Resource allocation method for target search and tracking in networked radar based on radio frequency stealth

Abstract

The present invention discloses a method for allocating target search and tracking resources for a networked radar based on radio frequency stealth, including: considering a networked radar composed of multiple synchronized phased array radars, which needs to simultaneously complete searches of multiple circular key observation areas and track a known number of moving targets; constructing a networked radar search scenario for multiple circular key observation areas, and using detection probability as a measure of search performance; constructing a networked radar multi-target tracking scenario, and using the predicted Bayesian Cramer-Rao lower bound of target position estimation as a measure of multi-target tracking performance; establishing a networked radar search and tracking resource allocation model based on radio frequency stealth; and solving the optimization model using a two-step solution algorithm of the interior point method and the cyclic minimum method to achieve optimal resource allocation. The present invention improves the radio frequency stealth performance of the networked radar when performing multi-spatial search and multi-target tracking tasks.

Description

Technical Field

[0001] The present invention relates to radar signal processing technology, and in particular to a networked radar target search and tracking resource allocation method based on radio frequency stealth. Background Art

[0002] Radar was originally used for target detection and location measurement. With the continuous advancement of technology and the increasing demand for radar capabilities, radar's functions have gradually diversified. Phased array radar, due to its inertial beam scanning and strong anti-interference capabilities, has been widely used in the military, especially for the two key tasks of target search and tracking. Compared to traditional single-station radar, networked radar can extract target feature information from multiple perspectives and dimensions, and through information fusion, it can achieve goals such as improving resolution and reducing interference errors, further enhancing radar target search and tracking performance. This brings us to the technology of networked radar resource allocation. How to improve the performance of networked radar by allocating the different radiation resources of different radars has become the research topic of many scholars.

[0003] However, if the signals transmitted into space by a radar during its mission are intercepted by enemy passive detection systems, the radar faces the risk of being attacked. Therefore, improving RF stealth performance has become a pressing need in combat. RF stealth technology is a technique that counters the interception, sorting, and identification of active RF signals emitted by enemy passive detection systems. While optimizing radar performance using limited RF radiation resources, it is also necessary to consider RF stealth performance and reduce radiation resource consumption.

[0004] While most existing research has optimized radar node selection and resource allocation, achieving improvements in networked radar multi-target tracking accuracy or RF stealth performance to a certain extent, these studies have not considered the node selection and resource allocation issues of radars operating under multiple missions, resulting in certain limitations.

[0005] There are currently no public reports on the allocation of target search and tracking resources for networked radars based on RF stealth. Summary of the Invention

[0006] Purpose of the invention: The purpose of the present invention is to provide a networked radar target search and tracking resource allocation method based on radio frequency stealth, which not only takes into account the scenario in which networked radars perform multiple tasks together, but also can jointly optimize parameters such as radar node selection, radiation power and dwell time of each radar under the condition of meeting certain target search performance and multi-target tracking performance, effectively reducing the total radio frequency radiation resource consumption and improving the radio frequency stealth performance of the networked radar.

[0007] Technical solution: The networked radar target search and tracking resource allocation method based on radio frequency stealth of the present invention comprises the following steps:

[0008] Establishing a system model: Consider a networked radar system consisting of multiple synchronized phased array radars. This system needs to simultaneously search multiple circular observation areas and track a known number of moving targets. The multi-target tracking task takes priority over the target search task, and each phased array radar can only generate one beam at a time.

[0009] Construct a networked radar search scenario for multiple circular key observation areas, and use detection probability as a measure of search performance;

[0010] A networked radar multi-target tracking scenario is constructed, and the predicted Bayesian Cramer-Rao lower bound of target position estimation is used as a measure of multi-target tracking performance.

[0011] Under the conditions of meeting the pre-set search and multi-target tracking performance and RF resource constraints, a networked radar search and tracking resource allocation model based on RF stealth is established with the goal of minimizing the total RF resource consumption of the networked radar and the radar node selection method, radiation power, and dwell time as optimization parameters.

[0012] The model is decomposed into two sub-optimization models, and the two sub-optimization models are solved using a two-step solution algorithm of the interior point method and the cyclic minimization method. Under the constraints of search and tracking performance and radio frequency resources, the node selection, radiation power and dwell time resource allocation during networked radar search and multi-target tracking are jointly optimized.

[0013] Furthermore, a networked radar search scenario for multiple circular key observation areas is constructed, and the detection probability is used as a measure of search performance. Specifically:

[0014] In a networked radar system consisting of N radars, M S The radar is used to perform search tasks 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 Radar search; the detection probability obtained after radar i scans the key observation area a n times at time k is for:

[0015]

[0016] Where a=1,2,…,A,P fa is the false alarm probability, is the echo signal-to-noise ratio that can be obtained when radar i searches the key observation area a at time k and illuminates the target;

[0017] There is LS The radar is used to search the key observation area a. The detection probability of the networked radar for the target in the circular key observation area a at time k is expressed as:

[0018]

[0019] Furthermore, the multi-target tracking performance is measured as follows:

[0020]

[0021] in, is the target state estimation error prediction Bayesian Cramer-Rao lower bound matrix, which is expressed as:

[0022]

[0023] in, represents the Bayesian information matrix of the target state at time k-1, The Bayesian information matrix representing the target prediction state at time k; The Jacobian matrix representing the target prediction state at time k; represents the covariance matrix of the target measurement error at time k; the superscript (·) -1 Indicates the inverse matrix of a matrix; superscript (·) T represents the transpose of the matrix; Q q represents the covariance matrix of the Gaussian process white noise with zero mean; F represents the state transfer matrix; N represents the number of radars in the networked radar; Indicates whether radar i illuminates target q at time k.

