CN110488276A - The optimal resource allocation method based on demand of isomery radar fence towards multiple target tracking task - Google Patents
The optimal resource allocation method based on demand of isomery radar fence towards multiple target tracking task Download PDFInfo
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- 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
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Abstract
The present invention relates to a kind of optimal resource allocation method based on demand of the isomery radar fence towards multiple target tracking task, this method initially sets up asynchronous radar netting and target movement model, resource allocation problem is established as convex problem by the asynchronous measurement value set being then based in time of fusion interval, it is broken down into Q mutually independent convex subproblems, Q convex problem is solved using antithesis rise method and obtains the resource allocation optimal solution of Q target, and then obtains the resource allocation optimal solution for all targets；Using resource allocation optimal solution and radar to the asynchronous measurement value set of target, target extended mode is estimated using maximum likelihood method, and the filter value of target extended mode is finally obtained using the state as the input of Kalman filter.The embodiment of the present invention is suitable for the resource allocation under the conditions of limited emission resource budget, and less resource can reach identical tracking accuracy, under the premise of meeting multiple target tracking accuracy requirement, minimize transmission resources.
Description
Technical field
The invention belongs to Radar Signal Processing Technology fields, and in particular to a kind of isomery thunder towards multiple target tracking task
Up to the optimal resource allocation method based on demand of net.
Background technique
Isomery radar netting (the Heterogeneous Radar being made of different working modes, different type radar
Network, abbreviation HRN) it is becoming increasingly popular in the application of various military and civilians.With the list for being only capable of acquisition finite goal information
Base radar is different, and HRN can obtain the enough information of different target with different view；When these information effective integrations, HRN
Target positioning more better than monostatic radar and tracking performance may be implemented, therefore HRN is commonly used for defending the inspection of purpose multiple target
It surveys and tracks.In general, multiple target tracking (Multiple Target Tracking, abbreviation MTT) performance is moved depending on target
Really degree, radar surveying accuracy and radar spatial distribution of model etc..The validity of each radar surveying is directly believed with it
It makes an uproar more related than (signal-to-noise ratio, abbreviation SNR).Each radar in order to realize higher measurement SNR, in HRN
All targets should all be detected.
However the transmission resources of radar netting are often limited, and with a large amount of targets, track all fingers
Resource needed for determining SNR target can exceed that the available resource of every radar, therefore, how towards multiple target tracking task pair
Isomery radar fence carries out resource distribution according to need and has become the major issue studied at present.
Existing research provides the method for the resource allocation problem of target following in some processing radar nettings.But this
A little methods still need to improve there are many aspect: (1) existing most of researchs all use synchro measure model, and in practical application
In, due to initial time and sample rate difference, the target data of multiple radar advisories is usually asynchronous；It is asked to solve this
Topic, researcher develop a kind of asynchronous resource allocation (Heterogeneous resource for monotrack application
Allocation, abbreviation HRA) scheme, however, the HRA scheme establish mathematic optimal model be it is non-convex and nonlinear, only
It can obtain the result of suboptimum.(2) HRN is made of several radars with different working modes, has different resources, example
Such as, the transmission power of centralized MIMO radar is adjustable but total transmission power is limited, and the residence time of phased-array radar is adjustable but total
Residence time is limited；These different types of resource variables coupling in tracking performance metric function (Bayes carat Metro lower bound)
It closes；And most of existing researchs consider RA (resource allocation, resource allocation) model of homogeneity radar netting,
Wherein all radars are all with the operation of identical operating mode, therefore the RA model resource to be optimized of homogeneity radar netting belongs to together
One type, is not directly applicable HRN.
