UAV swarm deception strategy and trajectory joint optimization method for trajectory deception

Abstract

The present invention discloses a drone swarm deception strategy and track joint optimization method for track deception, including: establishing a single drone track deception model; constructing a false track generation quantity indicator with the drone swarm deception strategy and drone swarm track as optimization variables; constructing a drone swarm total flight distance indicator with the false track rotation angle and drone swarm track as optimization variables; establishing a dual-objective optimization model for drone swarm track deception targeting networked radars; and combining the platform-reused drone swarm deception strategy with a particle swarm optimization (PSO) algorithm to solve the optimization model step by step. The present invention utilizes a low-speed drone swarm to generate as many high-speed false tracks as possible to achieve track deception of networked radars.

Description

Technical Field

[0001] The present invention relates to unmanned aerial vehicle (UAV) cluster control technology, and in particular to a UAV cluster deception strategy and a track joint optimization method for track deception. Background Art

[0002] In electronic warfare, networked radars have been widely used due to their strong anti-reconnaissance, anti-jamming, and anti-deception capabilities. Using drone swarms to conduct track deception jamming against networked radars has become an advanced active jamming method. Drones use their onboard digital radio frequency memory to modulate and delay the forwarding of intercepted enemy radar signals, tricking the enemy radar into identifying them as false targets. Multiple consecutive false target points can form a false track. However, due to the "same-source verification" strategy of networked radars, false targets must be identified by multiple radars simultaneously before they can be recognized as legitimate track points by the fusion center. Therefore, it is necessary to plan the track of the drone swarm in a coordinated manner to deceive and jam each radar in the network.

[0003] At present, many scholars at home and abroad have conducted in-depth research on drone swarm track deception technology. However, the existing research results still have the following defects: (1) The utilization rate of each drone in the drone swarm is low, each drone only generates one false target, and the number of false tracks generated when implementing track deception is small; (2) It is difficult for a low-speed drone swarm to generate a high-speed fighter-type false target. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a drone cluster deception strategy and track joint optimization method for track deception, so that a low-speed drone cluster can generate as many high-speed false tracks as possible.

[0005] Technical solution: The drone swarm deception strategy and track joint optimization method for track deception described in the present invention include the following steps:

[0006] S1. Establish a single UAV track deception model;

[0007] S2. Construct a false track generation quantity indicator with the drone swarm deception strategy and drone swarm track as optimization variables;

[0008] S3, constructing a total flight distance index of the UAV cluster with the false track rotation angle and the UAV cluster track as optimization variables;

[0009] S4. A dual-objective optimization model for drone swarm track deception targeting networked radars is established, with the optimization objectives of maximizing the number of false track generation and minimizing the total flight distance of the drone swarm, and with the drone flight dynamics performance as a constraint.

[0010] S5. Combining the platform-reused UAV cluster deception strategy and the particle swarm optimization (PSO) algorithm to solve the dual-objective optimization model of UAV cluster track deception for networked radar established in step S4; including: first decomposing the optimization model into a false track generation quantity optimization model and a UAV cluster total flight distance optimization model; combining the platform-reused UAV cluster deception strategy to solve the false track generation quantity optimization model; combining the PSO algorithm to solve the UAV cluster total flight distance optimization model; and finally outputting the optimization results.

[0011] Furthermore, the single UAV track deception model established in step S1 is:

[0012]

[0013] Among them, e k+1 represents the coordinate point of the drone at time (k+1); e' k+1 Indicates the coordinate point of the imaginary drone with the same speed and direction as the false target at time (k+1); Indicates e k+1 to e' k+1 vector of express The unit vector of f k+1 represents the coordinate point of the false target at time (k+1); θ represents the angle between the speed direction of the UAV and the speed direction of the false target. If θ>0, e k+1 Located in e' k+1 Above, on the contrary e k+1 Located in e' k+1 Below.

[0014] Further, e k+1 With e' k+1 Distance Expressed as:

[0015]

[0016] Among them, e k represents the coordinate point of the drone at time k, Indicates e k to e' k+1 vector, Represents ∠e k e' k+1 e k+1 :

[0017]

[0018] Among them, f k represents the false target coordinate point at time k, represents f kto f k+1 vector of

[0019] e' k+1 Coordinate (x e',k+1 ,y e',k+1 ,z e',k+1 )for:

[0020]

[0021] Among them, (x f,k ,y f,k ,z f,k ) is the coordinate point of the false target at time k; z e,k is the flight altitude of the UAV at time k.

[0022] Furthermore, the number index of false track generation constructed in step S2 is:

[0023]

[0024] Among them, J1 represents the number of false track generation indicators, G n represents the number of false tracks generated by the nth UAV; S represents the number of UAVs in the UAV cluster.

[0025] Furthermore, the total flight distance index of the UAV cluster constructed in step S3 is:

[0026]

[0027] Among them, J2 represents the total flight distance index of the drone cluster, S represents the number of drones in the drone cluster; K represents the total number of deception moments; and They represent the average flight height and average flight distance of false targets respectively; h min,e Indicates the lower limit of the drone's flight altitude; It represents the flight distance of the nth UAV in the kth time period.

