CN106872955B - Radar multi-target tracking optimization method based on joint probability data association algorithm - Google Patents

Radar multi-target tracking optimization method based on joint probability data association algorithm Download PDF

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CN106872955B
CN106872955B CN201710052740.3A CN201710052740A CN106872955B CN 106872955 B CN106872955 B CN 106872955B CN 201710052740 A CN201710052740 A CN 201710052740A CN 106872955 B CN106872955 B CN 106872955B
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CN106872955A (en
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王彤
张俊飞
李�杰
高海龙
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Xidian University
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • 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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Abstract

The invention discloses a radar multi-target tracking optimization method based on a joint probability data association algorithm, which adopts the following steps: respectively determining the total target number T' tracked by the radar and the measurement number n correspondingly contained at the moment kkCalculating the state one-step prediction of the tth target at the moment k, the measurement prediction information of the jth target at the moment k, the one-step prediction error covariance matrix of the tth target at the moment k, the innovation covariance matrix of the tth target at the moment k and the Kalman gain of the tth target at the moment k, and further calculating the n-th target at the moment kkMeasuring the X T' dimension, namely a target incidence matrix, measuring at the moment k, namely a target interconnection probability matrix, and measuring at the moment k, namely a target confirmation matrix; respectively obtain k time nkζ of measurements associated with T' targetskA join event, and ζkCalculating the probability of each combined event to calculate the k time nkAn accurate probability matrix of the interconnection of each measurement with T' targets, a state equation of the tth target at the k moment, and an error covariance matrix of the tth target at the k moment.

Description

Radar multi-target tracking optimization method based on joint probability data association algorithm
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a radar multi-target tracking optimization method based on a joint probability data association algorithm, which is suitable for a radar to track a plurality of targets in real time in a clutter environment.
Background
In recent years, along with the complexity and changeability of application environments, the radar is required to have multi-target tracking capability and simultaneously realize multi-target tracking; the basic concept of multi-target tracking is proposed by Wax in an article applying the physical journal in 1955, and then in 1964, stel published a paper named as "optimal data association problem in monitoring theory" on IEEE to become a leader of multi-target tracking, but then kalman filtering is not generally applied, and stel adopts a track bifurcation method to solve the data association problem; in the early 70 s of the 20 th century, under the condition that a false alarm exists, a Kalman filtering method (Kalman) is utilized to systematically track and process multiple targets; the nearest neighbor method proposed by Singer in 1971 is the simplest method for solving data association, but the correct association rate of the nearest neighbor method in a clutter environment is low; in the period, the Y.Bar-Shalom plays a role in lifting the weight, and a probability data association algorithm (PDA) particularly suitable for tracking a single target in a clutter environment is proposed in 1975, so that the problem of tracking the single target in the clutter environment is effectively solved; T.E.Formann and Y.Bar-Shalom and the like propose a joint probability data association algorithm (JPDA), the JPDA arranges and combines all targets and measurements and selects a reasonable joint event to calculate joint probability, the JPDA considers the possibility that a plurality of measurements from other targets are in the same target interconnected domain, and the measurement problem of multiple targets in one interconnected domain under a clutter environment can be well solved; meanwhile, the JPDA is complex and large in calculation amount, and the situation of combined explosion can occur when the splitting of the confirmation matrix is increased along with the increase of the number of targets; therefore, JPDA is difficult to implement in engineering.
Disclosure of Invention
In view of the problems in the prior art, the invention aims to provide a radar multi-target tracking optimization method based on a joint probability data association algorithm, which can effectively reduce the number of joint events split in the interconnection process, reduce the calculated amount, is easy to realize in engineering and simultaneously ensures acceptable tracking accuracy.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
A radar multi-target tracking optimization method based on a joint probability data association algorithm comprises the following steps:
step 1, respectively determining the total number of targets tracked by the radar as T', and determining the number of measurements correspondingly contained at the moment k as nkAnd respectively recording the state estimation of the tth target at the moment k-1 as
Figure BDA0001218152210000021
The state error covariance matrix of the t-th target at the moment k-1 is recorded as Pt(k-1| k-1) of the tth target at time k-1The state transition matrix is denoted Ft(k | k-1), and recording the measurement matrix of the t-th target at the time k as Ht(k) The process noise covariance matrix of the tth target at the time k-1 is recorded as Qt(k-1), recording the measured noise covariance matrix of the t target at the time k as Rt(k) Then, the state one-step prediction of the t-th target at the k moment is obtained through calculation in sequence
Figure BDA0001218152210000022
Metrology prediction of the t-th target at time k
Figure BDA0001218152210000023
Measurement prediction innovation v of jth measurement on tth target at k momentjt(k) And a one-step prediction error covariance matrix P of the t target at the moment kt(k | k-1), innovation covariance matrix S of the tth target at time kt(k) And the Kalman gain K of the t target at the moment Kt(k) And then k time n is calculatedkMeasuring the dimension of x T-target incidence matrix omega (k);
wherein j ∈ {1,2, …, nk}，t∈{1,2,…,T′}，nkThe total number of the measurement correspondingly contained at the moment k is represented, T' represents the total number of the targets tracked by the radar, and k is more than or equal to 1;
step 2, according to the k time nkMeasuring a target incidence matrix omega (k) at the time of multiplying T', calculating to obtain a measuring-target interconnection probability matrix A (k) at the time of k, and further calculating to obtain a measuring-target confirmation matrix U (k) at the time of k;
step 3, obtaining a k time n according to the measurement-target confirmation matrix U (k) at the k timekζ of measurements associated with T' targetskA joint event, in turn, obtaining ζkThe respective probabilities of the respective joint events;
step 4, according to the k time nkζ of measurements associated with T' targetskThe respective probability of each joint event is calculated to obtain k time nkThe exact probability matrix of each measurement interconnected with T' targets is B (k);
step 5, according to the k time nkExact probability of interconnection of individual measurements with T' targetsA matrix B (k) for calculating the state equation of the tth target at the moment k
Figure BDA0001218152210000024
Further calculating to obtain an error covariance matrix P of the t target at the moment kt(k|k)；
Let T take 1 to T' respectively, and further obtain the equation of state of the 1 st target at the moment k respectively
Figure BDA0001218152210000025
Equation of state for the T' th target to time k
Figure BDA0001218152210000026
And the 1 st target's error covariance matrix P at time k1Error covariance matrix P of the T' th target from (k | k) to time kT′(k | k) and recording as an error covariance matrix of the T ' targets at the k moment, and tracking the T ' targets by the radar according to the error covariance matrix of the T ' targets at the k moment.