Summary of the invention
In order to solve the above-mentioned problems in the prior art, the present invention provides a kind of towards multiple target tracking task
The optimal resource allocation method based on demand of isomery radar fence.The technical problem to be solved in the present invention is achieved through the following technical solutions:
The embodiment of the invention provides a kind of optimal resource distributions according to need of isomery radar fence towards multiple target tracking task
Method, comprising steps of
S1, isomery radar netting is established, the isomery radar netting includesA radar station
With a fusion center, whereinIndicate the quantity of centralized MIMO radar,Indicate the number of phased-array radar
Amount,Indicate the quantity of mechanical scanning radar；There are Q target in the observation area of the isomery radar netting, Q be greater than
Zero positive integer；
It initializes the isomery radar netting: enabling tkIndicate tkA fusion moment, the initial value of k be 1, k ∈ 1,2 ...,
K }, tKFor the preset maximum fusion moment, K is the positive integer greater than 0, (tk, tk+1) indicate k-th of time of fusion interval；
S2, the target q for setting in the search coverage of the isomery radar netting make linear uniform motion, q ∈ 1,
2 ..., Q }, and t is established under conditions of the target q makees linear uniform motionkThe extended mode vector of moment target q
S3, according to the extended mode vectorAsynchronously using N number of radar station in the isomery radar netting
All asynchronous measurement values that the target q is observed, and N number of radar station in k-th of time of fusion interval is obtained
ZQ, kIt is sent to the fusion center；
S4, the fusion center are made with carats of Bayes beautiful sieve's lower bounds of the target q in k-th of time of fusion interval
For the metric function of target tracking accuracy, target tracking accuracy is calculated according to the metric function, makes the target following
Precision meets the target tracking accuracy achieved when radar resource gives the reference of Q target；Resource allocation is asked
Topic is converted to convex optimization problem, then by the convex optimization problem be decomposed into Q independently of each other about target q (q=1,2 ...,
Q convex problem), and the convex problem about target q (q=1,2 ..., Q) is solved using antithesis rise method, it obtains in kth
The resource allocation solution of target q described in a fusion moment (q=1,2 ..., Q), according to the money of the target q (q=1,2 ..., Q)
Source distribution solution obtains the resource allocation solution at k-th of fusion moment
S5, according to all asynchronous measurement Z of target q in isomery radar netting in k-th of time of fusion intervalQ, kWith it is described
The resource allocation solution at k-th of fusion momentTarget q is calculated in fusion moment t using maximum-likelihood criterionk+1Estimated valueWith the estimated valueCorresponding covariance matrix
S6, by the estimated valueAnd the covariance matrixInput as Kalman filter carries out
Filtering obtains target q in fusion moment tk+1State estimationAnd the state estimationCorresponding filtering
Covariance matrix
S7, it enables k=k+1, return step S2 be recycled, obtains the 1st time of fusion interval between k-th time of fusion
Every heterogeneous resource allocation resultAnd target q is in fusion moment t1To fusion moment tKState estimationAnd the state estimationCorresponding covariance matrix
Compared with prior art, beneficial effects of the present invention:
1, transmission resources assignment problem is established as by resource allocation method based on demand of the invention according to resource consumption rate minimum
Convex optimization problem solves resource allocation problem non-convex in conventional method and can only obtain the resource allocation result of suboptimum and asks
Topic, to obtain optimal resource allocation result.
2, HRA scheme is expressed as convex optimization problem under the premise of meeting multiple target tracking accuracy requirement by the present invention, into
And resource allocation optimal solution is obtained, it requires to not only meet performance of target tracking but also radar emission resource is greatly saved, make
Transmission resources are obtained to minimize.
The present invention is described in further details below with reference to accompanying drawings and embodiments.
Detailed description of the invention
Fig. 1 is that a kind of optimal resource of isomery radar fence towards multiple target tracking task provided in an embodiment of the present invention is on-demand
The flow diagram of distribution method；
Fig. 2 is the target trajectory schematic diagram in a kind of isomery radar fence search coverage provided in an embodiment of the present invention；
Fig. 3 is the asynchronous-sampling model of target q in k-th of fusion section；
Fig. 4 is Radar Cross Section of the radar 2 in Fig. 2 to target 1；
Fig. 5 is a kind of optimal resource distribution according to need of isomery radar fence towards multiple target tracking provided in an embodiment of the present invention
The resource-effective rate schematic diagram of method；
Fig. 6 is resource allocation result of the embodiment of the present invention to target q=1；
Fig. 7 is resource allocation result of the embodiment of the present invention to target q=2；
Fig. 8 is a kind of carats of tracking Bayes beautiful sieve's lower bounds of each target provided in an embodiment of the present invention.
Specific embodiment
Further detailed description is done to the present invention combined with specific embodiments below, but embodiments of the present invention are not limited to
This.
Embodiment one
The basic ideas of the embodiment of the present invention are as follows: initially set up asynchronous radar netting and target movement model, target movement
The asynchronous measurement of each target from multiple radars is combined into single duplex measurement by model and isomery radar netting, and will
Its input for being used as state estimation tracking filter.The distribution method of the embodiment of the present invention is suitable for limited emission resource budget item
Resource allocation under part, it is only necessary to which less resource can meet so that multiple targets reach identical tracking accuracy
Under the premise of multiple target tracking accuracy requirement, minimize transmission resources.
Referring to Figure 1, Fig. 1 be a kind of isomery radar fence towards multiple target tracking task provided in an embodiment of the present invention most
The flow diagram of excellent resource allocation method based on demand, the distribution method the following steps are included:
S1, isomery radar netting is established, which includesA radar station and
One fusion center, whereinIndicate the quantity of centralized MIMO radar (C-MIMO-R),Indicate phased array
The quantity of radar (PAR),Indicate the quantity of mechanical scanning radar (MSR).There are Q in the observation area of isomery radar netting
A target, Q are the positive integer greater than zero.
