A method and device for secure aerial computing of multi-uav cooperative transmission

Abstract

The application discloses a kind of multi-unmanned aerial vehicle cooperative transmission's safe air computing method and device, it is difficult to effectively avoid the computing deviation caused by dynamic communication environment for existing multi-unmanned aerial vehicle cooperative transmission safe air computing method, cause the technical problem that the overall computing precision of unmanned aerial vehicle auxiliary air computing network is poor.Method includes obtaining the basic parameters of multi-unmanned aerial vehicle cooperative transmission safe air computing system and the horizontal position of multiple time slots of unmanned aerial vehicle, calculates channel information;Initialize unmanned aerial vehicle system parameter, generate transceiver received signal and noise reduction processing, output aggregated signal estimation value;Accordingly determine non-convex safe air computing joint optimization problem model and initial optimization iteration parameter, solve current iteration optimal system parameter, complete convergence precision determination, output system converged optimization configuration parameter.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a secure aerial computing method and apparatus for multi-UAV collaborative transmission. Background Technology

[0002] Over-the-air computing is an emerging paradigm of communication-computing convergence. Its core idea is to leverage the inherent broadcast and signal superposition characteristics of wireless channels to directly perform function calculations on data during signal transmission. Unlike the traditional communication system's separate processing approach of independent transmission followed by centralized computation, over-the-air computing allows all devices to share the same time-frequency resources for simultaneous transmission. Through carefully designed pre-processing and post-processing, the desired aggregation function value is directly obtained at the fusion center. This architecture is particularly suitable for distributed data aggregation tasks in scenarios such as the Internet of Things (IoT) and edge computing, including distributed machine learning model updates, environmental monitoring data statistics, and distributed sensor network data fusion. Compared to traditional orthogonal multiple access (OMA) technologies, over-the-air computing reduces the communication load from being proportional to the number of devices to a constant, significantly improving spectral efficiency and reducing communication latency, providing a new technological path for efficient collaboration of large-scale IoT devices.

[0003] With the rapid development of drone technology, aerial computing systems using drones as mobile convergence hubs have attracted widespread attention. Drones, with their high mobility and flexible deployment capabilities, can dynamically adjust their spatial position to optimize wireless channel quality with ground equipment. Especially in urban environments or complex terrains, drones can establish line-of-sight transmission links, effectively avoiding the impact of obstacles on communication quality. Furthermore, the three-dimensional mobility of drones provides a new dimension for system optimization. Through reasonable trajectory design, they can proactively avoid areas with poor channel conditions and balance channel differences between different devices, thereby mitigating the "bottleneck effect" in traditional ground-based aerial computing systems. Existing research shows that compared with traditional fixed base stations, drone-assisted aerial computing systems offer significant improvements in both computational accuracy and coverage.

[0004] Existing methods for secure aerial computing through multi-UAV collaborative transmission mostly rely on pre-set fixed flight trajectories to complete data acquisition and air-to-ground collaborative transmission within the airspace. They establish a basic communication transmission model based on static channel parameters, employ conventional signal precoding techniques for transmitted signal preprocessing, utilize fixed security constraints to construct anti-eavesdropping communication mechanisms, and solve aerial aggregation calculations using a fixed-form mean square error model. They rely on a basic iterative optimization model to coordinate and allocate operational resources such as UAV transmission power to achieve secure transmission and distributed aerial computing collaborative operation. However, this traditional implementation model fails to adequately consider the dynamic fluctuations in the time-slotted channel caused by real-time UAV position changes, lacks equivalent simplified derivations of security constraints based on worst-case eavesdropping scenarios, and lacks differentiated and precise solution methods for various non-convex sub-problems after decomposing the joint optimization problem. Furthermore, it fails to finely control the signal denoising and aggregation process at the receiving end, and cannot effectively offset various signal losses and interference effects in complex airspace environments. These design shortcomings fail to guarantee a high degree of consistency between the aggregated signal estimate and the actual sensor data, making it difficult to effectively avoid computational deviations caused by dynamic communication environments, ultimately resulting in poor overall computational accuracy of the UAV-assisted aerial computing network. Summary of the Invention

[0005] This invention provides a secure aerial computing method and apparatus for multi-UAV collaborative transmission, which solves the technical problem that existing secure aerial computing methods for multi-UAV collaborative transmission cannot effectively avoid the calculation deviation caused by dynamic communication environment, resulting in poor overall calculation accuracy of UAV-assisted aerial computing networks.

[0006] The first aspect of this invention provides a secure aerial computing method for multi-UAV cooperative transmission, comprising:

[0007] The system acquires the basic parameters of a multi-UAV collaborative transmission secure aerial computing system and the horizontal positions of UAVs in multiple time slots. Based on the basic parameters and the horizontal positions of UAVs in multiple time slots, it calculates the channel information between the UAVs and the receiver.

[0008] Initialize the UAV system parameters, and generate the transceiver received signal based on the channel information and the UAV system parameters;

[0009] The received signal at the transceiver is post-processed with the UAV system parameters to reduce noise and output an aggregated signal estimate.

[0010] Based on the aggregated signal estimate, the actual sensor aggregated signal and the UAV system parameters, determine the joint optimization problem model for non-convex secure aerial computing and the initial optimization iteration parameters.

[0011] Based on the non-convex secure aerial computing joint optimization problem model and the initial optimization iteration parameters, solve for the optimal system parameters in the current iteration;

[0012] Based on the current iterative optimal parameters, the convergence accuracy is determined, and the optimized configuration parameters of the multi-UAV collaborative transmission secure aerial computing system after convergence are output.

[0013] Optionally, the channel information includes UAV-fusion center channel coefficients and UAV-eavesdropper channel coefficients in multiple time slots; the step of calculating the channel information between the UAV and the receiver based on the basic parameters and the horizontal positions of the UAVs in the multiple time slots includes:

[0014] Extract the following basic parameters: number of time slots, constant flight altitude of the UAV, location of the ground fusion center, location of the eavesdropper, and channel power gain at a preset reference distance.

[0015] Based on the number of time slots, the constant flight altitude of the UAV, the location of the ground fusion center, the location of the eavesdropper, the channel power gain at the preset reference distance, and the horizontal position of the UAV in multiple time slots, channel coefficients are calculated for the air-to-ground communication links from the UAV to the ground fusion center and the air-to-ground communication links from the UAV to the eavesdropper in multiple time slots, to obtain the UAV-fusion center channel coefficient and the UAV-eavesdropper channel coefficient in each time slot.

[0016] Optionally, the transceiver received signal includes the fusion center received signal and the eavesdropper received signal; generating the transceiver received signal based on the channel information and the UAV system parameters includes:

[0017] Based on the channel information and the UAV transmission power in the UAV system parameters, the preset normalized UAV transmission signal is preprocessed, and the preprocessed UAV transmission signal is output.

[0018] Control multiple drones to collaboratively transmit pre-processed drone transmission signals, generating fusion center reception signals and eavesdropper reception signals.

[0019] Optionally, the aggregated signal estimate includes a fusion center aggregated signal estimate and an eavesdropper aggregated signal estimate; the step of using the UAV system parameters to perform noise reduction post-processing on the received signal at the transceiver end and outputting the aggregated signal estimate includes:

[0020] Based on the fusion center noise reduction factor in the UAV system parameters, the fusion center received signal is denoised and aggregated to obtain the estimated value of the fusion center aggregated signal.

[0021] The eavesdropper received signal is denoised and aggregated based on the eavesdropper denoising factor in the UAV system parameters to obtain an estimated value of the eavesdropper aggregated signal.

[0022] Optionally, determining the joint optimization problem model and initial optimization iteration parameters for non-convex secure aerial computing based on the aggregated signal estimate, the actual sensor aggregated signal, and the UAV system parameters includes:

[0023] The estimated value of the fusion center aggregated signal and the estimated value of the eavesdropper aggregated signal are compared with the actual sensor aggregated signal to calculate the error, and the mean square error of the fusion center and the mean square error of the eavesdropper are output.

[0024] With the minimization of the mean square error of the fusion center as the optimization objective, and with the eavesdropper security constraint that the mean square error of the eavesdropper is not lower than the security threshold, combined with the preset UAV motion constraints, a non-convex secure aerial computation joint optimization problem model is constructed.

[0025] The parameters of the unmanned aerial vehicle system are used as the initial optimization iteration parameters.

[0026] Optionally, the current iteration optimal system parameters include the current iteration optimal fusion center noise reduction factor, the current iteration optimal UAV transmit power, and the current iteration optimal UAV horizontal position; the step of solving for the current iteration optimal system parameters based on the non-convex secure aerial computation joint optimization problem model and the initial optimization iteration parameters includes:

[0027] The eavesdropper security constraints in the non-convex secure aerial computation joint optimization problem model are equivalently reconstructed and simplified using closed-form solutions, and simplified security constraint conditions are output.

[0028] The non-convex safe air computation joint optimization problem model is decomposed to obtain the non-convex optimization sub-problem of UAV launch power and the non-convex optimization sub-problem of UAV flight trajectory;

[0029] By fixing the UAV's transmit power and horizontal position in the initial optimization iteration parameters, and combining the simplified safety constraints, the optimal solution for the fusion center noise reduction factor is obtained, and the current iteration's optimal fusion center noise reduction factor is output.

