Joint optimization method of UAV trajectory and jamming resources for composite jamming network radar

Abstract

The present invention provides a joint optimization method for UAV tracks and jamming resources for composite jamming network radars, including: introducing suppression jamming while performing track deception to establish a UAV cluster composite jamming network radar model; establishing a joint optimization model for UAV tracks and jamming resources for composite jamming network radars by jointly optimizing the configuration of the UAV's beam pointing, track, and power resources, using the UAV's motion parameters as constraints and minimizing the probability of the network radar detecting the UAV performing the jamming mission as the optimization goal; and solving the optimization model using a hybrid optimization algorithm combining a particle swarm optimization algorithm and an interior point method to achieve composite jamming of the network radar. The present invention reduces the difficulty of UAV track deception and effectively improves the feasibility of track deception. Furthermore, on the basis of deceptive jamming, suppression jamming is introduced, and by rationally allocating jamming resources, the jamming effect on the network radar is further improved, thereby reducing the probability of the UAV being detected.

Description

Technical Field

[0001] The present invention relates to radar electronic countermeasure technology, and in particular to a method for jointly optimizing the trajectory and jamming resources of unmanned aerial vehicles (UAVs) for composite jamming network radars. Background Art

[0002] In modern military and defense fields, radar detection systems serve as a critical means of information acquisition, and their performance and reliability are directly linked to battlefield situational awareness and decision-making. With the continuous advancement of radar technology, networked radar systems, thanks to the collaborative operation of multiple radar nodes, information sharing, and fusion, enhance radar detection performance, expand detection range, and improve anti-interference capabilities compared to traditional single radars. Therefore, networked radars present new challenges to electronic countermeasures.

[0003] Currently, a variety of electronic jamming methods are available for networked radars, but traditional single jamming methods often fail to achieve optimal results, especially in complex electromagnetic environments where multiple types of jamming coexist and intertwine. As emerging aerial platforms, drones (UAVs) exhibit significant potential in electronic countermeasures due to their maneuverability, low cost, and ability to carry a variety of payloads. Currently, suppression jamming and deception jamming are the two primary methods of active jamming. Suppression jamming uses noise or pseudo-noise jamming signals to drown out or suppress echo signals carrying target status information, making it difficult for networked radars to detect targets and measure target parameters. Deception jamming, on the other hand, uses stored-delay forwarding radar signals to create a false target on the radar, effectively deceiving the networked radar. However, when UAVs perform complex jamming on networked radars, how to plan their flight paths to maximize jamming effectiveness and properly allocate limited jamming resources remains a pressing technical challenge. Traditional UAV trajectory planning methods, mostly based on static or simple dynamic environmental models, struggle to adapt to the complex and changing detection characteristics of networked radars and the rapidly changing electronic jamming environment. At the same time, the allocation of interference resources lacks systematicity and scientificity, resulting in low interference efficiency and difficulty in forming an effective interference system. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method for jointly optimizing the trajectory and jamming resources of UAVs for composite jamming networked radars, so as to realize composite jamming of networked radars.

[0005] Technical solution: The method for jointly optimizing the UAV track and jamming resources for composite jamming network radar of the present invention comprises the following steps:

[0006] M drones are used to spoof the track of a networked radar system consisting of N radars, forming P false tracks. At the same time, drones are introduced to suppress and interfere with the radars, and a model of drone cluster composite interference with networked radars is established.

[0007] By jointly optimizing the UAV's beam pointing, track, and power resources, and implementing track deception on the networked radar, with the UAV's motion parameters as constraints and the optimization goal of minimizing the probability of the networked radar detecting the UAV performing the jamming mission, a joint optimization model of UAV track and jamming resources for composite jamming networked radars was established.

[0008] A hybrid optimization algorithm combining the particle swarm optimization algorithm and the interior point method is used to solve the optimization model, and the UAV cluster beam pointing, trajectory and power resource allocation results that meet the constraints are obtained. In this way, composite interference to the networked radar is achieved while satisfying the pre-set UAV dynamic constraints and generating effective deception trajectory.

[0009] Furthermore, the motion control equation of the UAV when implementing the deception jamming mission is:

[0010]

[0011] Among them, β e is the flight pitch angle of the UAV, θ is the pitch angle of the UAV in the direction of the radar, α e is the flight angle of the UAV, φ is the direction angle of the UAV in the direction of the radar, φ' is the derivative of φ, θ' is the derivative of θ, r' is the derivative of r, and r is the distance from the UAV to the radar. is the square of the UAV’s flight speed;

[0012] The UAV always satisfies the coupling relationship between the radar, the UAV and the false target during the implementation of the track deception jamming mission. The position of the false target and the radar position are known a priori. The motion variables of the UAV will be constrained in one dimension, that is, only by controlling its flight direction angle α e It is possible to achieve track control under track deception coupling constraints;

[0013] The interference suppression adopts noise interference, and the noise interference signal is expressed as:

[0014]

[0015] Where J(t) is the noise interference signal, is the noise interference signal amplitude, f j is the center frequency of the noise interference signal, K FM is the frequency modulation slope, μ(t') is the modulation noise, ψ is the phase function of the noise interference signal, exp is the exponential operation, j represents the imaginary operation, t represents the signal change over time, and ['] is the derivative operation; the above formula is simplified to:

[0016]

[0017] Among them, s m,n,k (t) is the normalized complex envelope of the suppressed interference signal.

