CN106054151B - Radar Multi Target based on data association algorithm tracks optimization method - Google Patents
Radar Multi Target based on data association algorithm tracks optimization method Download PDFInfo
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Abstract
The invention discloses a kind of, and the Radar Multi Target based on data association algorithm tracks optimization method, and thinking is：The target total number T ' for determining radar tracking respectively, determines that the k moment corresponds to the measurement number n for includingk, then the candidate of t-th of target of k moment after calculation optimization measures collection Z successivelyt' (k), k moment nkA vector C (k) for measuring a targets of each leisure T ' corresponding correlation Bo Mennei occurrence numbers composition and k moment fall into candidate's measurement of the related Bo Mennei of t-th of target in nkThe vector C of the number composition occurred in × T ' dimensions measurement-target association matrix Ωt' (k), and then calculate the k moment successively and fall into i-th of t-th target correlation Bo Mennei and candidate measure in nkThe number c occurred in × T ' dimensions measurement-target association matrix ΩitThe candidate of t-th of target of k moment after ' (k), optimization measures collection ZtI-th of candidate measurement z in ' (k)it' (k) is derived from the probability β of t-th of targetit(k) the candidate of t-th of target of k moment and after optimization measures collection ZtThe candidate probability β measured derived from t-th of target of no one of ' (k)0t(k), the state equation of t-th of target of k moment and then is calculated successivelyWith the error co-variance matrix P of t-th of target of k momentt(k|k)。
Description
Technical field
The invention belongs to Radar Technology field, more particularly to a kind of Radar Multi Target tracking based on data association algorithm is excellent
Change method, be suitable under clutter environment radar to single target into line trace or to multiple targets into line trace.
Background technology
In recent years, complicated and changeable with application environment, it is desirable that radar has multiple target tracking ability, and can realize simultaneously
Multiple target tracking；The basic conception of multiple target tracking is proposed in an article of applicating physical magazine in nineteen fifty-five by Wax
Come, 1964 later Si Teer deliver the paper of one entitled " the optimal data related question in monitoring theory " on IEEE
As the guide of multiple target tracking, but Kalman filtering is not yet commonly used at that time, and Si Teer is using a kind of Track Furcation
Method solves the problems, such as data correlation；Early 1970s start in the presence of having false-alarm, to utilize kalman filter method
(Kalman) it systematically to multiple target tracking and handles；The nearest neighbor method that Singer in 1971 is proposed is to solve data correlation
Simplest method, but correct association rate of the nearest neighbor method under clutter environment is relatively low；During this period, Y.Bar-Shalom is played
Very important effect, probability number to single goal into line trace under he proposed in 1975 especially suitable for clutter environment
According to association algorithm (PDA), the multiple target tracking under clutter environment is efficiently solved the problems, such as；T.E.Formann and Y.Bar-
Shalom etc. proposes Joint Probabilistic Data Association algorithm (JPDA), and JPDA is by all targets and measures progress permutation and combination,
And select rational joint event and calculate joint probability, JPDA considers multiple measurements from other targets and is in same mesh
The possibility in interworking domain is marked, the measurement problem of multiple target in the next interworking domain of clutter environment can be well solved；But with
This simultaneously, JPDA is more complicated, computationally intensive, and with the growth of number of targets, and it is quick-fried to confirm that the fractionation of matrix will appear combination
Fried situation.Therefore, JPDA is implemented relatively difficult in engineering.
Invention content
For the above problem of the existing technology, it is an object of the invention to propose a kind of tracking based on data correlation
The optimization method of multiple radar targets, the optimization method of tracking multiple radar targets of this kind based on data correlation is for solving needle
Occur accidentally with the higher feelings of rate when to carrying out data correlation using Probabilistic Data Association Algorithm (PDA) in multiple target tracking processing
Condition, computation complexity is almost the same with PDA, and is easily achieved in engineering.
To reach above-mentioned technical purpose, the present invention is realised by adopting the following technical scheme.
