (CSAR) has both as a kind of high-resolution imaging method over the ground and observes and obtain target for a long time
The advantage of 360 ° of omnidirectional's information in terms of moving-target processing, is observed since flying platform does Circular test movement using its long-time
Characteristic, radial component of the moving-target under different angle can be obtained.In image sequence, static target position is kept not
Becoming, moving target is because its position of the movement of itself constantly changes, since radial velocity causes orientation positional shift, movement
The imaging position of target is not actual position.Mainly for the moving target after circumference SAR image Sequence Detection, it is carried out with
Track processing, eliminates the Clutter of not motion feature, improves detection performance, and obtain position and the kinematic parameter of target.?
Moving target is usually multiple target in SAR image scene, remaining a large amount of clutters after conventional clutter recognition and CFAR detection, especially
In urban area, clutter background is stronger.For multiple target tracking problem under high clutter background, traditional target association is directlyed adopt
Algorithm needs to spend a large amount of calculating to solve the problems, such as data correlation, and high false alarm rate leads to the increase of false track quantity and track
Mistake is tracked, therefore practical need are all unable to satisfy in computational efficiency and tracking performance based on associated multi-object tracking method
It asks, is not suitable for the motion target tracking of data after SAR image target detection.
According to finite set statistics theory (FISST), by image sequence multiple target state and observation respectively with
Machine finite aggregate (RFS) characterization, using the observation RFS at each moment, using Bayesian frame to the posteriority multiple target state at each moment
RFS is estimated, to realize the Combined estimator to target number and corresponding each dbjective state.Compared to traditional more mesh
Track algorithm is marked, the multiple target tracking algorithm based on RFS theory no longer individually carries out single target state and single observation
Processing, but as a whole, all observations as a whole all dbjective state of each moment, to keep away
Complicated data correlation problem is opened.However the integral in multi-objective Bayesian filter is set valued integrals, can not usually be solved.
Therefore, the method for seeking suboptimum in practical applications carrys out approximate multi-objective Bayesian filter.Probability hypothesis density (PHD) filtering
Device be then by the first moment information of each moment multiple target state RFS of iterative estimate, as a kind of suboptimal solution of Bayesian filter,
Complicated data correlation problem is not only avoided, while solving set valued integrals double linear problems of difficulty for solving under Bayesian frame, there is reason
The Bayes's meaning and propinquity effect thought.
Summary of the invention
The purpose of the present invention is to solve tradition to calculate complicated problem based on the multi-object tracking method of data correlation,
And propose the circumference SAR multi-object tracking method based on stochastic finite collection.
Circumference SAR multi-object tracking method detailed process based on stochastic finite collection are as follows:
Step 1: Preliminary detection is carried out to moving target based on DPCA-CFAR method, obtains the measuring value of moving target；
Step 2: the moving target measuring value obtained according to step 1, establish moving target state vector and measure to
Amount according to the state vector of moving target and measures vector, establishes the state vector set of multiple mobile object and measures vector set
It closes；
Step 3: the measurement vector that step 2 obtains is modified, measures vector after being compensated；
Step 4: according to vector is measured after compensation, dbjective state model and measurement model are established；
Step 5: the dbjective state model and measurement model provided according to step 4 carries out the mesh based on GMPHD filter
Mark tracking；Target following based on GMPHD filter includes PHD prediction, and PHD updates, the trimming of Gaussian component, multiple target number
And state estimation；
The GMPHD is the filtering of gaussian sum probability hypothesis density；
The multiple mobile object is 2 and 2 or more moving targets.
The invention has the benefit that
The present invention is based on circumference SAR image sequences to realize SAR tracking of maneuvering target method, the present invention using GMPHD filter
It proposes a kind of circumference SAR multi-object tracking method based on stochastic finite collection, using the observation stochastic finite collection at each moment, uses
Bayesian frame estimates the posteriority multiple target state stochastic finite collection at each moment, to realize to target number and correspondence
Each dbjective state Combined estimator.Compared to traditional multiple target tracking algorithm, more mesh based on stochastic finite collection theory
Mark track algorithm is no longer individually handled single target state and single observation, but the target-like that each moment is all
State as a whole, to avoid complicated data correlation problem, solves as a whole, all observations
Tradition calculates complicated problem based on the multi-object tracking method of data correlation.
1, the present invention carries out tracking processing to it, elimination does not have for the moving target after circumference SAR image Sequence Detection
The Clutter of motion feature improves detection performance, and obtains position and the kinematic parameter of target.
2, the present invention can close compared with traditional multiple target tracking algorithm based on data correlation to avoid complicated data
Connection process.
3, the present invention can directly estimate the number of multiple target and state simultaneously, and have stringenter mathematics
Theoretical basis.
4, simulation result shows: the multi-object tracking method based on stochastic finite collection can effectively realize moving-target with
Track obtains the true motion state of moving-target.
