Unmanned aerial vehicle swarm detection and discrimination method and device based on kt and deanm

Abstract

The application discloses a kind of unmanned aerial vehicle group detection and distinguishing method and device based on KT and DeANM, the method includes: the three-dimensional echo signal of digital beam forming transformation is obtained to echo signal in space dimension;According to the acceleration and velocity ambiguity number of three-dimensional echo signal search target, and based on wedge stone conversion algorithm to the three-dimensional echo signal after preliminary filtering compensation;According to the distance, velocity and angle of three-dimensional echo signal after compensation to target rough estimate;According to distance rough estimate value, velocity rough estimate value and angle rough estimate value, the distance dimension and angle dimension of three-dimensional echo signal after compensation are extracted Fourier inverse transform and obtain two-dimensional echo signal;Two-dimensional echo signal is decoupled atomic norm minimization processing and obtains the topley matrix of target, and the distance super-resolution estimate value and angle super-resolution estimate value of target are obtained by Van der Monde decomposition to the topley matrix of target.The present application can realize high-precision detection and distinguish to unmanned aerial vehicle group.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a method and apparatus for detecting and distinguishing unmanned aerial vehicle (UAV) swarms based on KT and DeANM. Background Technology

[0002] Drone swarms are characterized by their high speed, maneuverability, and small size. They are applied in various scenarios, such as commercial performances, cargo transportation, agricultural protection, and military operations. Therefore, drone swarm control systems have a wider range of applications. However, swarm drones also pose a possibility of malicious use. In critical areas, even if only one swarm drone breaches defenses, the danger is enormous, making accurate detection and location crucial. However, compared to individual drones, which are typically weak targets with small radar cross-sections, long ranges, and time-varying motion, drone swarms exhibit a new characteristic: high density. This characteristic presents a significant challenge to radar sensors. Therefore, accurately detecting and locating drone swarms under low signal-to-noise ratio conditions is a vital aspect of ensuring safety, improving resource utilization efficiency, and environmental monitoring.

[0003] Current methods for detecting drone swarms either use long-term coherent accumulation techniques to improve the signal-to-noise ratio and Doppler resolution of targets in the echo signals, or employ sparse methods to search for targets.

[0004] Long-term coherent accumulation techniques can improve the signal-to-noise ratio and Doppler resolution of a target by increasing the coherent processing interval. Keystone (KT) transform and Radon-Fourier transform are typical long-term accumulation methods. The KT transform has lower computational complexity than the latter; however, it often suffers from Doppler frequency coupling, leading to energy diffusion.

[0005] Common sparse methods can be broadly categorized into on-mesh sparse methods, off-mesh sparse methods, and meshless sparse methods. However, both on-mesh and off-mesh sparse methods suffer from dictionary mismatch issues. To address this problem, some researchers have proposed implementing the sparse signal reconstruction process in a continuous parameter space, utilizing the total variational norm for signal recovery. However, methods based on this idea, such as atomic norm minimization, have high computational complexity. To reduce the computational burden, a decoupled atomic norm minimization (DeANM) method is proposed, which introduces a new set of atoms into the atomic norm minimization method.

[0006] However, while the KT transform, a long-term accumulation technique, can improve the signal-to-noise ratio of the target, its Doppler resolution is low, making it impossible to accurately locate the specific position of a single drone in a drone swarm. Although the DeANM sparse super-resolution method can separate drones in a drone swarm and obtain accurate information about individual drones, it has extremely high requirements for the signal-to-noise ratio of the echo signal.

[0007] Therefore, current methods for detecting and distinguishing drone swarms cannot simultaneously achieve both detection accuracy and resolution accuracy. Summary of the Invention

[0008] This invention provides a method and apparatus for detecting and distinguishing unmanned aerial vehicle (UAV) swarms based on KT and DeANM, which can solve the problem that current UAV swarm detection and distinguishing methods cannot simultaneously achieve detection accuracy and distinguishing accuracy.

[0009] In a first aspect, embodiments of the present invention provide a method for detecting and distinguishing unmanned aerial vehicle (UAV) swarms based on KT and DeANM, the method comprising:

[0010] A three-dimensional echo signal is obtained by performing a spatial-dimensional digital beamforming transformation on the echo signal. The three-dimensional echo signal includes information about the target in the range time domain, azimuth slow time domain, and spatial frequency domain.

