CN108333583A - The resource allocation methods of biobjective scheduling are searched for and tracked based on phased-array radar - Google Patents
The resource allocation methods of biobjective scheduling are searched for and tracked based on phased-array radar Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
- G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
- G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
- G01S13/726—Multiple target tracking
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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Abstract
The invention discloses a kind of based on phased-array radar search and tracks the resource allocation methods of biobjective scheduling, belongs to Radar Technology field, main thought is：There are Q for the region of search of phased-array radar when setting kth sub-distributionkA target, and the region of search of phased-array radar is divided into N when kth sub-distributionkA nonoverlapping search sector；It is kth sub-distribution to enable k, and the initial value of 1≤k≤K, k be 1, K for the even number more than 0；Phased-array radar distributes to N during respectively obtaining the 1st sub-distribution1A optimum search time resource for not being overlapped search sectorPhased-array radar distributes to N during being distributed to kthKA optimum search time resource for not being overlapped search sectorAnd the 1st phased-array radar during sub-distribution distribute to Q1The tracking time resource column vector optimal solution of a targetPhased-array radar distributes to Q during being distributed to kthKThe tracking time resource column vector optimal solution of a targetAnd it is denoted as the resource allocation result that biobjective scheduling is searched for and tracked based on phased-array radar.
Description
Technical field
The invention belongs to Radar Technology fields, more particularly to a kind of phased-array radar that is based on to search for and track biobjective scheduling
Resource allocation methods, be suitable for finite time resource budget under the conditions of resource allocation, to the maximum extent improve phased array thunder
The tracking accuracy of the search capability and target that reach.
Background technology
Recently, the progress of technology makes quick, multitask phased array radar system exploitation be achieved；In general, phased array
Radar utilizes electronic control array antenna, therefore has high beam flexibility, and this characteristic enables phased-array radar to hold
Row multiple tasks；In fact, different radar functions may have system resource the demand vied each other, it is therefore desirable to according to thunder
The ability and their target reached distributes resource using automatic technology；For search lighting and tracking (SAT) application, if
One phased-array radar detects target using insufficient time resource, then multiple low detectable targets may still will not be by
It was found that；It at the same time, may production if a phased-array radar does not have time enough resource come the tracking target before illuminating
Raw discontinuous track.
Before this, the problem of many methods have been applied to resource allocation, either search function or tracing function
Or two function collective effects；For search lighting application, challenge is to expand radar surveillance region and raising target
Detection probability, while resource is used as few as possible；For target following, can seek by optimize tracking-again access interval,
Target Signal Strength and detection threshold value make total radar resource needed for tracking target minimize, and existing work, as SAT are answered
With the Resource Allocation Formula of design, it is broadly divided into two classes:It is rule-based and based on optimization；In rule-based scheme, root
According to some operation needs or radar signature, series of rules is formulated, these methods are although highly effective, in bayesian theory
In be not optimal, and be likely to occur uncertain behavior；Another method is by using single cost function
To calculate SAT tasks；Radar resource assignment problem can be formulated as a kind of mathematical optimization scheme, in general, cost function is
The weighted sum of Measure Indexes corresponding with search capability and tracking accuracy, for example, the probability of detection target, tracking Bayes gram
The ratio (SNR) of Latin America's sieve lower bound (BCRLB) and expected measuring signal and noise；But the shortcomings that these methods is to weight
The meaningless polymerization of selection and non-corresponding measurement.
Invention content
In view of the above-mentioned problems of the prior art, a kind of based on phased-array radar search it is an object of the invention to propose
With the resource allocation methods of tracking biobjective scheduling, this kind is searched for and is tracked the resource point of biobjective scheduling based on phased-array radar
Method of completing the square can solve it is budgetary in limited lighting hours, while to the maximum extent improve phased-array radar search capability and
The resource allocation of the tracking accuracy of target.
In view of the above-mentioned problems of the prior art, it is an object of the invention to the present invention by the resource allocation of SAT tasks
Conceptual design determines its famous Pareto subset (BK- at a Bi-objective constrained optimization problem, and using Pareto theory
PS).Resource Allocation Formula uses two cost functions：(i) just more search sector search minimum signal-to-noise ratio (are searched under worst case
Signal-to-noise ratio (WCS-SNR)) for, emphasize that target search ability maximizes；(ii) with regard to the tracking Bayes carat under worst case
For Metro lower bound (WCT-BCRLB), emphasize that multiple target tracking mean square deviation minimizes；It is more between the two targets in order to inquire into
Weigh again, needs the Pareto optimality disaggregation for finding out Bi-objective problem；However, for many Bi-objective problems, because solution is concentrated
There are many number of solution, therefore determine that entire Pareto optimality collection is practically impossible；Therefore, to a kind of reality of biobjective scheduling
It is to calculate BK-PS, and indicate Pareto optimality collection with BK-PS as much as possible with method, has this BK-PS, it will be able in SAT
A compromise appropriate is found between task, and correspondingly selects a Resource Allocation Formula, to meet specific application demand.
To reach above-mentioned technical purpose, the present invention is realised by adopting the following technical scheme.
A kind of resource allocation methods for being searched for and tracked biobjective scheduling based on phased-array radar, include the following steps：
Step 1, it initializes：It is kth sub-distribution to enable k, and the initial value of 1≤k≤K, k be 1, K for the even number more than 0；Setting
There are Q for the region of search of phased-array radar when kth sub-distributionkA target, and when kth sub-distribution phased-array radar the field of search
Domain is divided into NkA nonoverlapping search sector；
Step 2, phased-array radar searches for search model and the kth sub-distribution phase of sector at i-th when determining kth sub-distribution
Between q-th of target trace model；Wherein, 0≤q≤Qk, QkIndicate that the region of search of phased-array radar when kth sub-distribution exists
Target number；1≤i≤Nk, NkIndicate phased array search lighting sector total number when kth sub-distribution；
Step 3, the search model for searching for sector at i-th according to phased-array radar when kth sub-distribution obtains kth time point
The switch target letter of searching resource allocation plan during object function and kth sub-distribution with period searching resource allocation plan
Number；
Step 4, it according to the trace model of q-th of target during kth sub-distribution, determines and tracks resource during kth sub-distribution
The target criteria function of allocation plan；
Step 5, according to during the switch target function of searching resource allocation plan during kth sub-distribution and kth sub-distribution
The target criteria function for tracking Resource Allocation Formula obtains the mathematical optimization of Bi-objective Resource Allocation Formula during kth sub-distribution
Model；
Step 6, the mathematic optimal model for solving Bi-objective Resource Allocation Formula during kth sub-distribution, respectively obtains kth time
Phased-array radar distributes to N during distributionkA optimum search time resource for not being overlapped search sectorWith during kth sub-distribution
Phased-array radar distributes to QkThe tracking time resource column vector optimal solution of a target
Step 7, the value of k is enabled to add 1, return to step 2, phased-array radar distributes to N during obtaining the 1st sub-distribution1It is a
It is not overlapped the optimum search time resource of search sectorPhased-array radar distributes to N during being distributed to kthKA be not overlapped is searched
The optimum search time resource of rope sectorAnd the 1st phased-array radar during sub-distribution distribute to Q1When the tracking of a target
Between resource column vector optimal solutionPhased-array radar distributes to Q during being distributed to kthKThe tracking time resource of a target arrange to
Measure optimal solutionIt is denoted as the resource allocation result that biobjective scheduling is searched for and tracked based on phased-array radar.
