Three-Dimensional Space Swarm Target Detection and Information Estimation Method Based on Phased Array Radar

Abstract

The present invention discloses a three-dimensional space swarm target detection and information estimation method based on a phased array radar. First, starting from the three-dimensional distribution model of the space swarm target, an echo model under the phased array radar system is established. The echo model is preprocessed, the sparsity of the echo matrix is used as a regularization constraint term, super-resolution processing is performed on the azimuth dimension and the elevation dimension, and noise is suppressed for target resolution detection. Then, three-dimensional condensation processing is performed on the super-resolution result to condense the broadened targets into one target. Finally, three-dimensional convex hull solving is performed on the condensation result to obtain the contour estimation of the space swarm target, and the swarm scale is estimated under this contour. The method of the present invention effectively solves the problems of resolving and detecting three-dimensional space swarm targets in a real scene and information estimation using existing radar systems, and has high prediction accuracy and excellent performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar, and particularly relates to a three-dimensional space swarm target detection and information estimation method based on a phased array radar. Background Art

[0002] Swarm targets originate from the research of human society on the behaviors of animals in nature, referring to a large number of individuals with similar sizes and motion patterns, gathering together within a certain period of time and exhibiting decentralized and self-organized group behaviors. Typical swarm targets include bird flocks, insect swarms, unmanned aerial vehicle (UAV) swarms, etc. The detection requirements for spatial swarm targets exist in various scenarios of the real world. For example, airport bird detection radars need to detect and track bird flocks near airports to prevent impacts on aircraft takeoff, landing, etc.; insect radars need to detect large-scale insect swarms and predict and estimate the scale, density, migration routes, etc. of insect swarms, so as to effectively prevent and control insect disasters; in the future urban environment, services such as UAV food delivery and UAV express delivery will gradually become popular, and the effective detection and supervision of UAV swarms over cities are related to the lives of citizens and the safety of cities, which is an important part of urban governance. For these spatial swarm target scenarios, it is necessary to accurately detect them as much as possible and obtain sufficient information about the swarm targets. Therefore, it is of great practical significance to detect swarm targets in the three-dimensional space of range-azimuth-elevation using radar and estimate information such as the scale and three-dimensional contour of the swarm as accurately as possible.

[0003] Currently, there is relatively little research on radar detection of three-dimensional space dense swarm targets. Since swarm targets have a large number, are densely distributed, and the individuals in the swarm have a high degree of autonomy in motion, the swarm structure is variable, and there are also situations involving individual increase and decrease, therefore, many situations need to be considered for the detection of spatial swarm targets.

[0004] The literature "Zheng Jibin et al. An Efficient Strategy for Accurate Detection and Localization of UAV Swarms. IEEE Internet of Things Journal, 2021, 8(20): 15372 - 15381" proposed an effective strategy for accurate detection and localization of UAV swarms. By using a radar equipped with a co-prime array, the UAVs in the swarm are detected and located using coherent long-time integration technology and meshless sparse technology. However, this method has special requirements for the radar array and is not applicable to traditional array radars; moreover, this method requires long-time accumulation, has poor real-time performance and high computational complexity; in addition, this method only considers the two-dimensional plane of range-azimuth. When it comes to real-world spatial swarm targets, corresponding array forms, algorithms, etc. all need to be greatly changed.

[0005] The literature "Chen Weishi, Huang Yifeng, Lu Xianfeng, Zhang Jie, Chen Xiaolong. Estimation of the Number of Bird Targets around Airports Based on Bird Detection Radar. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(08): 1533-1542" proposed a multi-target track automatic initiation and tracking algorithm, which realized the statistical analysis of the number of bird targets in the hot spots of bird activities around airports. However, this method requires accurate measurement data of swarm targets, and can only estimate the number of targets in the swarm through tracking in the two-dimensional plane of range-azimuth dimension, and cannot effectively estimate the swarm contour.