[0011] The acceleration and velocity ambiguity number of the target are searched based on the three-dimensional echo signal. Based on the wedge transform algorithm, the three-dimensional echo signal after preliminary filtering is compensated according to the acceleration estimate and velocity ambiguity number estimate to obtain the compensated three-dimensional echo signal. The three-dimensional echo signal after preliminary filtering is obtained from the three-dimensional echo signal.

[0012] Based on the compensated three-dimensional echo signal, the target's distance, velocity, and angle are coarsely estimated to obtain the target's coarse distance estimate, velocity estimate, and angle estimate.

[0013] Based on the coarse estimates of distance, velocity, and angle, the range and angle dimensions of the compensated three-dimensional echo signal are extracted and subjected to inverse Fourier transform to obtain a two-dimensional echo signal. The two-dimensional echo signal includes information about the target in the range and angle dimensions.

[0014] The toplitz matrix of the target is obtained by decoupling and minimizing the atomic norm of the two-dimensional echo signal. Then, the target's toplitz matrix is ​​decomposed by Vandermonde to obtain the range super-resolution estimate and angle super-resolution estimate of the target.

[0015] Secondly, embodiments of the present invention provide a drone swarm detection and resolution device based on KT and DeANM, comprising:

[0016] The first transformation unit is used to perform spatial-dimensional digital beamforming transformation on the echo signal to obtain a three-dimensional echo signal, wherein the three-dimensional echo signal includes information about the target in the range time domain, azimuth slow time domain, and spatial frequency domain.

[0017] The compensation unit is used to search for the acceleration and velocity ambiguity number of the target based on the three-dimensional echo signal, and based on the wedge transform algorithm, it compensates the initially filtered three-dimensional echo signal according to the acceleration estimate and velocity ambiguity number estimate to obtain the compensated three-dimensional echo signal. The initially filtered three-dimensional echo signal is obtained from the three-dimensional echo signal.

[0018] The coarse estimation unit is used to coarsely estimate the target's distance, velocity, and angle based on the compensated three-dimensional echo signal to obtain coarse estimates of the target's distance, velocity, and angle.

[0019] The second transformation unit is used to extract the range dimension and angle dimension of the compensated three-dimensional echo signal based on the coarse range estimate, coarse velocity estimate and coarse angle estimate, and perform inverse Fourier transform to obtain a two-dimensional echo signal, wherein the two-dimensional echo signal includes information about the target in the range dimension and angle dimension.

[0020] The fine estimation unit is used to decouple the two-dimensional echo signal and minimize the atomic norm to obtain the target's Toplitz matrix, and then perform Vandermonde decomposition on the target's Toplitz matrix to obtain the target's range super-resolution estimate and angle super-resolution estimate.

[0021] The beneficial effects of the embodiments of the present invention compared with the prior art are as follows: According to the method provided by the present invention, the signal-to-noise ratio of the echo signal can be improved by compensating the echo signal through the wedge transform algorithm, and the resolution of the target in the echo signal can be improved by minimizing the atomic norm. Thus, high-precision detection and high-resolution resolution of small targets in a group of targets can be achieved, with good robustness. At the same time, by transforming the echo signal into a three-dimensional echo signal in space-distance-frequency and then performing subsequent processing, compared with the current two-dimensional super-resolution in space-distance, the resolution performance of cluster targets can be further improved, and the resolution can be improved. Attached Figure Description

[0022] Figure 1 The present invention provides a flowchart of the implementation of a method for detecting and distinguishing unmanned aerial vehicle swarms based on KT and DeANM;

[0023] Figure 2 A schematic diagram showing the geometric position of the target relative to the radar;

[0024] Figure 3A schematic diagram of a single-pulse, single-channel echo signal provided in an embodiment of the present invention;

[0025] Figure 4 A schematic diagram of velocity acceleration after parameter search provided in an embodiment of the present invention;

[0026] Figure 5 A schematic diagram of a three-dimensional echo signal after wedge transformation provided in an embodiment of the present invention;

[0027] Figure 6 This is a distance-Doppler diagram after constant false alarm rate (CFAR) detection, provided in an embodiment of the present invention.

[0028] Figure 7 This is a schematic diagram of a drone swarm detection and resolution device based on KT and DeANM, provided for an embodiment of the present invention. Detailed Implementation

[0029] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0030] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0031] It should also be understood that the term “and / or” as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0032] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if [described condition or event] is detected" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once [described condition or event] is detected," or "in response to detection of [described condition or event]."