Initialization isomery radar netting: t is enabledkIndicate tkMoment, the initial value of k are 1, k ∈ { 1,2 ..., K }, tKIt is pre-
If the maximum fusion moment, K is the positive integer greater than 0, (tk, tk+1) indicate k-th of time of fusion interval.
Specifically, the position of radar 1 is set, and using 1 due east direction 70km of radar, due south direction 0.5km as origin O,
It is that X-axis establishes plane right-angle coordinate by Y-axis, due east direction of direct north.
Fig. 2 is referred to, Fig. 2 is that the target in a kind of isomery radar fence search coverage provided in an embodiment of the present invention moves rail
Mark schematic diagram.Isomery radar fence includes in Fig. 2A radar station and a fusion center, N,WithIt is the positive integer greater than 0；Wherein,Indicate centralized MIMO radar number,Indicate phase
Battle array radar number is controlled,Indicate mechanical scanning radar number；N value is 8 in the present embodiment,Value is 4,Value
It is 3,Value is 1；It sets there are Q target in the search coverage of N number of radar station, Q is the positive integer greater than zero, this implementation
Q value is 2 in example.Enable tkIndicate k-th of fusion moment, k indicates the index at fusion moment, the initial value of k for 1, k ∈ 1,
2 ..., K }, tKFor the preset maximum fusion moment, K is the positive integer greater than 0, and the present embodiment K is taken as 20；(tk, tk+1) table
Show k-th of time of fusion interval, T0=(tk, tk+1), the present embodiment T0=6s, tK=121s；
S2, the target q for setting in search coverage in isomery radar fence carry out linear uniform motion, q ∈ { 1,2 ..., Q }, and
It establishes under conditions of target q makees linear uniform motion in tkThe extended mode vector of moment target q
Target q is in fusion moment tkState are as follows:
In (1),WithRespectively indicate target position and speed.In the present embodiment, at the beginning of target 1
Beginning state are as follows:The original state of target 2 are as follows:
The motion model of target q can be write as:
Wherein fq() is the transition function of target q, be can simplify in this example are as follows:
Wherein, I2Indicate 2 dimension unit matrixs,Indicate direct product operation, T0Indicate time of fusion interval, the present embodiment T0=
6s；In (3),It indicates process noise, and is assumed to that there is known covariance matrixZero-mean gaussian.
The covariance matrixIt can simplify are as follows:
Wherein rqIndicate process noise intensity.
The Radar Cross Section metastasis model of target q are as follows:
Indicate target q in fusion moment tkWhite Gaussian noise, covarianceEqual to target q at the fusion moment
tkProcess noise covarianceExpression channel status vector (It indicates in fusion moment tkRadar Cross Section of the radar i to target q
Real and imaginary parts, subscript T indicate transposition).In the present embodiment, target 1 is in fusion moment t1Initial channel state vector set
It is set toTarget 2 is in fusion moment t1Initial channel state vector be set asBy target q in fusion moment tkStateWith channel status vectorMerge, is q-th
Target forms an extended mode vector, is defined asState transfer equation be:
Wherein,It is integral transition function, γq(T0) indicate target q in fusion moment tkExpansion process make an uproar
Sound obeys zero-mean, covarianceGaussian Profile.Wherein,Indicate target q in fusion moment tkMotion process noise covariance,Indicate target q at the fusion moment
tkChannel noise covariance.
S3, according to the extended mode vectorAsynchronously target q is carried out using N number of radar station in isomery radar fence
Observation, and all asynchronous measurement value Z that N number of radar station in k-th of time of fusion interval is obtainedQ, kIt is sent to fusion center；
Fig. 3 is referred to, Fig. 3 is the asynchronous-sampling model of target q in k-th of fusion section.MI, q, kIt is between k-th of fusion
Every (tk, tk+1) during the pendulous frequency that is acquired from target q of radar i,Radar i is expressed as in tI, q, k(m) provided when
M measurement,It is indicated using measurement functions are as follows:
Wherein,It is target q in sampling instant tI, q, k(m) extended mode, h () are measurement functions:
In (8),Indicate radar i in k-th of time of fusion interval to m-th of distance measure of target q,
Indicate radar i in k-th of time of fusion interval to the m azimuth determination value of target q,It indicates in sampling instant
tI, q, k(m) Radar Cross Section measured value of the radar i to target q；WithTarget q is respectively indicated to sample
Moment tI, q, k(m) component of the position in X-axis and Y direction；X (i) indicates the component of the position of radar i in the X-axis direction,
Y (i) indicates the component of the position of radar i in the Y-axis direction, and the position of the present embodiment radar, which refers to, is shown in Table 1；arctan(·)
Indicate arc tangent operation,Indicate nxThe n-th of the null vector of+N-dimensionalx+ i elements are 1, and subscript T indicates transposition.
