CN109035301A - A kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm - Google Patents
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Abstract
A kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm, the present invention relates to group's method for tracking target based on repulsion Modifying model random matrix algorithm.The present invention is low in order to solve the problems, such as existing method computation complexity height and precision.The present invention includes: one: establishing the space repulsion model and proper subspace repulsion model when the movement of group's target；Two: space repulsion model and proper subspace repulsion when group's target that step 1 is established is moved are transformed under rectangular coordinate system；Three: the proper subspace repulsion Modifying model radar measurement value being transformed into step 2 under rectangular coordinate system, and the equation of motion for the space repulsion Modifying model random matrix algorithm being transformed under rectangular coordinate system with step 2 and the Predicting Performance Characteristics covariance for correcting measurement equation.The present invention is compared with Interactive Multiple-Model random matrix algorithm, and queue estimated accuracy improves 11.79%, and position estimation accuracy improves 21.12%.The present invention is used for group's target tracking domain.
Description
Technical field
The present invention relates to group's target tracking domains, and in particular to the group based on repulsion Modifying model random matrix algorithm
Method for tracking target.
Background technique
Many years have been developed in target following technology, regardless of suffering from huge in military or civil field, the technology
Development space, practical value and commercial value.And in recent years, fast with space technology, telecommunication technology and computer technology
Exhibition is hailed, target following technology is in every field all by the concern of scholars.
In group's Target Tracking Problem, traditional tracking often will cause huge data correlation problem, such as
Arest neighbors Kalman filtering, multiple hypotheis tracking method, joint probability data association method etc., these methods when carrying out tracking filter all
Individual in group's target is individually taken out into consideration, the specific pass between measured value and target individual is determined by data correlation
System, to being predicted one by one objective monomer, be updated.Due to it needs to be determined that association in tracking gate between measured value and target
Relationship, even for multiple tracking gate overlapping regions a variety of associative combinations that may be present, this will cause these algorithms to explode
Calculation amount.However, in the case where for modern electromagnetic increasingly complexity, when radar echo signal bring destination number will be
Become, if also with traditional track algorithm, it is likely that the case where causing data association combination to be exploded.Therefore, it is badly in need of a kind of calculation
Method reduces in the case where guaranteeing certain filtering accuracy and even avoids computation complexity caused by data correlation, thus preferably
Handle Radar Multi Target, group's Target Tracking Problem.
Summary of the invention
The purpose of the present invention is to solve the low problems of existing method computation complexity height and precision, and propose a kind of base
In group's method for tracking target of repulsion Modifying model random matrix algorithm.
A kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm the following steps are included:
Step 1: the space repulsion model and proper subspace repulsion when the movement of group's target are established；
Establish the space repulsion model when movement of group's target are as follows:
Wherein θt-1For the orientation angles measured value of t-1 moment target, θtFor t moment angle measurement, FNFor N number of target
Transfer matrix is moved, subscript N is the target number in group, RNFor repulsion matrix, HR,t-1For the repulsion vector at t-1 moment,
QNFor noise covariance, p (θt|θt-1) it is conditional probability of the t moment angle measurement at the t-1 moment,For Gaussian Profile；
Establish the detailed process of proper subspace repulsion model are as follows:
Proper subspace repulsion model is established by estimating that the angle difference Δ θ of angle and pre-estimation is determined after iteration；
Other than the repulsion described in the above-mentioned modeling, in radar spatial spectral estimation algorithm, when non-on two target angles
Very close to when, the spectral peak that spatial spectrum algorithm obtains often has overlapping situation, this be as caused by algorithm precision itself, therefore calculate
The repulsion on a kind of spatial spectrum is implied in method to offset the mistake of this overlapping initiation, so that the target angle interval of estimation
It is wider than actual angle interval.In this case, angle dimension can be carried out to signal first with basic spatial spectrum algorithm
Pre-estimation, then single direction signal is reconstructed, iteration signal amplitude is simultaneously subtracted each other with original signal, calculate spatial spectrum simultaneously look for
To the peak value of magnitude in an iterative process is detected, estimation angle corresponding to peak value is the angle estimation for subtracting other signals and obtaining
Value, therefore the overlapping influence of spectral peak is reduced, so that angle estimation interval reduces, angle estimation is more accurate, and estimates after iteration
The repulsion that meter angle and the angle difference Δ θ of pre-estimation are used to describe to need to introduce in spatial spectrum algorithm, the present invention are referred to as
It is characterized subspace repulsion.It is worth noting that, the space repulsion of the foregoing description allow for mutually collided between avoiding target and
Definition, therefore inversely with the differential seat angle of two targets；And the proper subspace repulsion proposed here is by spatial spectrum
It is proportional with the difference at estimation angle and pre-estimation angle after iteration caused by angle estimation algorithm itself.
Step 2: space repulsion model and proper subspace repulsion when group's target that step 1 is established moves are converted
To under rectangular coordinate system；
Step 3: the proper subspace repulsion Modifying model radar measurement value being transformed into step 2 under rectangular coordinate system,
And the equation of motion and correction amount of the space repulsion Modifying model random matrix algorithm under rectangular coordinate system are transformed into step 2
Survey the Predicting Performance Characteristics covariance of equation.
For radar when tracking to group's target, traditional track algorithm under Bayesian frame can not often avoid complexity
Data correlation and problem of data fusion, this by force radar system need to carry out huge mathematical operation, so as to cause system
Effective tracking in real time can not be carried out to target in first time.For such problem, invention introduces Random Matrices Theory,
It is right along with the amendment of dynamic Multiple Models Algorithm using the special relationship of the distribution character and itself and positive definite matrix of random matrix
Traditional filtering algorithm under Bayesian frame improves, and show that joint random matrix algorithm is tracked to group's target
When, either in terms of sensitivity or tracking accuracy and arithmetic speed, all there is huge improvement than traditional algorithm.
