Small snapshot direction finding method and system for marine target by unmanned aerial vehicle group

Abstract

The invention discloses a small-snapshot direction finding method and system for a marine target by an unmanned aerial vehicle group, relates to the field of array signal processing, and aims to solve the problems that an existing minimum redundant array is insufficient in direction finding precision and robustness under a small-snapshot condition and is easily influenced by model errors. The method is technically characterized by comprising the following steps: step 1, establishing a small snapshot signal receiving model of a minimum redundant array of an unmanned aerial vehicle group for a marine target, and establishing a maximum likelihood estimation target function; 2, initializing a turtledove population; 3, constructing a fitness function based on the established maximum likelihood estimation target function, calculating the fitness value of the turtledove group, and determining a local optimal position and a global optimal position; 4, updating the turtledove population; 5, calculating the fitness of the newly generated position of each turtledove individual, updating the local optimal position and the global optimal position, screening elite individuals, and carrying out iterative updating on the belief space; and step 6, completing iteration to obtain an optimal solution of the incoming wave direction of the marine target.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically, to a method and system for finding the direction of a maritime target using a swarm of unmanned aerial vehicles (UAVs). Background Technology

[0002] Direction finding, also known as direction of arrival (DOA) estimation, is an important component of array signal processing. Traditional high-resolution direction finding methods typically utilize second-order statistics for modeling and analysis, exhibiting good estimation performance under Gaussian noise. However, the noise characteristics in real-world environments are complex and variable, making traditional direction finding methods prone to performance degradation or even failure.

[0003] Most existing direction-finding methods are based on the Uniform Linear Array (ULA) model, whose degrees of freedom are limited by the number of physical array elements. When the number of signal sources exceeds the number of array elements, effective direction finding becomes difficult. Minimum Redundancy Array (MRA), as a special type of non-uniform linear array structure, is characterized by the completely continuous expansion of its Kirchhoff difference set. By optimizing element positions, it can achieve a larger equivalent aperture and higher degrees of freedom with fewer physical array elements. However, its non-uniformity introduces higher sidelobes and grating lobes, leading to ambiguity in spatial spectrum estimation. Furthermore, the complex mutual coupling effects between array elements make the direct application of traditional algorithms less than ideal. Especially under small snapshot conditions, the estimation error of the sample covariance matrix is ​​further amplified, resulting in deteriorated direction-finding performance.

[0004] A search of existing technical literature revealed that Zhang Liqiang et al., in their paper "DOA Estimation of Minimum Redundancy Linear Array" published in Firepower and Command Control (2012, 37(10):10-13), discussed the direction-finding performance of minimum redundancy linear arrays using the MUSIC algorithm. This method effectively expands the array aperture by reducing array redundancy. However, this method was verified under ideal Gaussian noise conditions and did not consider the influence of actual noise environments. Furthermore, the simulation snapshot count was high, which could not reflect the performance of the algorithm under small snapshot conditions. Zhang Xiuqing et al., in their paper "Joint Correction Robust Beamforming Algorithm Based on Small Snap Scenarios" published in Radio Engineering (2024, 54(8):1900-1907), proposed a new method. This method improves the robustness of beamforming under small snapshot conditions by jointly performing covariance matrix reconstruction and steering vector optimization. This algorithm uses the uncertainty set to solve the interference steering vector and uses power spectrum integration to achieve covariance matrix reconstruction. However, it still relies on second-order statistics and does not consider special array structures such as minimum redundancy arrays.

[0005] In summary, while existing direction-finding methods have achieved certain results, they cannot achieve high-precision direction finding of maritime targets by UAV swarms under minimum redundancy array architecture, small snapshot conditions, and multi-coherent source environments. Summary of the Invention

[0006] The technical problem to be solved by this invention is:

[0007] Existing minimum redundancy arrays suffer from insufficient direction finding accuracy and robustness under small snapshot conditions and are susceptible to model errors.

[0008] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0009] This invention provides a method for quick-image direction finding of maritime targets by a swarm of unmanned aerial vehicles (UAVs), comprising the following steps:

[0010] Step 1: Establish a model for receiving small snapshots of maritime targets using a minimum redundancy array of UAV swarms; construct a fractional low-order covariance matrix using the small snapshot data received by the minimum redundancy array composed of multiple UAV swarms, and establish a maximum likelihood estimation objective function.