[0033] Furthermore, in the description of this invention and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0034] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of the invention include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0035] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0036] The UAV swarm detection and differentiation method based on KT and DeANM provided in this embodiment of the invention can be applied to electronic devices such as mobile terminals, personal laptops, and supercomputers. This embodiment of the invention does not impose any restrictions on the specific type of electronic device.

[0037] Figure 1 The diagram illustrates an implementation flowchart of a UAV swarm detection and discrimination method based on KT and DeANM, provided by an embodiment of the present invention. As an example and not a limitation, this method can be applied to the aforementioned electronic device. The method may include steps S101-S107, which are described below.

[0038] S101, the echo signal is transformed by spatial-dimensional digital beamforming to obtain a three-dimensional echo signal.

[0039] For example, a three-dimensional echo signal may include information about a target (e.g., a drone) in the range time domain, azimuth slow time domain, and spatial frequency domain.

[0040] In one possible implementation, the echo signal can be obtained by reflecting the emitted signal from the target.

[0041] In one example, if the radar is an N-ary digital array radar, and its transmitted signal is a pulse linear frequency modulated signal, and M pulses are transmitted within one correlation processing interval, then the transmitted signal can satisfy the following formula:

[0042]

[0043] in, In order to transmit signals, It is a rectangular window function, where j is the imaginary unit. B is the modulation bandwidth. To save time, t m =mT r m is a positive integer less than or equal to M-1, T r T is the pulse repetition period. P f is the pulse width. c For carrier frequency, For all times.

[0044] In one example, see Figure 2 If the target is in the radar's line-of-sight direction, due to the radar's low resolution, there may be K targets within each beam, then the echo signal (see...) Figure 3 The waveform shown in the figure can satisfy the following formula:

[0045]

[0046] in, The echo signal is represented by l, which is a positive integer less than or equal to N-1, indicating the index of the transmitting antenna element, and A0 is the amplitude of the echo signal. See Figure 2 R k0 v k0 a k0 θ k0 These represent the initial distance, velocity, acceleration, and azimuth angle between the k-th target within the beam and the radar, respectively, where k is a positive integer less than or equal to K. c is the speed of light, and n... r0 It is Gaussian white noise with zero mean and constant variance, and d is the element spacing.

[0047] In one possible implementation, a three-dimensional echo signal can be obtained by performing spatial-dimensional digital beamforming operations on the echo signal based on the steering vector of the echo signal.

[0048] In one example, the steering vector of the echo signal can satisfy the following formula:

[0049]

[0050] Where a(θ) is the steering vector of the echo signal in the θ direction, θ=zδ θ (z = 1, ..., Z), where z is the index of the grid number, δ θ Z represents the angular resolution, Z represents the total number of grids, and λ represents the wavelength.

[0051] In one example, the three-dimensional echo signal can satisfy the following formula:

[0052]

[0053] in, For three-dimensional echo signals, A DBF The amplitude of the three-dimensional echo signal. Similarly, to represent Gaussian white noise with zero mean and constant variance, sin c(x) = sin(πx) / πx.

[0054] S102, based on the three-dimensional echo signal, search for the target's acceleration and velocity ambiguity number, and obtain the target's acceleration estimate and velocity ambiguity number estimate.

[0055] In one possible implementation, the first operation can be performed twice on the three-dimensional echo signal to obtain a pre-filtered three-dimensional echo signal. Then, the pre-filtered three-dimensional echo signal can be searched to obtain the target's acceleration estimate and velocity ambiguity number estimate.

[0056] For example, see Figure 4 The two peaks found in the search have X, Y, and Z coordinate values ​​that represent the estimated acceleration, velocity ambiguity number, and signal amplitude, respectively.

[0057] For example, the first operation, in the order of execution, may include range pulse compression processing and range fast Fourier transform.

[0058] In one example, the three-dimensional echo signal Y obtained after the first operation is performed for the first time. DBF (f,t m ,θ) can satisfy the following formula:

[0059]

[0060] Where f represents the distance frequency, f r n is the pulse repetition frequency. amb The velocity fuzzy number for the target.

[0061] Similarly, the pre-filtered three-dimensional echo signal can satisfy the following formula:

[0062]

[0063] Among them, A PC n represents the amplitude of the pre-filtered three-dimensional echo signal. PC (f,t m ,z) represents Gaussian noise.

