CN115561748A - Networked radar target search tracking resource allocation method based on radio frequency stealth - Google Patents
Networked radar target search tracking resource allocation method based on radio frequency stealth Download PDFInfo
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The invention discloses a networked radar target searching and tracking resource allocation method based on radio frequency stealth, which comprises the following steps: considering a networked radar consisting of a plurality of synchronous phased array radars, searching a plurality of circular key observation areas and tracking a known number of moving targets need to be completed simultaneously; constructing a search scene of a networked radar for a plurality of circular key observation areas, and adopting detection probability as a measurement index of search performance; constructing a multi-target tracking scene of the networked radar, and adopting a predicted Bayesian-Lame lower bound of target position estimation as a measurement index of multi-target tracking performance; establishing a networked radar search tracking resource allocation model based on radio frequency stealth; and solving the optimization model by adopting a two-step solving algorithm of an interior point method and a cyclic minimum method to realize resource optimization allocation. The invention improves the radio frequency stealth performance of the networked radar when the networked radar executes multi-airspace searching and multi-target tracking tasks.
Description
Technical Field
The invention relates to a radar signal processing technology, in particular to a networked radar target searching and tracking resource allocation method based on radio frequency stealth.
Background
Radars were originally used for target detection and positioning measurements, and as technology has advanced and the demand for radar capability has increased, the functions of radars have become increasingly diverse. The phased array radar has the characteristics of no inertial scanning of wave beams, strong anti-interference capability and the like, and is widely applied to the military field, particularly two key tasks of searching and tracking a target. Compared with the traditional single-station radar, the networked radar can extract the characteristic information of the target from multiple visual angles and multiple dimensions, the purposes of improving the resolution, reducing interference errors and the like are achieved through information fusion, and the performances of radar target searching and tracking and the like are further improved. Thus, techniques for networked radar resource allocation are involved. How to improve the performance of the networked radar by allocating different radiation resources of different radars becomes the research content of a plurality of scholars.
However, if the radar intercepts the signals transmitted to the space while performing the task, the radar is at risk of being attacked. Therefore, the improvement of radio frequency stealth performance also becomes an urgent need in the battle process. The radio frequency stealth technology is a technology for actively intercepting, sorting and identifying a radio frequency device radiation signal by an anti-enemy passive detection system, and the radio frequency stealth performance of the radio frequency device is required to be considered while the performance of a radar is optimized by using limited radio frequency radiation resources, so that the radiation resource consumption is reduced.
Although most of the existing research results are optimized in the aspects of radar node selection and resource allocation, the multi-target tracking accuracy of the networked radar or the radio-frequency stealth performance is improved to a certain extent. However, these studies do not consider the problem of node selection and resource allocation of radar when multiple tasks coexist, and have certain limitations.
At present, no public report in the aspect of searching and tracking resource allocation of a networked radar target based on radio frequency stealth exists.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a networked radar target searching and tracking resource allocation method based on radio frequency stealth, which considers the scene of the common multitask implementation of the networked radar, can perform joint optimization on parameters such as radar node selection, radiation power and residence time of each radar and the like under the condition of meeting certain target searching performance and multi-target tracking performance, effectively reduces the total radio frequency radiation resource consumption and improves the radio frequency stealth performance of the networked radar.
The technical scheme is as follows: the invention discloses a networked radar target searching and tracking resource allocation method based on radio frequency stealth, which comprises the following steps of:
establishing a system model: considering a networked radar consisting of a plurality of synchronous phased array radars, searching a plurality of circular key observation areas and tracking a known number of moving targets need to be completed simultaneously; the priority of the multi-target tracking task is higher than that of the target searching task, and each phased array radar can only generate one wave beam at each moment;
constructing a search scene of a networked radar for a plurality of circular key observation areas, and adopting detection probability as a measurement index of search performance;
constructing a multi-target tracking scene of the networked radar, and adopting a predicted Bayesian-Lame lower bound of target position estimation as a measurement index of multi-target tracking performance;
under the condition of meeting preset searching and multi-target tracking performance and radio frequency resource constraint, taking the total radio frequency resource consumption of the minimized networked radar as an optimization target, and taking a radar node selection mode, radiation power and residence time as optimization parameters, and establishing a radio frequency stealth-based networked radar searching and tracking resource allocation model;
the model is decomposed into two sub-optimization models, the two sub-optimization models are solved by adopting a two-step solving algorithm of an interior point method and a circular minimum method, and node selection, radiation power and residence time resource allocation during networked radar searching and multi-target tracking are jointly optimized under the constraints of searching and tracking performance and radio frequency resources.