[0011] Step 2: Set the dove flock types as basic dove flock, reverse dove flock, and cultural dove flock, initialize the dove flock and set the relevant parameters;

[0012] Step 3: Construct a fitness function based on the established maximum likelihood estimation objective function, calculate the fitness value of the dove flock, and determine the local optimal position and the global optimal position;

[0013] Step 4: Perform updates for the three population types: basic dove flock, reverse dove flock, and cultural dove flock, respectively;

[0014] Step 5: Calculate the newly generated position fitness for each individual dove, update the local optimal position and the global optimal position, select elite individuals with better fitness in the group through the acceptance function, and iteratively update the belief space according to the cultural evolution mechanism;

[0015] Step Six: Determine if the preset maximum number of iterations has been reached. If the preset maximum number of iterations has not been reached, then set the iteration count... If not, return to step four; otherwise, output the global optimal position of the dove flock as the optimal solution for the direction of incoming waves from the sea target.

[0016] Furthermore, step one includes the following process:

[0017] Build a A model for receiving signals from maritime targets using a minimum redundancy array of UAVs, consisting of one array element per UAV. The drones form a special array group, and the array element positions are set as follows: With half wavelength As a unit, Indicates the first The relative positions of each array element with respect to the reference array element satisfy the following conditions: , ; Array element position difference set , The minimum distance between two array elements. When there is A far-field narrowband signal from the sea surface one direction When incident on the minimum redundancy array of the UAV swarm, the array is at the... The sampling data received in the second snapshot is ,in express Data volume received by the 3D array express 3D space signal vector, express Additive noise vector express 3D steering vector matrix; corresponding direction of arrival angle is The steering vector of the incident signal is , Under the condition of small snapshots, only a limited number of time sampling points can be obtained. The number of snapshots is denoted as... And meet the conditions , The sub-snapshot receiver matrix is ​​represented as follows: ,in Represents the source signal matrix. Represents the impulse noise matrix;

[0018] use The fractional low-order covariance matrix is ​​constructed from the small snapshot data received by the minimum redundancy array consisting of a swarm of drones, denoted as follows: , for 3D matrix , , No. Line 1 Column elements are , , , The first normalized form of the infinite norm The data from the second quick snapshot dimension, These are the parameters of a low-order matrix; ,in , ;

[0019] The infinite norm weighted fractional matrix of the minimum redundancy array Extended to an infinite norm weighted fractional low-order matrix of a virtual uniform array , ,in , , To represent the number of elements in the expanded virtual uniform array. , , This indicates the calculation of mathematical expectation. , The guiding matrix for the virtual uniform array is: The direction of arrival is The virtual steering vector of the incident signal is ;

[0020] The objective function for maximizing the maximum likelihood estimation is obtained based on the low-order matrix of the infinite norm weighted fraction and the steering vector matrix. , , This represents the trace function of a matrix. This represents the guidance matrix.

[0021] Furthermore, step two includes the following process:

[0022] Set the size of the dove flock to be ,exist Three types of dove flocks were generated in the 3D search space: basic dove flocks, reverse dove flocks, and cultural dove flocks, with the following numbers respectively. , and ,and ;No. A flock of doves has Only a turtledove, The maximum number of iterations is ;No. During the nth iteration, the 1st The first flock of doves The location of only the dove Its speed The cultural doves, following the rules of the cultural algorithm, generate an initial belief space and initialize normative knowledge, defining... Indicates the first The lower bound of normative knowledge. Indicates the first The upper bound of normative knowledge, Indicates the first The generation Lower bound of normative knowledge The corresponding evaluation value, Indicates the first The generation Upper bound of normative knowledge The corresponding evaluation value, and Take the corresponding boundary values ​​of the domain of the variable respectively. and In the first generation, all were initialized to... .

[0023] Furthermore, step three includes the following process:

[0024] No. During the nth iteration, the 1st The first flock of doves The location of only the dove The fitness function is Based on fitness values, determine each individual up to the [number]th [level]. Substitute local optimal position The entire group until the first The global optimal position is as follows: .