[0028] Furthermore, the dual-objective optimization model for drone cluster track deception targeting networked radar established in step S4 is:

[0029]

[0030] Among them, μ represents the UAV cluster deception strategy; θ represents the angle between the UAV speed direction and the false target speed direction; z0 represents the initial height of the UAV; γ represents the false track rotation angle; ω1 and ω2 represent the weight coefficients of the optimization targets J1 and J2 respectively; S represents the number of UAVs in the UAV cluster, G n represents the number of false tracks generated by the nth UAV, and K represents the total number of deception moments; and They represent the average flight height and average flight distance of false targets respectively; h min,e Indicates the lower limit of the drone's flight altitude; represents the flight distance of the nth UAV in the kth time period; v max,e and v min,e Respectively represent the upper and lower limits of the drone's flight speed; Indicates drone e n Flight speed in the kth time period; △α max,e and △α min,e Respectively represent the upper and lower limits of the UAV flight turning angle; Indicates drone e n The turning angle at the kth time period; β max,e and β min,e Respectively represent the upper and lower limits of the drone's flight pitch angle; Indicates drone e n The flight pitch angle in the kth time period; h max,e and h min,e Respectively represent the upper and lower limits of the drone's flight altitude; Indicates drone e n Flight altitude at time k; Indicates drone e n1 and drones n2 Spacing; d safe Indicates the safe distance between drones; γ max and γ min Respectively represent the upper and lower limits of the false track rotation angle; N R Indicates the number of radars whose false tracks need to pass the homology test; R indicates the number of radars in the networked radar system; H m,r is a Boolean variable, representing the homology test parameter. If there is a drone on the line connecting the track point of the false track m and any radar r, record H m,r =1, otherwise H m,r =0;μ n,m,r is a Boolean variable, which is an element in the UAV cluster deception strategy μ. If the nth UAV deceives the rth radar to produce a false track m, μ is recorded. n,m,r =1, otherwise μ n,m,r =0.

[0031] Furthermore, the effect of the false track rotation angle γ on the false track is expressed as:

[0032]

[0033] Among them, (x' f,k ,y' f,k ,z' f,k) represents the new false track generated by rotating the original false track, (x f,k ,y f,k ,z f,k ) is the false target coordinate point at time k; (x f,mid ,y f,mid ,z f,mid ) represents the position coordinates of the false track at the intermediate moment.

[0034] Furthermore, the optimization model for the number of false track generation in step S5 is expressed as:

[0035]

[0036] Among them, μ represents the drone cluster deception strategy, S represents the number of drones in the drone cluster, G n Indicates the number of false tracks generated by the nth UAV, N R Indicates the number of radars that need to pass the homology test for false tracks; R indicates the number of radars in the networked radar system; H m,r is a Boolean variable, indicating the homology test parameter; μ n,m,r is a Boolean variable, which is an element in the drone cluster deception strategy μ;

[0037] The platform reuse UAV swarm deception strategy is used to solve the optimization model for the number of false track generation:

[0038] i) Based on the scaling factor By false track Generate false tracks

[0039]

[0040] Among them, the proportional factor of the false target m2 corresponding to the false target m1 at time k is Expressed as:

[0041]

[0042] in, and They represent the distances from the false target m1 and the false target m2 to the radar at time k respectively; It represents a constant proportional factor that does not change with time, and gives the basic activity range of the false target m2; represents the fluctuation scale factor at time k, which makes the shape of the false track m2 different from the false track m1;

[0043] ii) Given the number of false tracks, the UAV swarm deception strategy reused by the platform is used to generate corresponding false targets by the UAVs: the UAV swarm deception strategy is obtained according to subscript 1;

[0044] Table 1 Drone swarm deception strategy table

[0045]

[0046] iii) Given a given number of drones, a platform-reused drone swarm deception strategy is used to generate corresponding false targets from the drones; specifically:

[0047] A drone cluster consisting of S drones is divided into q drone groups, S≥N R , where q must satisfy the following formula:

[0048] q=SL(N R -1).

[0049] In order to maximize the total number of false tracks L generated, it is necessary to minimize q and q ≥ 1. The maximum number of false tracks L generated is obtained by the following formula: max :

[0050]

[0051] in, Indicates rounding down, the maximum value of L max Substitute the calculation formula of q to obtain the minimum value q of the drone group min ;

[0052] Then the number of false tracks L generated by the i-th UAV group i To distribute, it is necessary to satisfy the following formula:

[0053]

[0054] The number of drones in the i-th drone group S i Calculated by the following formula:

[0055] S i =N R +(L i -1)(N R -1).

[0056] Finally, the deception strategy of the i-th drone group is obtained from Table 1.

[0057] Furthermore, the total flight distance optimization model of the UAV cluster is expressed as:

[0058]

[0059] Among them, θ represents the angle between the UAV speed direction and the false target speed direction; z0 represents the initial height of the UAV; γ represents the rotation angle of the false track; S represents the number of UAVs in the UAV cluster; K represents the total number of deception moments; represents the flight distance of the nth UAV in the kth time period; v max,e and v min,e Respectively represent the upper and lower limits of the drone's flight speed; Indicates drone e n Flight speed in the kth time period; △α max,e and △α min,e Respectively represent the upper and lower limits of the UAV flight turning angle; Indicates drone e n The flight turning angle in the kth time period; β max,e and β min,e Respectively represent the upper and lower limits of the drone's flight pitch angle; Indicates drone e n The flight pitch angle in the kth time period; h max,e and h min,e Respectively represent the upper and lower limits of the drone's flight altitude; Indicates drone e n Flight altitude at time k; Indicates drone e n1 and drones n2 Spacing; d safe Indicates the safe distance between drones; γ max and γ min Respectively represent the upper and lower limits of the false track rotation angle;

[0060] The particle swarm optimization algorithm (PSO) is used to solve the total flight distance optimization model of UAV clusters:

[0061] i) Initialization: Initialize the position and velocity of a group of particles, the position of the i-th particle in the 0th generation speed in, Any vector in Indicates that drones n The vector formed by the initial height and the angle between the velocity at each moment; represents the false track rotation angle vector, for The corresponding particle velocity value; the fitness value of each particle is evaluated by optimizing the target;

[0062] ii) Iterative update: Find the optimal individual position of each particle in the tth generation and the optimal value of group position The particle velocity is updated according to the following formula:

[0063]

