A multi-jammer cooperative resource allocation method and device for networked radars

Abstract

The application discloses a kind of multi-jammer cooperative resource allocation method and equipment for networking radar, the method includes: determining multi-jammer cooperative jamming networking radar scene;Scene contains opposite radar, our target and our jammer;Obtain the position and speed of each opposite radar, our target and our jammer at current time;According to position and speed, determine the measurement value of each opposite radar to each our target at current time;According to measurement value, calculate the bayesian information matrix of each our target at current time;Based on the resource constraint of our jammer and the bayesian information matrix of each our target at current time, construct multi-jammer cooperative resource allocation model;Using augmented lagrange multiplier method, solve multi-jammer cooperative resource allocation model, obtain the solution result that the interference residence time of each our jammer to each opposite radar at current time is characterized.The application can quickly allocate the resource of our jammer, and the calculation complexity is low.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a method and device for collaborative resource allocation of multiple jammers in networked radar systems. Background Technology

[0002] In recent years, the increasingly severe situation of modern warfare has posed a serious threat to traditional monostatic radar systems, which struggle to counter stealth targets and complex electronic jamming. To improve radar resource utilization and enhance detection and tracking performance, networked radar systems have emerged. These systems break away from the traditional independent operation of individual radars, enabling them to cooperate and significantly improve operational performance, particularly in anti-jamming capabilities. Faced with such powerful networked radar systems, single jammers often have limited effectiveness; only through coordinated operation of multiple jammers, centrally managed, can optimal jamming be achieved. Existing multi-jamming cooperative jamming technologies mostly employ open-loop, loosely coupled networking, resulting in low jamming resource utilization and weak cooperative jamming capabilities. Therefore, establishing a flexible and efficient resource allocation mechanism for multi-jamming network systems, under conditions of limited jamming resources, is of significant practical importance for improving target survivability.

[0003] The jamming resource allocation problem can be viewed as optimizing a certain objective function under resource or performance constraints. The construction of the objective function is crucial for evaluating the jamming effect of a jammer on radar and thus guiding jamming resource allocation, and a substantial foundation of related research already exists. Some scholars have used the posterior Cramer-Rao bound of target tracking error as an evaluation index for jamming effect, proposing a two-step method based on particle swarm optimization to solve for jammer power and beam pointing. Existing research results on jamming resource allocation methods provide a reference for the jamming resource allocation problem in networked radar systems. However, most studies construct non-convex jamming resource allocation models, which to some extent face problems of high computational complexity and susceptibility to getting trapped in local optima. Therefore, a reasonable and objective evaluation index is urgently needed to measure the jamming impact of a jammer on the opposing radar. Furthermore, to further achieve rapid allocation of jamming resources in networked radar systems, the established mathematical model should also be easy to solve. In other words, a low-complexity resource allocation method that is not prone to getting trapped in local optima is urgently needed to quickly guide the resource allocation of jammers. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, this invention provides a method and device for collaborative resource allocation among multiple jammers in networked radar systems.

[0005] The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a method for collaborative resource allocation among multiple jammers in networked radar systems, comprising:

[0007] A scenario involving multiple jammers coordinating to jam a networked radar system is identified; this scenario includes multiple enemy radars, multiple friendly targets, and multiple friendly jammers.

[0008] Obtain the current position and velocity of each enemy radar, each friendly target, and each friendly jammer;

[0009] Based on the position and the speed, determine the measurement value of each enemy radar for each friendly target at the current moment;

[0010] Calculate the Bayesian information matrix of each of our targets at the current moment based on the measured values;

[0011] Based on the resource constraints of our jammers and the Bayesian information matrix of each of our targets at the current moment, a multi-jammer collaborative resource allocation model is constructed.

[0012] The augmented Lagrange multiplier method is used to solve the multi-jamming machine cooperative resource allocation model to obtain the solution results; the solution results represent the jamming dwell time of each friendly jammer on each opposing radar at the current moment.

[0013] This invention also provides a multi-jammer cooperative resource allocation device for networked radar, comprising:

[0014] The scenario determination module is used to determine the scenario of multi-jamming machine cooperative jamming network radar; the scenario includes multiple enemy radars, multiple friendly targets, and multiple friendly jammers;

[0015] The information acquisition module is used to acquire the position and velocity of each enemy radar, each friendly target, and each friendly jammer at the current moment; and to determine the measurement value of each enemy radar for each friendly target at the current moment based on the position and velocity.