Further, a networked radar is constructed to search scenes of a plurality of circular key observation areas, and detection probability is used as a measurement index of search performance, and the method specifically comprises the following steps:
in a networked radar consisting of N radars, M S The partial radar is used for executing a search task on A circular key observation areas; a single radar can only illuminate one area at a time, and each area needs to be simultaneously L S Searching by a radar; detection probability obtained by scanning the observation area a for n times by radar i at moment k
Comprises the following steps:
wherein, a =1,2, …, A, P fa In order to be the probability of a false alarm,
the echo signal-to-noise ratio which can be obtained after the radar i irradiates the target when searching the key observation area a at the moment k;
has L S The partial radar is used for searching the key observation area a, and the detection probability of the networked radar at the moment k on the target in the circular key observation area a is represented as follows:
further, the measurement indexes of the multi-target tracking performance are as follows:
wherein, the first and the second end of the pipe are connected with each other,
predicting a Bayesian Classmei-Rou lower bound matrix for the target state estimation error, wherein the expression is as follows:
wherein the content of the first and second substances,
a Bayesian information matrix representing the state of the target at time k-1,
a Bayesian information matrix representing a target prediction state at the moment k;
a Jacobian matrix representing the target prediction state at the time k;
representing a covariance matrix of target measurement errors at the moment k; superscript (·) -1 An inverse matrix representing a matrix; superscript (·) T Represents a transpose of a matrix; q q A covariance matrix representing white gaussian process noise with a mean of zero; f represents a state transition matrix; n represents the number of radars in the networked radar;
indicating whether the radar i irradiates the target q at the time k.
Further, the networked radar search and tracking resource allocation model based on radio frequency stealth is as follows:
wherein E is tot,k Representing the total radio frequency resource consumption; u. of k ＝[u S,k ,u T,k ] T Indicating the networked radar node selection mode at the time k,
the node selection mode of searching the key observation area a is shown,
represents a networked radar search node selection mode,
represents a node selection manner of the tracking target q,
representing a networked radar tracking node selection mode; p k ＝[P S,k ,P T,k ] T And T k ＝[T S,k ,T T,k ] T Respectively representing the radiation power and residence time resource allocation of the networked radar at the moment k;
the detection probability of the networked radar to the target in the key observation area a at the moment k is shown;
representing a measurement index representing the tracking precision of the target; p is a radical of d,min And
respectively meeting the requirements of target searching performance and multi-target tracking precision; for search tasks, P S,max And P S,min Respectively representing the upper and lower limits of the search radiation power, T S,max And T S,min Respectively representing the upper limit and the lower limit of the search beam residence time;
indicating mineThe radiation power when the key observation area a is searched by the radar;
representing the beam residence time when the radar i searches for the key observation area a; for trace tasks, P T,max And P T,min Respectively representing the upper and lower limits of the tracking radiation power, T T,max And T T,min Respectively representing the upper limit and the lower limit of the residence time of the tracking wave beam;
and
respectively determining the radiation power and the residence time of the radar i at the moment k for irradiating the target q once; l is S Representing the number of radars searching the same circular key observation area at the same time; a represents the number of circular key observation areas; m is a group of S Representing the number of radars for performing a search task on a circular key observation regions;
whether the radar i at the moment k is selected or not is shown, and a key observation area a is searched;
indicating whether the radar i irradiates the target q at the moment k; l is T Representing the number of radars required to illuminate the same target simultaneously; q represents the number of moving objects; m is a group of T Representing a number of radars for performing tracking tasks on a plurality of targets; 1 N×1 Representing an N x 1 dimensional full 1 matrix.
Further, total radio resource consumption E tot,k Defined as the sum of the search and tracking radio frequency resource consumption, expressed as:
wherein, E S,k Indicating the consumption of the search radio frequency resources,E T,k representing tracking radio frequency resource consumption; alpha is alpha 1 And alpha 2 Weight coefficients representing radiation power and dwell time, respectively.
Further, the two sub-optimization models of the decomposition are:
and
wherein E is S,k Indicating search radio frequency resource consumption, E T,k Representing tracking radio frequency resource consumption;
node selection mode u representing search key observation area a S,k Represents a networked radar search node selection mode,
means for indicating the node selection of the tracking target q, u T,k Representing a networked radar tracking node selection mode;
the detection probability of the networked radar to the target in the key observation area a at the moment k is shown;
representing a measurement index representing the tracking precision of the target; p is a radical of d,min And
respectively meeting the requirements of target searching performance and multi-target tracking precision; for search tasks, P S,max And P S,min Respectively representing the upper and lower limits of the search radiation power, T S,max And T S,min Respectively representing search beam dwell timesA lower limit;
representing the radiation power when the radar i searches for the key observation area a;
representing the beam residence time when the radar i searches for the key observation area a; for trace tasks, P T,max And P T,min Respectively representing the upper and lower limits of the tracking radiation power, T T,max And T T,min Respectively representing the upper limit and the lower limit of the residence time of the tracking wave beam;
and
respectively determining the radiation power and the residence time of the radar i at the moment k for irradiating the target q once; l is a radical of an alcohol S Representing the number of radars searching the same circular key observation area at the same time; a represents the number of circular key observation areas; m S Representing the number of radars for performing a search task on a circular key observation regions;
whether the radar i at the moment k is selected or not is shown, and a key observation area a is searched;
indicating whether the radar i irradiates the target q at the moment k; l is T Representing the number of radars required to illuminate the same target simultaneously; q represents the number of moving objects; m T Representing a number of radars for performing tracking tasks on a plurality of targets; 1 N×1 An all-1 matrix representing N × 1 dimensions;
will be provided with
And
are respectively relaxed to
And
further, a method for solving the two sub-optimization models by adopting a two-step solving algorithm of an interior point method and a cyclic minimum method comprises the following steps:
(1) Tracking node selection and resource allocation;
(a) Initializing a prediction Bayesian information matrix of k time to a target q
(b) Allocating initial tracking radiation power and tracking residence time for each radar node;
(c) Continuous variable obtained after relaxation
The contribution degree of the radar i tracking target q at the moment k is regarded as the contribution degree; by optimizing the variable u in the case of current resource allocation T,k Minimizing the tracking error to the target q; solving the sub-optimization model by adopting an interior point method:
obtaining the contribution degree of each radar tracking the target q under the current resource allocation
