CN106980114A - Target Track of Passive Radar method - Google Patents
Target Track of Passive Radar method Download PDFInfo
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- CN106980114A CN106980114A CN201710207225.8A CN201710207225A CN106980114A CN 106980114 A CN106980114 A CN 106980114A CN 201710207225 A CN201710207225 A CN 201710207225A CN 106980114 A CN106980114 A CN 106980114A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
- G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
- G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
- G01S13/726—Multiple target tracking
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Abstract
The present invention relates to Target Track of Passive Radar technology.The invention discloses a kind of passive radar multi-object tracking method, positioned according to the direction angle information of multistation passive radar, operating speed, acceleration, the direct-vision method of angle restriction carry out track initiation；Maneuvering target is tracked using IMM algorithms, tracking system nonlinear problem is solved using UKF algorithms, multiple target related question is solved using JPDA methods, so as to obtain targetpath and Target state estimator.Then interrupt flight path to certain measurement to be predicted, to T after the break periodth+TsmNew flight path in time is reversely estimated, then associates new and old flight path using sequential correlating method and obtains test matrix ΨN×M, then again to ΨN×MEnter the association confirmation matrix Ω that row constraint processing solves optimal trajectory associationN×M.The present invention not only can carry out locating and tracking to passive radar multiple target, the target state estimator precision in the track initiation time be improved, while the interruption track association in threshold time can also be solved the problems, such as.
Description
Technical field
The present invention relates to Radar Technology, more particularly to Target Track of Passive Radar technology.Particularly tracing area exists many
Individual target and disruption occurs in each targetpath, it is in the mesh under discrete state to cause the flight path after tracking filter
Mark tracking technique.
Background technology
In radio detection technical field, passive radar itself is without launching electromagnetic wave, by the electricity for receiving target emanation
Magnetic information is positioned and tracked to target.Passive Radar System has the advantages that operating distance is remote, good concealment, for improving
Survival ability of the system under electronic station environment plays an important roll.Passive Radar System is the electromagnetic wave ginseng based on target emanation
Number come determine radiation source and its carry platform or target position information, the key technology of system is the processing of metric data
And form stable flight path.The conventional data processing method of passive radar is similar to monostatic radar, consists predominantly of data prediction,
Data correlation, track initiation, filter tracking, flight path termination forms the steps such as flight path.Data prediction solves systematic error and matched somebody with somebody
The problems such as standard, time synchronized, spacial alignment and unruly-value rejecting.Track initiation is that target is moved under radar observation region with termination
Flight path set up and the process that terminates of flight path, especially track initiation is the significant process of radar data processing, and can decision to mesh
Mark realizes tracking.Data correlation and filter tracking solve associating for measuring point mark and target, and by measuring value to target-like
The problems such as estimation of state.It is the mistake that the dbjective state estimated by the measurement set of same target is formed to same flight path to form flight path
Journey.
For Passive Radar System pre-process (time synchronized, unruly-value rejecting) after orientation angle measurements set positioned with
Track, has very strong non-linear relation, so using unscented kalman filter due to measuring azimuth and target location in space
Device (Unscented Kalman Filter, UKF) is filtered.For the tracking of maneuvering target, using interactive multi-model
The adaptive algorithm of (Interacting Multiple Model Algorithm, IMM) is tracked.For multiple targets
Data correlation, using joint probabilistic data association algorithm (Joint Probabilistic Data Association
Algorithm, JPDA) solve the multiple target interconnection problem under clutter environment, and echo falls into the related ripples door of multiple tracking
Intersecting area data correlation problem., can be by interactive multi-model (IMM) algorithm and unwise karr to maneuvering target tracking
Graceful filtering (UKF) algorithm is combined, i.e., the wave filter in IMM algorithms is replaced with UKF wave filters, obtain IMM_UKF algorithms.This
Method can solve the tracking problem in passive radar, can with effective detection target move mobility, can improve target with
The state estimation of track.
Stable flight path can be formed by these based process methods to measuring point set substantially.Yet with passive radar
The intrinsic speciality of itself not emission detection signal, situations such as no longer radiation signal or ground obstacle are blocked radiant source target
Cause target metric data discontinuous so that interruption phenomenon occurs in the flight path formed using the above method to same target, especially
When under complex environment, when multiple targets are interrupted simultaneously, same stable flight path being formed to target and bring difficulty.
The content of the invention
, not only can be to continual continuous quantity it is an object of the invention to provide a kind of passive radar multi-object tracking method is counted
Survey data to be associated to form stable flight path, (flight path can also occur to the metric data for having partial loss in threshold time
Disruption) it is associated, can be to forming corresponding one stable flight path with each target in a collection of multiple target.