[0016] The calculation module is used to calculate the Bayesian information matrix of each of our targets at the current moment based on the measurement values;

[0017] The model building module is used to build a multi-jamming machine collaborative resource allocation model based on the Bayesian information matrix of each of our targets at the current time and the resource constraints of our jammers.

[0018] The solution module is used to solve the multi-jamming machine cooperative resource allocation model and obtain the solution result; the solution result represents the jamming dwell time of each friendly jammer on each opposing radar at the current moment.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0020] This invention constructs a multi-jammer collaborative resource allocation model based on the resource constraints of our jammers and the Bayesian information matrix of our targets. The augmented Lagrange multiplier method is then used to solve the constructed allocation model, ultimately yielding the collaborative resource allocation results. This model enables rapid resource allocation for our jammers with low computational complexity, effectively reducing the tracking accuracy of the opposing networked radar system. Even with limited beam counts, it maintains good jamming performance and rapid solution capability, achieving optimal jamming effects and ultimately enhancing the survivability of our targets.

[0021] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating a multi-jammer collaborative resource allocation method for networked radar provided by an embodiment of the present invention;

[0023] Figure 2 This is a two-dimensional scene diagram of an exemplary multi-jammer cooperative jamming network radar provided in an embodiment of the present invention;

[0024] Figure 3 This is an exemplary schematic diagram of the positional relationship between the enemy radar, our target, and our jammer at time k, provided by an embodiment of the present invention.

[0025] Figure 4 This is an exemplary schematic diagram of the movement of our target and our jammer within the detection area of ​​the opposing network radar, provided by an embodiment of the present invention.

[0026] Figure 5 This is a schematic diagram comparing the BCRLB and RMSE performance of each target under three exemplary interference conditions provided by embodiments of the present invention.

[0027] Figure 6 This is a schematic diagram showing the dwell time allocation results of each jammer under three exemplary interference conditions provided by the embodiments of the present invention;

[0028] Figure 7 This is an exemplary schematic diagram comparing the ARMSE performance of three different methods under the condition of limited number of interfering beams, provided by an embodiment of the present invention.

[0029] Figure 8 This is an exemplary schematic diagram comparing the average running time of three different methods under the condition of limited number of interfering beams, provided by an embodiment of the present invention. Detailed Implementation

[0030] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0031] Figure 1 This is a flowchart illustrating a multi-jammer cooperative resource allocation method for networked radar provided by an embodiment of the present invention. The method includes:

[0032] S101. Determine the scenario of multi-jamming machine cooperative jamming network radar; the scenario includes multiple enemy radars, multiple friendly targets and multiple friendly jammers.

[0033] Here, the scenario of multi-jamming aircraft coordinating to jam a networked radar system includes both the opposing networked radar system and our formation. The opposing networked radar system consists of N... R The formation consists of phased array radars, and our formation includes N. Q One goal and N J jammer; N R N Q N J All are positive integers greater than 0.

[0034] Reference Figure 2 This is a two-dimensional scene diagram of a multi-jammer cooperative jamming network radar provided by the present invention; as shown below. Figure 2 As shown, the enemy's network radar system consists of multiple phased array radars. Our formation includes multiple penetrating targets and multiple jamming aircraft. Each jamming aircraft escorts the targets while carrying out suppressive jamming against the enemy's network radar.

[0035] S102. Obtain the position and velocity of each enemy radar, each friendly target, and each friendly jammer at the current moment.

[0036] Here, after determining the position of each phased array radar of the other side, we can establish an XOY plane rectangular coordinate system with the midpoint of all phased array radars as the origin O, and the north direction as the X-axis and the east direction as the Y-axis.

[0037] Here, at time k, the enemy radar r (r = 1, 2, ..., N) R The position at time k is Our objective is q (q = 1, 2, ..., N) Q The position and velocity at time k are: and Our jammer j (j=1,2,…,N) J The position and velocity at time k are: and For example, when our target q is moving at a constant velocity in a straight line, its state transition model is as follows: in, For the state of our target q, F and These represent the state transition matrix and the process noise, respectively. It follows a zero-mean covariance matrix. The state transition model is Gaussian distributed. When our jammer is moving at a constant velocity in a straight line, its state transition model is consistent with that of our target.

[0038] S103. Based on position and speed, determine the measurement values ​​of each enemy radar for each friendly target at the current moment.