[0030] By fixing the noise reduction factor of the current iteration's optimal fusion center and the horizontal position of the UAV in the initial optimization iteration parameters, and combining the simplified safety constraints, the non-convex optimization subproblem of UAV transmission power is solved, and the current iteration's optimal UAV transmission power is output.

[0031] By fixing the noise reduction factor of the current iteration's optimal fusion center and the current iteration's optimal UAV transmission power, and combining the simplified safety constraints, the non-convex optimization subproblem of the UAV flight trajectory is solved, and the current iteration's optimal UAV horizontal position is output.

[0032] Optionally, the step of determining the convergence accuracy based on the current iterative optimal parameters and outputting the converged optimized configuration parameters of the multi-UAV cooperative transmission safe aerial computing system includes:

[0033] Based on the current optimal parameters, calculate the objective function value for this round;

[0034] The difference between the objective function value in this round and the objective function value at a historical time is compared with the preset algorithm convergence accuracy.

[0035] If the difference is greater than or equal to the preset algorithm convergence accuracy, then the current iteration optimal parameter is used as the new initial optimization iteration parameter, and the process jumps to the step of solving the current iteration optimal system parameter based on the non-convex safe air computation joint optimization problem model and the initial optimization iteration parameter, until the difference is less than the preset algorithm convergence accuracy;

[0036] The optimal parameters for the current iteration, determined when the difference is less than the preset algorithm convergence accuracy, are used as the optimized configuration parameters after convergence of the multi-UAV collaborative transmission secure aerial computing system.

[0037] A second aspect of the present invention provides a secure aerial computing device for multi-UAV collaborative transmission, comprising:

[0038] The acquisition module is used to acquire the basic parameters of the multi-UAV collaborative transmission secure aerial computing system and the horizontal position of the UAVs in multiple time slots, and to calculate the channel information between the UAVs and the receiver based on the basic parameters and the horizontal positions of the UAVs in multiple time slots.

[0039] An initialization module is used to initialize the UAV system parameters and generate a transceiver signal based on the channel information and the UAV system parameters.

[0040] The noise reduction post-processing module is used to perform noise reduction post-processing on the received signal from the transceiver using the UAV system parameters, and output the aggregated signal estimate.

[0041] The model building module is used to determine the joint optimization problem model for non-convex secure aerial computing and the initial optimization iteration parameters based on the aggregated signal estimate, the real sensor aggregated signal and the UAV system parameters.

[0042] The solution module is used to solve for the optimal system parameters in the current iteration based on the non-convex safe air computation joint optimization problem model and the initial optimization iteration parameters;

[0043] The output module is used to determine the convergence accuracy based on the current iteration optimal parameters and output the converged optimized configuration parameters of the multi-UAV collaborative transmission safe aerial computing system.

[0044] A third aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the secure aerial computing method for multi-UAV cooperative transmission as described above.

[0045] The fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed, implements the secure aerial computing method for multi-UAV cooperative transmission as described above.

[0046] As can be seen from the above technical solutions, the present invention has the following advantages:

[0047] The above-mentioned technical solution of the present invention provides a secure aerial computing method for multi-UAV cooperative transmission. This method acquires the basic parameters of the secure aerial computing system for multi-UAV cooperative transmission and the horizontal positions of the UAVs in multiple time slots. Based on the basic parameters and the horizontal positions of the UAVs in multiple time slots, it calculates the channel information between the UAVs and the receiver. It initializes the UAV system parameters and generates the received signal at the transceiver end based on the channel information and the UAV system parameters. It then performs noise reduction post-processing on the received signal at the transceiver end using the UAV system parameters, outputting an aggregated signal estimate. Based on the aggregated signal estimate, the actual sensor aggregated signal, and the UAV system parameters, it determines the joint optimization problem model for non-convex secure aerial computing and the initial optimization iteration parameters. Based on the joint optimization problem model for non-convex secure aerial computing and the initial optimization iteration parameters, it solves for the optimal system parameters for the current iteration. Finally, based on the optimal system parameters for the current iteration... The parameters are used to determine the convergence accuracy, and the optimized configuration parameters of the multi-UAV collaborative transmission safe aerial computing system are output after convergence. Based on the above scheme, this invention integrates the dynamic horizontal position of UAVs in each time slot for modeling calculation in the channel calculation stage. This changes the shortcomings of traditional schemes that rely on fixed parameter modeling and cannot adapt to the real-time channel fluctuations caused by the dynamic flight of UAVs. It avoids the basic calculation deviation caused by the dynamic communication environment from the source. At the same time, it effectively optimizes the signal aggregation effect through a standardized signal denoising post-processing process, reduces the error gap between the estimated value of the aggregated signal and the actual sensor aggregated signal, and achieves multi-parameter joint optimization by relying on a non-convex joint optimization model that fits the actual operation constraints. With the help of iterative solution and convergence determination mechanism, it continuously corrects the accumulated calculation error generated in the dynamic communication process, thereby improving the accuracy of multi-UAV collaborative safe aerial computing in dynamic airspace. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart illustrating the steps of a secure aerial computing method for multi-UAV collaborative transmission provided in Embodiment 1 of the present invention.

[0050] Figure 2 This is a schematic diagram of a secure aerial computing network system with multiple UAVs acting as transmitters, provided in Embodiment 1 of the present invention.

[0051] Figure 3 An iterative graph showing the average mean square error of the proposed scheme at different heights, as provided in Embodiment 1 of the present invention;

[0052] Figure 4 The drone trajectory optimized by the proposed solution in Embodiment 1 of the present invention when there is no eavesdropper.

[0053] Figure 5 The drone trajectory optimized by the proposed solution in Embodiment 1 of this invention when an eavesdropper is present;

[0054] Figure 6 The flight duration provided in Embodiment 1 of the present invention At that time, the mean square error of the fusion center varies with the maximum transmit power. A schematic diagram of the change curve;

[0055] Figure 7 The maximum transmission power provided in Embodiment 1 of the present invention At that time, the mean square error of the fusion center varies with flight time. A schematic diagram of the change curve;

[0056] Figure 8 This is a structural block diagram of a secure aerial computing device for multi-UAV collaborative transmission provided in Embodiment 2 of the present invention. Detailed Implementation

[0057] This invention provides a secure aerial computing method and apparatus for multi-UAV collaborative transmission, specifically involving the intersection of aerial computing, UAV communication, and physical layer security. It solves the technical problem that existing secure aerial computing methods for multi-UAV collaborative transmission cannot effectively avoid computational deviations caused by dynamic communication environments, resulting in poor overall computational accuracy of UAV-assisted aerial computing networks.

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that in the optional embodiments of the present invention, the object information and other related data involved require the permission or consent of the object when the embodiments of the present invention are applied to specific products or technologies, and the collection, use, and processing of related data must comply with relevant laws, regulations, and standards. That is to say, if the embodiments of the present invention involve data related to the object, it needs to be obtained with the authorization and consent of the object, the authorization and consent of relevant departments, and in compliance with relevant laws, regulations, and standards. If personal information is involved in the embodiments, the acquisition of all personal information requires the consent of the individual. If sensitive information is involved, the separate consent of the information subject is required, and the embodiments also need to be implemented with the authorization and consent of the object.

[0059] Please see Figure 1 , Figure 1 The flowchart illustrates the steps of a secure aerial computing method for multi-UAV collaborative transmission provided in Embodiment 1 of the present invention.

[0060] This invention provides a secure aerial computing method for multi-UAV cooperative transmission, comprising:

[0061] Step 101: Obtain the basic parameters of the multi-UAV collaborative transmission secure aerial computing system and the horizontal positions of the UAVs in multiple time slots, and calculate the channel information between the UAVs and the receiver based on the basic parameters and the horizontal positions of the UAVs in multiple time slots.

[0062] The basic parameters are a set of fixed parameters preset before the operation of the multi-UAV collaborative transmission secure aerial computing system. These parameters include the number of UAVs, the initial horizontal position of the UAVs, the final horizontal position of the UAVs, the maximum flight speed of the UAVs, the minimum safe distance between UAVs, the total flight time of the UAVs, the number of time slots, the constant flight altitude of the UAVs, the location of the ground fusion center, the location of the eavesdropper, the channel power gain at the reference distance, the additive white Gaussian noise power, the maximum transmit power of the UAVs, the mean square error safety threshold of the eavesdropper, and the algorithm convergence accuracy.

[0063] A time slot is a continuous time unit obtained by evenly dividing the total flight time of multiple UAVs in collaborative transmission. The horizontal position of the UAVs remains fixed within each time slot.