It in the gesture statistics of 500 Monte Carlo simulations, carves, due to the intensity inaccuracy of newborn target, needs at the beginning
Certain time is wanted to obtain correct estimated value.Increase with the tracking time, real goal number can be converged on.The OPSA of GMPHD
Distance is smaller, and in 2m hereinafter, gesture error is equipped with large error in start bit, subsequent fluctuation is smaller for position error control.Pass through reality
The feasibility that this method is illustrated is verified, the multi-object tracking method based on GMPHD can effectively realize the tracking of moving-target, obtain
The true motion state of moving-target.
Detailed description of the invention
Fig. 1 is binary channels circumference SAR system geometrical relationship figure, Pa(Rgcosθ,Rgsinθ,Zh) it is radar in the side of running to
Momentary position coordinates when parallactic angle is the position θ, RcFor radar to the distance at observation area center, RgFor radar uniform motion circumference
Radius note, ZhFor carrier of radar height, it is set in Ptm(xtm,ytm, 0) and it is moving target position coordinate in scene, Rrt(θ) is thunder
Up to carrier aircraft platform to the oblique distance of target, θiFor radar beam incidence angle at the center of observation area, θ is azimuth, and V (θ) is radar
Platform moves linear velocity；
Fig. 2 is the circumference SAR multi-object tracking method flow chart based on stochastic finite collection；
Fig. 3 is GM-PHD filter tracks effect picture；
Fig. 4 is GM-PHD filter tracking result figure at any time；
Fig. 5 a is the OSPA distance for carrying out 500 Monte Carlo simulations in emulation experiment of the present invention using GM-PHD filter
Result figure；
Fig. 5 b is to be positioned in emulation experiment of the present invention using the OSPA that GM-PHD filter carries out 500 Monte Carlo simulations
Error result figure；
Fig. 5 c is the OSPACard for carrying out 500 Monte Carlo simulations in emulation experiment of the present invention using GM-PHD filter
Gesture error result figure；
Fig. 6 is to estimate analysis chart using the gesture of GM-PHD filter in emulation experiment of the present invention.
Specific embodiment
Specific embodiment 1: the circumference SAR multi-object tracking method detailed process of present embodiment stochastic finite collection are as follows:
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, below with reference to Fig. 1, Fig. 2, Fig. 3,
Fig. 4, the present invention is described in further detail for Fig. 5, Fig. 6 and specific embodiment；
Wherein Fig. 2 is the stream of the present invention based on the circumference SAR motion target tracking method for improving GMPHD filter
Cheng Tu.
Step 1: Preliminary detection is carried out to moving target based on DPCA-CFAR method, obtains the measuring value of moving target；
Step 2: the moving target measuring value obtained according to step 1, establish moving target state vector and measure to
Amount according to the state vector of moving target and measures vector, establishes the state vector set of multiple mobile object and measures vector set
It closes；
Step 3: the measurement vector that step 2 obtains is modified, measures vector after being compensated；
Step 4: according to vector is measured after compensation, dbjective state model and measurement model are established；
Step 5: the dbjective state model and measurement model provided according to step 4 carries out the mesh based on GMPHD filter
Mark tracking；Target following based on GMPHD filter includes PHD prediction, and PHD updates, the trimming of Gaussian component, multiple target number
And state estimation；
The GMPHD is the filtering of gaussian sum probability hypothesis density；
The multiple mobile object is 2 and 2 or more moving targets.
Specific embodiment 2: the present embodiment is different from the first embodiment in that, it is based in the step 1
DPCA-CFAR method carries out Preliminary detection to moving target, obtains the measuring value of moving target；Detailed process are as follows:
Binary channels circumference SAR system geometrical relationship as shown in Figure 1, for multichannel circumference SAR system carrier aircraft platform away from
From objective plane z=ZhPlane on RgFor radius, circumferentially uniform motion is made in path, and it is V that carrier aircraft platform, which moves linear velocity, because
And carrier aircraft platform angular velocity of satellite motion is expressed as ω=V/Rg；
For multichannel circumference SAR, it is horizontally arranged N width antenna along radar track tangential direction, the spacing between antenna is equal
For d, knocked off operation mode using single-shot, by reference channel (antenna C more1) emitting linear FM signal, all antennas receive simultaneously
Echo-signal；
The multichannel is 2 and 2 with upper channel；
Momentary position coordinates of the reference channel when running to azimuth and being the position θ are Pa(Rgcosθ,Rgsinθ,Zh),
Middle θ ∈ [0,2 π) it is azimuth, azimuth represents synthetic aperture domain, i.e. tmSlow time-domain；
When circumferentially track moves carrier aircraft platform, the radar beam center in carrier aircraft platform is radiated at always with R0It is half
Diameter, O are in the circumference observation area Ω in the center of circle；The distance at radar to observation area center isObservation area
Radar beam incidence angle is at centerI indicates incidence angle；If certain moving target in observation area
Positioned at Pt(x(tm)), the state vector of moving target is expressed as
Wherein [x (tm),y(tm)] indicate moving target position,Indicate moving target in Descartes
The speed of coordinate system x-axis and y-axis direction；tmIndicate slow time-domain；
The instantaneous oblique distance of twin-channel two channel distance moving targets is expressed as Ri(tm), i=1,2；
Since moving target is submerged in strong clutter, it is difficult to obtain target measuring value.Therefore, first with DPCA technology
It realizes clutter recognition, the Preliminary detection of moving target is used for extracting the measuring value of target by constant false alarm detector realization
In subsequent Moving Target Tracking Algorithm.Based on displaced phase center principle, it is necessary first to carry out time calibration and phase to signal
Position compensation carries out DPCA processing to two channel images, realizes clutter recognition.
