Unmanned aerial vehicle cluster flight path deception method based on weak feedback and weak communication conditions

Abstract

The invention discloses an unmanned aerial vehicle cluster flight path deception method based on weak feedback and weak communication conditions, and the method comprises the steps: determining an unmanned aerial vehicle cluster flight path deception model which comprises a motion control model and a control instruction model; constructing an unmanned aerial vehicle cluster flight path deception optimization model based on weak feedback and weak communication conditions, wherein the unmanned aerial vehicle cluster flight path deception optimization model comprises an unmanned aerial vehicle cluster flight path deception optimization model based on weak feedback and an unmanned aerial vehicle cluster flight path deception optimization model under the weak communication conditions; and solving the unmanned aerial vehicle cluster flight path deception optimization model based on weak feedback and the unmanned aerial vehicle cluster flight path deception optimization model under the weak communication condition by adopting a particle swarm algorithm to obtain a stable false trajectory. Through collaborative optimization calculation of the flight path of the unmanned aerial vehicle and the DRFM parameters, a control instruction capable of effectively maintaining a deception task in a complex battlefield environment is output, so that reliable flight path deception of a networking radar system is realized under the condition that platform errors and communication interruption exist.

Description

Technical Field

[0001] This invention belongs to the technical field of radar electronic countermeasures, and specifically proposes a method for deceiving the flight paths of UAV swarms under weak feedback and weak communication conditions. Background Technology

[0002] With the rapid development of radar technology, networked radar, through multi-radar node collaborative detection and information fusion, has significantly improved the high-precision positioning, identification, and anti-jamming capabilities of targets, becoming a core means of modern battlefield situational awareness. In the field of modern electronic warfare, UAV swarm trajectory deception technology, with its advantages of multi-platform collaboration, resource redundancy, and dynamic reconstruction, has become a key technical means to counter networked radar. However, in practical applications, this technology faces multiple challenges: UAVs are affected by factors such as airflow disturbances and power system fluctuations during flight, resulting in position jitter errors; Digital Radio Frequency Memory (DRFM) devices generate forwarding delay errors due to signal processing link delays or clock synchronization deviations; the complex and variable battlefield electromagnetic environment makes UAV swarm communication susceptible to interference, leading to interruptions in status information feedback or failures in command transmission, which in turn causes problems such as cluster leader decision delays and swarm control disorder. In addition, the "same source verification" mechanism of networked radar requires that false targets must strictly meet the consistency constraints of multi-radar observations, placing extremely high demands on the spatial accuracy of false trajectories. Existing track deception methods generally suffer from the following shortcomings: First, they lack a dynamic compensation mechanism for UAV jitter error and DRFM delay error, causing false targets to deviate beyond the radar resolution unit; second, they do not fully consider the robust design for loss of state information and delay of control commands in weak communication scenarios, making them susceptible to communication interruptions that could affect the deception mission; and third, they have not established a joint optimization model for multiple error coupling and communication uncertainty, making it difficult to balance deception effectiveness and system stability. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a method for deceiving UAV swarm tracks under weak feedback and weak communication conditions, so as to achieve highly reliable deception tracks for networked radar in complex battlefield environments.

[0004] Technical solution: The method described in this invention includes the following steps:

[0005] A drone swarm trajectory deception model is established, including a motion control model for drones when performing trajectory deception tasks and a model for drones within the swarm to receive control commands from the swarm leader drone. The drone swarm consists of a swarm leader drone and multiple drones within the swarm. Each drone within the swarm sends its own information to the swarm leader drone at every moment. The swarm leader drone performs real-time trajectory planning and deception parameter calculation based on the information sent by each drone and sends the actual control parameters to each drone.

[0006] With minimizing the flight distance of the UAV platform as the optimization objective and UAV dynamic performance as the constraint, an optimization model for UAV swarm trajectory deception under weak feedback and weak communication conditions is constructed, which includes two parts: an optimization model for UAV swarm trajectory deception under weak feedback and an optimization model for UAV swarm trajectory deception under weak communication conditions.

[0007] The particle swarm optimization algorithm is used to solve the UAV swarm trajectory deception optimization model based on weak feedback and the UAV swarm trajectory deception optimization model under weak communication conditions, and stable false trajectories are obtained.

[0008] Furthermore, the model for intra-cluster UAVs receiving control commands from the cluster leader UAV is represented as follows:

[0009] ;

[0010] in, Indicates the first drone receiver Real-time self-control command information; , and They represent Time of the first The flight speed command, heading angle command, and pitch angle command for the drone; express Time of the first The delay parameter command for the drone.

[0011] Furthermore, the optimization model for drone swarm trajectory deception based on weak feedback is expressed as follows:

[0012] ;

[0013] in, Indicates the first The drone in Flight distance over a period of time; express Time of the first The actual position coordinates of the drone; express Time of the first The actual spatial coordinates of the false target generated by the drone; express The target location of a constantly deceptive target; express Time of the first The flight speed of the drone; and These represent the upper and lower limits of the drone's flight speed, respectively. express Time of the first The azimuth angle of the drone; express Time of the first The yaw angle of the drone; and These represent the upper and lower limits of the drone's yaw angle, respectively. express Time of the first The pitch angle of the drone; and These represent the upper and lower limits of the drone's pitch angle, respectively. and These represent the upper and lower limits of the drone's flight altitude, respectively. express Time of the first The flight altitude of the drone is restricted. ~ Constraints on the dynamic performance of the UAV To constrain the flight altitude of drones.

[0014] Furthermore, a method for constructing an optimization model for UAV swarm trajectory deception under weak communication conditions includes:

[0015] First, we introduce the intra-cluster UAV transmission state variable. ,express The first time within the cluster The drone sends a state vector, with a value of 1 indicating that the drone has successfully sent its own state information, and a value of 0 indicating that communication between the drone and the cluster leader drone has been interrupted.

[0016] like If communication is interrupted, the cluster leader drone cannot receive the status information of the drones within the cluster and therefore cannot perform trajectory planning. Consequently, if communication is interrupted, the cluster leader drone needs to predict the current spatial coordinates of the drones within the cluster based on historical information. In this case, assuming that the flight control of the drones within the cluster is error-free and the forwarding delay is error-free, the cluster leader drone can then predict the current spatial coordinates of the drones within the cluster based on historical information. Prediction of spatial coordinates of drones at any time The spatial coordinates of the drone at any given time are then calculated, and the cluster leader drone is then used to determine its position. Prediction of spatial coordinates of drones at any time Real-time drone relay latency Finally, the status information of the cluster head UAV received by the UAVs within the cluster under weak communication conditions was obtained;

[0017] Secondly, introduce intra-cluster UAV reception state variables. ,express The first time within the cluster When the drone receives the state vector, a value of 1 indicates that the drone has successfully received its own state information, and a value of 0 indicates that communication between the drone and the cluster leader drone has been interrupted.

