Black flight unmanned aerial vehicle DoA estimation method based on cooperation unmanned aerial vehicle auxiliary domain self-adaption

Abstract

The invention discloses a black flight unmanned aerial vehicle DoA estimation method based on cooperation unmanned aerial vehicle auxiliary domain self-adaption, and the method comprises the steps: defining an operation domain as an actual environment with multipath interference, and defining a reference domain as an ideal multipath-free free space environment through employing a domain self-adaption idea; constructing a linear mapping matrix from the operation domain to the reference domain based on a structural relationship between the reference domain covariance matrix and the operation domain covariance matrix so as to map a received signal of the operation domain to the reference domain; the method comprises the following steps: firstly, constructing a reference domain covariance matrix, and determining an operation domain covariance matrix by using a multi-snapshot broadcast signal of a cooperative unmanned aerial vehicle; converting the black flight unmanned aerial vehicle signal acquired by the receiving array into a reference domain signal by using an optimal solution of the linear mapping matrix, and then determining a covariance matrix of the black flight unmanned aerial vehicle signal by using the reference domain signal; and finally, determining the DoA of the black flight unmanned aerial vehicle based on eigenvalue decomposition of the covariance matrix in combination with a spatial spectrum function.

Description

Technical Field

[0001] This invention relates to the fields of array signal processing and radio monitoring technology, specifically to a DoA estimation method for unauthorized drones based on cooperative drone-assisted domain adaptation, which can be applied to scenarios such as anti-drone systems, airspace security management, key area protection, and radio frequency positioning of moving targets. Background Technology

[0002] In recent years, with the rapid popularization and widespread application of drone technology, unauthorized "black flight" drones have posed an increasingly serious threat to public safety, critical infrastructure, and personal privacy. Statistics show that thousands of such incidents occur globally each year, frequently causing flight delays, event cancellations, and other safety accidents. Therefore, real-time detection and precise location of "black flight" drones has become an urgent technological need.

[0003] Among numerous detection technologies, radio frequency (RF) signal-based detection methods have garnered widespread attention due to their advantages of passive reception, independence from optical characteristics, and all-weather operation. Within these methods, Direction of Arrival (DoA) estimation is a crucial step in achieving spatial positioning and tracking of unmanned aerial vehicles (UAVs). By accurately estimating the direction of arrival of the UAV's RF signals, its location can be further deduced, enabling real-time monitoring and early warning. Therefore, DoA estimation holds a central position in "black flight" UAV detection systems.

[0004] DoA estimation is a classic problem in array signal processing, widely used in radar, sonar, and wireless communication systems. Traditional DoA estimation algorithms include delayed summation beamforming, minimum variance distortionless response (MVDR), and multiple signal classification (MUSIC), which can achieve high direction estimation accuracy in ideal environments. However, DoA estimation faces severe challenges in complex real-world environments, especially in urban scenarios. Multipath propagation, electromagnetic interference, and non-stationary noise significantly degrade algorithm performance, leading to increased estimation bias and false alarm rate. Furthermore, detecting unauthorized drones ("black-flying" drones) presents several unique challenges: their radio frequency (RF) signals are typically weak and rapidly changing; their operating frequency bands (e.g., 2.4 GHz, 5.8 GHz) overlap with those of civilian devices like Wi-Fi, making signal extraction and differentiation difficult; the lack of prior signal features or location information further weakens the applicability of traditional DoA algorithms; simultaneously, the multipath effect in urban environments generates spurious spectral peaks, leading to multiple false peaks in subspace algorithms (such as MUSIC), increasing the risk of misjudgment; in addition, drones possess high maneuverability and a low radar cross section (RCS), resulting in radar-based detection methods having short detection ranges, high costs, and limited deployment. Therefore, researching robust and high-precision DoA estimation algorithms for the RF signals of unauthorized drones in complex electromagnetic environments is of significant theoretical and practical value for achieving rapid detection and accurate localization of drones. Summary of the Invention

[0005] The purpose of this invention is to provide a DoA estimation method for unauthorized UAVs based on cooperative UAV-assisted domain adaptation, in order to solve the problems of low accuracy, poor environmental adaptability, and reliance on a large amount of calibration data in the existing technology for DoA estimation of unauthorized UAVs in complex electromagnetic environments such as multipath interference.

