CN108333583B - Resource allocation method based on dual-target optimization of phased array radar search and tracking - Google Patents
Resource allocation method based on dual-target optimization of phased array radar search and tracking Download PDFInfo
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Abstract
The invention discloses a resource allocation method based on phased array radar searching and tracking dual-target optimization, which belongs to the technical field of radar and mainly comprises the following steps: setting search area existence Q of time-controlled array radar distributed for the kth timekThe search area of the phased array radar is divided into N when the k-th distribution is carried outkA plurality of non-overlapping search sectors; let K be the kth distribution, K is more than or equal to 1 and less than or equal to K, the initial value of K is 1, and K is an even number greater than 0; obtaining the phased array radar allocation N during the 1 st allocation period1Optimal search time resources for non-overlapping search sectors
Phased array radar allocation to N during allocation up to KthKOptimal search time resources for non-overlapping search sectors
And phased array radar allocation to Q during the 1 st allocation1Tracking time resource column vector optimal solution of each target
Phased array radar allocation to Q during the Kth allocationKTracking time resource column vector optimal solution of each target
And recording as a resource allocation result based on phased array radar searching and tracking dual-target optimization.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a resource allocation method based on phased array radar searching and tracking dual-target optimization, which is suitable for resource allocation under the condition of limited time resource budget and improves the searching capability of a phased array radar and the tracking precision of a target to the maximum extent.
Background
Recently, advances in technology have enabled the development of agile, multi-tasking phased array radar systems; generally, a phased array radar uses an electronically steered array antenna and thus has extremely high beam flexibility, a characteristic that enables the phased array radar to perform multiple tasks; in fact, different radar functions may have competing demands on system resources, and therefore require the use of automated techniques to allocate resources depending on the capabilities of the radars and their goals; for radar search and tracking (SAT) applications, if one phased array radar detects targets with insufficient time resources, multiple low detectable targets may still not be found; at the same time, if a phased array radar does not have enough time resources to illuminate the previously tracked target, a discontinuous trajectory may result.
Heretofore, many approaches have been applied to the problem of resource allocation, whether a search function or a tracking function or both functions act together; for radar search applications, the challenge is to expand the radar surveillance area and improve the probability of target detection while using as few resources as possible; for target tracking, one may seek to minimize the total radar resources needed to track a target by optimizing the tracking-revisit interval, target signal strength, and detection threshold, and existing work, i.e., resource allocation schemes designed for SAT applications, can be broadly divided into two categories, rule-based and optimization-based; in rule-based schemes, a series of rules are formulated according to some operation requirements or radar features, and although the methods are very effective, the methods are not optimal in Bayesian theory and unpredictable behaviors can occur; another approach is to compute the SAT task by using a single cost function; the radar resource allocation problem may be formulated as a mathematical optimization scheme, and typically the cost function is a weighted sum of metrics corresponding to search capability and tracking accuracy, e.g., probability of detecting a target, tracking bayesian cralmelo lower bound (BCRLB), and expected measured signal-to-noise ratio (SNR); however, the disadvantage of these methods is the selection of weights and the meaningless aggregation of non-corresponding metrics.
Disclosure of Invention
In view of the problems in the prior art, the present invention is directed to a resource allocation method based on dual target search and tracking optimization for a phased array radar, which can solve the problem of resource allocation in a limited illumination time budget and simultaneously improve the search capability of the phased array radar and the tracking accuracy of a target to the maximum extent.
In view of the above problems with the prior art, it is an object of the present invention to design the SAT task resource allocation scheme as a dual target constrained optimization problem and to determine its well-known pareto subset (BK-PS) using the pareto theory. The resource allocation scheme employs two cost functions: (i) emphasizing that the target search capability is maximized in terms of multi-search sector search minimum signal-to-noise ratio (worst case search signal-to-noise ratio (WCS-SNR)); (ii) emphasizing multi-target tracking mean square error minimization in terms of a worst-case tracking Bayesian Cramer lower bound (WCT-BCRLB); in order to discuss the multiple balance between the two targets, a pareto optimal solution set of the two-target problem needs to be found; however, for many dual-objective problems, because the number of solutions in a solution set is large, determining the entire pareto optimal set is practically impossible; thus, a practical approach to dual target optimization is to calculate the BK-PS and represent the pareto optimal set with BK-PS as much as possible, with which one can find a suitable compromise between SAT tasks and select a resource allocation scheme accordingly to meet the specific application requirements.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
A resource allocation method based on phased array radar searching and tracking dual-target optimization comprises the following steps:
Step 7, let
Adds 1 to the value of (1), returns to step 2 until the phased array radar assignment during the 1 st assignment is obtained
Optimal search time resources for non-overlapping search sectors
To the first
Phased array radar allocation during sub-allocation
Optimal search time resources for non-overlapping search sectors
And phased array radar assignment during the 1 st assignment
Tracking time resource column vector optimal solution of each target
To the first
Phased array radar allocation during sub-allocation
Tracking time resource column vector optimal solution of each target
And recording the resource allocation result as a resource allocation result based on dual target searching and tracking of the phased array radar.
The invention has the beneficial effects that:
firstly, the method utilizes the unique structure of a dual-target constraint optimization problem, and can obtain a pareto subset BK-PS by solving a salient pole small maximum optimization (CMO) problem in parallel; in previous studies, in order to obtain the pareto subset BK-PS, researchers developed many methods such as the weighted sum method, the ant colony optimization algorithm, and the genetic algorithm; the method of the invention develops a parallel minimization scheme to research the pareto subset BK-PS by utilizing the unique structure of the dual-objective optimization problem, so that the method of the invention is used as an alternative method for obtaining BK-PS, different pareto solutions can be obtained by solving a plurality of dual-objective problems with different SAT requirements in parallel, each complex dual-objective problem can be divided into two CMO problems, one for a search task and the other for a tracking task, and the solutions of search resource allocation (S-RA) problems corresponding to different SAT requirements are proportional.