To overcome prior art to form stable flight path to the continuous sampling metric data of target, it is impossible to same target surrounding time
The problem of metric data for having disruption forms same flight path.
The present invention solves the technical problem, and the technical scheme of use is, Target Track of Passive Radar method, including as follows
Step：
A, tracking pretreatment：According to radar station up to collection orientation angle measurements set Z (k) carry out cross bearing, obtain with
Position the measurement set U (k) of target association；Track initiation is carried out according to positioning result operating speed, acceleration, angle restriction,
And obtain the Initial state estimation and corresponding covariance matrix of target；
B, Track In Track filtering：The flight path that target following obtains each moment of target is carried out to the target for meeting starting flight path
And state estimation；
C, interruption flight path pretreatment：It is predicted to interrupting the old flight path before the moment by the multi-model probability for interrupting the moment
T after being interrupted to the targetpathth+TsmOld Trajectory Prediction state estimation in time, wherein TthBe new, old displacement most
Big time, TsmIt is sequential correlation time window length；
D, the interruption sequential association of flight path：Interrupted according to flight path after the target number N that moment flight path is interrupted, and flight path interruption
Tth+TsmNew starting flight path target number M, initialization Testing Association matrix Ψ in timeN×M；To the target prediction of every Geju City flight path
State estimation is estimated in sequential association window length T with new flight path adverse statesmInterior progress sequential method association obtains test matrix
ΨN×M；At most there is a new flight path again according to every Geju City flight path, corresponding association, every new flight path at most have one therewith
Inspection thresholding γ under constraint criterion and level of confidence α that old flight path is associated1-αTo test matrix ΨN×MHandled,
Obtain last association and confirm matrix ΩN×M；
E, track confirmation：Confirm matrix Ω according to associationN×MAssociation results, old boat is assigned to the new flight path being successfully associated
The flight path number of mark, and replace dbjective state in target break period section to estimate with the status predication value of the old flight path in the break period
Evaluation；The flight path number of remaining new flight path is constant, and is designated fresh target appearance；Not associated successfully old flight path is terminated with flight path
Processing.
Specifically：Step b is specifically, the measurement that flight path is originated to meeting carries out target using IMM_UKF and JPDA algorithms
Tracking obtains the flight path and state estimation at each moment of target.
Specifically：Choose TsmFor sampling time Ts3~5 times.
Further：Step c also includes, to interrupting T after the momentth+TsmThe fresh target occurred in time temporally inversely enters
Row filtering obtains the T that its flight path startssmNew flight path state estimation in time.
Specifically：The radar station is included not at least three movement of same position and/or fixed radar station.
Specifically：The radar station is in the same plane.
Specifically：The radar station quantity is 3.
Further：In 3 radar stations, one of radar station is in the vertical of two other radar station connecting line
On bisector.
Specifically：
Z (k)={ Z1(k), Z2(k), Z3(k)}
Z in formulas(k) be s-th of radar station of k moment orientation angle measurements set, and meet
WhereinIt is the i-th of s-th of radar station of k momentsIndividual orientation angle measurements；nsRepresent s-th of radar station of k moment
Measurement number；N represents the number of radar station；M (k) represents the target number in k moment systematic observations region；Work as isWhen=0
Expression there is no measurement, i.e. missing inspection target or exist without target.
Specifically：In step a, the cross bearing is to calculate institute in all moment according to orientation angle measurements set Z (k)
There is the position coordinates of target.
The present invention is positioned according to the direction angle information of multistation passive radar, operating speed, acceleration, angle restriction
Direct-vision method carries out track initiation；Maneuvering target is tracked using IMM algorithms, tracking system non-thread is solved using UKF algorithms
Sex chromosome mosaicism, solves multiple target related question, so as to obtain targetpath and Target state estimator using JPDA methods.Then to certain
Measure interruption flight path to be predicted, to T after the break periodth+TsmNew flight path in time is reversely estimated, then using sequence
Correlating method is passed through to associate new and old flight path and obtain test matrix ΨN×M, then again to ΨN×MEnter row constraint processing and solve optimal boat
The association of mark association confirms matrix ΩN×M.The present invention not only can carry out locating and tracking to passive radar multiple target, improve flight path
Target state estimator precision in initial time, while the interruption track association in threshold time can also be solved the problems, such as.Overcome existing
There is technology to form stable flight path to the continuous sampling metric data of target, it is impossible to have interruption existing to same target surrounding time
The metric data of elephant forms the defect of same flight path.