[0024] Furthermore, the networked radar search and tracking resource allocation model based on RF stealth is:

[0025]

[0026] Among them, E tot,k Indicates the total radio frequency resource consumption; u k =[u S,k ,u T,k ] T represents the networked radar node selection method at time k, Indicates the node selection method for searching the key observation area a. Indicates the network radar search node selection method, Indicates the node selection method for tracking target q, represents the networked radar tracking node selection method; P k =[P S,k ,P T,k ] T and Tk =[T S,k ,T T,k ] T They represent the radiated power and dwell time resource allocation of the networked radar at time k respectively; represents the detection probability of the networked radar for the target in the key observation area a at time k; represents the measurement index of target tracking accuracy; p d,min and are target search performance and multi-target tracking accuracy requirements respectively; for the search task, P S,max and P S,min Respectively represent the upper and lower limits of the search radiation power, T S,max and T S,min Respectively represent the upper and lower limits of the search beam dwell time; represents the radiation power of radar i when searching the key observation area a; represents the dwell time of the beam when radar i searches for the key observation area a; for tracking tasks, P T,max and P T,min Respectively represent the upper and lower limits of the tracking radiation power, T T,max and T T,min Respectively represent the upper and lower limits of the tracking beam dwell time; and are the radiation power and dwell time of radar i illuminating target q at time k; L S Indicates the number of radars simultaneously searching the same circular key observation area; A indicates the number of circular key observation areas; M S Indicates the number of radars used to perform search missions for A circular key observation areas; Indicates whether radar i is selected to search the key observation area a at time k; Indicates whether radar i illuminates target q at time k; L T Indicates the number of radars required to illuminate the same target at the same time; Q indicates the number of moving targets; M T Indicates the number of radars used to perform tracking tasks for multiple targets; 1 N×1 Represents an N×1 matrix of all ones.

[0027] Furthermore, the total radio frequency resource consumption E tot,k It is defined as the sum of search and tracking radio frequency resource consumption, expressed as:

[0028]

[0029] Among them, E S,k Indicates the search radio resource consumption, E T,kIndicates tracking of radio resource consumption; α1 and α2 are weight coefficients of radiation power and dwell time, respectively.

[0030] Furthermore, the two sub-optimization models are decomposed into:

[0031]

[0032] and

[0033]

[0034] Among them, E S,k Indicates the search radio resource consumption, E T,k Indicates tracking of radio resource consumption; Indicates the node selection method for searching the key observation area a, u S,k Indicates the network radar search node selection method, Indicates the node selection method for tracking target q, u T,k Indicates the networked radar tracking node selection method; represents the detection probability of the networked radar for the target in the key observation area a at time k; represents the measurement index of target tracking accuracy; p d,min and are target search performance and multi-target tracking accuracy requirements respectively; for the search task, P S,max and P S,min Respectively represent the upper and lower limits of the search radiation power, T S,max and T S,min Respectively represent the upper and lower limits of the search beam dwell time; represents the radiation power of radar i when searching the key observation area a; represents the dwell time of the beam when radar i searches for the key observation area a; for tracking tasks, P T,max and P T,min Respectively represent the upper and lower limits of the tracking radiation power, T T,max and T T,min Respectively represent the upper and lower limits of the tracking beam dwell time; and are the radiation power and dwell time of radar i illuminating target q at time k; L S Indicates the number of radars simultaneously searching the same circular key observation area; A indicates the number of circular key observation areas; M S Indicates the number of radars used to perform search missions for A circular key observation areas; Indicates whether radar i is selected to search the key observation area a at time k; Indicates whether radar i illuminates target q at time k; L TIndicates the number of radars required to illuminate the same target at the same time; Q indicates the number of moving targets; M T Indicates the number of radars used to perform tracking tasks for multiple targets; 1 N×1 Represents an N×1-dimensional all-1 matrix;

[0035] Will and Relaxed to and

[0036] Furthermore, the method of solving the two sub-optimization models using the two-step solution algorithm of the interior point method and the cyclic minimum method is as follows:

[0037] (1) Tracking node selection and resource allocation;

[0038] (a) Initialize the predicted Bayesian information matrix for the target q at time k

[0039] (b) Allocate initial tracking radiation power and tracking dwell time to each radar node;