[0006] To achieve the above objectives, the present invention employs the following technical solution: A DoA estimation method for unauthorized drones based on cooperative drone-assisted domain adaptation includes: Using the concept of domain adaptation, the operational domain is defined as the actual environment with multipath interference, and the reference domain is defined as the ideal free space environment without multipath interference. Based on the structural relationship between the covariance matrix of the reference domain and the covariance matrix of the operational domain, a linear mapping matrix from the operational domain to the reference domain is constructed to map the received signal from the operational domain to the reference domain. Based on the reference steering vector matrix, construct the autocorrelation matrix of each reference steering vector; use the autocorrelation matrix under different reference angles to obtain the reference domain covariance matrix; A cooperative drone remote identification method is adopted, in which cooperative drones are deployed in the region of interest and continuously broadcast RID signals; based on the coordinate information contained in the RID signals, the incident angle of the cooperative drones relative to the receiving array is determined; and the covariance matrix of the operating domain is determined by using multiple acquired snapshot RID signals. The objective function for solving the linear mapping matrix is ​​constructed using the reference domain covariance matrix and the operation domain covariance matrix, and the optimal solution of the linear mapping matrix is ​​obtained through Cholesky decomposition. For the signal of the unauthorized drone acquired by the receiving array, the optimal solution of the linear mapping matrix is ​​used to transform it into a reference domain signal, and then the covariance matrix of the unauthorized drone signal is determined using the reference domain signal. The covariance matrix of the signal from the unauthorized UAV is decomposed into eigenvalues, and a spatial spectral function is constructed based on the decomposed signal subspace and the steering vector. The DoA of the unauthorized UAV is determined by spectral peak search.

[0007] Furthermore, in order to construct the reference structure of the reference domain, we first define the reference steering vector matrix; assuming in angle space... Inner uniform sampling Reference angle Then the reference steering vector matrix can be represented as:

[0008] In the above formula For the minimum and maximum values ​​in the angle space, Indicates the first One reference angle, Each reference steering vector for:

[0009] in, This represents the element spacing of the uniform linear array at the receiving end. For the signal wavelength, The number of array elements; for each reference angle Calculate the autocorrelation matrix of its reference steering vector:

[0010] in These are positive constants used for numerical stability. for Identity matrix; parameter superscript Indicates conjugate transpose; takes all reference angles. The corresponding autocorrelation matrix The average value is used to obtain the reference domain covariance matrix: .

[0011] Furthermore, the incident angle of the cooperative drone relative to the receiving array The following is calculated based on the broadcast location coordinates in the RID signal and the known location of the receiving array:

[0012] in, For the horizontal coordinates of the cooperative drones, These are the position coordinates of the reference array element of the receiving array.

[0013] Furthermore, the receiving array collects the RID signal broadcast by the cooperative drone during the environmental correction phase, during which no unauthorized drones are flying in the actual environment; and collects data within the region of interest using the cooperative drone. The first snapshot data, the first The signals received by the array at each snapshot moment are:

[0014] in, The complex envelope of the RID signal. This is the guide vector corresponding to the direct path. For the first The guide vector corresponding to the multipath. This is the multipath coefficient; This is the noise vector; Indicates the direct path, which exists in both directions. Multiple diameters.

[0015] Furthermore, based on the collected data A snapshot of data, operating on the domain covariance matrix. Through the sample covariance matrix estimate:

[0016] in For the first Each snapshot receives the signal received by the array.