[0064] in, represents the velocity of particle i of the (t+1)th generation in the dth dimension; ω represents the inertia factor; represents the speed of particle i of the tth generation in the dth dimension; c1 and c2 represent acceleration factors; r1 and r2 are random numbers between (0,1); represents the optimal value of the individual position of particle i in the tth generation in the dth dimension; represents the position of particle i of generation t in the dth dimension; represents the optimal value of the position of the t-th generation group in the d-th dimension;

[0065] Update the particle position according to the following formula:

[0066]

[0067] in, and denote the positions of particle i in the (t+1)th and tth generations in the dth dimension respectively; represents the velocity of particle i of the (t+1)th generation in the dth dimension;

[0068] iii) Check the termination condition: Check whether the maximum number of iterations is reached or the difference in fitness between two iterations is less than the termination index ε: If it is met, the algorithm terminates; otherwise, return to step ii) and execute the next iteration;

[0069] iv) Output: (x1, x2, …, x S ),in Indicates that drones n The vector formed by the initial height and the velocity angle at each moment; the false track rotation angle vector x (S+1) .

[0070] Based on the same inventive concept, the present invention also provides a drone swarm deception strategy and track joint optimization system for track deception, including:

[0071] A single UAV track deception model building unit is used to build a single UAV track deception model;

[0072] A false track generation quantity indicator construction unit is used to construct a false track generation quantity indicator with the drone swarm deception strategy and the crowd-free track as optimization variables;

[0073] The UAV swarm flight total distance index construction unit is used to construct the UAV swarm flight total distance index with the false track rotation angle and the UAV swarm track as optimization variables;

[0074] An optimization model building unit is used to establish a dual-objective optimization model for drone swarm track deception targeting networked radars, with the optimization objectives of maximizing the number of false tracks generated and minimizing the total flight distance of the drone swarm, and with the drone flight dynamics performance as a constraint;

[0075] The optimization model solving unit is used to solve the dual-objective optimization model of drone cluster track deception for networked radar established in the optimization model establishment unit by combining the platform-reused drone cluster deception strategy and the PSO algorithm; it includes: first decomposing the optimization model into a false track generation quantity optimization model and a drone cluster total flight distance optimization model; combining the platform-reused drone cluster deception strategy to solve the false track generation quantity optimization model; combining the PSO algorithm to solve the drone cluster total flight distance optimization model; and finally outputting the optimization results.

[0076] Beneficial effects: Compared with the existing technology, the significant advantages of the present invention are: (1) by constructing a false track generation number index and a UAV cluster flight total distance index, with maximizing the false track generation number and minimizing the UAV cluster flight total distance as optimization goals, and with the UAV flight dynamics performance as a constraint condition, a dual-objective optimization model for UAV cluster track deception for networked radar is established, and the UAV cluster deception strategy, UAV cluster track, and false track rotation angle are optimized to achieve the purpose of making the low-speed UAV cluster generate as many high-speed false tracks as possible; (2) a better UAV cluster deception strategy selection, UAV cluster track planning, and false track rotation angle selection are achieved, so that the low-speed UAVs generate as many high-speed false tracks as possible, thereby efficiently realizing track deception for the networked radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 Flowchart of the UAV swarm deception strategy and trajectory joint optimization method for trajectory deception;

[0078] Figure 2 This is a schematic diagram of the spatial relationship between radar, UAV, and false targets;

[0079] Figure 3 Generate a graph of the number of false tracks for different numbers of drones in simulation scenario 1;

[0080] Figure 4 This is the effect of drone cluster deceiving network radar tracks in simulation scenario 2;

[0081] Figure 5 This is the flight speed diagram in simulation scenario 2;

[0082] Figure 6 This is the flight direction angle diagram in simulation scenario 2;

[0083] Figure 7 This is the flight pitch angle diagram in simulation scenario 2;

[0084] Figure 8 This is the effect of drone cluster deceiving network radar tracks in simulation scenario 3;

[0085] Figure 9 This is the flight speed diagram in simulation scenario 3;

[0086] Figure 10 This is the flight direction angle diagram in simulation scenario 3;

[0087] Figure 11 This is the flight pitch angle diagram in simulation scenario 3. DETAILED DESCRIPTION

[0088] The results and working process of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0089] Based on actual combat scenarios, this paper proposes a joint optimization method for drone swarm track deception strategies and tracks for track deception. Under given drone flight dynamics constraints, the method optimizes the drone swarm deception strategy, track, and false track rotation angle, aiming to maximize the number of false tracks generated and minimize the total flight distance of the drone swarm. This method aims to maximize the number of high-speed false tracks generated by a low-speed drone swarm. First, the flight model of a single drone performing track deception against a single radar is analyzed. The number of false tracks generated and the total flight distance of the drone swarm are then used as metrics to measure the effectiveness of the track deception mission. Finally, a dual-objective optimization model for drone swarm track deception targeting networked radars is established, with the optimization objectives of maximizing the number of false tracks generated and minimizing the total flight distance of the drone swarm, and the drone flight dynamics constraints as constraints. The method optimizes the drone swarm deception strategy, track, and false target rotation angle to maximize the number of high-speed false tracks generated by a low-speed drone swarm.

[0090] like Figure 1 As shown, the drone cluster deception strategy and track joint optimization method for track deception of the present invention include the following steps:

[0091] S1. Establish a single UAV track deception model. The radar, UAV, and false target should meet the line of sight (LOS) criterion at any time, that is, the three should be on the same straight line. Therefore, the three must meet a strict position coupling relationship. To achieve UAV cluster track deception, the flight model of any UAV with a known false track should be considered first. In the spatial rectangular coordinate system with the radar as the origin, the coordinates of UAV (k+1) at time are shown as formula (1):

[0092]

[0093] Among them, e k+1 represents the coordinate point of the drone at time (k+1); e' k+1 represents the coordinate point of the imaginary drone with the same speed direction as the false target at time (k+1), Indicates e k+1 to e' k+1 A vector such as Figure 2 As shown; express The unit vector of the UAV; θ represents the angle between the UAV speed direction and the false target speed direction. If θ>0, e k+1 Located in e' k+1 Above, on the contrary e k+1 Located in e' k+1 below; f k+1 Represents the false target coordinate point at time (k+1).