If two channel image sequences after time calibration are expressed as I1,k(x, y) and I2,k(x, y), wherein k=1,2 ..., K
Indicate frame number；
The relationship of two channel image sequences is expressed as
Wherein λ indicates wavelength；J is imaginary number, j2=-1；vrIndicate the radial velocity of moving target；Using DPCA technology to two
Channel image obtain after offseting processing | IDPCA,k(x, y) |, realize clutter recognition；
According to above formula it is found that DPCA treated that amplitude is related with target radial speed, above formula is realized for static target
It is zero, to realize clutter recognition.
After clutter recognition, OS-CFAR Preliminary detection is carried out to each frame image and obtains target measuring value, examined in constant false alarm
Higher false-alarm probability P is set in surveyfa, to ensure based on higher detection probability PdThe measuring value of moving target is obtained, so that
The observation of most moving targets is detected, and guarantees the complete track of moving target.Without the clutter of motion feature
It is eliminated by subsequent track algorithm, therefore further decreases false-alarm probability under the premise of compared with high detection probability.
Specific embodiment 3: the present embodiment is different from the first and the second embodiment in that, it is described to each frame figure
Target measuring value is obtained as carrying out OS-CFAR Preliminary detection, higher false-alarm probability P is set in CFAR detectionfa, to ensure
Based on higher detection probability PdObtain the measuring value of moving target；Detailed process are as follows:
The detection threshold η in OS-CFAR detectorkBy false-alarm probability PfaWith | IDPCA,k(x, y) | probability statistics determine,
OS-CFAR Preliminary detection result is expressed as
Wherein detection threshold ηkBy false-alarm probability PfaAnd IDPCA,kThe probability statistics of (x, y) determine；
To OS-CFAR Preliminary detection result Bk(x, y) carries out image procossing, obtains the measuring value of moving target；Process are as follows:
The target area that connection is obtained by morphologic corrosion expansive working, carries out edge detection to target area and obtains
The center point for taking target, using the center of target point as the measuring value of moving target.
Other steps and parameter are the same as one or two specific embodiments.
Specific embodiment 4: the false-alarm is general unlike one of present embodiment and specific embodiment one to three
Rate Pfa=0.01.
Other steps and parameter are identical as one of specific embodiment one to three.
Specific embodiment 5: unlike one of present embodiment and specific embodiment one to four, the step 2
The middle moving target observation obtained according to step 1 establishes the state vector of moving target and measures vector, according to movement mesh
Target state vector and measurement vector establish the state vector set of multiple mobile object and measure vector set；Detailed process are as follows:
The state vector of target is expressed as[xk,yk] indicate moving target position,
Indicate moving target in the speed of cartesian coordinate system x-axis and y-axis direction；
The measuring value of moving target is expressed as z in SAR imagek=[x'k,y'k]TIt (is obtained by step 1 Preliminary detection
Measuring value), measuring value is the position of target on the image, due to moving target in SAR image there are orientation displacement, because
The measuring value of this target is unable to the actual position of accurate response target, the only apparent position of target；
Assuming that there are a moving target of N (k) and a measuring value of M (k) in kth frame, then multiple mobile object state vector collection
The form of stochastic finite set can be regarded as by closing and measure vector set, be expressed as
Wherein, xk,1Indicate the state vector of first moving target in kth frame, xk,N(k)Indicate that N (k) is a in kth frame
The state vector of moving target；zk,1Indicate the measurement vector of first moving target in kth frame, zk,M(k) indicate the in kth frame
The measurement vector of a moving target of M (k)；WithThe respectively state space of moving targetWith measurement space
The set that upper all finite subsets are constituted.