[0040] (c) The continuous variable obtained after relaxation As the contribution of radar i to tracking target q at time k; under the current resource allocation, by optimizing the variable u T,k , minimize the tracking error of the target q; use the interior point method to solve the sub-optimization model:

[0041]

[0042] Obtain the contribution of each radar to tracking target q under the current resource allocation Choose the largest L T The radar irradiation target q corresponding to the element is selected, that is, the L that contributes the most to tracking the target q is selected. T Department of radar;

[0043] (d) Select the node obtained in step (c) Based on this, under the constraints of target tracking accuracy and RF resources, the radiation power and dwell time of the corresponding radar are jointly optimized to minimize the total RF resource consumption; the interior point method is used to solve the sub-optimization model:

[0044]

[0045] Obtain the tracking resource allocation result P T,k,0 and T T,k,0, substitute the result as the new resource allocation scheme into step (b) and jump to step (b) until the difference between the two consecutive calculated total tracking radio frequency resource consumption is less than the preset value; the radar corresponding to the target q that is finally designated to track is Set to 1 and the rest to 0, and the result of tracking node selection and resource allocation at time k is obtained;

[0046] (2) Search node selection and resource allocation;

[0047] (a) After the tracking node selection is determined, node selection for the multi-domain search task will be performed among the remaining radar nodes, and initial search resources will be allocated to the remaining radars.

[0048] (b) The continuous variable obtained after relaxation Considered as the contribution of radar i to the search effect of key observation area a at time k; Under the current resource allocation, the optimal search node selection variable u S,k , maximize the target detection probability; solve the sub-optimization model:

[0049]

[0050] Obtain the contribution of each radar to the target detection probability in the key observation area a under the current resource allocation, and select the L with the largest contribution S Department radar search key observation area a;

[0051] (c) Under the current node selection, jointly optimize the corresponding radar's radiated power and dwell time to minimize the total RF resource consumption; solve the sub-optimization model:

[0052]

[0053] After the search resource allocation result is obtained, jump to step (a) and update the initial search resource allocation plan until the difference between the total search RF resource consumption obtained twice is less than the preset value; the radar corresponding to the radar that is finally designated to search the key observation area a is allocated. Set it to 1 and the rest to 0, and the search node selection and resource allocation results at time k are obtained.

[0054] The networked radar target search and tracking resource allocation system based on radio frequency stealth of the present invention comprises:

[0055] A system modeling module is used to build a networked radar consisting of multiple synchronized phased array radars. The networked radar needs to simultaneously search multiple circular observation areas and track a known number of moving targets.

[0056] A measurement index calculation module is used to calculate the detection probability of the networked radar in the circular key observation area as a measurement index of the search performance based on the networked radar searching scenario of multiple circular key observation areas; and to calculate the predicted Bayesian Cramer-Rao lower bound of the target position estimate as a measurement index of the multi-target tracking performance based on the networked radar tracking scenario;

[0057] The optimization model construction module is used to establish a networked radar search and tracking resource allocation model based on RF stealth, with the goal of minimizing the total RF resource consumption of the networked radar, while satisfying pre-defined search and multi-target tracking performance and RF resource constraints. The module uses radar node selection, radiation power, and dwell time as optimization parameters.

[0058] The optimization model solving module is used to decompose the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models, and solve the two sub-optimization models using a two-step solving algorithm of the interior point method and the cyclic minimum method.

[0059] A device of the present invention includes a memory and a processor, wherein:

[0060] a memory for storing computer programs capable of running on the processor;

[0061] The processor is configured to execute the steps of the above-mentioned method for allocating resources for networked radar target search and tracking based on radio frequency stealth when running the computer program.

[0062] A storage medium of the present invention stores a computer program, which, when executed by at least one processor, implements the steps of the above-mentioned networked radar target search and tracking resource allocation method based on radio frequency stealth.

[0063] Beneficial Effects: Compared with existing technologies, the present invention achieves significant technical benefits: by jointly optimizing parameters such as radar node selection, radiation power, and dwell time during multi-domain search and multi-target tracking tasks, the total RF resource consumption of the networked radar is minimized, while simultaneously meeting pre-defined target search and multi-target tracking performance requirements, thereby improving the RF stealth performance of the networked radar. This advantage is achieved by deriving target detection probabilities and predicting Bayesian Cramer-Rao lower bounds based on binary variables such as radar node selection, radiation power, and dwell time of each radar as independent variables, respectively, as metrics for measuring target search performance and multi-target tracking performance. Based on this, the present invention jointly optimizes parameters such as radar node selection, radiation power, and dwell time of each radar, with the goal of minimizing the total RF radiation consumption of the networked radar, based on the networked radar's limited RF radiation resources, pre-defined detection probabilities for targets within each domain, and tracking accuracy requirements for each moving target. This method effectively improves the RF stealth performance of the networked radar during multi-target tracking, while simultaneously meeting search and tracking performance requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0065] The present invention will be further described below with reference to the accompanying drawings.