[0094] In formula (1), e k+1 With e' k+1 Distance Expressed as:

[0095]

[0096] Among them, e k represents the coordinate point of the drone at time k, Indicates e k to e' k+1 vector, Represents ∠e k e' k+ 1e k+1 :

[0097]

[0098] Among them, f k represents the false target coordinate point at time k, represents f k to f k+1 vector.

[0099] In formula (1), e'k+1 Coordinate (x e',k+1 ,y e',k+1 ,z e',k+1 )for:

[0100]

[0101] Among them, (x f,k ,y f,k ,z f,k ) is the coordinate point of the false target at time k; z e,k is the flight altitude of the UAV at time k.

[0102] S2. Construct a false track generation quantity index with the drone swarm deception strategy and drone swarm track as optimization variables, as shown in formula (5):

[0103]

[0104] Among them, J1 represents the number of false track generation indicators, G n represents the number of false tracks generated by the nth UAV; S represents the number of UAVs in the UAV cluster.

[0105] S3. Construct the total flight distance index of the UAV cluster with the false track rotation angle and the UAV cluster track as the optimization variables, as shown in formula (6):

[0106]

[0107] Among them, J2 represents the total flight distance index of the drone cluster, S represents the number of drones in the drone cluster; K represents the total number of deception moments; and They represent the average flight height and average flight distance of false targets respectively; h min,e Indicates the lower limit of the drone's flight altitude; It represents the flight distance of the nth UAV in the kth time period.

[0108] S4. With the optimization objectives of maximizing the number of false tracks generated and minimizing the total flight distance of the UAV swarm, and the UAV flight dynamics performance as the constraint, a dual-objective optimization model for UAV swarm track deception targeting networked radars is established:

[0109]

[0110] Among them, μ represents the UAV cluster deception strategy; θ represents the angle between the UAV speed direction and the false target speed direction; z0 represents the initial height of the UAV; γ represents the false track rotation angle; ω1 and ω2 represent the weight coefficients of the optimization targets J1 and J2 respectively; S represents the number of UAVs in the UAV cluster, G nrepresents the number of false tracks generated by the nth UAV, and K represents the total number of deception moments; and They represent the average flight height and average flight distance of the false targets respectively; v max,e and v min,e Respectively represent the upper and lower limits of the drone's flight speed; Indicates drone e n Flight speed in the kth time period; △α max,e and △α min,e Respectively represent the upper and lower limits of the UAV flight turning angle; Indicates drone e n The flight turning angle in the kth time period; β max,e and β min,e Respectively represent the upper and lower limits of the drone's flight pitch angle; Indicates drone e n The flight pitch angle in the kth time period; h max,e and h min,e Respectively represent the upper and lower limits of the drone's flight altitude; Indicates drone e n Flight altitude at time k; Indicates drone e n1 and drones n2 Spacing; d safe Indicates the safe distance between drones; γ max and γ min They represent the upper and lower limits of the false track rotation angle respectively; γ represents the false track rotation angle; N R Indicates the number of radars that need to pass the same-source verification for false tracks; N R Indicates the number of radars whose false tracks need to pass the homology test; R indicates the number of radars in the networked radar system; H m,r is a Boolean variable, representing the homology test parameter. If there is a drone on the line connecting the track point of the false track m and any radar r, record H m,r =1, otherwise H m,r =0;μ n,m,r is a Boolean variable, which is an element in the UAV cluster deception strategy μ. If the nth UAV deceives the rth radar to produce a false track m, μ is recorded. n,m,r =1, otherwise μ n,m,r =0.

[0111] The effect of the false track rotation angle γ on the false track is shown in formula (8):

[0112]

[0113] Among them, (x' f,k ,y' f,k ,z'f,k ) represents the new false track generated by rotating the original false track; (x f,mid ,y f,mid ,z f,mid ) represents the position coordinates of the false track at the intermediate moment.

[0114] S5. Combining the platform reused drone swarm deception strategy and the particle swarm optimization (PSO) algorithm, the optimization model (7) is solved step by step;

[0115] Step 1: Decompose the optimization model (7) into the optimization model for the number of false track generation and the optimization model for the total flight distance of the UAV cluster;

[0116] The optimization model for the number of false track generation is expressed as:

[0117]

[0118] The total flight distance optimization model of UAV cluster is expressed as:

[0119]

[0120] Step 2: Use the platform reused UAV swarm deception strategy to solve the optimization model (9) for the number of false track generation:

[0121] i) Based on the scaling factor By false track Generate false tracks The expression is:

[0122]

[0123] Among them, the proportional factor of the false target m2 corresponding to the false target m1 at time k is Expressed as:

[0124]

[0125] in, and They represent the distances from the false target m1 and the false target m2 to the radar at time k respectively; It represents a constant proportional factor that does not change with time, and gives the basic activity range of the false target m2; represents the fluctuation scale factor at time k, which makes the shape of the false track m2 different from the false track m1;

[0126] ii) Given a given number of false tracks, a platform-reused drone swarm deception strategy is used to generate corresponding false targets from the drones:

[0127] Assume that L false tracks need to be generated. Each UAV only deceives the same radar and can generate at most two false targets. The corresponding false targets are generated by the UAV according to the deception strategy given in Table 1.