[0064] It should be noted that the schematic diagram of the multi-UAV collaborative transmission secure aerial computing system (i.e., a secure aerial computing system in which multiple UAVs act as transmitters / aerial transmission nodes) is as follows: Figure 2 As shown. Figure 1 As shown, this invention considers a secure aerial computing network in which multiple drones act as transmitters. In this network, the drones, as aerial transmitting nodes, collaboratively send pre-processed signals to a ground-based fusion center, while a potential eavesdropper attempts to intercept these transmissions. The network includes... A single-antenna UAV, with the following index set: A place located A single-antenna ground fusion center at the location, and a center located at A single-antenna eavesdropper at a location. Where i is the index of a single drone; This is the horizontal coordinate vector of the ground fusion center, which is the location of the ground fusion center in the basic parameters; The horizontal coordinate vector of the eavesdropper is the basic parameter, i.e., the eavesdropper's position.

[0065] Furthermore, the constant flight altitude of the UAV, the location of the ground fusion center, the location of the eavesdropper, and the channel power gain at a preset reference distance are extracted from the basic parameters. Combined with the horizontal position of the UAV corresponding to each time slot, the air-to-ground link channel coefficients between the UAV and the ground fusion center and between the UAV and the eavesdropper are calculated using a free space path loss model in each time slot. This yields complete channel information between the UAV and the receiver in each time slot, providing a calculation basis for the subsequent generation of received signals at the transceiver end.

[0066] Further, step 101 may include the following sub-steps:

[0067] S11. Extract the number of time slots, constant flight altitude of the UAV, location of the ground fusion center, location of the eavesdropper, and channel power gain at a preset reference distance from the basic parameters.

[0068] S12. Based on the number of time slots, the constant flight altitude of the UAV, the location of the ground fusion center, the location of the eavesdropper, the channel power gain at the preset reference distance, and the horizontal position of the UAV in multiple time slots, calculate the channel coefficients for the air-to-ground communication links from the UAV to the ground fusion center and from the UAV to the eavesdropper in multiple time slots, and obtain the UAV-fusion center channel coefficients and the UAV-eavesdropper channel coefficients in each time slot.

[0069] The channel information includes the UAV-fusion center channel coefficients and the UAV-eavesdropper channel coefficients in multiple time slots.

[0070] It should be noted that the drone flight time (i.e., the total drone flight time) is... Divide it evenly into There are 1 time slot, and the length of each time slot is 1. All drones maintained a constant altitude during flight. .make Indicates drone In the time slot The horizontal position. Limited by the drone's maximum flight speed. The maximum horizontal displacement of the drone in each time slot is In addition, to ensure a safe distance, drones must meet a minimum distance constraint (i.e., the minimum safe distance between drones). And its starting and ending positions are fixed as follows: and Therefore, the motion constraints of the UAV can be expressed as:

[0071] (1)

[0072] (2)

[0073] (3)

[0074] in, The number of time slots to be divided; Let be the horizontal position coordinate vector of the i-th UAV in time slot m; m is the time slot index, representing the number of the current time slot; A set of time slot indexes; Let be the initial horizontal position coordinate vector of the i-th UAV, which is the initial horizontal position of the UAV in the basic parameters; Let be the coordinate vector of the terminal horizontal position of the i-th UAV, which is the terminal horizontal position of the UAV in the basic parameters;

[0075] Similarly, this invention uses a free-space path loss model to model the air-to-ground link. Based on this, the UAV... With the integration center in time slot The channel coefficients between them can be expressed as:

[0076] (4)

[0077] in, Let be the channel coefficient of the air-to-ground communication link between the i-th UAV and the ground fusion center in time slot m, which is the channel coefficient of UAV i-fusion center in time slot m; This represents the channel power gain at a reference distance of 1 meter. This represents the channel phase of that time slot. Similarly, the channel coefficient between the drone and the eavesdropper can be expressed as:

[0078] (5)

[0079] in, Let be the channel coefficient of the air-to-ground communication link between the i-th UAV and the eavesdropper in time slot m, i.e., the channel coefficient of UAV i-eavesdropper in time slot m; To test the channel power gain of the communication link between the UAV and the eavesdropper at a distance of 1 meter, that is, the channel power gain at a reference distance of 1 meter (eavesdropper link part) included in the basic parameters. Let be the channel phase between the i-th UAV and the eavesdropper in time slot m, and be a parameter that affects the phase of the received signal.

[0080] In this embodiment, the following basic parameters are extracted: the number of time slots, the constant flight altitude of the UAV, the location of the ground fusion center, the location of the eavesdropper, and the channel power gain at a preset reference distance. The number of time slots determines the time granularity of dynamic channel modeling, the constant flight altitude of the UAV determines the vertical transmission distance of the air-to-ground link, the location of the ground fusion center and the location of the eavesdropper determine the two-dimensional coordinate references for the two types of receivers, and the channel power gain at the preset reference distance is used as the reference parameter for path loss calculation. Subsequently, based on the number of time slots, the constant flight altitude of the UAV, the location of the ground fusion center, the location of the eavesdropper, the channel power gain at the preset reference distance, and the horizontal position of the UAV in multiple time slots, the following parameters are calculated for each time slot: The three-dimensional transmission distances from the UAV to the ground fusion center and from the UAV to the eavesdropper were calculated based on the UAV's horizontal position and constant flight altitude. Substituting these distances into the free space path loss model and introducing the channel phase term, the channel coefficients of the air-to-ground communication links from the UAV to the ground fusion center and from the UAV to the eavesdropper were calculated for multiple time slots. This yielded the UAV-fusion center channel coefficients and the UAV-eavesdropper channel coefficients for each time slot. This process enabled accurate modeling of the channel state under dynamic UAV flight scenarios, reflecting in real time the link loss fluctuations caused by changes in the UAV's position in different time slots. This provides a channel foundation that fits the actual dynamic scenario for the subsequent generation of received signals at the transceiver end.

[0081] Step 102: Initialize the UAV system parameters and generate the transceiver signal based on the channel information and the UAV system parameters.

[0082] The unmanned aerial vehicle (UAV) system parameters are a set of adjustable parameters used to support signal generation, noise reduction processing, and optimization solutions in a multi-UAV collaborative transmission secure aerial computing system. These parameters include UAV transmit power, fusion center noise reduction factor, eavesdropper noise reduction factor, and UAV horizontal position.

[0083] It should be noted that the initialization of UAV system parameters, including UAV transmit power, fusion center noise reduction factor, eavesdropper noise reduction factor, and UAV horizontal position, combined with the channel information of each time slot UAV and receiver, uses a phase compensation precoding strategy to preprocess the preset UAV normalized transmit signal, and then controls multiple UAVs to transmit the preprocessed signal in a coordinated manner to generate fusion center received signal and eavesdropper received signal, providing raw received data for subsequent noise reduction post-processing steps.

[0084] Furthermore, step 102 may include the following sub-steps:

[0085] S21. Based on the channel information and the UAV transmission power in the UAV system parameters, preprocess the preset normalized UAV transmission signal and output the UAV preprocessed transmission signal.

[0086] S22. Control multiple drones to collaboratively send drone preprocessed transmission signals, and generate fusion center reception signals and eavesdropper reception signals.

[0087] The signals received at the transceiver end include signals received by the fusion center and signals received by the eavesdropper.

[0088] It should be noted that each drone Send a pre-processed normalized signal (i.e., a preset UAV normalized transmission signal). ,satisfy The objective function that this network aims to compute is:

[0089] (6)

[0090] Assume each drone uses a phase-compensated precoding strategy and transmits signals using the following coefficients:

[0091] (7)

[0092] in, For time slot m, the target aggregation signal for multi-UAV collaborative aerial computation is defined as the average value of the normalized transmitted signals of all UAVs, which is the objective function value that the network needs to obtain through safe aerial computation, and represents the theoretical calculation form of the real sensor aggregation signal; Let m be the transmit power of the i-th UAV in time slot m in the UAV system parameters. This power is used to control the signal transmit power of the UAV in the corresponding time slot. In the time slot Transmission power; superscript This indicates the conjugate operation.

[0093] Therefore, by transmitting simultaneously, the received signals at the fusion center and the eavesdropper can be represented as follows:

[0094] (8)

[0095] (9)

[0096] in, The signal received by the ground fusion center at time slot m is the fusion center reception signal. The signal received by the potential eavesdropper in time slot m is the eavesdropper's received signal. The variance (power) of additive white Gaussian noise is the power of additive white Gaussian noise in the basic parameters, which characterizes the power intensity of the noise. and These represent the additive white Gaussian noise at the fusion center and the eavesdropper, respectively.

[0097] In this embodiment, a phase-compensated precoding strategy is adopted. The conjugate component of the UAV-fusion center channel coefficient in the channel information is used to cancel the channel phase offset. At the same time, the signal amplitude is adjusted by combining the UAV transmit power. The pre-processed normalized transmit signal of the UAV is preprocessed to obtain the preprocessed transmit signal corresponding to each UAV. Then, multiple UAVs are controlled to transmit their respective preprocessed transmit signals in the same time slot. After the signal is transmitted through the air-to-ground link, channel attenuation and additive white Gaussian noise are superimposed. The received signals are formed at the ground fusion center and the eavesdropper, respectively, providing raw data for the subsequent noise reduction post-processing steps. The phase-compensated preprocessing method effectively reduces the impact of dynamic channel phase fluctuations on the received signal and reduces the distortion error in the signal transmission process.

