CN106707272A - Multi-target tracking method based on theory of random sets - Google Patents

Multi-target tracking method based on theory of random sets Download PDF

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CN106707272A
CN106707272A CN201610522044.XA CN201610522044A CN106707272A CN 106707272 A CN106707272 A CN 106707272A CN 201610522044 A CN201610522044 A CN 201610522044A CN 106707272 A CN106707272 A CN 106707272A
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target
probability
subset
label
density function
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CN106707272B (en
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易伟
王佰录
李帅
李溯琪
孔令讲
杨晓波
崔国龙
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
    • G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
    • G01S13/726—Multiple target tracking

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention provides a multi-target tracking method based on the theory of random sets, and aims at realizing multi-target state effective tracking in a complex scene under the restricted condition of limited resources. According to the method, firstly each continue live track is further predicted according to the Bayes rule in the track prediction stage, and then a target track is self-adaptively generated according to target prior information; and in the track updating stage, firstly the corresponding existence weight probability and a combined multi-target probability density function are computed under each assumption, and then the posterior probability parameter of each target mark number is computed, including the existence probability and the corresponding probability density function. The method has the advantages of being low in approximation cost and excellent in performance under the limited resources and has the robustness suitable for any measurement models. Besides, the algorithm occupies less system computing resources so as to have great engineering application prospect.