[0039] Here, at time k, the nonlinear measurement model of the enemy radar r against our target q can be expressed as: Among them, Z r,q,k =[R r,q,k ,Θ r,q,k ] T R is the measurement value of the target q by the enemy's radar r. r,q,k and Θ r,q,k h represents the radial distance and azimuth angle, respectively. r,q,k (·) represents the measurement function of the opposing radar r, ω r,q,k The zero-mean covariance matrix is ​​Σ r,q,k Gaussian noise, Σ r,q,k It can be represented as: Here, diag(·) is the operation for constructing a diagonal matrix. and The Cramer-Rao boundaries for radial distance and azimuth measurement errors are as follows: Where k1 and k2 are the corresponding coefficients, B r For the effective bandwidth of the radar, γ r Let λ be the antenna aperture of the opposing radar r. r Let r be the wavelength of the opposing radar. μ is the number of coherent pulses accumulated. r,q,k This represents the signal-to-interference-plus-noise ratio (SINR) of the opposing radar r to our target q.

[0040] Here, the SINR of the opposing radar r on our target q includes not only the echo signal energy of our target q, but also thermal noise energy and interference signal energy from all directions. At time k, the echo signal energy received by the opposing radar r from our target q is: in, For radar transmission power, For radar antenna gain, For the radar wavelength, σ q For the target RCS, Let r be the distance between the enemy radar r and our target q. The comprehensive loss coefficient, Let be the coherent pulse accumulation period. When the beam of the opposing radar r is pointed at our target q, the energy of the interference signal received from our jammer j is: in, The transmit power of our jammer j against the enemy radar r, t r,j,k The jamming dwell time of our jammer j against the enemy radar r. For the jammer antenna gain, For the interference wavelength, The distance from the enemy radar r to our jamming device j. The comprehensive loss coefficient, Let the receiving gain of the antenna of the opposing radar r in the interference direction be expressed as:

[0041] For example, such as Figure 3 As shown, Let θ be the antenna gain of the opposing radar r. 0.5 For half-beamwidth (3dB), θ r,q,j,k This represents the angle between the main lobe of the radar r and the main lobe of the jammer j when the radar r illuminates our target q. The jamming signal can enter the receiver from the main lobe of the radar antenna (main lobe jamming) or from the side lobe (side lobe jamming). Due to the existence of the radar antenna directional gain, the energy of the jamming signal received by the radar in each direction is different. For jamming signals using radio frequency noise, the radar receiver must process them in the same way as thermal noise. If we assume that the jamming signals are incoherent, the total jamming signal energy can be obtained by superimposing the jamming signal energy in each direction. The thermal noise energy E0 can be expressed as: E0=k'T0(8), where k' is the Boltzmann constant and T0 is the total noise temperature of the system (including internal and external noise temperatures). In a shorter pulse accumulation period, the energy ratio can be approximated as the power ratio, and the final SINR is:

[0042] S104. Calculate the Bayesian information matrix of each of our targets at the current moment based on the measurement values.

[0043] Here, the Bayesian information matrix is ​​a function of the jamming dwell time vector at time k; the jamming dwell time vector at time k represents the jamming dwell time of each of our jammers against each of the opposing radars at time k.

[0044] Specifically, the expression for the Bayesian information matrix of our target q at time k is as follows:

[0045]

[0046] Where q = 1, 2, ..., N Q N QLet r represent the number of our targets, where r = 1, 2, ..., N R N R J represents the number of enemy radars. q,k (t k Let be the Bayesian information matrix of our target q at time k, and k-1 represent the previous time step. Let be the Bayesian information matrix of our target q at time k-1. t k Let N be the dwell time of each friendly jammer against each enemy radar at time k. J The number of our jammers, T represents the transpose, t k The dimension is N R ×N J Dimension, t k In Let j be the dwell time vector of our jammer j against each enemy radar, j = 1, 2, ..., N J , Let q be the state of our target at time k. Let h be the state of our target q at time k-1, where the state represents position and velocity. r,q,k (·) represents the measurement function of the opposing radar r, H r,q,k At time k, the measurement value of the enemy radar r of our target q is related to... Jacobian matrix, Let q be the predicted state of our target q at time k. Let F be a zero-mean covariance matrix, and let Σ be the state transition matrix. r,q,k Let be another zero-mean covariance matrix.