[0025] Furthermore, step four includes the following process:

[0026] In the basic dove flock, the first The turtledove updates its velocity and position according to the basic operators, and the update equation is:

[0027]

[0028]

[0029] in , Indicates map and compass factors, This represents the chaotic random numbers generated by the chaotic equation. Update according to the following rules:

[0030]

[0031] in A uniformly random number between [0,1];

[0032] In the reverse-flying dove flock, the first Individual doves update their own position by jumping backwards, based on the probability of the jump. The formula for determining whether to perform a population jump for the updated individual is:

[0033] ,

[0034] In the formula It is a uniformly random number between [0,1]. , ;

[0035] The cultural dove flock generates new dove individuals based on an influence function. The influence functions for position, step size, and direction of movement are adjusted jointly based on the normative knowledge of the cultural mechanism and the local optimum. The update formula is:

[0036]

[0037] in This represents the scaling factor for the Cultural Doves flock. This represents a random number that follows a standard normal distribution.

[0038] Furthermore, step five includes the following process:

[0039] No. During the nth iteration, the 1st The first flock of doves The location of only the dove The fitness function is Based on fitness values, determine each individual up to the [number]th [level]. Replace the local optimum position to determine the entire population up to the th... The global optimal position is determined by substitution.

[0040] Subsequently, an elite individual with better fitness from the population is selected as the knowledge source through an acceptance function. The position information of the elite individual is used to update the normative knowledge base within the belief space. The local optimal positions of the doves that influence the update of the lower bound and upper bound of the normative function are respectively... and ;

[0041] The specific update equations for the parameters related to the normative knowledge are as follows:

[0042]

[0043]

[0044]

[0045] .

[0046] This invention provides a small-scale, quick-photo direction finding system for unmanned aerial vehicle (UAV) swarms targeting maritime targets. This system has a program module corresponding to the steps of any of the above-described technical solutions, and executes the steps in the above-described small-scale, quick-photo direction finding method for unmanned aerial vehicle (UAV) swarms targeting maritime targets during operation.

[0047] The present invention provides a computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps of the method for finding the direction of a maritime target by a swarm of unmanned aerial vehicles (UAVs) as described in any of the above technical solutions.

[0048] Compared with the prior art, the beneficial effects of the present invention are:

[0049] This invention effectively solves the problem of traditional optimization algorithms easily getting trapped in local optima when dealing with high-dimensional nonlinear maximum likelihood functions by co-evolutionizing the belief space and the population space. Utilizing the extended aperture and degrees of freedom provided by the minimum redundancy array, and through a structurally adapted steering vector generation mechanism, it effectively overcomes the inherent grating lobe and mutual coupling effects of non-uniform arrays, significantly improving array utilization efficiency and direction-finding performance, and achieving high-precision direction finding even with small snapshot data. The adaptive optimization characteristics of the "cultural dove" mechanism can also effectively cope with uncertainties in various practical application scenarios, providing a reliable direction-of-arrival estimation solution for radar, sonar, and other applications in maritime and air environments. Simulation results show that the direction-finding method designed in this invention exhibits superior direction-finding performance and robustness in complex environments such as small snapshots, low signal-to-noise ratios, and multi-coherent sources. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method for quick-snap direction finding of a maritime target by a swarm of drones in an embodiment of the present invention;

[0051] Figure 2 The figure shows the fitness convergence curves and DOA estimation results of the three swarm intelligence optimization algorithms in the embodiments of the present invention.

[0052] Figure 3 This is a graph showing the relationship between DOA estimation performance and GSNR of the cultural dove mechanism in this embodiment of the invention.

[0053] Figure 4 This is a graph showing the relationship between DOA estimation performance and feature index in an embodiment of the present invention.