Selecting the largest L T The radar corresponding to each element irradiates a target q, namely, the L which has the maximum contribution to a tracking target q is selected T A radar;
(d) Selection of nodes obtained in step (c)
Foundation of (2)In the above, under the constraints of target tracking precision and radio frequency resources, the radiation power and residence time of the corresponding radar are optimized in a combined manner, so that the total radio frequency resource consumption is minimized; solving the sub-optimization model by adopting an interior point method:
deriving trace resource allocation result P T,k,0 And T T,k,0 Substituting the result into the step (b) as a new resource allocation scheme and skipping to the step (b) until the difference between the total tracking radio frequency resource consumption calculated in two adjacent times is smaller than a preset value; corresponding to the radar to which the tracking target q is finally assigned
Setting 1 and setting 0 for the rest to obtain k moment tracking node selection and resource allocation results;
(2) Searching node selection and resource allocation;
(a) After the selection of the tracking nodes is determined, the nodes for multi-airspace search tasks are selected from the rest radar nodes, and initial search resources are distributed to the rest radars;
(b) Continuous variable obtained after relaxation
The contribution degree of the radar i at the moment k to the effect of the search key observation area a is regarded as; optimizing search node selection variable u under current resource allocation S,k Maximizing the target detection probability; solving the sub-optimization model:
obtaining the contribution degree of each radar to the target detection probability in the gravity observation area a under the current resource allocation, and selecting the L with the maximum corresponding contribution S Searching a key observation area a by the partial radar;
(c) Under the current node selection, the radiation power and the residence time of the corresponding radar are optimized in a combined mode, and the aim of minimizing the total radio frequency resource consumption is taken as an optimization target; solving the sub-optimization model:
after obtaining the search resource allocation result, jumping to the step (a), updating the initial search resource allocation scheme until the difference value between the total search radio frequency resource consumption obtained in two adjacent times is smaller than a preset value; corresponding to the radar finally assigned to search the key observation area a
And setting 1 and setting 0 for the rest, thus obtaining the search node selection and resource allocation result at the moment k.
The invention discloses a networked radar target searching and tracking resource distribution system based on radio frequency stealth, which comprises:
the system modeling module is used for establishing a networked radar consisting of a plurality of synchronous phased array radars, and the networked radar needs to complete the search of a plurality of circular key observation areas and the tracking of a known number of moving targets at the same time;
the measurement index calculation module is used for searching scenes for a plurality of circular key observation areas based on the networked radar and calculating the detection probability of the networked radar on the target in the circular key observation areas as the measurement index of the search performance; calculating a predicted Bayesian-Rous lower bound of target position estimation as a measurement index of multi-target tracking performance based on a networked radar to a multi-target tracking scene;
the optimization model building module is used for building a networked radar search and tracking resource distribution model based on radio frequency stealth by taking the total radio frequency resource consumption of the minimized networked radar as an optimization target and taking a radar node selection mode, radiation power and residence time as optimization parameters under the condition of meeting preset search and multi-target tracking performance and radio frequency resource constraint;
and the optimization model solving module is used for decomposing the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models and solving the two sub-optimization models by adopting a two-step solving algorithm of an interior point method and a cyclic minimum method.
An apparatus of the present invention includes a memory and a processor, wherein:
a memory for storing a computer program capable of running on the processor;
and the processor is used for executing the steps of the networked radar target searching and tracking resource allocation method based on radio frequency stealth when the computer program is run.
A storage medium of the present invention stores thereon a computer program, which when executed by at least one processor implements the steps of the above-mentioned radio frequency stealth-based networked radar target search tracking resource allocation method.
Has the advantages that: compared with the prior art, the invention has the remarkable technical effects that: by jointly optimizing parameters such as radar node selection, radiation power, residence time and the like when multi-airspace searching and multi-target tracking tasks coexist, the total radio frequency resource consumption of the networked radar is reduced to the maximum extent under the condition of simultaneously meeting the preset requirements of target searching and multi-target tracking performance, and the radio frequency stealth performance of the networked radar is improved. The reason for the advantage is that the target detection probability and the prediction Bayesian-Luo Xiajie which take the radar node selection binary variable, the radar radiation power and the residence time as independent variables are deduced and are respectively used as indexes for measuring the target searching performance and the multi-target tracking performance; on the basis, limited radio frequency radiation resources of the networked radar, preset detection probability of targets in each airspace and tracking precision requirements of each moving target are taken as constraint conditions, the total radio frequency radiation consumption of the networked radar is minimized as an optimization target, and parameters such as radar node selection, each radar radiation power and residence time are jointly optimized. The method can effectively improve the radio frequency stealth performance of the networked radar during multi-target tracking under the condition of simultaneously meeting the requirements of searching and tracking performance.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Aiming at a networked radar which consists of a plurality of time-synchronized phased array radars and needs to complete multi-region searching and multi-target tracking tasks at the same time, parameters such as radar node selection, radiation power, residence time and the like are adaptively and jointly optimized under the condition of meeting preset target detection probability, multi-target prediction tracking precision and networked radar emission resource constraint, the total radio frequency resource consumption of the networked radar is minimized, searching and tracking models are respectively constructed, the target detection probability with radar node selection binary variables, each radar radiation power and residence time as arguments and the prediction Bayesian-Luo Xiajie are deduced and are respectively used as indexes for measuring the target searching performance and the multi-target tracking performance. Using preset target searching performance, multi-target tracking performance and limited radio frequency resources as constraint conditions, and using radar node selection scheme u k Each radar radiation power P k And a residence time T k In order to optimize variables, a mathematical model for searching and tracking the resource allocation of the networked radar target based on radio frequency stealth is established by taking the total radio frequency resource consumption of the minimized networked radar as an optimization target. And a two-step solving algorithm based on an interior point method and a cyclic minimum method is provided to solve the optimization model, and the radio frequency stealth performance of the networked radar is improved when search and tracking tasks coexist under the condition of ensuring the preset search and tracking performance.