[0006] CN113109804A discloses a working mode of phased array radar swarm target tracking, which tracks the equivalent measurement of the swarm target while scanning the spatial area occupied by the predicted value of the swarm target scale, and predicts the scanning area of the next cycle through the maximum and minimum measurement values of the swarm target in the range, azimuth and elevation dimensions in the previous scanning cycle; simultaneously tracks the overall swarm and swarm members through a hybrid swarm target tracking method. However, this method only relies on beam scanning to obtain swarm target information, does not solve the resolution detection of swarm targets under the condition of limited beam width, and only relies on the measurement of swarm targets to estimate the scanning range, without considering the acquisition of information such as the scale and contour of swarm targets. The above methods only solve the problem of spatial swarm target detection in certain specific scenarios, have their own limitations, do not consider the three-dimensional spatial distribution of swarm targets, and do not effectively estimate the scale and contour information of swarm targets. Summary of the Invention

[0007] To solve the above technical problems, the present invention proposes a three-dimensional space swarm target detection and information estimation method based on a phased array radar.

[0008] The technical solution of the present invention is as follows: A three-dimensional space swarm target detection and information estimation method based on a phased array radar, and the specific steps are as follows:

[0009] S1. Establish a three-dimensional space swarm target echo model based on a phased array radar,

[0010] Starting from the radar echo of a single array element of a point target, combining the characteristics of a phased array radar, according to the radar array element distribution and the spatial distribution characteristics of the swarm target, obtain the three-dimensional echo of range-azimuth-elevation of multiple targets in space to different array elements of the radar, and then combine the vector superposition model of the swarm target to establish a spatial swarm target echo model based on the phased array radar.

[0011] where K is the number of targets in the swarm, l = 0, 1, …, L - 1 is the sampling point in the range dimension, m = 0, 1, …, M - 1 is the number of array elements in the azimuth dimension, n = 0, 1, …, N - 1 is the number of array elements in the elevation dimension, L is the number of sampling points in the range dimension, M is the total number of array elements in the azimuth dimension, N is the total number of array elements in the elevation dimension; x k (l, m, n) is the echo of the k-th target in the swarm at the l-th sampling point in the range dimension, relative to the m-th array element in the azimuth dimension and the n-th array element in the elevation dimension.

[0012] S2. Preprocess the echo model in step S1 to obtain a preprocessing result.

[0013] Preprocessing the echo model in step S1 includes range dimension pulse compression and beamforming in the azimuth-elevation dimension to obtain a preprocessing result X(R, A, E).

[0014] where R is the variable in the range dimension, A is the variable in the azimuth dimension, E is the variable in the elevation dimension, and X(R, A, E) represents the three-dimensional space swarm target echo under the three variables.

[0015] S3. Use a regularization method based on sparse constraints to perform two-dimensional super-resolution processing on the azimuth-elevation dimension, taking the Frobenius norm of the azimuth and elevation dimension echo matrices as the regularization constraint term, and solving the optimization problem under this constraint.

[0016] Due to the limitation of the antenna aperture, the beam in step S2 cannot be infinitely narrow. Therefore, the target has a large angular dimension broadening under the modulation of the antenna pattern, which is not conducive to subsequent resolution detection and quantity estimation of adjacent targets. Therefore, a regularization method based on sparse constraints is used to perform two-dimensional super-resolution processing on the azimuth-elevation dimension, taking the Frobenius norm of the azimuth and elevation dimension echo matrices as the regularization constraint term, and solving the optimization problem under this constraint.

[0017] where H is the convolution matrix corresponding to the azimuth-elevation dimension antenna pattern, x(A, E) is the distribution of the target in the azimuth-elevation dimension, y is the three-dimensional space swarm target echo X(R, A, E) in step S2, ||·||2 is the matrix two-norm operation, μ is the regularization parameter, ||·|| F is the Frobenius norm of the matrix. is the azimuth-elevation dimension super-resolution result of the target.

[0018] S4. Use a three-dimensional condensation algorithm based on spatial density to cluster multiple targets located in adjacent azimuth-elevation resolution cells into a cluster, and re-condense this cluster into a single target point to facilitate subsequent accurate information estimation of the swarm targets.