The state of target and measurement are unordered in finite aggregate；For the multiple target state vector at given k-1 moment
Set Xk-1, each dbjective state vector xk-1∈Xk-1With Probability pS,k-1(xk-1) it is transferred to new state vector xk, or with general
Rate 1-pS,k-1(xk-1) disappear；Therefore, for the state vector x at given k-1 momentk∈Xk-1, the state vector of subsequent time can
With with stochastic finite collection Sk|k-1(xk-1) indicate, when target exists, Sk|k-1(xk-1) it is { xk, when target disappears,
Sk|k-1(xk-1) it is empty set；In addition, in the new target that the k moment is likely to occur, so the multiple target state at given k-1 moment
Xk-1, the multiple target state X at k momentkThen by the target and newborn target configuration survived, i.e.,
Wherein, ΓkIndicate k moment new life target random set, Sk|k-1(xk-1) indicate subsequent time state vector it is random
Finite aggregate, Xk-1Indicate the multiple target state vector set at k-1 moment；
The measurement model of target usually require to consider uncertainty in measurement and false-alarm there are the case where.When for given k
Carve dbjective state vector xk∈XkWith Probability pD,k(xk) be detected, or with probability 1-pD,k(xk) be not detected；When target quilt
When detecting, from xkThe measurement z of acquisitionkProbability density be gk(zk|xk), then in k moment each target xk∈XkGenerate one
Stochastic finite collection, i.e. Θk(xk), when target is detected, Θk(xk) it is { zk, when target is not detected, Θk(xk)
For empty set；In addition, there is also the set K that false-alarm or clutter are constituted in addition to the measurement from targetk, so more at the given k moment
Dbjective state Xk, the measurement Z of multiple targetkThe measurement and clutter generated by target is constituted, i.e.,
Wherein, KkIndicate false-alarm or the set that clutter is constituted；Θk(xk) indicate k moment each target xk∈XkGenerate one
Stochastic finite collection.
Other steps and parameter are identical as one of specific embodiment one to four.
Specific embodiment 6: unlike one of present embodiment and specific embodiment one to five, the step 3
In the measurement vector that step 2 obtains is modified, measure vector after being compensated；
Due to the radial velocity of target, so that moving target shifts in orientation, the observation of acquisition is simultaneously non-targeted
Actual position, this has an adverse effect to the tracking of target, needs to be modified observation, and compensation is drawn due to radial velocity
The orientation offset risen；Specific steps are as follows:
The target P in kth frame image sequencet(xk) radial velocity be expressed as
Wherein θa,kIndicate the azimuth of kth frame radar platform, carrier of radar platform to target Pt(xk) oblique distance RkIt is expressed as
Since the initial oblique distance of radar to moving target is larger, oblique distance change over time it is smaller, therefore for microinching
Target puts aside that oblique distance caused by target and radar motion changes in analysis, i.e. hypothesis Rk=R, is caused by radial velocity
Orientation offset be
Wherein, oblique distance of the R expression radar platform to target；
ATI technology is primarily based on by two channel image sequence I after time calibration1,k(x, y) and I2,k(x, y) is conjugated phase
Multiply, obtains interferometric phase Δ φk, realize the estimation to target bearing to offsetTherefore it is mended
Measurement vector after repayingWithIt is denoted as
Wherein, xk' indicate moving target in cartesian coordinate system x-axis coordinate, yk' indicate moving target in cartesian coordinate
It is y-axis coordinate (measuring value obtained by step 1 Preliminary detection).
Other steps and parameter are identical as one of specific embodiment one to five.
Specific embodiment 7: unlike one of present embodiment and specific embodiment one to six, the step 4
It is middle according to vector is measured after compensation, establish dbjective state model and measurement model；Specific steps are as follows:
Target dynamic equation (dbjective state model) is expressed as
xk=Fk-1xk-1+vk-1
Wherein, process noise vectorO is 0 vector of 4*1；Covariance isσvTable
Show the standard deviation of process noise, GkFor process noise distribution matrix, FkFor dynamic model state-transition matrix；
Assuming that the forms of motion of target is CV (constant velocity model (constant velocity model)) mould in scene
Type, FkAnd GkIt is expressed as
In formula, T is the sampling period；
Measurement equation (measurement model) is expressed as
zk=Hkxk+wk
Wherein measure noise wk~Ν (O ', Rk), O ' is 0 vector of 2*1；CovarianceσwIt indicates to measure noise
Standard deviation, I2For 2 × 2 unit matrix；
Observing matrix can be expressed as
Other steps and parameter are identical as one of specific embodiment one to six.
Specific embodiment 8: unlike one of present embodiment and specific embodiment one to seven, the step 5
The middle dbjective state model provided according to step 4 and measurement model carry out the target following based on GMPHD filter；It is based on
The target following of GMPHD filter includes PHD prediction, and PHD updates, the trimming of Gaussian component, multiple target number and state estimation；
Detailed process are as follows:
The dbjective state model and measurement model of moving target in SAR scene belong to linear Gauss model, are expressed as
In formula, xkFor the state vector of kth frame prediction；ζ is the state vector of -1 frame of kth；zkTo measure vector；
Following step needs to set up under this condition in satisfaction；
Step 5 one: PHD is predicted:
Assuming that the posteriority intensity of -1 frame of kth and the intensity of newborn target stochastic finite collection are Gaussian Mixture form, then kth
The predicted intensity of frame is expressed as
Wherein, pS,kIndicate the survival probability of target,Indicate the mean value of Gaussian term after PHD is predicted, Indicate the mean value in each Gaussian term of -1 frame of kth；Indicate Gaussian term after PHD is predicted
Variance, Indicate the variance in each Gaussian term of -1 frame of kth；Indicate the intensity of newborn target stochastic finite collection, Jk-1Indicate -1 vertical frame dimension of kth this
The number of item, Jγ,kIndicate that, in kth frame new life Gaussian term number, i indicates the index value of newborn Gaussian term；With
Respectively indicate the weight of each newborn Gaussian term, mean value and variance.