[0018] like If the cluster drones cannot receive the control commands from the cluster leader drone, they cannot control the drones. Therefore, we consider that when the cluster leader drone sends the control command at each moment, it also sends the control command at the current moment and the control command at several predicted moments in the future, so as to obtain the control command information sent by the cluster leader drone under weak communication conditions.

[0019] The expression for the optimization model of drone swarm trajectory deception under weak communication conditions is:

[0020] ;

[0021] in, Indicates the first The drone in Flight distance over a period of time; express Time of the first The actual position coordinates of the drone; express Time of the first The actual spatial coordinates of the false target generated by the drone; express The target location of a constantly deceptive target; express Time of the first The flight speed of the drone; and These represent the upper and lower limits of the drone's flight speed, respectively. express Time of the first The azimuth angle of the drone; express Time of the first The yaw angle of the drone; and These represent the upper and lower limits of the drone's yaw angle, respectively. express Time of the first The pitch angle of the drone; and These represent the upper and lower limits of the drone's pitch angle, respectively. and These represent the upper and lower limits of the drone's flight altitude, respectively. express Time of the first The flight altitude of the drone is restricted. ~ Constraints on the dynamic performance of the UAV To constrain the flight altitude of drones.

[0022] Furthermore, the cluster-headed drones, based on Prediction of spatial coordinates of drones at any time The spatial coordinates of the UAV at any given time can be expressed by the recursive formula as follows:

[0023] ;

[0024] in, Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Spatial coordinates of the drone; Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Spatial coordinates of the drone; Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Displacement vector of the drone; according to calculate, Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first The displacement vector of the drone is calculated using the following formula:

[0025] ;

[0026] in, , and These represent the results obtained by solving the optimization model under the assumptions of error-free flight control and error-free forwarding delay for the UAV. Time of the first Prediction of the status information of drones Time of the first The flight speed, heading angle, and pitch angle of the drone;

[0027] Cluster-headed drones according to Prediction of spatial coordinates of drones at any time Real-time drone relay latency Represented as:

[0028] ;

[0029] in, Indicates that the cluster-headed drone is based on Prediction of False Target Information Fusion Results at Any Time The target location of the false target at all times. Represents the speed of light;

[0030] Under weak communication conditions, the cluster leader UAV receives status information from UAVs within the cluster. for:

[0031] ;

[0032] in, Indicates the first The DRFM carried by the drone The actual forwarding delay at any given moment. This indicates the moment when the cluster leader drone last successfully received status information from drones within the cluster. Indicates based on the first The predicted time of the last successful reception of cluster drone status information by the drone. Time of the first Control command vectors for drones, To indicate from the first The time interval between the moment when the drone last successfully received the status information of the drone in the cluster and the current moment.

[0033] Furthermore, under weak communication conditions, cluster-headed UAVs can send control command information. for:

[0034] ;

[0035] in, Indicates the length of the prediction window; Indicates cluster-headed drones Time Prediction Time of the first Control commands for the drone Specifically, it is expressed as:

[0036] ;

[0037] in, Indicates cluster-headed drones Time Prediction Time of the first The flight speed of the drone Indicates cluster-headed drones Time Prediction Time of the first The yaw angle of the drone, Indicates cluster-headed drones Time Prediction Time of the first The pitch angle of the drone;

[0038] Actual control commands for UAVs within a cluster under weak communication conditions for:

[0039] ;

[0040] in, This indicates the moment when the drone within the cluster last successfully received control commands. This indicates that the nth drone has successfully received the control command. This represents the moment when the nth drone last successfully received a control command. The predicted control commands received by the nth UAV at the current time k.

[0041] Furthermore, the particle swarm optimization algorithm is used to solve the drone swarm trajectory deception optimization model based on weak feedback, including the following steps:

[0042] (1) Calculate the spatial coordinates of the false target of a single UAV, traverse each UAV in the cluster, and calculate the actual spatial coordinates of the false target generated by each UAV.

[0043] (2) The unified false target coordinates are obtained by fusion. Based on the false target coordinates of each UAV obtained in step (1), the false targets generated by different UAVs are fused to obtain the globally unified false target spatial coordinates.

[0044] (3) Update the coordinates of the false target at the next moment. Based on the current fused false target coordinates, update the target space coordinates of the false target at the next moment.

[0045] (4) Solve for the optimal heading angle of the UAV. Then, traverse each UAV in the cluster again and use PSO to solve the optimization model to obtain the optimal heading angle of each UAV.

[0046] (5) Based on the optimal heading angle obtained in step (4), calculate the control command corresponding to each UAV, and determine the time delay parameter and Doppler parameter of DRFM;

[0047] (6) All UAVs in the cluster receive the corresponding control commands, fly to the designated location, and forward the signals carrying the corresponding time delay and Doppler parameters.

[0048] Furthermore, the particle swarm optimization algorithm is used to solve the UAV swarm trajectory deception optimization model under weak communication conditions, including the following steps:

[0049] (1) Determine the transmission status and obtain the UAV location and DRFM delay;

[0050] (2) Calculate the spatial coordinates of the false target of a single UAV, traverse each UAV in the cluster, and calculate the actual spatial coordinates of the false target generated by each UAV based on the UAV position obtained in step (1).

[0051] (3) The coordinates of the false targets are fused together. Based on the coordinates of the false targets of each UAV obtained in step (2), the information of the false targets generated by different UAVs is fused to obtain the global unified spatial coordinates of the false targets.

[0052] (4) Update the false target coordinates at the next moment. Based on the current fused false target coordinates and combined with the preset false target velocity vector, update the target space coordinates of the false target at the next moment.

[0053] (5) Solve for the optimal heading angle of the UAV. Then, traverse each UAV in the cluster again and use PSO to solve the optimization model to obtain the optimal heading angle of each UAV.

[0054] (6) Generate control commands and signal parameters. Based on the optimal heading angle obtained in step (5), calculate the flight control commands corresponding to each UAV and determine the time delay parameters and Doppler parameters of DRFM.

[0055] (7) Determine the reception status. If the reception is successful, send the control command at the current time directly. If the reception fails, predict the control command at several future times.

[0056] The UAV swarm trajectory deception system based on weak feedback and weak communication conditions described in this invention includes:

[0057] The deception model construction unit is used to establish the UAV swarm trajectory deception model, including the motion control equations of the UAVs when carrying out the trajectory deception task and the model of the UAVs in the swarm receiving the control command information of the swarm leader UAV. The UAV swarm includes a swarm leader UAV and multiple UAVs in the swarm. Each UAV in the swarm sends its own information to the swarm leader UAV at every moment. The swarm leader UAV performs real-time trajectory planning and deception parameter calculation based on the information sent by each UAV, and sends the actual control parameters to each UAV.