[0066] The present invention targets a networked radar composed of multiple time-synchronized phased array radars that needs to simultaneously complete multi-area search and multi-target tracking tasks. Under the conditions of satisfying the pre-set target detection probability and multi-target prediction tracking accuracy as well as the networked radar transmission resource constraints, the radar node selection, radiation power, and dwell time parameters are adaptively and jointly optimized to minimize the total RF resource consumption of the networked radar. The search and tracking models are constructed separately, and the target detection probability and the predicted Bayesian Cramer-Rao lower bound are derived with the radar node selection binary variable, the radar radiation power and the dwell time as independent variables. These are used as indicators to measure the target search performance and multi-target tracking performance respectively. With the pre-set target search performance, multi-target tracking performance and limited RF resources as constraints, the radar node selection scheme u is used to select the target node and the target tracking accuracy. k , Radiation power P of each radar k and residence time T k To optimize variables and minimize the total RF resource consumption of a networked radar, a mathematical model for target search and tracking resource allocation based on RF stealth was established. A two-step solution algorithm based on the interior point method and the cyclic minimization method was proposed to solve the optimization model. This algorithm improves the RF stealth performance of the networked radar when performing both search and tracking tasks, while maintaining the pre-defined search and tracking performance.

[0067] Based on the needs of actual engineering applications, this paper proposes a networked radar target search and tracking resource allocation method based on radio frequency stealth. With limited radio frequency radiation resources and pre-set target search performance and multi-target tracking performance as constraints, and minimizing the total radio frequency resource consumption of the networked radar as the optimization goal, the radio frequency stealth performance of the networked radar when performing target search and tracking tasks is improved by jointly optimizing parameters such as radar selection, radar radiation power and dwell time.

[0068] like Figure 1 As shown, the networked radar target search and tracking resource allocation method based on radio frequency stealth of the present invention includes the following steps:

[0069] 1. Establish system model:

[0070] Consider a networked radar system consisting of multiple synchronized phased array radars, which must simultaneously search multiple circular observation areas and track a known number of moving targets. Assuming that the multi-target tracking task takes priority over the target search task, each phased array radar can only generate a single beam at a time. This means that a single radar can only search a single area of ​​airspace or illuminate a single target at a time, and each radar can only receive and process the echo of its own transmitted signal.

[0071] 2. Build a networked radar search scenario for multiple circular key observation areas, and use detection probability as a measure of search performance:

[0072] In a networked radar system consisting of N radars, M S The radar is used to perform search tasks on S circular key observation areas. Assuming that a single radar can only illuminate one area at a time, each area needs to be simultaneously L S The detection probability obtained after radar i scans the key observation area a (a=1,2,…,A) n times at time k is for:

[0073]

[0074] Among them, P fa is the false alarm probability, is the echo signal-to-noise ratio that can be obtained when radar i searches the key observation area a at time k and illuminates the target, expressed as:

[0075]

[0076] Among them, the binary variable Indicates whether radar i is selected to search the key observation area a at time k; A represents the radiation power of radar i when searching the key observation area a;e and σ represent the effective area of ​​the antenna and the radar cross section of the target, respectively; k represents the dwell time of the beam when radar i searches for the key observation area a; B 、T e and L represent the Boltzmann constant, radar system temperature and system loss respectively; search distance range is the maximum distance between radar i and the boundary of key observation area a, and the search angle range is the angle value of radar i covering the key observation area a.

[0077] As mentioned above, there is L S The radars are used to search the key observation area a, so the detection probability of the networked radar for the target in the circular key observation area a at time k can be expressed as:

[0078]

[0079] 3. Construct a multi-target tracking scenario using a networked radar and use the predicted Bayesian Cramer-Rao lower bound of target position estimation as a measure of multi-target tracking performance:

[0080] In a networked radar system consisting of N radars, there are M T The radar performs the tracking task of multiple targets. The state vector of the moving target q (q=1,2,…,Q) at time k can be expressed as in, and They represent the position and velocity of the qth target at time k respectively. Assuming that the target moves in a uniform straight line, the state equation of the moving target can be expressed as:

[0081]

[0082] in, represents the state transfer matrix, T represents the sampling interval, represents the Kronecker product, and I2 is the second-order identity matrix. W represents the state vector of the moving target q at time k+1; q Represents Gaussian process white noise with zero mean, and its covariance matrix Q q It can be expressed as:

[0083]

[0084] Among them, r q Indicates the process noise intensity.

[0085] The present invention assumes that when the networked radar performs a multi-target tracking task, a single radar can only illuminate one target at a time, and each target needs to be simultaneously LT Radar illumination. Binary variable Indicates whether radar i illuminates target q at time k. Therefore, the measurement model of radar i on target q at time k can be expressed as:

[0086]

[0087] in, represents the measurement vector corresponding to the radar i tracking the target q at time k, Represents a nonlinear observation function containing target range and azimuth information, which can be expressed as:

[0088]

[0089] Among them, (x i ,y i ) represents the position coordinates of radar i, represents the measurement noise vector that obeys the zero-mean Gaussian distribution, and its covariance matrix and The lower bounds of the mean square error for distance and azimuth information are estimated as follows:

[0090]

[0091] Where c is the speed of light; β is the effective bandwidth of the transmitted signal; λ and γ are the signal wavelength and antenna aperture, respectively. and are the radiation power and dwell time of radar i illuminating target q at time k, T r is the pulse repetition period, then the radar can perform The coherent accumulation of pulses can obtain the echo signal-to-noise ratio of radar i to target q after coherent accumulation. The signal-to-noise ratio is about and function.

