Unmanned aerial vehicle swarm SAR configuration optimization method and system based on low-orbit communication satellite

Abstract

The application provides a UAV swarm SAR configuration optimization method and system based on a low-orbit communication satellite, relates to the technical field of radar signal processing and optimization, and comprises the following steps: constructing a wave number spectrum geometric constraint, designing a decision variable, and then constructing a target function; a Cubic chaotic mapping method is used to generate an initial population, the decision variable is mapped into a gene segment of an individual in the population, and a child population is obtained according to the initial population; the decision variable is crossed according to a correlation chromosome strategy and an extended correlation chromosome strategy in sequence; an adaptive mutation mechanism is used to update the child population for the correlation chromosome group; the updated child population is non-dominantly sorted, the crowding degree of the individual is calculated, and then an approximate Pareto front surface of a multi-objective problem is constructed, a candidate configuration data set is screened, the optimal configuration is selected from the configuration data set in combination with the actual application scene requirement, and finally, the configuration scheme is output. The application realizes efficient and stable UAV swarm SAR imaging.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing and optimization technology, and in particular to a method and system for optimizing the SAR configuration of unmanned aerial vehicle swarms based on low-Earth orbit communication satellites. Background Technology

[0002] Low-Earth orbit (LEO) communication satellite signals, with their global all-weather coverage, long-range operation, and high-frequency revisit capabilities, are widely used in various fields such as military reconnaissance, aerospace security, and emergency rescue. However, for Synthetic Aperture Radar (SAR) imaging applications, LEO-COS signals suffer from narrow bandwidth and low echo signal-to-noise ratio, severely limiting the acquisition of high-quality image information. Using UAV swarms for collaborative observation can effectively compensate for this deficiency.

[0003] In collaborative observation using unmanned aerial vehicle (UAV) swarms, efficient and stable UAV swarm configuration optimization technology is particularly important. It can minimize system costs and optimize detection performance under multiple constraints such as platform motion characteristics, swarm size, and imaging resolution. This allows for effective evaluation of system performance, optimization of real-time imaging processing hardware, and reduction of development risks. This technology not only improves R&D efficiency and accuracy but also expands the application potential of low-Earth orbit (LEO) communication satellites in military and civilian fields, promoting the progress and development of related technologies.

[0004] LEO-COS-driven UAV swarm SAR imaging relies on cluster configuration optimization to adapt to the dynamic observation geometry of the "constellation-swarm" architecture. Traditional UAV swarm configuration design methods are mainly based on static array structures (such as circular arrays or cross arrays) or low-dynamic platform assumptions, achieving topology planning through single-dimensional optimization (such as resolution or signal-to-noise ratio). While these methods can theoretically meet the imaging requirements of simple scenarios, they suffer from the following problems in practical applications involving high-speed movement of low-Earth orbit satellites and dynamic coordination of UAV swarms:

[0005] I. Insufficient Dynamic Adaptability: Traditional configuration designs often assume fixed observation geometry or low-dynamic platform motion, failing to consider the significant motion differences between low-Earth orbit satellites and UAVs. When the observation geometry of the "constellation-swarm" continuously changes dynamically, static configurations are prone to wavenumber spectrum overlap, misalignment, or gaps, leading to decreased imaging resolution, sidelobe defocus, and an inability to maintain stable performance for all-weather, wide-area detection.

[0006] II. Weak Multi-Constraint Optimization Capability: UAV swarm configuration optimization needs to simultaneously meet multiple objective constraints, such as UAV swarm size and motion constraints, imaging resolution and signal-to-noise ratio requirements, and engineering deployment costs. Traditional methods often decompose multiple constraints into single-dimensional solutions or make linear approximations of strongly nonlinear coupling relationships, making it difficult to achieve a balance between "minimizing system cost and optimizing detection performance," and easily leading to a disconnect between the theoretical performance of the configuration and actual needs.

[0007] Third, there is a disconnect between engineering feasibility and performance: Traditional array designs focus on theoretical imaging performance but fail to fully incorporate the engineering constraints of UAV swarms. While traditional array configurations can improve resolution, in scenarios with low-Earth orbit satellite external radiation sources, the lack of consideration for the UAV's endurance limits leads to frequent trajectory adjustments during actual deployment, introducing additional errors. Furthermore, traditional methods cannot adapt to the "separate transmission and reception" external radiation source system and are difficult to reconcile with the space-time coupling characteristics of low-Earth orbit satellite signals, further limiting practical application.

[0008] Therefore, developing a UAV swarm configuration optimization method that can adapt to the high dynamic characteristics of "low-orbit satellite-UAV swarm" and take into account both multi-constraint optimization and engineering feasibility has become an urgent problem to be solved in the current technical field. Summary of the Invention

[0009] Based on this, the purpose of this invention is to provide a method and system for optimizing the SAR configuration of UAV swarms based on low-orbit communication satellites, in order to solve the problems of low resource utilization and weak robustness in traditional UAV topology configurations, so as to achieve efficient and stable UAV swarm SAR imaging.

[0010] This invention provides a method for optimizing the SAR configuration of unmanned aerial vehicle (UAV) swarms based on low-Earth orbit (LEO) communication satellites, comprising:

[0011] Parameters of low-Earth orbit communication satellites and UAV swarms are obtained to construct wavenumber spectrum geometric constraints and design decision variables; the decision variables are substituted into the calculation to construct the objective function; the decision variables include core decision variables and auxiliary decision variables; wherein, the core decision variables include the UAV swarm size and the relative motion parameters between the satellites and UAVs; the auxiliary decision variables include the orbital phase factor and the cross-platform synchronization threshold;

[0012] The Cubic chaotic mapping method is used in conjunction with the objective function to generate an initial population. The decision variables are mapped to gene fragments of individuals in the population, and the initial population is made to exhibit random distribution characteristics through chaotic operators to obtain the offspring population.

[0013] The core decision variables are first cross-referenced using the associated chromosome strategy, and the auxiliary decision variables are cross-referenced by extending the associated chromosome strategy. Then, an adaptive mutation mechanism is used to update the offspring population of the associated chromosome set to ensure that the association constraints between the decision variables are not broken.