[0064] S103, based on the wedge transformation algorithm, compensates the initially filtered three-dimensional echo signal according to the acceleration estimate and the velocity ambiguity number estimate to obtain the compensated three-dimensional echo signal.

[0065] In one example, a two-dimensional matched filter function can be constructed in the range-time domain and the slow-time dimension based on the target's acceleration estimate and velocity ambiguity number estimate. Then, a wedge transform ((f+f)) is performed on the pre-filtered three-dimensional signal in the range-frequency domain. c )t m =f c t′ m ), by combining this two-dimensional matched filter function with the three-dimensional echo signal after wedge transformation (see Figure 5 The signal is compensated by multiplying the two signals to obtain the compensated three-dimensional echo signal.

[0066] For example, a two-dimensional matched filter function can satisfy the following formula:

[0067]

[0068] in, It is a two-dimensional matched filter function. These are the target's acceleration estimate and velocity ambiguity number estimate, t′, respectively. m This is the slow time after scaling.

[0069] For example, the compensated three-dimensional echo signal can satisfy the following formula:

[0070]

[0071] Among them, Y DK (f,t′ m A, θ) represents the compensated three-dimensional echo signal. DK To calculate the amplitude of the compensated three-dimensional echo signal, n DK (f,t m ,z) also represents Gaussian noise.

[0072] By performing wedge transformation, velocity ambiguity number estimation, and azimuth quadratic term estimation and compensation on the echo signal in the range frequency domain, the range migration and Doppler frequency migration of the target can be compensated.

[0073] S104. Based on the compensated three-dimensional echo signal, the target's distance, velocity, and angle are coarsely estimated to obtain the target's coarse distance estimate, velocity estimate, and angle estimate.

[0074] In one possible implementation, the compensated three-dimensional echo signal can be subjected to inverse Fourier transform and Fourier transform in the range frequency domain and slow time domain, respectively, to obtain the transformed three-dimensional echo signal; then constant false alarm detection is performed on the transformed three-dimensional echo signal in the range dimension, velocity dimension and angle dimension to obtain the target's coarse range estimate, velocity estimate and angle estimate.

[0075] For example, see Figure 6 The waveform shown is obtained by constant false alarm rate detection. The X, Y, and Z coordinates of the waveform correspond to the coarse estimate of the target's distance, coarse estimate of its velocity, and amplitude, respectively.

[0076] In one example, the transformed three-dimensional echo signal can satisfy the following formula:

[0077]

[0078] in, For the transformed three-dimensional echo signal, A F The amplitude of the transformed three-dimensional echo signal. Similarly, f represents Gaussian noise. m and T M These are the Doppler frequency variable and the coherent accumulation time, respectively.

[0079] S105. Based on the coarse distance estimate, coarse velocity estimate, and coarse angle estimate, the distance dimension and angle dimension of the compensated three-dimensional echo signal are extracted and subjected to inverse Fourier transform to obtain the two-dimensional echo signal in the distance dimension and angle dimension.

[0080] In one example, the two-dimensional echo signal can satisfy the following formula:

[0081]

[0082] Among them, S n-l (n,l) represents a two-dimensional echo signal, A n-l e n-l These represent the amplitude and noise in the distance, velocity, and angle domains, respectively. For the distance-frequency domain sampling index, N r Where is the number of frequency domain sampling points, l is the spatial domain sampling index, N is the number of spatial domain sampling points, and F s The sampling frequency.

[0083] S106, the toplitz matrix of the target is obtained by decoupling and minimizing the atomic norm of the two-dimensional echo signal.

[0084] In one possible implementation, the two-dimensional echo signal can be rewritten based on the normalized frequencies of the target along the distance and angle dimensions to obtain the rewritten two-dimensional echo signal. Then, the two-dimensional echo signal is decoupled and subjected to atomic norm minimization processing based on the atomic norm minimization model to obtain the Toplitz matrix of the target.

[0085] In one example, the rewritten two-dimensional echo signal can satisfy the following formula:

[0086]

[0087] Where S is the rewritten two-dimensional echo signal, f Rk f θk These are the normalized frequencies in the angle dimension and the distance dimension, respectively, S, y, and e. n Both are one-dimensional vectors, e n G is the noise vector. k The amplitude of the received signal.