Description

A kind of multi-object tracking method theoretical based on random set
Technical field
The invention belongs to multiple target tracking field, its more particularly to theoretical lower Multitarget Tracking field of random set.
Background technology
In recent years, the multi-target detection tracking technique based on random set statistical theory has obtained extensive concern, this kind of side Method avoids the data correlation of traditional multiple target tracking, and can process that target number is unknown and situation of time-varying.At present, mostly Several random set track algorithms, such as probability hypothesis density wave filter, the probability hypothesis density wave filter of radix, label multiple target Bernoulli Jacob's wave filter etc. both for standard measurement model (referring to document R.Mahler, Statistical Multisource-Multitarget Information Fusion,Norwood,MA:Artech House, 2007.) and set Meter.However, in actual multiple target tracking scene, the measurement model of standard has many limitation, many sensor models Can not be described with standard measurement model, such as before detections of radar in trace model, wireless sensor network multi-user positioning, it is many Multi-target position in input multi output radar, sonar amplitude sensor, radio frequency chromatography imaging tracing system, video frequency following system Deng.
Asked for the multiple target tracking under the measurement model (the especially non-standard measurement model of nonlinearity) of broad sense Topic, document (F.Papi, B.N.Vo, B.T.Vo, C.Fantacci and M.Beard, " Generalized labeled multi-Bernoulli Approximation of multi-object densities,”IEEE Trans.on Signal Process.Vol.63, No.20, pp.5487-5497,2015.) a kind of broad sense label multiple target Bernoulli Jacob's wave filter is proposed, The wave filter realizes effective tracking of multiple target under off-gauge measurement model, and can effectively recognize target identities, shape Into targetpath.But, the multiple target posteriority component number of the wave filter is presented super exponential increase with the growth of target number, makes Greatly, poor real is limited by very large computing resource needed for it in actual applications.
The content of the invention
The technical problems to be solved by the invention are, the existing random set multiple target tracking side for non-standard measurement model The system resources in computation that method takes increases with target number in super index, so as to be unfavorable for its practical engineering application.
The present invention solves the technical scheme that is used of above-mentioned technical problem, a kind of multiple target theoretical based on random set with Track method, it is comprised the following steps：
Step 1, initialization system parameter
Initialization system parameter includes：Radar surveillance scope：That is datum plane, radar resolution ratio △ r, radar scanning Cycle T, observation totalframes K；Target survival probabilitySingle goal probability density function fk|k-1(xk|xk-1)；Birth mesh Mark model is distributed for multiple target Bernoulli JacobWhereinRepresent theThe presence probability of individual birth targetpath,Represent theThe individual corresponding distribution probability density function of targetpath of being born,Represent birth target label ensemble space； Multiple target likelihood function g (Z | X), wherein Z represents measurement set, and X represents multiple target state set；
Step 2：Initialization label multiple target-Bernoulli parameterAnd makeWhereinRepresent current The target label ensemble space of frame；Initialization iteration time k=1,Represent theThe individual presence for continuing survival targetpath is general Rate,Represent theThe individual probability density function for continuing survival target；
Step 3, the prediction flight path for calculating kth frame：
3.1st, according to the prior information of target birth position, and based on target birth model birth fresh target flight path, birth Object module is distributed for multiple target Bernoulli Jacob
3.2 predictions for continuing survival flight path, according to Bayesian forecasting equation, theBar continues Trajectory Prediction of surviving Presence probabilityWith corresponding probability density functionIt is as follows respectively,
Wherein, mathematic sign<f1(x),f2(x)>Representative function f1(x) and function f2Inner product between (x)；Represent and continue Survival targetpath label ensemble space；
Step 3, the finite subset space for building the target label set predicted；
3.1 determine target label setTarget label collection is combined into target birth label set and continues mark of surviving with target Number union of sets collection；
3.2 build target label setAll finite subsets space, its mathematical symbolism isFinite subset number beHere I is defined+It is finite subset spaceAny one have Subset is limited, and its mathematical symbolism is
Step 4, according to bayesian criterion, calculate each finite subset of kth framePosteriority weight probability and its Corresponding multiple target probability density function；
4.1. each subset is calculatedPriori weight probability w+(I+)：
Wherein mathematic sign ∏ represents that company multiplies symbol,Represent theThe presence probability of individual prediction targetpath,Table Show indicator function, it is defined as follows：Indicator function
4.2. each subset is calculatedMultiple target posterior probability density function normalization factor ηZ(I+)：
WhereinRepresent theThe probability density function of individual prediction targetpath；
4.3. each subset is calculatedPosteriority weight probability w (I+)：
w(I+)=w+(I+)ηZ(I+)
4.4. each subset is calculatedMultiple target posterior probability density function：
Step 5, to each subsetPosteriority weight probability w (I+) be normalized：
Step 6, each target label of calculatingPresence probabilityAnd its corresponding probability density function
6.1st, each target label is calculatedPresence probabilityBy each subset of step 5In forgive target labelPosteriority weight probability w (I+) sued for peace, obtain target labelPresence probability
6.2nd, each target label is calculatedPosterior probability density functionBy each subset of step 5In forgive target labelMarginal probability density functionSummation is weighted, its weighting weight is The posteriority weight probability w (I of corresponding subset+), and the presence probability obtained with step 6.1The posteriority obtained to weighted sum is general Rate density functionIt is normalized：