[0014] The updated offspring population is non-dominated and the crowding degree of individuals is calculated. Based on the non-dominated sorting results and the crowding degree calculation results, an approximate Pareto front for the multi-objective problem is constructed, and a candidate configuration dataset is formed. The optimal configuration is selected from the configuration dataset in combination with the actual application scenario requirements, and the imaging effect of the UAV swarm SAR under the optimal configuration is verified to meet the system evaluation criteria, so as to output the final configuration scheme.

[0015] The aforementioned method for optimizing the SAR configuration of UAV swarms based on low-Earth orbit communication satellites deeply integrates non-dominated sorting genetic algorithms with wavenumber spectrum geometric constraints. It iteratively optimizes the algorithm by establishing an optimization method that alternates between Cubic chaotic mapping initialization, associated chromosome crossover mutation, and non-dominated sorting screening. Finally, by inputting low-Earth orbit satellite parameters and UAV swarm parameters, the optimal configuration scheme is obtained, realizing the optimization of UAV swarm SAR configuration in highly dynamic scenarios. This effectively solves the dynamic mismatch problem of traditional static configurations, enabling UAV swarms to maintain high resolution and low sidelobe imaging performance even under complex observation geometry.

[0016] In addition, the UAV swarm SAR configuration optimization method based on low-Earth orbit communication satellites according to the present invention may also have the following additional technical features:

[0017] Furthermore, in the step of obtaining parameters of low-Earth orbit communication satellites and UAV swarms to construct wavenumber spectrum geometric constraints and design decision variables, the expression for the geometric constraints is:

[0018] ;

[0019] In the formula, The azimuth wavenumber vector representing the overall distributed SAR system; The wavenumber spectrum of the distributed unmanned aerial vehicle swarm SAR system at the receiver n The range of the upward projection of a distance of -1; γ max This represents the maximum permissible wavenumber spectral gap factor; Indicates receiver n azimuth wavenumber vector; Indicates receiver azimuth wavenumber vector magnitude; Indicates receiver n -1 azimuth wavenumber vector; Indicates receiver -1 is the azimuth wavenumber vector magnitude.

[0020] Furthermore, in the step of substituting decision variables into the calculation to construct the objective function, the objective function includes the imaging resolution and echo signal-to-noise ratio of the UAV swarm SAR system. The imaging resolution of the UAV swarm SAR system includes ground range resolution, ground azimuth resolution, resolution angle, and resolution cell area. The formula for calculating the ground range resolution is:

[0021] ;

[0022] In the formula, ρ r Indicates the ground distance resolution; c Indicates the population size; B r It is the bandwidth of the transmitted signal; P g Represents the ground projection matrix; The unit vector from the launch station to the target point; The unit vector from the receiving station to the target point;

[0023] The formula for calculating ground azimuth resolution is:

[0024] ;

[0025] In the formula, ρ a Indicates the ground azimuth resolution; λ The radar carrier wavelength; T a P represents the time for synthesizing the pore size. T and P R They are respectively by and The determined projection matrix; P g Represents the ground projection matrix; Represents the velocity vector of the receiving station; Represents the velocity vector of the launching station; R T This indicates the distance between the launch station and the target point; R R This indicates the distance between the receiving station and the target point;

[0026] The formula for calculating the angle is:

[0027] ;

[0028] In the formula, α Indicates the angle to be distinguished; Represents a distance-to-unit vector; Represents the azimuth unit vector;

[0029] The formula for calculating the area of ​​a distinguishing unit is:

[0030] ;

[0031] In the formula, S This indicates the area of ​​the resolvable unit.

[0032] Furthermore, the formula for calculating the echo signal-to-noise ratio is:

[0033] ;

[0034] In the formula, SNR Indicates the echo signal-to-noise ratio; P av The average power of the transmitted signal; G t For the transmit antenna gain, G r For receiving antenna gain; λ σ is the radar carrier wavelength; s The bistatic radar cross section of the target; T a The time for synthesizing the aperture; R T This indicates the distance between the launch station and the target point; R R This indicates the distance between the receiving station and the target point; k Boltzmann's constant, T 0 represents the temperature at which noise is received; F 0 represents the noise figure of the receiving station; L s The system's loss factor;

[0035] The echo power received by the UAV swarm SAR system is:

[0036] ;

[0037] In the formula, P r This indicates the echo power.

[0038] Furthermore, in the steps of generating an initial population using the Cubic chaotic mapping method and combining it with the objective function, mapping decision variables to gene segments of individuals in the population, and using chaotic operators to make the initial population exhibit random distribution characteristics to obtain the offspring population, the decision variables are encoded using binary encoding, the chromosome length is L, the population size is C, and the real value of a gene segment of a certain chromosome in the population is represented by... It means that, among them, i Indicates chromosome number within the population. j Representing the location of gene segments in a chromosome, the population expression for the Cubic chaotic mapping is:

[0039] ;

[0040] In the formula, ρ For control parameters, For chaos operators, i Indicates chromosome number within the population. j It indicates the location of a gene segment in a chromosome.

[0041] Another aspect of the present invention provides a SAR configuration optimization system for unmanned aerial vehicle swarms based on low-Earth orbit communication satellites, the system comprising:

[0042] The acquisition module is used to acquire parameters of low-Earth orbit communication satellites and UAV swarms to construct wavenumber spectrum geometric constraints and design decision variables; substitute the decision variables into the calculation to construct the objective function; the decision variables include core decision variables and auxiliary decision variables; wherein, the core decision variables include the UAV swarm size and the relative motion parameters between the satellites and UAVs; the auxiliary decision variables include the orbital phase factor and the cross-platform synchronization threshold;

[0043] The mapping module is used to generate an initial population by using the Cubic chaotic mapping method and combining it with the objective function. It maps decision variables to gene fragments of individuals in the population and uses chaotic operators to make the initial population exhibit random distribution characteristics in order to obtain the offspring population.