[0092] The elements representing the lower bound of the mean square error of the target position estimation are extracted from the diagonal elements of the Bayesian Cramer-Rao lower bound matrix predicted at time k as a measure of the target tracking accuracy:

[0093]

[0094] Among them, the Bayesian information matrix of the target prediction state at time k is and the Jacobian matrix Target state estimation error prediction Bayesian Cramer-Rao lower bound matrix The expression is:

[0095]

[0096] in, represents the Bayesian information matrix of the target state at time k-1, The Bayesian information matrix representing the target prediction state at time k; The Jacobian matrix representing the target prediction state at time k; represents the covariance matrix of the target measurement error at time k; the superscript (·) -1 Indicates the inverse matrix of a matrix; superscript (·) T Represents the transpose of a matrix.

[0097] 4. Under the conditions of meeting the pre-defined search and multi-target tracking performance and RF resource constraints, with minimizing the total RF resource consumption of the networked radar as the optimization goal, and using radar node selection method, radiation power, and dwell time as optimization parameters, a networked radar search and tracking resource allocation model based on RF stealth is established:

[0098]

[0099] Among them, E tot,k Indicates total radio frequency resource consumption; represents the networked radar node selection method at time k, Indicates the node selection method for searching the key observation area a. Indicates the network radar search node selection method, Indicates the node selection method for tracking target q, Represents the networked radar tracking node selection method; similarly, P k =[P S,k ,P T,k ] T and T k =[T S,k ,T T,k ] T They represent the radiation power and residence time resource allocation of the networked radar at time k; 1 N×1 represents an N×1-dimensional all-1 matrix; p d,min and are target search performance and multi-target tracking accuracy requirements respectively; for the search task, P S,max and P S,min Respectively represent the upper and lower limits of the search radiation power, T S,max and T S,min Respectively represent the upper and lower limits of the search beam dwell time; for tracking tasks, P T,max and P T,min Respectively represent the upper and lower limits of the tracking radiation power, T T,max and T T,minThey represent the upper and lower limits of the tracking beam dwell time respectively.

[0100] Total radio frequency resource consumption E tot,k It is defined as the sum of search and tracking radio frequency resource consumption and can be expressed as:

[0101]

[0102] Among them, E S,k Indicates the search radio resource consumption, E T,k Indicates tracking of radio frequency resource consumption; α1 and α2 represent the weight coefficients of radiation power and dwell time respectively; p d,min and are target search performance and multi-target tracking accuracy requirements respectively; for the search task, P S,max and P S,min Indicates the upper and lower limits of the search radiation power, T S,max and T S,min Represents the upper and lower limits of the search beam dwell time; similarly, for multi-target tracking tasks, the radiated power is between P T,min With P T,max The dwell time is between T T,min and T T,max between.

[0103] 5. A two-step solution algorithm based on the interior point method and the cyclic minimum method is proposed to solve the above optimization model. Under the constraints of search and tracking performance and radio frequency resources, the node selection, radiation power and dwell time resource allocation in networked radar search and multi-target tracking are jointly optimized. Considering that there is no coupling relationship between the allocation of search resources and tracking resources, the networked radar search and tracking resource allocation model (11) based on radio frequency stealth can be decomposed into the following two sub-optimization models:

[0104]

[0105] and

[0106]

[0107] Since the optimization variables and is a discrete integer variable. The above optimization models are all non-convex, nonlinear mixed integer programming models that are difficult to solve. Therefore, to simplify the solution, and Relaxed to and Considering the high priority of the multi-target tracking task, a two-step solution algorithm based on the interior point method and the cyclic minimum method is proposed. The specific solution steps are as follows:

[0108] (1) Tracking node selection and resource allocation;

[0109] (a) Initialize the predicted Bayesian information matrix for the target q at time k

[0110] (b) Allocate initial tracking radiation power and tracking dwell time to each radar node;

[0111] (c) The continuous variable obtained after relaxation As the contribution of radar i to tracking target q at time k. Under the current resource allocation, by optimizing the variable u T,k , minimize the tracking error of the target q. Use the interior point method to solve the sub-optimization model:

[0112]

[0113] The contribution of each radar to tracking target q under the current resource allocation can be obtained Choose the largest L T The radar irradiation target q corresponding to the element is selected, that is, the L that contributes the most to tracking the target q is selected. T Department of radar.