[0018] Furthermore, the radar adopts a self-transmitting and self-receiving working mode. Each radar only receives and processes the echo signal sent by itself and scattered by the target. Each radar can detect M drones at time k, so each radar will receive M echo signals. Under the interference suppression condition, the radar will also receive interference signals transmitted by multiple drones. The signal received by radar n at time k is:

[0019]

[0020] Among them, r n,k (t) represents the signal received by radar n at time k, r m,n,k (t) represents the echo signal of the mth UAV received by radar n at the kth moment; j m,n,k (t) represents the suppression jamming signal received by radar n from the mth UAV at the kth moment; w n,k (t) represents the radar receiver thermal noise of radar n at time k, and t indicates that these signals vary with time;

[0021] When M drones cooperate to suppress a single radar, the total interference signal power received by the radar is the sum of the power of each interference signal. According to the power superposition principle, the total interference signal power received by radar n when detecting drone m is for:

[0022]

[0023] in, is the suppression jamming signal power received by radar n from the mth UAV at the kth moment, u m,n,k is the beam pointing situation of the mth UAV to the nth radar at the kth moment, P m,n,k is the interference power of the mth UAV on the nth radar at the kth moment.

[0024] Furthermore, the established UAV track and jamming resource joint optimization model for composite jamming network radar is expressed as follows:

[0025]

[0026] in, To improve the detection performance of networked radar on drone clusters, Pd k (u k ,P k ,R k ) is the detection probability of the networked radar to the drone cluster at the kth moment, u kis the UAV cluster beam pointing matrix at the kth moment, P k is the UAV cluster interference power matrix at the kth moment, R k is the distance matrix between the UAV cluster and the radar at the kth moment, is the detection probability requirement, P m,n,k is the interference power of the mth UAV to the nth radar at the kth moment, P min is the lower limit of UAV beam interference power, P max is the upper limit of the UAV beam interference power, u m,n,k is the beam pointing situation of the m-th UAV to the n-th radar at the k-th moment, is the total power of the jammer, L is the number of beams generated by each UAV, S is the maximum number of jammed beams, △α e is the change in the UAV flight angle, △α max is the maximum value of the change in the UAV flight direction angle, △α min is the minimum value of the change in the UAV flight direction angle, △β e is the change in the pitch angle of the UAV, △β max is the maximum value of the change in the pitch angle of the UAV flight, △β min is the minimum value of the change in the pitch angle of the UAV flight, v e is the flight speed of the UAV, v max is the upper limit of the UAV flight speed, v min The lower limit of the drone's flight speed.

[0027] Furthermore, the networked radar adopts the KN criterion, that is, when the number of radar nodes in the networked radar that have detected drone m exceeds the detection threshold K, 1≤K≤N, it is determined that the networked radar has detected drone m; otherwise, it is determined that the drone has not been detected; as shown in the following formula:

[0028]

[0029] in, represents the judgment result of the network radar on UAV m at the kth moment; represents the decision result of radar n on drone m at the kth moment and According to the KN criterion, the detection probability of the networked radar to the drone m at time k is:

[0030]

[0031] in, is the detection probability of UAV m by the networked radar at the kth moment, is the equivalent expression of the detection probability of the networked radar to the UAV m at the kth moment, u k is the UAV cluster beam pointing matrix at the kth moment, Pk is the UAV cluster interference power matrix at the kth moment, R k is the distance matrix between the UAV cluster and the radar at the kth moment, is the detection probability of radar n to drone m at the kth moment, represents the permutation and combination in which the sum of the judgment results of N radar nodes on UAV m is j;

[0032] The vector Pd formed by the detection probability of the networked radar for M drones k As a performance evaluation indicator for suppression jamming network radar:

[0033]

[0034] Among them, Pd k (u k ,P k ,R k ) is the detection probability matrix of the networked radar to the UAV cluster at the kth moment;

[0035] Detection probability requirements for multiple targets for:

[0036]

[0037] in, To meet the detection requirements for the first drone, To meet the detection requirements for the second drone, The detection requirement for the Mth drone;

[0038] Based on the principle of quality of service, a global cost function is established:

[0039]

[0040] in, To improve the detection performance of networked radar on drone clusters, Pd k (u k ,P k ,R k ) is the detection probability matrix of the networked radar to the UAV cluster at the kth moment, The detection performance of the networked radar for the mth UAV is: is the detection probability of the networked radar to the mth UAV cluster at the kth moment, is the detection requirement for the mth UAV.

[0041] Furthermore, the optimization model solution method is:

[0042] (1) Based on the preset false target and radar position prior information, the optimal trajectory of the UAV that satisfies the dynamic constraints of the optimization model in this scenario is obtained using the particle swarm optimization algorithm, and the optimal distance correspondence between the UAV and the radar at each moment is obtained.

[0043] (2) In seeking Based on this, it is assumed that the UAV can interfere with all radar nodes at the same time and the transmission power of each beam is evenly distributed. is the UAV interference power under the condition of uniform power distribution, is the total power of the jammer; for the convenience of solving, point the beam to the variable u k Relaxed to a continuous variable in the interval [0,1]

[0044] At this point, the optimization problem is simplified to:

[0045]

[0046] in, In order to simplify the detection performance of the networked radar on the drone cluster, is the detection probability matrix of the networked radar to the drone cluster, is the UAV cluster interference power matrix under average radiation power, is the pointing direction of the mth UAV to the nth radar under the average radiated power;

[0047] The interior point method is used to solve the above equation to obtain the beam pointing variable u k The relaxation result And initialize the beam pointing result Under the constraints, The maximum value is Set 1 in the middle and repeat the The maximum value is Set 1 in the middle until all beam resources of M jammers are exhausted, and finally get the optimal allocation method of beam pointing

[0048] (3) In seeking and Based on the above, the interference power allocation result is solved. At this point, the optimization problem has been simplified to:

[0049]