[0054] Figure 5 This is a graph showing the relationship between the direction-finding performance of the cultural dove mechanism for coherent sources and the number of snapshots in an embodiment of the present invention. Detailed Implementation

[0055] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are merely some, not all, of the embodiments or examples of the present invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0057] Combination Figure 1 As shown, this invention provides a method for quick-snap direction finding of maritime targets by a swarm of unmanned aerial vehicles (UAVs), comprising the following steps:

[0058] Step 1: Establish a model for receiving signals from maritime targets using a minimum redundancy array of UAV swarms; utilize... The fractional low-order covariance matrix is ​​constructed from the small snapshot data received by the minimum redundancy array consisting of a swarm of drones, and the maximum likelihood estimation objective function is established.

[0059] A minimum redundancy array is a non-uniform linear array that maximizes the array's degrees of freedom by optimizing the distribution of its elements. Constructing a minimum redundancy array... A minimum redundancy array consisting of 1000 elements, with 1 element placed for each UAV. The drones form a special array group, and the array element positions are set as follows: With half wavelength As a unit, Indicates the first The relative positions of each array element with respect to the reference array element satisfy the following conditions: , Array element position difference set It should be as continuous as possible and with minimal redundancy. The minimum distance between two array elements. When there is A far-field narrowband signal from the sea surface one direction When incident on the minimum redundancy array of the UAV swarm, the array is at the... The sampling data received in the second snapshot is ,in express Data volume received by the 3D array express 3D space signal vector, express Additive noise vector express 3D steering vector matrix. The corresponding direction of arrival angle is... The steering vector of the incident signal is , Under the condition of small snapshots, only a limited number of time sampling points can be obtained. The number of snapshots is denoted as... And meet the conditions , The sub-snapshot receiver matrix is ​​represented as follows: ,in Represents the source signal matrix. This represents the impulse noise matrix.

[0060] The infinite norm weighted fractional low-order matrix representation of a minimum redundancy array is as follows: , for 3D matrix , , No. Line 1 Column elements are , , , The first normalized form of the infinite norm The data from the second quick snapshot dimension, These are the parameters of a low-order matrix; ,in , .

[0061] The infinite norm weighted fractional matrix of the minimum redundancy array Extended to an infinite norm weighted fractional low-order matrix of a virtual uniform array Then the low-order matrix of the infinite norm weighted fraction is expressed as: ,in , , To represent the number of elements in the expanded virtual uniform array. , , This indicates the calculation of mathematical expectation. , The guiding matrix for the virtual uniform array is: The direction of arrival is The virtual steering vector of the incident signal is , .

[0062] The objective function for maximizing the maximum likelihood estimation is obtained based on the low-order matrix of the infinite norm weighted fraction and the steering vector matrix. , , This represents the trace function of a matrix. Represents the guidance matrix. This represents a low-order matrix of weighted fractions with infinite norm.

[0063] Step 2: Set the dove flock types as basic dove flock, reverse dove flock, and cultural dove flock, initialize the dove flock and set the relevant parameters.

[0064] Set the size of the dove flock to be ,exist Three types of dove flocks were generated in the 3D search space: basic dove flocks, reverse dove flocks, and cultural dove flocks, with the following numbers respectively. , and ,and . No. A flock of doves has Only a turtledove, The maximum number of iterations is The number of iterations is marked as an integer. . No. During the nth iteration, the 1st The first flock of doves The location of only the dove Its speed The cultural doves, following the rules of the cultural algorithm, generate an initial belief space and initialize normative knowledge. Indicates the first The lower bound of normative knowledge. Indicates the first The upper bound of normative knowledge, Indicates the first The generation Lower bound of normative knowledge The corresponding evaluation value, Indicates the first The generation Upper bound of normative knowledge The corresponding evaluation value, and Take the corresponding boundary values ​​of the domain of the variable respectively. and In the first generation, all were initialized to... , .

[0065] Step 3: Construct a fitness function based on the established maximum likelihood estimation objective function, calculate the fitness value of the dove flock, and determine the local optimal position and the global optimal position.

[0066] No. During the nth iteration, the 1st The first flock of doves The location of only the dove The fitness function is Based on fitness values, determine each individual up to the [number missing]. Substitute local optimal position , The entire group until the... The global optimal position is as follows: .

[0067] Step 4: Implement different renewal strategies for the three types of populations: basic dove flocks, reverse dove flocks, and cultural dove flocks.