The invention has the benefit that
For radar when tracking to group's target, traditional track algorithm under Bayesian frame can not often avoid complexity
Data correlation and problem of data fusion, this by force radar system need to carry out huge mathematical operation, so as to cause system
Effective tracking in real time can not be carried out to target in first time.For such problem, invention introduces Random Matrices Theory,
Using the special relationship of the distribution character and itself and positive definite matrix of random matrix, in addition amendment and the repulsion of dynamic Multiple Models Algorithm
The optimization of model improves traditional filtering algorithm under Bayesian frame, and the improved multi-model random matrix obtained is calculated
Method either in terms of sensitivity or tracking accuracy and arithmetic speed, all compares traditional algorithm when tracking to group's target
There is huge improvement.
The present invention will start with from positive definite matrix and elliptical physical relationship, draw random matrix algorithm.Utilize random matrix
Special distribution character, by track algorithm frame under Bayesian frame, provide basic random matrix track algorithm and amendment with
The proof of machine matrix algorithm, and utilize simulation results show advantage of the algorithm in arithmetic speed and estimated accuracy.Finally, knot
Dynamic multi-model and repulsion model theory are closed, random matrix algorithm, dynamic Multiple Models Algorithm and repulsion model are combined, from
And greatly improve the estimated accuracy and sensitivity of algorithm.
The method of the present invention is compared with the essentially random matrix algorithm that Koch is proposed, queue estimated accuracy is relative to classic algorithm
Improve 68.91% (relative value)；Compared with Interactive Multiple-Model random matrix algorithm, queue estimated accuracy improves the present invention
11.79% (relative value), position estimation accuracy improve 21.12% (relative value).
Detailed description of the invention
Fig. 1 is characterized subspace repulsion coordinate transformation relation figure；
Fig. 2 is true queue scene figure；Abscissa is the x-axis under rectangular coordinate system, unit km, ordinate y in figure
Axis, unit km；
The queue scene figure that Fig. 3 is plus makes an uproar；Abscissa is the x-axis under rectangular coordinate system in figure, and unit km, ordinate is
Y-axis, unit km；
Fig. 4 is the dynamic multi-model random matrix track algorithm result figure of repulsion model refinement；Abscissa is rectangular co-ordinate
X-axis under system, unit km, ordinate is y-axis, unit km；
Fig. 5 is the partial enlarged view of Fig. 4；Abscissa is the x-axis under rectangular coordinate system, and unit km, ordinate is y-axis,
Unit is km；
Fig. 6 is model probability distribution map；Abscissa pendulous frequency in figure, ordinate are the probability size that model occurs；
Fig. 7 is the proper subspace repulsion figure of iterative method estimation；Abscissa is the time in figure, and unit 10s, ordinate is
The proper subspace repulsion size of angle dimension, unit are degree；
Fig. 8 is quene state mean square error figure；Abscissa is the time in figure, and unit 10s, ordinate is the team of angle dimension
The mean square error of column-shaped state is relative value without unit；
Fig. 9 is center position mean square error figure；Abscissa is the time in figure, and unit 10s, ordinate is the square of position
Error, unit are rice；
Figure 10 is four kinds of algorithm comparison diagrams；Abscissa is rectangular co-ordinate x-axis, and unit m, ordinate is y-axis, and unit is
km；
Figure 11 is that quene state mean square error calculates comparison diagram；Abscissa is the time, and unit 10s, ordinate is angle
The mean square error of the quene state of dimension is relative value without unit；
Figure 12 is center position mean square error figure；Abscissa is the time in figure, and unit 10s, ordinate is the equal of position
Square error, unit m
Figure 13 is practical radar surveying scene figure；Abscissa is rectangular co-ordinate x-axis in figure, and unit km, ordinate is y-axis,
Unit is km；
Figure 14 is the lower four kinds of algorithm comparison diagrams of actual scene；Abscissa is rectangular co-ordinate x-axis in figure, and unit km is indulged and sat
It is designated as y-axis, unit km；
Figure 15 is the mean square error figure of formation state；Abscissa is the time in figure, and unit 10s, ordinate is angle dimension
Quene state mean square error, be relative value without unit；
Figure 16 is center position mean square error figure；Abscissa is the time, and unit 10s, ordinate is the mean square error of position
Difference, unit km.
Specific embodiment
Specific embodiment 1: a kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm includes
Following steps:
In order to solve the problems, such as in group's target following that conventional method needs data correlation and caused by huge operand and
Ellipse fitting method has the problem of rigors to measurement point property, and the present invention will propose core of the invention algorithm, that is, give
Group's target tracking algorism of random matrix.The thought of similar ellipse fitting method, the algorithm of random matrix is also by group's target
It is considered as an entirety, and is gone to describe its profile information with ellipse.And unlike ellipse fitting algorithm, in random matrix algorithm
It is Wishart distribution by object queue state reasonable assumption, so that algorithm is dissolved into Bayes using the theory of random matrix
It is pushed under frame, final result is a large amount of quasi- without doing it is only necessary to give a forecast and update similar to Kalman filtering
It is total to calculate, to substantially reduce calculation amount and system complexity.Later, sensor error is considered random square again by the present invention
In battle array algorithm, amendment random matrix algorithm is described, the larger problem of former algorithm profile evaluated error is compensated for.Finally, this hair
It is bright to incorporate dynamic Multiple Models Algorithm in amendment random matrix algorithm, and repulsion model is added, place is optimized to the equation of motion
Reason, obtains new algorithm proposed by the present invention, i.e., based on the joint track algorithm of dynamic multi-model, repulsion model and random matrix.
The algorithm had both remained the advantage that random matrix algorithm model is simple, arithmetic speed is fast, had incorporated dynamic Multiple Models Algorithm to machine
The high sensitivity of tracking of maneuvering target, and repulsion model is introduced to the high-precision of group's target following, it is suitble in actual radar
It is used in system.