[0047] S105. Based on the resource constraints of our jammers and the Bayesian information matrix of each of our targets at the current moment, construct a multi-jammer collaborative resource allocation model.

[0048] Specifically, S105 is implemented in the following way:

[0049] S1051. Based on the Bayesian information matrix of each of our targets at the current time, determine the BCRLB of each of our targets.

[0050] Specifically, when J q,k (t k When ) is the Bayesian information matrix of our target q at time k, Let BCRLB be the BCRLB of our target q at time k.

[0051] S1052. Determine the state estimation error of each of our targets based on the BCRLB of each target at the current time.

[0052] From the perspective of jammer transmission parameters, changing the jammer's radiation resources to the radar can affect the radar's target echo SINR, thereby affecting target tracking performance, which can be characterized by the BCRLB of the target tracking error.

[0053] Here, for each friendly target, the product of the Bayesian Craméro lower bound of the friendly target at the current time and the preset normalized matrix and the transpose of the preset normalized matrix can be determined; the trace operation is performed on the product to obtain the state estimation error of the friendly target.

[0054] Specifically, the expression for the state estimation error of our target q at time k is as follows:

[0055]

[0056] in, Let be the state estimation error of our target q at the current moment. Let be the BCRLB of our target q at the current moment, and Λ be the preset normalization matrix. Δt is the sampling interval, I is the identity matrix, T represents the transpose, and Tr(·) represents the trace operation.

[0057] S1053. Based on the state estimation error of each of our targets at the current moment and the resource constraints of our jammers, construct a multi-jamming machine collaborative resource allocation model.

[0058] Here, the state estimation errors of each of our targets at the current moment can be summed to obtain the overall tracking error; the preset total jamming dwell time of each of our jammers is used as the resource constraint of our jammers; based on the overall tracking error and the preset total jamming dwell time of each of our jammers, a multi-jamming machine collaborative resource allocation model is constructed.

[0059] To minimize the overall tracking accuracy of the enemy's networked radar on our targets, i.e., to maximize the tracking error, a minimum tracking accuracy method is adopted. To evaluate the cooperative jamming performance of multiple jammers, a cooperative resource allocation model for multiple jammers is established under the constraint of jammer dwell time resources. Specifically, the cooperative resource allocation method aims to optimize the allocation of transmission resources of multiple jammers under the condition of limited jamming resources, so as to minimize the overall tracking accuracy (maximum tracking error) of the networked radar against the target, that is, to make Therefore, the expression for the constructed multi-interference machine cooperative resource allocation model is as follows:

[0060]

[0061] in, t is the preset total jamming dwell time of our jammer j. kLet t be the dwell time of each friendly jammer against each enemy radar at time k. r,j,k Let Et be the dwell time of our jammer j against the enemy radar r at time k. Furthermore, the constraint condition can be rewritten as: Et k =T total Where E is the corresponding coefficient matrix. This is the preset total jamming dwell time for all our jammers.

[0062] S106. The augmented Lagrange multiplier method is used to solve the multi-jamming machine cooperative resource allocation model and obtain the solution results. The solution results represent the jamming dwell time of each of our jammers on each of the opposing radars at the current moment.

[0063] Here, based on the multi-interference machine cooperative resource allocation model, a corresponding augmented Lagrangian function is constructed; the constructed augmented Lagrangian function is iteratively solved to obtain the solution result.

[0064] Here, the time subscript k is omitted, and the inequality constraints of the above formula (12) are written in matrix form At. k ≥0 N×1 (When A is an N×N dimensional identity matrix), the expression for the constructed augmented Lagrange function is:

[0065] in, Let σ be the dual vector, and μ be the penalty factor of the ALMM. n As auxiliary variables, μ = (μ1, μ2, ..., μ) N The penalty factor σ = 10, and the threshold ε = 10. -6 t is the original variable, E is the corresponding coefficient matrix, and T total This is the preset total jamming dwell time for all our jammers.