Secondly, for different SAT parameters, the minimum search resource allocation problem only needs to be solved once, and as the target function of target tracking resource allocation is nonlinear, the method can obtain a pareto subset BK-PS with a base number of M by solving M +1 CMO problems in parallel; the result shows that the infinitesimal maximum radar search resource allocation problem generates a linear programming model, so that the problem can be solved easily by a famous linear programming method; for the target tracking resource allocation scheme, the generated minimum maximum problem consists of a set of separable monotonically decreasing convex functions, and a minimum maximum solution algorithm can be used for solving the T-RA problem.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a resource allocation method based on dual target optimization for phased array radar search and tracking according to the present invention;
FIG. 2 is a schematic diagram of quantizing the search area of a phased array radar to non-overlapping sectors;
FIG. 3 is a schematic diagram of target deployment within a detection range of a phased array radar;
FIG. 4(a) is a schematic diagram comparing the performance of the resource-averaging allocation scheme with the pareto-based dual-target-optimized resource allocation scheme during the 5 th allocation;
fig. 4(b) is a schematic diagram comparing the performance of the resource average allocation scheme with the pareto-based dual target optimized resource allocation scheme during the 15 th allocation.
Detailed Description
Referring to fig. 1, it is a flowchart of a resource allocation method based on dual target optimization of phased array radar search and tracking according to the present invention; the resource allocation method based on the phased array radar searching and tracking dual-target optimization comprises the following steps:
Specifically, a phased array radar is determined, and the south-plus-south direction 93km and the west-plus-45 km of the phased array radar are taken as the origin points
And establishing a plane rectangular coordinate system by taking the north direction as the Y axis and the east direction as the X axis.
As shown in FIG. 2, let
Is as follows
The number of the sub-distribution is equal to the number of the sub-distribution,
is set to an initial value of 1,
is an even number greater than 0, in the present embodiment
A value of 20; is set to
Search area existence of time-controlled array radar in sub-distribution
Object, in the present embodiment
The value is 5; and a first
The search area of the sub-distributed time-controlled array radar is divided into
Non-overlapping search sectors
Front side
The search regions of the sub-distributed time phased array radar are respectively divided into
A number of non-overlapping search sectors that are,rear end
The search regions of the sub-distributed time phased array radar are respectively divided into
A plurality of non-overlapping search sectors; in this example
Specifically, in order to find an undetected target, the phased array radar needs to allocate its time resources to different search sectors; to further obtainTo the first
Time phased array radar in sub-distribution
Search sector
The search model of (2) is:
wherein,
a represents an intermediate variable which is,
is shown as
Time-controlled array radar allocation to the second
Search sector
The time resources of the search of (2),
is shown as
Time phased array radar in sub-distribution
Search sector
The target search signal-to-noise ratio of (c),
represents the average transmit power of the phased array radar,
indicating the set effective receive aperture of the phased array radar antenna,
is shown as
Time phased array radar in sub-distribution
Search sector
The cross-sectional area of scattering of the target,
which represents the boltzmann constant, represents,
indicating the set phased array radar temperature,
the loss of the phased array radar is shown,
is shown as
Time-controlled array radar scanned by sub-distribution
Search sector
Angle of (2), in the present embodiment
Taking the empirical value of the raw material to be tested,
the empirical values of (A) are 6 °, 8 °, 12 °, 16 °;
is shown as
Time phased array radar in sub-distribution
Search sector
Target distance search value of, in the present embodiment
Taking the empirical value of the raw material to be tested,
the empirical values of (A) are 200km, 240km, 295km, 300km and 310 km;
can be directly measured according to prior information.
Is set to
Number of targets during sub-allocation
Is known, in this embodiment
Will be first
During the sub-distribution period
The state vector of each object is recorded as
Which represents the transpose of the row vector,
is shown as
During the sub-distribution period
The X-axis directional position of the individual target,
is shown as
During the sub-distribution period
The Y-axis directional position of the individual target,
is shown as
During the sub-distribution period
The velocity of the individual target in the direction of the X-axis,
is shown as
During the sub-distribution period
The speed of the object along the Y-axis direction with the constraint of the first
During the sub-distribution period
State vector of individual target
Dimension of (2)
In this example
Is shown as
And distributing the number of targets in the search area of the phased array radar in time.
Then, first
During the sub-distribution period
The tracking model for each target is as follows:
wherein,
is shown as
During the sub-distribution period
The process noise of the individual target is,
is shown as
During the sub-distribution period
The state vector of the individual objects is,
is as follows
During the sub-distribution period
The transformation matrix of the individual objects is,
the expression of the kronecker operator,
representing a 2 x 2 dimensional identity matrix, assuming the process is noisy
Subject to a mean-zero Gaussian process that is noisy
Has a covariance matrix of
Indicating the duration of each dispensing period, in this embodiment
When in use
The 0 th allocation period when the value is 1
The state vector of the individual target is noted as
Initial state vector of individual target
First, the
Process noise of initial state vector of individual target
Is as follows
The process of each target is noisy with respect to the random number during initial assignment.