Group's target tracking algorism principle based on random matrix
Group's method for tracking target based on random matrix is proposed that his principle is divided into following several by Germany scientist Koch
A step:
(1) the target following Novel Modeling based on random matrix and bayesian theory
In tkIt moment, can be the motion state vector x of group targetkRepresent, the shape of target (being approximately oval) and it
Queue situation matrix XkIt represents.xkIn can indicate the speed, acceleration etc. of target, XkIn can indicate target size,
Semiaxis ratio and direction etc..
Define tkMoment measurement value sensor is Zk, then p (xk,Xk∣Zk) it can indicate that radar measured data is Zk's
When, dbjective state is [xk,Xk] probability.
Assuming that nkFor the quantity of measured value, thenIt can indicate in nkTo each target in a measured value
Measured valueSet, re-defineRepresenting includes tkAll measurement value sensors before moment.
It is prediction process first:
According to Bayes' theorem, it is clear that there is following formula establishment:
Whether to do is to can pass through belowTo predict [xk,Xk], there is following push over:
Furthermore it is filtering:
It is a filtering after prediction, substantially idea is as follows:
It is finally estimation procedure:
For tlMoment, (l > k)
(2) state renewal equation
By above-mentioned model, p (xk,Xk|Zk) given by formula (1-1), wherein several important probability density are as follows:
p(Zk,nk|xk,Xk)=p (Zk|nk,xk,Xk)p(nk|xk,Xk)
In the t at momentkKinestate vector xkIt is expressed from the next:
R is known as spatiality vector in formula, and vector length d, it describes the quene state situation of current goal.And r·
And r··Respectively indicate the velocity and acceleration of target.(acceleration is put aside in emulation)
(3) target following dynamic modeling
In Kalman filter, the motion state of target is modeled are as follows:
xk=Φk|k-1xk-1+vk
p(vk)=N (vk；o,Δk|k-1)
It is long-pending by matrix Φ using Kroneckerk|k-1It decomposes as follows:
Wherein
In subsequent proof, it will be found that can be allowed and be pushed over simply much using Kronecker product.
For dynamic noise covariance Δk|k-1, have
Wherein
(4) construction of prediction probability density
In terms of target state, it is assumed that the t of motion state density after the filteringk-1Moment Gaussian distributed, i.e.,
By model before, have:
According to Kronecker product, xk|k-1And Pk|k-1It can indicate are as follows:
Object queue state aspect, it is assumed that quene state density p (Xk-1|Zk-1) obey Wishart distribution:
In above-mentioned model, it is assumed that it is expected that density answers the equal expectation to previous filter step, then:
Xk|k-1=(υk|k-1- 2d-2)=Xk-1|k-1=(υk-1|k-1-2d-2)
Definition time interval is Δ tk=tk-tk-1, time attenuation constant is τ, and prediction can be written as with new equation
In order to tighter obtain mathematically accessible more new formula, it is assumed here that the transfering density of object queue state
p(Xk|Xk-1) Wishart distribution is obeyed, and assume that the desired value of transition density should be equal to Xk-1.It is related to description rotation, expansion and receives
The more complicated summary of the state matrix of contracting rate is possible.Characterize the freedom degree δ of this Wishart distributionk|k-1, it is similar to
Noise statistics in usual Kalman filtering.Therefore, it can be concluded that
Wherein E [Xk|Xk-1]=Xk-1.It is obvious that the precision of quene state prediction is spaced t with updatek-tk-1Increase and
Reduce.Using the attenuation constant τ of the time model parameter additional as one, conclusion below can be obtained:
The formula is using the amount δ and τ that two queue extensions are developed out as parameter.It, can using the evolutionary model of the object extension
To calculate predicted density p (Xk|Zk-1).According to Bayesian frame and inverse Wishart distribution, predicted density p (Xk|Zk-1) can be under
Formula statement:
By match by moment, the inverse Vichy spy that this predicted density can be estimated with equating expections and same scalar covariance is close
Degree carrys out approximate representation.By this approximation, the class of used density is retained in iteration renewal process, then in above-mentioned equation
Parameter can be expressed asPredicted density can be by following
Estimation:
However, obtainedMore new formula seem intuitively to explain.Furthermore in this theoretical frame
Under frame, the transition density p (X of quene state matrixk|Xk-1) the characteristics of be only single scalar parameter.Therefore, not phase
Hope this method that there is bigger predictive ability than pervious heuristic.The present invention recalls discussed above: according to previous
A word, compared with the gain in filter step, the predicted portions during tracking be in any case it is unessential, than
As if it is considered that having the extension target or group's target of sufficient amount sensor measurement, then the predicted portions for tracking process do not weigh
It wants.