[0088] In one example, the decoupled atomic norm minimization process for the objective can be transformed into a semi-definite program (SDP) problem by using an atomic norm minimization model.

[0089] For example, the atomic norm minimization model can satisfy the following formula:

[0090]

[0091] Wherein, T(u R ), T(u θ The first row of sequences corresponding to distance and angle are u. R and u θ The optimal Toplitz matrix, Tr() represents the trace of the matrix, and λ1 is the regularization coefficient used to balance signal sparsity and data fidelity.

[0092] S107. Perform Vandermonde decomposition on the Toplitz matrix of the target to obtain the range super-resolution estimate and angle super-resolution estimate of the target.

[0093] In one example, the Vandermonde decomposition of the target's Toplitz matrix can be performed using matrix bundle or subspace class methods.

[0094] For example, the range super-resolution estimate and angle super-resolution estimate of the target can satisfy the following formula:

[0095]

[0096] in, These are the range super-resolution estimates and angle super-resolution estimates of the target, respectively. These are the estimates of the normalized frequencies for the angular and distance dimensions, respectively.

[0097] According to the method provided by the present invention, the signal-to-noise ratio of the echo signal can be improved by compensating the echo signal through the wedge transform algorithm, and the resolution of the target in the echo signal can be improved by minimizing the atomic norm. Thus, high-precision detection and high-resolution resolution of small targets in a group of targets can be achieved, with good robustness. At the same time, by transforming the echo signal into a three-dimensional echo signal in space-range-frequency and then performing subsequent processing, compared with the current two-dimensional super-resolution in space-range only, the resolution performance of cluster targets can be further improved, and the resolution can be increased.

[0098] Figure 7 The diagram shown is a structural schematic of a drone swarm detection and resolution device based on KT and DeANM provided in an embodiment of the present invention. As an example and not a limitation, the device may include a first transformation unit 710, a compensation unit 720, a coarse estimation unit 730, a second transformation unit 740, and a fine estimation unit 750.

[0099] For example, the first transformation unit is used to perform spatial-dimensional digital beamforming transformation on the echo signal to obtain a three-dimensional echo signal, wherein the three-dimensional echo signal includes information about the target in the range time domain, azimuth slow time domain, and spatial frequency domain; the compensation unit is used to search for the target's acceleration and velocity ambiguity number based on the three-dimensional echo signal, and based on the wedge transform algorithm, compensate the initially filtered three-dimensional echo signal according to the acceleration estimate and velocity ambiguity number estimate to obtain a compensated three-dimensional echo signal, wherein the initially filtered three-dimensional echo signal is obtained from the three-dimensional echo signal; the coarse estimation unit is used to estimate the target's range based on the compensated three-dimensional echo signal. The first unit performs coarse estimation of the target's distance, velocity, and angle to obtain coarse estimates of the target's distance, velocity, and angle. The second transformation unit extracts the distance and angle dimensions of the compensated three-dimensional echo signal based on the coarse estimates of distance, velocity, and angle, and performs inverse Fourier transform to obtain a two-dimensional echo signal, which includes information about the target in the distance and angle dimensions. The fine estimation unit performs decoupling atomic norm minimization processing on the two-dimensional echo signal to obtain the target's Toplitz matrix, and performs Vandermonde decomposition on the target's Toplitz matrix to obtain the target's distance super-resolution estimate and angle super-resolution estimate.

[0100] In one example, the three-dimensional echo signal can satisfy the following formula:

[0101]

[0102] in, For three-dimensional echo signals, A DBF The amplitude of the three-dimensional echo signal. Let represent Gaussian white noise with zero mean and constant variance, sin c(x) = sin(πx) / πx, and K be the total number of targets within one radar beam. To save time, t m =mT r m is a positive integer less than or equal to M-1, T r T is the pulse repetition period. P f is the pulse width. c Where c is the carrier frequency and c is the speed of light. R k0 ν k0 a k0 θ k0 These represent the initial distance, velocity, acceleration, and azimuth angle between the k-th target within a radar beam and the radar.

[0103] In one example, the two-dimensional echo signal can satisfy the following formula:

[0104]

[0105] Among them, S n-l (n,l) represents a two-dimensional echo signal, A n-l e n-l These represent the amplitude and noise in the distance, velocity, and angle domains, respectively. For the distance-frequency domain sampling index, N r Where is the number of frequency domain sampling points, l is the spatial domain sampling index, N is the number of spatial domain sampling points, and F s The sampling frequency.