A kind of Radar Multi Target tracking optimization method based on data association algorithm, includes the following steps：
Step 1, the target total number T ' for determining radar tracking respectively, determines that the k moment corresponds to the measurement number n for includingk, and
The state estimation of t-th of target of k-1 moment is denoted as respectivelyBy the state error of t-th of target of k-1 moment
Covariance matrix is denoted as Pt(k-1 | k-1), by the k-1 moment, the state-transition matrix of t-th of target is denoted as Ft(k | k-1), when by k
The measurement matrix for carving t-th of target is denoted as Ht(k), the process noise covariance matrix of t-th of target of k-1 moment is denoted as Qt(k-
1) the measurement noise covariance matrix of t-th of target of k moment, is denoted as Rt(k), t-th of target of k moment is then calculated successively
State one-step predictionThe measurement of t-th of target of k moment is predictedThe k moment, j-th of measurement was to t
The new breath v of measurement prediction of a targetjt(k), the one-step prediction error co-variance matrix P of t-th of target of k momenttWhen (k | k-1), k
Carve the kalman gain K of t-th of targett(k) and the new breath covariance matrix S of t-th of target of k momentt(k), it and then is calculated
nk× T ' dimensions measurement-target association matrix Ω；
Wherein, j ∈ { 1,2 ..., nk, t ∈ { 1,2 ..., T ' }, nkIndicate that the k moment corresponds to the measurement number for including, T ' tables
Show the target total number of radar tracking, k >=1；
Step 2, the candidate collection that measures of t-th of target of k moment is denoted as Zt(k), t-th of mesh of k moment after being optimized
Target candidate measures collection Z 't(k), and according to nk× T ' dimensions measurement-target association matrix Ω, is calculated k moment n successivelykIt is a
The vector C (k) and k moment for measuring the corresponding correlation Bo Mennei occurrence numbers composition of a targets of each leisure T ' fall into t-th of target
The candidate of related Bo Mennei measures in nkThe vector C ' of the number composition occurred in × T ' dimensions measurement-target association matrix Ωt
(k), it and then obtains the k moment and falls into i-th of t-th target correlation Bo Mennei and candidate measure in nk× T ' dimensions measurement-target is closed
The number c occurred in connection matrix Ωi′t(k), i ∈ { 1,2 ..., mkt, mktIndicate the candidate measurement that t-th of target of k moment includes
Number；
Step 3, the m that t-th of target of k moment includes is definedktI-th of candidate measurement is to t-th of target in a candidate measurement
The new breath of measurement prediction be v 'it(k), and t-th of the candidate of target correlation Bo Mennei is fallen into according to the k moment to measure in nk× T ' dimensions
The vector C ' of the number composition occurred in measurement-target association matrix Ωt(k) and the new breath covariance of t-th of target of k moment
Matrix St(k), the candidate of t-th of target of k moment and after optimization measures collection Z 't(k), when calculating separately the k after being optimized
It carves t-th of the candidate of target and measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from the probability β of t-th of targetit(k) and
The candidate of t-th of target of k moment after optimization measures collection Z 't(k) zero candidates measure the probability β derived from t-th of target in0t
(k)；
Step 4, according to the state one-step prediction of t-th of target of k momentThe karr of t-th of target of k moment
Graceful gain Kt(k), the candidate of t-th of target of k moment after optimizing measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from
The probability β of t-th of targetit(k), the candidate of t-th of target of k moment after optimizing measures collection Z 't(k) zero candidates measure source in
In the probability β of t-th of target0t(k), the m that t-th of target of k moment includesktI-th of candidate measurement is to t in a candidate measurement
The new breath v ' of measurement prediction of a targetit(k), the one-step prediction error co-variance matrix P of t-th of target of k momentt(k|k-1)、k
The measurement matrix H of t-th of target of momentt(k), the state equation of t-th of target of k moment is calculated successivelyWhen with k
Carve the error co-variance matrix P of t-th of targett(k|k)；Wherein, the target of t ∈ { 1,2 ..., T ' }, T ' expression radar tracking is total
Number, i ∈ { 1,2 ..., mkt, mktIndicate that the candidate of t-th of target of k moment measures number.
Beneficial effects of the present invention：
First, the method for the present invention combines the advantage of Probabilistic Data Association Algorithm, it is contemplated that all targets fall into related wave
The candidate echo acknowledgement of door measures, and calculates the interconnection probability of candidate echo acknowledgement measurement and all targets, uses probability weight
The echo of the equivalent all targets of form so that when carrying out multiple target following processing under clutter environment, the probability with losing is relatively low；
Second, the method for the present invention confirms that measuring corresponding interconnection probability cuts to specific in Probabilistic Data Association Algorithm
Subtract so that track cross target can be better achieved flight path separation, reduce target accidentally with probability；
The computation complexity of third, the method for the present invention is low, and Project Realization is easy.
Description of the drawings
Invention is further described in detail with reference to the accompanying drawings and detailed description.
Fig. 1 is that a kind of Radar Multi Target based on data association algorithm of the present invention tracks the flow chart of optimization method；
Fig. 2 (a) is the result schematic diagram that target following is carried out using two cross-goal of Probabilistic Data Association Algorithm pair,
Fig. 2 (b) is the result schematic diagram that target following is carried out using two cross-goal of the method for the present invention pair；
Fig. 3 is the metric data distribution schematic diagram of four cross-goals；
Fig. 4 (a) is the result schematic diagram that target following is carried out using four cross-goal of Probabilistic Data Association Algorithm pair,
Fig. 4 (b) is the result schematic diagram that target following is carried out using four cross-goal of the method for the present invention pair.
Specific implementation mode
Referring to Fig.1, it is that a kind of Radar Multi Target based on data association algorithm of the present invention tracks the flow of optimization method
Figure；The Radar Multi Target based on data association algorithm tracks optimization method, includes the following steps：
Step 1, the target total number T ' for determining radar tracking respectively, determines that the k moment corresponds to the measurement number n for includingk, and
The state estimation of t-th of target of k-1 moment is denoted as respectivelyBy the state error of t-th of target of k-1 moment
Covariance matrix is denoted as Pt(k-1 | k-1), by the k-1 moment, the state-transition matrix of t-th of target is denoted as Ft(k | k-1), when by k
The measurement matrix for carving t-th of target is denoted as Ht(k), the process noise covariance matrix of t-th of target of k-1 moment is denoted as Qt(k-
1) the measurement noise covariance matrix of t-th of target of k moment, is denoted as Rt(k), t-th of target of k moment is then calculated successively
State one-step predictionThe measurement of t-th of target of k moment is predictedThe k moment, j-th of measurement was to t
The new breath v of measurement prediction of a targetjt(k), the one-step prediction error co-variance matrix P of t-th of target of k momenttWhen (k | k-1), k
Carve the kalman gain K of t-th of targett(k) and the new breath covariance matrix of t-th of target of k moment is St(k), it and then calculates
To nk× T ' dimensions measurement-target association matrix Ω.
Wherein, j ∈ { 1,2 ..., nk, t ∈ { 1,2 ..., T ' }, nkIndicate that the k moment corresponds to the measurement number for including, T ' tables
Show the target total number of radar tracking, k >=1.