[0044] The update module is used to first cross-reference the core decision variables according to the associated chromosome strategy, and then cross-reference the auxiliary decision variables by extending the associated chromosome strategy; then, an adaptive mutation mechanism is used to update the offspring population of the associated chromosome set to ensure that the association constraints between decision variables are not broken.

[0045] The optimization module is used to perform non-dominated sorting on the updated offspring population and calculate the crowding degree of individuals. Based on the non-dominated sorting results and the crowding degree calculation results, an approximate Pareto front for the multi-objective problem is constructed, and a candidate configuration dataset is formed by screening. The optimal configuration is selected from the configuration dataset in combination with the actual application scenario requirements, and the imaging effect of the UAV swarm SAR under the optimal configuration is verified to meet the system evaluation criteria, so as to output the final configuration scheme.

[0046] In another aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for optimizing the SAR configuration of unmanned aerial vehicle swarms based on low-Earth orbit communication satellites.

[0047] In another aspect, the present invention provides a data processing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described method for optimizing the SAR configuration of unmanned aerial vehicle swarms based on low-Earth orbit communication satellites. Attached Figure Description

[0048] Figure 1 This is a flowchart of a method for optimizing the SAR configuration of unmanned aerial vehicle swarms based on low-Earth orbit communication satellites, as described in an embodiment of the present invention.

[0049] Figure 2 This is a wavenumber spectrum geometric constraint configuration diagram provided in an embodiment of the present invention.

[0050] Figure 3 This is a schematic diagram of associated chromosome variations provided in an embodiment of the present invention.

[0051] Figure 4 This is a schematic diagram of associated chromosome variations provided in an embodiment of the present invention.

[0052] Figure 5 This is a scene scattering coefficient diagram provided in an embodiment of the present invention.

[0053] Figure 6 The diagram shows the SAR image results obtained by performing SAR imaging processing on the SAR simulation echo signals obtained by the method of this invention and the traditional unmanned structure. Among them, (a) is the SAR image obtained by receiving with a single platform, (b) is the SAR image obtained by using the cross-shaped configuration method, and (c) is the SAR image obtained by using the unmanned structure method proposed in this invention.

[0054] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0055] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Several embodiments of the invention are illustrated in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0056] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0057] Analysis reveals the following problems and shortcomings of existing technologies: how to design a configuration optimization model that adapts to high-dynamic observation geometry to avoid configuration mismatch caused by differences in motion between low-orbit satellites and UAVs; how to accurately solve strongly nonlinear optimization problems under multiple constraints to achieve multi-objective collaborative optimization; and how to embed engineering feasibility constraints into the configuration design to ensure that the solution is feasible and can stably support the imaging requirements of low-orbit satellite external radiation source SAR.

[0058] Therefore, this application provides a method and system for optimizing the SAR configuration of unmanned aerial vehicle swarms based on low-Earth orbit communication satellites to solve the above problems, thereby giving the technical solution of this application the following significance:

[0059] First, this invention innovatively integrates wavenumber spectrum constraints with non-dominated sorting genetic algorithms. By constructing a dynamic configuration optimization model for UAV swarms, it can generate the globally optimal configuration solution set without approximating the strong nonlinear constraints. This effectively solves the dynamic mismatch problem of traditional static configurations, enabling UAV swarms to maintain high resolution and low sidelobe imaging performance even under complex observation geometry.

[0060] Secondly, the multi-objective optimization framework designed in this invention has significant global optimization advantages compared to traditional single-dimensional optimization algorithms. By incorporating objectives such as resolution, signal-to-noise ratio, and cluster energy consumption into a unified optimization model, this invention can output multiple Pareto optimal configuration schemes in a single iteration, eliminating the need for multiple constraint decomposition and solution steps. This greatly accelerates the dynamic trajectory change response of low-Earth orbit satellites and significantly improves the system's dynamic adaptability and mission flexibility.

[0061] Furthermore, this invention provides a method for optimizing UAV swarm configurations that is compatible with both theoretical performance and engineering feasibility. By embedding engineering parameters such as UAV payload constraints, cross-platform synchronization error tolerance, and endurance limits into the optimization model, it avoids the shortcomings of traditional methods that prioritize theory over practical application. While saving system integration costs and manpower, it provides a feasible topology solution for collaborative passive imaging of constellations and swarms, helping to improve the practicality of such applications in scenarios such as military reconnaissance, aerospace security, and emergency rescue.

[0062] To facilitate understanding of the present invention, several embodiments are given below. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that the disclosure of the present invention will be more thorough and complete.

[0063] Example 1

[0064] Please see Figure 1 The figure shows a method for optimizing the SAR configuration of an unmanned aerial vehicle swarm based on low-Earth orbit communication satellites in the first embodiment of the present invention. The method includes steps S101 to S105:

[0065] S101. Obtain parameters of low-Earth orbit communication satellites and UAV swarms to construct wavenumber spectrum geometric constraints and design decision variables.

[0066] As a specific example, parameters of the low-Earth orbit communication satellite and the UAV swarm are extracted based on the SAR imaging requirements of the LEO-COS UAV swarm to construct wavenumber spectrum geometric constraints and design decision variables. Specifically, wavenumber spectrum geometric constraints with non-overlapping, gapless, misaligned, and isomorphic distribution characteristics are constructed, and decision variables including UAV spatial coordinates and flight trajectory parameters are designed. The decision variables are then substituted into the calculation to construct the objective function. Furthermore, the decision variables include UAV spatial coordinates and flight trajectory parameters.

[0067] Specifically, before extracting the core parameters of the low-orbit communication satellite and the UAV swarm according to the SAR imaging requirements of the LEO-COS UAV swarm, constructing the wavenumber spectrum geometric constraint system, and completing the multi-target optimization adaptation step, the initialization preprocessing of the core parameters is also included. The initialization preprocessing specifically includes (1) and (2):

[0068] (1) Only when the wavenumber spectra of each receiver in an unmanned aerial vehicle (UAV) SAR system satisfy the conditions of non-overlapping, gapless, misaligned, and homogeneous distribution can the system balance imaging quality and configuration feasibility. Specifically, for example... Figure 2 As shown, where, Figure 2 (a) shows the overlap of wavenumber spectra of each receiver; Figure 2 (b) shows the wavenumber spectrum splitting of each receiver; Figure 2 (c) shows the wavenumber spectrum misalignment of each receiver; Figure 2 In the middle (d), the wavenumber spectrum distribution directions of each receiver are inconsistent.