Step 5 two: PHD updates: according to the predicted intensity v of kth framek|k-1(xk) and measurement vector set Zk, calculate kth
The posteriority intensity v of framek(xk)；
Assuming that the predicted intensity of kth frame is Gaussian Mixture form, then the posteriority intensity v of kth framek(xk) Gaussian Mixture form
It indicates are as follows:
In formula, pD,kIndicate target detection probability, Jk|k-1=Jk-1+Jγ,kIndicate of Gaussian Mixture item in predicted intensity
Number, with stochastic finite collection Sk|k-1(xk-1) indicate,Indicate the weight of each Gaussian term,Indicate kth frame PHD
The mean value of jth Gaussian term after update,Indicate the variance of j-th of Gaussian term after kth frame PHD updates；Indicate pre-
Survey the mean value of i-th of Gaussian term in intensity；Indicate the weight of i-th of Gaussian term in predicted intensity；Indicate prediction
The mean value of i-th of Gaussian term in intensity；Indicate the variance of i-th of Gaussian term in predicted intensity；
vk|k-1(xk) in each Gaussian component obtain 1+ after PHD updates | Zk| a update Gaussian component, | Zk| it indicates to measure
It is worth number；They represent the same target, therefore this 1+ | Zk| a mark value and the prediction Gaussian component for updating Gaussian component
Mark value it is identical, then updated vk(xk) Gaussian component mark value are as follows:
In formula, Lk|k-1Gauss mark value after indicating prediction, LkIndicate the Gauss mark value of k frame,It indicates by z1More
The Gauss mark value newly obtained Indicate by z |Zk| update obtained Gauss mark value Indicate the | Zk| a measurement vector；
Step 5 three: the trimming of Gaussian component with merge: since the Gaussian Mixture item of GMPHD filter constantly increases at any time
Add, therefore algorithm merged by trimming and effectively reduces the number of Gaussian Mixture item, retain the biggish Gaussian term of weight, delete weight compared with
Small Gaussian term.Multiple Gaussian components in certain thresholding will be merged into one.
To vk(xk) in Gaussian componentIt is trimmed and is merged to effectively reduce Gauss
The number of mixed term, during being merged；Detailed process are as follows:
If the v being mergedk(xk) in Gaussian componentMark value having the same, then
Gaussian term (v after mergingk(xk) in Gaussian component) mark value with merge before Gaussian term
(vk(xk) in Gaussian component) mark value is identical；
On the contrary, if the v being mergedk(xk) in Gaussian componentMark value it is different,
Then take the Gaussian term (v before merging with maximum weightk(xk) in Gaussian component) mark
Mark value of the note value as Gaussian term after merging.
After trimming union operation, if being needed to them again there is also different Gaussian term mark values is identical
Mark value is distributed, the mark value of the maximum Gaussian term of weight is retained, and the Gaussian term of other same label is then assigned other only
One mark value.
Step 5 four: multiple target number and state estimation are calculated based on step 6 three:
Since the mean value of each Gaussian component corresponds to a Local Extremum of posteriority intensity, weight indicates the Gauss point
Amount is to the desired contribution of target number, therefore the state estimation of multiple target can be obtained directly according to the weight of Gaussian Mixture item and mean value
, it is the weighting of Gaussian component weight in kth frame target numberThe posteriority intensity v of kth framek(xk) in front ofIt is a
The mean value of the corresponding Gaussian component of maximum weight is Target state estimator；
In formula,Indicate the weight of the remaining Gaussian term after the processing of step 6 three.
Remaining Gaussian term weight after six or three processing is weighted to obtain target number, to the posteriority intensity v of kth framek(xk) warp
It is preceding after crossing six or three processingThe mean value of the corresponding Gaussian component of a maximum weight is Target state estimator.
Other steps and parameter are identical as one of specific embodiment one to seven.
Specific embodiment 9: unlike one of present embodiment and specific embodiment one to eight, it is described each high
This weightThe mean value of jth Gaussian term after kth frame PHD updatesKth frame PHD is j-th high after updating
This varianceExpression formula are as follows:
In formula,Indicate the mean value of j-th of Gaussian term in predicted intensity,It indicates in i-th of Gaussian term of kth frame
Gain matrix, zkIt indicating to measure vector, I indicates 4 × 4 unit matrix,Indicate the gain matrix in j-th of Gaussian term of kth frame,Indicate the variance of j-th of Gaussian term in predicted intensity,Indicate the weight of j-th of Gaussian term in predicted intensity,Indicate the likelihood function of j-th of Gaussian term, κk(zk) it is noise intensity,Indicate first of Gauss in predicted intensity
The weight of item,Indicate that the likelihood function of first of Gaussian term, l indicate Gauss item number in predicted intensity.
Other steps and parameter are identical as one of specific embodiment one to eight.