Specifically, it is determined that the target total number of radar tracking is T ', and the state of t-th of target of k-1 moment is estimated respectively
Meter is denoted asThe state error covariance matrix of t-th of target of k-1 moment is denoted as Pt(k-1 | k-1), by k-
The state-transition matrix of 1 t-th of moment target is denoted as Ft(k | k-1), by the k moment, the measurement matrix of t-th of target is denoted as Ht(k),
The process noise covariance matrix of t-th of target of k-1 moment is denoted as Qt(k-1), by the measurement noise of t-th of target of k moment
Covariance matrix is denoted as Rt(k)；Wherein, the target total number of t ∈ { 1,2 ..., T ' }, T ' expression radar tracking.
It is assumed that Z (k) indicates the measurement set at k moment, and Z (k)={ zj(k) | j=1,2 ..., nk, nkIndicate the k moment pair
The measurement number that should include, zj(k) j-th of measurement in the measurement set Z (k) at k moment is indicated.
Then calculate separately the state one-step prediction of t-th of target of k momentIts expression formula is：
Calculate the measurement prediction of t-th of target of k momentIts expression formula is：
Then calculate separately the new breath v of measurement prediction for obtaining j-th of the measurement of k moment to t-th of targetjt(k), expression formula
For：
And then it calculates separately to obtain the one-step prediction error co-variance matrix P of t-th of target of k momentt(k | k-1), table
It is up to formula：
Pt(k | k-1)=Ft(k|k-1)Pt(k-1|k-1)Ft T(k|k-1)+Qt(k-1)
The kalman gain K of t-th of target of k moment is calculatedt(k), expression formula is：
Kt(k)=Pt(k|k-1)Ht T(k)St -1(k)
The new breath covariance matrix S of t-th of target of k moment is calculatedt(k), expression formula is：
St(k)=Ht(k)Pt(k|k-1)Ht T(k)+Rt(k)
Wherein, Ft(k | k-1) indicates the state-transition matrix of t-th of target of k-1 moment,Indicate k-1
The state estimation of t-th of target of moment, Ht(k) measurement matrix of t-th of target of k moment is indicated,Indicate the k moment
The state one-step prediction of t-th of target, zj(k) j-th of measurement in the measurement set Z (k) at k moment is indicated,It indicates
The measurement prediction of t-th of target of k moment, Ft(k | k-1) indicates the state-transition matrix of t-th of target of k-1 moment, Pt(k-1|k-
1) the state error covariance matrix of t-th of target of k-1 moment, Q are indicatedt(k-1) process of t-th of target of k-1 moment is indicated
Noise covariance matrix, Pt(k | k-1) indicates the one-step prediction error co-variance matrix of t-th of target of k moment, j ∈ 1,
2,…,nk, t ∈ { 1,2 ..., T ' }, nkIndicate that the k moment corresponds to the measurement number for including, the target of T ' expression radar trackings is always a
Number.
It is assumed that space where a targets of the T ' of radar tracking is tracking space, measured in advance so that a targets of k moment T ' are respective
It surveysCentered on, the tracking space is corresponded to and is divided
For T ' sub-spaces V1,V2,…,Vt,…,VT′, and by t-th of subspace VtTracking gate or phase as corresponding t-th of target
Guan Bomen, and there is the situation mutually overlapped mutually in the T ' sub-spaces；The design of related wave door ensures radar with determining general
Rate PGThe echo of corresponding tracked target is received, therefore j-th in the measurement set Z (k) at k moment is measured and is used as t-th of mesh
The new breath v of measurement prediction of target candidate's echo, i.e. j-th of the measurement of k moment to t-th of targetjt(k) and k moment t-th of target
New breath covariance matrix St(k) meet following formula：
Wherein, subscript T indicates that transposition, subscript -1 indicate inversion operation, vjt(k) indicate j-th of the measurement of k moment to t-th
The new breath of measurement prediction of target, St(k) the new breath covariance matrix of t-th of target of k moment, j ∈ { 1,2 ..., n are indicatedk, t ∈
{ 1,2 ..., T ' }, nkIndicate that the k moment corresponds to the measurement number for including, the target total number of T ' expression radar trackings；γ indicates phase
The size of wave door is closed, value is corresponded to the probability P for receiving tracked target echo by the dimension and radar of single measuring valueGJointly
It determines.
Therefore, n is calculatedk× T ' dimensions measurement-target association matrix Ω, expression formula are：
Wherein, wjtIt indicates to measure for j-th and falls into the binary variable of t-th of target correlation Bo Mennei, j ∈ 1,2 ...,
nk, t ∈ { 1,2 ..., T ' }, nkIndicate that the k moment corresponds to the measurement number for including, the target total number of T ' expression radar trackings,
wjt=1 j-th of measurement of expression falls into t-th of target correlation Bo Mennei, also meetswjt=0 indicates
J-th of measurement does not fall within t-th of target correlation Bo Mennei, is unsatisfactory for yetSubscript T indicates to turn
It sets, subscript -1 indicates inversion operation, vjt(k) j-th of new breath for measuring the measurement prediction to t-th of target of k moment, S are indicatedt
(k) the new breath covariance matrix of t-th of target of k moment, k >=1 are indicated；γ indicates the size of related wave door, and value is by individually measuring
The dimension and radar of measured value correspond to the probability P for receiving tracked target echoGIt codetermines.