[0098] Step 103: Use UAV system parameters to perform noise reduction post-processing on the received signal at the transceiver end, and output the aggregated signal estimate.

[0099] It should be noted that, based on the fusion center noise reduction factor and the eavesdropper noise reduction factor in the UAV system parameters, the fusion center received signal and the eavesdropper received signal are subjected to weighted noise reduction and aggregation processing to remove noise interference components in the signal, and the estimated values ​​of the fusion center aggregated signal and the eavesdropper aggregated signal are obtained respectively, providing processed signal data for subsequent error calculation and optimization model construction.

[0100] Furthermore, step 103 may include the following sub-steps:

[0101] S31. Based on the noise reduction factor of the fusion center in the UAV system parameters, perform noise reduction and aggregation processing on the fusion center received signal to obtain the estimated value of the fusion center aggregated signal.

[0102] S32. Based on the eavesdropper noise reduction factor in the UAV system parameters, perform noise reduction and aggregation processing on the eavesdropper received signal to obtain the estimated value of the eavesdropper aggregated signal.

[0103] The aggregated signal estimates include the fusion center aggregated signal estimates and the eavesdropper aggregated signal estimates.

[0104] It should be noted that after receiving the signal, both the fusion center and the eavesdropper apply the fusion center's noise reduction factor. And the noise reduction factor of the eavesdropper To obtain an estimate of the average message (i.e., the aggregation signal estimate at the fusion center). Estimated aggregated signal of the eavesdropper ):

[0105] (10)

[0106] (11)

[0107] In this embodiment, at each time slot, the fusion center received signal is scaled using a fusion center noise reduction factor to suppress noise interference components in the received signal, restore the effective components of the target aggregated signal, and obtain the estimated value of the fusion center aggregated signal. Simultaneously, the eavesdropper received signal is denoised and aggregated based on the eavesdropper noise reduction factor in the UAV system parameters. That is, the eavesdropper received signal is scaled using an eavesdropper noise reduction factor to simulate the eavesdropper noise reduction reception process under the worst eavesdropping scenario, and obtain the estimated value of the eavesdropper aggregated signal. This process effectively reduces the impact of noise on the received signal through targeted noise reduction and aggregation processing, and improves the accuracy of the aggregated signal estimate.

[0108] Step 104: Based on the aggregated signal estimate, the actual sensor aggregated signal, and the UAV system parameters, determine the joint optimization problem model for non-convex secure aerial computation and the initial optimization iteration parameters.

[0109] The real sensor aggregated signal is the true value of the target aggregated signal that needs to be transmitted and processed by the multi-UAV collaborative aerial computing network. It serves as a benchmark for evaluating the accuracy of the aggregated signal estimate and is used to calculate the mean square error of the fusion center and the mean square error of the eavesdropper.

[0110] It should be noted that, in order to calculate the error between the estimated value of the fusion center aggregated signal and the estimated value of the eavesdropper aggregated signal and the actual sensor aggregated signal, respectively, the mean square error of the fusion center and the mean square error of the eavesdropper are obtained. The optimization objective is to minimize the mean square error of the fusion center. The eavesdropper safety constraint that the mean square error of the eavesdropper is not lower than the safety threshold and the preset UAV motion constraints are combined to construct a non-convex safe aerial computation joint optimization problem model. At the same time, the UAV system parameters are used as the initial optimization iteration parameters to provide the model foundation and initial conditions for subsequent iterative solutions.

[0111] Furthermore, step 104 may include the following sub-steps:

[0112] S41. Calculate the error between the estimated value of the fusion center aggregated signal and the estimated value of the eavesdropper aggregated signal and the actual sensor aggregated signal, and output the mean square error of the fusion center and the mean square error of the eavesdropper.

[0113] S42. Taking the minimization of the mean square error of the fusion center as the optimization objective, and the eavesdropper security constraint that the mean square error of the eavesdropper is not lower than the security threshold, combined with the preset UAV motion constraints, a non-convex secure aerial computation joint optimization problem model is constructed.

[0114] S43. Use the unmanned aerial vehicle system parameters as the initial optimization iteration parameters.

[0115] It should be noted that the present invention recovers the average value. (or ) and the true average value (i.e., the true sensor aggregated signal) Distortion is quantified by the mean square error between the two sides, and it is defined as follows:

[0116] (12)

[0117] (13)

[0118] in , The mean square error of the fusion center; The mean square error of the eavesdropper; Let m be the horizontal position coordinate vector of the i-th UAV in time slot m; The power of the additive white Gaussian noise at the fusion center; The power of additive white Gaussian noise applied to the eavesdropper; Under the worst-case assumption, the equivalent channel gain between the i-th UAV and the eavesdropper in time slot m represents the magnitude part of the UAV-eavesdropper channel coefficient (ignoring the phase term), which is used to construct strict eavesdropper security constraints. This invention adopts a worst-case assumption, namely that the eavesdropper can achieve phase alignment, thereby enhancing its eavesdropping capability. This assumption makes the design of security constraints more stringent.

[0119] Furthermore, the objective of this invention is to jointly optimize the UAV's launch power. Fusion center noise reduction factor and drone trajectories Under the constraints of minimum mean square error of the eavesdropper, maximum transmit power, and UAV motion, the goal is to minimize the time-averaged mean square error of the fusion center. Based on this, the optimization problem (i.e., the joint optimization problem model of non-convex secure aerial computation) P0 can be expressed as:

[0120] (14)

[0121] Among them, P max This is the maximum transmit power of the drone; Let r be the horizontal position coordinate vector of the r-th UAV in time slot m; Let be the horizontal position coordinate vector of the i-th UAV at the initial moment; The operator that minimizes the objective function of the optimization problem; st is the identifier of the constraints in the optimization problem; For the worst-case eavesdropping scenario (i.e., the eavesdropper's noise reduction factor) When taking the optimal value to minimize its mean square error), the minimum value of the eavesdropper's mean square error is used to construct strict eavesdropper security constraints. It is worth noting that the eavesdropper noise reduction factor is not a controllable variable in this invention, but rather an auxiliary quantity used to derive the optimal eavesdropper reception capability and reconstruct security constraints under the worst-case assumption. For drone transmission power and fusion center noise reduction factor The non-negativity constraint means that the values ​​of the optimization variables must be non-negative, which conforms to the actual physical meaning of the transmission power and the noise reduction factor; This represents the minimum mean square error threshold allowed at the location of the eavesdropper.

[0122] In this embodiment, the estimated values ​​of the fusion center aggregated signal and the eavesdropper aggregated signal are compared with the actual sensor aggregated signal to calculate errors, outputting the mean square error of the fusion center and the mean square error of the eavesdropper signal. Specifically, in each time slot, the differences between the estimated values ​​of the fusion center aggregated signal and the eavesdropper aggregated signal and the actual sensor aggregated signal are calculated, and then the squares of the differences are taken and the expected value is calculated to obtain the mean square error of the fusion center and the mean square error of the eavesdropper signal for each time slot. This quantifies the degree of estimation distortion of the target aggregated signal by the two types of receivers. Subsequently, minimizing the time average value of the mean square error of the fusion center in each time slot is used as the overall optimization. The objective is to introduce a constraint that the mean square error of the eavesdropper is not lower than a preset safety threshold to ensure the security of the transmission process. At the same time, preset motion constraints such as the maximum flight speed of the UAV, the minimum safe distance between UAVs, and the fixed start and end positions of the UAVs are superimposed to construct a non-convex joint optimization problem model for secure aerial computation, which includes three types of optimization variables: UAV transmission power, fusion center noise reduction factor, and UAV horizontal position. Then, the UAV system parameters, including the initial value of the UAV transmission power, the initial value of the fusion center noise reduction factor, and the initial horizontal position of the UAV, are used as the initial optimization iteration parameters for iteratively solving the optimization model, providing an initial starting point for the subsequent solution process.

[0123] Step 105: Based on the non-convex secure aerial computation joint optimization problem model and the initial optimization iteration parameters, solve for the optimal system parameters in the current iteration.

[0124] It should be noted that the initial optimization iteration parameters are used as the starting point for iterative optimization. The block coordinate descent algorithm is used to decompose the optimization problem into three sub-problems: UAV launch power, fusion center noise reduction factor, and UAV trajectory. In each iteration, closed-form solution, successive convex approximation, and convex optimization solver are used to update each sub-problem, respectively, to obtain the optimal system parameters that satisfy all constraints under the current iteration.

[0125] Furthermore, step 105 may include the following sub-steps:

[0126] S51. Perform equivalent reconstruction and closed-form solution simplification on the eavesdropper security constraints in the non-convex secure aerial computation joint optimization problem model, and output simplified security constraint conditions.

[0127] S52. Decompose the joint optimization problem model of non-convex safe air computation to obtain the non-convex optimization sub-problem of UAV launch power and the non-convex optimization sub-problem of UAV flight trajectory.

[0128] S53. Fix the UAV's transmit power and horizontal position in the initial optimization iteration parameters, and combine the simplified safety constraints to solve the optimal solution of the fusion center noise reduction factor, and output the optimal fusion center noise reduction factor of the current iteration.