[0017] Furthermore, in obtaining the reference domain covariance matrix and the covariance matrix of the operating domain Then, the linear mapping matrix from the operation domain to the reference domain is defined as follows: This ensures that the covariance of the mapped signal satisfies:

[0018] Linear mapping matrix The solution is achieved by minimizing the following objective function:

[0019] in, Let Frobenius norm be denoted; the derivation of the closed-form solution is as follows: make The above formula can be written as:

[0020] The optimization problem becomes:

[0021] right Perform Cholesky decomposition:

[0022] in The lower triangular matrix obtained from Cholesky decomposition; but The optimal solution is:

[0023] Therefore, the linear mapping matrix is: The optimal solution is: .

[0024] Furthermore, the signal received by the receiving array from the unauthorized drone during practical application is... Then the reference domain signal after the domain transformation is:

[0025] The covariance matrix of the transformed UAV signal is:

[0026] in, This indicates the operation of finding the expected value. Let be the theoretical covariance matrix of the UAV signal.

[0027] Furthermore, DoA estimation based on the MUSIC algorithm is used to estimate the covariance matrix. Perform eigenvalue decomposition:

[0028] in: For the signal subspace, corresponding to the previous The largest eigenvalues ; For the noise subspace, corresponding to the following Smaller eigenvalues ; The signal eigenvalues ​​are a diagonal matrix. This is a diagonal matrix of noise eigenvalues. This refers to the number of elements in the receiving array. For the number of signal sources, express 3D complex space, It is a diagonal matrix; The MUSIC spatial spectral function is defined as:

[0029] in For drone signals in The angular direction of the guide vector; By searching in angular space The DoA estimate of the "black flight" drone can be obtained by finding the peak position. .

[0030] Furthermore, the MDL criterion is used to estimate the number of signal sources:

[0031] in, Covariance matrix of 1 eigenvalue, For the first 1 eigenvalue, The number of array elements. For signal snapshots, The number of signal sources to be tested; The number of signal sources is estimated as follows: .

[0032] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the DoA estimation method for black-flying drones based on cooperative drone-assisted domain adaptation.

[0033] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the DoA estimation method for black-flying drones based on cooperative drone-assisted domain adaptation.

[0034] Compared with the prior art, the present invention has the following technical features: This method constructs an ideal signal reference domain by introducing a cooperative UAV as a reference node with known angles. It then uses a domain adaptive learning mechanism to map observation data contaminated by multipath interference to this ideal signal reference domain, thereby achieving mapping correction from the actual multipath environment to the ideal signal distribution. This suppresses the rank deficiency problem caused by multipath coherence and restores the signal subspace structure. As a result, it provides high-precision and robust direction-of-arrival estimation for "black flight" UAVs in complex environments with strong interference, offering an effective technical means for UAV supervision in complex electromagnetic environments. Attached Figure Description

[0035] Figure 1 This is a schematic flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the application scenario model of the present invention; Figure 3 This is a schematic diagram illustrating the failure of the MUSIC algorithm due to multipath effect in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the effect of using cooperative drones for domain adaptation in an embodiment of the present invention. Detailed Implementation

[0036] In recent years, Domain Adaptation (DA) technology has developed rapidly in the field of machine learning. Its core idea is to improve the model's generalization ability in different environments by aligning the feature distributions of the source and target domains, and it has achieved significant results in fields such as computer vision and speech recognition. This technology provides a new approach to solving the problem that traditional methods rely on fixed distribution assumptions in complex scenarios.

[0037] Deploy a containing A uniform linear array system with 1000 elements is used to receive narrowband signals from the far field. Let the first element in the uniform linear array system be the reference element. Then the received signal of the reference element can be expressed as: (1) in, Indicates the echo angular frequency. Indicates the incident signal (narrowband signal) The phase of ) It is a natural exponential function. The imaginary unit, For time parameters, This indicates additive noise.

[0038] Then the first The expression for the received signal of each array element can be written as: (2) in, Indicates narrowband signal Reaching the The time delay of each array element relative to the reference array element Indicates the spacing between array elements. At the speed of light, Narrowband signal The angle between the direction of arrival and the array normal. For the first The additive noise received by each array element.