[0106] In one example, the precise estimation unit 750 can specifically be used for:

[0107] The Toplitz matrix of the target is obtained by decoupling the atomic norm of the two-dimensional echo signal based on the atomic norm minimization model.

[0108] The atomic norm minimization model satisfies the following formula:

[0109]

[0110] Wherein, T(u R ), T(u θ The first row of sequences corresponding to distance and angle are u. R and u θ The optimal Toplitz matrix is ​​given by Tr(), where Tr() represents the trace of the matrix, λ1 is the regularization coefficient, S is the rewritten two-dimensional echo signal, and y is the noise-free signal.

[0111] In one example, the range super-resolution estimate and the angle super-resolution estimate of the target can satisfy the following formula:

[0112]

[0113] in, These are the range super-resolution estimates and angle super-resolution estimates of the target, respectively. These are the normalized frequency estimates for the angular distance dimension of the target.

[0114] According to the apparatus provided by the present invention, the signal-to-noise ratio of the echo signal can be improved by compensating the echo signal through the wedge transform algorithm, and the resolution of the target in the echo signal can be improved by minimizing the atomic norm. Thus, high-precision detection and high-resolution resolution of small targets in a group of targets can be achieved, with good robustness. At the same time, by transforming the echo signal into a three-dimensional echo signal in space-range-frequency and then performing subsequent processing, compared with the current two-dimensional super-resolution in space-range only, the resolution performance of cluster targets can be further improved, and the resolution can be increased.

[0115] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

Claims

1. A method for detecting and distinguishing unmanned aerial vehicle (UAV) swarms based on KT and DeanmM, characterized in that, include: A three-dimensional echo signal is obtained by performing a spatial-dimensional digital beamforming transformation on the echo signal, wherein the three-dimensional echo signal includes information about the target in the range time domain, azimuth slow time domain, and spatial frequency domain; The acceleration and velocity ambiguity number of the target are searched based on the three-dimensional echo signal, and the pre-filtered three-dimensional echo signal is compensated based on the acceleration estimate and velocity ambiguity number estimate using the wedge transform algorithm to obtain the compensated three-dimensional echo signal. The pre-filtered three-dimensional echo signal is obtained based on the three-dimensional echo signal. Based on the compensated three-dimensional echo signal, the distance, velocity, and angle of the target are coarsely estimated to obtain the coarse estimates of the target's distance, velocity, and angle. Based on the coarse distance estimate, the coarse velocity estimate, and the coarse angle estimate, the distance dimension and angle dimension of the compensated three-dimensional echo signal are extracted and subjected to inverse Fourier transform to obtain a two-dimensional echo signal, wherein the two-dimensional echo signal includes information about the target in the distance dimension and angle dimension; The toplitz matrix of the target is obtained by decoupling and minimizing the atomic norm of the two-dimensional echo signal, and then the toplitz matrix of the target is decomposed by Vandermonde to obtain the range super-resolution estimate and angle super-resolution estimate of the target.

2. The method according to claim 1, characterized in that, The three-dimensional echo signal satisfies the following formula: in, For the three-dimensional echo signal, A DBF The amplitude of the three-dimensional echo signal, Let represent Gaussian white noise with zero mean and constant variance, sin c(x) = sin(πx) / πx, and K be the total number of targets within one radar beam. To save time, t m =mT r m is a positive integer less than or equal to M-1, T r T is the pulse repetition period. P f is the pulse width. c Where c is the carrier frequency and c is the speed of light. R k0 v k0 a k0 θ k0 These are the initial distance, velocity, acceleration, and azimuth angle between the k-th target within one beam of the radar and the radar, respectively, where k is a positive integer less than or equal to K, and z is the index of the number of grid cells.

3. The method according to claim 1, characterized in that, The two-dimensional echo signal satisfies the following formula: Among them, S n-l (n, l) represents the two-dimensional echo signal, A n-l e n-l These represent the amplitude and noise in the distance, velocity, and angular domains, respectively. For the distance-frequency domain sampling index, N r Where is the number of frequency domain sampling points, l is the spatial domain sampling index, and F s The sampling frequency.