(5) bottom sensor model
In the case where observed object is extension or group's target, the importance individually measured extends feelings by following target
Condition (quene state situation) is dominated.Given scattering center, the bigger measurement error of sensor accuracy is smaller, the actual arrays of object
The bigger measurement error of range is bigger.Therefore, single measurement must be construed to the measurement of the mass center to extension or group's target, because
It is not important for target following task for extending for it, and these different scattering centers are actually to have shadow to measured value
Loud.Therefore, each individual measurement that target generates will be extended and is construed to the measurement to object mass center, corresponding " measurement
Error " and the object queue state X to be estimatedkIt is directly proportional.However, by the measurement error, object queue queue XkBy explicitly
Become likelihood function p (Zk,nk|xk,Xk) a part, which depict the amount Z of measurementk.As this explanation as a result, can be with
By estimating object queue state X using sensing datak(in addition to kinestate vector xk)。
Establish measurement model are as follows:
For the k moment to j-th of target measure as a result, H be measure transfer matrix,It is the k moment to jth
A target measures existing sensor error.Range and the scene of azimuthal measurement are that can obtain after being converted into cartesian coordinate
?.According to before the considerations of corresponding measurement error and covariance matrix estimate quene state Xk。
(6) likelihood function
Note center measured value zkCollision matrix corresponding with its is Zk, have:
Method in order to use random matrix in Bayesian frame needs to define the likelihood function decomposited.For letter
For the sake of list, the case where excluding false or unnecessary measurement.Under approximation, it is assumed that the measured value n in ZkWith state variable XkNothing
It closes, that is, say present invention assumes that p (nk|xk,Xk) when it is constant so that
Wherein there is following approximation relation to set up:
(7) filtering frame
For motion state part, filter frame is as follows:
Wherein, newly breath matrix S and gain matrix K is defined as follows:
For queue formation state, filter frame is as follows:
First factor on right side is independent of motion state variable x in likelihood function formulak, can rewrite are as follows:
The factor due to above formula independent of state variable, this innovation matrix Nk|k-1It is defined as follows:
It is also contemplated that:
It is as follows to obtain simple more new formula:
Xk|k=Xk|k-1+Nk|k-1+Zk
υk|k=υk|k-1+nk
(8) sensor noise is corrected
Feldmann has incorporated the influence of sensor error on the basis of Koch algorithm, and derives under Bayes frame
Modified group's method for tracking target based on random matrix is gone out.Feldmann points out, sensor noiseIt can do and assume
Approximation is in normal distribution, variance zXk+ R, so that
Other than sensor error covariance matrix, Feldmann also adds a zoom factor z, makes target formation
It contributes bigger.The latter is mainly technical interest, enable the invention to explain assume formation contribution and may be practical
Hypothesis between difference.
New breath matrix S changes are as follows:
In the update of queue situation, formula amendment are as follows:
xk|k=xk|k-1+Kk|k-1(zk-Hxk|k-1)
αk|k=αk|k-1+nk
Predictor formula amendment are as follows:
xk|k-1=Fk|k-1xk-1|k-1
Xk|k-1=Xk-1|k-1
αk|k-1=2+exp (- T/ τ) (αk-1|k-1-2)
Zk|k-1=zXk|k-1+R
Group's method for tracking target based on repulsion Modifying model random matrix algorithm the following steps are included:
Step 1: the space repulsion model and proper subspace repulsion model when the movement of group's target are established；
Establish the space repulsion model when movement of group's target are as follows:
Wherein θt-1For the orientation angles measured value of t-1 moment target, θtFor t moment angle measurement, FNFor N number of target
Transfer matrix is moved, subscript N is the target number in group, RNFor repulsion matrix, HR,t-1For the repulsion vector at t-1 moment,
QNFor noise covariance, p (θt|θt-1) it is conditional probability of the t moment angle measurement at the t-1 moment,For Gaussian Profile；H
Lower footnote R be in following model measure transfer matrix distinguish and add, represent the H in repulsion model.
Establish the detailed process of proper subspace repulsion model are as follows:
Proper subspace repulsion model is established by estimating that the angle difference Δ θ of angle and pre-estimation is determined after iteration；
Other than the repulsion described in the above-mentioned modeling, in radar spatial spectral estimation algorithm, when non-on two target angles
Very close to when, the spectral peak that spatial spectrum algorithm obtains often has overlapping situation, this be as caused by algorithm precision itself, therefore calculate
The repulsion on a kind of spatial spectrum is implied in method to offset the mistake of this overlapping initiation, so that the target angle interval of estimation
It is wider than actual angle interval.In this case, angle dimension can be carried out to signal first with basic spatial spectrum algorithm
Pre-estimation, then single direction signal is reconstructed, iteration signal amplitude is simultaneously subtracted each other with original signal, calculate spatial spectrum simultaneously look for
To the peak value of magnitude in an iterative process is detected, estimation angle corresponding to peak value is the angle estimation for subtracting other signals and obtaining
Value, therefore the overlapping influence of spectral peak is reduced, so that angle estimation interval reduces, angle estimation is more accurate, and estimates after iteration
The repulsion that meter angle and the angle difference Δ θ of pre-estimation are used to describe to need to introduce in spatial spectrum algorithm, the present invention are referred to as
It is characterized subspace repulsion.It is worth noting that, the space repulsion of the foregoing description allow for mutually collided between avoiding target and
Definition, therefore inversely with the differential seat angle of two targets；And the proper subspace repulsion proposed here is by spatial spectrum
It is proportional with the difference at estimation angle and pre-estimation angle after iteration caused by angle estimation algorithm itself.
Step 2: space repulsion model and proper subspace repulsion when group's target that step 1 is established moves are converted
To under rectangular coordinate system；
Step 3: the proper subspace repulsion Modifying model radar measurement value being transformed into step 2 under rectangular coordinate system,
And the equation of motion and correction amount of the space repulsion Modifying model random matrix algorithm under rectangular coordinate system are transformed into step 2
Survey the Predicting Performance Characteristics covariance of equation.
The present invention mainly introduces the dynamic change and ruler of a kind of group target that the tracking based on stochastic matrix models is complicated
Very little method.This method is a kind of estimation method of approximate bayesian theory, it joins target state and formation state
It closes, can not only track the speed, acceleration, distance, direction of target, additionally it is possible to size, the shape situation of monitoring group target.And
And the present invention is easy to consider the noise factor in reality in this method, and reduces influence of the noise to measurement result.Together
When, the present invention will also use Interactive Multiple-Model tracking filter algorithm and improve to stochastic matrix models, so that former algorithm
It is more accurate when tracking dynamic object.
Specific embodiment 2: the present embodiment is different from the first embodiment in that: group is established in the step 1
The detailed process of repulsion model when group target movement are as follows:
It is pointed out in high-energy physics, if two protons or neutron will be deposited between the two protons at a distance of too closely
In a kind of strong interaction, this power is a kind of short-range contingence, and has symmetry.For group's target, between target such as
If fruit is closer, in order to avoid mutually colliding between target, each objective monomer all can automatically be generated peripheral object
One repulsive interaction, therefore this repulsion model can be introduced in group's target following, and this repulsion is referred to as space repulsion.