The invention provides a method for distributing target searching and tracking resources of a networked radar based on radio frequency stealth, which is based on practical engineering application requirements, takes limited radio frequency radiation resources and preset target searching performance and multi-target tracking performance as constraints, takes the total radio frequency resource consumption of the networked radar as an optimized target, and improves the radio frequency stealth performance of the networked radar when executing target searching and tracking tasks by jointly optimizing parameters such as radar selection, radar radiation power, residence time and the like.
As shown in fig. 1, the method for allocating resources for searching and tracking a networked radar target based on radio frequency stealth according to the present invention includes the following steps:
1. establishing a system model:
considering a networked radar composed of multiple synchronous phased array radars, it is necessary to complete the search of multiple circular key observation areas and the tracking of a known number of moving targets at the same time. The priority of the multi-target tracking task is higher than that of the target searching task, each phased array radar can only generate one beam at each moment, namely, a single radar can only search one airspace or irradiate one target at each moment, and each radar can only receive and process echoes of self-transmitted signals.
2. A networked radar is constructed to search scenes of a plurality of circular key observation areas, and the detection probability is used as a measurement index of the search performance:
in a networked radar consisting of N radars, M S The partial radar is used for executing a search task on the S circular key observation areas. Assuming that only one area can be illuminated by a single radar at a time, each area needs to be simultaneously illuminated by L S And searching radar. Detection probability obtained after scanning a counterweight observation area a (a =1,2, …, A) n times by using radar i at time k
Comprises the following steps:
wherein, P fa In order to be the probability of a false alarm,
the signal-to-noise ratio of the echo which can be obtained after the radar i irradiates the target when searching the key observation area a at the moment k is expressed as follows:
wherein, the two variables are
Whether the radar i is selected to search a key observation area a at the moment k is shown;
representing the radiation power when the radar i searches for the key observation area a; a. The e And σ represents the effective area of the antenna and the radar scattering cross section of the target, respectively;
representing the beam residence time when the radar i searches for the key observation area a; k is a radical of B 、T e And L represents Boltzmann constant, radar system temperature and system loss, respectively; searching for a range of distances
Searching the angle range for the farthest distance between the radar i and the boundary of the key observation area a
Covering the angle value of the key observation area a for the radar i.
As previously mentioned, has L S The partial radar is used for searching the important observation area a, and then the detection probability of the networked radar at the time k on the target in the circular important observation area a can be expressed as:
3. constructing a multi-target tracking scene of the networked radar, and adopting a predicted Bayesian-Role lower bound of target position estimation as a measurement index of multi-target tracking performance:
in a networked radar composed of N radars, M is shared T The radar performs tracking on multiple targetsThe task is tracked. The state vector of the k-time moving object Q (Q =1,2, …, Q) can be represented as
Wherein the content of the first and second substances,
and
respectively, the position and velocity of the qth object at time k. Assuming that the target makes a uniform linear motion, the equation of state of the moving target can be expressed as:
wherein, the first and the second end of the pipe are connected with each other,
representing the state transition matrix, T represents the sampling interval,
denotes the kronecker product, I 2 Is an identity matrix of order 2.
A state vector representing the moving target q at the time k + 1; w q Representing white Gaussian process noise with mean zero, its covariance matrix Q q Can be expressed as:
wherein r is q Representing the process noise strength.
The invention assumes that when the networked radar executes the multi-target tracking task, only one target can be irradiated by a single radar at each moment, and each target needs to be simultaneously L-shaped T And (4) irradiating by radar. Binary variable
Indicating whether the radar i irradiates the target q at the time k. Therefore, the measurement model of the target q by the radar i at the time k can be represented as:
wherein the content of the first and second substances,
represents the corresponding measurement vector when the radar i tracks the target q at the moment k,
the non-linear observation function, which represents information including the target distance and azimuth, can be expressed as:
wherein (x) i ,y i ) The position coordinates of the radar i are represented,
representing a measured noise vector, whose covariance matrix follows a zero-mean Gaussian distribution
And
estimating the lower limit of the mean square error for the range and azimuth information, respectively:
wherein c is the speed of light; beta is the effective bandwidth of the transmitted signal; λ and γ are the signal wavelength and antenna aperture, respectively. Suppose that
And
respectively the radiation power and the residence time T of the radar i at the moment k to irradiate the target q once r For a pulse repetition period, the radar can be operated at time k
Coherent accumulation of each pulse can obtain the signal-to-noise ratio of the echo irradiated by the radar i to the target q after coherent accumulation
The signal-to-noise ratio is related to
And
as a function of (c).