[0050] Similarly, the interior point method is used to obtain the optimal interference power allocation result

[0051] Furthermore, step (1) includes the following steps:

[0052] (a) Initialize the population size, population inertia, particle state and fitness function;

[0053] (b) Iteratively optimizing the flight speed, flight direction angle, and flight pitch angle parameters of the UAV at that moment;

[0054] (c) Return to step (b) and repeat until the absolute value of the difference between the two optimization objective functions is less than an arbitrary minimum value ε>0, thereby obtaining the optimal UAV flight speed, flight direction angle, and flight pitch angle motion state parameters at the current moment;

[0055] (d) Determine the initial position of the UAV at the next moment based on the coupling relationship between the false target, the UAV, and the radar;

[0056] (e) Repeat steps (b) to (d) until the distributed online decision-making of the UAV cluster flight trajectory is completed, that is, the optimal distance correspondence between the UAV and the radar at each moment is obtained.

[0057] The system corresponding to the above method includes:

[0058] The composite jamming model construction unit is used to implement track deception on a networked radar system consisting of N radars using M drones, forming P false tracks. At the same time, it introduces drone suppression jamming on the radars to establish a drone cluster composite jamming networked radar model.

[0059] The optimization model construction unit is used to jointly optimize the configuration of the UAV's beam pointing, track, and power resources. Based on the implementation of track deception on the networked radar, the unit uses the UAV's motion parameters as constraints and takes minimizing the probability of the networked radar detecting the UAV performing the jamming mission as the optimization goal. This unit establishes a joint optimization model of the UAV's track and jamming resources for the composite jamming networked radar.

[0060] The optimization model solving unit is used to solve the optimization model using a hybrid optimization algorithm that combines the particle swarm optimization algorithm with the interior point method, and obtain the drone cluster beam pointing, trajectory and power resource allocation results that meet the constraints, thereby achieving composite interference to the networked radar while satisfying the pre-set drone dynamic constraints and generating effective deception tracks.

[0061] The control device of the above method includes a processor, a communication interface, a memory and a communication bus;

[0062] The processor, the communication interface, and the memory communicate with each other via the communication bus.

[0063] The memory is used to store computer programs;

[0064] The processor is used to implement the steps of the method for jointly optimizing the UAV track and interference resources for the composite interference networking radar when executing the program stored in the memory.

[0065] A storage medium for storing the above method, wherein a computer program is stored on the storage medium, and when the computer program is executed by at least one processor, the steps of the above-mentioned method for jointly optimizing the trajectory and interference resources of drones for composite interference networking radar are implemented.

[0066] Beneficial effects: Compared with the existing technology, the significant technical effects of the present invention are: (1) Under the condition of limited interference resources, by jointly optimizing the configuration of the UAV's beam pointing, track and power resources, on the basis of implementing track deception on the networked radar, the probability of the networked radar detecting the UAV implementing the interference mission is minimized, thereby reducing the exposure risk of the UAV and effectively improving the success rate of the interference mission and the survivability of the UAV; (2) The two interference methods of deception interference and suppression interference are integrated to effectively weaken and disrupt the detection and tracking capabilities of the radar system, which not only meets the pre-set strict UAV dynamic constraints, reduces the difficulty of the UAV to implement track deception, and effectively improves the feasibility of track deception, but also introduces suppression interference on the basis of deception interference. By reasonably allocating interference resources, the interference effect on the networked radar is further improved, and the probability of the UAV being discovered is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Flow chart of the method of the present invention;

[0068] Figure 2 It is a schematic diagram of composite interference;

[0069] Figure 3 This is a composite interference simulation scenario diagram;

[0070] Figure 4 Schematic diagram of UAV motion parameters, where (a) is the UAV's flight direction angle, (b) is the UAV's flight pitch angle, and (c) is the UAV's flight speed;

[0071] Figure 5 Schematic diagram of the distance between the UAV and the radar;

[0072] Figure 6 Schematic diagram of the interference resource optimization results, where (a) is the interference resource allocation result of the drone cluster to radar 1, (b) is the interference resource allocation result of the drone cluster to radar 2, and (c) is the interference resource allocation result of the drone cluster to radar 3;

[0073] Figure 7 Schematic diagram of the probability of radar detecting a drone when no suppression jamming is implemented;

[0074] Figure 8 Schematic diagram of the detection probability of each radar for a drone after suppressing interference is implemented;

[0075] Figure 9 Schematic diagram of the detection probability of the networked radar against the drone after the suppression interference is implemented;

[0076] Figure 10 Schematic diagram of networked radar detection performance after implementing composite interference. DETAILED DESCRIPTION

[0077] The structure and working process of the present invention will be further described below with reference to specific embodiments and drawings.

[0078] like Figure 1 As shown, the optimization method of the present invention comprises the following steps:

[0079] 1. Establish the radar model for the UAV cluster composite jamming network:

[0080] M drones are used to spoof the track of a networked radar system composed of N radars, forming P false tracks. In order to reduce the probability of the enemy networked radar detecting the friendly drone, the drone is used to perform deceptive jamming on the networked radar while also exerting suppressive jamming. Assuming that the parameters of each enemy radar (such as radar position, carrier frequency, pulse width, etc.) have been obtained, and the radar position, drone position, and false target position are all known, the composite jamming diagram is shown as follows: Figure 2 shown.

[0081] The motion control equation of the UAV when implementing the deception jamming mission is as follows:

[0082]

[0083] Among them, β e is the flight pitch angle of the UAV, θ is the pitch angle of the UAV in the direction of the radar, α e is the flight angle of the UAV, φ is the direction angle of the UAV in the direction of the radar, φ' is the derivative of φ, θ' is the derivative of θ, r' is the derivative of r, and r is the distance from the UAV to the radar. is the square of the UAV’s flight speed.