Step 2, the candidate collection that measures of t-th of target of k moment is denoted as Zt(k), t-th of mesh of k moment after being optimized
Target candidate measures collection Z 't(k), and according to nk× T ' dimensions measurement-target association matrix Ω, is calculated k moment n successivelykIt is a
The vector C (k) and k moment for measuring the corresponding correlation Bo Mennei occurrence numbers composition of a targets of each leisure T ' fall into t-th of target
The candidate of related Bo Mennei measures in nkThe vector C ' of the number composition occurred in × T ' dimensions measurement-target association matrix Ωt
(k), it and then obtains the k moment and falls into i-th of t-th target correlation Bo Mennei and candidate measure in nk× T ' dimensions measurement-target is closed
The number c ' occurred in connection matrix Ωit(k), i ∈ { 1,2 ..., mkt, mktIndicate the candidate measurement that t-th of target of k moment includes
Number.
Specifically, n is investigatedkThe t of × T ' dimensions measurement-target association matrix Ω is arranged, if wjt=1, then it represents that j-th
Measurement is that t-th of the candidate of target measures；The candidate collection that measures of t-th of target of k moment is denoted as Zt(k), Zt(k)={ zj(k)|
wjt=1 }, wherein zj(k) j-th of measurement, w in the measurement set Z (k) at k moment are indicatedjt=1 j-th of measurement of expression falls into t
A target correlation Bo Mennei；Then collection Z is measured to the candidate of t-th of target of k momentt(k) it optimizes, the k after being optimized
The candidate of t-th of target of moment measures collection Z 't(k), Z 't(k)={ z 'it(k) | i=1,2 ... mkt, z 'it(k) the k moment is indicated
I-th of t-th of target is candidate to be measured, mktIndicate that the candidate of t-th of target of k moment measures number, wjtIndicate j-th of measurement
Fall into the binary variable of t-th of target correlation Bo Mennei.
Investigate nkThe jth row of × T ' dimensions measurement-target association matrix Ω calculates all w of jth rowjt=1 number, and make
The number occurred in the corresponding correlation Bo Mennei of a targets of T ', w are measured for the k moment j-thjtIndicate that j-th of measurement is fallen into t-th
The binary variable of target correlation Bo Mennei.
The number that j-th of the measurement of k moment occurs in the corresponding correlation Bo Mennei of a targets of T ' is denoted as cj(k), it expresses
Formula is：
cj(k)=sum (wjt| t=1,2 ..., T '),
Wherein, sum () indicates summation, wjtIt indicates to measure the binary system change for falling into t-th of target correlation Bo Mennei j-th
Amount, j ∈ { 1,2 ..., nk, t ∈ { 1,2 ..., T ' }, nkIndicate that the k moment corresponds to the measurement number for including, T ' expression radar trackings
Target total number.
And then calculate k moment nkA vector for measuring the corresponding correlation Bo Mennei occurrence numbers composition of a targets of each leisure T '
C (k), expression formula are：
C (k)={ (zj(k),cj(k)) | j=1,2 ..., nk}
Wherein, zj(k) j-th of measurement, c in the measurement set Z (k) at k moment are indicatedj(k) indicate that j-th of the measurement of k moment exists
The number that the corresponding correlation Bo Mennei of a targets of T ' occurs, j ∈ { 1,2 ..., nk, nkIndicate that the k moment corresponds to the measurement number for including
Mesh.
Collection Z ' is measured to the candidate of t-th of target of k moment after optimizationt(k) each element in, respectively in k moment nkIt is a
Measure the member found in the vector C (k) of the corresponding correlation Bo Mennei occurrence numbers composition of a targets of each leisure T ' corresponding thereto
Element, and be calculated the k moment and fall into the candidate of t-th target correlation Bo Mennei and measure in nk× T ' dimensions measurement-target association square
The vector C ' of the number composition occurred in battle array Ωt(k), expression formula is：
C′t(k)={ c 'it(k) | i=1,2 ..., mkt}
Wherein, c 'it(k) indicate that the k moment falls into i-th of candidate measurement of t-th of target correlation Bo Mennei in nk× T ' dimensions
The number occurred in measurement-target association matrix Ω, i ∈ { 1,2 ..., mkt, mktIndicate the time that t-th of target of k moment includes
Choosing measures number, t ∈ { 1,2 ..., T ' }, the target total number of T ' expression radar trackings.
Step 3, the m that t-th of target of k moment includes is definedktI-th of candidate measurement is to t-th of target in a candidate measurement
The new breath of measurement prediction be v 'it(k), and t-th of the candidate of target correlation Bo Mennei is fallen into according to the k moment to measure in nk× T ' dimensions
The vector C ' of the number composition occurred in measurement-target association matrix Ωt(k), the new breath covariance square of t-th of target of k moment
Battle array St(k), the candidate of t-th of target of k moment and after optimization measures collection Z 't(k), the k moment after being optimized is calculated separately
T-th of the candidate of target measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from the probability β of t-th of targetit(k) and it is excellent
The candidate of t-th of target of k moment after change measures collection Z 't(k) zero candidates measure the probability β derived from t-th of target in0t(k)。
Specifically, in order to calculate interconnection probability, the m that t-th of target of k moment includes is definedktI-th of time in a candidate measurement
It is v ' that choosing, which measures the new breath of the prediction of the measurement to t-th of target,it(k), expression formula is：
Wherein, z 'it(k) indicate that the candidate of t-th of target of k moment after optimization measures collection Z 't(k) i-th of candidate amount in
It surveys,Indicate the measurement prediction of t-th of target of k moment, t ∈ { 1,2 ..., T ' }, the target of T ' expression radar trackings
Total number, i ∈ { 1,2 ..., mkt, mktIndicate the candidate measurement number that t-th of target of k moment includes.