[0069] Specifically, let's set up the receiver. n The range wavenumber vector and azimuth wavenumber vector are:

[0070] ;

[0071] In the formula, B represents the signal bandwidth; T represents the wavenumber vector; a Indicates the time for synthesizing the aperture; This represents the range wavenumber vector of receiver n; Indicates receiver n The azimuth wavenumber vector.

[0072] First, establish a range-azimuth orthogonal optimization objective. Orthogonality between the range and azimuth directions is equivalent to... and Since they are orthogonal, the objective function for optimizing the orthogonality of range and orientation can be obtained as follows:

[0073] ;

[0074] In the formula, dot(﹒) represents the vector dot product operation.

[0075] Secondly, an optimization objective for wavenumber spectrum parallelism is established, and the range wavenumber vectors of different receivers are... The azimuth wavenumber vectors of different receivers should be as parallel as possible. Parallelism should also be maintained as much as possible. Based on this, the objective function for optimizing wavenumber spectrum parallelism is:

[0076] ;

[0077] In the formula, cross(﹒) represents the cross product operation of vectors.

[0078] Finally, an optimization objective for wavenumber spectrum misalignment suppression is established. After determining the optimization objective descriptions for range-azimuth orthogonality and wavenumber spectrum parallelism, constraints on wavenumber spectrum misalignment are also required. (The last part, "assume the receiver...", appears to be incomplete and lacks context.) n -1 and receiver n offset vector for:

[0079] ;

[0080] To reduce the degree of wavenumber spectrum misalignment, the offset vector in the above equation is related to the receiver. n -1 azimuth wavenumber vector The included angle should be as small as possible, therefore the optimization objective for wavenumber spectrum misalignment suppression is:

[0081] ;

[0082] (2) Give the constraints of the optimization problem.

[0083] Specifically, let's set up the receiver. n The configuration of -1 is known, including the receiver. n -1 is the starting point of the trajectory I n-1 (0) and velocity , among which, I n-1 (0)=[ x R(n-1) (0), y R(n-1) (0), z R(n-1) (0)], where, x R(n-1) (0) represents the X-axis coordinate of the receiver's n-1 track starting point in the spatial coordinate system; y R(n-1) (0) represents the Y-axis coordinate of the receiver's n-1 track starting point in the spatial coordinate system; zR(n-1) (0) represents the Z-axis coordinate of the receiver's n-1 trajectory starting point in the spatial coordinate system; based on this, the configuration of the transmitter and receiver is planned. Receiver n The decision variables are:

[0084] g=(△ x ,△ y ,△z,△ θ vRn ,△ θ vT ,△ θ TR(n-1) );

[0085] In the formula, (△ x ,△ y ,△z) represents the receiver n track start point and receiver n -1 Track Start Point I n-1 (0) difference in rectangular space coordinates, △ θ vRn Indicates receiver n Relative to receiver n -1 yaw angle, △ θ vT Indicates the transmitter relative to the receiver n -1 yaw angle, △ θ TR(n-1) Indicates receiver n -1 is the angle between the coordinates of the transmitter's trajectory start point and the coordinates projected onto the ground.

[0086] According to the spatial configuration design criteria, the wavenumber spectra of each receiver should, as far as possible, satisfy the conditions of non-overlapping and gapless operation. This leads to the following geometric constraints:

[0087] ;

[0088] In the formula, The azimuth wavenumber vector representing the overall distributed SAR system; The wavenumber spectrum of the distributed unmanned aerial vehicle swarm SAR system at the receiver n The range of the upward projection of a distance of -1; γ max This represents the maximum permissible wavenumber spectral gap factor; Indicates receiver n azimuth wavenumber vector; Indicates receiver azimuth wavenumber vector magnitude; Indicates receiver n -1 azimuth wavenumber vector; Indicates receiver -1 is the azimuth wavenumber vector magnitude.

[0089] S102. Substitute the decision variables into the calculation to construct the objective function.

[0090] In this embodiment, substituting the decision variables into the calculation to construct the objective function specifically includes (I) and (II):

[0091] (I) The imaging resolution of an unmanned aerial vehicle (UAV) swarm SAR system is closely related to its spatial configuration. Let the position vector from the launch station to the target point be... The velocity vector of the launch station is The bistatic projection angle between the receiving station and the transmitting station is... The receiving station's flight altitude is H The horizontal distance from the receiving station to the target point is R The flight velocity vector of the receiving station is If the flight direction of the receiving station is consistent with the projection of the position vector from the receiving station to the target point, then the expression for the position vector from the receiving station to the target point is:

[0092] ;

[0093] Where M is the rotation matrix, its expression can be written as:

[0094] ;

[0095] Therefore, the expression for the velocity vector of the receiving station is:

[0096] ;

[0097] Due to the position vector from the launch station to the target point Height of receiving station H The speed of the receiving station v R All of these are fixed: the horizontal distance R from the receiving station to the target point and the angle between the bistatic projections. Together they determine the velocity vector of the receiving station. and the position vector from the receiving station to the target point .