[0084] From formula (1), we can see that since the UAV needs to always satisfy the coupling relationship between the radar, the UAV and the false target during the implementation of the track deception jamming mission, and the false target position and the radar position are known a priori, the UAV's motion variables will be constrained in one dimension, that is, only by controlling its flight direction angle α eTrack control under track deception coupling constraints can be achieved.

[0085] Based on the implementation of track deception on networked radars, the present invention introduces suppression interference to increase the success rate of deception, thereby enhancing the interference effect on networked radars. The present invention mainly uses noise interference. The noise interference signal implemented by drone m on radar n can be expressed as:

[0086]

[0087] Where J(t) is the noise interference signal, is the noise interference signal amplitude, f j is the center frequency of the noise interference signal, K FM is the frequency modulation slope, μ(t') is the modulation noise, ψ is the phase function of the noise interference signal, exp is the exponential operation, j represents the imaginary operation, t represents the signal change over time, and ['] is the derivative operation. Equation (2) can be simplified to:

[0088]

[0089] Among them, s m,n,k (t) is the normalized complex envelope of the suppressed interference signal.

[0090] The present invention considers radars operating in a self-transmitting and self-receiving mode. Each radar only receives and processes the echo signals it transmits and scattered by the target. If each radar can detect M drones at time k, then each radar will receive M echo signals. Under interference suppression conditions, the radar will also receive interference signals from multiple drones. The signal received by radar n at time k is:

[0091]

[0092] Among them, r n,k (t) represents the signal received by radar n at time k, r m,n,k (t) represents the echo signal of the mth UAV received by radar n at the kth moment; j m,n,k (t) represents the suppression jamming signal received by radar n from the mth UAV at the kth moment; w n,k (t) represents the radar receiver thermal noise of radar n at time k, and t represents the time variation of the signal.

[0093] When M drones cooperate to suppress a single radar, the total interference signal power received by the radar is the sum of the power of each interference signal. According to the power superposition principle, the total interference signal power received by radar n when detecting drone m is for:

[0094]

[0095] in, is the suppression jamming signal power received by radar n from the mth UAV at the kth moment, u m,n,k is the beam pointing situation of the mth UAV to the nth radar at the kth moment, P m,n,k is the interference power of the mth UAV on the nth radar at the kth moment.

[0096] 2. Construct a joint optimization model of UAV trajectory and jamming resources for composite jamming network radar:

[0097] Considering that the UAV adopts a multi-beam jamming system, it can generate multiple power-controllable beams to interfere with multiple radar nodes at the same time. and To represent the variables of the jamming task. Define the beam pointing vector of the UAV cluster Indicates whether UAV m is assigned beam jammer radar n,u m,n,k is the beam pointing situation of the m-th UAV to the n-th radar at the k-th moment, n=1,…,N; define the UAV’s transmission power vector represents the interference power emitted by each UAV at the kth moment, P m,n,k is the interference power of the mth UAV on the nth radar at the kth moment; [·] T represents the transpose operation, u m,n,k and P m,n,k The following constraints need to be met:

[0098]

[0099] Among them, L is the number of beams generated by each UAV, S is the maximum number of beams interfered with, and P min is the lower limit of UAV beam interference power, P max is the upper limit of the UAV beam jammer power, is the total power of the jammer.

[0100] Among them, considering the limitations of UAV equipment, constraint 1 means that each UAV can generate a maximum of L beams; considering that all radar nodes can be interfered, constraint 2 means that the number of beams allocated to each radar does not exceed S; constraint 3 means that the transmission power of the beam must be within the set power range; constraint 4 means that the total power of each UAV is certain; constraints 5 and 6 mean that when UAV m allocates a beam to interfere with radar n, the power of this beam is not 0; otherwise, the transmission power is 0.

[0101] Consider the KN criterion (rank K criterion) used by networked radars. That is, when the number of radar nodes in the networked radar that have detected drone m exceeds the detection threshold K (1≤K≤N), the networked radar is considered to have detected drone m; otherwise, it is considered to have not detected the target. This is shown in the following formula:

[0102]

[0103] in, represents the judgment result of the network radar on UAV m at the kth moment; represents the decision result of radar n on drone m at the kth moment and According to the rank K fusion criterion, the detection probability of the networked radar to the drone m at time k is:

[0104]

[0105] in, is the detection probability of UAV m by the networked radar at the kth moment, is the equivalent expression of the detection probability of the networked radar to the UAV m at the kth moment, u k is the UAV cluster beam pointing matrix at the kth moment, P k is the UAV cluster interference power matrix at the kth moment, R k is the distance matrix between the UAV cluster and the radar at the kth moment, is the detection probability of radar n to drone m at the kth moment, is the decision of radar n on drone m at the kth moment, It represents the permutation and combination in which the sum of the judgment results of N radar nodes on UAV m is j.

[0106] The vector Pd formed by the detection probability of the networked radar for M drones k Can be used as a performance evaluation indicator for suppressing interference network radars:

[0107]

[0108] Among them, Pd k (u k ,P k ,R k ) is the detection probability matrix of the networked radar to the drone cluster at the kth moment.

[0109] Considering that in the actual execution of the composite jamming task, each UAV has the same importance, that is, the detection probability requirement for each UAV is approximately the same, the detection probability requirement for multiple targets is defined as for:

[0110]

[0111] in, To meet the detection requirements for the first drone, To meet the detection requirements for the second drone, It is the detection requirement for the Mth drone.