The stochastic differential equation for describing the repulsion that one group acts on group's target is written as:
θt,iIt is the azimuth of i-th of target of t moment,It is θt,iCorresponding angular speed, BtIndicate Blang's fortune of a d dimension
It is dynamic, in all targets, it is the same；Wt,iIndicate the d dimension Brownian movement that i-th of target carries out, it is assumed that in group
Each target i is independently generated.So BtIt is the modeling of the randomness in group movement for group entirety, and Wt,iIt is pair
The modeling of the randomness of each target individual in group.α, β and γ are the restoring force factors, indicate that dbjective state is returned to class mean
Restoring force intensity.It is to inhibit item, prevents angular speed from rising to very high values at any time.Function f (θt) andIt is state
Function is relied on, is discussed below, θt=[θt,1,...,θt,N] andRespectively indicate N number of target of a certain specific group
Azimuth set and angular speed set；
In the simplest case, f (θt) andIt is the mean value at the azimuth of N number of target and angular speed in group, point
Not are as follows:
WhereinFor θtFirst derivative, θt,iFor i-th of target t moment angle measurement,For θt,iSingle order lead
Number；
All space repulsion summation r for acting on target i in pairsi(θt) expression are as follows:
Wherein θt,kFor k-th of target t moment angle measurement, r (θt,i,θt,k) it is i-th of target and k-th of target
Active force；
For the target that shape in two planes is more regular, the stress point of the target of the regular shape is considered as center
Point, the direction of the mutually exclusive power of two more regular targets of shape obviously should be the lines along two mid-points
's.This space repulsion is defined as r (θ by the present inventiont,1,θt,2)；
dt,1,2=θt,2-θt,1
dt,1,2Representative is the distance between two targets (can be in angle, be also possible on coordinate), ft,1,2Generation
The table space repulsion factor；R1And R2It is control ft,1,2The magnitude control parameter of magnitude, the parameter have different radar systems
Institute is different, needs to measure in the actual environment.The targets very close for two, the active force between them in reality not
It may be infinitely great, therefore R1And R2Effect be exactly that the size of the power in the case of this kind is limited in R1/R2, so that system
Stablize, high forces cause target to be rapidly separated and indeterminable situation when avoiding target too close.
Obviously it can be seen that r (θt,1,θt,2) it is nonlinear, therefore want to obtain numerical solution and be difficult.For simplification
The problem of stochastic differential equation solves, the present invention select fixed using the size of repulsive force as one between time t and t+ τ
Controllable constantIt is modeled, constant space repulsionIt is to be calculated based on the status architecture in time t, such as it can be with
Are as follows:
τ is any time with the same magnitude of radar scanning time interval；
If enabledThen the linear random differential equation of joint objective state equation simplifies
Are as follows:
dθt=A θtdt+HRdt+DdMt
Wherein repulsion vector
Repulsion matrix A is defined as:
MtIt is for description covarianceBrownian movement, A1And A2For intermediate variable, intermediary matrix
Above-mentioned stochastic differential equation is solved, is obtained:
Using Eigenvalues Decomposition method, matrix is calculatedValue；T moment angle measurement
Conditional probability approximation of the value at the t-1 moment is considered as normal distribution:
p(θt|θt-1)=N (FNθt-1+RNHR,QN)。
The calculating of model of the present invention is very simple and effective, this is because for there is the feelings of N number of target in a group
Condition, it is thus only necessary to calculate a RN, and repulsion vector can be according to the state θ of previous momentt-1It calculates, so operand is very
It is small.
Other steps and parameter are same as the specific embodiment one.
Specific embodiment 3: the present embodiment is different from the first and the second embodiment in that: it will in the step 2
Space repulsion model and proper subspace repulsion when group's target movement that step 1 is established are transformed under rectangular coordinate system
Detailed process are as follows:
What general spatial spectrum algorithm obtained is the angle of target echo signal, and passes through the equidistant calculation of maximum-signal method
Method, it can be deduced that target is at a distance from radar, therefore basic radar system is all built upon under polar coordinate system.However, being
Beneficial to target following and facilitate display, need for system polar coordinates to be transformed under rectangular co-ordinate, therefore the space reprimand in angle
Power is also required to be converted to the space repulsion under rectangular co-ordinate.
Space repulsion to the definition of space repulsion in angle in similar step 1, under rectangular co-ordinate is defined as:
If the state matrix for defining two targets isDirectly
Corresponding repulsion vector correction is under angular coordinate
Wherein dt,1,2For the space length under 2 rectangular coordinate system of t moment target 1 and target, xt,1It is sat for target 1 at right angle
Mark is the coordinate of lower x-axis, yt,1For the coordinate of the y-axis under rectangular coordinate system of target 1, xt,2For target 2 under rectangular coordinate system x-axis
Coordinate, yt,2For the coordinate of the y-axis under rectangular coordinate system of target 2, ft,1,2For under 2 rectangular coordinate system of t moment target 1 and target
The size of space repulsion, r (st,1,st,1) it is 2 rectangular coordinate system down space repulsion of t moment target 1 and target,For t moment mesh
The component of x-axis under mark 1 and 2 rectangular coordinate system of target,For point for y-axis under 2 rectangular coordinate system of t moment target 1 and target
Power；
For proper subspace repulsion, it is assumed that the pre-estimation angle of single target is θ；Angle and pre-estimation are estimated after iteration
The difference of angle is Δ θ, the positive and negative plus-minus amendment represented to θ of Δ θ；As shown in Figure 1, according to geometrical relationship, for right angle
The target of coordinate system first quartile has following relationship to set up:
Wherein RsFor the target range that observation point measures, Δ x is the correction amount on abscissa, and Δ y is on ordinate
Correction amount.