It is calculated to simplify, defines t-th of target of k moment derived from i-th of candidate proportion e measuredit(k) with k when
It carves and measures the proportion b (k) being associated with t-th of target without candidate, expression formula is respectively：
B (k)=λ | 2 π St(k)|1/2(1-PDPG)/PD
Wherein,It indicates if the m that t-th of target of k moment includesktI-th of candidate amount in a candidate measurement
It surveys the number occurred in a correlation Bo Mennei of T ' and is more than 1, then the m for including to t-th of target of k momentktI-th in a candidate measurement
Candidate measures and is cut down so that flight path can be better achieved with all targets that t-th of target trajectory intersects and detach, reduce
Target is accidentally with probability；v′it(k) m that t-th of target of k moment includes is indicatedktI-th of candidate measurement is to t in a candidate measurement
The new breath of measurement prediction of a target, St(k) the new breath covariance matrix of t-th of target of k moment, c ' are indicatedit(k) the k moment is indicated
I-th of candidate measurement of t-th of target correlation Bo Mennei is fallen into nkOccur in × T ' dimensions measurement-target association matrix Ω
Number, λ indicate that the false space density measured, i.e. the false of unit area measure number, PDIndicate each in a targets of T '
The detectable probability of target, PGIndicate that radar receives the probability of corresponding tracked target echo, subscript T indicates transposition, subscript -1
Indicate inversion operation, t ∈ { 1,2 ..., T ' }, nkIndicate that the k moment corresponds to the measurement number for including, the mesh of T ' expression radar trackings
Mark total number, i ∈ { 1,2 ..., mkt, mktIndicate the candidate measurement number that t-th of target of k moment includes.
And then it calculates separately the candidate of t-th of target of k moment after optimization and measures collection Z 't(k) i-th of candidate measurement in
z′it(k) it is derived from the probability β of t-th of targetit(k) the candidate of t-th of target of k moment and after the optimization measures collection Z 't(k)
Middle zero candidates measure the probability β derived from t-th of target0t(k), expression formula is respectively：
Wherein, eit(k) t-th of target of k moment is indicated derived from i-th of candidate proportion measured, and b (k) indicates the k moment
The proportion being associated with t-th of target, t ∈ { 1,2 ..., T ' }, the target of T ' expression radar trackings are measured without candidate
Total number, i ∈ { 1,2 ..., mkt, mktIndicate the candidate measurement number that t-th of target of k moment includes.
Step 4, according to the state one-step prediction of t-th of target of k momentThe karr of t-th of target of k moment
Graceful gain Kt(k), the candidate of t-th of target of k moment after optimizing measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from
The probability β of t-th of targetit(k), the candidate of t-th of target of k moment after optimizing measures collection Z 't(k) zero candidates measure source in
In the probability β of t-th of target0t(k), the m that t-th of target of k moment includesktI-th of candidate measurement is to t in a candidate measurement
The new breath v ' of measurement prediction of a targetit(k), the one-step prediction error co-variance matrix P of t-th of target of k momentt(k|k-1)、k
The measurement matrix H of t-th of target of momentt(k), the state equation of t-th of target of k moment is calculated successivelyWhen with k
Carve the error co-variance matrix P of t-th of targett(k|k)；Wherein, the target of t ∈ { 1,2 ..., T ' }, T ' expression radar tracking is total
Number, i ∈ { 1,2 ..., mkt, mktIndicate that the candidate of t-th of target of k moment measures number.
Specifically, the state equation of described t-th of target of k momentIts expression formula is：
Wherein,Indicate the state one-step prediction of t-th of target of k moment, Kt(k) t-th of mesh of k moment is indicated
Target kalman gain, vt(k) indicate that the combination of the measurement prediction of t-th of target of k moment newly ceases,βitTable
Show that the candidate of t-th of target of k moment after simplifying measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from t-th of target
Probability βit(k), v 'itIndicate the m that t-th of target of k moment includesktI-th of candidate measurement is to t-th of mesh in a candidate measurement
Target measures the new breath v ' of predictionit(k)；The state equation of t-th of target of k moment is calculated hereinWhen use probability weight
Form is sought combining new breath, can realize when carrying out multiple target followings processing under clutter environment, effectively reduce target with
Lose probability.
The error co-variance matrix P of described t-th of target of k momentt(k | k), expression formula is：
Wherein, Pt(k | k-1) indicates the one-step prediction error co-variance matrix of t-th of target of k moment, βit(k) indicate excellent
The candidate of t-th of target of k moment after change measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from the general of t-th target
Rate, β0t(k) indicate that the candidate of t-th of target of k moment after optimization measures collection Z 't(k) zero candidates, which measure, in is derived from t-th of mesh
Target probability, Pt c(k | k)=[I-Kt(k)Ηt(k)]Pt(k | k-1),
Ηt(k) t-th of target of k moment is indicated
Measurement matrix,Indicate the one-step prediction of k moment target t states, Pt(k | k-1) indicate t-th of target of k moment
One-step prediction error co-variance matrix, Kt(k) indicate that the kalman gain of t-th of target of k moment, subscript T indicate transposition,
The target total number of t ∈ { 1,2 ..., T ' }, T ' expression radar tracking, i ∈ { 1,2 ..., mkt, mktIndicate the k moment
T-th of the candidate of target measures number.
So far, a kind of optimization method to Probabilistic Data Association Algorithm during multiple target tracking of the invention terminates.
Further verification explanation is made to effect of the present invention by following emulation experiment.
(1) emulation experiment data explanation.