Table 1
| Radar | I=1 | I=2 | I=3 | I=4 | I=5 | I=6 | I=7 | I=8 |
| Position/km | (- 70,0.5) | (- 40, -30) | (- 40,30) | (40,30) | (70,0.5) | (40, -30) | (0,30) | (0, -30) |
In formula (7)Indicate that radar i is to the measurement Gauss of m-th of measured value of target q in k-th of time of fusion interval
White noise, covariance matrix are as follows:
Wherein,Indicate that radar i is to the covariance square of m-th of measurement noise of target q in k-th of time of fusion interval
Battle array,Indicate radar i in k-th of time of fusion interval to the measurement variance of m-th of distance measure of target q,
Indicate radar i in k-th of time of fusion interval to the measurement variance of m-th of azimuth determination value of target q,Table
Show that radar i is to m-th of RCS (Radar-Cross Section, the radar cross section of target q in k-th of time of fusion interval
Product) measured value measurement variance.
Wherein, ζiAnd BiThe transmitted signal bandwidth and 3dB for indicating radar i receive beam angle, in the present embodiment, ζi=
1MHz, Bi=1 °；PI, q, k(m) indicate that radar i provides the transmission power of the m times measurement of target q in k-th of time of fusion interval
Source, TI, q, k(m) the residence time resource that radar i measures the m time of target q in k-th of time of fusion interval is indicated,It indicates in sampling instant tI, q, k(m) Radar Cross Section measured value of the radar i to target q.In extraction formula (10)
Public keysIt can obtain:
Wherein, subscript -1 indicates inversion operation,Indicate that radar i is to the m of target q in k-th of time of fusion interval
The matrix of the rest parameter composition of secondary measurement.
The vector Z that all measured values of target q are constituted in k-th of time of fusion intervalQ, kIt indicates are as follows:
Wherein,Indicate m-th measured value of the radar i to target q, M in k-th of time of fusion intervalI, q, kIndicate the
Radar i enables M to the measured value total number of target q in k time of fusion intervalQ, kIndicate fusion center in k-th of time of fusion
All measured value total numbers received in interval,Wherein, N indicates the sum of radar station；Melt at k-th
It closes in time interval, radar will be sent to fusion center to all asynchronous measurement values of target, for more fresh target q in fusion
Carve tk+1State and corresponding estimate covariance.
S4, the fusion center are made with carats of Bayes beautiful sieve's lower bounds of the target q in k-th of time of fusion interval
For the metric function of target tracking accuracy, target tracking accuracy is calculated according to the metric function, makes the target following
Precision meets the target tracking accuracy achieved when radar resource gives the reference of Q target；Resource allocation is asked
Topic is converted to convex optimization problem, then by the convex optimization problem be decomposed into Q independently of each other about target q (q=1,2 ...,
Q convex problem), and the convex problem about target q (q=1,2 ..., Q) is solved using antithesis rise method, it obtains in kth
The resource allocation solution of target q described in a fusion moment (q=1,2 ..., Q), according to the money of the target q (q=1,2 ..., Q)
Source distribution solution obtains the resource allocation solution at k-th of fusion moment
The embodiment of the present invention minimizes general power and residence time resource, this can regard an optimization problem as.More mesh
Mark the model of the heterogeneous resource allocation methods of tracking performance driving are as follows:
Wherein, min indicates to minimize, and s.t. indicates constraint condition, sI, q, kIndicate radar i in k-th of time of fusion interval
To the energy of target q transmitting signal, sI, q, k=PI, q, kTI, q, k, wherein PI, q, kI pairs of radar is indicated in k-th of time of fusion interval
The transmission power of target q, TI, q, kIndicate that radar i is to the residence time of target q in k-th of time of fusion interval；Q indicates target
Sum；The present embodiment SymbolIndicating all, symbol ∈ expression belongs to,Indicate centralized MIMO radar set,Indicate phased-array radar set, skIndicate k-th of all thunder in time of fusion interval
The adjustable transmission parameter reached.skIt indicates are as follows:
Wherein,Indicate the number of centralized MIMO radar,Indicate the number of phased-array radar, on
Marking T indicates transposition, pkIndicate the transmission power vector in k-th of time of fusion interval, tkIt indicates in k-th of time of fusion interval
Residence time vector.
Wherein, PI, q, kIndicate transmission power of the radar i to target q, T in k-th of time of fusion intervalI, q, kIt indicates k-th
Residence time of the radar i to target q in time of fusion interval.