First, the
During the sub-distribution period
The measured value of each target is
The expression is as follows:
in the formula (3)
Wherein,
is shown as
During the sub-distribution period
State vector of individual target
Is/are as follows
The dimensional non-linear distance and orientation measurement functions,
representing the coordinates of the phased array radar in a planar rectangular coordinate system,
the position of the phased array radar in the X-axis direction in a plane rectangular coordinate system is represented,
the position of the phased array radar in the Y-axis direction in a plane rectangular coordinate system is represented,
is shown as
During the sub-distribution period
The position information of the individual objects is determined,
is shown as
During the sub-distribution period
The radial distance of an individual target from the phased array radar,
is shown as
During the sub-distribution period
The X-axis directional position of the individual target,
is shown as
During the sub-distribution period
Y-axis position of individual target, superscript
Indicating transpose and arctan for arctan.
Will be first
During the sub-distribution period
The error of each target is recorded as
Set error
Is mean zero uncoupledResultant measurement error of
During the sub-distribution period
Error of individual target
Is a diagonal covariance matrix of
Wherein,
is shown as
During the sub-distribution period
The range of each target estimates the lower boundary of the cramer-circle of mean square error,
is shown as
During the sub-distribution period
The lower boundary of the Cramer-Rao bound of the mean square error of the azimuth information estimation of each target is respectively as follows:
wherein,
the speed of light is indicated and is,
it is shown that the set constant is,
is shown as
During the sub-distribution period
The expected measured echo signal to noise ratio (signal-to-noise ratio) for an individual target,
is shown as
During the sub-distribution period
The reflectivity of the individual target is such that,
is shown as
During the second allocation period phased array radar is allocated to the second
The tracking time resources of the individual targets,
is shown as
During the sub-distribution period
The radial distance of an individual target to the phased array radar,
is shown as
The-3 dB bandwidth of the electromagnetic wave signals transmitted by the phased array radar during the sub-distribution period is marked with the-1 to represent inversion,
is shown as
-3dB beamwidth of the phased array radar antenna during the secondary allocation; in this example
Due to the fact that
During the sub-distribution period
Cramer-Rao bound lower bound of mean squared error of range estimates for individual targets
First, the
During the sub-distribution period
Cramer-Rao bound lower bound of mean square error of azimuth information estimation of individual targets
Electromagnetic wave signal-3 dB bandwidth
-3dB beamwidth
Sum signal to noise ratio
All with tracking time resources
Is inversely proportional, therefore will be
During the sub-distribution period
Error of individual target
The diagonal covariance matrix of (A) extracts common factors
The post rewrite is:
wherein,
is shown as
During the sub-distribution period
The remaining matrix of the individual objects is,
Specifically, for the second
During the sub-distribution period
The search sectors are not overlapped, and the search resource allocation of the phased array radar aims to optimally allocate search time resources to a plurality of areas and maximize the search signal-to-noise ratio under the worst condition; by using
Is shown as
Phased array radar allocation during sub-allocation
Search time column vectors of non-overlapping search sectors, a
The objective function of searching the resource allocation scheme during the secondary allocation is:
wherein,
is shown as
During the sub-distribution period
A set of non-overlapping search sector numbers,
a constraint condition is expressed in terms of the number of the elements,
is shown as
Phased array radar allocation during sub-allocation
The total search time resources of the non-overlapping search sectors,
is shown as
During the second allocation period phased array radar is allocated to the second
Search time resources of the respective search sectors; the first constraint in equation (8) indicates that
Phased array radar allocation during sub-allocation
The total search time resources of the non-overlapping search sectors are
The second constraint states that
The search time resources allocated to each search sector by phased array radar during the sub-allocation are limited by a minimum value, i.e. the second
The search time resources allocated to each search sector by the phased array radar during the sub-allocation are greater than or equal to 0.
As is readily known, a maximized object type can be converted into a minimized object type by inversion; therefore, the search resource allocation problem of equation (8) can be newly formulated as the second
Search for the transfer objective function of the resource allocation scheme during the secondary allocation:
wherein,
is shown as
The convex function during the sub-allocation period,
is shown as
Search sector 1 to search sector 1 during sub-allocation
The search sectors search the accumulated sum of time resources, alpha represents an intermediate variable,
representation calculation
The minimum value of (a) is determined,
representing a set of computations
Ratio of each search sector in the search
Then obtain
A ratio is then compared
The ratio value is then used to select the maximum value operation.
Specifically, for multi-target tracking, the time resources can be optimized according to the previous tracking informationThe tracking performance of a plurality of targets under the worst condition is improved; here, WCT-BCRLB is used as a standard function, and a target function of a target tracking resource allocation problem is made to be the second
Target criteria function for tracking resource allocation scheme during sub-allocation:
wherein,
is shown as
During the sub-distribution period
A set of object numbers, each object number being,
is shown as
Phased array radar allocation during sub-allocation
A tracking time resource column vector for each target,
is shown as
During the second allocation period phased array radar is allocated to the second
The tracking time resources of the individual targets,
is shown as
Phased array radar allocation during sub-allocation
Total tracking time resources of the individual targets;
expression solution
The minimum value of (a) is determined,
representing normalized worst case
During the sub-distribution period
Tracking a Bayesian Claritrol lower bound convex function of each target; the first constraint indicates
Phased array radar allocation during sub-allocation
The total tracking time resource of each target is
And the second constraint denotes
The tracking time resources allocated to each target by the phased array radar during the secondary allocation are limited by a minimum value, i.e. the second
The tracking time resource allocated to each target by the phased array radar during the secondary allocation period is greater than or equal to 0; the normalized worst case first
During the sub-distribution period
Tracking Bayesian Claritrol lower bound convex function of each target
The expression is as follows:
wherein,
representation matrix
And Λ represents a standardized matrix, and shows that the elements of the bayesian cramer lower bound matrix are on different scales, and the expression is as follows:
wherein,
is shown as
During the sub-distribution period
A predicted Bayesian information matrix of the observed state of each target,
obtained by the following formula:
wherein,
is to show to
During the sub-distribution period
State vector of individual target
Is/are as follows
Dimensional non-linear distance and orientation measurement function
Is transferred to
With respect to state vectors
Δ represents the amount of change of the measured value,
is shown as
During the sub-distribution period
The state vector of the individual objects is,
is shown as
During the sub-distribution period
Of a single object
A matrix of the Wijacobi is formed,
it is shown that the set constant is,
show that
Value of
In (1),
to represent
Is given a value of
Calculating the value of the point; when in use
First 0 time during the dispensing
State vector of individual target
Is shown as
During the sub-distribution period
Process noise of individual target
The covariance matrix of (a) is determined,
is as follows
During the sub-distribution period
The transformation matrix of the individual objects is,
is shown as
Phased array radar allocation during sub-allocation
A tracking time resource column vector for each target,
is shown as
During the second allocation period phased array radar is allocated to the second
The tracking time resources of the individual targets,
is shown as
During the sub-distribution period
The remaining matrix of each object, superscript-1, represents the inversion,
representing a row vector transpose.