Wherein WhereinRepresent label subset I+IncludingMultiple target posterior probability density function P (X|Z)；Step 7, dbjective state are extracted；Radix corresponding to cardinal of the set distribution maximum is the estimation of k moment targets number Nk, and the N is estimated respectivelykThe state of individual target；
If step 8, k<K, makes k be equal to k+1, and return to step 3, wherein k are frame number.
Innovative point of the invention is, 1) in forecast period, independent prediction to be carried out between multiple Bernoulli Jacob's components, greatly section Computing resource needed for having saved multiple target tracking；2) in the more new stage, by building the finite subset space of target label, joint Multiple target probability density function under multiple hypotheses is considered, therefore the tracking is adapted to more broadly multiple target and measures mould Type.
An advantage of the invention is that it provides one kind take computing resource it is few, and the excellent effect of tracking performance multiple target tracking side Method, and target tracking algorism proposed by the present invention can be applicable any measurement model, with compared with strong algorithms robustness.
Brief description of the drawings
Fig. 1 is flow chart of the invention；
Fig. 2 is the schematic diagram of inventive algorithm；
Fig. 3 is simulating scenes figure under inventive algorithm typical scene；
Fig. 4 is the tracking effect figure of inventive algorithm.
Specific embodiment
The content of present invention description is described for convenience, and following term definition is done first：
Random collection：It refer to given state spaceByAll finite subsets constitute a superspaceThen It is defined onOn stochastic variable be referred to as random collection.
Cardinal of the set：It refer to the number of element in set.
The main method using Computer Simulation of the invention is verified that all steps, conclusion are all in MATLAB-R2014b Upper checking is correct.Specific implementation step is as follows：
Step 1, initialization system parameter.
Initialization system parameter includes：Radar surveillance scope [0,60m] × [0,60m], radar resolution ratio △ r=1m, thunder Up to scan period T=1s, observation totalframes K=28；Target survival probabilityBirth object module is multiple target Bernoulli Jacob DistributionWherein The measuring value vector of present frameRepresent, wherein mathematic signRepresent real number Domain, zjJ-th measuring value of radar resolution cell of (j=1 ..., M) expression, the number M=3600 of resolution cell, multiple target is seemingly The mathematical expression of right function g (Z | X) be for：
Wherein mathematic signRepresent the general of under the conditions of multiple target state X j-th measuring value of resolution cell Rate density function, here using Gaussian Profile, mathematic(al) representation is：
WhereinExpression average is μ, and covariance matrix is the Gaussian Profile of Γ,Represent dbjective state x To j-th power contribution amount of resolution cell, σNX () represents noise power.
Step 2：Initialization label multiple target-Bernoulli parameterAnd makeWhereinRepresent current The target label ensemble space of frame；Initialization iteration time k=1.
Step 3, the prediction flight path for calculating kth frame：
3.1st, according to the prior information of target birth position, and based on target birth model birth fresh target flight path, birth Object module is distributed for multiple target Bernoulli Jacob
3.2 predictions for continuing survival flight path.According to Bayesian forecasting equation, theBar continues Trajectory Prediction of surviving Presence probabilityWith corresponding probability density functionIt is as follows respectively,
Wherein, mathematic sign<f1(x),f2(x)>Representative function f1(x) and function f2X the inner product between (), its mathematics is determined Justice isRepresent and continue targetpath label ensemble space of surviving.
Step 3, the finite subset space for building the target label set predicted.
3.1 determine target label setTarget label collection is combined into target birth label set and continues mark of surviving with target Number union of sets collection, i.e.,Wherein.Element number is then in target label setWherein symbol | f | represents f Length.
3.2 build target label setAll finite subsets space, its mathematical symbolism isFinite subset number beHere I is defined+It is finite subset spaceAny one have Subset is limited, and its mathematical symbolism is
Step 4, according to bayesian criterion, calculate each finite subset of kth framePosterior probability and its correspondence Multiple target probability density function.
4.1. each subset is calculatedPriori weight probability w+(I+), its mathematical computations expression formula is
Wherein mathematic sign ∏ is represented and even multiply symbol.
4.2. each subset is calculatedMultiple target posterior probability density function normalization factor ηZ(I+), Its mathematical computations expression formula is
4.3. each subset is calculatedPosteriority weight probability w (I+), its mathematical computations expression formula is
w(I+)=w+(I+)ηZ(I+)
4.4. each subset is calculatedMultiple target posterior probability density function, its mathematical computations expression formula is
Step 5, to each subsetPosteriority weight probability w (I+) be normalized, i.e.,
Step 6, each target label of calculatingPresence probabilityAnd its corresponding probability density function
6.1st, each target label is calculatedPresence probabilityBy each subset of step 5In forgive target labelPosteriority weight probability w (I+) sued for peace, obtain target labelPresence probabilityI.e.
6.2nd, each target label is calculatedPosterior probability density functionBy each subset of step 5In forgive target labelMarginal probability density functionSummation is weighted, its weighting weight is The posteriority weight probability w (I of corresponding subset+), and the presence probability obtained with step 6.1The posteriority obtained to weighted sum is general Rate density functionIt is normalized：
Wherein WhereinRepresent that label set includesMultiple target posterior probability density function P (X |Z)；Step 7, dbjective state are extracted.Radix corresponding to cardinal of the set distribution maximum is k moment targets number and estimates Nk, And the N is estimated respectivelykThe state of individual target.
If step 8, k<K, makes k be equal to k+1, and return to step 3, wherein k are frame number.
By above step, it is possible to multiple target tracking under effectively realizing complex scene under system limited resources.