The invention has the beneficial effects that:
firstly, the method of the invention utilizes the advantages of the joint probability data association algorithm, fully considers the interconnection attribute between the measurement and the target, and calculates the interconnection probability between the measurement and the target by splitting the joint event, so that the algorithm can keep better tracking performance in the strong clutter environment.
Secondly, the method greatly reduces the number of low-probability combined events by thresholding the target-related wave gate, effectively reduces the calculated amount and improves the real-time property on the premise of acceptable tracking precision loss.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a radar multi-target tracking optimization method based on a joint probability data association algorithm of the present invention;
FIG. 2(a) is a schematic view of a measurement distribution under a four-cross target condition;
FIG. 2(b) is a schematic diagram of a four-cross target real route;
FIG. 2(c) is a diagram illustrating the results of target tracking for a quad-cross target using the method of the present invention;
FIG. 3(a) is a schematic diagram of measurement distribution under six-cross target conditions;
FIG. 3(b) is a schematic diagram of a six-cross target true course;
fig. 3(c) is a schematic diagram of the result of target tracking on a six-cross target by using the method of the present invention.
Detailed Description
Referring to fig. 1, it is a flow chart of a radar multi-target tracking optimization method based on joint probability data association algorithm of the present invention; the radar multi-target tracking optimization method based on the joint probability data association algorithm comprises the following steps:
step 1, respectively determining the total number of targets tracked by the radar as T', and determining the number of measurements correspondingly contained at the moment k as nkAnd respectively recording the state estimation of the tth target at the moment k-1 as
Figure BDA0001218152210000031
The state error covariance matrix of the t-th target at the moment k-1 is recorded as Pt(k-1| k-1), and the state transition matrix of the tth target at the time k-1 is denoted as Ft(k | k-1), and recording the measurement matrix of the t-th target at the time k as Ht(k) The process noise covariance matrix of the tth target at the time k-1 is recorded as Qt(k-1), recording the measured noise covariance matrix of the t target at the time k as Rt(k) Then, the state one-step prediction of the t-th target at the k moment is obtained through calculation in sequence
Figure BDA0001218152210000041
Metrology prediction of the t-th target at time k
Figure BDA0001218152210000042
Measurement prediction innovation v of jth measurement on tth target at k momentjt(k) And a one-step prediction error covariance matrix P of the t target at the moment kt(k | k-1), the tth target at time kIs given by the innovation covariance matrix St(k) And the Kalman gain K of the t target at the moment Kt(k) And then k time n is calculatedkThe x T' dimension measures the target correlation matrix Ω (k).
Wherein j ∈ {1,2, …, nk}，t∈{1,2,…,T′}，nkAnd the total number of the measurement correspondingly contained at the moment k is represented, T' represents the total number of the targets tracked by the radar, and k is more than or equal to 1.
Specifically, the total number of targets tracked by the radar is respectively determined to be T', and the measurement number correspondingly contained at the moment k is determined to be nkAnd respectively recording the state estimation of the tth target at the moment k-1 as
Figure BDA0001218152210000043
The state error covariance matrix of the t-th target at the moment k-1 is recorded as Pt(k-1| k-1), and the state transition matrix of the tth target at the time k-1 is denoted as Ft(k | k-1), and recording the measurement matrix of the t-th target at the time k as Ht(k) The process noise covariance matrix of the tth target at the time k-1 is recorded as Qt(k-1), recording the measured noise covariance matrix of the t target at the time k as Rt(k) (ii) a Wherein T ∈ {1,2, …, T '}, T' represents the total number of targets tracked by the radar.
Determining that Z (k) is a measurement set at time k, and Z (k) is { z }j(k)|j＝1,2,…,nk}，nkRepresents the total number of measurements, z, correspondingly included at time kj(k) Represents the jth measurement in the measurement set Z (k) at time k.