[0098] In this embodiment, the objective function includes the imaging resolution and echo signal-to-noise ratio of the UAV swarm SAR system. The imaging resolution of the UAV swarm SAR system includes ground range resolution, ground azimuth resolution, resolution angle, and resolution cell area. Based on the theory of bibasic generalized fuzzy functions, expressions for the ground range resolution, ground azimuth resolution, resolution angle, and resolution cell area of ​​the swarm UAV SAR system can be derived. The formula for calculating the ground range resolution is as follows:

[0099] ;

[0100] In the formula, ρ r Indicates the ground distance resolution; c Indicates the population size; B r It is the bandwidth of the transmitted signal; P g Represents the ground projection matrix; The unit vector from the launch station to the target point; The unit vector from the receiving station to the target point;

[0101] The formula for calculating ground azimuth resolution is:

[0102] ;

[0103] In the formula, ρ a Indicates the ground azimuth resolution; λ The radar carrier wavelength; T a P represents the time for synthesizing the pore size. T and P R They are respectively by and The determined projection matrix; P g Represents the ground projection matrix; Represents the velocity vector of the receiving station; Represents the velocity vector of the launching station; R T This indicates the distance between the launch station and the target point; R R This indicates the distance between the receiving station and the target point;

[0104] The formula for calculating the angle is:

[0105] ;

[0106] In the formula, α Indicates the angle to be distinguished; Represents a distance-to-unit vector; Represents the azimuth unit vector;

[0107] The formula for calculating the area of ​​a distinguishing unit is:

[0108] ;

[0109] In the formula, S This indicates the area of ​​the resolvable unit.

[0110] (II) Besides spatial resolution, imaging signal-to-noise ratio is also an important indicator for evaluating the imaging quality of a SAR system. Assume the transmitted signal power of the multi-base SAR system is... P t The transmit antenna gain is G t The receiving antenna gain is G r The echo power received by the UAV swarm SAR system is:

[0111] ;

[0112] In the formula, P r Indicates echo power; P t This indicates the transmitted signal power of the group multi-base SAR system; G t For the transmit antenna gain, G r For receiving antenna gain; λ σ is the radar carrier wavelength; s The bistatic radar cross section of the target; R T This indicates the distance between the launch station and the target point. R R This indicates the distance between the receiving station and the target point.

[0113] Let Boltzmann's constant be... k The temperature at which the noise is received is T 0, the noise figure of the receiving station is F 0, the system's loss factor is L s Then, the expression for the echo signal-to-noise ratio of the swarm UAV SAR system can be obtained as follows:

[0114] ;

[0115] In the formula, SNR Indicates the echo signal-to-noise ratio; P av The average power of the transmitted signal; G t For the transmit antenna gain, G r For receiving antenna gain; λ σ is the radar carrier wavelength; s The bistatic radar cross section of the target; T a The time for synthesizing the aperture; R T This indicates the distance between the launch station and the target point; RR This indicates the distance between the receiving station and the target point.

[0116] To quantify the critical threshold between noise and the minimum detectable backscattered signal in SAR images, this embodiment provides a calculation expression for the Noise-Equivalent Sigma-Zero (NESZ). NESZ is a core performance indicator of a Synthetic Aperture Radar (SAR) system. When the target's backscattering coefficient equals the NESZ, the power of the target's scattered signal is equal to the noise power of the radar system, at which point the target can just be identified from the noisy background. Specifically, the NESZ calculation expression is as follows:

[0117] ;

[0118] As can be seen from the above formula, when the launch station configuration parameters and system parameters are fixed, the imaging signal-to-noise ratio performance of the UAV swarm SAR system is mainly determined by the distance from the receiving station to the center point of the scene. R R Decide.

[0119] S103. The initial population is generated by using the Cubic chaotic mapping method and combining it with the objective function. The decision variables are mapped to gene fragments of individuals in the population. The initial population is made to exhibit random distribution characteristics by using chaotic operators to obtain the offspring population.

[0120] An initial population is generated using the Cubic chaotic mapping method, mapping decision variables to gene fragments of individuals in the population. Chaotic operators are then used to make the population exhibit random distribution characteristics. In this embodiment, the decision variable g = (Δ...) x ,△ y ,△z,△ θ vRn ,△ θ vT ,△ θ TR(n-1) The system uses binary encoding, with chromosome length L and population size C. The real value of a gene segment on a chromosome within the population is represented by... It means that, among them, i Indicates chromosome number within the population. j Representing the location of gene segments in a chromosome, the population expression for the Cubic chaotic mapping is:

[0121] ;

[0122] In the formula, i Indicates chromosome number within the population. j Indicates the location of gene segments within a chromosome; ρ For control parameters, For a chaotic operator, when ρ The chaotic variables generated when the value is 2.595 have better traversability.

[0123] S104. Based on the associated chromosome strategy, first cross the core decision variables, and then cross the auxiliary decision variables by extending the associated chromosome strategy; then use an adaptive mutation mechanism to update the offspring population to ensure that the association constraints between decision variables are not broken.

[0124] Specifically, the decision variables include core decision variables and auxiliary decision variables. The core decision variables include the UAV swarm size and the relative motion parameters between the satellite and the UAVs; the auxiliary decision variables include the orbital phase factor and the cross-platform synchronization threshold. Specifically, the core decision variables, such as the UAV swarm size and the relative motion parameters between the satellite and the UAVs, are first cross-referenced using the Linked Chromosome Strategy (LCS). Then, the auxiliary variables, such as the orbital phase factor and the cross-platform synchronization threshold, are cross-referenced using the Extended Linked Chromosome Strategy (ELCS). Finally, an adaptive mutation mechanism is used to update the offspring population of the Linked Chromosome Group (LCG) to ensure that the association constraints between the decision variables are not violated.

[0125] like Figure 3 As shown, in the decision variable g=(△ x ,△ y ,△z,△ θ vRn ,△ θ vT ,△ θ TR(n-1) In ) , △ x ,△ y △z is related. However, in the mutation process of traditional genetic algorithms, the direction of mutation is random and uncertain. This not only easily leads to the violation of constraints but also causes the failure of cooperation between variables. Furthermore, △ x ,△ y , △z are mutually complementary, if △ x △ changes with mutation y It hasn't changed; △ at this point... y For △ x It is meaningless to say that Δ is related to chromosomes. Therefore, this paper proposes the concept of associated chromosomes, which are relevant to different Δ chromosomes. x Pre-construct a matching △ y △z allows for a range of variations, and restricts variations of associated genes within this range. Specifically, △ xThe main gene mutates first, and then extends to its corresponding associated chromosome; subsequently, △ y The mutation occurs only within the extended associated chromosome, and the same applies to Δz, thus ensuring that Δ x ,△ y The collaborative update of Δz satisfies geometric constraints. In this process, the offspring chromosome is defined as the encoding result of the new individual obtained after one associated mutation. It consists of the mutated major gene Δz. x and the △ generated under the constraint of associated chromosomes y △z is combined with the other decision variables to form the complete decision variable g that satisfies the constraints.