In order to do performance comparison with classical Probabilistic Data Association Algorithm (PDA), the present invention intersects mesh two respectively
Implement two kinds of algorithms respectively under mark environment and four cross-goal environment to be compared, experimental data parameter is as follows：
(2) simulation result and analysis
Simulation result such as Fig. 2 (a) of the present invention, Fig. 2 (b), shown in Fig. 3 and Fig. 4 (a) and Fig. 4 (b), wherein Fig. 2 is
Target following result schematic diagram in the case of two cross-goals, wherein Fig. 2 (a) is to be handed over using Probabilistic Data Association Algorithm pair two
The result schematic diagram that target carries out target following is pitched, Fig. 2 (b) is to carry out target following using two cross-goal of the method for the present invention pair
Result schematic diagram, Fig. 3 be four cross-goals metric data distribution schematic diagram, Fig. 4 be four cross-goals in the case of target
Track schematic diagram, wherein Fig. 4 (a) is to show using the result of four cross-goal of Probabilistic Data Association Algorithm pair progress target following
It is intended to, Fig. 4 (b) is the result schematic diagram that target following is carried out using four cross-goal of the method for the present invention pair；Wherein, in above-mentioned institute
Have in schematic diagram, abscissa is the directions x position, unit m；Ordinate is the directions y position, unit m.
As can be seen that since target is intersected from Fig. 2 (a) and Fig. 2 (b), multiple measurement tight clusters depend merely on probability weight
Form be difficult to detach targetpath, there is target with Probabilistic Data Association Algorithm it can be seen from Fig. 2 (a)
Accidentally with the case where；It can be seen from Fig. 2 (b) the method for the present invention due to specifically confirm measure corresponding interconnection probability into
Reduction is gone, to preferably realize flight path separation, Fig. 2 (b) demonstrates this point well.
Fig. 3 is the metric data distribution schematic diagram of four cross-goals, it can be seen that due to the presence of error in measurement,
The area distribution that measuring point mark intersects in target trajectory it is very in disorder, have no rule.
From in Fig. 4 (a) and Fig. 4 (b) as can be seen that when number of targets increases, the method for the present invention still have preferably target with
Track performance.
In conclusion emulation experiment demonstrates the correctness of the present invention, validity and reliability.
Obviously, various changes and modifications can be made to the invention without departing from essence of the invention by those skilled in the art
God and range；In this way, if these modifications and changes of the present invention belongs to the range of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to include these modifications and variations.
Claims (6)
1. a kind of Radar Multi Target based on data association algorithm tracks optimization method, which is characterized in that include the following steps：
Step 1, the target total number T ' for determining radar tracking respectively, determines that the k moment corresponds to the measurement number n for includingk, and respectively
By the k-1 moment, the state estimation of t-th of target is denoted asBy the state error association side of t-th of target of k-1 moment
Poor matrix is denoted as Pt(k-1 | k-1), by the k-1 moment, the state-transition matrix of t-th of target is denoted as Ft(k | k-1), by k moment t
The measurement matrix of a target is denoted as Ht(k), the process noise covariance matrix of t-th of target of k-1 moment is denoted as Qt(k-1), will
The measurement noise covariance matrix of t-th of target of k moment is denoted as Rt(k), the state of t-th of target of k moment is then calculated successively
One-step predictionThe measurement of t-th of target of k moment is predictedThe k moment, j-th of measurement was to t-th of mesh
Target measures the new breath v of predictionjt(k), the one-step prediction state error covariance matrix P of t-th of target of k momenttWhen (k | k-1), k
Carve the kalman gain K of t-th of targett(k) and the new breath covariance matrix S of t-th of target of k momentt(k), it and then is calculated
nk× T ' dimensions measurement-target association matrix Ω；
Wherein, j ∈ { 1,2 ..., nk, t ∈ { 1,2 ..., T ' }, nkIndicate that the k moment corresponds to the measurement number for including, T ' expression thunders
Up to the target total number of tracking, k >=1；
Step 2, the candidate collection that measures of t-th of target of k moment is denoted as Zt(k), the time of t-th of target of k moment after being optimized
Choosing measures collection Z 't(k), and according to nk× T ' dimensions measurement-target association matrix Ω, is calculated k moment n successivelykIt is a to measure respectively
The related wave door of t-th of target is fallen at vector C (k) and the k moment of a targets of T ' corresponding correlation Bo Mennei occurrence numbers composition
Interior candidate measurement is in nkThe vector C ' of the number composition occurred in × T ' dimensions measurement-target association matrix Ωt(k), it and then obtains
The k moment falls into i-th of candidate measurement of t-th of target correlation Bo Mennei in nkGo out in × T ' dimensions measurement-target association matrix Ω
Existing number c 'it(k), i ∈ { 1,2 ..., mkt, mktIndicate the candidate measurement number that t-th of target of k moment includes；
Step 3, the m that t-th of target of k moment includes is definedktI-th of candidate amount measured to t-th of target in a candidate measurement
It is v ' to survey the new breath of predictionit(k), and t-th of the candidate of target correlation Bo Mennei is fallen into according to the k moment to measure in nk× T ' dimension amounts
The vector C ' of the number composition occurred in survey-target association matrix Ωt(k) and the new breath covariance matrix of t-th of target of k moment
St(k), the candidate of t-th of target of k moment and after optimization measures collection Z 't(k), the k moment after being optimized is calculated separately
T the candidate of target measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from the probability β of t-th of targetit(k) and optimize
The candidate of t-th of target of k moment afterwards measures collection Z 't(k) zero candidates measure the probability β derived from t-th of target in0t(k)；
Step 4, according to the state one-step prediction of t-th of target of k momentThe Kalman of t-th of target of k moment increases
Beneficial Kt(k), the candidate of t-th of target of k moment after optimizing measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from t
The probability β of a targetit(k), the candidate of t-th of target of k moment after optimizing measures collection Z 't(k) zero candidates measurement is derived from
The probability β of t-th of target0t(k), the m that t-th of target of k moment includesktI-th of candidate measurement is to t-th in a candidate measurement
The new breath v ' of measurement prediction of targetit(k), the one-step prediction state error covariance matrix P of t-th of target of k momentt(k|k-1)、
The measurement matrix H of t-th of target of k momentt(k), the state estimation of t-th of target of k moment is calculated successivelyAnd k
The state error covariance matrix P of t-th of target of momentt(k|k)；Wherein, t ∈ { 1,2 ..., T ' }, T ' expression radar tracking
Target total number, i ∈ { 1,2 ..., mkt, mktIndicate that the candidate of t-th of target of k moment measures number.