Respectively calculating the state one-step prediction of the t target at the k momentThe expression is as follows:
Figure BDA0001218152210000045
computing a metrology prediction of the tth target at time k
Figure BDA0001218152210000046
The expression is as follows:
Figure BDA0001218152210000047
then, respectively calculating to obtain the measurement prediction innovation v of the jth measurement to the tth target at the k momentjt(k) The expression is as follows:
Figure BDA0001218152210000048
calculating to obtain a one-step prediction error covariance matrix P of the t target at the moment kt(k | k-1), expressed as:
Pt(k|k-1)＝Ft(k|k-1)Pt(k-1|k-1)Ft T(k|k-1)+Qt(k-1)
calculating to obtain an innovation covariance matrix S of the t target at the moment kt(k) The expression is as follows:
St(k)＝Ht(k)Pt(k|k-1)Ht T(k)+Rt(k)
calculating to obtain the Kalman gain K of the t target at the moment Kt(k) The expression is as follows:
Kt(k)＝Pt(k|k-1)Ht T(k)St -1(k)
wherein, Ft(k | k-1) represents the state transition matrix for the tth target at time k-1,
Figure BDA0001218152210000051
representing the state estimate of the tth target at time k-1, Ht(k) A metrology matrix representing the t-th target at time k,
Figure BDA0001218152210000052
representing the state of the tth target at time k, one-step prediction, zj(k) Represents the jth measurement in the measurement set Z (k) at time k,
Figure BDA0001218152210000053
represents the measured prediction of the t-th target at time k, Rt(k) Represents the measured noise covariance matrix, P, of the t-th target at time kt(k-1| k-1) represents the state error covariance matrix for the tth target at time k-1, Qt(k-1) represents the process noise covariance matrix for the tth target at time k-1, Pt(k | k-1) represents the one-step prediction error covariance matrix for the tth target at time k, j ∈ {1,2, …, nk}，t∈{1,2,…,T′}，nkAnd T' represents the total number of targets tracked by the radar.
Taking the space where T 'targets tracked by the radar are located as a target tracking space, taking the respective measurement prediction of the T' targets at the k moment as the center, and correspondingly dividing the target tracking space into T 'subspaces, wherein the T' subspaces are respectively Lambda1,Λ2,…,Λt,…,ΛT′The measured predictions of T' targets at time k are respectively
Figure BDA0001218152210000055
Represents the measured prediction of the t-th target at time k, ΛtRepresenting the subspace of the tth target and dividing the subspace of the tth target by LambdatAs a tracking gate corresponding to the tth target or a correlation gate of the tth target, and the T' subspaces overlap each other; and T epsilon {1,2, …, T '}, T' represents the total number of targets tracked by the radar.
The design of the correlation gates ensures that the radar has a certain probability PGCorrespondingly receiving the echo of the tracked target, and recording the measurement prediction information of the jth measurement to the tth target at the k moment as vjt(k) If the jth measurement at the moment k falls within the correlation threshold of the tth target, the jth measurement at the moment k predicts the innovation v for the measurement of the tth targetjt(k) And the innovation covariance matrix S of the tth target at time kt(k) Satisfies the following formula:
where superscript T denotes transposition, superscript-1 denotes inversion, vjt(k) Represents the measurement prediction information of the jth measurement to the tth target at the k moment, St(k) The innovation covariance matrix, j ∈ {1,2, …, n, representing the tth target at time kk}，t∈{1,2,…,T′}，nkThe total number of the measurement correspondingly contained at the moment k is represented, and T' represents the total number of the targets tracked by the radar; gamma raytThe size of the t-th correlation gate is shown, and the value is an empirical value, gamma epsilon [9,16 ∈ ]](ii) a And the size gamma of the correlation gate is determined by the dimension of the individual measurement values and the probability P that a measurement falls within the corresponding target gateGJoint determination, in which the dimensions of the individual measurements are determined by the radar degrees of freedom, the probability P of said determinationGIs an empirical value, and PG∈[0.8,1]。
Thus, k is calculated as the time nkThe x T dimension is measured as a target correlation matrix Ω (k), and is expressed as:
Figure BDA0001218152210000062
wherein, wjt(k) Binary variable representing the jth measurement at time k falling within the relevant threshold of the tth target, j ∈ {1,2, …, nk}，t∈{1,2,…,T′}，nkThe total number of the measurement correspondingly contained at the moment k is shown, T' represents the total number of the targets tracked by the radar, wjt(k) 1 means that the j measurement at the time k falls within the correlation gate of the t target, and the conditionwjt(k) 0 means that the jth measurement at time k does not fall within the correlation gate of the tth target, nor does it satisfy
Figure BDA0001218152210000064
Superscript T denotes transposition, superscript-1 denotes inversion operation, vjt(k) Representing a measurement prediction of the jth measurement at time k on the tth targetInnovation, St(k) Representing an innovation covariance matrix of the t-th target at the moment k, wherein k is more than or equal to 1; gamma raytIndicating the size of the t-th correlation gate.
Step 2, according to the k time nkMeasuring the multiplied by T' dimension-a target incidence matrix omega (k), calculating to obtain a measuring-target interconnection probability matrix A (k) at the k moment, and further calculating to obtain a measuring-target confirmation matrix U (k) at the k moment.
In particular, the binary variable w falling within the correlation gate of the tth target is measured according to the jth measurement at time kjt(k) Calculating to obtain an effective likelihood function G of the j measurement at the k moment and the t target interconnectionjt(k) The expression is as follows:
Figure BDA0001218152210000071
further calculating to obtain a rough probability α of the j-th measurement and the t-th target interconnection at the time kjt(k) Comprises the following steps:
Figure BDA0001218152210000072
where superscript T denotes transposition, superscript-1 denotes inversion, St(k) An innovation covariance matrix, v, representing the t-th target at time kjt(k) Represents the measurement prediction information of the jth measurement to the tth target at the k moment, Gjt(k) Effective likelihood function, G, representing the interconnection of the jth measurement and the tth target at time kt(k) For the t target at the time k, n correspondingly included at the time k is shownkMeasuring the sum of the effective likelihood functions of the tth target interconnection respectively; gj(k) For the jth measurement at the time k, the sum of effective likelihood functions of the jth measurement at the time k and T' targets tracked by the radar, which are respectively interconnected, is represented, and the calculation mode is as follows:
Figure BDA0001218152210000073
Figure BDA0001218152210000074
b represents a set clutter distribution density correlation constant, which is correlated with the clutter distribution density, and in general, B is 0, which can obtain a good result; st(k) Innovation covariance matrix, n, representing the t-th target at time kkThe total number of the measurement correspondingly contained at the moment k is shown, T' represents the total number of the targets tracked by the radar, vjt(k) Indicating the measurement prediction innovation of the jth measurement to the tth target at the time k.