[0114] (d) Select the node obtained in step (c) Based on the target tracking accuracy and RF resource constraints, the radiation power and dwell time of the corresponding radar are jointly optimized to minimize the total RF resource consumption. The interior point method is used to solve the sub-optimization model:

[0115]

[0116] The tracking resource allocation result P can be obtained T,k,0 and T T,k,0 , substitute the result as the new resource allocation scheme into step (b) and jump to step (b) until the difference between the two consecutive total tracking radio frequency resource consumption calculations is less than a preset value. Set it to 1 and the rest to 0, and you can get the tracking node selection and resource allocation results at time k.

[0117] (2) Search node selection and resource allocation;

[0118] (a) After the tracking node selection is determined, node selection for the multi-domain search task will be performed among the remaining radar nodes. Similar to the tracking node selection, initial search resources are allocated to the remaining radars first.

[0119] (b) The continuous variable obtained after relaxation Considered as the contribution of radar i to the search of key observation area a at time k. Under the current resource allocation, the optimal search node selection variable u S,k , maximize the target detection probability. Solve the sub-optimization model:

[0120]

[0121] The contribution of each radar to the target detection probability in the key observation area a under the current resource allocation can be obtained, and the L with the largest contribution can be selected. S Department radar search key observation area a.

[0122] (c) Under the current node selection, jointly optimize the radiation power and dwell time of the corresponding radar to minimize the total RF resource consumption. Solve the sub-optimization model:

[0123]

[0124] After the search resource allocation result is obtained, jump to step (a) and update the initial search resource allocation plan until the difference between the total search RF resource consumption obtained twice is less than a preset value. Set it to 1 and the rest to 0, and you can get the search node selection and resource allocation results at time k.

[0125] The networked radar target search and tracking resource allocation system based on radio frequency stealth of the present invention comprises:

[0126] A system modeling module is used to build a networked radar consisting of multiple synchronized phased array radars. The networked radar needs to simultaneously search multiple circular observation areas and track a known number of moving targets.

[0127] A measurement index calculation module is used to calculate the detection probability of the networked radar in the circular key observation area as a measurement index of the search performance based on the networked radar searching scenario of multiple circular key observation areas; and to calculate the predicted Bayesian Cramer-Rao lower bound of the target position estimate as a measurement index of the multi-target tracking performance based on the networked radar tracking scenario;

[0128] The optimization model construction module is used to establish a networked radar search and tracking resource allocation model based on RF stealth, with the goal of minimizing the total RF resource consumption of the networked radar, while satisfying pre-defined search and multi-target tracking performance and RF resource constraints. The module uses radar node selection, radiation power, and dwell time as optimization parameters.

[0129] The optimization model solving module is used to decompose the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models, and solve the two sub-optimization models using a two-step solving algorithm of the interior point method and the cyclic minimum method.

[0130] A device of the present invention includes a memory and a processor, wherein:

[0131] a memory for storing computer programs capable of running on the processor;

[0132] The processor is used to execute the steps of the above-mentioned networked radar target search and tracking resource allocation method based on radio frequency stealth when running the computer program, and achieve the technical effect consistent with the above-mentioned method.

[0133] A storage medium of the present invention stores a computer program, which, when executed by at least one processor, implements the steps of the above-mentioned networked radar target search and tracking resource allocation method based on radio frequency stealth, and achieves the same technical effect as the above-mentioned method.

[0134] The working principle and working process of the invention are as follows:

[0135] This paper considers a networked radar consisting of multiple synchronized phased array radars, which must simultaneously search multiple circular key observation areas and track a known number of moving targets. Assuming that the multi-target tracking task takes precedence over the target search task, each phased array radar can only generate one beam at a time. That is, a single radar can only search a single airspace or illuminate a single target at a time, and each radar can only receive and process the echo of its own transmitted signal. First, a networked radar search scenario for multiple key observation areas is established, and the detection probability is derived as a performance metric for target search within each area. Simultaneously, a networked radar multi-target tracking scenario is constructed, and the predicted Bayesian Cramer-Rao lower bound is derived as a performance metric for target tracking. Then, with minimizing the networked radar's RF resource consumption as the optimization objective, using the radar node selection method, each radar's transmit power, and dwell time as optimization parameters, and subject to pre-defined target search and multi-target tracking performance, as well as limited RF resources, a networked radar search and tracking resource allocation model based on RF stealth is established. Finally, the above optimization model is solved by a two-step solution algorithm based on the interior point method and the cyclic minimum method. After solving the optimization model, the radar node selection scheme u is obtained. k , Radiation power P of each radar k and residence time T k Substituting into formula (11), we can obtain the networked radar search and tracking resource allocation result based on RF stealth that meets the constraints.