[0066] Here, to ensure that the solution during the iteration process is always in the feasible descent direction, the gradient projection method can be used to update the original variables, and multiple iterations can be performed to obtain the resource allocation results of the multi-jamming machine for each radar node. The inequality constraints of formula (12) can be written in matrix form At. k ≥0 N×1 (A is an N×N dimensional identity matrix),

[0067] Specifically, the principle for solving the constructed augmented Lagrangian function is as follows:

[0068] 1) Initialize parameter σ>0, iteration termination error 0<ε<1, iteration index i=1;

[0069] 2) Initialize variable t (0) ∈R N (Et(0) =T total ), and μ (1) ∈R N ;

[0070] 3) Loop:

[0071] 3-1) Divide the inequality constraints into A1t (i-1) =T total,1 and A2t (i-1) =T total,2 ,make If M is not empty, then let the projection matrix P = IM. T (MM T ) -1 M, otherwise P = I;

[0072] 3-2) Order in

[0073] 3-3) Update step size

[0074] 3-4) Update the original variable t (i) =t (i-1) +αd (i) ;

[0075] 3-5) Update the dual variable λ (i+1) =λ (i) -σ (i) (Et (i) -T total );

[0076] 3-6) Update auxiliary variables

[0077] 3-7)i=i+1;

[0078] 4) If Exit the loop, let

[0079] This invention takes minimizing target tracking accuracy (i.e. maximizing tracking error BCRLB) as the objective function and, in conjunction with the resource constraints of our jammers, constructs a multi-jamming machine collaborative resource optimization model. Subsequently, since this model is a convex optimization problem, the augmented Lagrange multiplier method is used to solve it quickly, effectively reducing the tracking accuracy of the enemy's networked radar system on our targets.

[0080] This invention also provides a multi-jammer cooperative resource allocation device for networked radar, comprising:

[0081] The scenario determination module is used to determine the scenario of multi-jamming machine cooperative jamming network radar; the scenario includes multiple enemy radars, multiple friendly targets, and multiple friendly jammers;

[0082] The information acquisition module is used to acquire the position and velocity of each enemy radar, each friendly target, and each friendly jammer at the current moment; and to determine the measurement value of each enemy radar for each friendly target at the current moment based on the position and velocity.

[0083] The calculation module is used to calculate the Bayesian information matrix of each of our targets at the current moment based on the measurement values;

[0084] The model building module is used to build a multi-jamming machine collaborative resource allocation model based on the Bayesian information matrix of each of our targets at the current time and the resource constraints of our jammers.

[0085] The solution module is used to solve the multi-jamming machine cooperative resource allocation model and obtain the solution result; the solution result represents the jamming dwell time of each friendly jammer on each opposing radar at the current moment.

[0086] The specific functions of each module are as described in the methods section above, and will not be repeated here.

[0087] The following simulations further verify and illustrate the effectiveness of the present invention.

[0088] 1. Simulation parameter settings

[0089] The simulation software for this invention is MATLAB (R2021b).

[0090] Since the jamming effect can only be evaluated in relation to the jammed enemy radar, it is assumed that the enemy's networked radar uses extended Kalman filtering for target tracking. The normalized root mean square error (RMSE) and average root mean square error (ARMSE) of our target q at time k are:

[0091]

[0092]

[0093] Where, N mc For Monte Carlo times, To estimate the error, Let N be the estimated state of our target q in the i-th Monte Carlo trial. track To track duration.

[0094] Reference Figure 4A coordinated jamming scenario with a range of 120km × 90km was set. The opposing network radar system consists of 8 phased array radars, the relevant parameters of which have been obtained by electronic reconnaissance equipment. Our formation consists of 5 aircraft, of which 2 aircraft form an attack group (i.e., are the targets), each with a RCS of 1m. 2 Three accompanying jammers form a jamming suppression group (i.e., act as jammers). Their operating frequencies are within the radar's operating frequency range. For example, within 80 frames (Δt = 1s), our formation moves towards the enemy's network radar at a speed of (0, -500) m / s, while our jammers simultaneously perform coordinated jamming tasks. The penalty factor σ = 10 for ALMM, and the threshold ε = 10. -6 .

[0095] The parameters of each radar and each jammer are the same, as shown in Table 1 and Table 2 respectively.

[0096] Table 1 Radar Parameters

[0097]

[0098] Table 2 Jammer Parameters

[0099]

[0100]

[0101] 2. Simulation Content

[0102] This invention presents a comparative simulation experiment on the tracking performance and resource allocation results of average allocation of interference resources and the proposed resource allocation method. To further verify its superiority, the interference effect and real-time performance of three different methods are compared under the condition of limited number of interference beams.

[0103] 3. Simulation Result Analysis

[0104] To verify the effectiveness of the method proposed in this invention, it is compared with the cases of equal distribution of jamming resources and no distribution of jamming resources. In the case of equal distribution of jamming resources, each jammer distributes its own jamming resources evenly to each radar node, while in the case of no distribution of jamming resources, the jammer does not interfere with the other radar.