[0039] When the signal bandwidth is much smaller than the carrier frequency (narrowband condition), the time delay If the resulting amplitude and phase changes are negligible, then: (3) After applying this approximation, the first The received signal of each array element is simplified as follows: (4) in, Represents the natural constant. After sampling the signals of each channel, Time by The received signal of a uniform linear array system composed of array elements can be represented as a column vector, and its signal vector expression is: (5) in, , , They represent the first The received signal, time delay, and additive noise of each array element ; For the incident signal at Directional guidance vector, The signal wavelength is indicated by the superscript. Indicates the transpose operation; Let be the noise vector; assume that the additive noise is Gaussian white noise that is uncorrelated with the received signal, and that the noise components corresponding to each array element are independent of each other.

[0040] Assuming there are at the same time Each narrowband signal, from the angle When incident on this uniform linear array system, the received signal model of the system can be expressed as: (6) in, Indicates the incident signal at Directional guidance vector, surface Narrowband signals in the direction of It is the array flow vector matrix.

[0041] Therefore, the output covariance matrix of the entire array can be calculated as follows: (7) in, The signal covariance matrix, express Narrowband signal at any given moment Indicates noise power. yes An identity matrix of dimension 1 This indicates the operation of finding the expected value. This indicates the conjugate transpose operation.

[0042] In urban environments, the drone signals captured by the receiving array exhibit strong coherence between the directly propagating direct signal (the desired signal) and the multipath signal formed by reflections from urban buildings.

[0043] In an urban environment, the receiver needs to capture the signal from a drone. In this case, there is one directly propagating signal. At the same time Multipath signals formed by reflection or diffraction from urban buildings, and these multipath signals are completely coherent with the direct signal, then the first... The multipath signal corresponding to a multipath path can be represented as: (8) in, Represents the multipath coefficient; in particular, .

[0044] Based on the characteristics of signal propagation in urban environments, the coherent signal model at the receiver is similar to that mentioned above. The corresponding array receiving signal model for a system under narrowband signal conditions is represented as follows: (9) in, This is a multipath coefficient vector. Represents the noise vector. Indicates the first multipath The multipath signal corresponding to the given time.

[0045] The array output covariance matrix of the coherent signal can then be expressed as: (10) in, This represents the signal power.

[0046] Under conditions of perfect coherence or severe multipath, the covariance matrix The rank of the eigenvalue drops to 1, making it difficult for traditional subspace methods based on eigenvalue decomposition to maintain their intended discriminative power, such as... Figure 3 As shown.

[0047] Based on the above system model, such as Figure 1 and Figure 2 As shown, the present invention provides a DoA estimation method for unauthorized drones based on cooperative drone auxiliary domain adaptation, comprising the following steps: Step 1: Array modeling and reference domain construction.

[0048] This invention introduces the concept of domain adaptation, defining the Operation Domain as the actual environment with multipath interference and the Reference Domain as the ideal free space environment without multipath interference. The mapped signal is aligned with second-order statistics, which is more consistent with the free space model in a statistical sense. This enables the recovery of stable subspace features and ensures that the subsequent DOA algorithm remains reliable in complex environments.

[0049] set up The reference domain covariance matrix is ​​generated by the reference array steering vector. To accommodate the operational domain covariance matrix obtained from stage observations; based on the structural relationship between the two, define... Let be the linear mapping matrix from the operating domain to the reference domain, for any received signal Perform the transformation: (11) This mapping guarantees the signal after mapping. The covariance satisfies This allows for the correction of the statistical characteristics of the operating domain environment, which can then be followed by the relevant DOA algorithm based on the covariance matrix.