Claims

1. A networked radar target search and tracking resource allocation method based on radio frequency stealth, characterized in that: The following steps are involved: Establishing a system model: Consider a networked radar system consisting of multiple synchronized phased array radars. This system needs to simultaneously search multiple circular observation areas and track a known number of moving targets. The multi-target tracking task takes priority over the target search task, and each phased array radar can only generate one beam at a time. Construct a networked radar search scenario for multiple circular key observation areas, and use detection probability as a measure of search performance; A networked radar multi-target tracking scenario is constructed, and the predicted Bayesian Cramer-Rao lower bound of target position estimation is used as a measure of multi-target tracking performance. Under the conditions of meeting the pre-set search and multi-target tracking performance and RF resource constraints, a networked radar search and tracking resource allocation model based on RF stealth is established with the goal of minimizing the total RF resource consumption of the networked radar and the radar node selection method, radiation power, and dwell time as optimization parameters. The model is decomposed into two sub-optimization models, and the two sub-optimization models are solved using a two-step solution algorithm of the interior point method and the cyclic minimization method. Under the constraints of search and tracking performance and radio frequency resources, the node selection, radiation power and dwell time resource allocation during networked radar search and multi-target tracking are jointly optimized.

2. The networked radar target search and tracking resource allocation method based on radio frequency stealth according to claim 1 is characterized in that: Construct a networked radar search scenario for multiple circular key observation areas, and use detection probability as a measure of search performance. Specifically: In a networked radar system consisting of N radars, M S The radar is used to perform search tasks 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 Radar search; the detection probability obtained after radar i scans the key observation area a n times at time k is for: Where a=1,2,…,A,P fa is the false alarm probability, is the echo signal-to-noise ratio that can be obtained when radar i searches the key observation area a at time k and illuminates the target; There is L S The radar is used to search the key observation area a. The detection probability of the networked radar for the target in the circular key observation area a at time k is expressed as:

3. The networked radar target search and tracking resource allocation method based on radio frequency stealth according to claim 1 is characterized in that: The metrics for multi-target tracking performance are: in, is the target state estimation error prediction Bayesian Cramer-Rao lower bound matrix, which is expressed as: in, represents the Bayesian information matrix of the target state at time k-1, The Bayesian information matrix representing the target prediction state at time k; The Jacobian matrix representing the target prediction state at time k; represents the covariance matrix of the target measurement error at time k; the superscript (·) -1 Indicates the inverse matrix of a matrix; superscript (·) T represents the transpose of the matrix; Q q represents the covariance matrix of the Gaussian process white noise with zero mean; F represents the state transfer matrix; N represents the number of radars in the networked radar; Indicates whether radar i illuminates target q at time k.

4. The networked radar target search and tracking resource allocation method based on radio frequency stealth according to claim 1 is characterized in that: The networked radar search and tracking resource allocation model based on RF stealth is: Among them, E tot,k Indicates the total radio frequency resource consumption; u k =[u S,k ,u T,k ] T represents the networked radar node selection method at time k, Indicates the node selection method for searching the key observation area a. Indicates the network radar search node selection method, Indicates the node selection method for tracking target q, represents the networked radar tracking node selection method; P k =[P S,k ,P T,k ] T and T k =[T S,k ,T T,k ] T They represent the radiated power and dwell time resource allocation of the networked radar at time k respectively; represents the detection probability of the networked radar for the target in the key observation area a at time k; represents the measurement index of target tracking accuracy; p d,min and are target search performance and multi-target tracking accuracy requirements respectively; for the search task, P S,max and P S,min Respectively represent the upper and lower limits of the search radiation power, T S,max and T S,min Respectively represent the upper and lower limits of the search beam dwell time; represents the radiation power of radar i when searching the key observation area a; represents the dwell time of the beam when radar i searches for the key observation area a; for tracking tasks, P T,max and P T,min Respectively represent the upper and lower limits of the tracking radiation power, T T,max and T T,min Respectively represent the upper and lower limits of the tracking beam dwell time; and are the radiation power and dwell time of radar i illuminating target q at time k; L S Indicates the number of radars simultaneously searching the same circular key observation area; A indicates the number of circular key observation areas; M S Indicates the number of radars used to perform search missions for A circular key observation areas; Indicates whether radar i is selected to search the key observation area a at time k; Indicates whether radar i illuminates target q at time k; L T Indicates the number of radars required to illuminate the same target at the same time; Q indicates the number of moving targets; M T Indicates the number of radars used to perform tracking tasks for multiple targets; 1 N×1 Represents an N×1 matrix of all ones.

5. The networked radar target search and tracking resource allocation method based on radio frequency stealth according to claim 4 is characterized in that: Total radio frequency resource consumption E tot,k It is defined as the sum of search and tracking radio frequency resource consumption, expressed as: Among them, E S,k Indicates the search radio resource consumption, E T,k Indicates tracking of radio resource consumption; α1 and α2 are weight coefficients of radiation power and dwell time, respectively.