Beneficial effects of the present invention：
First, the method for the present invention utilizes the unique texture of Bi-objective constrained optimization problem, can pass through Parallel implementation salient pole
Small very big optimization (CMO) problem obtains Pareto subset BK-PS；In previous research, to obtain Pareto subset BK-
PS, researcher develop many methods, such as weighted sum method, ant colony optimization algorithm and genetic algorithm；The method of the present invention passes through profit
With the unique texture of biobjective scheduling problem, a kind of parallel minimum scheme is developed to study Pareto subset BK-PS so that
The method of the present invention can have difference as a kind of alternative for obtaining BK-PS, different Pareto solutions by concurrently solving
Multiple Bi-objective problems of SAT demands obtain, and each complicated Bi-objective problem can be divided into two CMO problems, and one
A to be used for search mission, another is used for tracing task, the solution of corresponding searching resource distribution (S-RA) problem of different SAT demands
It is proportional.
Second, for different SAT parameters, minimum searching resource assignment problem only needs solution primary, due to target following
The object function of resource allocation is nonlinear, and therefore, the method for the present invention can be obtained by M+1 CMO problem of Parallel implementation
With the Pareto subset BK-PS that radix is M；The result shows that minimax search lighting resource allocation problem will generate one
Linear programming model, therefore easily solved by famous linear programming method；For target following resource allocation side
Case, the minimax problem generated are made of one group of separable monotone decreasing convex function, and minimax resolving Algorithm can be used
To solve the problems, such as T-RA.
Description of the drawings
Invention is further described in detail with reference to the accompanying drawings and detailed description.
Fig. 1 is a kind of resource allocation methods flow for being searched for and tracked biobjective scheduling based on phased-array radar of the present invention
Figure；
Fig. 2 is that the region of search of phased-array radar is quantified as not overlapping sector schematic diagram；
Fig. 3 is the target deployment schematic diagram within the scope of phased-array radar detections of radar；
Resource mean allocation scheme and the biobjective scheduling resource allocation based on Pareto during Fig. 4 (a) is the 5th distribution
The performance comparison schematic diagram of scheme；
Resource mean allocation scheme and the biobjective scheduling resource based on Pareto point during Fig. 4 (b) is the 15th sub-distribution
Performance comparison schematic diagram with scheme.
Specific implementation mode
Referring to Fig.1, it is a kind of resource allocation side for searching for and track biobjective scheduling based on phased-array radar of the present invention
Method flow chart；The wherein described resource allocation methods for searching for and tracking biobjective scheduling based on phased-array radar, including following step
Suddenly：
Step 1, it initializes：It is kth sub-distribution to enable k, and the initial value of 1≤k≤K, k be 1, K for the even number more than 0；Setting
There are Q for the region of search of phased-array radar when kth sub-distributionkA target, and when kth sub-distribution phased-array radar the field of search
Domain is divided into NkA nonoverlapping search sector.
Specifically, it is determined that phased-array radar, and using phased-array radar due south direction 93km, due west direction 45km as origin
O is that X-axis establishes plane right-angle coordinate by Y-axis, due east direction of direct north.
As shown in Fig. 2, it is kth sub-distribution to enable k, the initial value of 1≤k≤K, k be 1, K for the even number more than 0, the present embodiment
Middle K values are 20；There are Q for the region of search of phased-array radar when setting kth sub-distributionkA target, Q in the present embodimentkValue is
5；And the region of search of phased-array radar is divided into N when kth sub-distributionkA nonoverlapping search sectorBeforeThe region of search of phased-array radar is divided into respectively when sub-distributionIt is a nonoverlapping to search
Rope sector, afterThe region of search of phased-array radar is divided into respectively when sub-distributionA nonoverlapping search fan
Area；In the present embodiment
Step 2, phased-array radar searches for search model and the kth sub-distribution phase of sector at i-th when determining kth sub-distribution
Between q-th of target trace model；Wherein, 0≤q≤Qk, QkIndicate that the region of search of phased-array radar when kth sub-distribution exists
Target number；1≤i≤Nk, NkIndicate phased array search lighting sector total number when kth sub-distribution.
Specifically, in order to find the target not being detected, phased-array radar needs are distributed to its time resource not
Same search sector；And then it obtains phased-array radar when kth sub-distribution and searches for sector S at i-thi,kSearch model be：
Wherein, 1≤i≤Nk, α expression intermediate variables,TS,i,kIndicate phased-array radar point when kth sub-distribution
I-th of search sector S of dispensingi,kSearch time resource, SNRi,kIndicate that phased-array radar is searched at i-th when kth sub-distribution
Sector Si,kTarget search signal-to-noise ratio, PavIndicate the average emitted power of phased-array radar, Pav=300KW；AeIndicate setting
The effective receiving aperture of Phased Array Radar Antenna, Ae=10m；Indicate that phased-array radar searches for sector at i-th when kth sub-distribution
Si,kTarget scatter section area,kBIndicate Boltzmann constant, TeIndicate the phased-array radar temperature of setting, Te=
290K；LsIndicate phased-array radar loss, Ls=0.8dB；θi,kIndicate i-th of phased array radar scanning when kth sub-distribution
Search for sector Si,kAngle, θ in the present embodimenti,kTake empirical value, θi,kEmpirical value be 6 °, 8 °, 12 °, 16 °；Ri,kIndicate kth
Phased-array radar searches for sector S at i-th when sub-distributioni,kTarget range search value, R in the present embodimenti,kEmpirical value is taken,
Ri,kEmpirical value be 200km, 240km, 295km, 300km, 310km；θi,k、Ri,kIt can directly be measured according to prior information.
The quantity Q of target during setting kth sub-distributionkIt is known, Q in the present embodimentk=5；It will be during kth sub-distribution
The state vector of q-th of target is denoted as[·]TIndicate row vector transposition,Indicate kth time point
X-direction position with q-th of target of period,The Y direction position of q-th of target during expression kth sub-distribution,Table
Show the speed of q-th of target during kth sub-distribution along X-direction,Q-th of target is along Y direction during indicating kth sub-distribution
Speed, constraints be kth sub-distribution during q-th of target state vectorDimensionIn the present embodiment0
≤q≤Qk, QkIndicate target number existing for the region of search of phased-array radar when kth sub-distribution.