[0019] Affected by the performance of the super-resolution algorithm in step S3, when performing azimuth-elevation dimension super-resolution, the target energy obtained is not all concentrated at one point, resulting in the dispersion of target energy. A single target may be misdetected as multiple targets located in adjacent azimuth-elevation resolution units, which has a great impact on the subsequent estimation of the scale of the swarm target.

[0020] To address the above problems, a three-dimensional condensation algorithm based on spatial density is adopted. By setting two parameters, the condensation radius ε and the condensation scale Ω, multiple targets located in adjacent azimuth-elevation resolution units are clustered into one cluster, and this cluster is re-condensed into a single target point, thereby reducing the impact of the increase in the number of target points caused by limited super-resolution performance.

[0021] S5. To obtain the contour information of the spatial swarm target, the incremental method is used to solve the three-dimensional convex hull to obtain the spatial envelope of the swarm target, and then the estimation of its contour is obtained; based on this contour estimation, the scale of the swarm is estimated.

[0022] Furthermore, in the above step S1, the process of modeling the range-azimuth-elevation three-dimensional radar echo of the spatial swarm target is as follows:

[0023] First, the parameters of the phased array radar are preset. The phased array antenna array is a planar array, measuring the azimuth angle in the horizontal direction, with the number of array elements being M, the element spacing being half a wavelength, and the corresponding azimuth dimension beam width being Measuring the elevation angle in the vertical direction, with the number of array elements being N, the element spacing being half a wavelength, and the corresponding elevation dimension beam width being The radar adopts an azimuth-elevation two-dimensional electronic scanning mode to obtain the range and angle information of spatial targets through the spatial scanning of narrow beams.

[0024] The traditional phased array radar echo model only considers the two-dimensional echo of range-azimuth dimension or only considers the three-dimensional spatial echo model of a single target. The method of the present invention divides the formation process of the group target echo into three stages under the azimuth-elevation two-dimensional scanning mode of the phased array radar: First, the radar emits a narrow beam to a certain azimuth-elevation angle, and the target located at this angle reflects the transmitted signal, and the range information of the target is determined according to the time when the radar receives the reflected wave; then, the beam scans in the two-dimensional angle domain, and the targets at different angles are successively covered by the beam and generate reflected echoes, and the azimuth-elevation information of the target is determined according to the scanned angle; finally, combined with the vector superposition model of the radar echo signals of the group target, the three-dimensional radar echo signals of individual targets are vectorially superposed to obtain the phased array radar echo model of the entire spatial swarm target. Referring to these three stages, the following process of modeling the three-dimensional radar echo of the spatial swarm target is proposed:

[0025] First, study the range dimension radar echo of a single target, as shown in the following formula:

[0026]

[0027] where x k $x_k(\tau)$ is the echo of the $k$-th target in the swarm in the range dimension, rect(·) is the rectangular window function, $\tau$ is the fast time in the range dimension, $\tau_k$ is the time delay in the range dimension of the $k$-th target, $c$ is the speed of light, $R_k$ k is the radial distance from the $k$-th target to the radar, $T$ is the pulse width of the transmitted pulse, $s$ k is the target scattering coefficient, $f$ is the carrier frequency of the radar transmitted signal, and $\alpha$ is the frequency modulation slope of the linearly frequency-modulated signal transmitted by the radar.

[0028] Perform de-carrier processing on Equation (1), and then sample the continuous-time variable $\tau$ in the fast time dimension to achieve discretization. Let $\tau = t$ l $= l\cdot T$ s , $l = 0, 1, \ldots, L - 1$, $t$ l is the time variable in the discretized fast time dimension, $T$ s is the sampling interval, and $l$ is the sampling point in the range dimension. Then Equation (1) can be written as:

[0029]

[0030] where $\lambda$ is the wavelength of the transmitted signal, $c = f\cdot\lambda$. This equation is the range dimension echo model of a single target relative to the origin of the radar array.

