CN110032710A - A kind of improved JPDA plot-track Association Algorithm - Google Patents
A kind of improved JPDA plot-track Association Algorithm Download PDFInfo
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- CN110032710A CN110032710A CN201910147806.6A CN201910147806A CN110032710A CN 110032710 A CN110032710 A CN 110032710A CN 201910147806 A CN201910147806 A CN 201910147806A CN 110032710 A CN110032710 A CN 110032710A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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Abstract
The present invention relates to the computation complexities of joint probability data association (JPDA) class algorithm, it discloses a kind of based on the JPDA algorithm for measuring self adaptive elimination method, comprising steps of 1, by introducing experience JPDA method calculate interconnection probability, reduce algorithm calculation amount；2, threshold process is subject to Marshal probabilistic matrix, confirms matrix by rebuilding, advanced optimizes algorithm complexity；3, using self adaptive elimination method, remove the measurement for easily causing erroneous association in Marshal probabilistic matrix, reduce error of the JPDA algorithm when being associated with approaching target.The computation complexity of JPDA algorithm the invention has the benefit that innovatory algorithm can debase the standard, and 10% or so correct interconnection probability can be improved to avoid track from merging compared to standard JPDA algorithm when tracking approaching target, 10% or so correct interconnection probability is improved to avoid with wrong target compared to Scaled JPDA algorithm when tracking cross-goal.
Description
Technical field
The present invention relates to the computation complexities of joint probability data association (JPDA) class algorithm, in particular to a kind of based on amount
Survey the JPDA algorithm of self adaptive elimination method.
Background technique
JPDA algorithm is developed by PDA, it does not need any prior information about target and clutter, can pass through benefit
Possible posterior information is obtained with effective echoes all in tracking gate.But its calculation amount is larger, closes on airbound target in tracking
When be easy to produce track merge phenomenon, cause target with losing.It reduces one of the effective way of calculation amount: improving PDA algorithm, allow
It is suitable for multiple target tracking；The two of approach: simplify JPDA algorithm, be allowed to meet requirement of real-time.
General algorithm is all to avoid the generation of track consolidation problem by introducing the new algorithm of one kind in the algorithm, this must
So it is unable to reach the requirement of real-time for target following.Real-time and the preferable Scaled of tracking performance are then selected herein
JPDA algorithm improves, and is reprocessed by introducing threshold restriction method to experience JPDA algorithm, reduction is unnecessary can
The generation of row joint event, and propose that a kind of adaptive measurement removing method tracks to solve SJPDA algorithm for cross-goal
The excessive problem of error emulates the verifying for carrying out algorithm validity finally by Monte Carlo.
Summary of the invention
The object of the invention is to reduce the computation complexity of joint probability data association (JPDA) class algorithm, tracking is solved
The track consolidation problem occurred when approaching target proposes a kind of based on the JPDA algorithm for measuring self adaptive elimination method.
The present invention is a kind of based on the JPDA algorithm for measuring self adaptive elimination method, includes the following steps:
Step 1: Cheap JPDA algorithm
Empirical formula in Cheap JPDA algorithm has a feature of JPDA algorithm, i.e., only to appearing in a boat
Measurement in mark interconnection region weights again, and makees light weighting in the overlapping of several Trace Association regions and contradictory measurement.It should
Empirical algorithms give higher weighting to close to predicted position and the measurement that can be used minimum track number to make to interconnect.
Probability is interconnected in the algorithmIt can be expressed from the next:
In formula
WhereinIndicate that the k moment measures effective likelihood function of j and target t interconnection；vj(k) measure j's for the k moment
New breath；S (k) is new breath covariance, and is had:
There may be certain errors for the interconnection probability wherein calculated by formula (1), but as redefining confirmation square
The foundation of element value is feasible in battle array.
By (1) formula to (3) formula, Marshal probabilistic matrix can be obtained:
Wherein, target t=0,1 ..., T；J=0,1 is measured ..., mk。
Step 2: the experience JPDA algorithm of threshold value constraint
Calculate all feasible joint event probability of confirmation matrix, it is likely that exploding for calculation amount is caused to cause to be delayed
It is long, and then it is unsatisfactory for system real time requirement.However having in the feasible joint event decomposed most of is small probability event, very
What is played a leading role during tracking is the biggish joint event of those probability.Therefore during rebuilding confirmation matrix,
Some probability values can be ignored close to 0 small probability event.A threshold value κ can first be set in the algorithm first, value can be with
10-2Same magnitude, the value can be adjusted in real time during tracking；Afterwards by compared with element in Marshal probabilistic matrix, with mark
Based on confirmation matrix in quasi- JPDA algorithm, new confirmation matrix is established.