[0129] S54. Fix the current iteration's optimal fusion center noise reduction factor and the UAV's horizontal position in the initial optimization iteration parameters, and solve the non-convex optimization subproblem of UAV's transmit power by combining simplified safety constraints, and output the current iteration's optimal UAV transmit power.

[0130] S55. Fix the noise reduction factor of the current iteration's optimal fusion center and the current iteration's optimal UAV transmission power, and solve the non-convex optimization subproblem of the UAV flight trajectory by combining simplified safety constraints, and output the current iteration's optimal UAV horizontal position.

[0131] The optimal system parameters for the current iteration include the optimal fusion center noise reduction factor, the optimal UAV transmit power, and the optimal UAV horizontal position.

[0132] It should be noted that, given , and Under these conditions, ensure each time slot The mean square error of the eavesdropper is greater than Original constraints Can be rewritten as a noise reduction factor for eavesdroppers Optimization issues:

[0133] (15)

[0134] By applying the first-order optimality condition, the optimal closed-form expression can be obtained as follows:

[0135] (16)

[0136] Substitute the above expression back into the constraints Then, this constraint (i.e., the simplified safety constraint) can be rewritten as:

[0137] (17)

[0138] Based on the above transformation, the problem It can be equivalently restated as:

[0139] (18)

[0140] Given the drone's launch power and drone trajectory Under these conditions, the problem It can be naturally decomposed into a series of independent subproblems for each time slot, expressed as:

[0141] (19)

[0142] By order about The first derivative is zero, which yields the optimal value. The closed-form solution, i.e., solving for the optimal fusion center noise reduction factor in the current iteration. :

[0143] (20)

[0144] fixed and Then, the UAV transmission power is optimized by solving the following non-convex optimization subproblem of UAV transmission power. :

[0145] ;(twenty one)

[0146] Introducing variables ,question It can be converted into:

[0147] ;(twenty two)

[0148] It is worth noting that constraints It contains fractional quadratic terms and is nonconvex. To address this problem, this invention employs a successive convex approximation technique. Perform iterative solutions.

[0149] Specifically, in the In the next iteration, the present invention addresses non-convex terms. At the current point Performing a first-order Taylor expansion at this point yields its linear upper bound:

[0150] ;(twenty three)

[0151] Will Substitution constraints , No. Problems during the next iteration It can be approximated as:

[0152] ;(twenty four)

[0153] The problem at this time This is a convex quadratic programming problem, which can be solved efficiently using solvers such as CVX (Convex Optimization Toolbox). Iterative updates ensure that the algorithm converges to a stable point.

[0154] Fixed UAV transmission power and fusion center noise reduction factor Under these conditions, the problem Simplified to optimize the drone trajectory using the following formula That is, fixing the current iteration's optimal fusion center noise reduction factor and the current iteration's optimal UAV transmit power, and combining simplified safety constraints, solving the non-convex optimization subproblem of the UAV flight trajectory, and outputting the current iteration's optimal UAV horizontal position:

[0155] (25)

[0156] Introducing auxiliary variables and and define and The problem can be equivalently transformed into :

[0157] (26)

[0158] Although function and about They are non-convex, but they have respect to the squared distance term. and It is convex. (For processing) and Nonconvexity and constraints and Regarding the distance term in the expression, this invention employs a successive convex approximation technique to linearize these non-convex expressions. Through iterative points... Constructing a first-order Taylor expansion, we obtain the following compact convex lower bound:

[0159] (27)

[0160] (28)

[0161] (29)

[0162] (30)

[0163] Similarly, constraints The lower bound can be represented as:

[0164] (31)

[0165] Therefore, the first Problems during the next iteration It can be rewritten as:

[0166] (32)

[0167] This problem is a convex optimization problem, which can be solved efficiently using solvers such as CVX. This invention addresses this by... In the next iteration, the drone trajectory will be updated to... By repeating this process, the algorithm can be ensured to converge to a stable point in the problem.

[0168] In the above formula, The baseline path loss coefficient corresponding to the communication link of the fusion center; The baseline path loss coefficient corresponding to the eavesdropper's communication link; The auxiliary optimization variable obtained by taking the square root of the UAV's transmit power is used to simplify non-convex terms; Link auxiliary variables constructed for the distance from the drone to the fusion center; Link auxiliary variables constructed for the distance from the drone to the eavesdropper; This function calculates the Euclidean distance between two points in a two-dimensional plane. Let be the real-time communication channel coefficient from the i-th UAV to the fusion center in time slot m.

[0169] In this embodiment, the eavesdropper security constraints within the non-convex secure aerial computing joint optimization problem model are equivalently reconstructed and simplified using closed-form solutions, outputting simplified security constraint conditions. Specifically, without altering the actual limiting effect of the constraints, the original security constraints are mathematically transformed, redundant coupling terms are eliminated, and formula simplification is achieved through analytical derivation. Complex nonlinear relationships are removed, resulting in simplified security constraint conditions with a more concise and regular structure. Then, based on the coupling relationship between optimization variables, the overall non-convex secure aerial computing joint optimization problem model is systematically decomposed, separating the overall optimization objective from the constraint system. Independent sub-problems of UAV launch power non-convex optimization and UAV flight trajectory non-convex optimization are identified, achieving hierarchical decomposition of the multivariate joint optimization problem. In subsequent iterative solutions, the UAV launch power and non-convex optimization parameters in the initial optimization iteration parameters are first fixed. For the horizontal position of the drone, the simplified safety constraints are used as the basis for value determination to search for the optimal value and complete the optimal solution of the fusion center noise reduction factor. Then, the optimal fusion center noise reduction factor for the current iteration is determined. Then, the horizontal position of the drone in the initial optimization iteration parameters is kept fixed, and the non-convex optimization sub-problem of drone transmission power is specifically solved within the constraints of the simplified safety constraints. Finally, the optimal drone transmission power for the current iteration that meets the constraints is obtained. Finally, the determined optimal fusion center noise reduction factor and the optimal drone transmission power for the current iteration are kept unchanged. Combining the simplified safety constraints and the various flight restrictions of the drone, the non-convex optimization sub-problem of drone flight trajectory is solved, and the optimal horizontal position of the drone for the current iteration that fits the actual flight scenario is finally calculated.

[0170] Step 106: Based on the current iterative optimal parameters, determine the convergence accuracy and output the optimized configuration parameters of the multi-UAV collaborative transmission secure aerial computing system after convergence.

[0171] It should be noted that numerical calculations are completed by substituting the optimal parameters of each group in the current iteration into the preset objective function. The difference between the function values ​​obtained from two adjacent iterations is compared, and the convergence accuracy is determined according to the established standards. After determining that the convergence conditions are met, all the optimal parameter combinations obtained through hierarchical solution are integrated, and the optimized configuration parameters of the multi-UAV collaborative transmission safe aerial computing system are output after being standardized and summarized.

[0172] Furthermore, step 106 may include the following sub-steps:

[0173] S61. Based on the optimal parameters of the current iteration, calculate the objective function value for this round;

[0174] S62. Compare the difference between the objective function value in this round and the objective function value at historical time points with the preset algorithm convergence accuracy.

[0175] S63. If the difference is greater than or equal to the preset algorithm convergence accuracy, the current iteration optimal parameter is used as the new initial optimization iteration parameter, and the process jumps to the step of solving the current iteration optimal system parameter based on the non-convex safe air computation joint optimization problem model and the initial optimization iteration parameter, until the difference is less than the preset algorithm convergence accuracy.

[0176] S64. The current iteration optimal parameters determined when the difference is less than the preset algorithm convergence accuracy are used as the optimized configuration parameters after convergence of the multi-UAV collaborative transmission safe aerial computing system.

[0177] It should be noted that, based on the optimal parameters of the current iteration, the objective function value for this round is calculated by substituting all the optimal parameters obtained in this iteration (i.e., the optimal parameters of the current iteration) into the objective function calculation formula, along with the channel state data of the corresponding time slot. After completing the integration calculation, the objective function value for this round, which reflects the overall computational error level under the current parameter configuration, is obtained. Then, the difference between the objective function value for this round and the objective function value retained from the previous round's historical moments is calculated. This difference is compared with the pre-set algorithm convergence accuracy. If the calculated difference is greater than or equal to the pre-set algorithm convergence accuracy, it means that there is still room for optimization and adjustment of the current parameters. Then, the current iterative optimal parameters are updated to new initial optimization iteration parameters, and the process returns to the steps of solving for the current iterative optimal system parameters based on the non-convex secure aerial computation joint optimization problem model and the initial optimization iteration parameters to continue iterative optimization. This process is repeated continuously to complete the entire process of constraint simplification, sub-problem decomposition, and hierarchical parameter solving. The iteration process continues until the difference between the objective function values ​​of two iterations is less than the preset algorithm convergence accuracy. At this point, the iterative optimization process is considered to have stabilized and no longer exhibits significant fluctuations. The optimal parameters corresponding to the current iteration in this state are formally determined as the optimized configuration parameters after convergence of the multi-UAV collaborative transmission safe aerial computing system (i.e., a safe aerial computing system with multiple UAVs as transmitters / aerial transmission nodes). This iterative convergence determination method can reasonably control the timing of optimization termination, effectively reduce the consumption of computational resources caused by invalid iterations, and ensure that the final determined system parameters strictly conform to all safety constraints and flight motion constraints. It steadily reduces the signal estimation error in the aerial computing process and improves the practical problems of result fluctuations and low convergence efficiency in the iteration process of non-convex optimization models.