[0126] like Figure 4 As shown, the crossover process first occurs on chromosome Δ x In the process, after the intersection △ x Associating chromosomes and expanding their corresponding triangles y Together with △z, an intermediate chromosome is formed, and then based on this, △ y Crossing with Δz according to the crossover probability, a new chromosome is eventually obtained.

[0127] S105. Perform non-dominated sorting on the updated offspring population and calculate the crowding degree of individuals. Based on the non-dominated sorting results and the crowding degree calculation results, construct an approximate Pareto front for the multi-objective problem and filter to form a candidate configuration dataset. Combine the actual application scenario requirements to select the optimal configuration from the configuration dataset and verify whether the imaging effect of the UAV swarm SAR under the optimal configuration meets the system evaluation criteria to output the final configuration scheme.

[0128] From the approximate Pareto front, the optimal configuration is selected based on the requirements of the actual application scenario. This configuration is compared with the traditional static configuration method to verify whether the imaging resolution and signal-to-noise ratio of the UAV swarm SAR under this configuration meet the system evaluation criteria. The final configuration scheme is output to provide support for the performance evaluation of SAR system and the improvement and optimization of real-time imaging processing hardware system.

[0129] This invention discloses a method for optimizing the SAR configuration of UAV swarms based on low-Earth orbit communication satellites. It innovatively integrates the second-generation Non-dominated Sorting Genetic Algorithm II (NSGA-II) with wavenumber spectrum geometric constraints. Through Cubic chaotic mapping initialization of the population, associated chromosome strategies, and adaptive mutation mechanisms, it iterative optimization is performed to construct a multi-objective collaborative configuration optimization architecture. Specifically, NSGA-II is deeply integrated with wavenumber spectrum geometric constraints and engineering feasibility constraints. The configuration design is treated as a multi-constraint collaborative optimization problem in a high-dynamic scenario using a multi-objective optimization framework. The algorithm is iteratively optimized by establishing an optimization method that alternates between Cubic chaotic mapping initialization, associated chromosome crossover mutation, and non-dominated sorting selection. Finally, by inputting low-Earth orbit satellite parameters and UAV swarm parameters, the optimal configuration scheme is obtained, achieving SAR configuration optimization for UAV swarms in high-dynamic scenarios. This innovative combination not only achieves precise adaptation of the UAV swarm configuration to the high dynamic observation geometry of low-orbit communication satellites and UAVs, but also achieves an optimal balance between imaging performance and engineering feasibility. The resulting configuration scheme has high resolution, strong robustness and deployment feasibility, meeting the real-time needs of complex scenarios such as marine monitoring and emergency rescue.

[0130] The following field tests further verify the stability and adaptability of the configuration, providing support for the performance optimization and engineering implementation of the LEO-COS UAV swarm SAR system. Specifically:

[0131] The technical effects of the present invention will be described in detail below with reference to simulation experiments.

[0132] The simulation parameters used in this invention are shown in Table 1.

[0133] Table 1: Simulation Parameter Settings

[0134]

[0135] Specifically: Ku band, carrier frequency 12.5 GHz, bandwidth 250 MHz, sampling frequency 300 MHz, pulse repetition frequency 7000 Hz, satellite platform flying along a curve, flight altitude approximately 330 km, center of action distance approximately 1240 km, satellite platform speed 3000 m / s. The set imaging scene size is approximately 2000 m × 2000 m (X direction × Y direction), pixel array is 320 × 320 (X direction × Y direction), corresponding SAR complex image as follows. Figure 4 As shown in Table 1. Based on the radar parameters and... Figure 5 The scene scattering coefficients are shown, where, Figure 5The scene size is approximately 320m × 320m (X-direction × Y-direction), and the pixel array is 320 × 320 (X-direction × Y-direction). The echo signal simulation was performed using the method of this invention. The simulation conditions were a 64-bit Windows 11 system with MATLAB, and a PC hardware platform of i5 14500 CPU and 16GB of memory. Using the method of this invention, the average convergence generation for the entire unmanned structure optimization was 63, and the standard deviation of the optimal solution was 0.001. In contrast, under the same test environment and platform, the average convergence generation for optimization using a genetic algorithm was 311, and the standard deviation of the optimal solution was 0.135.

[0136] The comparison shows that the SAR imaging results of UAV swarms under different configuration optimization methods are as follows: Figure 6 As shown, where Figure 6 (a) is a SAR image obtained using a single platform. The image entropy value is 10.0392, and the image is noisy and the scene details are blurred. Figure 6 (b) is a SAR image obtained using the cross-shaped configuration method. The image entropy value is 7.1298. The noise is reduced, but the scene details are still obviously blurred. Figure 6 Image (c) shows the imaging results of the UAV swarm SAR configuration optimization method based on low-Earth orbit communication satellites according to this invention. The image entropy value is 5.8958, the image details are clearly discernible, and scene features such as buildings and terrain textures are intuitively presented, with noise effectively suppressed. From the comparison of imaging quality, the imaging results of the method of this invention are significantly better than traditional static configuration methods and insufficiently constrained optimization methods in terms of detail preservation and noise suppression. This proves that the present invention, through the deep coupling of non-dominated sorting genetic algorithm with wavenumber spectrum geometric constraints and engineering constraints, can effectively solve the problems of insufficient dynamic adaptability and poor multi-constraint synergy of traditional configurations. The generated configuration scheme enables UAV swarm SAR to obtain higher resolution and better imaging quality in the highly dynamic collaborative scenario of "constellation-swarm", fully verifying the feasibility and effectiveness of the method.