Other steps and parameter are the same as one or two specific embodiments.
Specific embodiment 4: unlike one of present embodiment and specific embodiment one to three: the step 3
The detailed process of middle amendment radar measurement value are as follows:
If the measuring value of radar at a certain moment is [(θ1,Rs,1),(θ2,Rs,2),...,(θi,Rs,i),...,(θN,Rs,N)],
Wherein (θi,Rs,i) respectively indicate the distance of the pre-estimation angle and observation point of i-th of measurement target to the target, N expression measurement
The number of target；To the loop iteration processing in all target carry out amplitudes, angle and pre-estimation are estimated after obtaining N number of iteration
Difference [the Δ θ of angle1,Δθ2,...,Δθi,...,ΔθN], which is the proper subspace that all targets need to introduce
Repulsion；Using transformational relation of the proper subspace repulsion under polar coordinates and rectangular co-ordinate, the coordinate measure at the moment is carried out
Amendment, result is after amendment
[(x1+Δx1,y1+Δy1),(x2+Δx2,y2+Δy2),...,(xN+ΔxN,yN+ΔyN)]；
It corresponds in the formula of random matrix, it may be assumed that
Wherein zkFor center measured value, nkTo measure target numbers,The measuring value of target is measured for j-th of the k moment,To measure the correction value on coordinates of targets to j-th of the k moment.
Other steps and parameter are identical as one of specific embodiment one to three.
Specific embodiment 5: unlike one of present embodiment and specific embodiment one to four: the step 3
The detailed process of the Predicting Performance Characteristics covariance of the equation of motion and amendment measurement equation of middle amendment random matrix algorithm are as follows:
Initially set up the motion state equation of target's center of group are as follows:
xt=Φt|t-1xt-1+vt
p(vt)=N (vt；o,Qt|t-1)
Wherein, xtFor the motion state of t moment target's center, vtIndicate the noise in state equation, it is assumed that for Gauss point
Cloth, Qt|t-1For t-1 to the noise covariance of t moment state equation；
It is long-pending by intermediary matrix Φ using Kroneckert|t-1It decomposes as follows
Ft|t-1For the movement transfer matrix of t-1 to t moment, IdFor the unit matrix of d dimension, d xtVector length；
Because being to carry out tracking filter to the motion state at group center, so the present invention needs in random matrix algorithm
Consider that each target influences the repulsion of central point in group, that is, after calculating N group repulsion (N group target generates N group repulsion),
Calculating N group repulsion influences the resultant force at center, specific formula are as follows:
After space repulsion model is introduced random matrix algorithm, the equation of motion of random matrix algorithm is corrected are as follows:
p(vt)=N (vt；o,Qt|t-1)
For measurement equation, there is no consideration sensor errors in basic random matrix track algorithm, present invention assumes that
Sensor error is in normal distribution, and Predicting Performance Characteristics covariance isWherein z is scaling
The factor, XtFor the quene state of group's target, R is sensor self-noise covariance；
After amendment in the prediction steps of random matrix track algorithm, predictor formula amendment are as follows:
Xt|t-1=Xt-1|t-1
αt|t-1=2+exp (- T/ ζ) (αt-1|t-1-2)
Wherein xt-1|t-1For the estimated value of t-1 moment dbjective state, xt|t-1To utilize t-1 moment estimated value to t moment mesh
The predicted value of mark state, Pt-1|t-1For the covariance of t-1 moment dbjective state, Pt|t-1To utilize t-1 moment estimated value to t moment
The predicted value of dbjective state state covariance, Xt-1|t-1For the estimated value of t-1 moment quene state, Xt|t-1To utilize the t-1 moment
Predicted value of the estimated value to t moment quene state；ζ is attenuation constant, and T is radar surveying time interval, αt-1|t-1For the t-1 moment
The freedom degree of Wishart distribution, αt|t-1For the predicted value using t-1 moment estimated value to t moment Wishart distribution freedom degree.
Other steps and parameter are identical as one of specific embodiment one to four.
Embodiment one:
It is as follows to establish scene: in the scene of 30 × 30km, 5 group's targets form a team to move in a manner of such as Fig. 2, mesh
Mark minimum spacing is 850m, and 10s is divided between measurement, and pendulous frequency is 130 times.Sensor noise diag (20 is added2,102), it obtains
As shown in Figure 3 (putting aside sensor Resolution herein, can be differentiated by sensor depending on all targets) to result.
Using the scene as Fig. 2, it is real that tracking emulation is carried out to group's target used here as amendment random matrix algorithm
It surveys, three kinds of motion models is set, and being respectively as follows: model 1 has lower sensor noise and lower formation sensitivity, and model 2 has
Higher biography original text device noise and higher formation sensitivity, model 3 have moderate sensor noise and moderate queue sensitivity,
It obtains based on dynamic multi-model, the track algorithm of repulsion model and random matrix and the multi-mode tracking that repulsion model is not added
Arithmetic result is as shown in figure 4, amplification result is as shown in Figure 5.In emulation, the probability distribution of each model at various moments such as Fig. 6
Shown, the estimation of proper subspace repulsion order of magnitude is as shown in fig. 7, quene state mean square error estimation such as Fig. 8 in angle
Shown, center mean square error is as shown in Figure 9.As it can be seen that unified algorithm proposed by the present invention compares in the state estimation of queue
Essentially random matrix algorithm is accurately very much, and sensitiveer than correcting random matrix algorithm when handling formation mutation, together
When, repulsion model not only has modified measured value, the case where even more optimizing measurement point close proximity and bad prediction, is more suitable
It is used in actual scene.(drawing for convenience, every three time intervals draw primary result).