[0128] Table 1 Drone swarm deception strategy table

[0129]

[0130]

[0131] iii) Given a given number of drones, a platform-reused drone swarm deception strategy is used to allocate drone tasks:

[0132] Assume that a drone cluster is composed of S drones (S≥N R ), in order to make use of each drone, it is divided into q drone groups, where q must satisfy formula (13):

[0133] q=SL(N R -1). (13)

[0134] In order to maximize the total number of generated false tracks L, it is necessary to minimize q and q ≥ 1. The maximum number of generated false tracks L can be obtained from formula (14): max :

[0135]

[0136] in, Indicates rounding down. The maximum value of L max Substituting into formula (13), we can get the minimum value q of the drone group: min .

[0137] Then the number of false tracks L generated by the i-th UAV group i To distribute, it is necessary to satisfy formula (15):

[0138]

[0139] The number of drones in the i-th drone group S i Calculated by the following formula:

[0140] S i =N R +(L i -1)(N R -1). (16)

[0141] Finally, the deception strategy of the i-th drone group is obtained from Table 1. After obtaining the deception strategies of all drone groups, the drone cluster deception strategy μ can be obtained, thereby solving Equation (9).

[0142] Step 3: Use the Particle Swarm Optimization (PSO) algorithm to solve the optimization model of the total flight distance of the UAV cluster:

[0143] i) Initialization: Initialize the position and velocity of a group of particles, the position of the i-th particle in the 0th generation speed in, Any vector in Indicates that drones n The vector formed by the initial height and the angle between the velocity at each moment; represents the false track rotation angle vector, for The corresponding particle velocity value. The fitness value of each particle is evaluated by optimizing the target;

[0144] ii) Iterative update: Find the optimal individual position of each particle in the tth generation and the optimal value of group position Update the particle velocity according to formula (17):

[0145]

[0146] in, represents the velocity of particle i of the (t+1)th generation in the dth dimension; ω represents the inertia factor; represents the speed of particle i of the tth generation in the dth dimension; c1 and c2 represent acceleration factors; r1 and r2 are random numbers between (0,1); represents the optimal value of the individual position of particle i in the tth generation in the dth dimension; represents the position of particle i of generation t in the dth dimension; Represents the optimal value of the t-th generation population position in the d-th dimension.

[0147] Update the particle position according to formula (18):

[0148]

[0149] in, and denote the positions of particle i of the (t+1)th and tth generations in the dth dimension, respectively. represents the velocity of particle i of the (t+1)th generation in the dth dimension;

[0150] iii) Check the termination condition: Check whether the maximum number of iterations is reached or the difference in fitness between two iterations is less than the termination index ε: If it is met, the algorithm terminates; otherwise, return to step ii) and execute the next iteration;

[0151] iv) Output: (x1, x2, …, x S ),in Indicates that drones n The vector formed by the initial height and the velocity angle at each moment; the false track rotation angle vector x (S+1) ; Thus, we can solve equation (10).

[0152] Simulation results:

[0153] In order to verify the feasibility and effectiveness of the method proposed in this invention, three simulation scenarios were designed for simulation verification.

[0154] Simulation scenario 1:

[0155] Simulation scenario 1 considers that a drone swarm consisting of 10, 15, 20, 25, and 30 drones respectively implements track deception on a distributed network radar system consisting of 4 pulse radars, and the false track needs to pass N R =Homologous inspection of 4 radars.

[0156] Figure 3 A comparison of the number of false tracks generated by different numbers of drones using two deception strategies is shown. Table 2-4 uses 30 drones for track deception as an example to show the deception strategies for each group in the drone swarm.

[0157] Table 2 Drone swarm deception strategy (Group 1)

[0158]

[0159] Table 3 Drone swarm deception strategy (Group 2)

[0160]

[0161] Table 4 Drone swarm deception strategy (group 3)

[0162]

[0163] It can be seen that with the same number of drones, the platform reuse deception strategy can generate more false tracks. By grouping the drone cluster, more false tracks can be generated and each drone can be utilized. If the platform reuse deception strategy is not adopted, Figure 3 Except for the drone cluster consisting of 20 drones, there are unused drones in other drone clusters, and the drone utilization rate is low.

[0164] Simulation scenario 2:

[0165] Simulation scenario 2 considers a distributed network radar system consisting of three pulse radars, and the false track needs to pass N R = Homologous inspection of three radars, where the radar coordinates are (60, 10, 1) km, (60, 30, 1.1) km, (-20, 20, 1.3) km, and the safe distance d between drones safe =50m. The upper and lower limits of the constraint conditions are shown in Table 5:

[0166] Table 5 Upper and lower limit parameters of constraint conditions

[0167]

[0168]

[0169] Among them, v e Indicates the flight speed of the drone; h e Indicates the flight altitude of the drone; △α e Indicates the UAV flight turning angle; β e represents the pitch angle of the UAV flight; γ represents the false track rotation angle.

[0170] The motion equation of the false track 1 is shown in formula (19):

[0171]

[0172] Where k represents the time; represents the coordinates of false target 1 at time k.

[0173] The remaining false track scaling factor is shown in formula (20):

[0174]

[0175] Among them, k represents the time; p 2,1,k , p 3,1,k , p 4,1,k , p 5,4,k They represent the proportional factors of false target 2 corresponding to false target 1, false target 3 corresponding to false target 1, false target 4 corresponding to false target 1, and false target 5 corresponding to false target 4 at time k.