[0068] In the basic dove flock, the first The turtledove updates its velocity and position according to the basic operators, and the update equation is:

[0069]

[0070]

[0071] in , , Indicates map and compass factors, This represents the chaotic random numbers generated by the chaotic equation. Update according to the following rules:

[0072]

[0073] in It is a uniform random number between [0,1].

[0074] In the reverse-flying dove flock, the first Individual doves update their own position by performing a reverse jump; the jump probability is used as... This indicates that the decision to perform a population jump on the updated individual is based on the following update formula:

[0075] ,

[0076] In the formula It is a uniformly random number between [0,1]. , .

[0077] The cultural dove flock generates new dove individuals based on an influence function. The influence functions for position variables, step size, and direction of movement are adjusted jointly based on normative knowledge of the cultural mechanism and the local optimum. Only

[0078]

[0079] in This represents the scaling factor for the Cultural Doves flock. This represents a random number that follows a standard normal distribution.

[0080] Step 5: Calculate the newly generated position fitness for each individual dove and update the local and global optimal positions. The cultural dove swarm algorithm selects elite individuals with better fitness in the group through an acceptance function and iteratively updates the belief space according to the cultural evolution mechanism.

[0081] No. During the nth iteration, the 1st The first flock of doves The location of only the dove The fitness function is Based on fitness values, determine each individual up to the [number missing]. Substitute local optimal position , The entire group until the... The global optimal position is as follows: .

[0082] Subsequently, an acceptance function is used to select elite individuals with better fitness from the population as knowledge sources, the size of which is approximately the population size. The location information of these elite individuals will be used to update the canonical knowledge base within the faith space. The local optimal positions of the doves that affect the update of the lower bound and upper bound of the canonical function are respectively... and , .

[0083] The specific update equations for the parameters related to normative knowledge are as follows:

[0084]

[0085]

[0086]

[0087]

[0088] Step 6: Determine if the preset maximum number of iterations has been reached. If the preset maximum number of iterations is not reached, then let If not, return to step four; otherwise, output the global optimal position of the dove flock as the optimal solution for the direction of incoming waves from the sea target.

[0089] The method (algorithm) for finding the direction of maritime targets by a swarm of unmanned aerial vehicles (UAVs) proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.

[0090] Based on the method proposed in this invention, a small-scale quick-shot orientation finding system for UAV swarms of maritime targets is developed using a programming language. This system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned small-scale quick-shot orientation finding method for UAV swarms of maritime targets when running.

[0091] The developed system (software) computer program is stored on a computer-readable storage medium. This computer program is configured to implement the steps of the aforementioned method for finding the direction of a maritime target using a swarm of unmanned aerial vehicles (UAVs) when invoked by a processor. In other words, the invention is materialized on a carrier, becoming a computer program product.

[0092] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0093] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0094] The effectiveness of the present invention will be verified by using specific embodiments below.

[0095] Example 1

[0096] In this embodiment, the UAV swarm's quick-shot direction finding method for sea targets based on the culture dove mechanism and minimum redundancy array proposed in this invention is denoted as MPIO-MRL-ML. Algorithms used for comparison include maximum likelihood algorithms based on particle swarm optimization (PSO-MRL-ML) and ULA arrays (PSO-ULA-ML), and maximum likelihood algorithms based on the culture cat swarm search algorithm (CCSA-MRL-ML). The CCSA-MRL-ML method uses an array consisting of 5 non-equidistant array elements, with the element placement positions as follows: The non-uniform linear array. Other methods still use 5 array elements, but they are equidistant uniform linear arrays. The simulation parameters for the MPIO algorithm are set as follows: population size Basic dove flock reverse dove flock Cultural doves Map and compass operators Cultural doves scaling factor Maximum number of iterations Select according to proportion =20% of the best individuals are used as knowledge sources; the MUSIC algorithm's peak search accuracy is .

[0097] Example 1: Compare the global search capabilities of the MPIO-MRL-ML, CCSA-MRL-ML, and PSO-MRL-ML algorithms, and set... , The coherent source is Fifty Monte Carlo experiments were conducted, and the average fitness value was calculated. The fitness convergence curve was plotted as follows: Figure 2 As shown.