Extracting elements which represent the lower bound of the target position estimation mean square error in diagonal elements of a Bayesian-Rou lower bound matrix predicted at the k moment as a measurement index for representing the target tracking precision:
wherein, the Bayesian information matrix of the target prediction state at the k moment is combined
And Jacobian matrix
Bayesian Classmei-Rou lower bound matrix for target state estimation error prediction
The expression of (a) is:
wherein, the first and the second end of the pipe are connected with each other,
a Bayesian information matrix representing the state of the target at time k-1,
a Bayesian information matrix representing a target prediction state at the moment k;
a Jacobian matrix representing the target prediction state at the time k;
representing a covariance matrix of target measurement errors at the moment k; superscript (·) -1 An inverse matrix representing a matrix; upper label (·) T Representing the transpose of the matrix.
4. Under the condition of meeting preset searching and multi-target tracking performance and radio frequency resource constraint, taking total radio frequency resource consumption of a minimized networked radar as an optimization target and taking a radar node selection mode, radiation power and residence time as optimization parameters, establishing a networked radar searching and tracking resource allocation model based on radio frequency stealth:
wherein E is tot,k Representing the total radio frequency resource consumption;
representing the networked radar node selection mode at the time k,
the node selection mode of searching the key observation area a is shown,
represents a networked radar search node selection mode,
represents a node selection manner of the tracking target q,
representing a networked radar tracking node selection mode; similarly, P k ＝[P S,k ,P T,k ] T And T k ＝[T S,k ,T T,k ] T Respectively representing the radiation power and residence time resource allocation of the networked radar at the moment k; 1 N×1 An all-1 matrix representing N × 1 dimensions; p is a radical of d,min And
respectively meeting the requirements of target searching performance and multi-target tracking precision; for search tasks, P S,max And P S,min Respectively representing the upper and lower limits of the search radiation power, T S,max And T S,min Respectively representing the upper limit and the lower limit of the search beam residence time; for trace tasks, P T,max And P T,min Respectively representing the upper and lower limits of the tracking radiation power, T T,max And T T,min Respectively representing the upper and lower limits of the tracking beam dwell time.
Total radio frequency resource consumption E tot,k Defined as the sum of the search and tracking radio frequency resource consumption, can be expressed as:
wherein, E S,k Indicating search radio frequency resource consumption, E T,k Representation tracking radio frequency resource cancellationConsumption; alpha (alpha) ("alpha") 1 And alpha 2 Weight coefficients respectively representing radiation power and dwell time; p is a radical of d,min And
respectively meeting the requirements of target searching performance and multi-target tracking precision; for search tasks, P S,max And P S,min Representing the upper and lower limits of the search radiation power, T S,max And T S,min Representing upper and lower limits of search beam dwell time; similarly, for multi-target tracking tasks, the radiation power is between P T,min And P T,max Between the residence time of T T,min And T T,max In the meantime.
5. And a two-step solving algorithm based on an interior point method and a circular minimum method is provided to solve the optimization model, and node selection, radiation power and residence time resource allocation during networked radar search and multi-target tracking are jointly optimized under the constraints of search tracking performance and radio frequency resources. Considering that the search resources and the tracking resources are not distributed in a coupling relation, the networked radar search and tracking resource distribution model (11) based on radio frequency stealth can be decomposed into two sub-optimization models as follows:
and
due to optimization of variables
And
the optimization models are non-convex and non-linear mixed integer programming models which are difficult to solve. Thus, to simplify the solution, one would
And
are respectively relaxed to
And
considering that the priority of the multi-target tracking task is higher, a two-step solving algorithm based on an interior point method and a circular minimum method is provided, and the specific solving steps are as follows:
(1) Tracking node selection and resource allocation;
(a) Initializing prediction Bayesian information matrix of k moment to target q
(b) Allocating initial tracking radiation power and tracking residence time for each radar node;
(c) Continuous variable obtained after relaxation
And (4) considering the contribution degree of the radar i tracking target q at the moment k. By optimizing the variable u in the case of current resource allocation T,k The tracking error to the target q is minimized. Solving the sub-optimization model by adopting an interior point method:
the contribution degree of each radar tracking target q under the current resource allocation can be obtained
Selecting the largest L T The radar corresponding to each element irradiates a target q, namely, the L which has the maximum contribution to a tracking target q is selected T And (4) radar.
(d) Selection of nodes obtained in step (c)
On the basis, under the constraints of target tracking precision and radio frequency resources, the radiation power and the residence time of the corresponding radar are optimized in a combined mode, so that the total radio frequency resource consumption is minimized. Solving the sub-optimization model by adopting an interior point method:
can obtain the trace resource allocation result P T,k,0 And T T,k,0 Substituting the result into step (b) as a new resource allocation scheme and skipping step (b) until the difference between the total tracking radio frequency resource consumptions calculated at two adjacent times is less than a preset value. Corresponding to the radar to which the tracking target q is finally assigned
And setting 1 and setting 0 for the rest, thus obtaining the tracking node selection and resource allocation result at the moment k.