Wherein, PI, q, k(1) indicate radar i in k-th of time of fusion interval to the transmission power of the 1st of target q measurement,
PI, q, k(MI, q, k) indicate that radar i is to the M of target q in k-th of time of fusion intervalI, q, kThe transmission power of a measurement, MI, q, kTable
Show that radar i is to the overall measurement number of target q in k-th of time of fusion interval；TI, q, k(1) it indicates in k-th of time of fusion interval
Residence time of the radar i to the 1st measurement of target q, TI, q, k(MI, q, k) indicate that radar i is to mesh in k-th of time of fusion interval
Mark the M of qI, q, kThe residence time of a measurement；
Define the tracking performance that following equation describes q-th of target:
Mark is sought in Tr () expression,For BCRLB matrix, subscript T indicates transposition.
Wherein, Λ indicates normalized matrix:
Wherein, blkdiag () representing matrix block diagonalization operates, I2Indicate 2 dimension unit matrixs, I2NRepresentation dimension is 2N
Unit matrix,Representing matrix direct product, T0Indicate time of fusion interval.Carats of Bayes beautiful sieve (BCRLB) matrixes
WhereinIt is Bayesian Information matrix (BIM):
Since (17) limit the error variance of the unbiased esti-mator of dbjective state, it by with measure target tracking accuracy
Metric function.Specifically, in time index tkOne group of candidate target s of middle analysisk, and calculate target q's in each case
Estimated performance index
Wherein, mark is sought in Tr () expression, and the expression of subscript -1 is inverted.
B in formula (20)q(sk) indicate that the prediction Bayesian Information matrix of target q owns about in k-th of time of fusion interval
The adjustable transmission parameter s of radarkFunction approximation.
Wherein,Indicate target q in fusion moment tk+1Extended mode, PI, q, kIt indicates in k-th of time of fusion interval
Transmission power of the radar i to target q, TI, q, kIndicate radar i in k-th of time of fusion interval to the residence time of target q,
MI, q, kRadar i in k-th of time of fusion interval is indicated to the overall measurement number of target q, subscript -1 indicates inversion operation,
Indicate that radar i belongs to centralized MIMO radar,Indicate that radar i belongs to phased-array radar,When indicating k-th of fusion
Between be spaced in radar i to m-th of target q measurement aboutJacobian matrix approximation,Indicate k-th of fusion
Radar i is to the one-step prediction value of the extended mode of target q in time interval,Indicate radar i in k-th of time of fusion interval
To the approximation of the matrix of the rest parameter composition of the m times measurement of target q, JP() indicates that taking for prior information avenges information square
Battle array.
Wherein,Indicate the extended mode vector ξ of target q in fusion moment tkProcess noise covariance,It indicates
The extended mode vector of target q is in fusion moment tkTransfer matrix,Indicate target q in fusion moment tkState
Bayesian Information matrix, the expression of subscript -1 are inverted, subscript T expression transposition, in formula (10):
Wherein,Indicate that radar i belongs to centralized MIMO radar,It indicates in k-th of time of fusion interval
The matrix of the unrelated parameter composition of m-th measurement adjustable transmission resource parameters of the centralized MIMO radar i to target q,
Indicate that radar j belongs to phased-array radar,Indicate m of the phased-array radar j to target q in k-th of time of fusion interval
The matrix of the unrelated parameter composition of a measurement adjustable transmission resource parameters,Indicate that radar l belongs to mechanical scanning radar,Indicate m-th measurement adjustable transmission resource parameters of the mechanical scanning radar l to target q in k-th of time of fusion interval
The matrix of unrelated parameter composition.
By the transmission resources vector s in k-th of time of fusion intervalkIt is cut into Q non-overlapping block sQ, k, each piece of length
Degree isIndicate centralized MIMO radar number,Indicate phased-array radar number.
Wherein, sQ, kIndicate the transmission resources vector s in k-th of time of fusion intervalkQ-th of transmission resources vector, formula
It (13) can be with restatement are as follows:
In (25),The convex subproblem of different target q, available one group of mesh are solved respectively
Mark q=1, the resource allocation optimal solution of 2 ..., QWhen may then pass through the relationship provided in (25) and obtaining k-th of fusion
The resource allocation optimal solution at quarterThe definition provided from (25) can obtainIt is monotonic decreasing function.In addition,It is a convex function, therefore its first derivativeIt is a monotonically increasing function.
It utilizesWithMonotonicity, the Ka Lushiku provided in meeting formula (26)-(29)
While grace Plutarch (KKT) condition, an antithesis rise method is designed to find the resource allocation optimal solution of target q
(1) enable l=0, initialization stop parameter ε and
(each element is setTo ensureTherefore)。
(2) initial Lagrange's multiplier is setIt changes accordingly
Ride instead of walk rapid Δ α, whereinSymbol/expression point direction vector deviation.