[0137] Because this invention combines multi-objective optimization algorithms with wavenumber spectrum constraint analysis, leveraging the algorithm's global optimization advantages in highly dynamic coupled scenarios to generate configuration schemes, it can effectively adapt to highly dynamic collaborative scenarios of low-Earth orbit communication satellites and unmanned aerial vehicles (UAVs). Simultaneously, it improves the performance balance and engineering feasibility of the configuration, solving the problems of dynamic mismatch and multi-constraint collaboration in existing technologies. It is applicable to various mission parameters and complex application scenarios, and has broad application prospects. Simulation tests also verified the feasibility and effectiveness of the proposed method.

[0138] In summary, the UAV swarm SAR configuration optimization method based on low-Earth orbit communication satellites in the above embodiments of the present invention deeply integrates non-dominated sorting genetic algorithm with wavenumber spectrum geometric constraints, and iteratively optimizes the algorithm by establishing an optimization method that alternates between Cubic chaotic mapping initialization, associated chromosome crossover mutation and non-dominated sorting screening. Finally, by inputting low-Earth orbit satellite parameters and UAV swarm parameters, the corresponding optimal configuration scheme is obtained, realizing UAV swarm SAR configuration optimization in high dynamic scenarios. This effectively solves the dynamic mismatch problem of traditional static configurations, enabling UAV swarms to maintain high resolution and low sidelobe imaging performance even under complex observation geometry.

[0139] Example 2

[0140] The second embodiment of the present invention provides a SAR configuration optimization system for unmanned aerial vehicle swarms based on low-Earth orbit communication satellites, the system comprising:

[0141] The acquisition module is used to acquire parameters of low-Earth orbit communication satellites and UAV swarms to construct wavenumber spectrum geometric constraints and design decision variables; substitute the decision variables into the calculation to construct the objective function; the decision variables include core decision variables and auxiliary decision variables; wherein, the core decision variables include the UAV swarm size and the relative motion parameters between the satellites and UAVs; the auxiliary decision variables include the orbital phase factor and the cross-platform synchronization threshold;

[0142] The mapping module is used to generate an initial population by using the Cubic chaotic mapping method and combining it with the objective function. It maps decision variables to gene fragments of individuals in the population and uses chaotic operators to make the initial population exhibit random distribution characteristics in order to obtain the offspring population.

[0143] The update module is used to first cross-reference the core decision variables according to the associated chromosome strategy, and then cross-reference the auxiliary decision variables by extending the associated chromosome strategy; then, an adaptive mutation mechanism is used to update the offspring population of the associated chromosome set to ensure that the association constraints between decision variables are not broken.

[0144] The optimization module is used to perform non-dominated sorting on the updated offspring population and calculate the crowding degree of individuals. Based on the non-dominated sorting results and the crowding degree calculation results, an approximate Pareto front for the multi-objective problem is constructed, and a candidate configuration dataset is formed by screening. The optimal configuration is selected from the configuration dataset in combination with the actual application scenario requirements, and the imaging effect of the UAV swarm SAR under the optimal configuration is verified to meet the system evaluation criteria, so as to output the final configuration scheme.

[0145] In summary, the UAV swarm SAR configuration optimization system based on low-Earth orbit communication satellites in the above embodiments of the present invention deeply integrates non-dominated sorting genetic algorithm with wavenumber spectrum geometric constraints, and iteratively optimizes the algorithm by establishing an optimization method that alternates between Cubic chaotic mapping initialization, associated chromosome crossover mutation and non-dominated sorting screening. Finally, by inputting low-Earth orbit satellite parameters and UAV swarm parameters, the corresponding optimal configuration scheme is obtained, realizing UAV swarm SAR configuration optimization in high dynamic scenarios. This effectively solves the dynamic mismatch problem of traditional static configurations, enabling UAV swarms to maintain high resolution and low sidelobe imaging performance even under complex observation geometry.

[0146] Furthermore, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the methods described above.

[0147] Furthermore, embodiments of the present invention also propose a data processing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the methods described above.

[0148] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0149] More specific examples (a non-exhaustive list) of computer-readable media include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which programs can be printed, because programs can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0150] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0151] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0152] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for optimizing the SAR configuration of unmanned aerial vehicle (UAV) swarms based on low-Earth orbit communication satellites, characterized in that, include: Parameters of low-Earth orbit communication satellites and UAV swarms are obtained to construct wavenumber spectrum geometric constraints and design decision variables; Substitute the decision variables into the calculation to construct the objective function; The decision variables include core decision variables and auxiliary decision variables; among them, the core decision variables include the size of the UAV swarm and the relative motion parameters between the satellite and the UAV; the auxiliary decision variables include the orbital phase factor and the cross-platform synchronization threshold. The Cubic chaotic mapping method is used in conjunction with the objective function to generate an initial population. The decision variables are mapped to gene fragments of individuals in the population, and the initial population is made to exhibit random distribution characteristics through chaotic operators to obtain the offspring population. The core decision variables are first cross-referenced using the associated chromosome strategy, and the auxiliary decision variables are cross-referenced by extending the associated chromosome strategy. Then, an adaptive mutation mechanism is used to update the offspring population of the associated chromosome set to ensure that the association constraints between the decision variables are not broken. The updated offspring population is sorted non-dominated and the crowding degree of individuals is calculated. Based on the non-dominated sorting results and the crowding degree calculation results, an approximate Pareto front for the multi-objective problem is constructed and a candidate configuration dataset is formed. The optimal configuration is selected from the configuration dataset in combination with the actual application scenario requirements, and the imaging effect of the UAV swarm SAR under the optimal configuration is verified to meet the system evaluation criteria in order to output the final configuration scheme. In the step of obtaining parameters of low-Earth orbit communication satellites and UAV swarms to construct wavenumber spectrum geometric constraints and design decision variables, the expression for the geometric constraints is: ； In the formula, The azimuth wavenumber vector representing the overall distributed SAR system; The wavenumber spectrum of the distributed SAR system at the receiver n The range of the upward projection of a distance of -1; γ max This represents the maximum permissible wavenumber spectral gap factor; Indicates receiver n azimuth wavenumber vector; Indicates receiver azimuth wavenumber vector magnitude; Indicates receiver n -1 azimuth wavenumber vector; Indicates receiver -1 is the azimuth wavenumber vector magnitude.