Claims (1)

1. a kind of multi-object tracking method theoretical based on random set, it is comprised the following steps：
Step 1, initialization system parameter
Initialization system parameter includes：Radar surveillance scope：That is datum plane, radar resolution ratio △ r, radar scanning cycle T, observation totalframes K；Target survival probability pS(l), single goal probability density function fk|k-1(xk|xk-1)；Birth target mould Type is distributed for multiple target Bernoulli JacobWhereinL-th presence probability of birth targetpath is represented,L-th corresponding distribution probability density function of targetpath of being born is represented,Represent birth target label ensemble space； Multiple target likelihood function g (Z | X), wherein Z represents measurement set, and X represents multiple target state set；
Step 2：Initialization label multiple target-Bernoulli parameterAnd makeWhereinRepresent present frame Target label ensemble space；Initialization iteration time k=1, r(l)Represent l-th presence probability of continuation survival targetpath, p(l)Represent l-th probability density function of continuation survival target；
Step 3, the prediction flight path for calculating kth frame：
3.1st, according to the prior information of target birth position, and based on target birth model birth fresh target flight path, target of being born Model is distributed for multiple target Bernoulli Jacob
3.2 predictions for continuing survival flight path, according to Bayesian forecasting equation, theBar continues depositing for survival Trajectory Prediction In probabilityWith corresponding probability density functionIt is as follows respectively,
r + , S l = p S ( l ) r ( l )
p + , S l ( x ) = < f ( x | &CenterDot; ) , p ( &CenterDot; , l ) >
Wherein, mathematic sign ＜ f1(x),f2(x)>Representative function f1(x) and function f2Inner product between (x)；Expression continues to deposit Targetpath label ensemble space living；
Step 3, the finite subset space for building the target label set predicted；
3.1 determine target label setTarget label collection is combined into target birth label set and continues label set of surviving with target The union of conjunction；
3.2 build target label setAll finite subsets space, its mathematical symbolism is 's Finite subset number isHere I is defined+It is finite subset spaceAny one finite subset, and its mathematics accord with Number it is expressed as
Step 4, according to bayesian criterion, calculate each finite subset of kth framePosteriority weight probability and its correspondence Multiple target probability density function；
4.1. each subset is calculatedPriori weight probability w+(I+)：
Wherein mathematic sign ∏ represents that company multiplies symbol,L-th presence probability of prediction targetpath is represented,Expression refers to Show function, it is defined as follows：Indicator function
4.2. each subset is calculatedMultiple target posterior probability density function normalization factor ηZ(I+)：
&eta; Z ( I + ) = &Integral; ( &Pi; i = 1 n p + ( x i , l i ) ) g ( Z | { ( x 1 , l 1 ) , ... , ( x n , l n ) } ) d ( x 1 , ... , x n )
WhereinRepresent theThe probability density function of individual prediction targetpath；
4.3. each subset is calculatedPosteriority weight probability w (I+)：
w(I+)=w+(I+)ηZ(I+)
4.4. each subset is calculatedMultiple target posterior probability density function：
P ( X | Z ) = ( &Pi; i = 1 n p + ( x i , l i ) ) g ( Z | X ) &eta; Z ( I + )
Step 5, to each subsetPosteriority weight probability w (I+) be normalized：
Step 6, each target label of calculatingPresence probability r(l)And its corresponding probability density function p(l)(x)；
6.1st, the presence probability r of each target label l is calculated(l)；By each subset of step 5In forgive target label l's Posteriority weight probability w (I+) sued for peace, obtain the presence probability r of target label l(l)：
6.2nd, each target label is calculatedPosterior probability density function p(l)(x)；By each subset of step 5 In forgive the marginal probability density function of target label lSummation is weighted, its weighting weight is corresponding subset Posteriority weight probability w (I+), and the presence probability r obtained with step 6.1(l)The posterior probability density letter obtained to weighted sum Number p(l)X () is normalized：
WhereinWherein P({(x,l)}∪{(x1,l1),…,(xn,ln) | Z) represent label subset I+Multiple target posterior probability density function P including l (X|Z)；
Step 7, dbjective state are extracted；Radix corresponding to cardinal of the set distribution maximum is k moment targets number and estimates Nk, And the N is estimated respectivelykThe state of individual target；
If step 8, k ＜ K, k is made to be equal to k+1, return to step 3, wherein k are frame number.
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CN109508444A (en) * 2018-12-18 2019-03-22 桂林电子科技大学 Section measures the fast tracking method of the more Bernoulli Jacob of lower interactive multimode broad sense label
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CN111457916A (en) * 2020-03-30 2020-07-28 中国人民解放军国防科技大学 Space debris target tracking method and device based on expansion mark random finite set
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CN114491413A (en) * 2022-01-25 2022-05-13 中国人民解放军海军航空大学航空作战勤务学院 Probability density hypothesis track generation method and system based on minimum cross entropy

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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109508444A (en) * 2018-12-18 2019-03-22 桂林电子科技大学 Section measures the fast tracking method of the more Bernoulli Jacob of lower interactive multimode broad sense label
CN109508444B (en) * 2018-12-18 2022-11-04 桂林电子科技大学 Quick tracking method for interactive multimode generalized label multi-Bernoulli under interval measurement
CN111414843A (en) * 2020-03-17 2020-07-14 森思泰克河北科技有限公司 Gesture recognition method and terminal device
CN111414843B (en) * 2020-03-17 2022-12-06 森思泰克河北科技有限公司 Gesture recognition method and terminal device
CN111457916A (en) * 2020-03-30 2020-07-28 中国人民解放军国防科技大学 Space debris target tracking method and device based on expansion mark random finite set
CN111457916B (en) * 2020-03-30 2021-05-07 中国人民解放军国防科技大学 Space debris target tracking method and device based on expansion mark random finite set
CN112215146A (en) * 2020-10-12 2021-01-12 西安交通大学 Weak and small target joint detection and tracking system and method based on random finite set
CN114491413A (en) * 2022-01-25 2022-05-13 中国人民解放军海军航空大学航空作战勤务学院 Probability density hypothesis track generation method and system based on minimum cross entropy

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