[0112] Based on the principle of quality of service, a global cost function is established:

[0113]

[0114] in, To improve the detection performance of networked radar on drone clusters, Pd k (u k ,P k ,R k ) is the detection probability matrix of the networked radar to the UAV cluster at the kth moment, The detection performance of the networked radar for the mth UAV is: is the detection probability of the networked radar to the mth UAV cluster at the kth moment, The detection requirement of the networked radar for the mth UAV at the kth moment.

[0115] The composite jamming algorithm for networked radars proposed in this paper aims to minimize the probability of networked radar detecting the jamming UAV by jointly optimizing the configuration of the UAV's beam pointing, track, and power resources under the condition of limited jamming resources, while implementing track deception on the networked radar. The optimization model can be established as follows:

[0116]

[0117] in, is the total power of the jammer, △α e is the change in the UAV flight angle, △α max is the maximum value of the change in the UAV flight direction angle, △α min is the minimum value of the change in the UAV flight direction angle, △β e is the change in the pitch angle of the UAV, △β max is the maximum value of the change in the pitch angle of the UAV flight, △β min is the minimum value of the change in the pitch angle of the UAV flight, v e is the flight speed of the UAV, v max is the upper limit of the UAV flight speed, v minis the lower limit of the UAV's flight speed; constraints 1 and 2 indicate that the interference beam direction and interference power are coupled with each other, and the interference power has upper and lower limits; constraint 3 indicates that each UAV has a corresponding interference power constraint; constraint 4 indicates that the number of interference beams generated by each UAV does not exceed L, and each radar will be interfered with and will be interfered with by a maximum of S beams; constraints 5, 6, and 7 represent the UAV's kinematic constraints, and the changes in the UAV's heading angle and pitch angle cannot exceed the upper and lower limits of the constraints.

[0118] 3. Use particle swarm optimization algorithm and interior point method to solve the optimization model:

[0119] The present invention adopts a three-step solution method, and the specific steps are as follows:

[0120] (1) Based on the prior information such as the preset false target and the radar position, the optimal trajectory that satisfies the UAV dynamic constraints of formula (13) in this scenario is obtained using the particle swarm optimization algorithm, and the optimal distance correspondence between the UAV and the radar at each moment is obtained.

[0121] The specific solution steps are as follows:

[0122] (a) Initialize the population size, population inertia, particle state and fitness function;

[0123] (b) Iteratively optimize the parameters of the UAV at that moment, such as flight speed, flight direction angle, and flight pitch angle;

[0124] (c) Return to step (b) and repeat until the absolute value of the difference between the two optimization objective functions is less than an arbitrary minimum value ε>0, thereby obtaining the optimal UAV flight speed, flight direction angle, flight pitch angle and other motion state parameters at the current moment;

[0125] (d) Determine the initial position of the UAV at the next moment based on the coupling relationship between the false target, the UAV, and the radar;

[0126] (e) Repeat steps (b)-(d) until the distributed online decision-making of the UAV cluster flight trajectory is completed, that is, the optimal distance correspondence between the UAV and the radar is obtained.

[0127] (2) In seeking Based on this, it is assumed that the UAV can interfere with all radar nodes at the same time and the transmission power of each beam is evenly distributed. is the UAV interference power under the condition of uniform power distribution, is the total power of the jammer. To facilitate the solution, the beam needs to be pointed to the variable u k Relaxed to a continuous variable in the interval [0,1]

[0128] At this point, the optimization problem (13) is simplified to:

[0129]

[0130] in, In order to simplify the detection performance of the networked radar on the drone cluster, is the detection probability matrix of the networked radar to the drone cluster, is the UAV cluster interference power matrix under average radiation power, is the pointing direction of the mth UAV to the nth radar under the average radiated power.

[0131] The interior point method is used to solve equation (14) to obtain the beam pointing variable u k Relaxation results And initialize the beam pointing result Under the constraints of formula (6), The maximum value is Set 1 in the middle and repeat the above steps (the above steps refer to continuously setting The maximum value is Set 1 in the middle) until all beam resources of M jammers are exhausted, and finally the optimal beam pointing allocation method is obtained

[0132] The specific solution steps are as follows:

[0133] (a) Initialization

[0134] (b) Solve equation (14) using the interior point method and obtain the optimal relaxation

[0135] (c) Find the The maximum value in , update the corresponding It represents the optimal allocation result of the beam pointing of the m-th UAV to the radar n at the k-th time;

[0136] (d) Repeat step (c) until the jammer beam resources are exhausted under the constraints;

[0137] (e) Output optimal beam pointing

[0138] (3) In seeking and Based on the above, the interference power allocation result is solved. At this point, the optimization problem has been simplified to:

[0139]

[0140] Similarly, the interior point method is used to obtain the optimal interference power allocation result

[0141] The system corresponding to the above method includes:

[0142] The composite jamming model construction unit is used to implement track deception on a networked radar system consisting of N radars using M drones, forming P false tracks. At the same time, it introduces drone suppression jamming on the radars to establish a drone cluster composite jamming networked radar model.

[0143] The optimization model construction unit is used to jointly optimize the configuration of the UAV's beam pointing, track, and power resources. Based on the implementation of track deception on the networked radar, the unit uses the UAV's motion parameters as constraints and takes minimizing the probability of the networked radar detecting the UAV performing the jamming mission as the optimization goal. This unit establishes a joint optimization model of the UAV's track and jamming resources for the composite jamming networked radar.

[0144] The optimization model solving unit is used to solve the optimization model using a hybrid optimization algorithm that combines the particle swarm optimization algorithm with the interior point method, and obtain the drone cluster beam pointing, trajectory and power resource allocation results that meet the constraints, thereby achieving composite interference to the networked radar while satisfying the pre-set drone dynamic constraints and generating effective deception tracks.