[0058] The optimization model building unit is used to construct an optimization model for UAV swarm trajectory deception under weak feedback and weak communication conditions, with the optimization objective of minimizing the flight distance of the UAV platform and the UAV dynamic performance as the constraint. It includes two parts: an optimization model for UAV swarm trajectory deception under weak feedback and an optimization model for UAV swarm trajectory deception under weak communication conditions.

[0059] The optimization model solving unit is used to solve the UAV swarm trajectory deception optimization model based on weak feedback and the UAV swarm trajectory deception optimization model under weak communication conditions using the particle swarm algorithm, so as to obtain stable false trajectories.

[0060] The present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the method described.

[0061] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: (1) In response to the problem that jitter error and DRFM forwarding delay error cause false targets to deviate and fail the same source test when UAV swarms are used to counter networked radar, the present invention proposes a weak feedback error dynamic compensation method; by interacting with the position, delay and other status information in real time within the swarm, the coordinates of the false targets are dynamically corrected by utilizing the error controllability characteristics, ensuring that they converge to the radar spatial resolution unit, solving the pain point of traditional deviation, and improving the effectiveness and stability of track deception; The advantage of the present invention is that a weak feedback optimization model is established with the goal of solving the failure of the same source test, and a feedback closed loop is constructed through real-time status interaction to ensure that the false targets are corrected. The false target continues to converge to the radar resolution unit, and the offset is corrected to ensure the same source verification, thereby improving the deception effectiveness and stability; (2) In view of the distributed network radar system composed of N pulse radars, and the problem that UAV clusters are prone to communication interruption and deception mission stagnation in the weak communication environment of the battlefield, this invention proposes a UAV state prediction and control command pre-sending collaborative adaptation method, which aims to realize the trajectory deception mission in the weak communication scenario; Assuming that the dynamic parameters such as the flight speed, yaw angle, and pitch angle of the UAV are known, and communication link stability monitoring data can be obtained, this invention designs a state prediction and pre-command collaborative adaptation scheme with the goal of ensuring mission continuity. Under the premise of unstable communication link, by establishing a mathematical model with the goal of ensuring the continuous execution of trajectory deception mission and minimizing false target offset, the collaborative adaptation of UAV state prediction and control command pre-sending is realized, thereby avoiding mission stagnation caused by communication interruption and ensuring the continuity of deception mission in the weak communication environment. Attached Figure Description

[0062] Figure 1 This is a flowchart of the method of the present invention;

[0063] Figure 2 A schematic diagram illustrating drone swarm trajectory deception;

[0064] Figure 3 A schematic diagram illustrating the geometric relationship between a drone's radar track deception.

[0065] Figure 4 This is a schematic diagram illustrating drone swarm trajectory deception in simulation scenario 1.

[0066] Figure 5 This is a schematic diagram illustrating the flight speed of the drone in simulation scenario 1.

[0067] Figure 6 This is a schematic diagram of the heading angle of the UAV in simulation scenario 1.

[0068] Figure 7 This is a schematic diagram of the drone's pitch angle in simulation scenario 1.

[0069] Figure 8 This is a schematic diagram illustrating the average splitting distance of the false target in simulation scenario 1.

[0070] Figure 9 This is a schematic diagram of the communication status of the UAV in simulation scenario 2.

[0071] Figure 10 This is a schematic diagram illustrating drone swarm trajectory deception in simulation scenario 2.

[0072] Figure 11 This is a schematic diagram of the average splitting distance of the false target in simulation scenario 2. Detailed Implementation

[0073] The structure and working process of the present invention will be further described below with reference to the accompanying drawings.

[0074] Consider using A drone A network of radar systems composed of pulse radars performs track deception and generates... False flight paths. Existing technologies face the dual challenges of inherent jitter errors in UAVs, forwarding delay errors in digital radio frequency memory, and unstable communication links caused by the battlefield electromagnetic environment during deception. These factors can cause the generated false targets to deviate or split, ultimately failing the homology check of the networked radar and being eliminated. This invention aims to design a highly robust intelligent flight path deception method for UAV swarms under the aforementioned weak feedback and weak communication conditions. It aims to ensure the generation of continuous, stable false flight paths that can pass the homology check of enemy radar through dynamic compensation and predictive control. Based on practical engineering application needs, this invention adopts a solution combining intelligent decision-making and state prediction mechanisms based on particle swarm optimization algorithms. Through collaborative optimization calculation of UAV flight paths and DRFM parameters, it outputs control commands that can effectively maintain the deception mission in complex battlefield environments, thereby achieving reliable flight path deception of networked radar systems even in the presence of platform errors and communication interruptions.

[0075] like Figure 1 As shown, the method described in this invention includes the following steps:

[0076] 1. Establish a drone swarm trajectory deception model:

[0077] (1) Dynamics model of unmanned aerial vehicles

[0078] Depend on A drone swarm consisting of drones A distributed networked radar system composed of pulse radars performs track deception and generates... A false flight path is generated. To improve the success rate of deception, considering the jitter error of the UAV and the time delay error of DRFM during the deception mission, a false flight path that passes the same-source verification of the networked radar is generated. A schematic diagram of the flight path deception is shown below. Figure 2 As shown.

[0079] Based on the pre-set false flight path for the combat mission, the flight motion parameters of the UAV can be obtained through the coupling relationship between the false target point, the UAV, and the radar. Further analysis of the coupling relationship between the radar, the false target, and the UAV establishes a three-dimensional Cartesian coordinate system, and the kinematic variables of the three are given as follows: Figure 3 As shown. A spherical coordinate system is established around the radar, and the corresponding false target positions are obtained as follows:

[0080] (1)

[0081] in, Indicates the location coordinates of the false target; Indicates the distance between the radar and the false target; Indicates the azimuth angle of the line connecting the radar and the false target; This indicates the elevation angle of the line connecting the radar and the decoy target.

[0082] Differentiating equation (1) and transforming it into matrix form, we can obtain:

[0083] (2)

[0084] in, , and They represent respectively to , and Differentiating, , , They are respectively , , The derivative of .

[0085] Based on geometric relationships, we obtain:

[0086] (3)

[0087] in, , and These represent the flight speed, heading angle, and pitch angle of the false target, respectively.

[0088] Similarly, the spatial state of the drone can be obtained as follows:

[0089] (4)

[0090] in, Indicates the distance between the radar and the drone; Indicates to Differentiate; , and These represent the drone's flight speed, heading angle, and pitch angle, respectively.

[0091] According to geometric analysis, we can obtain:

[0092] (5)

[0093] (6)

[0094] (7)

[0095] in, ; This indicates the radar's location coordinates.