(3) it in each iteration l, enablesAnd it is searched for by formula (28)
(4) l=l+1 is enabled, ifIt enablesIt turns to step (3), otherwise
Jump to step (5).
(5) if Δ α > ε, enables Δ α=Δ α/2 jump to step (3)；Otherwise α is enabledopt=αl,
S5, according to all asynchronous measurement Z of target q in isomery radar netting in k-th of time of fusion intervalQ, kWith it is described
The resource allocation solution at k-th of fusion momentTarget q is calculated in fusion moment t using maximum-likelihood criterionk+1Estimated valueWith the estimated valueCorresponding covariance matrix
The measured value of target q is independent from each other between different radars, therefore conditional probability density function:
Wherein, ZQ, kIndicate the vector that all measured values of target q in k-th of time of fusion interval are constituted,Indicate mesh
Q is marked in fusion moment tk+1Hybrid measurement estimated value,Indicate that the state of target q is being melted
Conjunction tk+1Estimated value,Indicate the Radar Cross Section of target q in fusion moment tk+1Estimated value；It indicatesZ under the conditions of knownQ, kConditional probability density function, subscript T indicate transposition, ∏ indicate
Quadrature operation,It indicatesObeying mean value isVariance is
Gaussian Profile,Indicate that radar i is to m-th of measured value of target q in k-th of time of fusion interval；It indicates
Sampling instant tI, q, k(m) extended mode of target q, h () indicate measurement functions,It indicates in k-th of time of fusion interval
Covariance matrix of the radar i to m-th of measurement noise of target q, maximal possibility estimation are as follows:
Wherein,It indicates to return to corresponding parameter x when f (x) obtains maximum value, ln () expression pair
Number function.It is asked by interative least square methodAfter iteration jValue are as follows:
Wherein,It indicates in fusion moment tk+1The estimated value of hybrid measurement value after target q iteration j,It indicates in fusion moment tk+1The measured value of hybrid measurement value after target q iteration j.
Wherein,Indicate radar i in sampling instant tI, q, k(m) to the measured value of target q, subscript T is indicated
Transposition；
By that can be predicted with minor function from t1, q, k(m) t is arrivedk+1Each measured value:
Wherein, tI, q, k(m) when indicating that radar i is to the sampling of m-th of measured value of target q in k-th of time of fusion interval
It carves, tk+1Indicate the fusion moment,Indicate sampling instant tI, q, k(m) the q extended mode of target.In formula (35), ∑Q, kTable
Show measuring assembly ZQ, kCorresponding noise covariance matrix:
Wherein, blkdiag () representing matrix block diagonalization,Indicate that radar i is to mesh in k-th of time of fusion interval
Mark the measurement noise covariance of m-th of measured value of q；The Jacobian matrix of iteration j can indicate are as follows:
Wherein,Indicate that radar i is to the Jacobi square of m-th of measured value of target q in k-th of time of fusion interval
Battle array.
Wherein,Indicate sampling instant tI, q, k(m) target q in extended mode,Expression is sampling
Moment tI, q, k(m) radar i is to the measurement functions of target q,Local derviation is sought in expression,It indicatesIt is rightLocal derviation is sought,Indicating willValue be assigned toFor mesh
Q is marked in fusion moment tk+1Hybrid measurement estimated value, corresponding estimate covariance can indicate with carat Metro lower boundZQ, kIndicate the vector that all measured values of target q in k-th of time of fusion interval are constituted,Indicate target q
In fusion moment tk+1Hybrid measurement value true value,It indicatesAbout ZQ, kTake snow information matrix.
Wherein, subscript N indicates the total number of radar, MI, q, kIndicate that radar i is to target q's in k-th of time of fusion interval
Overall measurement number, PI, q, kIndicate transmission power of the radar i to target q, T in k-th of time of fusion intervalI, q, kIt indicates to melt for k-th
Radar i is closed in time interval to the residence time of target q,Indicate that radar i is to target q's in k-th of time of fusion interval
The Jacobian matrix of m-th of measured value,Indicate the m times measurement of radar i in k-th of time of fusion interval to target q
The matrix of rest parameter composition, subscript -1 indicate that inversion operation, subscript T indicate transposition.
S6, by the estimated valueAnd the covariance matrixInput as Kalman filter carries out
Filtering obtains target q in fusion moment tk+1State estimationAnd the state estimationCorresponding filtering
Covariance matrix
Specifically, according to the maximum likelihood estimator of the extended mode of target qAnd its corresponding estimate covariance matrixAccording to the available target q of Kalman filtering in fusion moment tk+1State estimationAnd its it is corresponding
Covariance matrix
Wherein,Indicate target q extended mode from fusion moment tkTo fusion moment tk+1Predicted value,It indicates
The extended mode vector of target q is in fusion moment tkTransfer matrix,Indicate target q in fusion moment tkState estimation
Value,Indicate target q extended mode from fusion moment tkTo fusion moment tk+1Prediction covariance,
Indicate target q in fusion moment tkState estimation estimate covariance, subscript T indicate transposition.