Then, the trace model of q-th of target is as follows during kth sub-distribution:
Wherein,The process noise of q-th of target during expression -1 sub-distribution of kth,During indicating -1 sub-distribution of kth
The state vector of q-th of target, FqFor the transition matrix of q-th of target during kth sub-distribution, Expression gram
Luo Neike operators, I2Indicate 2 × 2 dimension unit matrixs,The process noise of q-th of target during expression -1 sub-distribution of kth, it is assumed that
The process noiseObey the Gaussian process that mean value is zero, the process noiseCovariance matrix be T0It indicates per duration during sub-distribution, T in the present embodiment0=2s；When k values are 1 0th time point
State vector with q-th of target of period is denoted as the initial state vector of q-th of targetQ-th of mesh
The process noise of target initial state vectorFor random number of the process noise during original allocation of q-th of target.
The measured value of q-th of target is Z during kth sub-distributionq,k, expression formula is：
In formula (3)
Wherein,The state vector of q-th of target during expression kth sub-distributionNz× 1 non-linear distance of dimension and
Azimuthal measurement function, (x, y) indicate that coordinate of the phased-array radar in plane right-angle coordinate, x indicate phased-array radar flat
X-direction position in the rectangular coordinate system of face, y indicate phased-array radar Y direction position in plane right-angle coordinate, φq,kTable
Show the azimuth information of q-th of target during kth sub-distribution, Rq,kQ-th of target and phased-array radar during expression kth sub-distribution
Radial distance,The X-direction position of q-th of target during expression kth sub-distribution,Q-th during expression kth sub-distribution
The Y direction position of target, subscript T indicate that transposition, arctan indicate arc tangent.
The error of q-th of target during kth sub-distribution is denoted as wq,k, setting error wq,kIt is the non-coupled survey that mean value is zero
Measure error, the error w of q-th of target during kth sub-distributionq,kDiagonal covariance matrix be Σq,k：
Wherein,The Cramér-Rao lower bound lower bound of the distance estimations mean square error of q-th of target during expression kth sub-distribution,Indicate that the azimuth information of q-th of target during kth sub-distribution estimates the Cramér-Rao lower bound lower bound of mean square error, value difference
For：
Wherein,C indicates the light velocity, c=3 × 108M/s, kbIndicate setting constant,μq,kIndicate kth time point
The expected ratio (signal-to-noise ratio) for measuring echo-signal and noise with q-th of target of period,γq,kIndicate kth
The reflectivity of q-th of target, T during sub-distributiont,q,kIndicate that phased-array radar distributes to q-th target during kth sub-distribution
Track time resource, Rq,kQ-th of target is to the radial distance of phased-array radar, β during indicating kth sub-distributionkIndicate kth time
Electromagnetic wave signal-three dB bandwidth that phased-array radar emits during distribution, the expression of subscript -1 are inverted, BkDuring indicating kth sub-distribution
- 3dB the beam angles of Phased Array Radar Antenna；β in the present embodimentk=2MHZ, Bk=0.022 °.
Due to the Cramér-Rao lower bound lower bound of the distance estimations mean square error of q-th of target during kth sub-distributionKth time
The Cramér-Rao lower bound lower bound of the azimuth information estimation mean square error of q-th of target during distributionElectromagnetic wave signal-three dB bandwidth
βk, -3dB beam angles BkWith signal-to-noise ratio μq,kAll with tracking time resource Tt,q,kIt is inversely proportional, therefore by q during kth sub-distribution
The error w of a targetq,kDiagonal covariance matrix extract common factorAfter be rewritten as：
Wherein, Yq,kThe residual matrix of q-th of target during expression kth sub-distribution,
Step 3, the search model for searching for sector at i-th according to phased-array radar when kth sub-distribution obtains kth time point
The switch target letter of searching resource allocation plan during object function and kth sub-distribution with period searching resource allocation plan
Number.
Specifically, for N during kth sub-distributionkA nonoverlapping search sector, the distribution of phased-array radar searching resource
Target is that search time resource is optimally assigned to multiple regions and the search signal-to-noise ratio under worst case is made to maximize；WithIndicate that phased-array radar distributes to N during kth sub-distributionkWhen the search of a nonoverlapping search sector
Between column vector, the object function of searching resource allocation plan is during kth sub-distribution：
Wherein, i indicates N during kth sub-distributionkThe set of a nonoverlapping search sector number composition, i=1,2 ...,
Nk, s.t. indicates constraints, Tk,SeaIndicate that phased-array radar distributes to N during kth sub-distributionkIt is a not to be overlapped search sector
Total search time resource, TS,i,kPhased-array radar distributes to the search time of i-th of search sector during expression kth sub-distribution
Resource；First constraint shows that phased-array radar distributes to N during kth sub-distribution in formula (8)kA be not overlapped searches for sector
Total search time resource is Tk,Sea, second constraints shows that phased-array radar distributes to each search during kth sub-distribution
The search time resource of sector is subjected to the limitation of minimum value, i.e., phased-array radar distributes to each search during kth sub-distribution
The search time resource of rope sector will be greater than or equal to 0.
It is apparent from, one maximizes target type and can be converted to minimum target type by inverting；Therefore, formula (8)
Searching resource assignment problem can be reformulated as the switch target function of searching resource allocation plan during kth sub-distribution：
Wherein,Indicate the convex function during kth sub-distribution,
It indicates to search for sector to N for the 1st during kth sub-distributionkA search sector search time resource cumulative and, α indicates intermediate
Variable,It indicates to calculateMinimum value,It indicates each to search in set of computations i
The ratio of rope sectorAfter obtain NkA ratio, then compares NkA ratio selects maxima operation in turn.
Step 4, it according to the trace model of q-th of target during kth sub-distribution, determines and tracks resource during kth sub-distribution
The target criteria function of allocation plan.