The present invention is described further with reference to the accompanying drawings and detailed description.The additional aspect of the present invention and excellent
Point will be set forth in part in the description, and partly will become apparent from the description below, or pass through the practice of the present invention
Solve.
Brief description of the drawings
The accompanying drawing for constituting the part of the application is used for providing a further understanding of the present invention, specific implementation of the invention
Mode, schematic description and description are used to explain the present invention, do not constitute inappropriate limitation of the present invention.In the accompanying drawings：
Fig. 1 is the schematic diagram of the IMM_UKF algorithms for the N number of model for tracking single target, is included in N number of model, figure in figure
Wave filter uses UKF wave filters.In figureBe based on N number of model basis on state estimation, For model j state estimation.For model possibility vector, ukIt is model probability vector. For the output of j-th of wave filter of k-1 moment.ForHand over
The result of interaction, it as k moment wave filters j input.Z (k) is the orientation angle measurements at k moment.It is mould
Type j one-step prediction state estimation.
Fig. 2 is that circle represents certain target in the adjustment location in three targets 120 seconds, figure in the specific embodiment of the invention
Some time carves position coordinates in space.
Fig. 3 is to include measurement in 6 sections of flight paths that metric data is traced into after the A in invention, step B in Fig. 2, figure
Point mark, old flight path 1, old flight path 2, old flight path 3, new flight path 1, new flight path 2, new flight path 3.
Fig. 4 is to include measuring point mark in the obtained result of Trajectory Prediction, figure by interrupting, old flight path 1, old flight path 2, old
Flight path 3, old Trajectory Prediction flight path 1, old Trajectory Prediction flight path 2, the direction filter of old Trajectory Prediction flight path 3 and three new flight paths
Ripple flight path.
Fig. 5 is Fig. 4 partial enlarged drawing.
Fig. 6 is the final flight path of three targets obtained after step D, E.
Embodiment
It should be noted that in the case where not conflicting, embodiment, embodiment in the application and therein
Feature can be mutually combined.Let us now refer to the figures and combine herein below and describe the present invention in detail.
In order that those skilled in the art are better understood from the present invention program, below in conjunction with specific embodiment party of the present invention
Accompanying drawing in formula, embodiment, clear, complete description is carried out to the technical scheme in the specific embodiment of the invention, embodiment,
Obviously, described embodiment is only the embodiment of a branch of the invention, rather than whole embodiments.Based in the present invention
Embodiment, embodiment, what those of ordinary skill in the art were obtained on the premise of creative work is not made
Every other embodiment, embodiment, should all belong to the scope of protection of the invention.
Technical scheme, the azimuthal measuring set obtained first to passive radar using sight cross bearings,
IMM, JPDA, UKF scheduling algorithm form continuously measure steady according to steps such as tracking pretreatment, Track In Track filtering to continuous measure
Determine flight path and estimate the state corresponding to each target.Secondly in the range of sequential time, exist when the flight path termination moment
Multiple targetpaths (are referred to as " old flight path 1, old flight path 2, old flight path 3 ... ") termination, and threshold timeframe occur one or
Multiple targetpaths (are referred to as " new flight path 1, new flight path 2, new flight path 3 ... ") starting, and old Trajectory Prediction flight path and new flight path is inverse
Sequential association is carried out to filtering flight path and forms Testing Association matrix, and Restriction condition treat is pressed to Testing Association matrix, obtains old
Flight path and new flight path associate confirmation matrix, wherein unpaired message is associated comprising old flight path and new flight path, to what is be successfully associated
Old flight path substitutes dbjective state and flight path in the break period with status predication value and Trajectory Prediction value, and steady with new flight path composition
Determine flight path, flight path finalization process is carried out to not associated successfully old flight path, not associated successfully new flight path is gone out as fresh target
Now handled, to the new flight path beyond the threshold range time it also hold that being the appearance of fresh target.The passive radar of the present invention
Method for tracking target, is not only applicable to fixed radar station and carries out target following, is equally applicable to Radar Jammer and carries out target lid
Chapter.Key step of the present invention is as follows：
Track pre-treatment step：Cross bearing is carried out up to the orientation angle measurements set Z (k) of collection according to radar station, obtained
Measurement set U (k) with positioning target association；Flight path is carried out according to positioning result operating speed, acceleration, angle restriction to rise
Begin, and obtain the Initial state estimation and corresponding covariance matrix of target.
Track In Track is filtered：Target following is carried out to the target for meeting starting flight path using IMM_UKF and JPDA algorithms to obtain
Obtain the flight path and state estimation at each moment of target.