[0098] Example 2: Verify the robustness of the proposed MPIO-MRL-ML small snapshot direction finding algorithm, with constraints. , One hundred Monte Carlo experiments were conducted with different GSNR levels. The experiments were conducted with waves originating from... The coherent sources of three equal-power complex Gaussian processes were analyzed, and their success probabilities of DOA estimation and root mean square errors (RMSE) were statistically evaluated. The estimation accuracy and stability of the algorithm under low snapshot conditions were comprehensively assessed. Figure 3 As shown.

[0099] Example 3: Evaluate the robustness of the proposed MPIO-MRL-ML algorithm in an impulsive noise environment by setting a fixed number of snapshots. Adjusting characteristic index Simulate impact noise environments of varying intensities, targeting One hundred Monte Carlo experiments were conducted using three coherent sources in the direction of travel. The focus was on examining two key metrics: the success probability of DOA estimation and RMSE. The accuracy and stability of the algorithm under non-Gaussian noise conditions were fully quantified. Figure 4 As shown.

[0100] Example 4: To test the direction finding performance of the proposed small snapshot direction finding algorithm under different snapshot numbers, the following settings were implemented. , The algorithm mentioned in the statistics is for the direction of incoming waves. The success probability and RMSE of DOA estimation for three coherent sources at different snapshot numbers are as follows: Figure 5 As shown.

[0101] pass Figures 2-5 Simulation results demonstrate that the MPIO-MRL-ML method proposed in this invention exhibits significant advantages and good robustness in small-shot direction finding methods. Under environments with low signal-to-noise ratio, strong impulse noise, and a small number of shots, this UAV swarm direction finding method for maritime targets demonstrates high estimation success rate and accuracy. Particularly in scenarios with a small number of shots, this method effectively suppresses noise influence and maintains superior performance, proving its feasibility and stability in practical applications.

[0102] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for quick-photo direction finding of maritime targets by a swarm of unmanned aerial vehicles (UAVs), characterized in that, Includes the following steps: Step 1: Establish a model for receiving small snapshots of maritime targets using a minimum redundancy array of UAV swarms; construct a fractional low-order covariance matrix using the small snapshot data received by the minimum redundancy array composed of multiple UAV swarms, and establish a maximum likelihood estimation objective function. Step 2: Set the dove flock types as basic dove flock, reverse dove flock, and cultural dove flock, initialize the dove flock and set the relevant parameters; Step 3: Construct a fitness function based on the established maximum likelihood estimation objective function, calculate the fitness value of the dove flock, and determine the local optimal position and the global optimal position; Step 4: Perform updates for the three population types: basic dove flock, reverse dove flock, and cultural dove flock, respectively; Step 5: Calculate the newly generated position fitness for each individual dove, update the local optimal position and the global optimal position, select elite individuals with better fitness in the group through the acceptance function, and iteratively update the belief space according to the cultural evolution mechanism; Step Six: Determine if the preset maximum number of iterations has been reached. If the preset maximum number of iterations has not been reached, then set the iteration count... Return to step four; Otherwise, output the global optimal position of the flock of doves as the optimal solution for the direction of incoming waves from the sea target.