Specifically, for multiple target tracking, its time resource can be optimized according to tracking information before, to change
It is apt to the tracking performance of multiple targets in the worst cases；Here, using WCT-BCRLB as canonical function, and by target following
The object function of resource allocation problem is established as tracking the target criteria function of Resource Allocation Formula during kth sub-distribution：
Wherein, q indicates Q during kth sub-distributionkThe set of a target designation composition, q={ 1,2 ..., Qk, Τt,kIt indicates
Phased-array radar distributes to Q during kth sub-distributionkThe tracking time resource column vector of a target,
Tt,q,kPhased-array radar distributes to the tracking time resource of q-th of target, T during expression kth sub-distributionk,TraIndicate kth time point
Q is distributed to period phased-array radarkTotal tracking time resource of a target；Expression is askedMinimum
Value,Q during kth sub-distribution under expression normalization worst casekThe tracking Bayes carat Metro lower bound of a target is convex
Function；First constraints shows that phased-array radar distributes to Q during kth sub-distributionkTotal tracking time resource of a target
For Tk,Tra, and during second constraint representation kth sub-distribution phased-array radar distribute to the tracking time resource of each target by
To the limitation of minimum value, i.e., phased-array radar is distributed to the tracking time resource of each target and will be more than during kth sub-distribution
Or it is equal to 0；Q during kth sub-distribution under the normalization worst casekThe tracking Bayes carat convex letter of Metro lower bound of a target
NumberIts expression formula is：
Wherein, Tr [Λ CCRLB(Tt,q,k)ΛT] representing matrix [Λ CCRLB(Tt,q,k)ΛT] mark, Λ indicate standardization square
Battle array shows the element of Bayes carat Metro lower bound matrix on different scales, and expression formula is：
T0It indicates per duration during sub-distribution, T in the present embodiment0=2s；Indicate set q
In each target it is correspondingMiddle maximum value；CCRLB(Tt,q,k) indicate phased array thunder during kth sub-distribution
Up to the tracking time resource T for distributing to q-th of targett,q,kBayes's carat Metro lower bound matrix, expression formula is：
Wherein,The prediction Bayesian Information matrix of q-th of target observation state during expression kth sub-distribution,
It is obtained by following formula：
Wherein,Indicate the state vector to q-th of target during kth sub-distribution's
nz× 1 non-linear distance and bearing measurement functions of dimensionTranspositionAbout state vectorVariable quantity, △ expression ask
Variable quantity,The state vector of q-th of target, G during expression kth sub-distributionq,kIndicate q-th target during kth sub-distributionTie up Jacobian matrix, nzIndicate setting constant, nz=2,Indicating willValue bring intoIn,It indicatesValue byValue be calculated；Q-th of target during the 0th sub-distribution as k=1
State vectorThe process noise of q-th of target during expression -1 sub-distribution of kthCovariance
Matrix, FqFor the transition matrix of q-th of target during kth sub-distribution, q={ 1,2 ..., Qk, Τt,kDuring indicating kth sub-distribution
Phased-array radar distributes to QkThe tracking time resource column vector of a target,Tt,q,kIndicate kth time point
The tracking time resource of q-th of target, Y are distributed to period phased-array radarq,kIndicate q-th target during kth sub-distribution
Residual matrix, the expression of subscript -1 are inverted, []TIndicate row vector transposition.
Step 5, according to during the switch target function of searching resource allocation plan during kth sub-distribution and kth sub-distribution
The target criteria function for tracking Resource Allocation Formula obtains the mathematical optimization of Bi-objective Resource Allocation Formula during kth sub-distribution
Model.
Specifically, the ability of phased-array radar proposes significant challenge to radar resource manager, and manager must be every
Determine whether radar should search for new target or the already present target of tracking during primary distribution；Ideally, energy is searched for
The maximization of power and multiple target tracking precision are two conflicting targets, it is necessary to be considered simultaneously；Therefore, the kth sub-distribution phase
Between phased-array radar integrate the mathematical models of Bi-objective Resource Allocation Formula of SAT applications and can be write as：
Wherein,Indicate the Τ acquiredS,kAnd Τt,kMake simultaneouslyWithIt is minimum
Change, Tk,SeaIndicate that phased-array radar distributes to N during kth sub-distributionkA total search time resource for not being overlapped search sector,
Tk,TraIndicate that phased-array radar distributes to Q during kth sub-distributionkTotal tracking time resource of a target, Tk,TotIndicate kth time point
The total time resource of phased-array radar search and tracking application is integrated with period；The last one constraints shows in kth time point
The total resources that phased-array radar search and tracking application are integrated with period are Tk,Tot, Tk,Tot≤ρkT0, ρkIndicate the kth sub-distribution phase
Between duty ratio, ρk∈[0,1]；TS,i,kWhen indicating that phased-array radar distributes to the search of i-th of search sector during kth sub-distribution
Between resource, Tt,q,kPhased-array radar distributes to the tracking time resource of q-th of target during expression kth sub-distribution,Table
Show the convex function during kth sub-distribution,Q during kth sub-distribution under expression normalization worst casekThe tracking of a target
Bayes carat Metro lower bound convex function, ΤS,kIndicate that phased-array radar distributes to N during kth sub-distributionkIt is a nonoverlapping to search
The search time column vector of rope sector, Τt,kIndicate that phased-array radar distributes to Q during kth sub-distributionkWhen the tracking of a target
Between resource column vector.
Phased-array radar during kth sub-distribution is distributed into NkThe search time column vector of a nonoverlapping search sector
ΤS,kQ is distributed to phased-array radar during kth sub-distributionkThe tracking time resource column vector Τ of a targett,kIt is integrated into single
Vector is denoted as Nk+QkDimensional vector Τk,[·]TIndicate row vector transposition；And then during obtaining kth sub-distribution
The mathematic optimal model of Bi-objective Resource Allocation Formula is：
Wherein,Indicate the convex function during kth sub-distribution,Indicate kth time point under normalization worst case
With period QkThe tracking Bayes carat Metro lower bound convex function of a target,Expression length is Nk+QkAnd preceding NkA element is
1, remaining element is zero row vector,Expression length is Nk+QkAnd from Nk+ 1 element is to Nk+QkA element
It is 0 row vector for 1, remaining element,Indicate row vectorIn j-th of element；First constraints shows
Phased-array radar distributes to N during kth sub-distributionkA total search time resource for not being overlapped search sector is Tk,Sea, kth time point
Q is distributed to period phased-array radarkTotal tracking time resource of a target is Tk,Tra；Second constraints shows kth time
The tracking time of search time and each target that sector is each searched for during distribution are both needed to be greater than or equal to 0；The last one is about
Beam condition shows that phased-array radar distributes to N during kth sub-distributionkA total search time resource T for not being overlapped search sectork,Sea
Q is distributed to phased-array radar during kth sub-distributionkTotal tracking time resource T of a targetk,TraAnd be the kth sub-distribution phase
Between integrate phased-array radar search and tracking application total time resource be Tk,Tot。
Step 6, the mathematic optimal model for solving Bi-objective Resource Allocation Formula during kth sub-distribution, respectively obtains kth time
Phased-array radar distributes to N during distributionkA optimum search time resource for not being overlapped search sectorWith during kth sub-distribution
Phased-array radar distributes to QkThe tracking time resource column vector optimal solution of a target
The sub-step of step 6 is：
6.1 in order to obtain Pareto subset, (it is mutual indepedent that different total search budgets solve the solution that formula (9) obtains, different
The obtained solution of total tracking budget Solve problems (10) it is mutual indepedent)；There are M total search budgets and M during setting kth sub-distribution
A total tracking budget, M=17 in the present embodiment always search for budget to m-th from the 1st total search budget and meet：WhereinJ-th of total search budget during indicating kth sub-distribution, by kth sub-distribution
Period, j-th of total tracking budget was denoted asAnd j-th of total search budget during kth sub-distributionWith during kth sub-distribution
J-th of total tracking budgetMeet：
WhereinTk,TotIt indicates to integrate phase during kth sub-distribution
Control the total time resource of battle array search lighting and tracking application.