(2) Searching node selection and resource allocation;
(a) After the selection of the tracking nodes is determined, node selection for multi-airspace search tasks is carried out in the remaining radar nodes, and initial search resources are distributed to the remaining radars firstly, similar to the tracking node selection;
(b) Continuous variable obtained after relaxation
And (4) considering the contribution degree of the radar i at the moment k to the effect of searching the key observation area a. Optimizing search node selection variable u under current resource allocation S,k The target detection probability is maximized. Solving the sub-optimization model:
the contribution degree of each radar to the target detection probability in the observation area a under the current resource allocation can be obtained, and the L with the maximum corresponding contribution is selected S And searching the key observation area a by the radar.
(c) Under the current node selection, the radiation power and the residence time of the corresponding radar are jointly optimized, and the aim of minimizing the total radio frequency resource consumption is taken as an optimization target. Solving the sub-optimization model:
and (b) after obtaining a search resource allocation result, skipping to the step (a) to update the initial search resource allocation scheme until the difference between the total search radio frequency resource consumption obtained in two adjacent times is less than a preset value. Corresponding to the radar to which the search space s is finally assigned
Setting 1 and setting 0 for the rest, thus obtaining the search node selection and resource allocation result at the moment k.
The invention discloses a networked radar target searching and tracking resource distribution system based on radio frequency stealth, which comprises:
the system modeling module is used for establishing a networked radar consisting of a plurality of synchronous phased array radars, and the networked radar needs to complete the search of a plurality of circular key observation areas and the tracking of a known number of moving targets at the same time;
the measurement index calculation module is used for searching scenes for a plurality of circular key observation areas based on the networked radar and calculating the detection probability of the networked radar on the target in the circular key observation areas as the measurement index of the search performance; calculating a predicted Bayesian-Lame lower bound of target position estimation as a measurement index of multi-target tracking performance based on a networked radar to a multi-target tracking scene;
the optimization model building module is used for building a networked radar search and tracking resource distribution model based on radio frequency stealth by taking the total radio frequency resource consumption of the minimized networked radar as an optimization target and a radar node selection mode, radiation power and residence time as optimization parameters under the condition of meeting preset search and multi-target tracking performance and radio frequency resource constraint;
and the optimization model solving module is used for decomposing the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models and solving the two sub-optimization models by adopting a two-step solving algorithm of an interior point method and a cyclic minimum method.
An apparatus of the present invention includes a memory and a processor, wherein:
a memory for storing a computer program capable of running on the processor;
and the processor is used for executing the steps of the networked radar target searching and tracking resource allocation method based on radio frequency stealth when the computer program is run, and achieving the technical effect consistent to the method.
The storage medium of the present invention stores thereon a computer program, and the computer program, when executed by at least one processor, implements the steps of the above method for allocating resources for searching and tracking a networked radar target based on radio frequency stealth, and achieves technical effects consistent with the above method.
The working principle and the working process of the invention are as follows:
the invention considers the networked radar consisting of a plurality of synchronous phased array radars, and needs to complete the search of a plurality of circular key observation areas and the tracking of a known number of moving targets at the same time. The priority of the multi-target tracking task is higher than that of the target searching task, each phased array radar can only generate one beam at each moment, namely, a single radar can only search one airspace or irradiate one target at each moment, and each radar can only receive and process echoes of self-transmitted signals. Firstly, a network radar searching scene for a plurality of key observation areas is established, and detection probability is deduced to be used as a target searching performance measurement index in each area; meanwhile, a networked radar is constructed for tracking multiple targets,and the predicted Bayesian Classmen-Luo Xiajie is deduced to be used as a target tracking performance measurement index. Then, a radio frequency stealth-based networked radar search and tracking resource allocation model is established by taking the minimized radio frequency resource consumption of the networked radar as an optimization target, taking a radar node selection mode, each radar transmitting power and the residence time as optimization parameters and taking preset target search performance, multi-target tracking performance and limited radio frequency resources as constraint conditions. And finally, solving the optimization model by adopting a two-step solving algorithm based on an interior point method and a cyclic minimum method. After the optimization model is solved, the obtained radar node selection scheme u is selected k Each radar radiation power P k And a residence time T k And (3) substituting an equation (11), obtaining a radio frequency stealth-based networked radar search tracking resource allocation result meeting the constraint condition.
Claims (10)
1. The networked radar target searching and tracking resource allocation method based on radio frequency stealth is characterized by comprising the following steps of:
establishing a system model: considering a networked radar consisting of a plurality of synchronous phased array radars, searching a plurality of circular key observation areas and tracking a known number of moving targets need to be completed simultaneously; the priority of the multi-target tracking task is higher than that of the target searching task, and each phased array radar can only generate one wave beam at each moment;
constructing a search scene of a networked radar for a plurality of circular key observation areas, and adopting detection probability as a measurement index of search performance;
constructing a multi-target tracking scene of the networked radar, and adopting a predicted Bayesian-Lame lower bound of target position estimation as a measurement index of multi-target tracking performance;
under the condition of meeting preset searching and multi-target tracking performance and radio frequency resource constraint, taking the total radio frequency resource consumption of the minimized networked radar as an optimization target, and taking a radar node selection mode, radiation power and residence time as optimization parameters, and establishing a radio frequency stealth-based networked radar searching and tracking resource allocation model;
the model is decomposed into two sub-optimization models, the two sub-optimization models are solved by adopting a two-step solving algorithm of an inner point method and a cyclic minimum method, and node selection, radiation power and residence time resource allocation during networked radar search and multi-target tracking are jointly optimized under the constraints of search tracking performance and radio frequency resources.