Interrupt flight path pre-treatment step：It is predicted to interrupting the old flight path before the moment by the multi-model probability for interrupting the moment
Obtain T after the targetpath is interruptedth+TsmOld Trajectory Prediction state estimation in time, wherein TthIt is new, old displacement
Maximum time, TsmIt is sequential correlation time window length.Simultaneously to interrupting T after the momentth+TsmThe fresh target occurred in time is on time
Between reverse be filtered obtain the T that its flight path startssmNew flight path state estimation in time.Here T is generally chosensmFor system
Sampling time Ts3~5 times.
Interrupt the sequential associated steps of flight path：The target number N that moment flight path is interrupted is interrupted according to flight path, and flight path is interrupted
T afterwardsth+TsmNew starting flight path target number M, initialization Testing Association matrix Ψ in timeN×M；Target to every Geju City flight path is pre-
State estimation is surveyed with new flight path adverse state to estimate in sequential association window length TsmInterior progress sequential method association obtains test matrix
ΨN×M；At most there is a new flight path again according to every Geju City flight path, corresponding association, every new flight path at most have one therewith
Inspection thresholding γ under constraint criterion and level of confidence α that old flight path is associated1-αTo test matrix ΨN×MHandled,
Obtain last association and confirm matrix ΩN×M。
Track confirmation step：Confirm matrix Ω according to associationN×MAssociation results, the new flight path being successfully associated is assigned to old
The flight path number of flight path, and dbjective state in target break period section is replaced with the status predication value of the old flight path in the break period
Estimate；The flight path number of remaining new flight path is constant, and is designated fresh target appearance；It is whole with flight path to not associated successfully old flight path
Knot processing.
Here above-mentioned steps are done with following supplementary notes：
1), in above-mentioned tracking pre-treatment step, with the orientation angle measurements set Z (k) for 3 radar stations being generally aligned in the same plane
Carry out cross bearing.I.e.
Z (k)={ Z1(k),Z2(k),Z3(k)} (1)
Z in formulas(k) be s-th of radar station of k moment orientation angle measurements set, and meet
WhereinIt is the i-th of s-th of radar station of k momentsIndividual orientation angle measurements；nsRepresent s-th of radar station of k moment
Measurement number；M (k) represents the target number in k moment systematic observations region；Work as isRepresent there is no azimuth when=0
Measure, i.e. missing inspection target.
Above-mentioned cross bearing is exactly the position that all targets in all moment are calculated according to orientation angle measurements set Z (k)
Coordinate, its process is as follows：K moment orientation angle measurements are chosen, the azimuth metric data at two radar station k moment of s1, s2 is entered
Row sight cross bearing obtains the possibility distribution total collection T (k) of multiple target, wherein
T in formulai(k) be the individual targets of M (k) i-th kind of possible distribution situation；It is the amount at two station k moment of s1, s2
Survey the sight crosspoint of data；C (k) represents the number of total possibility situation；Represent arrangement computing.
Radar station s3 is calculated to Ti(k) the orientation angle measurements estimate of m-th of target inMake Ti(k) institute in
There is the association probability between target and the true bearing angle measurements of s3 radar stations to be equal to
M=1,2 in formula ..., min ({ ns1,ns2})；is3=1,2 ..., ns3And ns3≤M(k)；α represents that probability is adjusted
Coefficient, according to measurement error value, typically takes 3~5 times of radar station error in measurement standard deviation.And then try to achieve in T (k) and each may be used
Can distribution situation and the n of s3 radar stationss3The maximum likelihood probability of individual orientation angle measurements association
WhereinEqual to 1 or 0, and meet
And byCorresponding Ti(k) andRadar station s1, s2, s3 rhumb line association results are obtained, i.e., to position mesh
Mark the measurement set U (k) of association.Assuming that including T in U (k)kIndividual target, then
Ut(k)={ βs1,m1,βs2,m2, βs3,m3} (10)
Wherein Ut(k) be three of k moment targets t stations measurement composition orientation angle measurements vector；And m1 ∈ 1,
2,...,ns1, m2 ∈ { 1,2 ..., ns2, m3 ∈ { 1,2 ..., ns3}.And according to Ut(k) in any combination of two and with phase
The radar station location answered calculates three location estimations of targetIt is taken and is worth to target position
Put and be estimated as
Wherein Xt(k)=[xt(k),yt(k)] ' expression k moment targets t position coordinates.The set of k moment target locations can
It is designated as
For continuous three moment target association location sets X (k), X (k+1), X (k+2), the target at corresponding moment is obtained
Location estimation respectively takes a target to obtain a combination flight path respectively from three set, and each group is tried to achieve in chronological order
Close the speed of correspondence target, acceleration, and velocity angle, then with prior agreed terms:Constraint of velocity, acceleration are about
Whether the condition judgments such as beam, angle restriction correspondence combination flight path is targetpath to carry out track initiation.Combination flight path is met
Constraints, confirm track initiation and carry out subsequent processing steps.