[0050] To construct the reference structure of the reference domain, we first define the reference steering vector matrix; assuming in angle space... Inner uniform sampling Reference angle Then the reference steering vector matrix can be represented as: (12) In the above formula For the minimum and maximum values ​​in the angle space, Indicates the first One reference angle, Each reference steering vector Calculated according to the ideal uniform linear array model: (13) in, This represents the element spacing of the uniform linear array at the receiving end. For the signal wavelength, Let be the angle between the direction of arrival of the incident signal and the array normal. The number of array elements; for each reference angle Calculate the autocorrelation matrix of its reference steering vector: (14) in It is a small positive constant used for numerical stability. for Identity matrix; parameter superscript This indicates the conjugate transpose, and the same applies below; this regularization term can be considered as an equivalent noise compensation under high signal-to-noise ratio conditions. (Take all reference angles) The corresponding autocorrelation matrix The average value is used to obtain the reference domain covariance matrix: (15) The reference domain covariance matrix is ​​not a simulation of the actual signal scenario, but an ideal spatial structure template that is independent of signal power, constructed based on the array steering vector, thus avoiding the dependence on prior signal power information in traditional methods.

[0051] Step 2: Collaborative UAV environmental calibration and operational domain modeling.

[0052] In practical applications, the operational domain covariance matrix Estimation requires receiving signals; this scheme uses cooperative drone remote identification (RID) signals to estimate the operational domain covariance matrix. RID is a standardized signal broadcast by drones, used for drone identification and location tracking; according to relevant regulations, drones must continuously broadcast RID signals during flight, which include the drone's unique identifier, real-time position, speed, altitude, and other information.

[0053] In this invention, the RID signal broadcast by the cooperative UAV is used as a known reference signal source. This signal is acquired by the receiving array at the receiving end to achieve accurate estimation of the operational domain covariance matrix. Since the position information of the cooperative UAV can be obtained by parsing the RID signal, its incident angle is... Since these are known quantities, they provide a reliable reference benchmark for environmental correction.

[0054] The estimation of the covariance matrix of the operating domain is accomplished through the following process: Deploy a cooperative drone in the "area of ​​interest" and continuously broadcast a standard-compliant RID signal. The incident angle of the cooperative drone relative to the receiving array is specified. It can be calculated based on the broadcast position coordinates in the RID signal and the known position of the receiving array: (16) in, For the horizontal coordinates of the cooperative drones, The coordinates of the reference array elements are used to receive the array. The "region of interest" refers to the area where the DoA (DoA) of the "black flight" drone needs to be estimated.

[0055] The receiving array collects the RID signal broadcast by the cooperative UAV during the environmental correction phase, assuming the collection time window is [missing information]. During this period, no unauthorized drones were detected in the actual environment; data was collected using cooperative drones within the area of ​​interest. The first snapshot data, the first At each snapshot moment, the signal received by the receiving array is: (17) in, The complex envelope of the RID signal. Direct path (the incident angle of the cooperative UAV relative to the receiving array) The corresponding path) and its corresponding guide vector. For the first The guide vector corresponding to the multipath. For multipath coefficients, in particular, ; This is the noise vector; Indicates the direct path, which exists in both directions. Multiple diameters.

[0056] Based on collection A snapshot of data, operating on the domain covariance matrix. It can be obtained through the sample covariance matrix estimate: (18) Due to the incident angle of the cooperative drone Since the RID signal power is known and can be estimated from the received data, the estimation of the operating domain covariance matrix has high reliability.

[0057] Step 3: Solve for the domain mapping matrix.

[0058] Obtaining the covariance matrix of the reference domain and the covariance matrix of the operating domain Then, the linear mapping matrix from the operation domain to the reference domain is defined as follows: This ensures that the covariance of the mapped signal satisfies: (19) Linear mapping matrix The solution can be achieved by minimizing the following objective function: (20) in, Let Frobenius norm be denoted; for a Hermitian positive definite matrix, it can be solved using the matrix square root transformation. The derivation of the closed-form solution is as follows: make The above formula can be written as: (twenty one) The optimization problem becomes: (twenty two) right Perform Cholesky decomposition: (twenty three) in This is the lower triangular matrix obtained from the Cholesky decomposition.

[0059] but The optimal solution is: (twenty four) Therefore, the linear mapping matrix is: The optimal solution is: (25) Step 4: Receive the signal from the "black flight" drone and perform domain transformation.