2. a kind of Radar Multi Target based on data association algorithm as described in claim 1 tracks optimization method, feature exists
In, in step 1, the state one-step prediction of described t-th of target of k momentDescribed t-th of target of k moment
Measure predictionMeasurement prediction new breath v of j-th of the measurement of the k moment to t-th of targetjt(k), the k moment
The one-step prediction state error covariance matrix P of t-th of targettThe kalman gain of (k | k-1), described t-th of target of k moment
Kt(k), the new breath covariance matrix S of described t-th of target of k momentt(k) and the nk× T ' dimensions measurement-target association matrix
Ω, expression formula are respectively：
Kt(k)=Pt(k|k-1)Ht T(k)St -1(k)
St(k)=Ht(k)Pt(k|k-1)Ht T(k)+Rt(k)
Wherein, Ft(k | k-1) indicates the state-transition matrix of t-th of target of k-1 moment,Indicate the k-1 moment the
The state estimation of t target, Ht(k) measurement matrix of t-th of target of k moment is indicated,Indicate t-th of mesh of k moment
Target state one-step prediction, zj(k) j-th of measurement in the measurement set Z (k) at k moment is indicated,Indicate the k moment the
The measurement prediction of t target, Ft(k | k-1) indicates the state-transition matrix of t-th of target of k-1 moment, Pt(k-1 | k-1) it indicates
The state error covariance matrix of t-th of target of k-1 moment, Qt(k-1) the process noise association of t-th of target of k-1 moment is indicated
Variance matrix, Pt(k | k-1) indicates the one-step prediction state error covariance matrix of t-th of target of k moment, wjtIt indicates j-th
Measure the binary variable for falling into t-th of target correlation Bo Mennei, j ∈ { 1,2 ..., nk, t ∈ { 1,2 ..., T ' }, nkIndicate k
Moment corresponds to the measurement number for including, the target total number of T ' expression radar trackings, wjt=1 j-th of measurement of expression is fallen into t-th
Target correlation Bo Mennei, wjt=0 indicates that j-th of measurement does not fall within t-th of target correlation wave door, and subscript T indicates transposition, on
Mark -1 indicates inversion operation, vjt(k) j-th of new breath for measuring the measurement prediction to t-th of target of k moment, S are indicatedt(k) it indicates
The new breath covariance matrix of t-th of target of k moment, k >=1.
3. a kind of Radar Multi Target based on data association algorithm as described in claim 1 tracks optimization method, feature exists
In for k moment n in step 2kA vector C for measuring the corresponding correlation Bo Mennei occurrence numbers composition of a targets of each leisure T '
(k), wherein the correlation wave door is：It is assumed that space where a targets of the T ' of radar tracking is tracking space, with a mesh of k moment T '
Mark respective measurement predictionCentered on, will it is described with
Track space corresponds to and is divided into T ' sub-spaces V1, V2..., Vt..., VT′, and by t-th of subspace VtAs corresponding t-th of target
Related wave door.
4. a kind of Radar Multi Target based on data association algorithm as claimed in claim 3 tracks optimization method, feature exists
In in step 2, described that the candidate collection that measures of t-th of target of k moment is denoted as Zt(k), t-th of the k moment after the optimization
The candidate of target measures collection Z 't(k), the k moment nkThe corresponding correlation Bo Mennei occurrence numbers of a measurement a targets of each leisure T '
The vector C (k) of composition and the k moment fall into related the candidate of Bo Mennei of t-th of target and measure in nk× T ' dimensions measurement-target
The vector C ' of the number composition occurred in incidence matrix Ωt(k), expression formula is respectively：
Zt(k)={ zj(k)|wjt=1 }
Z′t(k)={ z 'it(k) | i=1,2 ... mkt}
C (k)={ (zj(k), cj(k)) | j=1,2 ..., nk}
C′t(k)={ c 'it(k) | i=1,2 ..., mkt}
Wherein, zj(k) j-th of measurement, w in the measurement set Z (k) at k moment are indicatedjt=1 j-th of measurement of expression is fallen into t-th
Target correlation Bo Mennei；z′it(k) i-th of candidate measurement of t-th of target of k moment, z are indicatedj(k) the measurement collection at k moment is indicated
Close j-th of measurement, c in Z (k)j(k) j-th of time measured in the corresponding correlation Bo Mennei appearance of a targets of T ' of k moment is indicated
Number, j ∈ { 1,2 ..., nk, nkIndicate that the k moment corresponds to the measurement number for including, c 'it(k) indicate that the k moment falls into t-th of target
I-th of related Bo Mennei is candidate to be measured in nkThe number occurred in × T ' dimensions measurement-target association matrix Ω, i ∈ 1,
2 ..., mkt, mktIndicate that t-th of target of k moment includes it is candidate measure number, t ∈ { 1,2 ..., T ' }, T ' expressions radar with
The target total number of track.