2), in above-mentioned Track In Track filtering, the schematic diagram of IMM_UKF algorithms is as shown in figure 1, be tracking one shown in Fig. 1
IMM_UKF algorithm flows during target, during to the tracking of multiple targets, the algorithm, Tu Zhongbao are reused to each target
Containing N number of model, figure median filter uses UKF wave filters.In figureIt is to be estimated based on the state on N number of model basis
Meter,For model j state estimation.For model possibility vector, ukIt is model probability vector.For the output of j-th of wave filter of k-1 moment.ForInteractive result, it as k moment wave filters j input.Z (k) is the orientation angle measurements collection at k moment
Close.It is model j one-step prediction state estimation.Interaction process is：Model i is transferred to model j transfer
Probability is Πij
Use uk-1(j) model j probability, and u are representedk-1(j) it is model probability vector ukIn the j elements, then interact
N number of wave filter is as follows in the input at k moment after calculating
In formula
In formula,
The system equation of hypothesized model j discrete times is
X (k+1)=fj[k,X(k)]+Vj(k) (17)
The system measurements equation of model j discrete times is
Z (k)=hj[k,X(k)]+Wj(k) (18)
WillAnd Poj(k-1 | k-1) being input in UKF wave filters as j-th of model of k moment, meter
Calculate (2lx+ 1) individual δ sampled pointsWith corresponding weights Wi, wherein lxIt isDimension,
Subscript m represents the weights in state renewal in formula；Subscript c represents the weights in covariance renewal；κukf、αukfβukf
It is UKF algorithm parameters.
According to the one-step prediction δ points of system state equation δ sampled pointsRecycle one-step prediction δ points and power
Value WiObtain status predication estimation and status predication covariance
In formula,Qj(k) be system process covariance.Further according to
Measurement equation, i.e. formula (18), obtain measuring prediction δ points
Then the measurement prediction of target and corresponding covariance are
In formula,Rj(k) it is system measurements noise covariance matrix.
Assuming that k+1 moment sensor orientations angle measurements are Z (k+1), then state updates and state updates covariance and is represented by
In formula,
Obtain wave filter outputAnd Pj(k | k) computation model j afterwards possibility
In formula
More new model j probability is again
The interactive mode for finally obtaining k moment IMM algorithms is output as
3), the JPDA algorithms in above-mentioned Track In Track filtering are the calculation by orientation angle measurements and target following track association
Method, main process is：Assuming that being carved with T target during k, and there are J orientation angle measurements to fall into corresponding echo Bo Mennei.Calculating side
Parallactic angle measurement j associates likelihood probability β with target t'sj,t, obtain associating likelihood matrix BJ×T, then
In formula
S in formulat(k) k moment targets t new breath covariance, v are representedj(k) the corresponding new breaths of orientation angle measurements j are represented, and
MeetWherein
In formula,It is the measurement predictor of UKF wave filters in model j when tracking target t,It is
UKF wave filter measurement predictor covariances in model j when tracking target t.
Set up the confirmation incidence matrix W of J × T dimensionJ×T, and initialize its element ωjtFor 0.Seek BJ×TMatrix greastest element
Ranks value corresponding to element, and by WJ×TThe element of middle correspondence ranks is entered as 1；By BJ×TThe all elements of middle correspondence ranks are assigned
It is worth for 0.The step is repeated always, until BJ×TMiddle all elements are all 0, obtain final confirmation incidence matrix WJ×T, wherein
ωjtAssociated for 1 expression target t with orientation angle measurements j.
4), in above-mentioned interruption flight path pretreatment, to the old flight path of target before the interruption moment by the multi-model for interrupting the moment
Probability is predicted T after targetpath terminationth+TsmThe method of old Trajectory Prediction state estimation in time is：Assuming that target
N interrupts the moment for kn, calculate the predicted state estimation of target and corresponding estimate covariance matrix
WhereinIt is the status predication estimation of UKF wave filters in model j when tracking target t, i.e. formula
(22)；It isCorresponding state covariance matrix, i.e. formula (23).Wherein kseg's
Value is met
To kmThe new fresh target m that moment occurs, and assume that it is k in the time that flight path occursm~(km+Lm), then LmTs
It is that the target total time length occurs.Backward filtering process to fresh target m is：By in normal filtering, system used
State equation is changed to as follows,
XM, it is inverse(k-1 | k)=F-1(k)XM, it is inverse(k|k)+V(k) (42)
Wherein F (k) is the state-transition matrix of normal system.The process of other processing procedures and Track In Track filtering process
It is similar, and without considering JPDA algorithms.