[0031] Analyze the echo model of the azimuth-elevation two-dimensional angle. Considering the path difference for different array elements of the radar in Equation (2), assume that the azimuth angle and elevation angle of the $k$-th target to the origin of the radar array are $\theta$ k and The horizontal spacing of the radar array elements is $d$ y , and the vertical spacing is $d$ z . Then, according to the knowledge of solid geometry, the path difference from the target to the $(m, n)$-th radar array element is: in the horizontal direction in the vertical direction The time difference caused by the path difference will affect the phase information of the echo. Then the range-azimuth-elevation dimension echo of a single target can be written as:

[0032]

[0033] where $l = 0, 1, \ldots, L - 1$ is the sampling point in the range dimension, $m = 0, 1, \ldots, M - 1$ is the number of array elements in the azimuth dimension, and $n = 0, 1, \ldots, N - 1$ is the number of array elements in the elevation dimension.

[0034] Finally, expand the echo of a single target to the echo of a spatial swarm target. According to the vector superposition model of the swarm target echo, the phased array radar echo model of the spatial swarm target is finally derived as

[0035] Further, in step S2, the echo model shown in step S1 is preprocessed:

[0036] First, pulse compression in the range dimension is performed. Let the range dimension variable The result of pulse compression is:

[0037]

[0038] Among them, Y(R, m, n) represents the echo of the spatial swarm target relative to the m-th element in the azimuth dimension and the n-th element in the elevation dimension of the radar under the range dimension variable R after pulse compression.

[0039] Beamforming in the azimuth and elevation dimensions is performed on Equation (4). Generally speaking, the azimuth angle scanning range of a phased array radar is large and the angular resolution is higher; the elevation angle scanning range is small and the angular resolution is generally poor. Assume that the scanning range of the azimuth angle variable θ is (-30°, 30°) and the scanning interval is 0.5°; the elevation angle variable The scanning range is (0°, 20°) and the scanning interval is 1°. Then θ = -30°, -29.5°, -29°, …, 0, …, 29.5, 30°; Let the azimuth dimension variable The elevation dimension variable The azimuth-elevation dimension beamforming result is obtained as:

[0040]

[0041] Further, in step S3, the beamforming result is processed using a regularization method based on sparse constraints to complete the super-resolution processing of the azimuth-elevation dimension:

[0042] Among them, the regularization method is to establish a corresponding regularization equation for solution according to prior information, such as the characteristics of the spatial distribution of the swarm target. For one-dimensional super-resolution, such as super-resolution in the azimuth dimension, a regularization equation with a single variable can be directly established is the estimated value of the variable x to be solved. x satisfies the formula: y = Hx, and H and y are known. ||·||2 and ||·||1 represent the matrix two-norm and the matrix one-norm respectively, and μ is the regularization parameter, which generally takes empirical values. The sparse regularization model of the above formula is solved through an iterative algorithm to obtain the target azimuth dimension distribution under a certain range dimension variable, thereby realizing the azimuth dimension super-resolution processing of the target.

[0043] For a swarm target with a three-dimensional spatial distribution, due to the limitation of the beam width of the phased array radar, two-dimensional super-resolution processing needs to be carried out separately for the azimuth dimension and the elevation dimension, so as to form the three-dimensional distribution of the target's range-azimuth-elevation. Considering that the distribution of the target in space is sparse relative to the continuous airspace, and in order to retain the information of the target in the azimuth dimension and the elevation dimension as completely as possible, two-dimensional sparse constraints in the azimuth dimension and the elevation dimension are introduced, and the original one-norm for vectors is improved to the Frobenius norm for two-dimensional matrices. According to the convex optimization theory, the Frobenius norm also has sparsity. Based on this, the regularization equation is improved to Then, the linear Bregman iterative algorithm for solving convex optimization problems is applied. By presetting the algorithm accuracy, the two-dimensional distribution of the target's azimuth-elevation under a certain range dimension is solved through multiple iterations. Finally, the two-dimensional super-resolution results of all range dimensions are integrated in a dimension-raising manner based on matrices of the same dimension, and the super-resolution processing results of the echoes of the three-dimensional space swarm target are obtained

[0044] Further, in the agglomerative algorithm in step S4, all data points are divided into three categories:

[0045] (1) Core point: If an object contains more than Ω number of points within its radius ε, then the object is a core point;

[0046] (2) Boundary point: If an object contains less than Ω number of points within its radius ε, but the object falls within the neighborhood of a core point, then the object is a boundary point;

[0047] (3) Noise point: If an object is neither a core point nor a boundary point, then the object is a noise point.