[0105] Reference Figure 5 Figures (a) and (b) show the comparison of BCRLB and RMSE for two targets under three different scenarios after 500 Monte Carlo tests. The tracking error curves of the two targets are relatively consistent because the two targets are close to each other and their spatial positions are relatively symmetrical relative to each radar node and jammer. Figure 5(a) and (b) show that: (1) in the absence of interference resource allocation, the tracking error decreases rapidly in a short time due to the fusion of information from each node in the networked radar system; (2) compared with the absence of interference, the tracking error of the networked radar on the target increases significantly when the interference resources are evenly allocated; (3) after the interference resources are optimized, the tracking error of the networked radar on the target increases further, indicating that the method proposed in this invention has a good interference effect. It should be noted that although the interference signal is transmitted one way while the target echo signal is transmitted two ways, that is, the attenuation of the target echo signal received by the radar is greater at the same distance, the radar transmission power is much greater than the jammer transmission power. As the formation continues to approach the other side, the SINR will continue to increase, that is, the tracking error will continue to decrease. Therefore, overall, the curves in the three cases show a downward trend. When our formation is close to the other side's networked radar, the radar signal energy is strong. At this time, the space for improving the interference effect is limited. Figure 5 In (a) and (b), it is shown that the BCRLB of the method proposed in this invention gradually flattens out and tends to be consistent with that of the case where interference resources are evenly distributed.

[0106] Reference Figure 6 In the table, (a), (b), and (c) represent the normalized allocation results of disturbance dwell time resources. For example... Figure 6 As shown in (a), (b), and (c), each jammer allocates jamming resources to different radars, resulting in a decrease in overall tracking accuracy. Factors affecting the jammer's resource allocation include, but are not limited to:

[0107] (1) The distance between the jammer and the radar. For example, jammer 2 allocates more resources to radars 3-6 because when jamming radars that are closer together, it is easier to obtain better jamming effect using the same jamming resources.

[0108] (2) The gain obtained when jamming energy enters the radar antenna when the enemy radar illuminates our target. For example, jammer 1 allocates more jamming resources to the farther radars 1-4 instead of the closer radars 5-8. This is because when radar 1-4 illuminates our target, the angle θ between its radar main lobe and the main lobe of jammer 1 is smaller. r,q,j,k The smaller the gain, the greater the receiving gain of the radar antenna according to formula (7). Compared with the influence of distance factors, it is easier to obtain a greater improvement in interference performance using the same interference resources.

[0109] In summary, the multi-jamming machine cooperative resource allocation method proposed in this invention can comprehensively consider the influence of various factors and achieve differentiated allocation of jamming resources for different adversary radars in a networked radar system, thereby reducing the overall tracking accuracy of the adversary networked radar. This also indicates that, in order to obtain better jamming effects during cooperative jamming, self-defense jamming or escort jamming should be used as much as possible, while the jamming signals of long-range support jammers are more likely to enter through the radar sidelobes, thus reducing the jamming effect.

[0110] The simulation results above verify the effectiveness of the method proposed in this invention. To further verify its superiority, the interference effect and real-time performance of different methods are compared under the condition that the number of interference beams is limited. At this time, the above formula (9) can be written as:

[0111] Among them, u r,j,k This is a binary variable representing the direction of the jamming beam. A value of 1 indicates that the jammer j is jamming the radar r, and a value of 0 indicates that the jammer j is not jamming the radar r. Therefore, the jamming dwell time variable t... r,j,k satisfy:

[0112] Consider the RJBSP method, a two-step joint optimization method based on Particle Swarm Optimization (PSO), denoted as S1. The dwell time allocation result obtained by the proposed method is processed using the Rounding Technique (TRT) to finally obtain a suboptimal beam pointing and a new dwell time allocation result, denoted as S2. The method of randomly allocating beam pointing while uniformly allocating dwell time is denoted as S3. It should be noted that all methods assume that no more than two beams are allocated to each radar, and no more than three beams are generated by each jammer. The iteration count for method S1 is set to 50, the population size to 100, the group learning factor to 1.5, and the self-learning factor to 1. The simulation environment is MATLAB R2021b.