[0178] Furthermore, the Matlab platform of this invention was used to conduct simulation experiments on the proposed secure aerial computing system with multiple UAVs as launchers / airborne launch nodes. The simulation results verified the effectiveness and feasibility of the proposed scheme.

[0179] The parameters required for the simulation experiment are shown in Table 1.

[0180] Table 1 Simulation Parameter Settings

[0181]

[0182] To evaluate the performance of the proposed solution, this invention compares it with the following four benchmark solutions:

[0183] (1) Transceiver design scheme under flight-hover-flight trajectory: In this scheme, the UAV first flies from the starting position to the optimized hovering point. Hover at that position for as long as possible, then fly to the destination position at maximum speed. Optimize the hovering point. The feasible region is determined through a two-dimensional exhaustive search, with the objective of minimizing the mean square error at the fusion center. Based on this, the flight time is calculated as follows: The hovering duration at the optimized hovering point is , This represents the initial horizontal position of the drone. Given the final horizontal position of the UAV and its trajectory, solve the following problem: and Optimize transceiver parameters.

[0184] (2) Transceiver design scheme under straight trajectory: In this scheme, the UAV moves at a constant speed Fly directly from the starting position to the ending position along a straight path. Given this trajectory, solve the problem... and Optimize transceiver parameters.

[0185] (3) Constant power design scheme: In this scheme, power constraints are used to achieve the desired power output. Simplified to and on the issue The solution is performed to achieve joint optimization of transceiver parameters and UAV trajectory.

[0186] (4) Design scheme without eavesdroppers: by removing the minimum mean square error constraint of the eavesdropper. and on the issue The solution is performed to achieve joint optimization of transceiver parameters and UAV trajectory.

[0187] Figure 3The convergence curve of the mean square error at the fusion center as a function of the number of iterations is shown under the multi-UAV cooperative launch scheme proposed in this invention. Observation reveals that the mean square error continuously decreases as the iteration process progresses, reflecting the gradual improvement of system performance during iteration. The fundamental reason for this phenomenon is that the algorithm alternately optimizes the launch power of multiple UAVs, the denoising factor at the fusion center, and the flight trajectories of multiple UAVs, causing the system parameter configuration to continuously approach the optimal operating point, thereby driving a successive reduction in computational error.

[0188] From the perspective of the phased characteristics of the convergence process, the mean squared error decreases rapidly in the early stages of iteration, indicating that the algorithm makes significant adjustments to the system parameters in the initial stage, quickly narrowing the gap with the optimal solution. This is because in the early stages of iteration, the transmit power allocation and flight trajectory of each UAV are far from the optimal configuration, allowing the algorithm to rapidly improve the system state through substantial parameter adjustments. As the number of iterations increases, the slope of the curve gradually slows down, the error value tends to stabilize, and eventually converges to a certain stable level, indicating that the algorithm has entered the local fine-tuning stage, and the performance gain of subsequent iterations gradually decreases.

[0189] In summary, the multi-UAV cooperative scheme proposed in this invention achieves efficient convergence within a finite number of iterations, reflecting both the algorithm's rapid response capability in the initial stage and its good numerical stability in the later stages. This convergence characteristic verifies the reliability and robustness of the proposed optimization algorithm, providing effective performance assurance for multi-UAV assisted safe aerial computing systems.

[0190] Figure 4 The flight trajectories of three drones in a scenario without eavesdroppers are shown. From the overall trajectory, all three drones start from their respective starting points and gradually approach the fusion center. This trend is expected, as drones need to move closer to the fusion center to shorten communication distances, improve line-of-sight link quality, and thus enhance data aggregation accuracy. Specifically, drones 1 and 3 start from the upper left and upper right respectively, flying directly towards the fusion center with symmetrical trajectories, demonstrating the spatial symmetry of path planning; drone 2 starts directly above, its trajectory descending vertically along the central axis. During flight, the trajectories of each drone maintain a certain distance, without intersections or excessively close proximity, indicating that the proposed trajectory optimization algorithm effectively avoids the risk of collisions between drones. In summary, in a scenario without eavesdroppers, the proposed scheme can plan smooth flight trajectories that are beneficial to communication quality based on the drones' starting and ending positions, verifying the effectiveness and robustness of the trajectory optimization algorithm.

[0191] Figure 5The flight trajectories of three drones in a scenario with an eavesdropper present are shown. From the overall trajectory, all three drones start from their respective starting points, but unlike in a scenario without an eavesdropper, they do not directly approach the fusion center. Instead, they exhibit a clear tendency to disperse and fly around it. This change is expected because, in the presence of an eavesdropper, the system needs to balance aggregation accuracy and communication security. The drones actively avoid the eavesdropper's coverage area by adjusting their flight paths. Specifically, drones 1 and 3 start at the upper left and upper right, respectively, but their trajectories are no longer symmetrically distributed. Drone 3 clearly shifts to the left to move away from the eavesdropper located slightly to the right in the diagram. Drone 2 starts directly above, and its trajectory no longer descends vertically but exhibits some twists and turns. Notably, drone 3 maintains a tendency to move away from the eavesdropper throughout its flight, while still gradually approaching the fusion center later on. This allows it to achieve better security performance while ensuring a certain level of aggregation accuracy. During flight, the trajectories of the various drones were further spaced, with no intersections or excessively close proximity observed. This demonstrates that the proposed trajectory optimization algorithm can effectively avoid collisions between drones even in the presence of eavesdropping threats. In summary, in scenarios with eavesdroppers, the proposed scheme can plan smooth, safe, and anti-eavesdropping flight trajectories based on the drones' starting positions and the eavesdropper's position, validating the effectiveness and robustness of the trajectory optimization algorithm in complex environments.

[0192] Comprehensive comparison Figure 4 and Figure 5 It can be seen that the proposed scheme can adaptively adjust the drone trajectory based on the presence of eavesdroppers. In scenarios without eavesdroppers, the drones fly in a converging manner, with smooth and symmetrical trajectories, prioritizing aggregation accuracy. In scenarios with eavesdroppers, the drones fly in a dispersed, circling manner, with tortuous and deviating trajectories, prioritizing communication security. Furthermore, the trajectories in both scenarios do not intersect or become too close together, indicating that the algorithm can effectively avoid the risk of collisions between drones while meeting security or accuracy requirements. The above results demonstrate that the proposed joint optimization framework can dynamically balance aggregation accuracy and physical layer security performance according to actual environmental needs, exhibiting good adaptability and robustness.

[0193] Figure 6 Demonstrates fixed flight duration Under the given conditions, the mean square error of the fusion center in each scheme varies with the maximum transmit power. The graph shows the relationship between the changes. As can be seen, the mean square error (MSE) of all schemes decreases with increasing maximum transmit power. This trend aligns with theoretical expectations; higher transmit power helps improve the system's ability to resist channel fading and eavesdropping interference, thus effectively reducing aggregation error. Compared to the three control schemes (i.e., transceiver design under a "fly-hover-fly" trajectory, transceiver design under a straight trajectory, and a constant power scheme), the proposed scheme achieves lower MSE under all power values, fully demonstrating the significant advantage of jointly optimizing UAV trajectory and transceiver parameters in improving aerial computational accuracy.

[0194] Figure 7 Demonstrated at maximum transmission power Under fixed conditions, the mean square error of the fusion center in each scheme varies with flight time. The graph shows the relationship between the changes. As can be seen, the mean square error (MSE) of all schemes decreases with increasing flight duration. This trend aligns with theoretical expectations; longer flight durations provide more freedom for UAV trajectory optimization. The UAV can adjust its flight and hovering strategies to remain in optimal communication positions for longer periods, effectively reducing fusion errors. Compared to the three control schemes (i.e., transceiver design under a "fly-hover-fly" trajectory, transceiver design under a straight trajectory, and a constant power scheme), the proposed scheme achieves lower MSE for all flight durations, with performance approaching the benchmark scheme in scenarios without eavesdroppers. This fully demonstrates the significant advantage of jointly optimizing UAV trajectories and transceiver parameters in improving aerial computational accuracy, effectively ensuring system performance even in scenarios with eavesdroppers.

[0195] Furthermore, the proposed solution performs slightly worse than the baseline solution in scenarios without eavesdroppers. This is because the system requires additional resources (such as transmission power and trajectory planning) to build a security protection mechanism, which to some extent reduces the resource investment used to optimize the mean square error of the fusion center. In summary, the proposed solution, while ensuring system security, can adaptively adjust the UAV trajectory and power allocation according to the presence of eavesdroppers, achieving an effective trade-off between aggregation accuracy and physical layer security, and verifying its effectiveness and robustness in eavesdropping environments.