In particular, the capabilities of phased array radars present a significant challenge to radar resource managers, which must determine during each assignment whether the radar should search for new targets or track existing targets; under the ideal condition, the maximization of the searching capability and the multi-target tracking precision are two mutually conflicting targets and must be considered simultaneously; thus, first
The mathematical model of a dual target resource allocation scheme for phased array radar integrated SAT application during sub-allocation can be written as:
wherein,
showing obtained
And
at the same time make
And
the size of the particles is minimized and,
is shown as
Phased array radar allocation during sub-allocation
The total search time resources of the non-overlapping search sectors,
is shown as
Phased array radar allocation during sub-allocation
The total tracking time resources of the individual targets,
is shown as
Integrating the total time resources of phased array radar search and tracking applications during the secondary allocation; the last constraint is indicated in
The total resource of the integrated phased array radar search and tracking application during the sub-allocation is
Is shown as
The duty cycle during the sub-dispensing period,
is shown as
During the second allocation period phased array radar is allocated to the second
The search time resources of each search sector,
is shown as
During the second allocation period phased array radar is allocated to the second
The tracking time resources of the individual targets,
is shown as
The convex function during the sub-allocation period,
representing normalized worst case
During the sub-distribution period
The tracked Bayesian Clarithrome lower bound convex function of each target,
is shown as
Phased array radar allocation during sub-allocation
A search time column vector of non-overlapping search sectors,
is shown as
Phased array radar allocation during sub-allocation
A tracking time resource column vector for each target.
Will be first
Phased array radar allocation during sub-allocation
Search time column vector of non-overlapping search sectors
And a first
Phased array radar allocation during sub-allocation
Tracking time resource column vector of individual targets
Integrated into a single vector, denoted
Dimension vector
Representing a row vector transpose; further obtain the first
The mathematical optimization model of the dual-target resource allocation scheme during the secondary allocation period is as follows:
wherein,
is shown as
The convex function during the sub-allocation period,
representing normalized worst case
During the sub-distribution period
The tracked Bayesian Clarithrome lower bound convex function of each target,
is expressed as length of
And before
A row vector with 1 element and zero elements,
is expressed as length of
And from the second
Element to element
A row vector with 1 element and 0 elements,
representing row vectors
To middle
An element; the first constraint indicates
Phased array radar allocation during sub-allocation
The total search time resources of the non-overlapping search sectors are
First, the
Phased array radar allocation during sub-allocation
The total tracking time resource of each target is
The second constraint indicates
The searching time of each searching sector and the tracking time of each target in the secondary distribution period are both more than or equal to 0; the last constraint indicates
Phased array radar allocation during sub-allocation
Total search time resources for non-overlapping search sectors
And a first
Phased array radar allocation during sub-allocation
Total tracking time resource of each target
Is a sum of
The total time resource of the integrated phased array radar search and tracking application during the sub-allocation is
The substep of step 6 is:
6.1 in order to obtain pareto subsets (the solutions obtained by different overall search budget solutions (9) are mutually independent, and the solutions obtained by different overall tracking budget solution problems (10) are mutually independent); is set to
During the sub-distribution period
Total search budget and
an overall tracking budget, in this embodiment
From 1 st total search budget to
The total search budget satisfies:
wherein
Is shown as
During the sub-distribution period
Total search budget, will
During the sub-distribution period
Total tracking budget as
And the first
During the sub-distribution period
Total search budget
And a first
During the sub-distribution period
Total tracking budget
Satisfies the following conditions:
6.2 according to the first
During the sub-distribution period
Total search budget
And linear programming to solve equation (9)
During the sub-distribution period
Total search budget
Substituting the right side of the first constraint condition in the formula (9) to obtain the second constraint condition according to a linear programming method
Phased array radar allocation during sub-allocation
Search time vector pair of non-overlapping search sectors
Optimal solution for individual search budget resource allocation
According to the first
During the sub-distribution period
Total tracking budget
And maximum and minimum solution algorithm solving equation (10), i.e. the first
During the sub-distribution period
Total tracking budget
Substituting the right side of the first constraint condition in the step (10), and obtaining the second constraint condition according to a maximum and minimum solution algorithm
Phased array radar allocation during sub-allocation
Tracking time resource column vector pair of individual targets
Optimal solution for individual total tracking budget resource allocation
Subscript
Is shown as
Sub-distribution period, subscript
Denotes a search, subscript
Denotes trace, subscript
Representing an optimal solution; will be the first
Total searchOptimal solution for allocation of cable budget resources
And the said first
Optimal solution for individual total tracking budget resource allocation
Form two target resources
The second of the sub-distribution (equation (16))
Pareto optimal solution
(parallel minimization scheme) in which superscripts are applied
Second to indicate transposed, dual target resource allocation
Pareto optimal solution
Included
And (4) each element.