[0113] Reference Figure 7The results show that the ARMSE of each target after 100 Monte Carlo experiments is compared in S1, S2 and S3. The results show that the ARMSE of S3 is lower. This is because the beam pointing of the jammer is random and some jamming energy enters from the radar sidelobe, thus affecting the jamming effect. The ARMSE of S2 is the highest, indicating that the tracking accuracy of the network radar for each target is the worst at this time, that is, the jamming effect of our jammer is the best. The jamming performance of S1 is close to that of S2. This is because the model described in formula (12) is a convex problem in the case of continuous variables. Theoretically, the two-step method based on particle swarm optimization in S1 can solve the optimal solution of the current step in each step. However, the performance of the PSO algorithm is affected by the number of populations, the number of iterations and the learning factor, and it is difficult to accurately solve the global optimal solution. Therefore, the jamming effect is reduced.

[0114] Reference Figure 8 To compare the average running times of S1 and S2 at each moment after convergence, it can be seen that the running time of S2 is much shorter than that of S1, indicating that it can meet the real-time requirements of networked radar systems. In summary, by adding beam constraints to the original convex problem, a two-step solution can still be achieved by combining the TRT method and the convex optimization method.

[0115] In summary, simulation experiments have verified the correctness, effectiveness, and reliability of the method proposed in this invention.

[0116] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0117] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0118] In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple instances. While different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce a good effect.

[0119] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for collaborative resource allocation among multiple jammers in networked radar systems, characterized in that, include: A scenario involving multiple jammers coordinating to jam a networked radar system is identified; this scenario includes multiple enemy radars, multiple friendly targets, and multiple friendly jammers. Obtain the current position and velocity of each enemy radar, each friendly target, and each friendly jammer; Based on the position and the speed, determine the measurement value of each enemy radar for each friendly target at the current moment; Calculate the Bayesian information matrix of each of our targets at the current moment based on the measured values; Based on the resource constraints of our jammers and the Bayesian information matrix of each of our targets at the current moment, a multi-jammer collaborative resource allocation model is constructed. The augmented Lagrange multiplier method is used to solve the multi-jamming machine cooperative resource allocation model to obtain the solution results; the solution results represent the jamming dwell time of each friendly jammer on each opposing radar at the current moment. Among them, the target of our side at the current moment q The expression for the Bayesian information matrix is ​​as follows: ； in, , The quantity of our targets. , The number of enemy radars. k Indicates the current time. For the current moment, our target q Bayesian information matrix, k -1 indicates the time before the current time. For the target of our side at the previous moment q Bayesian information matrix, , For the first k The duration of interference from each of our jamming devices to each of the enemy's radars at any given time. The number of our jamming devices. Indicates transpose. The dimension is dimension, In For our jamming machine j The dwell time vector of interference against each enemy radar. , For the first k Our target at all times q state, For the first k -1 moment our target q The state, which represents position and velocity. For the other side's radar r The measurement function, It is the first k Constant enemy radar r For our target q The measured value is about Jacobian matrix, For the predicted first k Our target at all times q state, Let be the first zero-mean covariance matrix. Here is the state transition matrix. This is the second zero-mean covariance matrix; The expression for the multi-interference machine cooperative resource allocation model is as follows: ； in, , The number of our jamming devices. , The quantity of our targets. , The number of enemy radars. For the first k Our target at all times q The state estimation error, For our jamming machine The preset total interference dwell time, For the first k The duration of interference from each of our jamming devices to each of the enemy's radars at any given time. For the first k Our jamming machine at all times j against the other side's radar r Interference dwell time.

2. The multi-jammer cooperative resource allocation method for networked radar according to claim 1, characterized in that, The multi-jammer cooperative resource allocation model is constructed based on the resource constraints of our jammers and the Bayesian information matrix of each of our targets at the current moment, including: Based on the Bayesian information matrix of each friendly target at the current moment, determine the Bayesian Cramer-Rao lower bound for each friendly target; the Bayesian information matrix is ​​a function of the jamming dwell time vector at the current moment; the jamming dwell time vector at the current moment represents the jamming dwell time of each friendly jammer against each enemy radar at the current moment. Based on the Bayesian Cramerlow lower bound of each of our targets at the current moment, determine the state estimation error of each of our targets; Based on the state estimation error of each of our targets at the current moment and the resource constraints of our jammers, the multi-jamming machine cooperative resource allocation model is constructed.