[0096] Combining equations (4), (5), (6), and (7), we can obtain the motion control equations for the UAV when performing a flight deception mission, namely:

[0097] (8)

[0098] As can be seen from equation (8), since the UAV needs to satisfy the coupling relationship between the radar, the UAV and the false target at all times during the flight deception mission, and the false flight path and radar site are known in advance, the motion variables of the UAV will be constrained to one dimension, that is, only by controlling its flight direction angle. This enables UAV trajectory planning under trajectory deception coupling constraints.

[0099] (2) Unmanned Aerial Vehicle (UAV) Control Command Model

[0100] Assuming the radar transmitted signal is a linear frequency modulated (LFM) signal, then the radar transmitted signal... Represented as:

[0101] (9)

[0102] in, Indicates the amplitude of the radar transmitted signal; This indicates the center frequency of the signal; This indicates the linear modulation frequency of the frequency modulation signal; Indicates the pulse width of the rectangular window signal. For gate functions, For timestamps.

[0103] Let the time delay modulation parameter and the Doppler modulation parameter be respectively and Then, it will deceive and interfere with the signal. Represented as:

[0104] (10)

[0105] The coordinates of the false target obtained from the above deception and interference signals are calculated by the following formula:

[0106] (11)

[0107] in, Represents the speed of light; This indicates the location coordinates of the drone.

[0108] Define a drone swarm consisting of drones generating the same false target using different radars. The swarm employs a star-shaped communication topology. Figure 2 As shown. Each UAV within the cluster needs to send its own information to the cluster leader UAV at every moment. The cluster leader UAV performs real-time trajectory planning and spoofing parameter calculation based on the information sent by the UAVs in the cluster, and then sends the actual control parameters to the UAVs in the cluster. The status information sent by each UAV in the cluster is represented as follows:

[0109] (12)

[0110] in, Indicates the first Send by drone Real-time self-state information; express Time of the first The actual position coordinates of the drone; Indicates the first The DRFM carried by the drone The actual forwarding delay at any given moment.

[0111] The control command information received by the UAV within the cluster from the UAV in the cluster head is represented as follows:

[0112] (13)

[0113] in, Indicates the first drone receiver Real-time self-control command information; , and They represent Time of the first The flight speed command, heading angle command, and pitch angle command for the drone; express Time of the first The delay parameter command for the drone.

[0114] 2. Construct an optimization model for UAV swarm trajectory deception under weak feedback and weak communication conditions; including the following steps:

[0115] (1) Optimization model for UAV swarm trajectory deception based on weak feedback;

[0116] Because the UAV has jitter error and DRFM has time delay error during the deception mission, there is an offset between the actual generated false target and the preset false target. If the offset is not compensated, the distance between the false targets generated by each UAV will continue to increase, eventually causing them to fail the same source test of the enemy's networked radar and be eliminated. Therefore, each UAV needs to communicate in real time, exchange its own actual position information and DRFM actual forwarding delay according to equation (13), and perform trajectory planning and deception parameter calculation based on real-time information, so as to ensure that the generated false targets can pass the same source test of the enemy's radar. Since the UAV and DRFM have a certain accuracy, their related parameter errors can be controlled within a certain range. Therefore, this kind of small-range error feedback is called weak feedback.

[0117] Considering that the networked radar performs information fusion on false targets that pass the same-source test, the coordinates of the false targets after information fusion can be expressed as:

[0118] (14)

[0119] in, express The spatial coordinates of the false target after fusion of time-series information; express Time of the first The actual spatial coordinates of the false target generated by the drone are calculated using the following formula:

[0120] (15)

[0121] in, Indicates the first Deceiving radar with drones Spatial coordinates; express Time of the first The actual location of the drone was transferred to the radar. The distance.

[0122] To ensure that the generated false targets can pass the network radar source detection, the target position of the false targets at the next moment needs to be calculated in real time based on the coordinates of the false targets after information fusion.

[0123] (16)

[0124] in, express The target location of a constantly deceptive target; express The velocity vector of the false target is preset at all times; Indicates a time interval.

[0125] In actual combat missions, to enable low-speed UAVs to generate high-speed false targets and complete trajectory deception tasks, optimal trajectory planning for the UAVs is necessary. The cluster leader UAV receives status information from all UAVs within the cluster. With minimizing the flight distance of the UAV platform as the optimization objective and UAV dynamic performance as the constraint, a UAV trajectory deception optimization model based on weak feedback is established. By solving this model, control command information for each UAV within the cluster is obtained and sent to each UAV within the cluster. The UAV swarm trajectory deception optimization model based on weak feedback is expressed as follows:

[0126] (17)

[0127] in, Indicates the first The drone in Flight distance over a period of time; express Time of the first The flight speed of the drone; and These represent the upper and lower limits of the drone's flight speed, respectively. express Time of the first The azimuth angle of the drone; express Time of the first The yaw angle of the drone; and These represent the upper and lower limits of the drone's yaw angle, respectively. express Time of the first The pitch angle of the drone; and These represent the upper and lower limits of the drone's pitch angle, respectively. and These represent the upper and lower limits of the drone's flight altitude, respectively. This refers to the drone's flight altitude. (Constraint) ~ Constraints on the dynamic performance of the UAV To constrain the flight altitude of drones.

[0128] (2) Optimization model for UAV swarm trajectory deception under weak communication conditions;

[0129] In actual combat scenarios, UAV swarm communication is affected by factors such as the battlefield electromagnetic environment and platform movement, and is prone to weak communication characteristics such as communication failure or intermittent interruption. That is, the control command obtained by equation (13) cannot be guaranteed to be continuous and uninterrupted, which seriously affects the control command decision of the UAV head and the control command execution of UAVs in the swarm. Therefore, it is necessary to study the intelligent trajectory deception algorithm of UAV swarm under weak communication conditions.

[0130] To characterize the communication state of a drone swarm at any given time, we first introduce the state vector transmitted by the drones within the swarm:

[0131] (18)

[0132] in, express The state vector sent by the UAV within the cluster at each time step; It is the transpose symbol. This indicates the state variables sent by the drones within the cluster. ,satisfy:

[0133] (19)

[0134] Similarly, an intra-cluster UAV reception state vector is introduced:

[0135] (20)

[0136] in, express The intra-cluster UAV received state vector at time t; The state variable received by the UAV within the cluster satisfies:

[0137] (twenty one)

[0138] like If communication interruption occurs, the cluster leader drone will be unable to receive status information from other drones within the cluster and will be unable to plan its flight path. Therefore, if communication is interrupted, the cluster leader drone needs to predict the current spatial coordinates of other drones within the cluster based on historical information. In this case, assuming that the flight control of the drones within the cluster is error-free and the forwarding delay is error-free, the cluster leader drone will then... Prediction of spatial coordinates of drones at any time The recursive formula for the spatial coordinates of the UAV at any given time is as follows:

[0139] (twenty two)

[0140] in, Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Spatial coordinates of the drone; Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Spatial coordinates of the drone; Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Displacement vector of the drone Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first The displacement vector of the drone is calculated using the following formula:

[0141] (twenty three)

[0142] in, , and These represent the results obtained by solving the optimization model (17) under the assumptions of error-free flight control and error-free forwarding delay of the UAV. Time of the first Prediction of the status information of drones Time of the first The flight speed, heading angle, and pitch angle of the drone.