5. a kind of Radar Multi Target based on data association algorithm as described in claim 1 tracks optimization method, feature exists
In, in step 3, the m for defining t-th of target of k moment and includingktI-th of candidate measurement is to t-th of mesh in a candidate measurement
It is v ' that target, which measures the new breath of prediction,it(k), expression formula is：
The candidate of t-th of target of k moment after the optimization measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from t
The probability β of a targetit(k) the candidate of t-th of target of k moment and after the optimization measures collection Z 't(k) zero candidates measure in
Derived from the probability β of t-th of target0t(k), expression formula is respectively：
Wherein, z 'it(k) indicate that the candidate of t-th of target of k moment after optimization measures collection Z 't(k) i-th of candidate measurement in,Indicate the measurement prediction of t-th of target of k moment, eit(k) indicate t-th of target of k moment derived from i-th of candidate amount
The proportion of survey, the proportion that b (k) the expression k moment is associated without candidate measurement with t-th of target, t ∈ 1,
2 ..., T ' }, the target total number of T ' expression radar trackings, i ∈ { 1,2 ..., mkt, mktIndicate that t-th of target of k moment includes
Candidate measure number.
6. a kind of Radar Multi Target based on data association algorithm as described in claim 1 tracks optimization method, feature exists
In, in step 4, the state estimation of described t-th of target of k momentIt is missed with the state of described t-th of target of k moment
Poor covariance matrix Pt(k | k), expression formula is respectively：
Wherein,Indicate the state one-step prediction of t-th of target of k moment, Kt(k) t-th of target of k moment is indicated
Kalman gain, vt(k) indicate that the combination of the measurement prediction of t-th of target of k moment newly ceases,βitIndicate letter
The candidate of t-th of target of k moment after change measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from the general of t-th target
Rate βit(k), v 'itIndicate the m that t-th of target of k moment includesktIt is a it is candidate measure in candidate measure to t-th target for i-th
Measure the new breath v ' of predictionit(k), Pt(k | k-1) indicates the one-step prediction state error covariance matrix of t-th of target of k moment, βit
(k) indicate that the candidate of t-th of target of k moment after optimization measures collection Z 't(k) i-th of candidate measurement z ' init(k) it is derived from t-th
The probability of target, β0t(k) indicate that the candidate of t-th of target of k moment after optimization measures collection Z 't(k) zero candidates measure source in
In the probability of t-th of target, Pt c(k | k)=[I-Kt(k)Ht(k)]Pt(k | k-1),
Ht(k) the measurement square of t-th of target of k moment is indicated
Battle array,Indicate the one-step prediction of k moment target t states, Pt(k | k-1) indicate that a step of t-th of target of k moment is pre-
Survey state error covariance matrix, Kt(k) kalman gain of expression t-th of target of k moment, subscript T expression transposition, t ∈ 1,
2 ..., T ' }, the target total number of T ' expression radar trackings, i ∈ { 1,2 ..., mkt, mktIndicate the time of t-th of target of k moment
Choosing measures number.
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| CN106970370B (en) * | 2017-04-25 | 2019-10-01 | 西安电子科技大学 | Radar Multi Target based on chaotic neural network tracks optimization method |
| CN107390180A (en) * | 2017-07-18 | 2017-11-24 | 中国人民解放军国防科学技术大学 | The multifunction radar signal estimation method of model is represented based on predicted state |
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| CN107977987B (en) * | 2017-11-20 | 2021-08-31 | 北京理工大学 | Unmanned aerial vehicle-mounted multi-target detection tracking and indicating system and method |
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| CN110297221B (en) * | 2019-06-19 | 2021-04-06 | 西安电子科技大学 | Data association method based on Gaussian mixture model |
| CN110542885B (en) * | 2019-08-13 | 2021-09-21 | 北京理工大学 | Millimeter wave radar target tracking method in complex traffic environment |
| CN110673134B (en) * | 2019-10-18 | 2023-06-13 | 南京市德赛西威汽车电子有限公司 | Track tracking optimization method under radar far-near alternating ranging mode |
| CN112114309B (en) * | 2020-08-10 | 2023-04-07 | 西安电子科技大学 | JPDA multi-target tracking method based on optimal contour coefficient self-adaptive K-means clustering |
| CN113376626A (en) * | 2021-06-23 | 2021-09-10 | 西安电子科技大学 | High maneuvering target tracking method based on IMMPDA algorithm |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101770024A (en) * | 2010-01-25 | 2010-07-07 | 上海交通大学 | Multi-target tracking method |
| CN104931952A (en) * | 2015-06-26 | 2015-09-23 | 西安电子科技大学 | Radar detection method based on multi-frame joint for moving target track |
-
2016
- 2016-05-23 CN CN201610344866.3A patent/CN106054151B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101770024A (en) * | 2010-01-25 | 2010-07-07 | 上海交通大学 | Multi-target tracking method |
| CN104931952A (en) * | 2015-06-26 | 2015-09-23 | 西安电子科技大学 | Radar detection method based on multi-frame joint for moving target track |
Non-Patent Citations (2)
| Title |
|---|
| Multiple Hypotheses Tracking for Multiple Target Tracking;S. S. Blackman;《IEEE Aerospace and Electronic Systems Magazine》;20040131;全文 * |
| 杂波环境下雷达/红外融合跟踪的修正概率数据互联滤波算法;崔彦凯，梁晓庚;《计算机工程与科学》;20131231;第35卷(第12期);全文 * |
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