By formula (5) it is found that threshold value κ is smaller, the feasible event decomposed is more, and computational load is bigger, and time delay is got over
Seriously, but tracking effect is better；It is opposite then real-time is preferable, but tracking effect is deteriorated.The size of threshold value can be according to the essence of system
Degree requires and the prior information of target is set.
Step 3: the calculating of interconnection probability
After obtaining the confirmation matrix that newly constructs, each feasible joint event can be obtained by decomposing to it, after according to standard
The joint event posterior probability at JPDA algorithm calculating k moment.
WhereinIt is the detection probability of target t；μF(φ) is the prior probability mass function of false measurement number；δt(θi(k))
For target association mark, to indicate target t whether with combine correlating event θi(k) any measurement association in； φ(θi(k))
For false measurable amount mark, to indicate joint correlating event θi(k) number measured in vain in；τj(θiIt (k)) is measurement
Associated flag, to indicate measure j whether with θi(k) any one target association in event,！Indicate factorial mark.
Posterior probability after normalization are as follows:
Wherein normalization coefficient are as follows:
Finally by the feasible joint event summation to decomposition, the interconnection of j-th of measurement Yu t-th of target can be obtained
Probability, shown in form such as formula (9):
WhereinAnd ziThe predicted position and physical location of target i are respectively represented, and is setWithRespectively target i's
The falseness as caused by clutter measures 1 and 2 in tracking gate.It can be seen from the figure that target 1 and the actual measurements of target 2 are all fallen within
In overlapping region, for target 1, z is measured2It is most likely to be larger than with the interconnection probability of target 1 and measures z1With the interconnection of target 1
Probability；Same situation also occurs in target 2.If introducing a scale factor greater than 1, it is likely that amount of error can be amplified
The interconnection probability of survey causes the deterioration of tracking performance, therefore set forth herein adaptive elimination algorithm is measured, the method is as described below.
β is obtained by formula (9)jt(k) these interconnection probability for belonging to target t are subjected to statistical arrangement by ascending order method after:
Definition:
If nminIt is to meet inequality γnThe maximum n value of >=ρ, definition (12) are as follows:
Wherein ρ is to measure the threshold value adaptively eliminated, and size can carry out designed, designed by system parameter.Pass through choosing
With m rear in ascending orderk-nmin+ 1 measures to be updated to target t, remaining measurement is given up.And when with each sampling
It carves the difference measured and its interconnects the variation of probability, resulting nminAlso it changes with system, so more new system shape
The measurement of state also changes constantly, that is, plays the purpose for measuring and adaptively eliminating.As Fitagerald thinks, more
When fresh target state, 2~3 measurements with high probability should be only used.In fact, there is also the choosings of parameter for this paper algorithm
Take problem.In formula (12), detection threshold ρ is played a very important role in terms of avoiding Track Fusion.As ρ=0, substantially
On be reduced into standard JPDA algorithm；As ρ=1, algorithm is simplified to ENNPDA algorithm.In order to avoid track merges phenomenon, ρ's
Value should be influenced between 0 and 1, and by target density, noise intensity and sensor performance etc..
Detailed description of the invention
Fig. 1 show the corresponding relationship between target of the present invention and measurement.
Fig. 2 show the present invention and measures adaptive elimination algorithm flow chart.
Fig. 3 show target true motion track of the present invention.
Fig. 4 show the pursuit path after standard JPDA association of the present invention.
Fig. 5 show the pursuit path after innovatory algorithm association of the present invention.
Fig. 6 show SJPDA algorithm of the present invention for the position RMSE of target a.
Fig. 7 show innovatory algorithm of the present invention for the position RMSE of target a.
Fig. 8 show the position RMSE of target a of the present invention.
Fig. 9 show target live flying of the present invention track.
Figure 10 show this paper algorithm keeps track of the present invention track.
Figure 11 show SJPDA algorithm keeps track of the present invention track.
Figure 12 show SJPDA algorithm of the present invention for the position RMSE of target a.
Figure 13 show innovatory algorithm of the present invention for the position RMSE of target a.
Figure 14 show the position RMSE of target a of the present invention.
Figure 15 show target live flying of the present invention track.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts it is all its
His embodiment, shall fall within the protection scope of the present invention.