[0143] Cluster-headed drones according to Prediction of spatial coordinates of drones at any time Real-time drone relay latency for:

[0144] (twenty four)

[0145] in, Indicates that the cluster-headed drone is based on Prediction of False Target Information Fusion Results at Any Time The target location of a false target at all times.

[0146] Therefore, under weak communication conditions, the cluster leader UAV receives the status information of the UAVs within the cluster. for:

[0147] (25)

[0148] in, This indicates the moment when the cluster leader drone last successfully received status information from drones within the cluster. This represents the control command vector of the nth drone at time k, predicted based on the moment when the nth drone last successfully received the state information of drones within the cluster. Let represent the time interval from the moment when the nth drone last successfully received the drone status information within the cluster to the current moment.

[0149] like If the cluster's drones cannot receive control commands from the cluster leader drone, they will be unable to control the drones. Therefore, considering that the cluster leader drone sends both the current control command and predicted control commands for several future times at each moment, the cluster leader drone's control command information transmission under weak communication conditions is... for:

[0150] (26)

[0151] in, Indicates the length of the prediction window; Indicates cluster-headed drones Time Prediction Time of the first Control commands for the drone Specifically, it is expressed as:

[0152] (27)

[0153] in, Indicates cluster-headed drones Time Prediction Time of the first The flight speed of the drone Indicates cluster-headed drones Time Prediction Time of the first The yaw angle of the drone, Indicates cluster-headed drones Time Prediction Time of the first The pitch angle of the drone.

[0154] Therefore, the actual control commands for UAVs within a cluster under weak communication conditions for:

[0155] (28)

[0156] in, This indicates the moment when the drone within the cluster last successfully received control commands. This indicates that the nth drone has successfully received the control command. This represents the moment when the nth drone last successfully received a control command. The predicted control commands received by the nth UAV at the current time k.

[0157] Finally, an optimization model for drone swarm trajectory deception based on weak communication is established, with the same expression as equation (17).

[0158] 3. Solve the optimization model using particle swarm optimization:

[0159] The optimization problem (17) is a nonlinear optimization problem. The PSO algorithm is one of the commonly used algorithms for solving nonlinear problems. Considering its simplicity and ease of implementation and the absence of complex parameter adjustments, this invention uses the PSO algorithm to solve this optimization problem.

[0160] The idea behind Particle Swarm Optimization (PSO) is derived from the study of bird flock foraging behavior. Bird flocks find the optimal destination through collective information sharing. Each iteration generates a new positional state based on the individual's own position vector, velocity vector, individual historical information, group information, and perturbations. Assume the flock consists of... Composed of the nth particle, the algorithm in the nth... Individual particles The formula for calculating the algebra is as follows:

[0161] (29)

[0162] (30)

[0163] in, Indicates the first The generation The speed of each particle Indicates the first The generation The position of each particle. Indicates the first The generation The position of each particle, in this invention, specifically represents the heading angle of the drone; Indicates the first The generation The velocity of each particle; Indicates the inertia factor; and Indicates the acceleration factor; and for Random numbers between; This represents the optimal value of an individual particle's position; This represents the optimal position for the group.

[0164] Combining the particle swarm optimization algorithm, this invention introduces a UAV swarm trajectory deception algorithm based on weak feedback, and the solution steps are as follows:

[0165] Step 1: Calculate the spatial coordinates of the false target of a single UAV. Traverse each UAV in the cluster and calculate the actual spatial coordinates of the false target generated by each UAV using Equation (15).

[0166] Step 2: Fusion to obtain unified false target coordinates. Based on the false target coordinates of each UAV obtained in Step 1, information fusion is performed through Equation (14) to obtain globally unified false target spatial coordinates.

[0167] Step 3: Update the coordinates of the false target at the next moment. Using Equation (16), based on the current fused false target coordinates, update the target space coordinates of the false target at the next moment.

[0168] Step 4: Solve for the optimal heading angle of the UAV. Iterate through each UAV in the cluster again and use the particle swarm optimization algorithm (PSO) to solve the optimization model (17) to obtain the optimal heading angle of each UAV.

[0169] Step 5: Based on the optimal heading angle obtained in Step 4, calculate the control command corresponding to each UAV, and at the same time determine the time delay parameter and Doppler parameter of DRFM.

[0170] Step Six: All UAVs within the cluster receive the corresponding control commands, fly to the designated location, and forward signals carrying the corresponding time delay and Doppler parameters.

[0171] The PSO method is used to solve the UAV swarm trajectory deception optimization model based on weak feedback to obtain the UAV state and latency, generate stable false trajectories, and feed the information back to the UAV swarm trajectory deception optimization model based on weak feedback to solve the UAV state and latency at the next moment.

[0172] The algorithm for spoofing drone swarm tracks based on weak communication is solved as follows:

[0173] Step 1: Determine the transmission status and obtain the drone's location and DRFM delay.

[0174] Step 2: Calculate the spatial coordinates of the false target of a single UAV. Traverse each UAV in the cluster and calculate the actual spatial coordinates of the false target generated by each UAV based on the UAV position obtained in Step 1 using Equation (15).

[0175] Step 3: Fusion to obtain unified false target coordinates. Based on the false target coordinates of each UAV obtained in Step 2, information fusion is performed through Equation (14) to obtain globally unified false target spatial coordinates.

[0176] Step 4: Update the coordinates of the false target at the next moment. Using Equation (16), based on the current fused false target coordinates and combined with the preset false target velocity vector, update the target space coordinates of the false target at the next moment.

[0177] Step 5: Solve for the optimal heading angle of the UAV. Iterate through each UAV in the cluster again and use PSO to solve the optimization model to obtain the optimal heading angle of each UAV.

[0178] Step Six: Generate control commands and signal parameters. Based on the optimal heading angle obtained in Step Five, calculate the flight control commands corresponding to each UAV, and determine the time delay parameters and Doppler parameters of DRFM.

[0179] Step 7: Determine the reception status. If the reception is successful, directly send the control command for the current moment. If the reception fails, predict the control command for several future moments.