[0060] In obtaining the linear mapping matrix optimal solution Then, a domain transformation is performed on the actual "black flight" drone signal to be tested; assuming that the "black flight" drone signal received by the receiving array in actual application is... Then the transformed reference domain signal is: (26) The covariance matrix of the transformed UAV signal is: (27) in, Let be the theoretical covariance matrix of the UAV signal.

[0061] Step 5, Subspace DoA estimation.

[0062] Due to the covariance matrix of the transformed UAV signal The statistical properties have been corrected to approximate the reference structure of the ideal domain, its rank deficiency problem has been alleviated, and the subspace structure has been restored. Therefore, the traditional DoA estimation algorithm can be directly applied.

[0063] DoA estimation based on the MUSIC algorithm is used to estimate the covariance matrix. Perform eigenvalue decomposition: (28) in: For the signal subspace, corresponding to the previous The largest eigenvalues ; For the noise subspace, corresponding to the following Smaller eigenvalues ; The signal eigenvalues ​​are a diagonal matrix. This is a diagonal matrix of noise eigenvalues. This refers to the number of elements in the receiving array. For the number of signal sources, express 3D complex space, It is a diagonal matrix.

[0064] The MUSIC spatial spectral function is defined as: (29) in For drone signals in The angular direction of the guide vector.

[0065] By searching in angular space The DoA estimate of the "black flight" drone can be obtained by finding its peak position. (30) In practical applications, the number of signal sources It is usually unknown and needs to be estimated using information theory criteria, such as the MDL (Minimum Description Length) criterion: (31) in, The number of signal sources to be tested is MDL value at that time; Covariance matrix of 1 eigenvalue, For the first 1 eigenvalue, The number of array elements. This represents the number of signal snapshots.

[0066] The number of signal sources is estimated as follows: (32) The application results of the embodiments of the present invention are as follows: Figure 4 As shown in the figure; the results indicate that this scheme can achieve high-precision direction-of-arrival estimation for unmanned aerial vehicles (UAVs) flying without a license.

[0067] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A DoA estimation method for unauthorized UAVs based on cooperative UAV-assisted domain adaptation, characterized in that, include: Using the concept of domain adaptation, the operational domain is defined as the actual environment with multipath interference, and the reference domain is defined as the ideal free space environment without multipath interference. Based on the structural relationship between the reference domain covariance matrix and the operational domain covariance matrix, a linear mapping matrix from the operational domain to the reference domain is constructed to map the received signal from the operational domain to the reference domain. Based on the reference steering vector matrix, construct the autocorrelation matrix of each reference steering vector; By using the autocorrelation matrices under different reference angles, the reference domain covariance matrix is ​​obtained; A cooperative drone remote identification method is adopted, in which cooperative drones are deployed in the region of interest and continuously broadcast RID signals; based on the coordinate information contained in the RID signals, the incident angle of the cooperative drones relative to the receiving array is determined; and the covariance matrix of the operating domain is determined by using multiple acquired snapshot RID signals. The objective function for solving the linear mapping matrix is ​​constructed using the reference domain covariance matrix and the operation domain covariance matrix, and the optimal solution of the linear mapping matrix is ​​obtained through Cholesky decomposition. For the signal of the unauthorized drone acquired by the receiving array, the optimal solution of the linear mapping matrix is ​​used to transform it into a reference domain signal, and then the covariance matrix of the unauthorized drone signal is determined using the reference domain signal. The covariance matrix of the signal from the unauthorized drone is decomposed into eigenvalues, and a spatial spectrum function is constructed based on the decomposed signal subspace and the steering vector. The DoA (DoA) of unauthorized UAVs was determined based on spectral peak search.