[0145] The control device of the above method includes a processor, a communication interface, a memory and a communication bus;

[0146] The processor, the communication interface, and the memory communicate with each other via the communication bus.

[0147] The memory is used to store computer programs;

[0148] The processor is used to implement the steps of the method for jointly optimizing the UAV track and interference resources for the composite interference networking radar when executing the program stored in the memory.

[0149] A storage medium for storing the above method, wherein a computer program is stored on the storage medium, and when the computer program is executed by at least one processor, the steps of the above-mentioned method for jointly optimizing the trajectory and interference resources of drones for composite interference networking radar are implemented.

[0150] Simulation results:

[0151] Assume that the networked radar system consists of N = 3 radars, M = 12 drones interfere with the networked radar system, and the networked radar adopts the rank 2 fusion criterion. The composite interference simulation scenario is as follows: Figure 3 As shown. The upper and lower limits of the UAV beam interference power are and The parameters of each UAV and each radar are the same, as shown in Table 1 and Table 2 respectively.

[0152] Table 1 Jammer operating parameters

[0153]

[0154] Table 2 Radar operating parameters

[0155]

[0156] The motion trajectory, false track and spatial position of the UAV cluster when implementing composite interference on the network radar are as follows: Figure 3 The motion parameters of the UAV are shown as Figure 4 As shown in (a) to (c).

[0157] Depend on Figure 4 From (a) to (c), we can see that the heading angle of the UAV is used as the control parameter of its navigation. Under the given conditions of the scene, the heading angle, pitch angle and speed of the UAV are coupled. At the same time, it can be seen from Table 1 that since the objective function to be optimized has only one minimum value, Figure 4 In the [0,5] moment of (a), the change in the heading angle of the UAV has a large fluctuation, and it approaches the optimal value of the objective function as much as possible within the constraint range; in the remaining moments, the UAV adjusts its heading angle according to the spatial position relationship between the preset false target and the radar. At this time, the change in the heading angle tends to be gentle. It can be seen from formula (1) that in the coupling relationship, the flight speed of the UAV is positively correlated with its pitch angle. Therefore, Figure 4 (b) and Figure 4 The changing trends of motion parameters in (c) are similar.

[0158] Figure 6 This is the optimization result of suppression jamming resources for networked radar in this scenario. Figure 6 (a) is the result of UAV's interference resource allocation to radar 1. Figure 6 (b) is the result of UAV's interference resource allocation to radar 2. Figure 6 (c) shows the interference resource allocation result of the UAV to radar 3. Figure 7 =The detection probability of the three radars for the 12 drones when no suppression jamming is implemented. In this case, the detection probability of the networked radar for each drone is 100%.

[0159] Combine Figure 6 、 Figure 7 It can be seen that the result of interference resource optimization is related to the detection probability of each radar to the corresponding UAV when no suppression interference is implemented. For example, in the simulation scenario, radar 2 has the highest detection probability to UAVs 2, 5, 8, and 11. Therefore, these four UAVs will allocate more resources to suppress radar 2 to reduce the interference performance of the networked radar. In addition, combined with Figure 3 、 Figure 5 and Figure 7 It can be seen that the distance between the UAV and each radar is between [50, 100] km. The spatial position change caused by the low-speed movement of the UAV has a negligible effect on the detection probability of the radar. Figure 6 The optimal jamming resource strategy of each UAV remains basically stable to achieve the best jamming effect.

[0160] Figure 8 The detection probability of each radar for the drone after the suppression jamming is implemented is shown. Figure 9 The figure shows the detection probability of 12 UAVs by a networked radar system consisting of three radar systems. Figure 10 The figure shows the degradation of drone detection performance of networked radar under composite interference.

[0161] Combine Figure 5 、 Figure 9 and Figure 10 It can be seen that since the distance between UAVs 3, 6, and 9 and the three radars is closer than that of other UAVs, the probability of their detection by the networked radar is higher. When optimizing the detection performance of the networked radar for the UAV cluster, the algorithm prioritizes allocating more resources to reduce the detection probability of the networked radar for other UAVs to ensure the optimal algorithm performance. Therefore, Figure 9 and Figure 10 In the data, the networked radar has a higher detection probability for drones 3, 6, and 9 than for other drones. However, the networked radar's detection performance for drones 3, 6, and 9 decreases by approximately 60%, while its detection performance for other drones decreases by approximately 80%.

[0162] Working principle and working process of the present invention:

[0163] Considering the risk of drone swarms being detected by networked radars in real-world scenarios, this paper proposes using M drones to jam a networked radar system consisting of N early warning radars using a composite jamming method that combines deceptive jamming with suppressive jamming. Specifically, while effectively deceiving the networked radars, suppressive jamming is applied to suppress the networked radar system's detection and tracking of drone swarms. This method improves the success rate of track deception, reduces the risk of drone swarms being detected by networked radars, and enhances the jamming effect on the networked radars. It assumes that the parameters of each enemy radar (such as radar position, carrier frequency, pulse width, etc.) are known, and the radar positions, drone positions, and false target positions are all known. Furthermore, the motion of the drones and false tracks satisfies dynamic constraints. Guided by the effectiveness of composite jamming, this paper designs a joint optimization method for UAV tracks and jamming resources. Using certain UAV motion parameters as constraints, the method aims to minimize the probability of detection of UAVs performing jamming missions by networked radars by jointly optimizing the UAVs' beam pointing, track, and power resources under limited jamming resources. Based on track deception against networked radars, a joint optimization model for UAV tracks and jamming resources is established for composite jamming networked radars. This optimization model is solved using a hybrid optimization algorithm combining a particle swarm optimization algorithm and an interior point method. The optimization model obtains a constrained UAV cluster beam pointing, track, and power resource allocation result. Simultaneously, the deceptive signal parameters are designed in real time, achieving composite jamming against networked radars while satisfying pre-set UAV dynamic constraints and generating effective deceptive tracks.