So as to obtain a measurement-target interconnection probability matrix A (k) at the time k, which has the following form:
wherein, αjt(k) Represents the coarse probability of the j-th measurement at time k interconnecting with the t-th target, j ∈ {1,2, …, nk}，t∈{1,2,…,T′}，nkAnd T' represents the total number of targets tracked by the radar.
According to the measurement-target interconnection probability matrix A (k) at the moment k, calculating to obtain a measurement-target confirmation matrix U (k) at the moment k, wherein the expression is as follows:
wherein u isjt(k) Binary variable, u, representing the confirmation gate at time k, with the jth measurement falling into the tth targetjt(k) 1 denotes that the jth measurement at time k falls within the validation gate of the tth target, ujt(k) 0 means that the jth measurement at time k does not fall within the validation gate of the tth target; the 1 st column elements in the measurement-target validation matrix u (k) at time k are all 1, which means that each measurement is likely to be due to clutter, and the jth measurement at time k falls into the binary variable u of the validation gate of the tth targetjt(k) The values of (A) are as follows:
Figure BDA0001218152210000082
αjt(k) indicating a coarse probability of interconnecting the jth measurement and the tth target at time k, α0Indicates a set acknowledgment threshold, and α0∈[0.1,0.3]。
Wherein the identifying gates of the tth target are a subset of the associated gates of the tth target, and the method comprises examining all the measurements of the associated gates falling within the tth target, i.e. examining the t-th column of the target interconnection probability matrix A (k) which is the measurement at time k, and if the j-th measurement at time k is associated with the t-th target with a rough probability αjt(k) Satisfy αjt(k)>α0Then the jth measurement at time k falls within the validation gate of the tth target.
Let j take 1 to n respectivelykAnd further obtain the k timeEach measurement falls within the validation wave gate of the t-th target;
Figure BDA0001218152210000085
indicating the number of measurements falling within the correlation threshold of the t-th target at time k α0Indicating a set confirmation gate threshold.
Through the processing, the number of split combined events in subsequent operation can be effectively reduced, and the calculated amount in the splitting process can be effectively reduced; thus, the measurement-target confirmation matrix u (k) at time k is obtained.
Step 3, obtaining a k time n according to the measurement-target confirmation matrix U (k) at the k timekζ of measurements associated with T' targetskA joint event, in turn, obtaining ζkThe respective probabilities of the individual joint events.
The substep of step 3 is:
3.1 splitting the measurement-target confirmation matrix U (k) at the moment k to obtain the moment n of kkζ of measurements associated with T' targetskThe ith joint event at the moment k is recorded as thetai(k)，i∈{1,2,…,ζk}，ζkRepresenting the number of the combined events contained after splitting the measurement-target confirmation matrix U (k) at the moment k, and further dividing the ith combined event theta (theta) at the moment ki(k) The corresponding interconnection matrix is marked as
Figure BDA0001218152210000091
The expression is as follows:
Figure BDA0001218152210000092
Figure BDA0001218152210000093
represents the ith join event θ at time ki(k) The j-th measure in the set of binary variables, i ∈ {1,2, …, ζ } interconnected with the t-th targetk}，ζkRepresents the number of the combined events contained after the measurement-target confirmation matrix U (k) at the time k is split, and j belongs to {1,2, …, nk}，t∈{1,2,…,T′}，nkAnd T' represents the total number of targets tracked by the radar.
The splitting of the k-time measurement-target validation matrix u (k) follows two principles: first, one and only one 1 is selected from each row in the measurement-target validation matrix u (k) at time k as nkMeasuring the X T' dimension, namely measuring unique non-zero elements corresponding to each row in a target interconnection matrix; second, nkIn the xT 'dimension measurement-target interconnection matrix, except the 1 st column, the rest T' -1 columns only have one non-zero element respectively, so that the ith joint event theta at the k momenti(k) The j-th measurement and t-th target interconnected binary variable
Figure BDA0001218152210000094
The following relationships are satisfied:
Figure BDA0001218152210000095
Figure BDA0001218152210000096
represents the ith join event θ at time ki(k) The jth measurement is interconnected with the tth target,
represents the ith join event θ at time ki(k) The jth measurement and the tth target are not interconnected; i ∈ {1,2, …, ζ ∈ [ ]k}，ζkRepresents the number of the combined events contained after the measurement-target confirmation matrix U (k) at the time k is split, and j belongs to {1,2, …, nk}，t∈{1,2,…,T′}，nkAnd T' represents the total number of targets tracked by the radar.