6.3 order
Are respectively 1 to
Repeatedly executing 6.2 until obtaining the second target resource
First pareto optimal solution of sub-distribution
To the two target resources
Second of the sub distribution
Pareto optimal solution
Is expressed as a base number
Pareto subsets of
Due to the fact that for the first
Any two different total search budgets during sub-allocation
And
upper label
Is shown as
Individual total search budget, superscript
Is shown as
The total search budget for the search is,
is shown as
During the sub-distribution period
The total search budget for the search is,
is shown as
During the sub-distribution period
Total search budget, of
During the sub-distribution period
Optimal solution for individual search budget resource allocation
And a first
During the sub-distribution period
Optimal solution for individual search budget resource allocation
Has the following relationship
Therefore, it is caused by
One of the total search budgets during the sub-allocation and the optimal solution sum of the search budget resource allocation
The proportional relationship between the total search budgets can be obtained
The total search budget is related to the solution of equation (9) respectively.
According to the cardinality of
Pareto subsets of
The calculation base is
Pareto subsets of
The function value of each optimal solution in the system is defined as the base number
Pareto subsets of
The function value of each optimal solution is respectively marked as a pareto point, and then the second solution is obtained
Pareto point set of time-controlled array radar for sub-distribution
(just before calculation)
One element), a represents an intermediate variable,
is shown as
Time phased array radar in sub-distribution
Search sector
Is calculated from the target distance of (a) to the target distance search value,
is shown as
Time-controlled array radar scanned by sub-distribution
Search sector
The angle of (a) is determined,
is shown as
During the sub-distribution period
A set of non-overlapping search sector numbers,
is shown as
Sub-distribution phase-controlled array radar 1 st pareto optimal solution
The function value of (a) is determined,
is shown as
Time phased array radar with sub-distribution
Pareto optimal solution
The function value of (a) is determined,
is shown as
Time phased array radar with sub-distribution
Pareto optimal solution
The function value of (1).
By using the first
During the sub-distribution periodConvex function of
Monotonicity of, i.e.
Indicating two target resources
Sub-assigned [ gamma ] pareto optimal solution
The function value of (a) is determined,
indicating two target resources
Pareto optimal solution of the beta of the sub-distribution
The function value of (a) is determined,
is shown as
The optimal solution for the beta total search budget resource allocation during the secondary allocation,
represents the optimal solution for the beta total tracking budget resource allocation,
is shown as
The optimal solution for the gamma th overall search budget resource allocation during the sub-allocation,
an optimal solution representing the gamma total tracking budget resource allocation; the upper level t represents the transpose,
is shown as
During the sub-distribution period
The worst-case search signal-to-noise ratio in the non-overlapping search sectors,
and
are the function values of two adjacent pareto optimal solutions.
From two pareto optimal solutions
And
two total search budgets can be derived
And
is shown as
The beta total search budget during the secondary allocation period is the second of the dual target resources
Pareto optimal solution of the beta of the sub-distribution
Middle front
A cumulative sum of the elements;
is shown as
The gamma total search budget during the sub-allocation period is the second of the dual target resources
Sub-assigned [ gamma ] pareto optimal solution
Middle front
A cumulative sum of the elements; budget for two total searches
And
using a dichotomy to obtain
Phased array radar allocation during sub-allocation
Maximum of non-overlapping search sectorsOptimal total search time resources
And a first
Phased array radar allocation during sub-allocation
Optimal total tracking time resource of each target
The optimal total search time resource
Substitute into
Searching the conversion objective function of the resource allocation scheme during the sub-allocation period, and solving by using a linear programming method to obtain the second
Phased array radar allocation during sub-allocation
Optimal search time resources for non-overlapping search sectors
The optimal total tracking time resource
Substitute into
Tracking the target standard function of the resource allocation scheme during the sub-allocation period, and obtaining the first time by utilizing a minimum maximum solution algorithm
Phased array radar allocation during sub-allocation
Tracking time resource column vector optimal solution of each target
Wherein,
is the first
The optimal search resource allocation result during the sub-allocation,
is the first
Optimal target tracking resource allocation results during sub-allocation, the first
Phased array radar allocation during sub-allocation
Optimal total search time resources for non-overlapping search sectors
And the said first
Phased array radar allocation during sub-allocation
Optimal total tracking time resource of each target
As a sum of
Total time resources for integrated phased array radar search and tracking applications during sub-allocation
The method comprises the following specific steps:
6a) separately setting iteration indexes
And a stop threshold ε of 10-3And is provided with
Searching for lower bounds of resources during secondary allocation
And a first
Searching for upper bounds of resources during secondary allocation
Is shown as
The beta total search budget during the secondary allocation,
is shown as
A gamma total search budget during the secondary allocation; wherein, gamma is beta +1,
is shown as
The total search budget number or the total tracking budget number set in the secondary allocation period.
6b) According to the first
Searching for lower bounds of resources during secondary allocation
And a first
Searching for upper bounds of resources during secondary allocation
Calculate the first
After the second iteration
Total search resources for phased array radar during secondary allocation
Then use the first
After the second iteration
Total search resources for phased array radar during secondary allocation
And linear programming method to solve
Searching resource allocation during secondary allocationConverting the objective function of the scheme to obtain
After the second iteration
Phased array radar allocation during sub-allocation
Search time column vector optimal solution for non-overlapping search sectors
6c) If it is not
Updating
Order to
Add 1 to the value of (6 b); otherwise 6d) is executed.