5), in the above-mentioned sequential association of interruption flight path, the sequential correlation method to old flight path and new flight path is by according to old flight pathPredict in 0~(Tth+Tsm)/TsFlight path in time windowWherein i=0,1 ...,
(Tth+Tsm)/TsWith the reverse estimation flight path of new flight pathIt is associated by sequential method, wherein i=0,
1,...,Tsm/Ts.Order
K in formulamSpan be 0,1,2 ..., Tsm/Ts.Then inspected numberFor
It is obeyedThe χ of the free degree2Distribution, wherein nxRepresentDimension；Further obtain test matrix ΨN×M
For
Again by according to per Geju City flight path, at most in the presence of a new flight path, corresponding association, every new flight path at most have one therewith
Inspection thresholding γ under constraints that the old flight path of bar is associated, level of confidence α1-αAnd examine moment matrix ΨN×MObtain
Track association confirms matrix ΩN×M.Wherein inspected numberInspection thresholding γ under certain level of confidence α1-αMeet formula
(48)
Formula (48) represents inspected numberLess than inspection thresholding γ1-αProbability be 1- α.Track association confirms square simultaneously
Battle array ΩN×MMeet
ω in formulan,mIt is ΩN×MIn element.
Embodiment
The Target Track of Passive Radar method of the present embodiment, it is assumed that passive radar tracking system is three stations on two dimensional surface
Fixed station tracking system (i.e. system is separated by a certain distance including 3, fixed radar station in the same plane), and use
Matlab softwares are emulated.
If the position coordinates of three radar stations is respectively O1(-20km,0)、O2(20km,0)、O3(0,20km), and set three
Orientation angle measurements are independent mutually between standing, and azimuth error in measurement average is 0, and standard deviation is all σβ=0.02 °, and obey Gauss
Distribution.
It is assumed that systematic sampling interval Ts=1s, Tth=22s, Tsm=3s, emulates total time T=120s.
If there is three targets in observation scope：Target T1 moved with uniform velocity in 0~120 second, and its initial position is XT1(-
21km, 75km), its initial velocity VT1(55m/s,60m/s)；Target T2 did uniform circular motion in 0~120 second, and its is initial
Position is XT2(- 20km, 82km), its initial velocity VT2(50m/s, -50m/s), angular speed isTarget T3 is 0
Moved with uniform velocity in~120 seconds, its initial position is in XT3(- 21km, 79km), its initial velocity VT3(60m/s,0m/s)；And set
Orientation angle measurements of the target 1 within 51~67s times are lost at fixed three stations simultaneously, while losing target 2 within 51~65s times
Orientation angle measurements, while losing orientation angle measurements of the target 3 within 51~64s times.
If the antenna sensing of radar station is Y-axis positive direction, and k moment radar stations j position isWhen
Now target i position isIt is β that then radar station j, which obtains orientation angle measurements,ji(k) it is
D β are azimuth measurement errors in formula, and its covariance is
If the process noise covariance Q containing a uniform motion model in IMM_UKF algorithmscv=1.8∧2I, six turn
It is curved motion rate of turn beThe process noise covariance of Turn Models is Qtr=2.5∧
2I.Wherein I represents unit matrix.And assume the probabilities of 7 models in IMM algorithms for u=[0.1,0.1,0.1,0.4,
0.1,0.1,0.1]′；Transition probability between model
If the parameter that UKF is calculated is：αukf=0.01, βukf=2, κukf=0.