Algorithm effect comparison
Using the scene as Fig. 2, simulation comparisons are carried out to three kinds of algorithms, model and algorithm parameter all be previously mentioned
It is identical, obtain that the results are shown in Figure 10.In three kinds of method emulation, the mean square error of target formation state can use following formula meter
It calculates.
Obtained result is as shown in figure 11.Center mean square error is as shown in figure 12.
By simulation result as it can be seen that essentially random matrix algorithm has preferable sensitivity to formation mutation, but in formation shape
Profile is larger in the estimation of state, fails to reflect truth.Modified random matrix algorithm estimates that upper precision is higher in formation, wheel
Exterior feature tallies with the actual situation, but is that there are insensibilityes in formation mutation.And it joined repulsion model and Interactive Multiple-Model is random
Matrix algorithm can not only drip estimation formation state very well, and formation has preferable sensitivity when being mutated, and does not add reprimand than common
The multi-model random matrix algorithm of power model has more accurate estimation in queue estimation and center estimation.Pass through meter
The RMSE value of calculation, more it can be seen that advantage of the unified algorithm in quene state estimation.
Algorithm simulating compares under practical radar scene
Radar range resolution is set as 400m, angular resolution is 0.35 degree, and radar fix is located at (0,0) in Figure 14
Point.Using radar baseband signal model and MUSIC algorithm, the target under Fig. 2 scene can be substantially distinguished, the group in similar Fig. 2
Group movement, carries out the emulation of radar actual measurement, and obtained true measurement scene is as shown in figure 13.Under the scene, algorithm is imitated
It very will more tally with the actual situation, the result obtained is also more convincing.Therefore, above-mentioned four kinds of algorithms are repeated, in actual scene
Under to obtain tracking effect as shown in figure 14.The mean square error of target formation state is as shown in figure 15.Target's center of group position
Mean square error is as shown in figure 16.Simulation result and the simulation result under virtual scene before are essentially identical under actual scene, still
It is used it is concluded that unified algorithm is more in line in real system.But as seen from Figure 13, the measurement of practical radar
The case where being in the presence of target in group can not be differentiated, and this Resolution has biggish shadow to the algorithm based on random matrix
It rings, therefore influence of the low radar resolution situation to algorithm will be a kind of following challenge to the serial algorithm.
Pass through and carry out four kinds of emulation based on random matrix algorithm, it was demonstrated that unified algorithm proposed by the invention regardless of
Sensitivity still has in estimated accuracy and has biggish advantage than other three kinds of algorithms, is to have drawn other algorithms respectively
Advantage to solving their own disadvantage, be well suited for using in actual radar system.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications all should belong to
The protection scope of the appended claims of the present invention.
Claims (5)
1. a kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm, it is characterised in that: described to be based on
Group's method for tracking target of repulsion Modifying model random matrix algorithm the following steps are included:
Step 1: the space repulsion model and proper subspace repulsion model when the movement of group's target are established；
Establish the space repulsion model when movement of group's target are as follows:
Wherein θt-1For the orientation angles measured value of t-1 moment target, θtFor t moment angle measurement, FNFor the movement of N number of target
Transfer matrix, subscript N are the target number in group, RNFor repulsion matrix, HR,t-1For the repulsion vector at t-1 moment, QNFor
Noise covariance, p (θt|θt-1) it is conditional probability of the t moment angle measurement at the t-1 moment,For Gaussian Profile；
Establish the detailed process of proper subspace repulsion model are as follows:
The pre-estimation for carrying out angle dimension to signal first with basic spatial spectrum algorithm, then carries out weight for single direction signal
Structure, iteration signal amplitude are simultaneously subtracted each other with original signal, are calculated spatial spectrum and are found the peak value of detection magnitude in an iterative process, peak value
Corresponding estimation angle is the angle estimation value for subtracting other signals and obtaining, the differential seat angle of angle and pre-estimation is estimated after iteration
Value Δ θ is used to the repulsion for describing to need to introduce in spatial spectrum algorithm；
Step 2: space repulsion model and proper subspace repulsion model conversion when group's target that step 1 is established moves
To under rectangular coordinate system；
Step 3: the proper subspace repulsion Modifying model radar measurement value being transformed under rectangular coordinate system with step 2 is used in combination
Step 2 is transformed into the equation of motion and the amendment measurement side of the space repulsion Modifying model random matrix algorithm under rectangular coordinate system
The Predicting Performance Characteristics covariance of journey.