6d) If it is not
Updating
Order to
Add 1 to the value of (6 b); otherwise 6e) is executed.
6e) If it is not
Get
Search for the optimal solution for resource allocation as
Is shown as
Phased array radar allocation during sub-allocation
The optimal search time resources of the non-overlapping search sectors,
is shown as
After the second iteration
Phased array radar allocation during sub-allocation
The search time vector optimal solution of the non-overlapping search sectors.
6f) Calculate the first
Phased array radar allocation during sub-allocation
Optimal total tracking time resource of each target
Wherein,
is shown as
The total resources of the integrated phased array radar search and tracking application during the sub-allocation,
is shown as
The duty cycle during the sub-dispensing period,
indicating the duration of each dispensing period, in this embodiment
6g) The optimal total tracking time resource
Substitute into
Tracking the target standard function of the resource allocation scheme during the sub-allocation period, and obtaining the first time by utilizing a minimum maximum solution algorithm
Phased array radar allocation during sub-allocation
Tracking time resource column vector optimal solution of each target
Step 7, let
Adds 1 to the value of (1), returns to step 2 until the phased array radar assignment during the 1 st assignment is obtained
Of non-overlapping search sectorsOptimal search time resource
To the first
Phased array radar allocation during sub-allocation
Optimal search time resources for non-overlapping search sectors
And phased array radar assignment during the 1 st assignment
Tracking time resource column vector optimal solution of each target
To the first
Phased array radar allocation during sub-allocation
Tracking time resource column vector optimal solution of each target
Recording as a resource allocation result based on phased array radar searching and tracking dual-target optimization; this example is to get
The invention makes a resource allocation scheme into a dual-target optimization framework, and obtains a cardinal number of the resource allocation scheme according to a parallel minimization scheme
Pareto subsets of (a); then using linear programmingThe method and the minimum and maximum solution algorithm effectively solve the problem of dual-target resource allocation.
The effects of the present invention are further verified and explained by the following simulations.
1. Simulation parameters:
the fixed position of the phased array radar is (93,45) km, and the effective signal bandwidth and the half-power beam width are respectively set to be
And
the total time resource is
The simulation was performed using a 20 dispense period, with the duration of each dispense being set to
In practice, phased array radars may have different search requirements. Thus, two types of search models are considered
And
to describe two different search requirements, see tables I and II for details, Table I is a model
Table II is a model of the search parameters for each sector in
Of the search parameter per sector.
The first 10 dispensing periods
Phased array radar adopts a first search model
Wherein the number of sectors is set to
During the last 10 dispensing sessions
The phased array radar adopts a second search model
The number of sectors is
TABLE I
| |
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
| |
1 | 2 | 3 | 4 | 5 | 6 |
| Ri,k(km) | 240 | 240 | 240 | 300 | 200 | 300 |
| θi,k(○) | 8 | 8 | 16 | 8 | 8 | 8 |
In the simulation, the number of targets to be tracked is set to
Each target state parameter is given in table III.
TABLE III
| |
1 | 2 | 3 | 4 | 5 |
| Location (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 |
| |
2 | 0.8 | 1.5 | 1 | 1 |
Referring to fig. 3, a schematic diagram of target deployment in a detection range of a phased array radar; figure 3 shows the angular distribution of these targets with respect to the radar system.
To obtain a base number of
The pareto sub-set of (a),
individual search time budget setting
For a given
Denotes a reference solution (solution of the resource equal allocation scheme) in which
Is shown as having
A vector of all 1 columns of the elements,
is shown as
During the sub-distribution period
The total resource budget is solved by a resource equal allocation scheme,
is shown as
During the sub-distribution period
The total search resource budget is a solution to the search resource even allocation scheme,
is shown as
During the sub-distribution period
The total tracking resource budget adopts the solution of the tracking resource average allocation scheme, and the reference set is
The objective function value of each reference solution is called the reference result, the curve formed by the reference results is called the reference curve, and the same pareto subset
The objective function value of each pareto solution is called a pareto result, and a curve formed by the pareto results is called a pareto curve.
2. Simulation content:
the invention aims at the resource average allocation scheme and the allocation result of the dual-target optimization resource allocation scheme based on the pareto theory to compare simulation experiments.
3. And (3) simulation result analysis:
the results of FIG. 4(a) show that the demand model was searched
For the worst case search signal-to-noise ratio and the worst case tracking bayesian cramer lower bound, the pareto curve is significantly better than the reference curve; the results of FIG. 4(b) show that the demand model was searched
For the worst case search signal-to-noise ratio and the worst case lower bound of the Bayesian-Cramer-Role boundary, PaThe cumulative-over curve is obviously superior to the reference curve; with the pareto curve, the best search and tracking performance can be easily obtained using the dichotomy for any mission requirements.