Embodiment 1
Airbound target is closed on, in order to obtain optimum efficiency, first three parameters for influencing algorithm performance are divided herein
Analysis, it is assumed that two at a distance of flying in parallel compared with close-target, and initial flight state is such as
Shown in table 1:
1 initial position of table and speed
Table 2 correctly interconnects probability and runing time
Embodiment 2
Cross-pair flies target, it is assumed that the target original state of two at the uniform velocity cross flyings is as shown in table 3:
3 initial position of table and speed
When tracking cross-goal, performance is declined two kinds of algorithms.But this paper innovatory algorithm is because giving up smaller interconnection
The measurement of probability, and retain the measurement for meeting (10-12) formula, substantially belong to after rejecting unnecessary measurement and re-starts
The normalization of probability is interconnected, this will lead to remaining a part measurement and final association results are all played compared to before more
Important role, such situation are particularly evident when target is intersected；And SJPDA algorithm is only to interconnection maximum probability
Probability amplifies, when target carries out crisscross motion, it is likely that cause wrong amplification, this necessarily causes under the algorithm performance
Drop, error becomes larger, take for tracing property efficiency of the two algorithm to target a shown in；
Innovatory algorithm tracking performance under crossing instances changes less compared with when closing on flight progress, but correct interconnection
Probability will be substantially better than SJPDA algorithm, although being declined compared with standard JPDA algorithm, its tracking accuracy is sufficient for making
War requires and real-time is significantly improved, so compared to other two kinds of algorithms more suitable for being applied to airborne platform.
Embodiment 3
Long distance accompanying flying target, lower surface analysis efficiency-cost ratio of three kinds of association algorithms for target following under normal circumstances.Wherein
Two target motion conditions are first to move with uniform velocity, after move in a circle half-turn, continue uniform motion later.Wherein to cadion-acceleration
Degree is respectively aa=18m/s2, ab=16m/s2, two targets take distance relatively far away from carry out accompanying flying.Specific motion conditions are such as
Shown in Figure 15.
When tracking multiple target apart from each other, the error of generation be heavily dependent on the kinetic model of selection with
Filtering method, there is a situation where erroneous associations will not occur substantially.And since three is all based on identical power mould in this example
The kalman filter method of type, thus in tracking error difference and it is few.The wherein efficiency-cost ratio of three kinds of correlating methods such as table 4
It is shown.
Table 4 correctly interconnects probability and runing time
As can be seen from Table 4: when target is apart from each other, can seldom exist and effectively measure the phase in multiple targets simultaneously
Bo Mennei is handed over, two targets are considered as a case where target is handled during tracking and are also greatly reduced, it, which is improved, at this time calculates
The effect of method is also not obvious, and in terms of tracking accuracy compared with standard JPDA algorithm also and be not present advantage, but the used time compared with
It is small, the validity of algorithm is equally demonstrated to a certain extent.
The invention has the benefit that being directed to JPDA algorithm calculation amount problems of too, the experience of threshold restriction is introduced herein
JPDA algorithm reduces the quantity of feasible joint event, reduces algorithm complexity；In order to solve standard JPDA algorithm to closing on mesh
Mark and SJPDA algorithm merge phenomenon to the track occurred during the tracking of cross-goal, propose that a kind of measurement is adaptive and eliminate
Method avoids track from merging phenomenon by eliminating false a possibility that measuring, reducing erroneous association event generation in associated domain
Generation.Herein by the improvement to SJPDA algorithm, correlating method is made to stabilize tracking accuracy, reduces algorithm complexity,
Illustrate that this paper algorithm exists by comparing the efficiency-cost ratio of three kinds of algorithms finally by the validity of simulating, verifying innovatory algorithm
Value in terms of engineer application.Finally it should be noted that.