[0048] According to this classification idea, the three-dimensional agglomerative algorithm based on spatial density can cluster adjacent points in space into one category. In the present invention, multiple adjacent detection points generated by one target can be agglomerated. For the selection of the parameters of the agglomerative algorithm, firstly, the agglomeration radius ε is an important factor affecting whether multiple points can be clustered into one category. If ε is selected too large, several detection points that are far apart and generated by multiple targets will be judged as the same category, and in the present invention, they will be agglomerated into one target point, bringing an error in scale estimation. If ε is selected too small, multiple detection points generated by one target will not be successfully clustered into one category and will be judged as multiple target points, still bringing an error in scale estimation. Secondly, the agglomeration scale Ω affects whether the target point will ultimately be classified into one category or into noise points. Therefore, the selection of ε and Ω needs to comprehensively consider the angular resolution of the radar and the angular distribution of the target.

[0049] Further, the incremental method in step S5 is used to solve the three-dimensional convex hull to estimate the contour of the swarm target. The specific steps are as follows:

[0050] (1) All the target points detected in step S4 form a point set. In this point set, any four points are taken to form an initial tetrahedron: two points p1 and p2 are selected, then a point p3 that is not collinear with p1 and p2 is selected. The three points form a face, and then any point p4 that is not on this face is selected, thus forming an initial tetrahedron;

[0051] (2) Study the remaining points. If a point is inside the tetrahedron, skip this point; if a point is outside the tetrahedron, delete the faces that this point can "see" to expand the volume of the convex hull;

[0052] (3) Until all points have been traversed, the final convex polyhedron obtained is the required convex hull.

[0053] The required three-dimensional convex hull is the spatial contour estimation of the spatial swarm target. Under this contour estimation, further estimation of the scale of the swarm target can be obtained.

[0054] Advantages of the present invention: The method of the present invention first starts from the three-dimensional distribution model of the spatial swarm target, establishes an echo model under the phased array radar system, preprocesses the echo model, uses the sparsity of the echo matrix as a regularization constraint term, performs super-resolution processing on the azimuth dimension and elevation dimension, and suppresses noise for target resolution detection. Then, three-dimensional condensation processing is performed on the super-resolution result to condense the broadened targets into one target. Finally, based on the incremental method, the three-dimensional convex hull of the condensation result is solved to obtain the contour estimation of the spatial swarm target, and the scale of the swarm is estimated under this contour. The method of the present invention effectively solves the problems of resolution detection and information estimation of three-dimensional spatial swarm targets in real scenarios using existing radar systems, has high prediction accuracy and excellent performance, and is applicable to real problems such as bird detection at airports, insect migration and control, and countermeasure against unmanned aerial vehicle swarms. Description of the Drawings

[0055] Figure 1 It is a flowchart of a method for detecting and information estimating three-dimensional spatial swarm targets based on a phased array radar according to the present invention.

[0056] Figure 2 It is a schematic diagram of the distribution of array elements of the phased array radar system used in the embodiment of the present invention.

[0057] Figure 3 It is a schematic diagram of the distribution of the spatial swarm targets set in the embodiment of the present invention.

[0058] Figure 4 It is an effect diagram during the specific implementation in the embodiment of the present invention.

[0059] Figure 5 It is a curve diagram of the information estimation error of the method of the present invention under different target scales. Detailed implementation manners

[0060] The method of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0061] The present invention mainly uses computer simulation methods for verification, and all steps and conclusions are verified correctly on MATLAB-R2019b. As Figure 1 shown, the flowchart of a three-dimensional space swarm target detection and information estimation method based on a phased array radar according to the present invention is as follows:

[0062] Figure 2 shows the element distribution of the phased array radar system used in the present invention. The radar emits a linear frequency modulated pulse signal, and the phase of the transmitted signal is adjusted through a phase shifter to achieve the scanning process of the transmitting beam in the azimuth-elevation two-dimensional angular domain. The parameters of the radar system are shown in Table 1. Under these parameters, the range resolution of the radar system is 3m, the angular resolution of the azimuth dimension and the elevation dimension is about 4°, and the maximum unambiguous detection range is 12km.