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the method.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (7)
1. A resource allocation method based on phased array radar searching and tracking dual-target optimization is characterized by comprising the following steps:
step 1, initialization: order to
Is as follows
The number of the sub-distribution is equal to the number of the sub-distribution,
is set to an initial value of 1,
an even number greater than 0; is set to
Search area existence of time-controlled array radar in sub-distribution
An object, and
time control of sub-distributionThe search area of the array radar is divided into
A plurality of non-overlapping search sectors;
step 2, determining
Time phased array radar in sub-distribution
Search model and method for searching sector
During the sub-distribution period
A tracking model of the individual target; wherein,
is shown as
Distributing the number of targets in a search area of the time-controlled array radar in a secondary mode;
is shown as
The time-controlled array radar searches the total number of sectors in the time distribution;
step 3, according to
Time phased array radar in sub-distribution
A search model of the search sector, get
Searching for objective function and second order of resource allocation scheme during secondary allocation
Searching a conversion objective function of the resource allocation scheme during the secondary allocation period;
step 4, according to
During the sub-distribution period
A tracking model of the object, determining
Tracking a target standard function of a resource allocation scheme during the secondary allocation;
step 5, according to
Search for transfer objective function and the second of resource allocation scheme during sub-allocation
Tracking a target criteria function of the resource allocation scheme during the sub-allocation period to obtain a second
A mathematical optimization model of a dual target resource allocation scheme during secondary allocation;
step 6, solving
The mathematical optimization model of the double-target resource allocation scheme in the secondary allocation period respectively obtains
Phased array radar allocation during sub-allocation
Optimal search time resources for non-overlapping search sectors
And a first
Phased array radar allocation during sub-allocation
Tracking time resource column vector optimal solution of each target
Step 7, let
Adds 1 to the value of (1), returns to step 2 until the phased array radar assignment during the 1 st assignment is obtained
Optimal search time resources for non-overlapping search sectors
To the first
Phased array radar allocation during sub-allocation
Optimal search time for non-overlapping search sectors(Resource)
And phased array radar assignment during the 1 st assignment
Tracking time resource column vector optimal solution of each target
To the first
Phased array radar allocation during sub-allocation
Tracking time resource column vector optimal solution of each target
And recording the resource allocation result as a resource allocation result based on dual target searching and tracking of the phased array radar.
2. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 2, the first step
Time phased array radar in sub-distribution
The search model for each search sector is:
wherein, alpha represents an intermediate variable,
is shown as
Time-controlled array radar allocation to the second
Search sector
The time resources of the search of (2),
is shown as
Time phased array radar in sub-distribution
Search sector
The target search signal-to-noise ratio of (c),
represents the average transmit power of the phased array radar,
indicating the set effective receive aperture of the phased array radar antenna,
is shown as
Time phased array radar in sub-distribution
Search sector
The cross-sectional area of scattering of the target,
which represents the boltzmann constant, represents,
indicating the set phased array radar temperature,
the loss of the phased array radar is shown,
is shown as
Time-controlled array radar scanned by sub-distribution
Search sector
The angle of (a) is determined,
is shown as
Time phased array radar in sub-distribution
Search sector
The target distance search value of (1);
the first mentioned
During the sub-distribution period
The tracking model of each target is as follows:
wherein,
is shown as
During the sub-distribution period
The process noise of the individual target is,
is shown as
During the sub-distribution period
The state vector of the individual objects is,
is as follows
During the sub-distribution period
The transformation matrix of the individual objects is,
the expression of the kronecker operator,
representing a 2 x 2 dimensional identity matrix,
indicating the duration of each dispense.
3. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 3, the first step
The objective function of searching the resource allocation scheme during the secondary allocation is:
wherein,
is shown as
During the sub-distribution period
A set of non-overlapping search sector numbers,
a constraint condition is expressed in terms of the number of the elements,
is shown as
Phased array radar allocation during sub-allocation
The total search time resources of the non-overlapping search sectors,
is shown as
During the second allocation period phased array radar is allocated to the second
The search time resources of each search sector,
is shown as
Time phased array radar in sub-distribution
Search sector
The target search signal-to-noise ratio of (c),
is shown as
Phased array radar allocation during sub-allocation
A search time column vector of non-overlapping search sectors,
upper label
The transpose is represented by,
the first mentioned
The transfer objective function for searching the resource allocation scheme during the secondary allocation is:
wherein,
is shown as
The convex function during the sub-allocation period,
is shown as
Search sector 1 to search sector 1 during sub-allocation
The accumulated sum of the search time resources of each search sector, wherein alpha represents an intermediate variable;
is shown as
Time phased array radar in sub-distribution
Search sector
Is calculated from the target distance of (a) to the target distance search value,
is shown as
Time-controlled array radar scanned by sub-distribution
Search sector
The angle of (d);
representation calculation
The minimum value of (a) is determined,
representing a set of computations
Ratio of each search sector in the search
Then obtain
A ratio is then compared
The ratio value is then used to select the maximum value operation.
4. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 4, the first step
The objective criteria function for tracking the resource allocation scheme during the secondary allocation is:
wherein,
is shown as
During the sub-distribution period
A set of object numbers, each object number being,
is shown as
Phased array radar allocation during sub-allocation
A tracking time resource column vector for each target,
upper label
The transpose is represented by,
is shown as
During the second allocation period phased array radar is allocated to the second
The tracking time resources of the individual targets,
is shown as
Phased array radar allocation during sub-allocation
Total tracking time resources of the individual targets;
expression solution
The minimum value of (a) is determined,
representing normalized worst case
During the sub-distribution period
And tracking a Bayesian Claritrol Laurve lower bound convex function of each target.
5. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 5, the first step
The mathematical optimization model of the double-target resource allocation scheme during the secondary allocation period comprises the following processes:
firstly, first, the
The mathematical model of the dual target resource allocation scheme during the secondary allocation is represented as:
wherein,
showing obtained
And
at the same time make
And
the size of the particles is minimized and,
is shown as
Phased array radar allocation during sub-allocation
The total search time resources of the non-overlapping search sectors,
is shown as
Phased array radar allocation during sub-allocation
The total tracking time resources of the individual targets,
is shown as
The total time resources of the integrated phased array radar search and tracking application during the sub-allocation,
is shown as
The duty cycle during the sub-dispensing period,
is shown as
During the second allocation period phased array radar is allocated to the second
The search time resources of each search sector,
is shown as
During the second allocation period phased array radar is allocated to the second
The tracking time resources of the individual targets,
is shown as
The convex function during the sub-allocation period,
representing normalized worst case
During the sub-distribution period
The tracked Bayesian Clarithrome lower bound convex function of each target,
is shown as
Is divided into sub-divisionsAllocation of phased array radar to allocation periods
A search time column vector of non-overlapping search sectors,
is shown as
Phased array radar allocation during sub-allocation
A tracking time resource column vector for each target;
then it will be
Phased array radar allocation during sub-allocation
Search time vector of non-overlapping search sectors
And a first
Phased array radar allocation during sub-allocation
Tracking time resource column vector of individual targets
Integrated into a single vector, denoted
Dimension vector
Representing a row vector transpose; thereby obtaining the first
The mathematical optimization model of the dual-target resource allocation scheme during the secondary allocation period is as follows:
wherein,
is shown as
The convex function during the sub-allocation period,
representing normalized worst case
During the sub-distribution period
The tracked Bayesian Clarithrome lower bound convex function of each target,
is expressed as length of
And before
A row vector with 1 element and zero elements,
is expressed as length of
And from the second
Element to element
A row vector with 1 element and 0 elements,
representing row vectors
To middle
The number of the elements is one,
is shown as
The total time resources of the phased array radar search and tracking application are integrated during the secondary allocation.
6. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 6, the first step
Phased array radar allocation during sub-allocation
Optimal search time resources for non-overlapping search sectors
And a first
Phased array radar allocation during sub-allocation
Tracking time resource column vector optimal solution of each target
The obtaining process comprises the following steps:
6a) separately setting iteration indexes
And a stop threshold epsilon, and setting
Searching for lower bounds of resources during secondary allocation
And a first
Searching for upper bounds of resources during secondary allocation
Is shown as
The beta total search budget during the secondary allocation,
is shown as
A gamma total search budget during the secondary allocation; wherein, gamma is beta +1,
is shown as
The total search budget number or the total tracking budget number set in the secondary allocation period;
6b) according to the first
Searching for lower bounds of resources during secondary allocation
And a first
Searching for upper bounds of resources during secondary allocation
Calculate the first
After the second iteration
Total search resources for phased array radar during secondary allocation
Then use the first
After the second iteration
Total search resources for phased array radar during secondary allocation
And linear programming method to solve
Searching a conversion objective function of the resource allocation scheme during the sub-allocation period to obtain a first step
After the second iteration
Phased array radar allocation during sub-allocation
Search time column vector optimal solution for non-overlapping search sectors
6c) If it is not
Updating
Order to
Add 1 to the value of (6 b); otherwise 6d) is executed,
is shown as
After the second iteration
Phased array radar allocation during sub-allocation
Function values of the search time vector optimal solution of the non-overlapping search sectors;
is shown as
During the sub-distribution period
Worst case search signal-to-noise ratios in non-overlapping search sectors; a represents an intermediate variable which is,
is shown as
Time phased array radar in sub-distribution
Search sector
Is calculated from the target distance of (a) to the target distance search value,
is shown as
Time-controlled array radar scanned by sub-distribution
Search sector
The angle of (d);
6d) if it is not
Updating
Order to
Add 1 to the value of (6 b); otherwise 6e) is executed;
6e) if it is not
Get
Search for the optimal solution for resource allocation as
Is shown as
Phased array radar allocation during sub-allocation
The optimal search time resources of the non-overlapping search sectors,
is shown as
After the second iteration
Phased array radar allocation during sub-allocation
Search time vector optimal solutions of non-overlapping search sectors;
6f) calculate the first
Phased array radar allocation during sub-allocation
Optimal total tracking time resource of each target
Wherein,
is shown as
The total resources of the integrated phased array radar search and tracking application during the sub-allocation,
is shown as
The duty cycle during the sub-dispensing period,
indicating the duration of each dispensing period;
6g) tracking time resources according to the optimal total tracking time resources
And minimum maximum solution method
Tracking a target criteria function of the resource allocation scheme during the sub-allocation period to obtain a second
Phased array radar allocation during sub-allocation
Tracking time resource column vector optimal solution of each target
7. The method for resource allocation based on dual target optimization for phased array radar search and tracking according to claim 6, wherein in 6(a), the method comprises
Is shown as
Beta total search budget during secondary allocation and the
Is shown as
A γ th total search budget during the secondary allocation, further comprising:
the two target resources are treated as
Second of the sub distribution
The pareto optimal solution is recorded as
The obtaining process comprises the following steps:
6.1 setting of
Sub-distribution periodThere is a
Total search budget and
total tracking budget from 1 st total search budget to
The total search budget satisfies:
wherein
Is shown as
During the sub-distribution period
Total search budget, will
During the sub-distribution period
Total tracking budget as
And the first
During the sub-distribution period
Total search budget
And a first
During the sub-distribution period
Total tracking budget
Satisfies the following conditions:
6.2 according to the first
During the sub-distribution period
Total search budget
And linear programming method to solve
Searching a conversion objective function of the resource allocation scheme during the sub-allocation period to obtain a first step
Phased array radar allocation during sub-allocation
Search time vector pair of non-overlapping search sectors
Optimal solution for individual search budget resource allocation
According to the first
During the sub-distribution period
Total tracking budget
And maximum and minimum solution algorithm solving
Tracking a target criteria function of the resource allocation scheme during the sub-allocation period to obtain a second
Phased array radar allocation during sub-allocation
Tracking time resource column vector pair of individual targets
Optimal solution for individual total tracking budget resource allocation
Will be the first
Optimal solution for individual search budget resource allocation
And the said first
Optimal solution for individual total tracking budget resource allocation
Form two target resources
Second of the sub distribution
Pareto optimal solution
Upper label
Second to indicate transposed, dual target resource allocation
Pareto optimal solution
Included
And (4) each element.
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