2. The method for allocating the radio frequency stealth-based networked radar target search tracking resources according to claim 1, wherein a search scene of the networked radar for a plurality of circular key observation areas is constructed, and detection probability is used as a measure index of search performance, and specifically the method comprises the following steps:
in a networked radar consisting of N radars, M S The partial radar is used for executing a search task on A circular key observation areas; a single radar can only illuminate one area at a time, and each area needs to be simultaneously L S Searching by a radar; the detection probability obtained after the radar i scans the observation area a of the counterweight n times at the moment k
Comprises the following steps:
wherein, a =1,2, …, A, P fa In order to be the probability of a false alarm,
the echo signal-to-noise ratio which can be obtained after the radar i irradiates the target when searching the key observation area a at the moment k;
has L S The partial radar is used for searching the key observation area a, and the detection probability of the networked radar at the moment k on the target in the circular key observation area a is represented as follows:
3. the method for allocating the resources for searching and tracking the networked radar target based on the radio frequency stealth according to claim 1, wherein the measurement indexes of the multi-target tracking performance are as follows:
wherein the content of the first and second substances,
predicting a Bayesian Classmei-Rou lower bound matrix for the target state estimation error, wherein the expression is as follows:
wherein, the first and the second end of the pipe are connected with each other,
a Bayesian information matrix representing the state of the target at time k-1,
a Bayesian information matrix representing a target prediction state at the moment k;
a Jacobian matrix representing the target prediction state at the time k;
representing a covariance matrix of target measurement errors at the moment k; superscript (·) -1 An inverse matrix representing a matrix; superscript (·) T Represents a transpose of a matrix; q q A covariance matrix representing white gaussian process noise with a mean of zero; f represents a state transition matrix; n meterIndicating the number of radars in the networked radar;
indicating whether the radar i is irradiating the target q at the time k.
4. The method for allocating the resources for searching and tracking the networked radar target based on the radio frequency stealth as claimed in claim 1, wherein the model for allocating the resources for searching and tracking the networked radar based on the radio frequency stealth is as follows:
wherein, E tot,k Representing the total radio frequency resource consumption; u. of k ＝[u S,k ,u T,k ] T Representing the networked radar node selection mode at the time k,
the node selection mode of searching the key observation area a is shown,
indicating a networked radar search node selection mode,
represents a node selection manner of the tracking target q,
representing a networked radar tracking node selection mode; p k ＝[P S,k ,P T,k ] T And T k ＝[T S,k ,T T,k ] T Respectively representDistributing the radiation power and residence time resources of the networked radar at the moment k;
the detection probability of the networked radar to the target in the key observation area a at the moment k is shown;
representing a measurement index representing the tracking precision of the target; p is a radical of d,min And
respectively meeting the requirements of target searching performance and multi-target tracking precision; for search tasks, P S,max And P S,min Respectively representing the upper and lower limits of the search radiation power, T S,max And T S,min Respectively representing the upper limit and the lower limit of the search beam residence time;
representing the radiation power when the radar i searches for the key observation area a;
representing the beam residence time when the radar i searches for the key observation area a; for trace tasks, P T,max And P T,min Respectively representing the upper and lower limits of the tracking radiation power, T T,max And T T,min Respectively representing the upper limit and the lower limit of the residence time of the tracking wave beam;
and
respectively determining the radiation power and the residence time of the radar i at the moment k for irradiating the target q once; l is S Representing the number of radars searching the same circular key observation area at the same time; a represents the number of circular key observation areas; m S Showing for A circular key observation regionsThe number of radars performing the search task;
whether the radar i at the moment k is selected or not is shown, and a key observation area a is searched;
indicating whether the radar i irradiates the target q at the moment k; l is T Representing the number of radars required to illuminate the same target simultaneously; q represents the number of moving objects; m is a group of T Representing a number of radars for performing tracking tasks on a plurality of targets; 1 N×1 Representing an N x 1 dimensional full 1 matrix.
5. The method for allocating the target search and tracking resources of the networked radar based on the radio frequency stealth as claimed in claim 4, wherein the total radio frequency resource consumption E tot,k Defined as the sum of the search and tracking radio frequency resource consumption, expressed as:
wherein E is S,k Indicating search radio frequency resource consumption, E T,k Representing tracking radio frequency resource consumption; alpha (alpha) ("alpha") 1 And alpha 2 Weight coefficients representing radiation power and dwell time, respectively.