3.2 obtaining all the joint events by the operation, and calculating the ith joint event theta at the k moment by the following formulai(k) Probability of (Pr { theta) { theta }i(k)|ZkThe expression is as follows:
Figure BDA0001218152210000103
wherein Z iskRepresents the cumulative set of measurements corresponding to time 1 to time k, C represents a set normalization constant,
Figure BDA0001218152210000104
v (k) represents the sum of the area of the T' gates associated with each target,
Figure BDA0001218152210000105
St(k) an innovation covariance matrix, τ, representing the tth target at time kj[θi(k)]Represents the ith join event θ at time ki(k) The measurement interconnect indicator of the jth measurement in (a) is,
Figure BDA0001218152210000106
δt[θi(k)]represents the ith join event θ at time ki(k) The target detection indication of the t-th target,
Figure BDA0001218152210000107
φ[θi(k)]represents the ith join event θ at time ki(k) The number of false measurements in (1) is,PDindicating a set target detectable probability, PD∈[0.8,1]；
Figure BDA0001218152210000109
The j measurement z in the measurement set Z (k) representing the time kj(k) Obeying a gaussian distribution, which is calculated in the form:
Figure BDA00012181522100001010
zj(k) the j measurement, t, in the measurement set Z (k) representing time kjRepresenting a target associated with the jth measurement; n is a continuous multiplication symbol,
Figure BDA0001218152210000111
representing target t associated with jth measurement at time kjThe new-information covariance matrix of (a),
Figure BDA0001218152210000112
representing target t associated with jth measurement at time kjExp represents an exponential function.
3.3 let i take 1 to ζ respectivelykRespectively obtain k times nkζ of measurements associated with T' targetskRespective probabilities of the respective joint events, respectivelyIs recorded as:
Figure BDA0001218152210000113
Pr{θi(k)|Zkdenotes the ith join event θ at time ki(k) The probability of (c).
Step 4, according to the k time nkζ of measurements associated with T' targetskThe respective probability of each joint event is calculated to obtain k time nkThe exact probability matrix for each measurement to interconnect with T' targets is B (k).
Specifically, the ith joint event θ according to the k timei(k) Probability of (Pr { theta) { theta }i(k)|Zkβ, calculating to obtain the accurate probability β of the interconnection between the jth measurement and the tth target at the k momentjt(k) The expression is as follows:
wherein the content of the first and second substances,
Figure BDA0001218152210000115
represents the ith join event θ at time ki(k) The j-th measurement and the t-th target of the binary variable, ζkRepresents the number of combined events, theta, contained after splitting the validation matrix U (k) of the measurement-target at the moment ki(k) Represents the ith join event at time k, j e {1,2, …, nk}，t∈{1,2,…,T′}，nkAnd T' represents the total number of targets tracked by the radar.
Let β0t(k) Representing the probability that the effective measurement of the t-th target at the moment k is all from the false measurement, wherein the false measurement is the measurement from clutter or interference;
Figure BDA0001218152210000116
further obtain k time nkThe exact probability matrix of the interconnection of each measurement with T' targets is B (k), and the expression is:
Figure BDA0001218152210000117
βjt(k) and representing the precise probability of the j-th measurement and the t-th target interconnection at the k moment.
Step 5, according to the k time nkMeasuring an accurate probability matrix B (k) interconnected with T' targets, and calculating to obtain a state equation of the T-th target at the k moment
Figure BDA0001218152210000121
Further calculating to obtain an error covariance matrix P of the t target at the moment kt(k|k)。
Finally, let T take 1 to T' respectively, and then get the equation of state of the 1 st target at the moment k respectively
Figure BDA0001218152210000122
Equation of state for the T' th target to time k
Figure BDA0001218152210000123
And the 1 st target's error covariance matrix P at time k1Error covariance matrix P of the T' th target from (k | k) to time kT′(k | k) and recording as an error covariance matrix of the T ' targets at the k moment, and tracking the T ' targets by the radar according to the error covariance matrix of the T ' targets at the k moment.
In particular, according to the k time nkMeasuring an accurate probability matrix B (k) interconnected with T' targets, and calculating to obtain a state equation of the T-th target at the k moment
Figure BDA0001218152210000124
The expression is as follows:
Figure BDA0001218152210000125
wherein the content of the first and second substances,
Figure BDA0001218152210000126
one-step prediction of state representing the tth target at time K, Kt(k) Kalman gain, v, representing the t-th target at time kt(k) A combined innovation representing the measured prediction of the tth target at time k,
Figure BDA0001218152210000127
βjt(k) represents the precise probability of the j measurement and t target interconnection at the k momentjt(k) Indicating the measurement prediction innovation of the jth measurement to the tth target at the time k.
Further calculating to obtain an error covariance matrix P of the t target at the moment kt(k | k), expressed as:
Figure BDA0001218152210000128
wherein, Pt(k | k-1) represents the one-step prediction error covariance matrix for the tth target at time k,
Figure BDA0001218152210000129
Ηt(k) a metrology matrix representing the t-th target at time k,
Figure BDA00012181522100001210
representing a one-step prediction of the state of the target t at time k,
Kt(k) showing the Kalman gain of the T-th target at the moment k, the superscript T showing transposition, T being equal to {1,2, …, T '}, T' showing the total number of targets tracked by the radar, and j being equal to {1,2, …, nk}，nkThe total number of measurements included at time k is shown.
Finally, let T take 1 to T' respectively, and then get the equation of state of the 1 st target at the moment k respectively
Figure BDA0001218152210000131
Equation of state for the T' th target to time k
Figure BDA0001218152210000132
And the 1 st target's moment of error covariance at time kArray P1Error covariance matrix P of the T' th target from (k | k) to time kT′(k | k) and recording as an error covariance matrix of the T ' targets at the k moment, and tracking the T ' targets by the radar according to the error covariance matrix of the T ' targets at the k moment.
The radar multi-target tracking optimization method based on the joint probability data association algorithm is finished.