By above-mentioned simulated conditions, it can learn in simulation time 120 seconds, the orientation angle measurements number at three station each moment
As much, then：
1), tracking pretreatment：Handle the orientation angle measurements of three radar stations at each moment, it is assumed that to three of the k moment
The orientation angle measurements stood, first choose the O at k moment1And O2The orientation angle measurements at two stations are calculated according to formula (52) obtains sight friendship
CrunodeAnd
I in formulaO1,iO2∈{1,2,3}；
Assuming that a target is corresponded with an orientation angle measurements, then obtain that total collection T (k) may be distributed, then
Wherein
T is sought againi(k) three targets are in O in3Observation under radar stationTake the σ of probability adjustment factor α=5β, then
Arrive
M in formula, is3∈{1,2,3}.Further obtain three target distribution situation TiAnd O (k)3Radar station true bearing angle
The association probability of measurement is
In formulaEqual to 1 or 0, and meet
Maximum is asked for againCorresponding Ti(k) andObtain the measurement of target 1 and be associated as U1(k)={ β11,β21,β31,
The measurement of target 2 is associated as U2(k)={ β12,β22,β32, the measurement of target 3 is associated as U3(k)={ β13,β23,β33}；
According to Ut(k) target t location estimation Z is calculatedt(k)=[xt(k),yt(k)] ', wherein t value is 1,2,3；
Then
In formula
The location estimation figure for drawing all targets all moment is as shown in Figure 2；
Error of covariance of the target t measurement errors under rectangular coordinate system, which can be calculated, simultaneously is
So the Initial state estimation and estimate covariance that are worth to target t according to the measurement of the azimuth at the first two moment are
2), Track In Track is filtered：The Initial state estimation and estimate covariance of all targets are obtained according to tracking pretreatment,
I.e. formula (62) and formula (63), are brought into IMM_UKF algorithms and are tracked filtering to all；
First according to target t the k-1 moment state estimationWith estimation association covariance Pt(k-1|k-1)
Measurement predictor is obtained to formula (26) by formula (19)With corresponding covariance matrix
Obtain associating likelihood matrix B further according to formula (35) to formula (38)J×T, set up and confirm incidence matrix WJ×T, and just
Its element of beginningization ωjtFor 0.Seek BJ×TRanks value corresponding to matrix greatest member, and by WJ×TThe element assignment of middle correspondence ranks
For 1；By BJ×TThe all elements of middle correspondence ranks are entered as 0.The step is repeated always, until BJ×TMiddle all elements are all 0,
Obtain final confirmation incidence matrix WJ×T；
According to WJ×TAssociation results, by the orientation angle measurements Z being associated with target tt(k) formula (27) is brought into arrive
Formula (34) obtains state estimations of all target t at the k momentWith estimate covariance Pt(k | k), and k moment mesh
Mark t multi-model probability
If sometime kePlay continuous 3 TsNo orientation angle measurements are successfully associated with target t in cycle, then target is in ke
Moment flight path is interrupted；
If sometime ksHave orientation angle measurements not with all ksThe target association success at -1 moment, then it is assumed that be fresh target
Occur, filtered for the Track In Track of fresh target, then according to target ksMoment and ksThe orientation angle measurements at+1 moment, according to upper
The processing mode for stating formula (58) to formula (63) in tracking pretreatment is obtained
Track In Track processing procedure is recycled to be filtered it；
The flight path for finally giving three targets in the case study on implementation after Track In Track is handled is as shown in Figure 3；
3) flight path pretreatment, is interrupted：There are all moment that flight path interruption occur in all targets in time search in order, and
All interrupt is handled by the interruption of following flight path：
Assuming that interrupting moment keHave N number of old target to interrupt, in keThreshold time T afterwardsth+TsmIt is interior and have M new
Targetpath occurs；
If flight path, which occurs, in old target n interrupts the moment for kn=ke, obtain all N number of old according to formula (39) to formula (41)
Target is in Tth+TsmStatus predication value and prediction covariance in time, whereinBe target n state it is pre-
Measured value, Pn(kseg+1|kseg+ 1) it isCorresponding prediction covariance, wherein ksegFormula (41) is met, and
By all N number of old targets in 0~Tth+TsmPredicted value in time window is designated asWherein k=1,2 ..., (Tth+
Tsm)/Ts；
If fresh target m is k at the time of occurringmFlight path total length is LmTs, according to what is obtained in the processing of above-mentioned Track In Track
Fresh target m is in km+LmThe estimated state at momentWith estimate covariance Pm(km+Lm|km+Lm).According to public affairs
Formula (42) sets the method for system equation to reset the system state equation of each IMM models, then according to above-mentioned Track In Track
IMM_UKF method carries out backward filtering in filtering, obtains new flight path backward filtering state estimationWithWherein i=1,2 ..., Lm, and by all M fresh targets in 0~TsmReverse estimation note in time window
ForWherein i=0,1,2 ..., Tsm/Ts；
So far obtain each interrupt flight path predicted value and new flight path reverse estimation as shown in figure 4, its partial enlargement such as
Shown in Fig. 5；
4) the sequential association of flight path, is interrupted：Above-mentioned interruption flight path pre-processed results, that is, the new flight path adverse state estimation obtainedWherein i=0,1,2 ..., Tsm/TsIt is designated as with the status predication value of old flight pathIts
Middle k=1,2 ..., (Tth+Tsm)/Ts, Testing Association matrix is obtained as shown in figure 4, being calculated according to formula (43) to formula (47)
ΨN×M, at most there is a new flight path further according to every Geju City flight path, to correspond to association, every new flight path therewith most old in the presence of one
Inspection thresholding γ under constraints that flight path is associated, level of confidence α1-αAnd examine moment matrix ΨN×MObtain flight path
Association confirms matrix ΩN×M；
5), track confirmation：Above-mentioned interruption track association result, obtains association and confirms matrix ΩN×M, according to ΩN×MTo have new
State in the old flight path break period of track association is replaced with status predication value, and stablizes flight path with new Track forming；To not
Terminated with the old track confirmation flight path of new track association；The new flight path not associated with old track confirmation is originated by fresh target and navigated
Mark；Finally give simulation result as shown in Figure 6.