[0180] By using PSO to solve the UAV swarm trajectory deception optimization model under weak communication conditions, the state and latency of the UAVs are obtained, a stable false trajectory is generated, and the information is fed back to the UAV swarm trajectory deception optimization model under weak communication conditions to solve the state and latency of the UAVs at the next moment.

[0181] 4. Simulation Results

[0182] Consider by A network radar system consisting of pulse radars has a range resolution of 100m. Assuming the "2 / 3" criterion is used for source detection of the network radars, the radar coordinates are (0,0,0)km, (3,4,0)km, and (4,-3,0)km. A swarm of drones was used to deceive the target's flight path. The initial coordinates of the false target were (-60, 80, 8) km, and the flight speeds of the false target along the x, y, and z axes were respectively... , , The DRFM delay accuracy error is... The drone's positional error was 5m within 25ns. The drone's dynamic performance parameters are shown in Table 1.

[0183] Table 1. Dynamic Performance Parameters of Unmanned Aerial Vehicles

[0184]

[0185] (1) Simulation Scenario 1

[0186] Simulation Scenario 1 considers intelligent flight path deception under the condition that the UAV has uninterrupted communication at all times. Figure 4 The simulation scenario 1 shows the movement trajectory of the UAV swarm, false tracks, and the spatial position of the network radar. It can be seen that the proposed algorithm can still generate false tracks that pass the network radar homology test even with UAV position errors and DRFM forwarding delay errors.

[0187] Figures 5 to 7 The flight parameter curves of each UAV in simulation scenario 1 are shown. It can be seen that at any given time, all flight parameters of the UAV conform to the UAV dynamic performance constraints. Figure 6 It can be seen that, due to the small distance between radars, the drones deceiving different radars fly in essentially the same direction to generate the same false track. Simultaneously, as the track deception mission progresses, the flight speed and pitch angle of each drone fluctuate within a small range, and the heading angle, while trending upward, also exhibits small fluctuations. These minor fluctuations in flight parameters primarily stem from the drones correcting their own positional deviations and compensating for time delay errors during DRFM relay.

[0188] To better measure the deception performance of false targets, the average splitting distance of the same false target generated by different UAVs is introduced as a performance index of the false target. The formula for calculating this performance index is as follows:

[0189] (31)

[0190] in, The average split distance for generating the same false target for different drones. Indicates to The number of pairs of false targets generated by drones; and Indicates the first drones and the first The actual coordinates of the false target generated by the drone.

[0191] Considering the randomness of UAV motion errors and DRFM forwarding delay errors, this study uses the Monte Carlo method to calculate the average splitting distance of false targets, such as... Figure 8 As shown, the average splitting distance of false targets continuously increases, but the upward trend of the average splitting distance slows down over time. Furthermore, the average splitting distance at any given time is less than the radar's range resolution, indicating that the generated false targets can pass the homology verification of the networked radar.

[0192] (2) Simulation Scenario 2

[0193] Simulation scenario 2 considers intelligent trajectory spoofing under weak communication conditions. In this scenario, drone 3 acts as the leader drone in a cluster, and is configured... The communication status between UAVs 1 and 2 and UAV 3 is as follows: Figure 9 As shown.

[0194] Figure 10 The simulation scenario 2 shows the movement trajectory, false tracks, and spatial position of the UAV swarm. It can be seen that despite communication interruptions between UAVs during the mission, the UAV swarm can still generate false tracks relatively well by predicting the state and control commands of each UAV.

[0195] Considering the randomness of UAV motion errors and DRFM forwarding delay errors, this study uses the Monte Carlo method to calculate the average splitting distance of false targets under weak communication conditions, such as... Figure 8 As shown. Comparison Figure 8 and Figure 11 It can be seen that the average splitting distance of the false target at each time step is basically the same in both simulation scenarios, indicating that the communication interruption at a single time step has little impact on the execution of the track deception task under this algorithm. Moreover, in 1000 Monte Carlo simulations, only one false track generated failed to pass the sameness test and was interrupted, which proves the stability of the proposed algorithm.

[0196] The working principle and process of this invention:

[0197] This invention presents a method for deceiving UAV swarm tracks under weak feedback and weak communication conditions. By integrating multi-source state compensation, predictive control, and collaborative optimization mechanisms, it achieves high-precision false track generation and interference maintenance against networked radar. Specifically, in the collaborative operation of the UAV swarm, the leader UAV acts as the core control node. Through a star-shaped communication topology, it receives flight state parameters and DRFM delay error information from each slave UAV in real time. First, it calculates the actual false targets generated by each UAV, then fuses them to obtain the fused false target at the current moment, and uses this to predict the false target position at the next moment. The leader UAV then establishes an optimization model with dynamic constraints, aiming to minimize the UAV flight distance, and solves it using the PSO algorithm. It dynamically corrects the UAV flight parameters to offset the impact of flight jitter error and DRFM delay error on the accuracy of the false target, ensuring that the false target can pass the same-source detection in multi-station observations of the networked radar. When communication is interrupted due to the complex electromagnetic environment on the battlefield, if the leader UAV does not receive the status information of a certain UAV, it calculates the current position and DRFM delay based on the historical position and predicted control commands of that UAV using a forward recursive method based on an ideal motion model, and generates control commands based on the prediction results. If UAVs within the cluster do not receive control commands, they execute flight strategies based on the last predicted control command received when communication was available, maintaining the continuity of the false trajectory until communication is restored and control parameters are updated synchronously. Based on this, the leader UAV constructs an optimization model that includes UAV dynamics and flight altitude constraints, aiming to minimize the UAV swarm flight distance. It uses the PSO algorithm to solve for the optimal trajectory planning scheme, dynamically adjusting the UAV flight path and DRFM delay parameters. By satisfying the geometric coupling relationship between the radar, UAV, and false target, it indirectly ensures that the false target passes the same-source verification of the networked radar. Based on optimized trajectory planning, the UAV swarm stores and delays radar signals via DRFM (Radar Radar Signal Detection and Forwarding) equipment, generating false echoes similar to the motion characteristics of real targets. By coordinating the forwarding delays and flight trajectories of multiple UAVs, the false targets meet the consistency requirements of multi-station radar observations in a network, thus misleading the radar tracking algorithm and achieving concealment or deception of real targets. During this process, the system continuously iterates and optimizes control commands based on weak feedback from the UAVs' own states and DRFM errors until the mission is completed, ultimately achieving highly reliable and high-precision trajectory deception of targets under conditions of weak feedback and weak communication.

[0198] In summary, this invention addresses the problem that when UAV swarms counter distributed networked radar, false targets deviate due to UAV jitter errors and DRFM forwarding delay errors, thus failing the same-source detection. This invention proposes a dynamic error compensation method based on weak feedback. By exchanging UAV position, DRFM delay, and other status information within the swarm in real time, the coordinates of false targets are dynamically corrected using the small-range controllable error characteristics. This ensures that false targets generated by multiple UAVs converge within the spatial resolution unit of the networked radar, improving the effectiveness and stability of track deception.