The foregoing is only a preferred embodiment of the present invention, is not intended to restrict the invention, although referring to aforementioned reality
Applying example, invention is explained in detail, for those skilled in the art, still can be to aforementioned each implementation
Technical solution documented by example is modified or equivalent replacement of some of the technical features, all in essence of the invention
Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (4)
1. a kind of improved JPDA plot-track Association Algorithm, spy, which helps, to be: the empirical formula tool in Cheap JPDA algorithm
There is the feature of JPDA algorithm, i.e., only the measurement appeared in a Trace Association region is weighted again, and in several tracks
Light weighting is made in interconnection region overlapping and contradictory measurements, and the empirical algorithms are to close to predicted position and can be used minimum track number work
The measurement of interconnection gives higher weighting:
Probability is interconnected in the algorithmIt can be expressed from the next:
In formula
WhereinIndicate that the k moment measures effective likelihood function of j and target t interconnection；vj(k) the new breath of j is measured for the k moment；S
(k) it is new breath covariance, and has:
Wherein by the interconnection probability of formula (1) calculating, there may be certain errors, but confirm in matrix as redefining
The foundation of element value is feasible；
By (1) formula to (3) formula, Marshal probabilistic matrix can be obtained:
Wherein, target t=0,1 ..., T；J=0,1 is measured ..., mk。
2. a kind of improved JPDA plot-track Association Algorithm according to claim 1, spy, which helps, to be: the experience JPDA of threshold value constraint is calculated
Method calculate confirmation matrix all feasible joint event probability, it is likely that cause calculation amount explode cause to be delayed it is too long, in turn
It is unsatisfactory for system real time requirement, however having in the feasible joint event decomposed most of is small probability event, is really being tracked
What is played a leading role in the process is the biggish joint event of those probability, therefore during rebuilding confirmation matrix, can be ignored
Some probability values can first set a threshold value κ close to 0 small probability event in the algorithm first, and value can be with 10-2Same amount
Grade, the value can be adjusted in real time during tracking；Afterwards by compared with element in Marshal probabilistic matrix, with standard JPDA algorithm
In confirmation matrix based on, establish new confirmation matrix:
By formula (5) it is found that threshold value κ is smaller, the feasible event decomposed is more, and computational load is bigger, and time delay is more serious,
But tracking effect is better；It is opposite then real-time is preferable, but tracking effect is deteriorated.The size of threshold value can be according to the required precision of system
And the prior information of target is set.
3. a kind of improved JPDA plot-track Association Algorithm according to claim 1, spy, which helps, to be: obtaining the confirmation matrix newly constructed
Afterwards, each feasible joint event can be obtained by decomposing to it, after according to standard JPDA algorithm calculate the k moment joint event after
Test probability:
WhereinIt is the detection probability of target t；μF(φ) is the prior probability mass function of false measurement number；δt(θiIt (k)) is mesh
Mark associated flag, to indicate target t whether with combine correlating event θi(k) any measurement association in；φ(θiIt (k)) is void
False measurable amount mark, to indicate joint correlating event θi(k) number measured in vain in；τj(θiIt (k)) is measurement association mark
Will, to indicate measure j whether with θi(k) any one target association in event,！Indicate factorial mark.
4. a kind of improved JPDA plot-track Association Algorithm according to claim 1, spy, which helps, to be: whereinAnd ziRespectively represent mesh
The predicted position and physical location of i are marked, and is setWithRespectively the falseness as caused by clutter measures 1 in the tracking gate of target i
With 2, it can be seen from the figure that the actual measurements of target 1 and target 2 have been all fallen in overlapping region, for target 1, z is measured2
It is most likely to be larger than with the interconnection probability of target 1 and measures z1With the interconnection probability of target 1；Same situation also occurs in target 2
On.If introducing a scale factor greater than 1, it is likely that the interconnection probability that can amplify mistake measurement causes the evil of tracking performance
Change, therefore set forth herein measure adaptive elimination algorithm.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112327290A (en) * | 2020-10-22 | 2021-02-05 | 北京理工大学 | Low-altitude flight small target tracking method based on multi-dimensional feature fusion JPDA |
| CN112654979A (en) * | 2020-04-29 | 2021-04-13 | 华为技术有限公司 | Data association method and device |
| CN115168787A (en) * | 2022-09-05 | 2022-10-11 | 中国电子科技集团公司第二十八研究所 | Flight trajectory associated tracking method based on speculative calculation |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112654979A (en) * | 2020-04-29 | 2021-04-13 | 华为技术有限公司 | Data association method and device |
| CN112327290A (en) * | 2020-10-22 | 2021-02-05 | 北京理工大学 | Low-altitude flight small target tracking method based on multi-dimensional feature fusion JPDA |
| CN112327290B (en) * | 2020-10-22 | 2024-02-27 | 北京理工大学 | Low-altitude flying small target tracking method based on multidimensional feature fusion JPDA |
| CN115168787A (en) * | 2022-09-05 | 2022-10-11 | 中国电子科技集团公司第二十八研究所 | Flight trajectory associated tracking method based on speculative calculation |
| CN115168787B (en) * | 2022-09-05 | 2022-11-25 | 中国电子科技集团公司第二十八研究所 | Flight trajectory associated tracking method based on speculative calculation |
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