2. a kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm according to claim 1,
It is characterized in that: establishing the detailed process of the repulsion model when movement of group's target in the step 1 are as follows:
The stochastic differential equation for acting on the repulsion of group's target is written as:
θt,iIt is the azimuth of i-th of target of t moment,It is θt,iCorresponding angular speed, BtIndicate the Brownian movement of d dimension, Wt,iTable
Showing the d dimension Brownian movement that i-th of target carries out, α, β and γ are the restoring force factors,It is to inhibit item, function f (θt) and
It is State-dependence function, θt=[θt,1,...,θt,N] andRespectively indicate N number of target azimuth set and
Angular speed set；
f(θt) andIt is the mean value at the azimuth of N number of target and angular speed in group, is respectively as follows:
WhereinFor θtFirst derivative, θt,iFor i-th of target t moment angle measurement,For θt,iFirst derivative；
All space repulsion summation r for acting on target i in pairsi(θt) expression are as follows:
Wherein θt,kFor k-th of target t moment angle measurement, r (θt,i,θt,k) be i-th of target and k-th of target effect
Power；
For the target of regular shape in two planes, the stress point of the target of the regular shape is considered as central point, shape rule
The repulsion of two targets then is defined as r (θt,1,θt,2)；
dt,1,2=θt,2-θt,1
dt,1,2Representative is the distance between two targets, ft,1,2Represent the space repulsion factor；R1And R2It is control ft,1,2Magnitude
Magnitude control parameter；
Select between time t and t+ τ using the size of repulsive force asIt is modeled, constant space repulsionBe based on when
Between t status architecture calculate, are as follows:
τ is any time with the same magnitude of radar scanning time interval；
If enabledThen the linear random differential equation of joint objective state equation simplifies are as follows:
dθt=A θtdt+HRdt+DdMt
Wherein repulsion vector
Repulsion matrix A is defined as:
MtIt is for description covarianceBrownian movement, A1And A2For intermediate variable, intermediary matrix
Stochastic differential equation is solved, is obtained:
Using Eigenvalues Decomposition method, matrix is calculatedValue；T moment angle measurement exists
The conditional probability at t-1 moment is considered as normal distribution:
p(θt|θt-1)=N (FNθt-1+RNHR,QN)。
3. a kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm according to claim 1 or claim 2,
It is characterized by: space repulsion model and proper subspace when the group's target for establishing step 1 in the step 2 moves
Repulsion is transformed into the detailed process under rectangular coordinate system are as follows:
Space repulsion under rectangular co-ordinate is defined as:
If the state matrix for defining two targets isRight angle is sat
Corresponding repulsion vector correction is under mark
Wherein dt,1,2For the space length under 2 rectangular coordinate system of t moment target 1 and target, xt,1It is target 1 in rectangular coordinate system
The coordinate of lower x-axis, yt,1For the coordinate of the y-axis under rectangular coordinate system of target 1, xt,2For the seat of the x-axis under rectangular coordinate system of target 2
Mark, yt,2For the coordinate of the y-axis under rectangular coordinate system of target 2, ft,1,2For 2 rectangular coordinate system down space of t moment target 1 and target
The size of repulsion, r (st,1,st,1) it is 2 rectangular coordinate system down space repulsion of t moment target 1 and target,For t moment target 1
With the component of x-axis under 2 rectangular coordinate system of target,For the component for y-axis under 2 rectangular coordinate system of t moment target 1 and target；
For proper subspace repulsion, it is assumed that the pre-estimation angle of single target is θ；Angle and pre-estimation angle are estimated after iteration
Difference be Δ θ, the positive and negative of Δ θ represents to the amendment of the plus-minus of θ；According to geometrical relationship, for rectangular coordinate system first quartile
Target, there is following relationship to set up:
Wherein RsFor the target range that observation point measures, Δ x is the correction amount on abscissa, and Δ y is the amendment on ordinate
Amount.
4. a kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm according to claim 3,
It is characterized in that: correcting the detailed process of radar measurement value in the step 3 are as follows:
If the measuring value of radar at a certain moment is [(θ1,Rs,1),(θ2,Rs,2),...,(θi,Rs,i),...,(θN,Rs,N)], wherein
(θi,Rs,i) respectively indicate i-th of measurement target pre-estimation angle and observation point to the target distance, N indicate measurement go out
The number of target in group；To the loop iteration processing in all target carry out amplitudes, obtain after N number of iteration estimation angle and
Difference [the Δ θ of pre-estimation angle1,Δθ2,...,Δθi,...,ΔθN], which is the feature that all targets need to introduce
Subspace repulsion；Using transformational relation of the proper subspace repulsion under polar coordinates and rectangular co-ordinate, to the coordinate amount at the moment
Survey is modified, and result is after amendment
[(x1+Δx1,y1+Δy1),(x2+Δx2,y2+Δy2),...,(xN+ΔxN,yN+ΔyN)]；
It corresponds in the formula of random matrix, it may be assumed that
Wherein zkFor center measured value, nkTo measure target numbers,The measuring value of target is measured for j-th of the k moment,To measure the correction value on coordinates of targets to j-th of the k moment.
5. a kind of group's method for tracking target based on repulsion Modifying model random matrix algorithm according to claim 4,
It is characterized in that: correcting the equation of motion of random matrix algorithm and the Predicting Performance Characteristics covariance of amendment measurement equation in the step 3
Detailed process are as follows:
Initially set up the motion state equation of target's center of group are as follows:
xt=Φt|t-1xt-1+vt
p(vt)=N (vt；o,Qt|t-1)
Wherein, xtFor the motion state of t moment target's center, vtIndicate the noise in state equation, Qt|t-1For t-1 to t moment shape
The noise covariance of state equation；
It is long-pending by intermediary matrix Φ using Kroneckert|t-1It decomposes as follows
Ft|t-1For the movement transfer matrix of t-1 to t moment, IdFor the unit matrix of d dimension, d xtVector length；
After calculating N group repulsion, calculating N group repulsion influences the resultant force at center, specific formula are as follows:
After space repulsion model is introduced random matrix algorithm, the equation of motion of random matrix algorithm is corrected are as follows:
p(vt)=N (vt；o,Qt|t-1)
Assuming that sensor error is in normal distribution, Predicting Performance Characteristics covariance isWherein
Z is zoom factor, XtFor the quene state of group's target, R is sensor self-noise covariance；
After amendment in the prediction steps of random matrix track algorithm, predictor formula amendment are as follows:
Xt|t-1=Xt-1|t-1
αt|t-1=2+exp (- T/ ζ) (αt-1|t-1-2)
Wherein xt-1|t-1For the estimated value of t-1 moment dbjective state, xt|t-1To utilize t-1 moment estimated value to t moment target-like
The predicted value of state, Pt-1|t-1For the covariance of t-1 moment dbjective state, Pt|t-1To utilize t-1 moment estimated value to t moment target
The predicted value of status covariance, Xt-1|t-1For the estimated value of t-1 moment quene state, Xt|t-1To be estimated using the t-1 moment
It is worth the predicted value to t moment quene state；ζ is attenuation constant, and T is radar surveying time interval, αt-1|t-1For the moment Vichy t-1
The freedom degree of spy's distribution, αt|t-1For the predicted value using t-1 moment estimated value to t moment Wishart distribution freedom degree.
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