[0063] Table 1

[0064] Parameter Symbol Value Carrier frequency f 10 GHz Bandwidth B 50 MHz Time width of transmitted signal T 80 μs Pulse sampling frequency PRF 50 MHz Number of array elements in horizontal direction M 30 Number of array elements in vertical direction N 30 Element spacing <![CDATA[d y 、d z > 1.5 cm (half wavelength)

[0065] Figure 3 shows the space swarm target scenario set by the present invention. The targets in the swarm are randomly distributed within a specific spatial range, and the minimum radial distance from the radar is 10km. The signal-to-noise ratio of the simulation scenario is set to 0dB. The relevant parameters of the swarm target scenario are shown in Table 2.

[0066] Table 2

[0067] Parameter Symbol Value Number of targets in swarm K 64 Expansion range in range dimension R_range 1000m Expansion range in azimuth dimension A_range 2000m Expansion range in elevation dimension E_range 2000m

[0068] The specific steps are as follows:

[0069] Step 1: Generate the original radar echoes of the swarm targets based on the radar system parameters and scenario parameters

[0070] Step 2: Perform range-dimensional pulse compression and angle-dimensional beamforming on the original radar echoes to obtain the preprocessed echo result X(R,A,E).

[0071] Step 3: Due to the limitations of the radar hardware conditions, the targets cannot be resolved in the angle dimension after beamforming. The preprocessed echo result is processed using a regularization super-resolution method based on sparse constraints. At the same time, due to the inherent properties of the sparse regularization method, the noise is suppressed simultaneously, and the resolved detection result of the swarm targets is obtained

[0072] Step 4: Since the super-resolution performance is limited, to solve the problem that one target is detected as multiple targets after broadening, a three-dimensional condensation algorithm based on spatial density is adopted. According to the radar and target parameters set by the method of the present invention, the condensation radius ε = 2 and the condensation scale Ω = 1 are set. Multiple targets located in adjacent azimuth-elevation resolution units are clustered into one cluster, and this cluster is re-condensed into a single target point to facilitate subsequent accurate information estimation of the swarm target.

[0073] Step 5: For the detected points of the swarm target in the condensation result, the incremental method is used to solve the three-dimensional convex hull to obtain the spatial envelope of the swarm target, and then the estimation of its contour is obtained; based on this contour estimation, the scale of the swarm is estimated.

[0074] Finally, the detection and information estimation results of the spatial swarm target are as Figure 4 (a), Figure 4 (b), Figure 4 (c), Figure 4 (d) shown, which are in sequence: the original target distribution, the original swarm target information, the target resolution detection result, and the swarm target information estimation result. Figure 5 (a), Figure 5 (b) gives the information estimation error curve graph of the method of the present invention for the spatial swarm target under different target scales. It can be seen from the figure that the method of the present invention can achieve the resolution detection and information estimation of the dense spatial swarm target under different target scales, and can reach a very high prediction accuracy under a certain signal-to-noise ratio, with a good information estimation effect.

[0075] It can be seen from the embodiments of the present invention that the method of the present invention can realize the phased array radar echo modeling of the spatial swarm target, and complete the resolution detection and information estimation of the swarm target. For swarm targets with different scales and densities, a very high information estimation accuracy can be achieved under a certain signal-to-noise ratio, with good robustness and reliability.