Beneficial effects of the present invention are verified using following embodiment:
Embodiment one:
Circumference SAR multi-object tracking method in the present embodiment one based on stochastic finite collection is specifically made according to the following steps
Standby:
Emulation experiment
Radar simulation parameter setting is as shown in table 1, and moving target is as shown in table 2, and GM realizes that parameter is as shown in table 3.
1 radar simulation parameter of table
| Parameter | Numerical value |
| Platform movement velocity (m/s) | 100 |
| Emit signal carrier frequency (GHz) | 10 |
| Transmitted signal bandwidth (MHz) | 600 |
| Scene center oblique distance (km) | 11.55 |
| Elevation angle (°) | 30 |
| Every frame total angle of rotation (°) | 3.6 |
| Duplication | 0.75 |
2 target component of table
Table 3GM realizes parameter setting
| Parameter | Numerical value |
| Sampling period T (s) | 0.4 |
| Process noise standard deviation sigmav(m/s2) | 1 |
| Measure noise criteria difference σw(m) | 3 |
| Survival probability pS,k | 0.99 |
| Detection probability pS,k | 0.98 |
In an experiment, using GM-PHD filter.During GM-PHD filter is realized, newborn target random set is pool
Loose finite aggregate, i.e.,Wherein
500 Monte Carlo simulations have been carried out to verify the filtering characteristic of filter and have carried out gesture statistics, and using OPSA away from
From with a distance from OPSA in position error and gesture error analysis filtering characteristic.By simulation result it can be seen that this method can be correct
Estimate target, occasional generates abnormal estimation, but erroneous estimation can disappear quickly.The gesture statistics of 500 Monte Carlo simulations
In, it carves at the beginning, due to the intensity inaccuracy of newborn target, certain time is needed to obtain correct estimated value.With tracking
Time increases, and can converge on real goal number.The OPSA distance of GMPHD is smaller, and position error control is in 2m hereinafter, gesture is missed
Difference is equipped with large error in start bit, and subsequent fluctuation is smaller.It is experimentally confirmed the feasibility of this method, based on GMPHD's
Multi-object tracking method can effectively realize the tracking of moving-target, obtain the true motion state of moving-target.
It is experimentally confirmed the feasibility of this method, the multi-object tracking method based on stochastic finite collection can be effectively real
The tracking of existing moving-target, obtains the true motion state of moving-target.The selection of its newborn target component directly influences target
Tracking effect, in addition, this method also needs to obtain the trace information of multiple target by effective track administrative skill.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications all should belong to
The protection scope of the appended claims of the present invention.
Claims (9)
1. the circumference SAR multi-object tracking method based on stochastic finite collection, it is characterised in that: the method detailed process are as follows:
Step 1: Preliminary detection is carried out to moving target based on DPCA-CFAR method, obtains the measuring value of moving target；
Step 2: the moving target measuring value obtained according to step 1 establishes the state vector of moving target and measures vector, root
According to the state vector and measurement vector of moving target, establishes the state vector set of multiple mobile object and measure vector set；
Step 3: the measurement vector that step 2 obtains is modified, measures vector after being compensated；
Step 4: according to vector is measured after compensation, dbjective state model and measurement model are established；
Step 5: the dbjective state model and measurement model provided according to step 4 carry out the target based on GMPHD filter with
Track；Target following based on GMPHD filter includes PHD prediction, and PHD updates, the trimming of Gaussian component, multiple target number and shape
State estimation；
The GMPHD is the filtering of gaussian sum probability hypothesis density；
The multiple mobile object is 2 and 2 or more moving targets.
2. the circumference SAR multi-object tracking method based on stochastic finite collection according to claim 1, it is characterised in that: described
Preliminary detection is carried out to moving target based on DPCA-CFAR method in step 1, obtains the measuring value of moving target；Detailed process
Are as follows:
For multichannel circumference SAR system carrier aircraft platform in distance objective plane z=ZhPlane on RgCircumferentially for radius
Uniform motion is made in path, and it is V that carrier aircraft platform, which moves linear velocity, and carrier aircraft platform angular velocity of satellite motion is expressed as ω=V/Rg；
For multichannel circumference SAR, it is horizontally arranged N width antenna along radar track tangential direction, the spacing between antenna is d,
Knocked off operation mode using single-shot more, linear FM signal is emitted by reference channel, all antennas receives echo-signal simultaneously；
The multichannel is 2 and 2 with upper channel；
Momentary position coordinates of the reference channel when running to azimuth and being the position θ are Pa(Rgcosθ,Rgsinθ,Zh)；
Wherein θ ∈ [0,2 π) be azimuth, azimuth represents synthetic aperture domain, i.e. tmSlow time-domain；
When circumferentially track moves carrier aircraft platform, the radar beam center in carrier aircraft platform is radiated at always with R0For radius, O
For in the circumference observation area Ω in the center of circle；The distance at radar to observation area center isObservation area center
Locating radar beam incidence angle isI indicates incidence angle；
If certain moving target is located at P in observation areat(x(tm)), the state vector of moving target is expressed as
Wherein [x (tm),y(tm)] indicate moving target position,Indicate moving target in cartesian coordinate system
The speed of x-axis and y-axis direction；tmIndicate slow time-domain；
The instantaneous oblique distance of twin-channel two channel distance moving targets is expressed as Ri(tm), i=1,2；
If two channel image sequences after time calibration are expressed as I1,k(x, y) and I2,k(x,y)；
Wherein k=1,2 ..., K indicates frame number；
The relationship of two channel image sequences is expressed as
Wherein λ indicates wavelength；J is imaginary number, j2=-1；vrIndicate the radial velocity of moving target；
Two channel images obtain after offseting processing using DPCA technology | IDPCA,k(x, y) |, realize clutter recognition；
After clutter recognition, OS-CFAR Preliminary detection is carried out to each frame image and obtains target measuring value, in CFAR detection
False-alarm probability P is setfa, obtain the measuring value of moving target.