[0199] To address the issues of communication interruptions and deception mission stalls in distributed networked radar systems composed of N pulse radars, and the susceptibility of UAV swarms to communication interruptions in weak battlefield communication environments, this invention establishes a mathematical model for the coordinated adaptation of UAV state prediction and control command pre-transmission, under the premise of unstable communication links and the goal of ensuring continuous execution of flight path deception missions and minimizing false target deviations. This model uses dynamic parameters such as UAV flight speed, yaw angle, and pitch angle as constraints to achieve seamless connection of deception missions in weak communication scenarios.

[0200] To address the multivariable and nonlinear solution requirements of weak feedback error compensation and weak communication adaptation models, this invention adopts a hybrid solution strategy combining particle swarm optimization algorithm and state prediction logic. First, the particle swarm optimization algorithm is used to solve the optimal UAV trajectory that satisfies dynamic constraints under weak feedback. Then, the state recursion formula for weak communication scenarios is incorporated to complete the prediction of UAV position, DRFM delay, and pre-command generation when communication is interrupted. Finally, the UAV control commands and DRFM modulation parameters are output, simultaneously achieving error compensation and weak communication adaptation.

[0201] This invention also provides a drone swarm trajectory deception system based on weak feedback and weak communication conditions, comprising:

[0202] The deception model construction unit is used to establish the UAV swarm trajectory deception model, including the motion control equations of the UAVs when carrying out the trajectory deception task and the model of the UAVs in the swarm receiving the control command information of the swarm leader UAV. The UAV swarm includes a swarm leader UAV and multiple UAVs in the swarm. Each UAV in the swarm sends its own information to the swarm leader UAV at every moment. The swarm leader UAV performs real-time trajectory planning and deception parameter calculation based on the information sent by each UAV, and sends the actual control parameters to each UAV.

[0203] The optimization model building unit is used to construct an optimization model for UAV swarm trajectory deception under weak feedback and weak communication conditions, with the optimization objective of minimizing the flight distance of the UAV platform and the UAV dynamic performance as the constraint. It includes two parts: an optimization model for UAV swarm trajectory deception under weak feedback and an optimization model for UAV swarm trajectory deception under weak communication conditions.

[0204] The optimization model solving unit is used to solve the UAV swarm trajectory deception optimization model based on weak feedback and the UAV swarm trajectory deception optimization model under weak communication conditions using the particle swarm algorithm.

[0205] The present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the method described.

Claims

1. A method for deceiving UAV swarm tracks under conditions of weak feedback and weak communication, characterized in that, Includes the following steps: A drone swarm trajectory deception model is established, including a motion control model for drones when performing trajectory deception tasks and a model for drones within the swarm to receive control commands from the swarm leader drone. The drone swarm consists of a swarm leader drone and multiple drones within the swarm. Each drone within the swarm sends its own information to the swarm leader drone at every moment. The swarm leader drone performs real-time trajectory planning and deception parameter calculation based on the information sent by each drone and sends the actual control parameters to each drone. With minimizing the flight distance of the UAV platform as the optimization objective and UAV dynamic performance as the constraint, an optimization model for UAV swarm trajectory deception under weak feedback and weak communication conditions is constructed, which includes two parts: an optimization model for UAV swarm trajectory deception under weak feedback and an optimization model for UAV swarm trajectory deception under weak communication conditions. The particle swarm optimization algorithm is used to solve the UAV swarm trajectory deception optimization model based on weak feedback and the UAV swarm trajectory deception optimization model under weak communication conditions, and stable false trajectories are obtained.

2. The method according to claim 1, characterized in that, The model of a UAV within a cluster receiving control commands from the cluster leader UAV is represented as follows: ； in, Indicates the first drone receiver Real-time self-control command information; , and They represent Time of the first The flight speed command, heading angle command, and pitch angle command for the drone; express Time of the first The delay parameter command for the drone.

3. The method according to claim 1, characterized in that, The optimization model for drone swarm trajectory deception based on weak feedback is expressed as follows: ； in, Indicates the first The drone in Flight distance over a period of time; express Time of the first The actual position coordinates of the drone; express Time of the first The actual spatial coordinates of the false target generated by the drone; express The target location of a constantly deceptive target; express Time of the first The flight speed of the drone; and These represent the upper and lower limits of the drone's flight speed, respectively. express Time of the first The azimuth angle of the drone; express Time of the first The yaw angle of the drone; and These represent the upper and lower limits of the drone's yaw angle, respectively. express Time of the first The pitch angle of the drone; and These represent the upper and lower limits of the drone's pitch angle, respectively. and These represent the upper and lower limits of the drone's flight altitude, respectively. express Time of the first The flight altitude of the drone is restricted. ~ Constraints on the dynamic performance of the UAV To constrain the flight altitude of drones.

4. The method according to claim 1, characterized in that, A method for constructing an optimization model for drone swarm trajectory deception under weak communication conditions, including: First, we introduce the intra-cluster UAV transmission state variable. ,express The first time within the cluster at time The drone sends a state vector, with a value of 1 indicating that the drone has successfully sent its own state information, and a value of 0 indicating that communication between the drone and the cluster leader drone has been interrupted. like If communication is interrupted, the cluster leader drone cannot receive the status information of the drones within the cluster and therefore cannot perform trajectory planning. Consequently, if communication is interrupted, the cluster leader drone needs to predict the current spatial coordinates of the drones within the cluster based on historical information. In this case, assuming that the flight control of the drones within the cluster is error-free and the forwarding delay is error-free, the cluster leader drone can then predict the current spatial coordinates of the drones within the cluster based on historical information. Prediction of spatial coordinates of drones at any time The spatial coordinates of the drone at any given time are then calculated, and the cluster leader drone is then used to determine its position. Prediction of spatial coordinates of drones at any time Real-time drone relay latency Finally, the status information of the cluster head UAV received by the UAVs within the cluster under weak communication conditions was obtained; Secondly, introduce intra-cluster UAV reception state variables. ,express The first time within the cluster at time When the drone receives the state vector, a value of 1 indicates that the drone has successfully received its own state information, and a value of 0 indicates that communication between the drone and the cluster leader drone has been interrupted. like If the cluster drones cannot receive the control commands from the cluster leader drone, they cannot control the drones. Therefore, we consider that when the cluster leader drone sends the control command at each moment, it also sends the control command at the current moment and the control command at several predicted moments in the future, so as to obtain the control command information sent by the cluster leader drone under weak communication conditions. The expression for the optimization model of drone swarm trajectory deception under weak communication conditions is: ； in, Indicates the first The drone in Flight distance over a period of time; express Time of the first The actual position coordinates of the drone; express Time of the first The actual spatial coordinates of the false target generated by the drone; express The target location of a constantly deceptive target; express Time of the first The flight speed of the drone; and These represent the upper and lower limits of the drone's flight speed, respectively. express Time of the first The azimuth angle of the drone; express Time of the first The yaw angle of the drone; and These represent the upper and lower limits of the drone's yaw angle, respectively. express Time of the first The pitch angle of the drone; and These represent the upper and lower limits of the drone's pitch angle, respectively. and These represent the upper and lower limits of the drone's flight altitude, respectively. express Time of the first The flight altitude of the drone is restricted. ~ Constraints on the dynamic performance of the UAV To constrain the flight altitude of drones.