[0176] Figure 4This diagram shows the effectiveness of a drone swarm spoofing networked radar tracks. The results show that a drone swarm consisting of 11 drones generates five different false tracks, and at any given moment, a drone is located on the line connecting the three radars and any false target. By forwarding spoofing signals with specified parameters, the drone swarm can generate multiple false tracks, achieving track deception against the networked radars. Because the constant scaling factor is greater than 1, the flight distance of false track 2 is greater than that of false track 1; while the flight distance of false track 4, with a constant scaling factor less than 1, is less than that of false track 1. Therefore, to ensure that the speed of the false tracks generated by the scaling factor is realistic, the constant scaling factor cannot be much greater than or much less than 1. Furthermore, by properly setting the scaling factor, the false targets can simulate formation flight within the same area, thereby increasing the authenticity of the false tracks.

[0177] Since the motion states of each drone in a drone cluster are similar, any drone can represent the motion states of each drone. Figures 5 to 7 Taking fake track 2 and drones 1, 4, and 5 as examples, the flight speed, heading, and pitch angle parameters of the fake targets and the three drones are displayed. The results show that all drones in this group meet dynamic performance constraints and generate high-speed fake targets at approximately 400 m / s at a low speed of approximately 50 m / s.

[0178] Simulation scenario 3:

[0179] Simulation scenario 3 considers a drone swarm consisting of 20 drones to implement track deception on a distributed network radar system consisting of 4 pulse radars, where the false track needs to pass N R = Homologous verification of 4 radars, with the radar coordinates being (-32, 15, 0.3) km, (62, 12, 0.8) km, (-22, 33, 0.5) km, and (54, 25, 1) km. The safe distance and upper and lower limits of the inter-UAV constraints are the same as those in simulation scenario 2. Calculations show that the UAV cluster needs to be divided into two groups, generating six false tracks. Each UAV group generates three false tracks, and the motion equations for the first false track generated by the two groups are set as follows:

[0180]

[0181] in, and They represent the coordinates of false target 1 and false target 4 at time k respectively.

[0182] The remaining false track scaling factors are as follows:

[0183]

[0184] Among them, p 2,1,k, p 5,4,k , p 3,1,k , p 6,4,k They represent the proportional factors of false target 2 corresponding to false target 1, false target 5 corresponding to false target 4, false target 3 corresponding to false target 1, and false target 6 corresponding to false target 4 at time k.

[0185] Figure 8 The figure shows the effect of drone cluster deceiving networked radar tracks in simulation scenario 3. Figures 9 to 11 Taking false track 2 and the 1st, 5th, 6th and 7th UAVs as an example, the flight speed, direction angle, pitch angle and altitude parameters of the false target and the three UAVs are displayed.

[0186] The results show that all drones were utilized and generated a high number of false tracks. Because the false tracks generated by each drone group met the Loss of Sight (LOS) criterion, the orientation of all false tracks relative to the radar was essentially the same as the first false track generated by that group. Therefore, by grouping the drone cluster, false targets flying in formation in different directions can be generated. Furthermore, each drone met its dynamic performance constraints, and its motion parameter curves were relatively smooth, eliminating the need for drone maneuvers. Therefore, the generated tracks are highly feasible.

[0187] The working principle and working process of the invention are as follows:

[0188] The present invention considers the efficient track deception of drone swarms against networked radars. Low-speed drone swarms generate as many high-speed false tracks as possible. To achieve this goal, a false track generation quantity index is constructed, with the drone swarm deception strategy and drone swarm track as optimization variables, and a false track rotation angle and drone swarm track as optimization variables are constructed for the total flight distance of the drone swarm. First, a single drone track deception model is established. Second, a false track generation quantity index is constructed, with the drone swarm deception strategy and drone swarm track as optimization variables, and a false track rotation angle and drone swarm track as optimization variables are constructed for the total flight distance of the drone swarm. Third, a dual-objective optimization model for drone swarm track deception against networked radars is established, with maximizing the number of false tracks generated and minimizing the total flight distance of the drone swarm as optimization objectives and drone flight dynamics performance as constraints. Finally, the optimization model is solved by combining the platform-reused drone swarm deception strategy with a particle swarm algorithm. By solving the optimization model, we can obtain the UAV swarm deception strategy μ, which makes the low-speed UAV swarm generate as many high-speed false tracks as possible under the conditions of satisfying the UAV flight dynamics constraints, and the speed direction angle between each UAV K moments and the false target (θ1, θ2, …, θ K ), the initial height z0 of the UAV and the false track rotation angle γ.

[0189] The UAV swarm deception strategy and track joint optimization system for track deception of the present invention includes:

[0190] A single UAV track deception model building unit is used to build a single UAV track deception model;

[0191] A false track generation quantity index construction unit is used to construct a false track generation quantity index with the drone swarm deception strategy and the drone swarm trajectory as optimization variables;

[0192] The UAV swarm flight total distance index construction unit is used to construct the UAV swarm flight total distance index with the false track rotation angle and the UAV swarm track as optimization variables;

[0193] An optimization model building unit is used to establish a dual-objective optimization model for drone swarm track deception targeting networked radars, with the optimization objectives of maximizing the number of false tracks generated and minimizing the total flight distance of the drone swarm, and with the drone flight dynamics performance as a constraint;

[0194] The optimization model solving unit is used to solve the dual-objective optimization model of drone cluster track deception for networked radar established in the optimization model establishment unit by combining the platform-reused drone cluster deception strategy and the PSO algorithm; it includes: first decomposing the optimization model into a false track generation quantity optimization model and a drone cluster total flight distance optimization model; combining the platform-reused drone cluster deception strategy to solve the false track generation quantity optimization model; combining the PSO algorithm to solve the drone cluster total flight distance optimization model; and finally outputting the optimization results.

[0195] An electronic device of the present invention comprises:

[0196] a memory storing executable program code;

[0197] a processor coupled to the memory;

[0198] The processor calls the executable program code stored in the memory to execute the steps of the above-mentioned drone cluster deception strategy and trajectory joint optimization method for trajectory deception.