3. the circumference SAR multi-object tracking method based on stochastic finite collection according to claim 2, it is characterised in that: described
OS-CFAR Preliminary detection is carried out to each frame image and obtains target measuring value, false-alarm probability P is set in CFAR detectionfa, obtain
To the measuring value of moving target；Detailed process are as follows:
OS-CFAR Preliminary detection result is expressed as
Wherein ηkFor detection threshold；
To OS-CFAR Preliminary detection result Bk(x, y) carries out image procossing, obtains the measuring value of moving target；Process are as follows:
The target area that connection is obtained by morphologic corrosion expansive working, carries out edge detection to target area and obtains mesh
Target center point, using the center of target point as the measuring value of moving target.
4. the circumference SAR multi-object tracking method based on stochastic finite collection according to claim 3, it is characterised in that: described
False-alarm probability Pfa=0.01.
5. the circumference SAR multi-object tracking method based on stochastic finite collection according to claim 4, it is characterised in that: described
The moving target measuring value obtained in step 2 according to step 1 establishes the state vector of moving target and measures vector, according to
The state vector and measurement vector of moving target, establish the state vector set of multiple mobile object and measure vector set；Specifically
Process are as follows:
The state vector of target is expressed as
Wherein, [xk,yk] indicate moving target position,Indicate moving target in cartesian coordinate system x-axis and y-axis side
To speed；
The measuring value of moving target is expressed as z in SAR imagek=[x'k,y'k]T, measuring value is the position of target on the image；
Assuming that there are a moving target of N (k) and a measuring value of M (k) in kth frame, then multiple mobile object state vector set and
Vector set is measured to be expressed as
Wherein, xk,1Indicate the state vector of first moving target in kth frame, xk,N(k)Indicate a movement of N (k) in kth frame
The state vector of target；zk,1Indicate the measurement vector of first moving target in kth frame, zk,M(k)Indicate M (k) in kth frame
The measurement vector of a moving target；WithThe respectively state space of moving targetWith measurement spaceUpper institute
The set for thering is finite subset to constitute；
The multiple target state X at given k-1 momentk-1, the multiple target state X at k momentkThen by the target survived and newborn mesh
Mark is constituted, i.e.,
Wherein, ΓkIndicate k moment new life target random set, Sk|k-1(xk-1) indicate subsequent time state vector stochastic finite
Collection, Xk-1Indicate the multiple target state vector set at k-1 moment；
In given k moment multiple target state Xk, the measurement Z of multiple targetkThe measurement and clutter generated by target is constituted, i.e.,
Wherein, KkIndicate false-alarm or the set that clutter is constituted；Θk(xk) indicate k moment each target xk∈XkGenerate one at random
Finite aggregate.
6. the circumference SAR multi-object tracking method based on stochastic finite collection according to claim 5, it is characterised in that: described
The measurement vector that step 2 obtains is modified in step 3, measures vector after being compensated；Specific steps are as follows:
The target P in kth frame image sequencet(xk) radial velocity be expressed asIts
Middle θa,kIndicate the azimuth of kth frame radar platform, carrier of radar platform to target Pt(xk) oblique distance RkIt is expressed as
Assuming that Rk=R, the orientation offset as caused by radial velocity are
Wherein, oblique distance of the R expression radar platform to target；
By two channel image sequence I after time calibration1,k(x, y) and I2,k(x, y) conjugate multiplication obtains interferometric phase Δ φk,
Realize the estimation to target bearing to offset
Therefore compensated measurement vector is obtainedWithIt is denoted as
Wherein, x 'kIndicate moving target in cartesian coordinate system x-axis coordinate, y 'kIndicate moving target in cartesian coordinate system y-axis
Coordinate.