5. The method according to claim 4, characterized in that, Cluster-headed drones according to Prediction of spatial coordinates of drones at any time The spatial coordinates of the UAV at any given time can be expressed by the recursive formula as follows: ； in, Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Spatial coordinates of the drone; Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Spatial coordinates of the drone; Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first Displacement vector of the drone; according to calculate, Indicates that the cluster-headed drone is based on Time of the first UAV spatial coordinate prediction Time of the first The displacement vector of the drone is calculated using the following formula: ； in, , and These represent the results obtained by solving the optimization model under the assumptions of error-free flight control and error-free forwarding delay for the UAV. Time of the first Prediction of the status information of drones Time of the first The flight speed, heading angle, and pitch angle of the drone; Cluster-headed drones according to Prediction of spatial coordinates of drones at any time Real-time drone relay latency Represented as: ； in, Indicates that the cluster-headed drone is based on Prediction of False Target Information Fusion Results at Any Time The target location of the false target at all times. Represents the speed of light; Under weak communication conditions, the cluster leader UAV receives status information from UAVs within the cluster. for: ； in, Indicates the first The DRFM carried by the drone The actual forwarding delay at any given moment. This indicates the moment when the cluster leader drone last successfully received status information from drones within the cluster. Indicates based on the first The predicted time of the last successful reception of cluster drone status information by the drone. Time of the first Control command vectors for drones, To indicate from the first The time interval between the moment when the drone last successfully received the status information of the drone in the cluster and the current moment.

6. The method according to claim 4, characterized in that, Cluster-headed UAVs transmit control command information under weak communication conditions for: ； in, Indicates the length of the prediction window; Indicates cluster-headed drones Time Prediction Time of the first Control commands for the drone Specifically, it is expressed as: ； in, Indicates cluster-headed drones Time Prediction Time of the first The flight speed of the drone Indicates cluster-headed drones Time Prediction Time of the first The yaw angle of the drone, Indicates cluster-headed drones Time Prediction Time of the first The pitch angle of the drone; Actual control commands for UAVs within a cluster under weak communication conditions for: ； in, This indicates the moment when the drone within the cluster last successfully received control commands. This indicates that the nth drone has successfully received the control command. This represents the moment when the nth drone last successfully received a control command. The predicted control commands received by the nth UAV at the current time k.

7. The method according to claim 1, characterized in that, The particle swarm optimization algorithm is used to solve the drone swarm trajectory deception optimization model based on weak feedback, including the following steps: (1) Calculate the spatial coordinates of the false target of a single UAV, traverse each UAV in the cluster, and calculate the actual spatial coordinates of the false target generated by each UAV. (2) The unified false target coordinates are obtained by fusion. Based on the false target coordinates of each UAV obtained in step (1), the false targets generated by different UAVs are fused to obtain the globally unified false target spatial coordinates. (3) Update the coordinates of the false target at the next moment. Based on the current fused false target coordinates, update the target space coordinates of the false target at the next moment. (4) Solve for the optimal heading angle of the UAV. Then, traverse each UAV in the cluster again and use PSO to solve the optimization model to obtain the optimal heading angle of each UAV. (5) Based on the optimal heading angle obtained in step (4), calculate the control command corresponding to each UAV, and determine the time delay parameter and Doppler parameter of DRFM; (6) All UAVs in the cluster receive the corresponding control commands, fly to the designated location, and forward the signals carrying the corresponding time delay and Doppler parameters.

8. The method according to claim 1, characterized in that, The particle swarm optimization algorithm is used to solve the UAV swarm trajectory deception optimization model under weak communication conditions, including the following steps: (1) Determine the transmission status and obtain the UAV location and DRFM delay; (2) Calculate the spatial coordinates of the false target of a single UAV, traverse each UAV in the cluster, and calculate the actual spatial coordinates of the false target generated by each UAV based on the UAV position obtained in step (1). (3) The coordinates of the false targets are fused together. Based on the coordinates of the false targets of each UAV obtained in step (2), the information of the false targets generated by different UAVs is fused to obtain the global unified spatial coordinates of the false targets. (4) Update the false target coordinates at the next moment. Based on the current fused false target coordinates and combined with the preset false target velocity vector, update the target space coordinates of the false target at the next moment. (5) Solve for the optimal heading angle of the UAV. Then, traverse each UAV in the cluster again and use PSO to solve the optimization model to obtain the optimal heading angle of each UAV. (6) Generate control commands and signal parameters. Based on the optimal heading angle obtained in step (5), calculate the flight control commands corresponding to each UAV and determine the time delay parameters and Doppler parameters of DRFM. (7) Determine the reception status. If the reception is successful, send the control command at the current time directly. If the reception fails, predict the control command at several future times.

9. A drone swarm trajectory deception system based on weak feedback and weak communication conditions, characterized in that, include: The deception model construction unit is used to establish the UAV swarm trajectory deception model, including the motion control equations of the UAVs when carrying out the trajectory deception task and the model of the UAVs in the swarm receiving the control command information of the swarm leader UAV. The UAV swarm includes a swarm leader UAV and multiple UAVs in the swarm. Each UAV in the swarm sends its own information to the swarm leader UAV at every moment. The swarm leader UAV performs real-time trajectory planning and deception parameter calculation based on the information sent by each UAV, and sends the actual control parameters to each UAV. The optimization model building unit is used to construct an optimization model for UAV swarm trajectory deception under weak feedback and weak communication conditions, with the optimization objective of minimizing the flight distance of the UAV platform and the UAV dynamic performance as the constraint. It includes two parts: an optimization model for UAV swarm trajectory deception under weak feedback and an optimization model for UAV swarm trajectory deception under weak communication conditions. The optimization model solving unit is used to solve the UAV swarm trajectory deception optimization model based on weak feedback and the UAV swarm trajectory deception optimization model under weak communication conditions using the particle swarm algorithm, so as to obtain stable false trajectories.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the method described in any one of claims 1-8.

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