3. The multi-jammer cooperative resource allocation method for networked radar according to claim 2, characterized in that, The step of determining the state estimation error of each friendly target based on the Bayesian Cramérault lower bound of each friendly target at the current time includes: For each of our objectives, determine the product of the Bayesian Craméro lower bound of the objective at the current time, the preset normalized matrix, and the transpose of the preset normalized matrix; The product is subjected to trace operation to obtain the state estimation error of our target.

4. The multi-jammer cooperative resource allocation method for networked radar according to claim 1, characterized in that, The measured values ​​include: radial distance and azimuth angle; the current moment's enemy radar... r For our target q The expression for the measured value is as follows: ； in, , The number of enemy radars. , The quantity of our targets. k Indicates the current time. For the first k Constant enemy radar r For our target q The measured value, For the other side's radar r The measurement function, For the first k Our target at all times q Position and velocity, The zero-mean covariance matrix is Gaussian noise.

5. The multi-jammer cooperative resource allocation method for networked radar according to claim 2, characterized in that, The step of constructing the multi-jamming machine cooperative resource allocation model based on the state estimation error of each friendly target at the current moment and the resource constraints of the friendly jammers includes: The total tracking error is obtained by summing the state estimation errors of each of our targets at the current moment. The preset total jamming dwell time of each of our jammers is used as the resource constraint of the jammers. Based on the overall tracking error and the preset total jamming dwell time of each of our jammers, the multi-jamming machine collaborative resource allocation model is constructed.

6. The multi-jammer cooperative resource allocation method for networked radar according to claim 1, characterized in that, The augmented Lagrange multiplier method is used to solve the multi-interference machine cooperative resource allocation model, and the solution results are as follows: Based on the multi-interference machine cooperative resource allocation model, the corresponding augmented Lagrangian function is constructed; The constructed augmented Lagrangian function is iteratively solved to obtain the solution result.

7. The multi-jammer cooperative resource allocation method for networked radar according to claim 3, characterized in that, Our target at the current moment q The expression for the state estimation error is as follows: ； in, k Indicates the current time. Our target at the current moment q The state estimation error, Our target at the current moment q Bayesian Clamello's lower bound, The preset normalized matrix is, and , The sampling interval is... It is the identity matrix. Indicates transpose. This indicates a trace operation.

8. A multi-jamming machine collaborative resource allocation device for networked radar, characterized in that, include: The scenario determination module is used to determine the scenario of a multi-jammer cooperative jamming network radar. The scenario includes multiple enemy radars, multiple friendly targets, and multiple friendly jammers; The information acquisition module is used to acquire the position and velocity of each enemy radar, each friendly target, and each friendly jammer at the current moment; and to determine the measurement value of each enemy radar for each friendly target at the current moment based on the position and velocity. The calculation module is used to calculate the Bayesian information matrix of each of our targets at the current moment based on the measurement values; The model building module is used to build a multi-jamming machine collaborative resource allocation model based on the Bayesian information matrix of each of our targets at the current time and the resource constraints of our jammers. The solution module is used to solve the multi-jamming machine cooperative resource allocation model and obtain the solution result; the solution result represents the jamming dwell time of each friendly jammer against each enemy radar at the current moment; Among them, the target of our side at the current moment q The expression for the Bayesian information matrix is ​​as follows: ； in, , The quantity of our targets. , The number of enemy radars. k Indicates the current time. For the current moment, our target q Bayesian information matrix, k -1 indicates the time before the current time. For the target of our side at the previous moment q Bayesian information matrix, , For the first k The duration of interference from each of our jamming devices to each of the enemy's radars at any given time. The number of our jamming devices. Indicates transpose. The dimension is dimension, In For our jamming machine j The dwell time vector of interference against each enemy radar. , For the first k Our target at all times q state, For the first k -1 moment our target q The state, which represents position and velocity. For the other side's radar r The measurement function, It is the first k Constant enemy radar r For our target q The measured value is about Jacobian matrix, For the predicted first k Our target at all times q state, Let be the first zero-mean covariance matrix. Here is the state transition matrix. This is the second zero-mean covariance matrix; The expression for the multi-interference machine cooperative resource allocation model is as follows: ； in, , The number of our jamming devices. , The quantity of our targets. , The number of enemy radars. For the first k Our target at all times q The state estimation error, For our jamming machine The preset total interference dwell time, For the first k The duration of interference from each of our jamming devices to each of the enemy's radars at any given time. For the first k Our jamming machine at all times j against the other side's radar r Interference dwell time.

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