6.2 according to j-th during kth sub-distribution total search budgetIt is with Linear Programming formula (9), i.e., kth is secondary
J-th of total search budget during distributionIn substitution formula (9) on the right of first constraints, kth is obtained according to linear programming technique
Phased-array radar distributes to N during sub-distributionkJ-th of total search budget of search time vector pair of a nonoverlapping search sector
The optimal solution of resource allocationAccording to j-th during kth sub-distribution total tracking budgetIt is solved with minimax resolving Algorithm
Formula (10), i.e., by j-th during kth sub-distribution total tracking budgetIt substitutes into (10) on the right of first constraints, and according to
Phased-array radar distributes to Q during minimax resolving Algorithm obtains kth sub-distributionkThe tracking time resource column vector pair of a target
The optimal solution of j-th of total tracking budget resources distributionDuring subscript k indicates kth sub-distribution, subscript Sea indicates search, under
It marks t and indicates that tracking, subscript opt indicate optimal solution；By the optimal solution of described j-th total search budget resources distributionWith it is described
The optimal solution of j-th of total tracking budget resources distributionJ-th of pa for forming Bi-objective resource kth sub-distribution (formula (16)) is tired
Hold in the palm optimal solution(minimizing scheme parallel), wherein subscript T indicate transposition, Bi-objective resource point
J-th of the Pareto optimal solution matchedIncluding Nk+QkA element.
6.3 enable the value of j take 1 to M respectively, repeat 6.2, until obtaining the 1st pa of Bi-objective resource kth sub-distribution
Tired support optimal solutionTo the m-th Pareto optimal solution of Bi-objective resource kth sub-distributionIt is denoted as the Pareto that radix is M
Subset Τk.opt,
Due to for the different total search budget of any two during kth sub-distributionWithSubscript n is indicated n-th
Total search budget, subscript m indicate m-th of total search budget, 1≤n≤M, 1≤m≤M；M-th during expression kth sub-distribution
Total search budget,N-th of total search budget during indicating kth sub-distribution, m-th of total search budget money during kth sub-distribution
The optimal solution of source distributionWith the optimal solution of n-th during kth sub-distribution total search budget resources distributionWith as follows
RelationshipTherefore by one of them total search budget during kth sub-distribution and the search budget resources point
Proportionate relationship between the optimal solution matched and M total search budgets can obtain solution of the M total search budgets respectively about formula (9).
According to the Pareto subset Τ that radix is Mk.opt, calculating basis is the Pareto subset Τ of Mk.opt
In each optimal solution functional value, by the Pareto subset Τ that radix is Mk.optIn each optimal solution letter
Numerical value is denoted as Pareto point respectively, and then obtains the Pareto point set of phased-array radar when kth sub-distribution (N before only calculatingkA element), α indicates intermediate variable, Ri,kWhen indicating kth sub-distribution
Phased-array radar searches for sector S at i-thi,kTarget range search value, θi,kIndicate that phased array radar is swept when kth sub-distribution
I-th of the search sector S retouchedi,kAngle, i indicate kth sub-distribution during NkThe collection of a nonoverlapping search sector number composition
It closes, i={ 1,2 ..., Nk,Indicate the 1st Pareto optimal solution of phased-array radar when kth sub-distributionLetter
Numerical value,Indicate j-th of Pareto optimal solution of phased-array radar when kth sub-distributionFunctional value,Table
The Μ Pareto optimal solution of phased-array radar when showing kth sub-distributionFunctional value.
Utilize the convex function during kth sub-distributionMonotonicity, i.e., Indicate Bi-objective resource kth
The γ Pareto optimal solution of sub-distributionFunctional value,Indicate the β pa of Bi-objective resource kth sub-distribution
Tired support optimal solutionFunctional value,Indicate kth sub-distribution
The optimal solution of period β total search budget resources distribution,Indicate the optimal solution of β total tracking budget resources distribution,The optimal solution of γ total search budget resources distribution during indicating kth sub-distribution,Indicate that γ total tracking are pre-
Calculate the optimal solution of resource allocation；Subscript Τ indicates transposition, SNR0N during expression kth sub-distributionkIt is a not to be overlapped in search sector most
Search signal-to-noise ratio in the case of bad, SNR0=mini∈i(SNRi),WithIt is two adjacent Pareto optimalities
The functional value of solution.
By two Pareto optimal solutionsWithIt can obtain two total search budgetsWithIndicate the
β total search budgets, are the β Pareto optimal solutions of Bi-objective resource kth sub-distribution during k sub-distributionIn preceding Nk
A element cumulative and；The total search budgets of γ during indicating kth sub-distribution are the of Bi-objective resource kth sub-distribution
γ Pareto optimal solutionIn preceding NkA element cumulative and；To two total search budgetsWithIt is obtained using dichotomy
N is distributed to phased-array radar during kth sub-distributionkA optimal total search time resource for not being overlapped search sectorAnd kth
Phased-array radar distributes to Q during sub-distributionkOptimal total tracking time resource of a target
By optimal total search time resourceThe conversion mesh of searching resource allocation plan during substitution kth sub-distribution
In scalar functions, and phased-array radar distributes to N during obtaining kth sub-distribution using Linear ProgrammingkIt is a not to be overlapped search
The optimum search time resource of sectorBy optimal total tracking time resourceMoney is tracked during substituting into kth sub-distribution
In the target criteria function of source allocation plan, and phased-array radar point during kth sub-distribution is obtained using minimax resolving Algorithm
Dispensing QkThe tracking time resource column vector optimal solution of a target
Wherein,Optimum search resource allocation result during being kth sub-distribution,Optimal objective during being kth sub-distribution
Resource allocation result is tracked, phased-array radar distributes to N during the kth sub-distributionkIt is a not to be overlapped the optimal total of search sector
Search time resourceQ is distributed to phased-array radar during the kth sub-distributionkOptimal total tracking time money of a target
SourceAnd as during kth sub-distribution integrate phased-array radar search and tracking application total time resource Tk,Tot。
The specific steps are：
Iteration index l=1 and outage threshold ε=10 6a) is respectively set-3, and searching resource during setting kth sub-distribution
Lower boundWith the searching resource upper bound during kth sub-distributionβ total search during indicating kth sub-distribution
Budget,γ total search budgets during indicating kth sub-distribution；Wherein, γ=β+1,1≤β≤M, 2≤γ≤M, M are indicated
The total search budget number or total tracking budget number set during kth sub-distribution.
6b) according to searching resource lower bound T during kth sub-distributionLWith searching resource upper bound T during kth sub-distributionU, calculate the
After l iteration during kth sub-distribution phased-array radar total searching resource Tl,Sea, Tl,Sea=(TL+TUThen)/2 utilize l
After secondary iteration during kth sub-distribution phased-array radar total searching resource Tl,SeaWith during Linear Programming kth sub-distribution
The switch target function of searching resource allocation plan, obtains after the l times iteration that phased-array radar distributes to N during kth sub-distributionk
The search time column vector optimal solution of a nonoverlapping search sector
If 6c)Update TU=Tl,Sea, the value of l is enabled to add
1, execute 6b)；Otherwise 6d is executed).