[0196] For comparison of technical effectiveness, existing technologies can be referenced. The open nature of wireless channels presents severe security challenges to in-flight computing systems. Since all devices share the same transmission resources, transmission signals naturally superimpose in the air. Any eavesdropper within the transmission range can receive the aggregated signal, potentially leading to the leakage of sensitive data. Physical layer security technology, as a lightweight security measure that does not rely on encryption algorithms, utilizes the physical characteristics of wireless channels to ensure information security. Its core idea is to improve the quality of legitimate channels while deteriorating the transmission conditions of eavesdropping channels through reasonable resource allocation and signal design. Specifically, in the in-flight computing scenario, the security objective transforms into ensuring the computational accuracy of the legitimate fusion center while preventing eavesdroppers from accurately recovering the aggregation function value from the received signal.

[0197] To enhance physical layer security in the over-the-air computing system, several countermeasures were implemented, including jamming, secure beamforming, and artificial noise. These techniques ensure that the mean square error between legitimate and intercepted signals exceeds a predetermined security threshold, thereby minimizing potential eavesdropping threats. The fusion center operates in full-duplex mode, performing the dual functions of receiving sensor data and transmitting jamming signals to degrade channel conditions for eavesdroppers. Simultaneously, artificial noise is incorporated into the over-the-air computing network to improve security without affecting legitimate sensor communications. This dual approach enhances the jamming capabilities against eavesdroppers while maintaining data security and transmission integrity at access points, and sustaining system-level mean square error performance.

[0198] Building upon existing research, this work proposes an enhanced secure aerial computing system assisted by unmanned aerial vehicles (UAVs). By treating the UAV as a transmitter, the transceiver configuration and the UAV's 3D flight path are jointly optimized to minimize the mean square error at the fusion center, while keeping the mean square error of eavesdroppers above a predefined security threshold. Although the formulaic optimization problem exhibits inherent non-convexity, this invention develops an innovative solution framework. The core technologies of this invention include joint optimization design based on UAV trajectory and communication parameters, and solving the transmission scheme under physical layer security constraints. By establishing a mathematical model of the non-convex optimization problem, the original problem is decomposed into three sub-problems—transmission coefficient optimization, noise reduction factor design, and UAV trajectory planning—using an alternating optimization framework. Continuous convex approximation techniques and closed-form solution derivation are used for efficient solving, achieving improved computational accuracy of the legitimate receiver while ensuring that the computational performance of the eavesdropper is not compromised. Furthermore, this invention combines alternating optimization with successive convex approximation techniques. Simulation results confirm that the proposed scheme simultaneously enhances the computational accuracy and security performance of the UAV-assisted aerial computing network, demonstrating the effectiveness of the design.

[0199] Specifically, this invention provides a secure aerial computing method for multi-UAV collaborative transmission, comprising multiple single-antenna UAVs, a single-antenna ground fusion center, and a single-antenna potential eavesdropper. The UAVs simultaneously transmit data, and the fusion center receives the data. During this process, the eavesdropper receives signals from the UAVs. This invention optimizes the transmission coefficients of the UAVs, the noise reduction factor of the fusion center, and the UAV trajectories to ensure that the mean square error of the signals received by all eavesdroppers is greater than a set threshold, while minimizing the mean square error of the signals received by the fusion center. Because the objective function obtained from the modeling is non-increasing, this method is convergent. The method proposed in this invention includes the following steps:

[0200] S2, the fusion center and the eavesdropper use the channel information obtained above to aggregate the information sent by the drone and process it using a noise reduction factor;

[0201] S3. The mean square error of the sensor aggregated signal obtained by the computational fusion center and the eavesdropper after post-processing and the real sensor aggregated signal is modeled and optimized.

[0202] S4. Initialize the drone transmission coefficients, fusion center and eavesdropper noise reduction factor, and drone flight trajectory, and solve the optimization problem using an alternating optimization framework;

[0203] S5. Reconstruct the security constraints for the eavesdropper in order to solve the problem;

[0204] S6. By fixing the transmission coefficient of the UAV and the trajectory of the UAV, the noise reduction factor can be solved, and its closed-form solution can be derived.

[0205] S7. With a fixed noise reduction factor and the drone's flight trajectory, solve for the transmission coefficient. It is found that the security constraints are simplified by the closed-form solution of the eavesdropper's noise reduction factor obtained above, but it is still non-convex. Use successive convex approximation to solve it.

[0206] S8, with fixed noise reduction factor and transmission coefficient, optimize the flight trajectory of the UAV, and solve using auxiliary variables and successive convex approximation;

[0207] S9. Substitute the result after one round of alternating optimization into the objective function and determine whether it converges.

[0208] S10. If yes, output the optimization result;

[0209] S11. If not, use the optimization result of this round as the initial value for the next round of alternating optimization, and repeat steps S6 to S10 until convergence.

[0210] As described above, this invention constructs a joint optimization model that integrates UAV transmit power, fusion center noise reduction factor, and UAV flight trajectory. This minimizes the mean square error of the fusion center calculation while ensuring the mean square error of the eavesdropper calculation is not lower than a preset safety threshold, thus achieving synergistic optimization of computational accuracy and physical layer security performance. Furthermore, this invention uses an alternating optimization framework to decompose the original non-convex problem into sub-problems such as eavesdropper security constraint reconstruction, fusion center noise reduction factor optimization, UAV transmit power optimization, and UAV trajectory optimization. This includes closed-form solution methods for the eavesdropper noise reduction factor and the fusion center noise reduction factor, as well as successive convex approximation solution methods for the power and trajectory sub-problems. Simultaneously, this invention incorporates auxiliary variable design during trajectory optimization and includes actual flight constraints such as the UAV's maximum speed, fixed start-end point, and minimum safe distance between UAVs in the solution process. Therefore, the protection points of this invention include not only the system modeling method for secure aerial computation but also the specific solution methods for the aforementioned joint optimization framework and its various sub-problems.

[0211] Compared with existing technologies, the advantages of this invention are as follows: it not only focuses on the computational accuracy of the fusion center, but also considers the eavesdropper's ability to recover the aggregation results, thus achieving joint protection of aerial computational accuracy and physical layer security performance at the system level; by utilizing the spatial maneuverability of multiple UAVs and jointly optimizing transmission power, noise reduction factor, and flight trajectory, it more effectively improves legitimate links and suppresses eavesdropping links, thereby enhancing the overall system performance; by actively avoiding eavesdropping risks through trajectory design, it has stronger spatial security enhancement capabilities compared to schemes that rely solely on fixed node power control or signal design; by combining closed-form solutions, alternating optimization, and successive convex approximation, it reduces solution complexity while ensuring performance and improves the implementation efficiency of the method; and by considering practical constraints such as UAV speed, origin-end point, and minimum safe distance between UAVs in the optimization, it is more in line with real deployment needs and has stronger engineering application value and scenario adaptability.

[0212] In this embodiment of the invention, a secure aerial computing method for multi-UAV cooperative transmission is provided. The method acquires the basic parameters of the secure aerial computing system for multi-UAV cooperative transmission and the horizontal positions of the UAVs in multiple time slots. Based on the basic parameters and the horizontal positions of the UAVs in multiple time slots, the method calculates the channel information between the UAVs and the receiver. The method initializes the UAV system parameters and generates the received signal at the transceiver end based on the channel information and the UAV system parameters. The received signal at the transceiver end is then denoised using the UAV system parameters to output an aggregated signal estimate. Based on the aggregated signal estimate, the actual sensor aggregated signal, and the UAV system parameters, a non-convex secure aerial computing joint optimization problem model and initial optimization iteration parameters are determined. Based on the non-convex secure aerial computing joint optimization problem model and the initial optimization iteration parameters, the optimal system parameters for the current iteration are solved. Based on the optimal system parameters for the current iteration... The optimal parameters are used to determine the convergence accuracy and output the optimized configuration parameters of the multi-UAV collaborative transmission safe aerial computing system after convergence. Based on the above scheme, this invention integrates the dynamic horizontal position of UAVs in each time slot for modeling calculation in the channel calculation stage. This changes the shortcomings of traditional schemes that rely on fixed parameter modeling and cannot adapt to the real-time channel fluctuations caused by the dynamic flight of UAVs. It avoids the basic calculation deviation caused by the dynamic communication environment from the source. At the same time, it effectively optimizes the signal aggregation effect through a standardized signal denoising post-processing process, reduces the error gap between the estimated value of the aggregated signal and the actual sensor aggregated signal, and achieves multi-parameter joint optimization by relying on a non-convex joint optimization model that fits the actual operation constraints. With the help of iterative solution and convergence determination mechanism, it continuously corrects the accumulated calculation error generated in the dynamic communication process, thereby improving the accuracy of multi-UAV collaborative safe aerial computing in dynamic airspace.

[0213] Please see Figure 8 , Figure 8 This is a structural block diagram of a secure aerial computing device for multi-UAV collaborative transmission provided in Embodiment 2 of the present invention.

[0214] This invention provides a secure aerial computing device for multi-UAV collaborative transmission, comprising:

[0215] The acquisition module 801 is used to acquire the basic parameters of the multi-UAV cooperative transmission secure aerial computing system and the horizontal position of the UAVs in multiple time slots, and to calculate the channel information between the UAVs and the receiver based on the basic parameters and the horizontal position of the UAVs in multiple time slots.