6. The method for allocating the radio frequency stealth-based networked radar target search and tracking resources according to claim 1, wherein the two decomposed sub-optimization models are as follows:
and
wherein E is S,k Indicating search radio frequency resource consumption, E T,k Representing tracking radio frequency resource consumption;
node selection means u representing search area a S,k Represents a networked radar search node selection mode,
means for indicating the node selection of the tracking target q, u T,k Representing a networked radar tracking node selection mode;
representing the detection probability of the networked radar at the moment k to the target in the key observation area a;
representing a measurement index representing the tracking precision of the target; p is a radical of d,min And
respectively meeting the requirements of target searching performance and multi-target tracking precision; for search tasks, P S,max And P S,min Respectively representing the upper and lower limits of the search radiation power, T S,max And T S,min Respectively representing the upper limit and the lower limit of the residence time of the search wave beam;
representing the radiation power when the radar i searches for the key observation area a;
representing the residence time of the wave beam when the radar i searches for the key observation area a; for trace tasks, P T,max And P T,min Respectively representing the upper and lower limits of the tracking radiation power, T T,max And T T,min Respectively representing the upper limit and the lower limit of the residence time of the tracking wave beam;
and
respectively determining the radiation power and the residence time of the radar i at the moment k for irradiating the target q once; l is S Representing the number of radars searching the same circular key observation area at the same time; a represents the number of circular key observation areas; m S Representing the number of radars for performing a search task on a circular key observation regions;
whether the radar i at the moment k is selected or not is shown, and a key observation area a is searched;
indicating whether the radar i irradiates the target q at the moment k; l is T Representing the number of radars required to illuminate the same target simultaneously; q represents the number of moving objects; m T Representing a number of radars for performing tracking tasks on a plurality of targets; 1 N×1 An all-1 matrix representing N × 1 dimensions;
will be provided with
And
are respectively relaxed to
And
7. the method for allocating the radio frequency stealth-based networked radar target search and tracking resources according to claim 6, wherein the two-step solving algorithm adopting the interior point method and the cyclic minimum method is used for solving the two sub-optimization models:
(1) Tracking node selection and resource allocation;
(a) Initializing a prediction Bayesian information matrix of k time to a target q
(b) Allocating initial tracking radiation power and tracking residence time for each radar node;
(c) Continuous variable obtained after relaxation
The contribution degree of the radar i tracking target q at the moment k is regarded as the contribution degree; by optimizing the variable u in the case of current resource allocation T,k Minimizing the tracking error to the target q; solving the sub-optimization model by adopting an interior point method:
obtaining the contribution degree of each radar tracking target q under the current resource allocation
Selecting the largest L T The radar corresponding to each element irradiates a target q, namely, the L which has the maximum contribution to a tracking target q is selected T A radar;
(d) Selection of nodes obtained in step (c)
On the basis, under the constraints of target tracking precision and radio frequency resources, the radiation power and the residence time of the corresponding radar are optimized in a combined mode so as to minimize the total consumption of the radio frequency resources; solving the sub-optimization model by adopting an interior point method:
deriving trace resource allocation result P T,k,0 And T T,k,0 Substituting the result into the step (b) as a new resource allocation scheme and skipping to the step (b) until the difference between the total tracking radio frequency resource consumption calculated in two adjacent times is smaller than a preset value; corresponding to the radar to which the tracking target q is finally assigned
Setting 1, and setting 0 for the rest to obtain a k moment tracking node selection and resource allocation result;
(2) Searching node selection and resource allocation;
(a) After the selection of the tracking nodes is determined, the nodes for multi-airspace search tasks are selected from the rest radar nodes, and initial search resources are distributed to the rest radars;
(b) Continuous variable obtained after relaxation
The contribution degree of the radar i at the moment k to the effect of the search key observation area a is regarded as; optimizing search node selection variable u under current resource allocation S,k Maximizing the target detection probability; solving the sub-optimization model:
obtaining the contribution degree of each radar to the target detection probability in the gravity observation area a under the current resource allocation, and selecting the L with the maximum corresponding contribution S Searching a key observation area a by the partial radar;
(c) Under the current node selection, the radiation power and the residence time of the corresponding radar are optimized in a combined mode, and the aim of minimizing the total radio frequency resource consumption is taken as an optimization target; solving the sub-optimization model:
after obtaining a search resource allocation result, skipping to the step (a) to update an initial search resource allocation scheme until the difference value between the total search radio frequency resource consumption obtained in two adjacent times is smaller than a preset value; corresponding to the radar finally designated to search the key observation area a
Setting 1 and setting 0 for the rest, namely obtaining the search node selection and resource distribution result at the moment k.
8. A networked radar target searching and tracking resource distribution system based on radio frequency stealth is characterized by comprising:
the system modeling module is used for establishing a networked radar consisting of a plurality of synchronous phased array radars, and the networked radar needs to complete the search of a plurality of circular key observation areas and the tracking of a known number of moving targets at the same time;
the measurement index calculation module is used for searching scenes for a plurality of circular key observation areas based on the networked radar and calculating the detection probability of the networked radar on targets in the circular key observation areas as a measurement index of the search performance; calculating a predicted Bayesian-Lame lower bound of target position estimation as a measurement index of multi-target tracking performance based on a networked radar to a multi-target tracking scene;
the optimization model building module is used for building a networked radar search and tracking resource distribution model based on radio frequency stealth by taking the total radio frequency resource consumption of the minimized networked radar as an optimization target and taking a radar node selection mode, radiation power and residence time as optimization parameters under the condition of meeting preset search and multi-target tracking performance and radio frequency resource constraint;
and the optimization model solving module is used for decomposing the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models and solving the two sub-optimization models by adopting a two-step solving algorithm of an interior point method and a cyclic minimum method.
9. An apparatus, comprising a memory and a processor, wherein:
a memory for storing a computer program capable of running on the processor;
a processor for executing the steps of the method for allocating radio frequency stealth based networked radar target search tracking resources according to any one of claims 1 to 7 when running the computer program.
10. A storage medium, characterized in that the storage medium has a computer program stored thereon, and the computer program when executed by at least one processor implements the steps of the method for allocating resources for searching and tracking a target of a networked radar based on radio frequency stealth according to any one of claims 1 to 7.
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