Claims

1. A method for three-dimensional space swarm target detection and information estimation based on a phased array radar, the specific steps are as follows: S1. Starting from the single-array-element radar echo of a point target, combined with the characteristics of a phased array radar, obtain the three-dimensional echo of distance-azimuth-pitch from multiple spatial targets to different array elements of the radar. Then, combined with the vector superposition model of a swarm target, establish a spatial swarm target echo model based on the phased array radar Among them, K is the number of targets in the bee swarm, l = 0, 1, …, L - 1 are the sampling points in the range dimension, m = 0, 1, …, M - 1 are the number of array elements in the azimuth dimension, n = 0, 1, …, N - 1 are the number of array elements in the elevation dimension, L is the number of sampling points in the range dimension, M is the total number of array elements in the azimuth dimension, N is the total number of array elements in the elevation dimension; x k (l, m, n) is the echo of the k-th target in the bee swarm at the l-th sampling point in the range dimension, relative to the m-th array element in the azimuth dimension and the n-th array element in the elevation dimension; S2. Preprocess the echo model in step S1, including range dimension pulse compression and azimuth-elevation dimension beamforming, to obtain a preprocessing result X(R, A, E); Among them, R is the range dimension variable, A is the azimuth dimension variable, E is the elevation dimension variable, and X(R, A, E) represents the three-dimensional space swarm target echo under the three variables; S3. Perform two-dimensional super-resolution processing on the azimuth-elevation dimension, use the Frobenius norm of the azimuth and elevation dimension echo matrices as the regularization constraint term, and solve the optimization problem under this constraint where \(H\) is the convolution matrix corresponding to the azimuth-elevation antenna pattern, \(x(A, E)\) is the distribution of the target in the azimuth-elevation dimension, \(y\) is the three-dimensional space swarm target echo \(X(R, A, E)\) in step S2, \(\|\cdot\|_2\) is the matrix two-norm operation, \(\mu\) is the regularization parameter, and \(\|\cdot\) F is the Frobenius norm of the matrix, and is the azimuth-elevation super-resolution result of the target; S4. Cluster multiple targets located in adjacent azimuth-elevation resolution units into a cluster, and re-condense this cluster into a target point; S5. Solve the three-dimensional convex hull to obtain the spatial envelope of the swarm target, and then obtain the estimation of its contour. Based on this contour estimation, estimate the scale of the swarm.

2. The three-dimensional space swarm target detection and information estimation method based on a phased array radar according to claim 1, characterized in that, In the said step S1: First, preset the parameters of the phased array radar. The phased array antenna array is a planar array, measuring the azimuth angle in the horizontal direction. The number of array elements is M, the element spacing is half a wavelength, and the corresponding beam width in the azimuth dimension is Measuring the elevation angle in the vertical direction. The number of array elements is N, the element spacing is half a wavelength, and the corresponding beam width in the elevation dimension is The radar adopts an azimuth-elevation two-dimensional electronic scanning mode, and obtains the distance and angle information of spatial targets through the spatial scanning of narrow beams; The range dimension radar echo of a single target is as follows: where x k (τ) is the echo of the k-th target in the range dimension of the swarm, rect(·) is the rectangular window function, τ is the fast time in the range dimension, is the range dimension time delay of the k-th target, c is the speed of light, R k is the radial distance from the k-th target to the radar, T is the transmit pulse width, s k is the target scattering coefficient, f is the carrier frequency of the radar transmit signal, and α is the frequency modulation slope of the radar transmit linear frequency modulation signal; Perform de - carrier processing on Equation (1), and then sample the fast - time - dimension continuous - time variable τ to achieve discretization. Let τ = t l = l·T s , l = 0, 1, …, L - 1, t l is the fast - time - dimension time variable after discretization, T s is the sampling interval, and l is the sampling point in the range dimension. Equation (1) can be written as: Among them, λ is the wavelength of the transmitted signal, and c = f·λ; Assume that the azimuth angle and elevation angle of the k-th target relative to the origin of the radar array are θ k and The horizontal spacing between radar elements is d y and the vertical spacing is d z The path difference from the target to the (m,n)-th radar element is: in the horizontal direction in the vertical direction The time difference caused by the path difference affects the phase information of the echo. Then the range-azimuth-elevation dimensional echo of a single target can be written as: Among them, l = 0, 1, …, L - 1 are the range dimension sampling points, m = 0, 1, …, M - 1 are the number of azimuth dimension array elements, and n = 0, 1, …, N - 1 are the number of elevation dimension array elements; Expand the echo of a single target into the echo of a spatial swarm target. According to the vector superposition model of the swarm target echo, the phased array radar echo model of the spatial swarm target is finally derived as 3. A three-dimensional space swarm target detection and information estimation method based on a phased array radar according to claim 1, characterized in that, The specific process of preprocessing the echo model in the said step S2 is as follows: Perform pulse compression in the range dimension, and let the range dimension variable The result of pulse compression is: Among them, Y(R, m, n) represents the echo of the spatial swarm target relative to the m-th array element in the azimuth dimension and the n-th array element in the elevation dimension of the radar under the range dimension variable R after pulse compression; Perform beamforming in the azimuth dimension and elevation dimension on Equation (4). Assume that the scanning range of the azimuth angle variable θ is (-30°, 30°), the scanning interval is 0.5°, and the elevation angle variable The scanning range is (0°, 20°), and the scanning interval is 1°. Then θ = -30°, -29.5°, -29°, …, 0°, …, 29.5°, 30°, Let the azimuth dimension variable The elevation dimension variable The azimuth-elevation beamforming result is obtained as follows: 。 4. A three-dimensional space swarm target detection and information estimation method based on a phased array radar according to claim 1, characterized in that, In the said step S3, a regularization method based on sparse constraints is used to perform two-dimensional super-resolution processing on the azimuth-elevation dimension.