2. The method for optimizing the SAR configuration of unmanned aerial vehicle swarms based on low-Earth orbit communication satellites according to claim 1, characterized in that, In the step of substituting decision variables into the calculation to construct the objective function, the objective function includes the imaging resolution and echo signal-to-noise ratio of the UAV swarm SAR system. The imaging resolution of the UAV swarm SAR system includes ground range resolution, ground azimuth resolution, resolution angle, and resolution cell area. The formula for calculating the ground range resolution is: ； In the formula, ρ r Indicates the ground distance resolution; c Indicates the population size; B r It is the bandwidth of the transmitted signal; P g Represents the ground projection matrix; The unit vector from the launch station to the target point; The unit vector from the receiving station to the target point; The formula for calculating ground azimuth resolution is: ； In the formula, ρ a Indicates the ground azimuth resolution; λ The radar carrier wavelength; T a P represents the time for synthesizing the pore size. T and P R They are respectively by and The determined projection matrix; P g Represents the ground projection matrix; Represents the velocity vector of the receiving station; Represents the velocity vector of the launching station; R T This indicates the distance between the launch station and the target point; R R This indicates the distance between the receiving station and the target point; The formula for calculating the angle is: ； In the formula, α Indicates the angle to be distinguished; Represents a distance-to-unit vector; Represents the azimuth unit vector; The formula for calculating the area of ​​a distinguishing unit is: ； In the formula, S This indicates the area of ​​the resolvable unit.

3. The method for optimizing the SAR configuration of unmanned aerial vehicle swarms based on low-Earth orbit communication satellites according to claim 2, characterized in that, The formula for calculating the echo signal-to-noise ratio is: ； In the formula, SNR Indicates the echo signal-to-noise ratio; P av The average power of the transmitted signal; G t For the transmit antenna gain, G r For receiving antenna gain; λ σ is the radar carrier wavelength; s The bistatic radar cross section of the target; T a The time for synthesizing the aperture; R T This indicates the distance between the launch station and the target point; R R This indicates the distance between the receiving station and the target point; k Boltzmann's constant, T 0 represents the temperature at which noise is received; F 0 represents the noise figure of the receiving station; L s The system's loss factor; The echo power received by the UAV swarm SAR system is: ； In the formula, P r Indicates echo power; P t This indicates the transmitted signal power of the multi-base SAR system.

4. The method for optimizing the SAR configuration of unmanned aerial vehicle swarms based on low-Earth orbit communication satellites according to claim 1, characterized in that, In the steps of generating an initial population using the Cubic chaotic mapping method and combining it with an objective function, mapping decision variables to gene fragments of individuals in the population, and using chaotic operators to make the initial population exhibit random distribution characteristics to obtain the offspring population, the decision variables are encoded using binary encoding, the chromosome length is L, the population size is C, and the real value of a gene fragment of a certain chromosome in the population is represented by... It means that, among them, i Indicates chromosome number within a population. j Representing the location of gene segments in a chromosome, the population expression for the Cubic chaotic mapping is: ； In the formula, ρ For control parameters, For chaos operators, i Indicates chromosome number within a population. j It indicates the location of a gene segment in a chromosome.

5. A SAR configuration optimization system for unmanned aerial vehicle swarms based on low-Earth orbit communication satellites, characterized in that, The system includes: The acquisition module is used to acquire parameters of low-Earth orbit communication satellites and UAV swarms to construct wavenumber spectrum geometric constraints and design decision variables; substitute the decision variables into the calculation to construct the objective function; the decision variables include core decision variables and auxiliary decision variables; wherein, the core decision variables include the UAV swarm size and the relative motion parameters between the satellites and UAVs; the auxiliary decision variables include the orbital phase factor and the cross-platform synchronization threshold; The mapping module is used to generate an initial population by using the Cubic chaotic mapping method and combining it with the objective function. It maps decision variables to gene fragments of individuals in the population and uses chaotic operators to make the initial population exhibit random distribution characteristics in order to obtain the offspring population. The update module is used to first cross-reference the core decision variables according to the associated chromosome strategy, and then cross-reference the auxiliary decision variables by extending the associated chromosome strategy; then, an adaptive mutation mechanism is used to update the offspring population of the associated chromosome set to ensure that the association constraints between decision variables are not broken. The optimization module is used to perform non-dominated sorting on the updated offspring population and calculate the crowding degree of individuals. Based on the non-dominated sorting results and the crowding degree calculation results, an approximate Pareto front for the multi-objective problem is constructed, and a candidate configuration dataset is formed by screening. The optimal configuration is selected from the configuration dataset in combination with the actual application scenario requirements, and the imaging effect of the UAV swarm SAR under the optimal configuration is verified to meet the system evaluation criteria in order to output the final configuration scheme. In the step of obtaining parameters of low-Earth orbit communication satellites and UAV swarms to construct wavenumber spectrum geometric constraints and design decision variables, the expression for the geometric constraints is: ； In the formula, The azimuth wavenumber vector representing the overall distributed SAR system; The wavenumber spectrum of the distributed SAR system at the receiver n The range of the upward projection of a distance of -1; γ max This represents the maximum permissible wavenumber spectral gap factor; Indicates receiver n azimuth wavenumber vector; Indicates receiver azimuth wavenumber vector magnitude; Indicates receiver n -1 azimuth wavenumber vector; Indicates receiver -1 is the azimuth wavenumber vector magnitude.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the SAR configuration optimization method for unmanned aerial vehicle swarms based on any one of claims 1-4.

7. A data processing apparatus, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the SAR configuration optimization method for unmanned aerial vehicle swarms based on low-orbit communication satellites as described in any one of claims 1-4.

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