Claims

1. A joint optimization method of UAV tracks and jamming resources for composite jamming network radar, characterized by: The following steps are involved: M drones are used to spoof the track of a networked radar system consisting of N radars, forming P false tracks. At the same time, drones are introduced to suppress and interfere with the radars, and a model of drone cluster composite interference with networked radars is established. By jointly optimizing the configuration of the UAV's beam pointing, track, and power resources, and implementing track deception on the networked radar, with the UAV's motion parameters as constraints and minimizing the detection probability of the networked radar for the UAV performing the jamming mission as the optimization goal, a joint optimization model of the UAV's track and jamming resources for the composite jamming networked radar is established. The optimization model expression is: in, To improve the detection performance of networked radar on drone clusters, Pd k (u k ,P k ,R k ) is the detection probability of the networked radar to the drone cluster at the kth moment, u k is the UAV cluster beam pointing matrix at the kth moment, P k is the UAV cluster interference power matrix at the kth moment, R k is the distance matrix between the UAV cluster and the radar at the kth moment, is the detection probability requirement, P m,n,k is the interference power of the mth UAV to the nth radar at the kth moment, P min is the lower limit of UAV beam interference power, P max is the upper limit of UAV beam interference power, u m,n,k is the beam pointing situation of the m-th UAV to the n-th radar at the k-th moment, is the total power of the jammer, L is the number of beams generated by each UAV, S is the maximum number of jammed beams, △α e is the change in the UAV flight angle, △α max is the maximum value of the change in the UAV flight direction angle, △α min is the minimum value of the change in the UAV flight direction angle, △β e is the change in the pitch angle of the UAV, △β max is the maximum value of the change in the pitch angle of the UAV flight, △β min is the minimum value of the change in the pitch angle of the UAV flight, v e is the flight speed of the UAV, v max is the upper limit of the UAV flight speed, v min The lower limit of the UAV flight speed; A hybrid optimization algorithm combining the particle swarm optimization algorithm and the interior point method is used to solve the optimization model, and the UAV cluster beam pointing, trajectory and power resource allocation results that meet the constraints are obtained. In this way, composite interference to the networked radar is achieved while satisfying the pre-set UAV dynamic constraints and generating effective deception trajectory.

2. The method for joint optimization of UAV tracks and jamming resources for composite jamming network radar according to claim 1 is characterized in that: The motion control equation of the UAV when implementing the deception jamming mission is: Among them, β e is the flight pitch angle of the UAV, θ is the pitch angle of the UAV in the direction of the radar, α e is the flight angle of the UAV, φ is the direction angle of the UAV in the direction of the radar, φ' is the derivative of φ, θ' is the derivative of θ, r' is the derivative of r, and r is the distance from the UAV to the radar. is the square of the UAV’s flight speed; The UAV always satisfies the coupling relationship between the radar, the UAV and the false target during the implementation of the track deception jamming mission. The position of the false target and the radar position are known a priori. The motion variables of the UAV will be constrained in one dimension, that is, only by controlling its flight direction angle α e It is possible to achieve track control under track deception coupling constraints; The suppression interference adopts noise interference, and the noise interference signal is expressed as: Where J(t) is the noise interference signal, is the noise interference signal amplitude, f j is the center frequency of the noise interference signal, K FM is the frequency modulation slope, μ(t') is the modulation noise, ψ is the phase function of the noise interference signal, exp is the exponential operation, j represents the imaginary operation, t represents the signal change over time, and ['] is the derivative operation; the above formula is simplified to: Among them, s m,n,k (t) is the normalized complex envelope of the suppressed interference signal.

3. The method for joint optimization of UAV tracks and jamming resources for composite jamming network radar according to claim 1 is characterized in that: The radars adopt a self-transmitting and self-receiving working mode. Each radar only receives and processes the echo signals sent by itself and scattered by the target. Each radar can detect M drones at time k, so each radar will receive M echo signals. Under the interference suppression condition, the radar will also receive interference signals from multiple drones. The signal received by radar n at time k is: Among them, r n,k (t) represents the signal received by radar n at time k, r m,n,k (t) represents the echo signal of the mth UAV received by radar n at the kth moment; j m,n,k (t) represents the suppression jamming signal received by radar n from the mth UAV at the kth moment; w n,k (t) represents the radar receiver thermal noise of radar n at time k, and t indicates that these signals vary with time; When M drones cooperate to suppress a single radar, the total interference signal power received by the radar is the sum of the power of each interference signal. According to the power superposition principle, the total interference signal power received by radar n when detecting drone m is for: in, is the suppression jamming signal power received by radar n from the mth UAV at the kth moment.

4. The method for joint optimization of UAV tracks and jamming resources for composite jamming network radar according to claim 1 is characterized in that: The networked radar adopts the KN criterion, that is, when the number of radar nodes that detect UAV m in the networked radar exceeds the detection threshold K, 1≤K≤N, it is determined that the networked radar has detected UAV m; otherwise, it is determined that the UAV has not been detected. As shown in the following formula: in, represents the judgment result of the network radar on UAV m at the kth moment; represents the decision result of radar n on drone m at the kth moment and According to the KN criterion, the detection probability of the networked radar to the drone m at time k is: in, is the detection probability of UAV m by the networked radar at the kth moment, is the equivalent expression of the detection probability of the networked radar to the UAV m at the kth moment, is the detection probability of radar n to drone m at the kth moment, represents the permutation and combination in which the sum of the judgment results of N radar nodes on UAV m is j; The vector Pd formed by the detection probability of the networked radar for M drones k As a performance evaluation indicator for suppression jamming network radar: Detection probability requirements for multiple targets for: in, To meet the detection requirements for the first drone, To meet the detection requirements for the second drone, The detection requirement for the Mth drone; Based on the principle of quality of service, a global cost function is established: in, The detection performance of the networked radar for the mth UAV is: is the detection requirement for the mth UAV.