[0199] A computer-readable storage medium of the present invention stores computer instructions, which, when called, are used to execute the steps of the above-mentioned drone cluster deception strategy and trajectory joint optimization method for trajectory deception.

Claims

1. UAV swarm deception strategy and trajectory joint optimization method for trajectory deception, characterized by: The following steps are involved: S1. Establish a single UAV track deception model; S2. Construct a false track generation quantity index with the drone swarm deception strategy and drone swarm track as optimization variables; expressed as: Among them, J1 represents the number of false track generation indicators, G n represents the number of false tracks generated by the nth UAV; S represents the number of UAVs in the UAV cluster; S3. Construct the total flight distance index of the UAV cluster with the false track rotation angle and the UAV cluster track as optimization variables; expressed as: Among them, J2 represents the total flight distance index of the drone cluster, and K represents the total number of deception moments; and They represent the average flight height and average flight distance of false targets respectively; h min,e Indicates the lower limit of the drone's flight altitude; represents the flight distance of the nth UAV in the kth time period; S4. Taking maximizing the number of false tracks generated and minimizing the total flight distance of the UAV cluster as the optimization goals and the UAV flight dynamics performance as the constraint condition, a dual-objective optimization model for UAV cluster track deception targeting networked radar is established; it is expressed as: Among them, μ represents the UAV swarm deception strategy; θ represents the angle between the UAV speed direction and the false target speed direction; z0 represents the initial height of the UAV; γ represents the false track rotation angle; ω1 and ω2 represent the weight coefficients of indicators J1 and J2 respectively; v max,e and v min,e Respectively represent the upper and lower limits of the drone's flight speed; Indicates drone e n Flight speed in the kth time period; △α max,e and △α min,e Respectively represent the upper and lower limits of the UAV flight turning angle; Indicates drone e n The turning angle at the kth time period; β max,e and β min,e Respectively represent the upper and lower limits of the drone's flight pitch angle; Indicates drone e n The flight pitch angle in the kth time period; h max,e and h min,e Respectively represent the upper and lower limits of the drone's flight altitude; Indicates drone e n Flight altitude at time k; Indicates drone e n1 and drones n2 Spacing; d safe Indicates the safe distance between drones; γ max and γ min Respectively represent the upper and lower limits of the false track rotation angle; N R Indicates the number of radars whose false tracks need to pass the homology test; R indicates the number of radars in the networked radar system; H m,r is a Boolean variable, representing the homology test parameter. If there is a drone on the line connecting the track point of the false track m and any radar r, record H m,r =1, otherwise H m,r =0;μ n,m,r is a Boolean variable, which is an element in the UAV cluster deception strategy μ. If the nth UAV deceives the rth radar to produce a false track m, μ is recorded. n,m,r =1, otherwise μ n,m,r =0; S5. Combining the platform-reused UAV cluster deception strategy and the particle swarm optimization (PSO) algorithm to solve the dual-objective optimization model of UAV cluster track deception for networked radar established in step S4; including: first decomposing the optimization model into a false track generation quantity optimization model and a UAV cluster total flight distance optimization model; combining the platform-reused UAV cluster deception strategy to solve the false track generation quantity optimization model; combining the PSO algorithm to solve the UAV cluster total flight distance optimization model; and finally outputting the optimization results.

2. The UAV swarm deception strategy and trajectory joint optimization method for trajectory deception according to claim 1 is characterized in that: The single UAV track deception model established in step S1 is: Among them, e k+1 represents the coordinate point of the drone at time (k+1); e' k+1 Indicates the coordinate point of the imaginary drone with the same speed and direction as the false target at time (k+1); Indicates e k+1 to e' k+1 vector of express The unit vector of f k+1 represents the coordinate point of the false target at time (k+1); θ represents the angle between the speed direction of the UAV and the speed direction of the false target. If θ>0, e k+1 Located in e' k+1 Above, on the contrary e k+1 Located in e' k+1 Below.

3. The UAV swarm deception strategy and track joint optimization method for track deception according to claim 2 is characterized in that: e k+1 With e' k+1 Distance Expressed as: Among them, e k represents the coordinate point of the drone at time k, Indicates e k to e' k+1 vector, Represents ∠e k e' k+1 e k+1 : Among them, f k represents the false target coordinate point at time k, represents f k to f k+1 vector of e' k+1 Coordinate (x e',k+1 ,y e',k+1 ,z e',k+1 )for: Among them, (x f,k ,y f,k ,z f,k ) is the coordinate point of the false target at time k; z e,k is the flight altitude of the UAV at time k.

4. The UAV swarm deception strategy and trajectory joint optimization method for trajectory deception according to claim 1 is characterized in that: The effect of the false track rotation angle γ on the false track is expressed as: Among them, (x' f,k ,y' f,k ,z' f,k ) represents the new false track generated by rotating the original false track, (x f,k ,y f,k ,z f,k ) is the false target coordinate point at time k; (x f,mid ,y f,mid ,z f,mid ) represents the position coordinates of the false track at the intermediate moment.