The effect of the present invention is further verified and explained by the following simulation experiment.
And (I) simulation experiment data show.
In order to verify the accuracy of the method, the method is proved by a simulation experiment; the experimental data parameters were as follows:
Figure BDA0001218152210000133
(II) simulation results and analysis
Simulation results of the present invention are shown in fig. 2(a), fig. 2(b), fig. 2(c), fig. 3(a), fig. 3(b), and fig. 3(c), respectively, where fig. 2(a) is a schematic diagram of measurement distribution under a four-cross target condition, fig. 2(b) is a schematic diagram of a real route of the four-cross target, fig. 2(c) is a schematic diagram of a result of target tracking performed on the four-cross target by using the method of the present invention, and fig. 3(a) is a schematic diagram of measurement distribution under a six-cross target condition; FIG. 3(b) is a schematic diagram of a six-cross target real route, and FIG. 3(c) is a schematic diagram of a result of target tracking on the six-cross target by using the method of the present invention; in fig. 2(a), 2(b), 2(c), 3(a), 3(b), and 3(c), the abscissa is the x-direction position and the unit is m; the ordinate is the y-direction position in m.
As can be seen from fig. 2(a), since the targets intersect and a plurality of measurements are tightly aggregated, it is difficult to separate the target tracks by using a conventional probabilistic data interconnection algorithm alone, and as can be seen from fig. 2(c), the targets can be accurately separated by using the method of the present invention, thereby ensuring higher tracking accuracy.
As can be seen from fig. 3(a), as the number of the targets tracked by the radar increases, the distribution of the trace of the measurement point in the region where the target tracks intersect is very messy, and a large amount of clutter is mixed. At the moment, if a conventional joint probability data association algorithm is adopted, a large number of joint events can be generated, the situation of combination explosion can occur when the matrix is confirmed to be split, the calculation complexity is increased sharply, and the engineering implementation cost is increased; the method can calculate the rough measurement-target association probability through an empirical formula, can effectively reduce the number of combined events through thresholding, is beneficial to engineering realization, and verifies the effectiveness of the processing method through the simulation experiments of the figure 3(b) and the figure 3 (c).
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the method.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention; thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (8)

1. A radar multi-target tracking optimization method based on a joint probability data association algorithm is characterized by comprising the following steps:
step 1, respectively determining the total number of targets tracked by the radar as T', and determining the number of measurements correspondingly contained at the moment k as nkAnd respectively recording the state estimation of the tth target at the moment k-1 asThe state error covariance matrix of the t-th target at the moment k-1 is recorded as Pt(k-1| k-1), and the state transition matrix of the tth target at the time k-1 is denoted as Ft(k | k-1), and recording the measurement matrix of the t-th target at the time k as Ht(k) The process noise covariance matrix of the tth target at the time k-1 is recorded as Qt(k-1), recording the measured noise covariance matrix of the t target at the time k as Rt(k) Then, the state one-step prediction of the t-th target at the k moment is obtained through calculation in sequence
Figure FDA0002267986090000012
Metrology prediction of the t-th target at time k
Figure FDA0002267986090000013
Measurement prediction innovation v of jth measurement on tth target at k momentjt(k) And a one-step prediction error covariance matrix P of the t target at the moment kt(k | k-1), innovation covariance matrix S of the tth target at time kt(k) And the Kalman gain K of the t target at the moment Kt(k) And then k time n is calculatedkThe measurement of the dimension of x T-target incidence matrix omega (k);
wherein j ∈ {1,2, …, nk}，t∈{1，2，…，T′}，nkThe total number of the measurement correspondingly contained at the moment k is represented, T' represents the total number of the targets tracked by the radar, and k is more than or equal to 1;
step 2, according to the k time nkMeasuring a target incidence matrix omega (k) in a multiplied by T' dimension, calculating to obtain a measuring-target interconnection probability matrix A (k) at the k moment, and further calculating to obtain a measuring-target confirmation matrix U (k) at the k moment;
step 3, obtaining a k moment n according to the measurement-target confirmation matrix U (k) at the k momentkζ of measurements associated with T' targetskA joint event, in turn, obtaining ζkThe respective probabilities of the respective joint events;
step 4, according to the k time nkζ of measurements associated with T' targetskThe respective probability of each joint event is calculated to obtain k time nkThe exact probability matrix of each measurement interconnected with T' targets is B (k);
step 5, according to the k time nkMeasuring an accurate probability matrix B (k) interconnected with T' targets, and calculating to obtain a state equation of the T-th target at the k moment
Figure FDA0002267986090000014
Further calculating to obtain an error covariance matrix P of the t target at the moment kt(k|k)；
Let T take 1 to T' respectively, and further get the 1 st mesh at the moment k respectivelyTarget equation of state
Figure FDA0002267986090000015
Equation of state for the T' th target to time k
Figure FDA0002267986090000021
And the 1 st target's error covariance matrix P at time k1Error covariance matrix P of the T' th target from (k | k) to time kT′(k | k) and recording as an error covariance matrix of the T ' targets at the k moment, and tracking the T ' targets by the radar according to the error covariance matrix of the T ' targets at the k moment.