Wherein,Indicate the extended mode of target q in fusion moment tk+1Information covariance,Indicate target q's
Extended mode is in fusion moment tk+1Kalman gain, ZQ, kIndicate all measured values of target q in k-th of time of fusion interval
The vector of composition,Indicate target q in fusion moment tk+1Hybrid measurement value true value,It indicatesAbout
ZQ, kTake snow information matrix.
S7, it enables k=k+1, return step S2 be recycled, obtains the 1st time of fusion interval between k-th time of fusion
Every heterogeneous resource allocation resultAnd target q is in fusion moment t1To fusion moment tKState estimationAnd the state estimation Corresponding covariance matrix
Transmission resources assignment problem is established as by the resource allocation method based on demand of the present embodiment according to resource consumption rate minimum
Convex optimization problem solves resource allocation problem non-convex in conventional method and can only obtain the resource allocation result of suboptimum and asks
Topic, to obtain optimal resource allocation result.
The present embodiment is expressed as convex optimization problem under the premise of meeting multiple target tracking accuracy requirement, by HRA scheme, into
And resource allocation optimal solution is obtained, it requires to not only meet performance of target tracking but also radar emission resource is greatly saved, make
Transmission resources are obtained to minimize.
Embodiment two
On the basis of example 1, the present embodiment makees further verifying explanation to effect of the present invention by emulation experiment.
(1) simulated conditions:
The simulated running system of the present embodiment be Intel (R) Core (TM) i5-4590CPU@3.30GHz, 64
Windows10 operating system, simulation software use MATLAB (R2016b).
(2) emulation content and interpretation of result:
Fig. 2 is referred to, radar total number is N=8 in isomery radar fence；Wherein, the number of centralized MIMO radar isCentralized MIMO radar is indicated with square；Phased-array radar number isIt uses the position of phased-array radar
Circle indicates；The number of mechanical scanning radar isMechanical scanning radar is indicated with triangle；The transmitting of i-th of radar
Signal effective bandwidth is ζi=1MHz, the 3dB beam angle of i-th of radar are Bi=1 °, the emission signal frequency of i-th of radar
For fi=(1+0.1i), i ∈ { 1,2 ..., N }；If i-th of radar is centralized MIMO radar, total transmission power resource
ForI-th of radar is phased-array radar, then its total residence time resource isRadial distance of the setting when i-th of radar and q-th of target in k-th of time of fusion intervalAnd in sampling instant tI, q, k(m) radar i is to the Radar Cross Section of target qWhen signal-to-noise ratio be 12dB；Being located at target number present in the search coverage of isomery radar fence is Q=2,
The initial position of target q=1 is (- 40,0) km, and initial velocity is (50,0) m/s；The initial position of target q=2 is (40,0)
Km, initial velocity are (- 50,0) m/s, it is assumed that target makees linear uniform motion；It is assumed that each centralization MIMO radar is using same
When multi-beam working method, therefore its correspond to different target sampling instant it is identical；Meanwhile each mechanical scanning radar is with solid
The fixed multiple targets of revolving speed Continuous irradiation, therefore it is also identical to the interval that revisits of multiple targets；On the contrary, phased-array radar
Due to the flexibility with wave beam, therefore it can illuminate multiple mesh in different initial times with different revisit time intervals
Mark；Table 2 illustrates the initial samples time of each radar and revisits interval corresponding to multiple targets.
Table 2
Fig. 4 is referred to, Fig. 4 is Radar Cross Section of the radar 2 in Fig. 2 to target 1；The radar of other all targets
Scattering resonance state parameter is set as 1, in this case, radar 2 and the constantly irradiation target 1, but their radar scattering of radar 5
Sectional area is different, therefore can analyze influence of the Radar Cross Section to resource allocation result of target.
In traditional heterogeneous network radar, resource allocation does not use any priori knowledge, the limited resources of each radar
It is uniformly allocated to multiple targets.In order to examine the optimal resource distribution according to need side of isomery radar fence towards multiple target tracking task
The optimality of method will meet the total resources consumption result and reference method of embodiment of the present invention when multiple target tracking BCRLB is required
Total resources consumption result be compared (reference method be each radar limited emission resource be uniformly allocated to multiple targets
The case where), and define a resource-effective rate parameter ρk:
Wherein,WithRespectively indicate the resource obtained from method designed by the embodiment of the present invention and reference method
Allocation result.