If 6d)Update TL=Tl,Sea, the value of l is enabled to add
1, execute 6b)；Otherwise 6e is executed).
If 6e)It takesSearching resource distributes
Optimal solution isIndicate that phased-array radar distributes to N during kth sub-distributionkIt is a not to be overlapped the optimal of search sector
Search time resource,Indicate that phased-array radar distributes to N during kth sub-distribution after the l times iterationkA nonoverlapping search
The search time vector optimal solution of sector.
Phased-array radar distributes to Q during 6f) calculating kth sub-distributionkOptimal total tracking time resource of a target Wherein, Tk,TotIt indicates to integrate the total resources that phased-array radar search and tracking are applied during kth sub-distribution,
Tk,Tot≤ρkT0, ρkDuty ratio during expression kth sub-distribution, ρk∈[0,1]；T0Duration during indicating per sub-distribution, the present embodiment
Middle T0=2s.
6g) by optimal total tracking time resourceThe target of Resource Allocation Formula is tracked during substituting into kth sub-distribution
In canonical function, and phased-array radar distributes to Q during obtaining kth sub-distribution using minimax resolving AlgorithmkA target with
Track time resource column vector optimal solution
Step 7, the value of k is enabled to add 1, return to step 2, phased-array radar distributes to N during obtaining the 1st sub-distribution1It is a
It is not overlapped the optimum search time resource of search sectorPhased-array radar distributes to N during being distributed to kthKA be not overlapped is searched
The optimum search time resource of rope sectorAnd the 1st phased-array radar during sub-distribution distribute to Q1When the tracking of a target
Between resource column vector optimal solutionPhased-array radar distributes to Q during being distributed to kthKThe tracking time resource of a target arrange to
Measure optimal solutionIt is denoted as the resource allocation result that biobjective scheduling is searched for and tracked based on phased-array radar；The present embodiment takes K=
20。
Resource Allocation Formula is established as a biobjective scheduling frame by the present invention, and base is obtained according to parallel minimum scheme
Number is the Pareto subset of M；Then linear programming technique and minimax resolving Algorithm are utilized, Bi-objective resource point is efficiently solved
With problem.
Further verification explanation is carried out to effect of the present invention by following emulation.
1. simulation parameter：
The fixed position of phased-array radar is (93,45) km, and signal effective bandwidth and half-power beam width are set respectively
It is set to βk=2MHZ and Bk=0.022 °, total time resource is Tk,Tot≤ρkT0,ρk∈[0,1]；It uses to come during 20 sub-distribution
It is simulated, the duration per sub-distribution is arranged to T0=2s；In fact, phased-array radar may have different search needs.
Accordingly, it is considered to two kinds of search model S1And S2It describes two different search needs, please refers to Table I and Table II in detail,
Table I is model S1In each sector search parameter, Table II be model S2In each sector search parameter.
(1≤k≤10) phased-array radar uses first search model S during preceding 10 sub-distribution1, the wherein quantity of sector
It is arranged to Nk=8；(11≤k≤20) phased-array radar uses second of search model S during being distributed at latter 102, sector
Quantity is Nk=6.
Table I
| Sector number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Ri,k(km) | 240 | 240 | 240 | 300 | 200 | 300 | 310 | 295 |
| θi,k(○) | 8 | 8 | 8 | 8 | 8 | 6 | 8 | 12 |
Table II
| Sector number | 1 | 2 | 3 | 4 | 5 | 6 |
| Ri,k(km) | 240 | 240 | 240 | 300 | 200 | 300 |
| θi,k(○) | 8 | 8 | 16 | 8 | 8 | 8 |
In simulations, it would be desirable to which the destination number of tracking is set as Qk=5, each dbjective state parameter is provided in Table III.
Table III
| Target number | 1 | 2 | 3 | 4 | 5 |
| Position (km) | (3,55) | (-23,85) | (233,60) | (300,30) | (52,80) |
| Speed (m/s) | (300,0) | (100,-150) | (200,-200) | (10,-200) | (200,100) |
| Initial range (m) | 127.28 | 126.32 | 169.19 | 86.45 | 122.09 |
| Target reflectivity | 2 | 0.8 | 1.5 | 1 | 1 |
It is the target deployment schematic diagram within the scope of phased-array radar detections of radar with reference to Fig. 3；Fig. 3 gives these targets
The angle of opposite radar system is distributed.
Radix is the Pareto subset of M in order to obtain, and M search time budget is set asJ=1,
2 ..., M, M=17；For what is givenExpression benchmark solution be (resource mean allocation scheme
Solution), wherein Indicate that there is NkComplete 1 column vector of a element,Indicate kth sub-distribution
J-th of total resources budget of period uses the solution of resource mean allocation scheme,J-th of total search during indicating kth sub-distribution
Resource budget uses the solution of searching resource mean allocation scheme,J-th of total tracking resource is pre- during indicating kth sub-distribution
The solution using tracking resource mean allocation scheme is calculated, benchmark set isThe target function value of each benchmark solution
Referred to as benchmark is as a result, the curve being made of benchmark result is known as datum curve, same Pareto subset
In the target function value of each Pareto solution be known as Pareto as a result, the curve being made of Pareto result is known as Pareto curve.
2. emulation content：
The present invention is for resource mean allocation scheme and the biobjective scheduling Resource Allocation Formula based on Pareto theory
Allocation result compares emulation experiment.
3. analysis of simulation result：
Fig. 4's (a) the results show that search need model S1With regard under the search signal-to-noise ratio and worst case under worst case
For tracking Bayes's Cramér-Rao lower bound lower bound, Pareto curve is substantially better than datum curve；Fig. 4's (b) the results show that search
Demand model S2For tracking Bayes's Cramér-Rao lower bound lower bound under the search signal-to-noise ratio and worst case under worst case,
Pareto curve is substantially better than datum curve；Therefore there is Pareto curve, it, can using dichotomy for arbitrary mission requirements
Easily to obtain best search and tracking performance.
In conclusion emulation experiment demonstrates the correctness of the present invention, validity and reliability.
Obviously, various changes and modifications can be made to the invention without departing from essence of the invention by those skilled in the art
God and range.In this way, if these modifications and changes of the present invention belongs to the range of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to include these modifications and variations.