[0216] The initialization module 802 is used to initialize the UAV system parameters and generate the transceiver received signal based on the channel information and the UAV system parameters.

[0217] The noise reduction post-processing module 803 is used to perform noise reduction post-processing on the received signal from the transceiver using UAV system parameters and output the aggregated signal estimate.

[0218] The model building module 804 is used to determine the joint optimization problem model and initial optimization iteration parameters for non-convex secure aerial computing based on the aggregated signal estimate, the aggregated signal from the real sensor, and the parameters of the UAV system.

[0219] Solver module 805 is used to solve for the optimal system parameters in the current iteration based on the joint optimization problem model of non-convex safe air computation and the initial optimization iteration parameters;

[0220] Output module 806 is used to determine the convergence accuracy based on the current iteration's optimal parameters and output the converged optimized configuration parameters of the multi-UAV collaborative transmission safe aerial computing system.

[0221] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the device and module described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0222] This invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program; when the computer program is executed by the processor, the processor performs the steps of the secure aerial computing method for multi-UAV cooperative transmission as described in the above embodiments.

[0223] This invention also provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the secure aerial computing method for multi-UAV cooperative transmission as described in the above embodiments.

[0224] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0225] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0226] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0227] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0228] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for secure in-flight computation of multi-UAV cooperative transmission, the method comprising: include: The system acquires the basic parameters of a multi-UAV collaborative transmission secure aerial computing system and the horizontal positions of UAVs in multiple time slots. Based on the basic parameters and the horizontal positions of UAVs in multiple time slots, it calculates the channel information between the UAVs and the receiver. Initialize the UAV system parameters, and generate the transceiver received signal based on the channel information and the UAV system parameters; The received signal at the transceiver is post-processed with the UAV system parameters to reduce noise and output an aggregated signal estimate. Based on the aggregated signal estimate, the actual sensor aggregated signal and the UAV system parameters, determine the joint optimization problem model for non-convex secure aerial computing and the initial optimization iteration parameters. Based on the non-convex secure aerial computing joint optimization problem model and the initial optimization iteration parameters, solve for the optimal system parameters in the current iteration; Based on the current iterative optimal parameters, the convergence accuracy is determined, and the optimized configuration parameters of the multi-UAV collaborative transmission secure aerial computing system after convergence are output.

2. The secure aerial computing method for multi-UAV cooperative transmission according to claim 1, characterized in that, The channel information includes UAV-fusion center channel coefficients under multiple time slots and UAV-eavesdropper channel coefficients under multiple time slots; The step of calculating the channel information between the UAV and the receiver based on the basic parameters and the horizontal position of the UAV in multiple time slots includes: Extract the following basic parameters: number of time slots, constant flight altitude of the UAV, location of the ground fusion center, location of the eavesdropper, and channel power gain at a preset reference distance. Based on the number of time slots, the constant flight altitude of the UAV, the location of the ground fusion center, the location of the eavesdropper, the channel power gain at the preset reference distance, and the horizontal position of the UAV in multiple time slots, channel coefficients are calculated for the air-to-ground communication links from the UAV to the ground fusion center and the air-to-ground communication links from the UAV to the eavesdropper in multiple time slots, respectively, to obtain the UAV-fusion center channel coefficient and the UAV-eavesdropper channel coefficient in each time slot.

3. The secure aerial computing method for multi-UAV cooperative transmission according to claim 1, characterized in that, The transceiver receives signals including signals received by the fusion center and signals received by the eavesdropper. The step of generating the transceiver received signal based on the channel information and the UAV system parameters includes: Based on the channel information and the UAV transmission power in the UAV system parameters, the preset normalized UAV transmission signal is preprocessed, and the preprocessed UAV transmission signal is output. Control multiple drones to collaboratively transmit pre-processed drone transmission signals, generating fusion center reception signals and eavesdropper reception signals.

4. The secure aerial computing method for multi-UAV cooperative transmission according to claim 3, characterized in that, The aggregated signal estimate includes the fusion center aggregated signal estimate and the eavesdropper aggregated signal estimate; the step of using the UAV system parameters to perform noise reduction post-processing on the received signal at the transceiver end and outputting the aggregated signal estimate includes: Based on the fusion center noise reduction factor in the UAV system parameters, the fusion center received signal is denoised and aggregated to obtain the estimated value of the fusion center aggregated signal. The eavesdropper received signal is denoised and aggregated based on the eavesdropper denoising factor in the UAV system parameters to obtain an estimated value of the eavesdropper aggregated signal.

5. The secure aerial computing method for multi-UAV cooperative transmission according to claim 4, characterized in that, The step of determining the joint optimization problem model and initial optimization iteration parameters for non-convex secure aerial computing based on the aggregated signal estimate, the actual sensor aggregated signal, and the UAV system parameters includes: The estimated value of the fusion center aggregated signal and the estimated value of the eavesdropper aggregated signal are compared with the actual sensor aggregated signal to calculate the error, and the mean square error of the fusion center and the mean square error of the eavesdropper are output. With the minimization of the mean square error of the fusion center as the optimization objective, and with the eavesdropper security constraint that the mean square error of the eavesdropper is not lower than the security threshold, combined with the preset UAV motion constraints, a non-convex secure aerial computation joint optimization problem model is constructed. The parameters of the unmanned aerial vehicle system are used as the initial optimization iteration parameters.

6. The secure aerial computing method for multi-UAV cooperative transmission according to claim 1, characterized in that, The current iteration optimal system parameters include the current iteration optimal fusion center noise reduction factor, the current iteration optimal UAV transmit power, and the current iteration optimal UAV horizontal position; The step of solving for the optimal system parameters in the current iteration based on the non-convex secure aerial computation joint optimization problem model and the initial optimization iteration parameters includes: The eavesdropper security constraints in the non-convex secure aerial computation joint optimization problem model are equivalently reconstructed and simplified using closed-form solutions, and simplified security constraint conditions are output. The non-convex safe air computation joint optimization problem model is decomposed to obtain the non-convex optimization sub-problem of UAV launch power and the non-convex optimization sub-problem of UAV flight trajectory; By fixing the UAV's transmit power and horizontal position in the initial optimization iteration parameters, and combining the simplified safety constraints, the optimal solution for the fusion center noise reduction factor is obtained, and the current iteration's optimal fusion center noise reduction factor is output. By fixing the noise reduction factor of the current iteration's optimal fusion center and the horizontal position of the UAV in the initial optimization iteration parameters, and combining the simplified safety constraints, the non-convex optimization subproblem of UAV transmission power is solved, and the current iteration's optimal UAV transmission power is output. By fixing the noise reduction factor of the current iteration's optimal fusion center and the current iteration's optimal UAV transmission power, and combining the simplified safety constraints, the non-convex optimization subproblem of the UAV flight trajectory is solved, and the current iteration's optimal UAV horizontal position is output.

7. The secure aerial computing method for multi-UAV cooperative transmission according to claim 1, characterized in that, The process of determining convergence accuracy based on the current iterative optimal parameters and outputting the converged optimized configuration parameters of the multi-UAV cooperative transmission safe aerial computing system includes: Based on the current optimal parameters, calculate the objective function value for this round; The difference between the objective function value in this round and the objective function value at a historical time is compared with the preset algorithm convergence accuracy. If the difference is greater than or equal to the preset algorithm convergence accuracy, then the current iteration optimal parameter is used as the new initial optimization iteration parameter, and the process jumps to the step of solving the current iteration optimal system parameter based on the non-convex safe air computation joint optimization problem model and the initial optimization iteration parameter, until the difference is less than the preset algorithm convergence accuracy; The optimal parameters for the current iteration, determined when the difference is less than the preset algorithm convergence accuracy, are used as the optimized configuration parameters after convergence of the multi-UAV collaborative transmission secure aerial computing system.

8. A secure aerial computing device for multi-UAV collaborative transmission, characterized in that, include: The acquisition module is used to acquire the basic parameters of the multi-UAV collaborative transmission secure aerial computing system and the horizontal position of the UAVs in multiple time slots, and to calculate the channel information between the UAVs and the receiver based on the basic parameters and the horizontal positions of the UAVs in multiple time slots. An initialization module is used to initialize the UAV system parameters and generate a transceiver signal based on the channel information and the UAV system parameters. The noise reduction post-processing module is used to perform noise reduction post-processing on the received signal from the transceiver using the UAV system parameters, and output the aggregated signal estimate. The model building module is used to determine the joint optimization problem model for non-convex secure aerial computing and the initial optimization iteration parameters based on the aggregated signal estimate, the real sensor aggregated signal and the UAV system parameters. The solution module is used to solve for the optimal system parameters in the current iteration based on the non-convex safe air computation joint optimization problem model and the initial optimization iteration parameters; The output module is used to determine the convergence accuracy based on the current iteration optimal parameters and output the converged optimized configuration parameters of the multi-UAV collaborative transmission safe aerial computing system.

9. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor causes the processor to perform the steps of the secure aerial computing method for multi-UAV cooperative transmission as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the secure aerial computing method for multi-UAV cooperative transmission as described in any one of claims 1-7.

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