Claims (10)
1. Target Track of Passive Radar method, comprises the following steps：
A, tracking pretreatment：Cross bearing is carried out up to the orientation angle measurements set Z (k) of collection according to radar station, obtains and positions
The measurement set U (k) of target association；Track initiation is carried out, and is obtained according to positioning result operating speed, acceleration, angle restriction
Obtain the Initial state estimation and corresponding covariance matrix of target；
B, Track In Track filtering：Flight path and shape that target following obtains each moment of target are carried out to the target for meeting starting flight path
State is estimated；
C, interruption flight path pretreatment：This is predicted by the multi-model probability for interrupting the moment to the old flight path before the interruption moment
T after targetpath is interruptedth+TsmOld Trajectory Prediction state estimation in time, wherein TthWhen being the maximum of new, old displacement
Between, TsmIt is sequential correlation time window length；
D, the interruption sequential association of flight path：T after the target number N that moment flight path is interrupted, and flight path interruption is interrupted according to flight pathth+
TsmNew starting flight path target number M, initialization Testing Association matrix Ψ in timeN×M；To the target prediction shape of every Geju City flight path
State is estimated with the estimation of new flight path adverse state in sequential association window length TsmInterior progress sequential method association obtains test matrix
ΨN×M；At most there is a new flight path again according to every Geju City flight path, corresponding association, every new flight path at most have one therewith
Inspection thresholding γ under constraint criterion and level of confidence α that old flight path is associated1-αTo test matrix ΨN×MHandled,
Obtain last association and confirm matrix ΩN×M；
E, track confirmation：Confirm matrix Ω according to associationN×MAssociation results, old flight path is assigned to the new flight path being successfully associated
Flight path number, and Target state estimator in target break period section is replaced with the status predication value of the old flight path in the break period
Value；The flight path number of remaining new flight path is constant, and is designated fresh target appearance；To it is not associated successfully old flight path with flight path termination at
Reason.
2. Target Track of Passive Radar method according to claim 1, it is characterised in that：Step b is specifically, to meeting
The flight path and state that the target of beginning flight path carries out target following acquisition each moment of target using IMM_UKF and JPDA algorithms are estimated
Meter.
3. Target Track of Passive Radar method according to claim 1, it is characterised in that：Choose TsmFor sampling time Ts's
3~5 times.
4. Target Track of Passive Radar method according to claim 1, it is characterised in that：Step c also includes, during to interrupting
T after quarterth+TsmThe fresh target occurred in time, which is temporally inversely filtered, obtains the T that its flight path startssmNew boat in time
Mark state estimation.
5. the Target Track of Passive Radar method according to Claims 1 to 4 any one, it is characterised in that：The radar
Stand including not at least three movement of same position and/or fixed radar station.
6. Target Track of Passive Radar method according to claim 5, it is characterised in that：The radar station is located at same flat
On face.
7. Target Track of Passive Radar method according to claim 6, it is characterised in that：The radar station quantity is 3.
8. Target Track of Passive Radar method according to claim 7, it is characterised in that：In 3 radar stations, wherein
One radar station is on the perpendicular bisector of two other radar station connecting line.
9. Target Track of Passive Radar method according to claim 8, it is characterised in that：
Z (k)={ Z1(k), Z2(k), Z3(k)}
Z in formulas(k) be s-th of radar station of k moment orientation angle measurements set, and meet
WhereinIt is the i-th of s-th of radar station of k momentsIndividual orientation angle measurements；nsRepresent the amount of s-th of radar station of k moment
Detecting number；N represents the number of radar station；M (k) represents the target number in k moment systematic observations region；Work as isRepresented when=0
There is no orientation angle measurements, i.e. missing inspection target or exist without target.
10. Target Track of Passive Radar method according to claim 9, it is characterised in that：In step a, the intersection is fixed
Position is the position coordinates that all targets in all moment are calculated according to orientation angle measurements set Z (k).
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