4. The method according to claim 1, characterized in that, The process of decoupling and minimizing the atomic norm of the two-dimensional echo signal to obtain the Toplitz matrix of the target includes: The Toplitz matrix of the target is obtained by decoupling and minimizing the atomic norm of the two-dimensional echo signal based on the atomic norm minimization model. The atomic norm minimization model satisfies the following formula: Wherein, T(u R ), T(u θ The first row of sequences corresponding to distance and angle are u. R and u θ The optimal Toplitz matrix is ​​given by Tr(), where Tr() represents the trace of the matrix, λ1 is the regularization coefficient, S is the rewritten two-dimensional echo signal, and y is the noise-free signal.

5. The method according to claim 1, characterized in that, The range super-resolution estimate and the angle super-resolution estimate of the target satisfy the following formula: in, These are the range super-resolution estimate and the angle super-resolution estimate of the target, respectively. These are the estimated normalized frequencies of the target in the angular and distance dimensions, respectively.

6. A device for detecting and distinguishing unmanned aerial vehicle (UAV) swarms based on KT and Deanm, characterized in that, include: The first transformation unit is used to perform spatial-dimensional digital beamforming transformation on the echo signal to obtain a three-dimensional echo signal, wherein the three-dimensional echo signal includes information about the target in the range time domain, azimuth slow time domain, and spatial frequency domain. The compensation unit is used to search for the acceleration and velocity ambiguity number of the target based on the three-dimensional echo signal, and to compensate the pre-filtered three-dimensional echo signal based on the wedge transform algorithm, according to the acceleration estimate and the velocity ambiguity number estimate, to obtain the compensated three-dimensional echo signal, wherein the pre-filtered three-dimensional echo signal is obtained based on the three-dimensional echo signal. A coarse estimation unit is used to perform coarse estimation of the target's distance, velocity, and angle based on the compensated three-dimensional echo signal to obtain coarse estimates of the target's distance, velocity, and angle. The second transformation unit is used to extract the distance dimension and angle dimension of the compensated three-dimensional echo signal based on the coarse distance estimate, the coarse velocity estimate and the coarse angle estimate, and perform inverse Fourier transform to obtain a two-dimensional echo signal, wherein the two-dimensional echo signal includes information about the target in the distance dimension and angle dimension; The fine estimation unit is used to perform decoupled atomic norm minimization processing on the two-dimensional echo signal to obtain the Toplitz matrix of the target, and to perform Vandermonde decomposition on the Toplitz matrix of the target to obtain the range super-resolution estimate and angle super-resolution estimate of the target.

7. The apparatus according to claim 6, characterized in that, The three-dimensional echo signal satisfies the following formula: in, For the three-dimensional echo signal, A DBF The amplitude of the three-dimensional echo signal, Let represent Gaussian white noise with zero mean and constant variance, sin c(x) = sin(πx) / πx, and K be the total number of targets within one radar beam. To save time, t m =mT r m is a positive integer less than or equal to M-1, T r T is the pulse repetition period. P f is the pulse width. c Where c is the carrier frequency and c is the speed of light. R k0 v k0 a k0 θ k0 These are the initial distance, velocity, acceleration, and azimuth angle between the k-th target within one beam of the radar and the radar, respectively, where k is a positive integer less than or equal to K, and z is the index of the number of grid cells.

8. The apparatus according to claim 6, characterized in that, The two-dimensional echo signal satisfies the following formula: Among them, S n-l (n, l) represents the two-dimensional echo signal, A n-l e n-l These represent the amplitude and noise in the distance, velocity, and angular domains, respectively. For the distance-frequency domain sampling index, N r Where is the number of frequency domain sampling points, l is the spatial domain sampling index, and F s The sampling frequency.

9. The apparatus according to claim 6, characterized in that, The precise estimation unit is specifically used for: The Toplitz matrix of the target is obtained by decoupling and minimizing the atomic norm of the two-dimensional echo signal based on the atomic norm minimization model. The atomic norm minimization model satisfies the following formula: Wherein, T(u R ), T(u θ The first row of sequences corresponding to distance and angle are u. R and u θ The optimal Toplitz matrix is ​​given by Tr(), where Tr() represents the trace of the matrix, λ1 is the regularization coefficient, S is the rewritten two-dimensional echo signal, and y is the noise-free signal.

10. The apparatus according to claim 6, characterized in that, The range super-resolution estimate and the angle super-resolution estimate of the target satisfy the following formula: in, These are the range super-resolution estimate and the angle super-resolution estimate of the target, respectively. These are the estimated normalized frequencies of the target in the angular and distance dimensions, respectively.

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