2. The DoA estimation method for unauthorized UAVs based on cooperative UAV auxiliary domain adaptation according to claim 1, characterized in that, To construct the reference structure of the reference domain, we first define the reference steering vector matrix; assuming in angle space... Inner uniform sampling Reference angle Then the reference steering vector matrix can be represented as: In the above formula For the minimum and maximum values ​​in the angle space, Indicates the first One reference angle, Each reference steering vector for: in, This represents the element spacing of the uniform linear array at the receiving end. For the signal wavelength, The number of array elements; for each reference angle Calculate the autocorrelation matrix of its reference steering vector: in These are positive constants used for numerical stability. for Identity matrix; parameter superscript Indicates conjugate transpose; takes all reference angles. The corresponding autocorrelation matrix The average value is used to obtain the reference domain covariance matrix: 。 3. The DoA estimation method for unauthorized UAVs based on cooperative UAV auxiliary domain adaptation according to claim 1, characterized in that, Angle of incidence of the cooperative drone relative to the receiving array The following is calculated based on the broadcast location coordinates in the RID signal and the known location of the receiving array: in, For the horizontal coordinates of the cooperative drones, These are the position coordinates of the reference array element of the receiving array.

4. The DoA estimation method for unauthorized UAVs based on cooperative UAV auxiliary domain adaptation according to claim 1, characterized in that, The receiving array collects the RID signal broadcast by the cooperative drone during the environmental calibration phase, during which no unauthorized drones are actually flying in the environment; data is collected within the region of interest using the cooperative drone. The first snapshot data, the first The signals received by the array at each snapshot moment are: in, The complex envelope of the RID signal. This is the guide vector corresponding to the direct path. For the first The guide vector corresponding to the multipath. This is the multipath coefficient; This is the noise vector; Indicates the direct path, which exists in both directions. Multiple diameters.

5. The DoA estimation method for unauthorized UAVs based on cooperative UAV auxiliary domain adaptation according to claim 1, characterized in that, Based on collection A snapshot of data, operating on the domain covariance matrix. Through the sample covariance matrix estimate: in For the first Each snapshot receives the signal received by the array.

6. The DoA estimation method for unauthorized UAVs based on cooperative UAV auxiliary domain adaptation according to claim 1, characterized in that, Obtaining the covariance matrix of the reference domain and the covariance matrix of the operating domain Then, the linear mapping matrix from the operation domain to the reference domain is defined as follows: This ensures that the covariance of the mapped signal satisfies: Linear mapping matrix The solution is achieved by minimizing the following objective function: in, Let Frobenius norm be denoted; the derivation of the closed-form solution is as follows: make The above formula can be written as: The optimization problem becomes: right Perform Cholesky decomposition: in The lower triangular matrix obtained from Cholesky decomposition; but The optimal solution is: Therefore, the linear mapping matrix is: The optimal solution is: 。 7. The DoA estimation method for unauthorized UAVs based on cooperative UAV auxiliary domain adaptation according to claim 1, characterized in that, The signal received by the receiving array from the unauthorized drone during practical application is as follows: Then the reference domain signal after the domain transformation is: The covariance matrix of the transformed UAV signal is: in, This indicates the operation of finding the expected value. Let be the theoretical covariance matrix of the UAV signal.

8. The DoA estimation method for unauthorized UAVs based on cooperative UAV auxiliary domain adaptation according to claim 1, characterized in that, DoA estimation based on the MUSIC algorithm is used to estimate the covariance matrix. Perform eigenvalue decomposition: in: For the signal subspace, corresponding to the previous The largest eigenvalues ; For the noise subspace, corresponding to the following Smaller eigenvalues ; The signal eigenvalues ​​are a diagonal matrix. This is a diagonal matrix of noise eigenvalues. This refers to the number of elements in the receiving array. For the number of signal sources, express 3D complex space, It is a diagonal matrix; The MUSIC spatial spectral function is defined as: in For drone signals in The angular direction of the guide vector; By searching in angular space The DoA estimate of the "black flight" drone can be obtained by finding the peak position. .

9. The DoA estimation method for unauthorized UAVs based on cooperative UAV auxiliary domain adaptation according to claim 1, characterized in that, The MDL criterion is used to estimate the number of signal sources: in, Covariance matrix of 1 eigenvalue, For the first 1 eigenvalue, The number of array elements. For signal snapshots, The number of signal sources to be tested; The number of signal sources is estimated as follows: 。 10. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the DoA estimation method for black-flying drones based on cooperative drone-assisted domain adaptation as described in any one of claims 1-9.

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