Fig. 5 is referred to, Fig. 5 is a kind of optimal money of isomery radar fence towards multiple target tracking provided in an embodiment of the present invention
The resource-effective rate schematic diagram of source allocation method based on demand, Fig. 5 show compared with reference method, and present invention method can be with
Save about 50% resource consumption.
Fig. 6 is referred to, Fig. 6 is resource allocation result of the embodiment of the present invention to target q=1；For specific objective, below
The radar of type is preferably: (1) being closer, the preferable radar of angular spread；(2) the relatively good thunder of propagation channel conditions
It reaches；(3) the lesser radar in interval is revisited.It can be to multiple target tracking precision property to these radars by a given resource allocation
Bigger raising is generated, in this case, only needs lesser resource consumption that can realize scheduled multiple target tracking precision
It is required that.For example, radar 2 and radar 5 have carried out system deployment to target 1, still, only radar 1 and radar 5 are designated tracking mesh
Mark 1, and radar 4 is not selected since its channel condition is unfavorable.Fig. 7 is similarly referred to, Fig. 7 is the embodiment of the present invention to target
The resource allocation result of q=2；Target 2 will not select radar 6, be spaced energy in each fusion because revisiting the lesser radar in interval
Enough generate more measured values.
Fig. 8 is referred to, Fig. 8 is under a kind of carats of tracking Bayes beautiful sieve of each target provided in an embodiment of the present invention
Boundary, tracking accuracy needed for Fig. 8 gives each target, and the corresponding tracking Bayes obtained using optimal HRA result
The beautiful sieve's lower bound of carat.In practical applications, different targets can generate different precision under index in different times, therefore
The dynamic accuracy requirement different to the two goal-settings.Due toIt is monotonic decreasing function, therefore works asWhen it is availableMinimum value.Simulation result also turns out, the embodiment of the present invention
The target following BCRLB realized can satisfy its required precision.
In conclusion the emulation experiment demonstrates the correctness of the embodiment of the present invention, validity and reliability.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, In
Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention
Protection scope.
Claims (1)
1. a kind of optimal resource allocation method based on demand of isomery radar fence towards multiple target tracking task, which is characterized in that including
Step:
S1, isomery radar netting is established, the isomery radar netting includesA radar station and one
A fusion center, whereinIndicate the quantity of centralized MIMO radar,Indicate the number of phased-array radar
Amount,Indicate the quantity of mechanical scanning radar；There are Q target in the observation area of the isomery radar netting, Q is big
In zero positive integer；
It initializes the isomery radar netting: enabling tkIndicate tkA fusion moment, the initial value of k are 1, k ∈ { 1,2 ..., K },
tKFor the preset maximum fusion moment, K is the positive integer greater than 0, (tk,tk+1) indicate k-th of time of fusion interval；
S2, the target q for setting in the search coverage of the isomery radar netting make linear uniform motion, q ∈ { 1,2 ..., Q },
And t is established under conditions of the target q makees linear uniform motionkThe extended mode vector of moment target q
S3, according to the extended mode vectorUsing N number of radar station in the isomery radar netting asynchronously to institute
All asynchronous measurement value Z for stating target q to be observed, and N number of radar station in k-th of time of fusion interval being obtainedq,kHair
It send to the fusion center；
S4, fusion center target q using in k-th of time of fusion interval the beautiful sieve's lower bounds of carats of Bayes as mesh
The metric function for marking tracking accuracy, is calculated target tracking accuracy according to the metric function, makes the target tracking accuracy
Meet the target tracking accuracy achieved when radar resource gives the reference of Q target；Resource allocation problem is turned
It is changed to convex optimization problem, the convex optimization problem is then decomposed into Q independently of each other about target q's (q=1,2 ..., Q)
Convex problem, and the convex problem about target q (q=1,2 ..., Q) is solved using antithesis rise method, it obtains melting at k-th
The resource allocation solution of target q described in the conjunction (q=1,2 ..., Q), according to the resource of the target q (q=1,2 ..., Q) point
The resource allocation solution at k-th of fusion moment is obtained with solution
S5, according to all asynchronous measurement Z of target q in isomery radar netting in k-th of time of fusion intervalq,kWith described k-th
Merge the resource allocation solution at momentTarget q is calculated in fusion moment t using maximum-likelihood criterionk+1Estimated value
With the estimated valueCorresponding covariance matrix
S6, by the estimated valueAnd the covariance matrixInput as Kalman filter is filtered
Wave obtains target q in fusion moment tk+1State estimationAnd the state estimationCorresponding filtering association
Variance matrix
S7, it enables k=k+1, return step S2 be recycled, obtains the 1st time of fusion interval to k-th time of fusion interval
Heterogeneous resource allocation resultAnd target q is in fusion moment t1To fusion moment tKState estimationAnd the state estimationCorresponding covariance matrix
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