7. the circumference SAR multi-object tracking method based on stochastic finite collection according to claim 6, it is characterised in that: described
According to vector is measured after compensation in step 4, dbjective state model and measurement model are established；Specific steps are as follows:
Target dynamic equation is expressed as
xk=Fk-1xk-1+vk-1
Wherein, process noise vectorCovariance isσvIndicate the standard deviation of process noise,
GkFor process noise distribution matrix, FkFor dynamic model state-transition matrix；
FkAnd GkIt is expressed as
In formula, T is the sampling period；
Measurement equation is expressed as
zk=Hkxk+wk
Wherein measure noise wk~Ν (O ', Rk), covarianceσwIndicate the standard deviation of measurement noise, I2It is 2 × 2
Unit matrix；
Observing matrix is expressed as
8. the circumference SAR multi-object tracking method based on stochastic finite collection according to claim 7, it is characterised in that: described
The dbjective state model and measurement model provided in step 5 according to step 4 carries out the target following based on GMPHD filter；
Target following based on GMPHD filter includes PHD prediction, and PHD updates, the trimming of Gaussian component, multiple target number and state
Estimation；Detailed process are as follows:
The dbjective state model and measurement model of moving target in SAR scene belong to linear Gauss model, are expressed as
In formula, ζ is the state vector of -1 frame of kth；
Step 5 one: PHD is predicted:
Assuming that the posteriority intensity of -1 frame of kth and the intensity of newborn target stochastic finite collection are Gaussian Mixture form, then kth frame
Predicted intensity is expressed as
Wherein, pS,kIndicate the survival probability of target,Indicate the mean value of Gaussian term after PHD is predicted, Indicate the mean value in each Gaussian term of -1 frame of kth；Indicate Gaussian term after PHD is predicted
Variance, Indicate the variance in each Gaussian term of -1 frame of kth；Indicate the intensity of newborn target stochastic finite collection, Jk-1Indicate -1 vertical frame dimension of kth this
The number of item, Jγ,kIndicate that, in kth frame new life Gaussian term number, i indicates the index value of newborn Gaussian term；With
Respectively indicate the weight of each newborn Gaussian term, mean value and variance；
Step 5 two: PHD updates: according to the predicted intensity v of kth framek|k-1(xk) and measurement vector set Zk, after calculating kth frame
Test intensity vk(xk)；
Assuming that the predicted intensity of kth frame is Gaussian Mixture form, then the posteriority intensity v of kth framek(xk) expression of Gaussian Mixture form
Are as follows:
In formula, pD,kIndicate target detection probability, Jk|k-1=Jk-1+Jγ,kIndicate the number of Gaussian Mixture item in predicted intensity,Indicate the weight of each Gaussian term,Indicate the mean value of jth Gaussian term after kth frame PHD updates,
Indicate the variance of j-th of Gaussian term after kth frame PHD updates；Indicate the mean value of i-th of Gaussian term in predicted intensity；
Indicate the weight of i-th of Gaussian term in predicted intensity；Indicate the mean value of i-th of Gaussian term in predicted intensity；It indicates
The variance of i-th of Gaussian term in predicted intensity；
vk|k-1(xk) in each Gaussian component obtain 1+ after PHD updates | Zk| a update Gaussian component, | Zk| indicate measuring value
Number；Then updated vk(xk) Gaussian component mark value are as follows:
In formula, Lk|k-1Gauss mark value after indicating prediction, LkIndicate the Gauss mark value of k frame,It indicates by z1Update obtains
Gauss mark value Indicate byUpdate obtained Gauss mark value Indicate the
|Zk| a measurement vector；
Step 5 three: the trimming of Gaussian component with merge:
If the v being mergedk(xk) in Gaussian componentMark value having the same, then after merging
Gaussian term mark value with merge before Gaussian term mark value it is identical；
If the v being mergedk(xk) in Gaussian componentMark value it is different, then before taking merging
Mark value of the mark value of Gaussian term with maximum weight as Gaussian term after merging；
Step 5 four: multiple target number and state estimation are calculated based on step 5 three:
It is the weighting of Gaussian component weight in kth frame target numberThe posteriority intensity v of kth framek(xk) in front ofIt is a
The mean value of the corresponding Gaussian component of maximum weight is Target state estimator；
In formula,Indicate the weight of the remaining Gaussian term after the processing of step 5 three.
9. the circumference SAR multi-object tracking method based on stochastic finite collection according to claim 8, it is characterised in that: described
The weight of each Gaussian termThe mean value of j-th of Gaussian term after kth frame PHD updatesAfter kth frame PHD updates
The variance of j-th of Gaussian termExpression formula are as follows:
In formula,Indicate the mean value of j-th of Gaussian term in predicted intensity,Indicate the gain in i-th of Gaussian term of kth frame
Matrix, zkIt indicating to measure vector, I indicates 4 × 4 unit matrix,Indicate the gain matrix in j-th of Gaussian term of kth frame,
Indicate the variance of j-th of Gaussian term in predicted intensity,Indicate the weight of j-th of Gaussian term in predicted intensity,Table
Show the likelihood function of j-th of Gaussian term, κk(zk) it is noise intensity,Indicate the weight of first of Gaussian term in predicted intensity,Indicate that the likelihood function of first of Gaussian term, l indicate Gauss item number in predicted intensity.
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