5. A three-dimensional space swarm target detection and information estimation method based on a phased array radar according to claim 4, characterized in that In step S3, the specific steps are as follows: First, introduce the two-dimensional sparse constraints in the azimuth dimension and the elevation dimension, improve the original l1-norm for vectors to the Frobenius norm for two-dimensional matrices, improve the regularization equation, apply the linear Bregman iteration algorithm for solving convex optimization problems, preset the algorithm accuracy, and solve the target azimuth-elevation two-dimensional distribution in a certain range dimension through multiple iterations. Finally, perform the dimension-raising integration based on the same-dimensional matrices for the two-dimensional super-resolution results of all range dimensions to obtain the super-resolution processing results for the echoes of the swarm targets in three-dimensional space.

6. The three-dimensional space swarm target detection and information estimation method based on a phased array radar according to claim 1, characterized in that In the said step S4, a three-dimensional condensation algorithm based on spatial density is used to cluster multiple targets located in adjacent azimuth-elevation resolution units into a cluster, and re-condense this cluster into a target point.

7. A three-dimensional space swarm target detection and information estimation method based on a phased array radar according to claim 6, characterized in that, In step S4, the specific steps are as follows: Divide all data points into three categories: (1) Core point: If an object contains more than Ω number of points within its radius ε, then this object is a core point; (2) Border point: If an object contains less than Ω number of points within its radius ε, but this object falls within the neighborhood of a core point, then this object is a border point; (3) Noise point: If an object is neither a core point nor a border point, then this object is a noise point; Then condense multiple adjacent detection points generated by a target.

8. A three-dimensional space swarm target detection and information estimation method based on a phased array radar according to claim 1, characterized in that In the said step S5, the incremental method is used to solve the three-dimensional convex hull to estimate the contour of the swarm target.

9. The three-dimensional space swarm target detection and information estimation method based on a phased array radar according to claim 8, characterized in that, In step S5, the specific steps are as follows: (1) All the target points detected in step S4 form a point set. In this point set, arbitrarily select four points to form an initial tetrahedron: Select two points p1, p2, then select a point p3 that is not collinear with p1 and p2. The three points form a face, and then arbitrarily select a point p4 that is not on this face. In this way, an initial tetrahedron is formed; (2) Examine the remaining points. If a point is inside the tetrahedron, skip it; if a point is outside the tetrahedron, delete the faces that this point can "see" to expand the volume of the convex hull. (3) Until all points have been traversed, the final convex polyhedron obtained is the required convex hull. The required three-dimensional convex hull is the spatial contour estimation of the spatial swarm target. Under this contour estimation, the scale estimation of the swarm target can be further obtained.

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