2. The radar multi-target tracking optimization method based on the joint probability data association algorithm as claimed in claim 1, wherein in step 1, the state of the tth target at the time k is predicted in one stepMetrology prediction of the t-th target at time k
Figure FDA0002267986090000023
Measurement prediction innovation v of jth measurement on tth target at k momentjt(k) And a one-step prediction error covariance matrix P of the t target at the moment kt(k | k-1), innovation covariance matrix S of the tth target at time kt(k) And the Kalman gain K of the t target at the moment Kt(k) The expressions are respectively:
Figure FDA0002267986090000024
Figure FDA0002267986090000025
Figure FDA0002267986090000026
Pt(k|k-1)＝Ft(k|k-1)Pt(k-1|k-1)Ft T(k|k-1)+Qt(k-1)
St(k)＝Ht(k)Pt(k|k-1)Ht T(k)+Rt(k)
Kt(k)＝Pt(k|k-1)Ht T(k)St -1(k)
wherein, Ft(k | k-1) represents the state transition matrix for the tth target at time k-1,
Figure FDA0002267986090000027
representing the state estimate of the tth target at time k-1, Ht(k) A metrology matrix representing the t-th target at time k,
Figure FDA0002267986090000028
representing the state of the tth target at time k, one-step prediction, zj(k) Represents the jth measurement in the measurement set Z (k) at time k,
Figure FDA0002267986090000029
represents the measured prediction of the t-th target at time k, Rt(k) Represents the measured noise covariance matrix, P, of the t-th target at time kt(k-1| k-1) represents the state error covariance matrix for the tth target at time k-1, Qt(k-1) represents the process noise covariance matrix for the tth target at time k-1, Pt(k | k-1) represents the one-step prediction error covariance matrix for the tth target at time k, j ∈ {1,2, …, nk}，t∈{1，2，…，T′}，nkThe total number of the measurement correspondingly contained at the moment k is represented, and T' represents the total number of the targets tracked by the radar; superscript T denotes transposition, superscript-1 denotes inversion operation, vjt(k) Represents the measurement prediction information of the jth measurement to the tth target at the k moment, St(k) And k is equal to or more than 1 and represents the innovation covariance matrix of the t target at the moment k.
3. The radar multi-target tracking optimization method based on the joint probability data association algorithm as claimed in claim 1, wherein in step 1, the k time n iskThe measurement-target correlation matrix Ω (k) in the x T' dimension is expressed as:
Figure FDA0002267986090000031
wherein, wjt(k) Binary variable representing the jth measurement at time k falling within the relevant threshold of the tth target, j ∈ {1,2, …, nk}，t∈{1，2，…，T′}，nkThe total number of the measurement correspondingly contained at the moment k is shown, T' represents the total number of the targets tracked by the radar, wjt(k) 1 denotes that the jth measurement at time k falls within the correlation bin of the tth target, wjt(k) 0 means that the jth measurement at time k does not fall within the correlation bin of the tth target;
the obtaining process of the correlation gate of the tth target is as follows: taking the space where T 'targets tracked by the radar are located as a target tracking space, taking the respective measurement prediction of the T' targets at the k moment as the center, and correspondingly dividing the target tracking space into T 'subspaces, wherein the T' subspaces are respectively Lambda1，Λ2，…，Λt，…，ΛT′，ΛtRepresenting the subspace of the tth target and dividing the subspace of the tth target by LambdatAs the correlation gate for the tth target.
4. The radar multi-target tracking optimization method based on the joint probability data association algorithm as claimed in claim 3, wherein in step 2, the measurement-target interconnection probability matrix A (k) at time k and the measurement-target confirmation matrix U (k) at time k are respectively expressed as:
Figure FDA0002267986090000032
Figure FDA0002267986090000033
wherein, αjt(k) Represents the coarse probability of the j-th measurement at time k interconnecting with the t-th target, j ∈ {1,2, …, nk}，t∈{1，2，…，T′}，nkThe total number of the measurement correspondingly contained at the moment k is represented, and T' represents the total number of the targets tracked by the radar; u. ofjt(k) Binary variable, u, representing the confirmation gate at time k, with the jth measurement falling into the tth targetjt(k) 1 denotes that the jth measurement at time k falls within the validation gate of the tth target, ujt(k) 0 means that the jth measurement at time k does not fall within the validation gate of the tth target; binary variable u of confirmation gate that jth measurement falls into tth target at time kjt(k) The values of (A) are as follows:
Figure FDA0002267986090000041
αjt(k) indicating a coarse probability of interconnecting the jth measurement and the tth target at time k, α0Indicating a set confirmation wave gate threshold;
wherein the identifying gates of the tth target are a subset of the associated gates of the tth target, the method comprising examining all measurements of the associated gates falling within the tth target, i.e. examining the measurements at time k-th column of a target interconnection probability matrix A (k), if the jth measurement at time k has a coarse probability of interconnection with the tth target αjt(k) Satisfy αjt(k)＞α0Then the jth measurement at time k falls within the validation gate of the tth target.
5. The radar multi-target tracking optimization method based on the joint probability data association algorithm as claimed in claim 4, wherein in step 2, α is performedjt(k) The rough probability of the interconnection between the jth measurement and the tth target at the time k is represented, and the obtaining process is as follows:
according to the binary variable w of j measurement falling into the correlation wave gate of t target at k timejt(k) Calculating to obtain an effective likelihood function G of the j measurement at the k moment and the t target interconnectionjt(k) The expression is as follows:
Figure FDA0002267986090000042
further calculating to obtain a rough probability α of the j-th measurement and the t-th target interconnection at the time kjt(k) Comprises the following steps:
where superscript T denotes transposition, superscript-1 denotes inversion, St(k) An innovation covariance matrix, v, representing the t-th target at time kjt(k) Represents the measurement prediction information of the jth measurement to the tth target at the k moment, Gjt(k) Effective likelihood function, G, representing the interconnection of the jth measurement and the tth target at time kt(k) For the t target at the time k, n correspondingly included at the time k is shownkThe sum of effective likelihood functions of each measurement and the t-th target are interconnected; gj(k) For the jth measurement at the time k, the sum of effective likelihood functions of the jth measurement at the time k and T' targets tracked by the radar, which are respectively interconnected, is represented, and the calculation mode is as follows:
Figure FDA0002267986090000051
Figure FDA0002267986090000052
b represents a set clutter distribution density correlation constant.