5. The method for joint optimization of UAV tracks and jamming resources for composite jamming network radar according to claim 1 is characterized in that: The optimization model solution method is: (1) Based on the preset false target and radar position prior information, the optimal trajectory of the UAV that satisfies the dynamic constraints of the optimization model in this scenario is obtained using the particle swarm optimization algorithm, and the optimal distance correspondence between the UAV and the radar at each moment is obtained. (2) In seeking Based on this, it is assumed that the UAV can interfere with all radar nodes at the same time and the transmission power of each beam is evenly distributed. is the UAV interference power under the condition of uniform power distribution; for the convenience of solution, the beam is directed to the variable u k Relaxed to a continuous variable in the interval [0,1] At this point, the optimization problem is simplified to: in, In order to simplify the detection performance of the networked radar on the drone cluster, is the detection probability matrix of the networked radar to the drone cluster, is the interference power matrix of the drone cluster under the average radiation power, is the pointing direction of the mth UAV to the nth radar under the average radiated power; The interior point method is used to solve the above equation to obtain the beam pointing variable u k The relaxation result And initialize the beam pointing result Under the constraints, The maximum value is Set 1 in the middle and repeat the The maximum value is Set 1 in the middle until all beam resources of M jammers are exhausted, and finally get the optimal allocation method of beam pointing (3) In seeking and Based on the above, the interference power allocation result is solved. At this point, the optimization problem has been simplified to: Similarly, the interior point method is used to obtain the optimal interference power allocation result 6. The method for joint optimization of UAV tracks and jamming resources for composite jamming network radar according to claim 5 is characterized in that: Step (1) includes the following steps: (a) Initialize the population size, population inertia, particle state and fitness function; (b) Iteratively optimizing the flight speed, flight direction angle, and flight pitch angle parameters of the UAV at that moment; (c) Return to step (b) and repeat until the absolute value of the difference between the two optimization objective functions is less than an arbitrary minimum value ε>0, thereby obtaining the optimal UAV flight speed, flight direction angle, and flight pitch angle motion state parameters at the current moment; (d) Determine the initial position of the UAV at the next moment based on the coupling relationship between the false target, the UAV, and the radar; (e) Repeat steps (b) to (d) until the distributed online decision-making of the UAV cluster flight trajectory is completed, that is, the optimal distance correspondence between the UAV and the radar at each moment is obtained.

7. UAV track and jamming resource joint optimization system for composite jamming network radar, characterized by: include: The composite jamming model construction unit is used to implement track deception on a networked radar system consisting of N radars using M drones, forming P false tracks. At the same time, it introduces drone suppression jamming on the radars to establish a drone cluster composite jamming networked radar model. The optimization model construction unit is used to jointly optimize the configuration of the UAV's beam pointing, track, and power resources. On the basis of implementing track deception on the networked radar, the UAV's motion parameters are used as constraints, and the optimization goal is to minimize the probability of the networked radar detecting the UAV performing the jamming mission. A joint optimization model of the UAV's track and jamming resources for the composite jamming networked radar is established. The optimization model expression is: in, To improve the detection performance of networked radar on drone clusters, Pd k (u k ,P k ,R k ) is the detection probability of the networked radar to the drone cluster at the kth moment, u k is the UAV cluster beam pointing matrix at the kth moment, P k is the UAV cluster interference power matrix at the kth moment, R k is the distance matrix between the UAV cluster and the radar at the kth moment, is the detection probability requirement, P m,n,k is the interference power of the mth UAV to the nth radar at the kth moment, P min is the lower limit of UAV beam interference power, P max is the upper limit of UAV beam interference power, u m,n,k is the beam pointing situation of the m-th UAV to the n-th radar at the k-th moment, is the total power of the jammer, L is the number of beams generated by each UAV, S is the maximum number of jammed beams, △α e is the change in the UAV flight angle, △α max is the maximum value of the change in the UAV flight direction angle, △α min is the minimum value of the change in the UAV flight direction angle, △β e is the change in the pitch angle of the UAV, △β max is the maximum value of the change in the pitch angle of the UAV flight, △β min is the minimum value of the change in the pitch angle of the UAV flight, v e is the flight speed of the UAV, v max is the upper limit of the UAV flight speed, v min The lower limit of the UAV flight speed; The optimization model solving unit is used to solve the optimization model using a hybrid optimization algorithm that combines the particle swarm optimization algorithm with the interior point method, and obtain the drone cluster beam pointing, trajectory and power resource allocation results that meet the constraints, thereby achieving composite interference to the networked radar while satisfying the pre-set drone dynamic constraints and generating effective deception tracks.

8. A control device, characterized in that: including a processor, a communication interface, a memory and a communication bus; The processor, the communication interface, and the memory communicate with each other via the communication bus. The memory is used to store computer programs; The processor is used to execute the program stored in the memory to implement the steps of the method for jointly optimizing the UAV track and interference resources for the composite interference networking radar as described in any one of claims 1-6.

9. 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 method for jointly optimizing the UAV track and interference resources for a composite interference networking radar as described in any one of claims 1 to 6.

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