5. The UAV swarm deception strategy and trajectory joint optimization method for trajectory deception according to claim 1 is characterized in that: The optimization model for the number of false track generation in step S5 is expressed as: The platform reuse UAV swarm deception strategy is used to solve the optimization model for the number of false track generation: i) Based on the scaling factor By false track Generate false tracks Among them, the proportional factor of the false target m2 corresponding to the false target m1 at time k is Expressed as: in, and They represent the distances from the false target m1 and the false target m2 to the radar at time k respectively; It represents a constant proportional factor that does not change with time, and gives the basic activity range of the false target m2; represents the fluctuation scale factor at time k, which makes the shape of the false track m2 different from the false track m1; ii) Given the number of false tracks, a swarm deception strategy of UAVs reused on the platform is used to generate corresponding false targets from UAVs; iii) Given the number of UAVs, a swarm deception strategy of UAVs reused on the platform is used to generate corresponding false targets from UAVs; specifically: A drone cluster consisting of S drones is divided into q drone groups, S≥N R , where q must satisfy the following formula: q=S-L(N R -1). In order to maximize the total number of false tracks L generated, it is necessary to minimize q and q ≥ 1. The maximum number of false tracks L generated is obtained by the following formula: max : in, Indicates rounding down, the maximum value of L max Substitute the calculation formula of q to obtain the minimum value q of the drone group min ; Then the number of false tracks L generated by the i-th UAV group i To distribute, it is necessary to satisfy the following formula: The number of drones in the i-th drone group S i Calculated by the following formula: S i =N R +(L i -1)(N R -1). Finally, the deception strategy of the i-th drone group is obtained from Table 1.

6. The UAV swarm deception strategy and track joint optimization method for track deception according to claim 1 is characterized in that: The total flight distance optimization model of UAV cluster is expressed as: The particle swarm optimization algorithm (PSO) is used to solve the total flight distance optimization model of UAV clusters: i) Initialization: Initialize the position and velocity of a group of particles, the position of the i-th particle in the 0th generation speed in, Any vector in Indicates that drones n The vector formed by the initial height and the angle between the velocity at each moment; represents the false track rotation angle vector, for The corresponding particle velocity value; the fitness value of each particle is evaluated by optimizing the target; ii) Iterative update: Find the optimal individual position of each particle in the tth generation and the optimal value of group position The particle velocity is updated according to the following formula: in, represents the velocity of particle i of the (t+1)th generation in the dth dimension; ω represents the inertia factor; represents the speed of particle i of the tth generation in the dth dimension; c1 and c2 represent acceleration factors; r1 and r2 are random numbers between (0,1); represents the optimal value of the individual position of particle i in the tth generation in the dth dimension; represents the position of particle i of generation t in the dth dimension; represents the optimal value of the position of the t-th generation group in the d-th dimension; Update the particle position according to the following formula: in, and denote the positions of particle i in the (t+1)th and tth generations in the dth dimension respectively; represents the velocity of particle i of the (t+1)th generation in the dth dimension; iii) Check the termination condition: Check whether the maximum number of iterations is reached or the difference in fitness between two iterations is less than the termination index ε: If it is met, the algorithm terminates; otherwise, return to step ii) and execute the next iteration; iv) Output: (x1, x2, …, x S ),in Indicates that drones n The vector formed by the initial height and the velocity angle at each moment; the false track rotation angle vector x (S+1) .

7. UAV swarm deception strategy and trajectory joint optimization system for trajectory deception, characterized by: include: A single UAV track deception model building unit is used to build a single UAV track deception model; The false track generation quantity indicator construction unit is used to construct the false track generation quantity indicator with the drone cluster deception strategy and the crowd-free track as the optimization variables; it is expressed as: Among them, J1 represents the number of false track generation indicators, G n represents the number of false tracks generated by the nth UAV; S represents the number of UAVs in the UAV cluster; The UAV swarm flight total distance index construction unit is used to construct the UAV swarm flight total distance index with the false track rotation angle and the UAV swarm track as optimization variables; it is expressed as: Among them, J2 represents the total flight distance of the drone cluster; K represents the total number of deception moments; and They represent the average flight height and average flight distance of false targets respectively; h min,e Indicates the lower limit of the drone's flight altitude; d en,k represents the flight distance of the nth UAV in the kth time period; The optimization model building unit is used to establish a dual-objective optimization model for UAV swarm track deception targeting networked radars, with the optimization objectives of maximizing the number of false tracks generated and minimizing the total flight distance of the UAV swarm, and with the UAV flight dynamics performance as the constraint condition. It is expressed as: Among them, μ represents the UAV swarm deception strategy; θ represents the angle between the UAV speed direction and the false target speed direction; z0 represents the initial height of the UAV; γ represents the false track rotation angle; ω1 and ω2 represent the weight coefficients of indicators J1 and J2 respectively; v max,e and v min,e Respectively represent the upper and lower limits of the drone's flight speed; Indicates drone e n Flight speed in the kth time period; △α max,e and △α min,e Respectively represent the upper and lower limits of the UAV flight turning angle; Indicates drone e n The turning angle at the kth time period; β max,e and β min,e Respectively represent the upper and lower limits of the drone's flight pitch angle; Indicates drone e n The flight pitch angle in the kth time period; h max,e and h min,e Respectively represent the upper and lower limits of the drone's flight altitude; Indicates drone e n Flight altitude at time k; Indicates drone e n1 and drones n2 Spacing; d safe Indicates the safe distance between drones; γ max and γ min Respectively represent the upper and lower limits of the false track rotation angle; N R Indicates the number of radars whose false tracks need to pass the homology test; R indicates the number of radars in the networked radar system; H m,r is a Boolean variable, representing the homology test parameter. If there is a drone on the line connecting the track point of the false track m and any radar r, record H m,r =1, otherwise H m,r =0;μ n,m,r is a Boolean variable, which is an element in the UAV cluster deception strategy μ. If the nth UAV deceives the rth radar to produce a false track m, μ is recorded. n,m,r =1, otherwise μ n,m,r =0; The optimization model solving unit is used to solve the dual-objective optimization model of drone cluster track deception for networked radar established in the optimization model establishment unit by combining the platform-reused drone cluster deception strategy and the PSO algorithm; it includes: first decomposing the optimization model into a false track generation quantity optimization model and a drone cluster total flight distance optimization model; combining the platform-reused drone cluster deception strategy to solve the false track generation quantity optimization model; combining the PSO algorithm to solve the drone cluster total flight distance optimization model; and finally outputting the optimization results.

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