2. The method according to claim 1, characterized in that, Step one includes the following process: Build a A model for receiving signals from maritime targets using a minimum redundancy array of UAVs, consisting of one array element per UAV. The drones form a special array group, and the array element positions are set as follows: With half wavelength As a unit, Indicates the first The relative positions of each array element with respect to the reference array element satisfy the following conditions: , ; Array element position difference set , The minimum distance between two array elements. When there is A far-field narrowband signal from the sea surface one direction When incident on the minimum redundancy array of the UAV swarm, the array is at the... The sampling data received in the second snapshot is ,in express Data volume received by the 3D array express 3D space signal vector, express Additive noise vector express 3D steering vector matrix; corresponding direction of arrival angle is The steering vector of the incident signal is , Under the condition of small snapshots, only a limited number of time sampling points can be obtained. The number of snapshots is denoted as... And meet the conditions , The sub-snapshot receiver matrix is ​​represented as follows: ,in Represents the source signal matrix. Represents the impulse noise matrix; use The fractional low-order covariance matrix is ​​constructed from the small snapshot data received by the minimum redundancy array consisting of a swarm of drones, denoted as follows: , for 3D matrix , , No. Line number Column elements are , , , The first normalized form of the infinite norm The data from the second quick snapshot dimension, These are the parameters of a low-order matrix; ,in , ; The infinite norm weighted fractional matrix of the minimum redundancy array Extended to an infinite norm weighted fractional low-order matrix of a virtual uniform array , ,in , , To represent the number of elements in the expanded virtual uniform array. , , This indicates the calculation of mathematical expectation. , The guiding matrix for the virtual uniform array is: The direction of arrival is The virtual steering vector of the incident signal is ; The objective function for maximizing the maximum likelihood estimation is obtained based on the low-order matrix of the infinite norm weighted fraction and the steering vector matrix. , , This represents the trace function of a matrix. This represents the guidance matrix.

3. The method according to claim 2, characterized in that, Step two includes the following process: Set the size of the dove flock to be ,exist Three types of dove flocks were generated in the 3D search space: basic dove flocks, reverse dove flocks, and cultural dove flocks, with the following numbers respectively. , and ,and ;No. A flock of doves has Only a turtledove, The maximum number of iterations is ;No. During the nth iteration, the 1st The first of the flocks of doves The location of only the dove Its speed The cultural doves, following the rules of the cultural algorithm, generate an initial belief space and initialize normative knowledge, defining... Indicates the first The lower bound of normative knowledge. Indicates the first The upper bound of normative knowledge, Indicates the first The generation Lower bound of normative knowledge The corresponding evaluation value, Indicates the first The generation Upper bound of normative knowledge The corresponding evaluation value, and Take the corresponding boundary values ​​of the domain of the variable respectively. and In the first generation, all were initialized to... .

4. The method according to claim 3, characterized in that, Step three includes the following process: No. During the nth iteration, the 1st The first of the flocks of doves The location of only the dove The fitness function is Based on fitness values, determine each individual up to the [number]th [level]. Substitute local optimal position The entire group until the first The global optimal position is as follows: .

5. The method according to claim 4, characterized in that, Step four includes the following process: In the basic dove flock, the first The turtledove updates its velocity and position according to the basic operators, and the update equation is: in , Indicates map and compass factors, This represents the chaotic random numbers generated by the chaotic equation. Update according to the following rules: in A uniformly random number between [0,1]; In the reverse-flying dove flock, the first Individual doves update their own position by jumping backwards, based on jump probability. The formula for determining whether to perform a population jump for the updated individual is: ， In the formula It is a uniformly random number between [0,1]. , ; The cultural dove flock generates new dove individuals based on an influence function. The influence functions for position, step size, and direction of movement are adjusted jointly based on the normative knowledge of the cultural mechanism and the local optimum. The update formula is: in This represents the scaling factor for the Cultural Doves flock. This represents a random number that follows a standard normal distribution.

6. The method according to claim 5, characterized in that, Step five includes the following process: No. During the nth iteration, the 1st The first of the flocks of doves The location of only the dove The fitness function is Based on fitness values, determine each individual up to the [number]th [level]. Replace the local optimum position to determine the entire population up to the th... The global optimal position is determined by substitution. Subsequently, an elite individual with better fitness from the population is selected as the knowledge source through an acceptance function. The position information of the elite individual is used to update the normative knowledge base within the belief space. The local optimal positions of the doves that influence the update of the lower bound and upper bound of the normative function are respectively... and ; The specific update equations for the parameters related to the normative knowledge are as follows: 。 7. A small-scale, rapid-photo direction-finding system for unmanned aerial vehicle (UAV) swarms targeting maritime targets, characterized in that: The system has a program module corresponding to the steps of the method described in any one of claims 1 to 6 above, and executes the steps in the above-described method for finding the direction of a maritime target by a swarm of UAVs during runtime.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the method for finding the direction of a maritime target by a swarm of unmanned aerial vehicles (UAVs) according to any one of claims 1 to 6.

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