Claims (7)
1. it is a kind of based on phased-array radar search for and track biobjective scheduling resource allocation methods, which is characterized in that including with
Lower step：
Step 1, initialization：It is kth sub-distribution to enable k, and the initial value of 1≤k≤K, k be 1, K for the even number more than 0；Set kth time
There are Q for the region of search of phased-array radar when distributionkA target, and when kth sub-distribution phased-array radar region of search quilt
It is divided into NkA nonoverlapping search sector；
Step 2, when determining kth sub-distribution phased-array radar searched at i-th sector search model and kth sub-distribution during
The trace model of q target；Wherein, 0≤q≤Qk, QkIndicate mesh existing for the region of search of phased-array radar when kth sub-distribution
Mark number；1≤i≤Nk, NkIndicate phased array search lighting sector total number when kth sub-distribution；
Step 3, the search model for searching for sector at i-th according to phased-array radar when kth sub-distribution obtains the kth sub-distribution phase
Between searching resource allocation plan object function and kth sub-distribution during searching resource allocation plan switch target function；
Step 4, it according to the trace model of q-th of target during kth sub-distribution, determines and tracks resource allocation during kth sub-distribution
The target criteria function of scheme；
Step 5, it is tracked according to during the switch target function of searching resource allocation plan during kth sub-distribution and kth sub-distribution
The target criteria function of Resource Allocation Formula obtains the mathematic optimal model of Bi-objective Resource Allocation Formula during kth sub-distribution；
Step 6, solve kth sub-distribution during Bi-objective Resource Allocation Formula mathematic optimal model, respectively obtain kth sub-distribution
Period phased-array radar distributes to NkA optimum search time resource for not being overlapped search sectorWith it is phased during kth sub-distribution
Battle array radar distributes to QkThe tracking time resource column vector optimal solution of a target
Step 7, the value of k is enabled to add 1, return to step 2, phased-array radar distributes to N during obtaining the 1st sub-distribution1It is a not to be overlapped
Search for the optimum search time resource of sectorPhased-array radar distributes to N during being distributed to kthKIt is a not to be overlapped search sector
Optimum search time resourceAnd the 1st phased-array radar during sub-distribution distribute to Q1The tracking time resource of a target
Column vector optimal solutionPhased-array radar distributes to Q during being distributed to kthKThe tracking time resource column vector of a target is optimal
SolutionIt is denoted as the resource allocation result that biobjective scheduling is searched for and tracked based on phased-array radar.
2. a kind of resource allocation methods for searching for and track biobjective scheduling based on phased-array radar as described in claim 1,
It is characterized in that, in step 2, the search model that phased-array radar searches for sector at i-th when the kth sub-distribution is：
Wherein, α indicates intermediate variable,TS,i,kPhased-array radar is distributed to i-th and is searched when expression kth sub-distribution
Rope sector Si,kSearch time resource, SNRi,kIndicate that phased-array radar searches for sector S at i-th when kth sub-distributioni,kMesh
Mark search signal-to-noise ratio, PavIndicate the average emitted power of phased-array radar, AeIndicate that the Phased Array Radar Antenna of setting effectively connects
Batter diameter,Indicate that phased-array radar searches for sector S at i-th when kth sub-distributioni,kTarget scatter section area, kBIndicate glass
The graceful constant of Wurz, TeIndicate the phased-array radar temperature of setting, LsIndicate phased-array radar loss, θi,kWhen indicating kth sub-distribution
I-th of search sector S that phased-array radar is scannedi,kAngle, Ri,kIndicate that phased-array radar is at i-th when kth sub-distribution
Search for sector Si,kTarget range search value；
The trace model of q-th of target is during the kth sub-distribution：
Wherein,The process noise of q-th of target during expression -1 sub-distribution of kth,Q-th during expression -1 sub-distribution of kth
The state vector of target, FqFor the transition matrix of q-th of target during kth sub-distribution, It indicates in Crow
Gram operator, I2Indicate 2 × 2 dimension unit matrixs, T0Duration during indicating per sub-distribution.
3. a kind of resource allocation methods for searching for and track biobjective scheduling based on phased-array radar as described in claim 1,
It is characterized in that, in step 3, the object function of searching resource allocation plan is during the kth sub-distribution：
s.t.∑i∈iTS,i,k=Tk,Sea
TS,i,k≥0,i∈i
Wherein, i indicates N during kth sub-distributionkThe set of a nonoverlapping search sector number composition, i={ 1,2 ..., Nk,
S.t. constraints, T are indicatedk,SeaIndicate that phased-array radar distributes to N during kth sub-distributionkIt is a not to be overlapped the total of search sector
Search time resource, TS,i,kPhased-array radar distributes to the search time money of i-th of search sector during expression kth sub-distribution
Source, SNRi,kIndicate that phased-array radar searches for sector S at i-th when kth sub-distributioni,kTarget search signal-to-noise ratio, ΤS,kIt indicates
Phased-array radar distributes to N during kth sub-distributionkThe search time column vector of a nonoverlapping search sector,Subscript T indicates transposition, 1≤i≤Nk；
The switch target function of searching resource allocation plan is during the kth sub-distribution：
TS,i,k≥0,i∈i
Wherein,Indicate the convex function during kth sub-distribution, Indicate the
During k sub-distribution sector is searched for N for the 1stkThe cumulative and α expression intermediate variables of a search sector search time resource；It indicates to calculateMinimum value,It indicates each to search for sector in set of computations i
RatioAfter obtain NkA ratio, then compares NkA ratio selects maxima operation in turn.
4. a kind of resource allocation methods for searching for and track biobjective scheduling based on phased-array radar as described in claim 1,
It is characterized in that, in step 4, the target criteria function that Resource Allocation Formula is tracked during the kth sub-distribution is：
s.t.∑q∈qTt,q,k=Tk,Tra
Tt,q,k≥0,q∈q
Wherein, q indicates Q during kth sub-distributionkThe set of a target designation composition, q={ 1,2 ..., Qk, Τt,kIndicate kth time
Phased-array radar distributes to Q during distributionkThe tracking time resource column vector of a target,Subscript T tables
Show transposition, Tt,q,kPhased-array radar distributes to the tracking time resource of q-th of target, T during expression kth sub-distributionk,TraIt indicates
Phased-array radar distributes to Q during kth sub-distributionkTotal tracking time resource of a target；Expression is asked
Minimum value,Q during kth sub-distribution under expression normalization worst casekThe tracking Bayes carat Metro of a target
Lower bound convex function.