6. The radar multi-target tracking optimization method based on the joint probability data association algorithm as claimed in claim 1, wherein the substep of step 3 is:
3.1 splitting the measurement-target confirmation matrix U (k) at the moment k to obtain a moment k nkζ of measurements associated with T' targetskThe ith joint event at the moment k is recorded as thetai(k)，i∈{1，2，…，ζk}，ζkRepresenting the number of the combined events contained after splitting the measurement-target confirmation matrix U (k) at the moment k, and further dividing the ith combined event theta (theta) at the moment ki(k) The corresponding interconnection matrix is marked as
Figure FDA0002267986090000053
The expression is as follows:
represents the ith join event θ at time ki(k) The j-th measure of the binary variable interconnected with the t-th target, j ∈ {1,2, …, nk}，t∈{1，2，…，T′}，nkThe total number of the measurement correspondingly contained at the moment k is represented, and T' represents the total number of the targets tracked by the radar;
3.2 calculate the ith join event θ at time k byi(k) Probability of (Pr { theta) { theta }i(k)|ZkThe expression is as follows:
Figure FDA0002267986090000061
wherein Z iskRepresents the cumulative set of measurements corresponding to time 1 to time k, C represents a set normalization constant,
Figure FDA0002267986090000062
v (k) represents the sum of the area of the T' gates associated with each target,
St(k) to representInnovation covariance matrix, τ, of the tth target at time kj[θi(k)]Represents the ith join event θ at time ki(k) The measurement interconnect indicator of the jth measurement in (a) is,
Figure FDA0002267986090000064
δt[θi(k)]represents the ith join event θ at time ki(k) The target detection indication of the t-th target,
Figure FDA0002267986090000065
φ[θi(k)]represents the ith join event θ at time ki(k) The number of false measurements in (1) is,
Figure FDA0002267986090000066
PDindicating the set target detectable probability that,
Figure FDA0002267986090000067
the j measurement z in the measurement set Z (k) representing the time kj(k) Obeying a gaussian distribution, which is calculated in the form:
Figure FDA0002267986090000068
zj(k) the j measurement, t, in the measurement set Z (k) representing time kjRepresenting a target associated with the jth measurement; pi is a successive multiplication symbol,
Figure FDA0002267986090000069
representing target t associated with jth measurement at time kjThe new-information covariance matrix of (a),
Figure FDA00022679860900000610
representing target t associated with jth measurement at time kjExp represents an exponential function;
3.3 let i take 1 to ζ respectivelykRespectively obtain k timenkζ of measurements associated with T' targetskThe respective probabilities of the joint events are respectively recorded as:
Figure FDA00022679860900000611
Pr{θi(k)|Zkdenotes the ith join event θ at time ki(k) The probability of (c).
7. The radar multi-target tracking optimization method based on the joint probability data association algorithm as claimed in claim 1, wherein in step 4, the k time n iskThe exact probability matrix of the interconnection of each measurement with T' targets is B (k), and the expression is:
Figure FDA0002267986090000071
wherein, βjt(k) Indicating the precise probability of the j-th measurement being interconnected with the t-th target at time k,
Figure FDA0002267986090000072
Figure FDA0002267986090000073
represents the ith join event θ at time ki(k) The j-th measurement and the t-th target of the binary variable, ζkRepresents the number of combined events, theta, contained after splitting the validation matrix U (k) of the measurement-target at the moment ki(k) Represents the ith join event at time k, j e {1,2, …, nk}，t∈{1，2，…，T′}，nkThe total number of the measurement correspondingly contained at the moment k is represented, and T' represents the total number of the targets tracked by the radar; pr { theta [ theta ])i(k)|ZkDenotes the ith join event θ at time ki(k) The probability of (c).
8. The radar multi-target tracking optimization method based on the joint probability data association algorithm as claimed in claim 1, whereinIn step 5, the equation of state of the tth target at the time k
Figure FDA0002267986090000074
And the error covariance matrix P of the t target at the time kt(k | k) expressed as:
Figure FDA0002267986090000076
wherein the content of the first and second substances,
Figure FDA0002267986090000077
one-step prediction of state representing the tth target at time K, Kt(k) Kalman gain, v, representing the t-th target at time kt(k) A combined innovation representing the measured prediction of the tth target at time k,
Figure FDA0002267986090000078
β0t(k) indicating the probability that the valid measurements for the t-th target at time k all originate from spurious measurements, which are measurements that originate from clutter or interference, βjt(k) Represents the precise probability of the j measurement and t target interconnection at the k momentjt(k) Represents the measurement prediction information of the jth measurement to the tth target at the k moment, Pt(k | k-1) represents the one-step prediction error covariance matrix for the tth target at time k, Pt c(k|k)＝[I-Kt(k)Ht(k)]Pt(k|k-1)，Ht(k) A measuring matrix representing the T-th target at the time k, superscript T represents transposition, T belongs to {1,2, …, T '}, T' represents the total number of targets tracked by the radar, j belongs to {1,2, …, nk}，nkIndicating the total number of measurements correspondingly contained at time kAnd (4) counting.
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