6. The networked radar target search and tracking resource allocation method based on radio frequency stealth according to claim 1 is characterized in that: The two sub-optimization models are decomposed as follows: and Among them, E S,k Indicates the search radio resource consumption, E T,k Indicates tracking of radio resource consumption; Indicates the node selection method of the search area a, u S,k Indicates the network radar search node selection method, Indicates the node selection method for tracking target q, u T,k Indicates the networked radar tracking node selection method; represents the detection probability of the networked radar for the target in the key observation area a at time k; represents the measurement index of target tracking accuracy; p d,min and are target search performance and multi-target tracking accuracy requirements respectively; for the search task, P S,max and P S,min Respectively represent the upper and lower limits of the search radiation power, T S,max and T S,min Respectively represent the upper and lower limits of the search beam dwell time; represents the radiation power of radar i when searching the key observation area a; represents the dwell time of the beam when radar i searches for the key observation area a; for tracking tasks, P T,max and P T,min Respectively represent the upper and lower limits of the tracking radiation power, T T,max and T T,min Respectively represent the upper and lower limits of the tracking beam dwell time; and are the radiation power and dwell time of radar i illuminating target q at time k; L S Indicates the number of radars simultaneously searching the same circular key observation area; A indicates the number of circular key observation areas; M S Indicates the number of radars used to perform search missions for A circular key observation areas; Indicates whether radar i is selected to search the key observation area a at time k; Indicates whether radar i illuminates target q at time k; L T Indicates the number of radars required to illuminate the same target at the same time; Q indicates the number of moving targets; M T Indicates the number of radars used to perform tracking tasks for multiple targets; 1 N×1 Represents an N×1-dimensional all-1 matrix; Will and Relaxed to and 7. The networked radar target search and tracking resource allocation method based on radio frequency stealth according to claim 6 is characterized in that: The method of solving the two sub-optimization models using the two-step solution algorithm of the interior point method and the cyclic minimum method is as follows: (1) Tracking node selection and resource allocation; (a) Initialize the predicted Bayesian information matrix for the target q at time k (b) Allocate initial tracking radiation power and tracking dwell time to each radar node; (c) The continuous variable obtained after relaxation As the contribution of radar i to tracking target q at time k; under the current resource allocation, by optimizing the variable u T,k , minimize the tracking error of the target q; use the interior point method to solve the sub-optimization model: Obtain the contribution of each radar to tracking target q under the current resource allocation Choose the largest L T The radar irradiation target q corresponding to the element is selected, that is, the L that contributes the most to tracking the target q is selected. T Department of radar; (d) Select the node obtained in step (c) Based on the target tracking accuracy and RF resource constraints, the radiation power and dwell time of the corresponding radar are jointly optimized to minimize the total RF resource consumption; Use the interior point method to solve the sub-optimization model: Obtain the tracking resource allocation result P T,k,0 and T T,k,0 , substitute the result as a new resource allocation scheme into step (b) and jump to step (b) until the difference between the total tracking radio frequency resource consumption calculated twice is less than a preset value; The radar that is ultimately assigned to track the target q Set to 1 and the rest to 0, and the result of tracking node selection and resource allocation at time k is obtained; (2) Search node selection and resource allocation; (a) After the tracking node selection is determined, node selection for the multi-domain search task will be performed among the remaining radar nodes, and initial search resources will be allocated to the remaining radars. (b) The continuous variable obtained after relaxation Considered as the contribution of radar i to the search effect of key observation area a at time k; Under the current resource allocation, the optimal search node selection variable u S,k , maximize the target detection probability; solve the sub-optimization model: Obtain the contribution of each radar to the target detection probability in the key observation area a under the current resource allocation, and select the L with the largest contribution S Department radar search key observation area a; (c) Under the current node selection, jointly optimize the corresponding radar's radiated power and dwell time to minimize the total RF resource consumption; solve the sub-optimization model: After the search resource allocation result is obtained, jump to step (a) and update the initial search resource allocation plan until the difference between the total search RF resource consumption obtained twice is less than the preset value; the radar corresponding to the radar that is finally designated to search the key observation area a is allocated. Set it to 1 and the rest to 0, and the search node selection and resource allocation results at time k are obtained.

8. A networked radar target search and tracking resource allocation system based on radio frequency stealth, characterized in that: include: A system modeling module is used to build a networked radar consisting of multiple synchronized phased array radars. The networked radar needs to simultaneously search multiple circular observation areas and track a known number of moving targets. A measurement index calculation module is used to calculate the detection probability of the networked radar in the circular key observation area as a measurement index of the search performance based on the networked radar searching scenario of multiple circular key observation areas; and to calculate the predicted Bayesian Cramer-Rao lower bound of the target position estimate as a measurement index of the multi-target tracking performance based on the networked radar tracking scenario; The optimization model construction module is used to establish a networked radar search and tracking resource allocation model based on RF stealth, with the goal of minimizing the total RF resource consumption of the networked radar, while satisfying pre-defined search and multi-target tracking performance and RF resource constraints. The module uses radar node selection, radiation power, and dwell time as optimization parameters. The optimization model solving module is used to decompose the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models, and solve the two sub-optimization models using a two-step solving algorithm of the interior point method and the cyclic minimum method.

9. A device, characterized in that: comprising a memory and a processor, wherein: a memory for storing computer programs capable of running on the processor; A processor, configured to execute the steps of the networked radar target search and tracking resource allocation method based on radio frequency stealth as described in any one of claims 1 to 7 when running the computer program.

10. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed by at least one processor, implements the steps of the networked radar target search and tracking resource allocation method based on radio frequency stealth as described in any one of claims 1 to 7.

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