5. a kind of resource allocation methods for searching for and track biobjective scheduling based on phased-array radar as described in claim 1,
It is characterized in that, in steps of 5, the mathematic optimal model of Bi-objective Resource Allocation Formula, process during the kth sub-distribution
For：
The mathematical model of Bi-objective Resource Allocation Formula during kth sub-distribution is expressed as first：
s.t.∑i∈iTS,i,k=Tk,Sea,∑q∈qTt,q,k=Tk,Tra
TS,i,k≥0,Tt,q,k≥0,i∈i,q∈q
Tk,Sea+Tk,Tra=Tk,Tot
Wherein,Indicate the Τ acquiredS,kAnd Τt,kMake simultaneouslyWithIt minimizes,
Tk,SeaIndicate that phased-array radar distributes to N during kth sub-distributionkA total search time resource for not being overlapped search sector, Tk,Tra
Indicate that phased-array radar distributes to Q during kth sub-distributionkTotal tracking time resource of a target, Tk,TotIndicate the kth sub-distribution phase
Between integrate phased-array radar search and tracking application total time resource, Tk,Tot≤ρkT0, ρkDuty during expression kth sub-distribution
Than ρk∈[0,1]；TS,i,kPhased-array radar distributes to the search time money of i-th of search sector during expression kth sub-distribution
Source, Tt,q,kPhased-array radar distributes to the tracking time resource of q-th of target during expression kth sub-distribution,Indicate kth
Convex function during sub-distribution,Q during kth sub-distribution under expression normalization worst casekThe tracking pattra leaves of a target
This carat of Metro lower bound convex function, ΤS,kIndicate that phased-array radar distributes to N during kth sub-distributionkA nonoverlapping search fan
The search time column vector in area, Τt,kIndicate that phased-array radar distributes to Q during kth sub-distributionkThe tracking time of a target provides
Source column vector；
Then phased-array radar during kth sub-distribution is distributed into NkThe search time vector Τ of a nonoverlapping search sectorS,k
Q is distributed to phased-array radar during kth sub-distributionkThe tracking time resource column vector Τ of a targett,kBe integrated into individually to
Amount, is denoted as Nk+QkDimensional vector Τk,[·]TIndicate row vector transposition；And then obtain the kth sub-distribution phase
Between the mathematic optimal model of Bi-objective Resource Allocation Formula be：
Tk,Sea+Tk,Tra=Tk,Tot
Wherein,Indicate the convex function during kth sub-distribution,Indicate the kth sub-distribution phase under normalization worst case
Between QkThe tracking Bayes carat Metro lower bound convex function of a target,Expression length is Nk+QkAnd preceding NkA element be 1, its
Remaining element is zero row vector,Expression length is Nk+QkAnd from Nk+ 1 element is to Nk+QkA element be 1,
Remaining element is 0 row vector,Indicate row vectorIn j-th of element, Tk,TotDuring indicating kth sub-distribution
The total time resource of integrated phased-array radar search and tracking application.
6. a kind of resource allocation methods for searching for and track biobjective scheduling based on phased-array radar as described in claim 1,
It is characterized in that, in step 6, phased-array radar distributes to N during the kth sub-distributionkIt is a not to be overlapped search sector most
Excellent search time resourceQ is distributed to phased-array radar during kth sub-distributionkThe tracking time resource column vector of a target is most
Excellent solutionIt obtains process：
Iteration index l=1 and outage threshold ε 6a) is respectively set, and searching resource lower bound during kth sub-distribution is setWith the searching resource upper bound during kth sub-distribution β total search budgets during indicating kth sub-distribution,γ total search budgets during indicating kth sub-distribution；Wherein, γ=β+1,1≤β≤M, 2≤γ≤M, M indicate kth time
The total search budget number or total tracking budget number set during distribution；
6b) according to searching resource lower bound T during kth sub-distributionLWith searching resource upper bound T during kth sub-distributionU, calculate the l times
After iteration during kth sub-distribution phased-array radar total searching resource Tl,Sea, Tl,Sea=(TL+TUThen)/2 utilize the l times and change
For total searching resource T of phased-array radar during rear kth sub-distributionl,SeaIt is searched for during Linear Programming kth sub-distribution
The switch target function of Resource Allocation Formula, obtains after the l times iteration that phased-array radar distributes to N during kth sub-distributionkIt is a not
The search time column vector optimal solution of the search sector of overlapping
If 6c)Update TU=Tl,Sea, enable the value of l add 1, hold
Row 6b)；Otherwise 6d is executed)；
If 6d)Update TL=Tl,Sea, enable the value of l add 1, hold
Row 6b)；Otherwise 6e is executed)；
If 6e)It takesSearching resource optimal scheme
Xie Wei Indicate that phased-array radar distributes to N during kth sub-distributionkWhen a optimum search for not being overlapped search sector
Between resource,Indicate that phased-array radar distributes to N during kth sub-distribution after the l times iterationkA nonoverlapping search sector
Search time vector optimal solution；
Phased-array radar distributes to Q during 6f) calculating kth sub-distributionkOptimal total tracking time resource of a target Wherein, Tk,TotIt indicates to integrate the total resources that phased-array radar search and tracking are applied during kth sub-distribution,
Tk,Tot≤ρkT0, ρkDuty ratio during expression kth sub-distribution, ρk∈[0,1]；T0Duration during indicating per sub-distribution；
6g) according to optimal total tracking time resourceResource is tracked during solving kth sub-distribution with minimax resolving Algorithm
The target criteria function of allocation plan, phased-array radar distributes to Q during obtaining kth sub-distributionkThe tracking time of a target provides
Source column vector optimal solution
7. a kind of resource allocation methods for searching for and track biobjective scheduling based on phased-array radar as claimed in claim 6,
It is characterized in that, in 6 (a), it is describedTotal search budgets of β and described during indicating kth sub-distributionIndicate kth time
Budget is always searched for during distribution for γ, further includes：
The total search budgets of β during indicating kth sub-distribution, be the β Pareto of Bi-objective resource kth sub-distribution most
Excellent solutionIn preceding NkA element cumulative and；γ total search budgets during indicating kth sub-distribution, are Bi-objective money
The γ Pareto optimal solution of source kth sub-distributionIn preceding NkA element cumulative and；
J-th of Pareto optimal solution of Bi-objective resource kth sub-distribution is denoted asIt obtains process：
There are M total search budgets and M total tracking budgets during 6.1 setting kth sub-distribution, from the 1st total search budget to M
A total search budget meets：WhereinJ-th of total search during indicating kth sub-distribution
J-th during kth sub-distribution total tracking budget is denoted as by budgetAnd j-th of total search budget during kth sub-distribution
With j-th during kth sub-distribution total tracking budgetMeet：
WhereinJ=1,2 ..., M, Tk,TotIt is integrated during indicating kth sub-distribution phased
The total time resource of battle array search lighting and tracking application；
6.2 according to j-th during kth sub-distribution total search budgetIt is provided with being searched for during Linear Programming kth sub-distribution
The switch target function of source allocation plan, phased-array radar distributes to N during obtaining kth sub-distributionkA nonoverlapping search fan
The optimal solution of j-th of total search budget resources distribution of search time vector pair in areaAccording to j-th during kth sub-distribution
Total tracking budgetThe target criteria function of Resource Allocation Formula is tracked during solving kth sub-distribution with minimax resolving Algorithm,
Phased-array radar distributes to Q during obtaining kth sub-distributionkJ-th of total tracking of tracking time resource column vector pair of a target is pre-
Calculate the optimal solution of resource allocationBy the optimal solution of described j-th total search budget resources distributionIt is total with described j-th
Track the optimal solution of budget resources distributionForm j-th of Pareto optimal solution of Bi-objective resource kth sub-distribution Subscript T indicates transposition, j-th of Pareto optimal solution of Bi-objective resource allocationIncluding Nk+QkIt is a
Element.
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