A multi-target array structure inversion method based on two-dimensional power spectrum imaging

Abstract

The present application belongs to the technical field of radar signal processing and target identification, and specifically provides a multi-target array structure inversion method based on two-dimensional power spectrum imaging, to solve the problem that the array structure in the multi-target scattering image is difficult to be stably recovered under the condition of strong aliasing, strong speckle and strong coherent interference background; the present application converts the collected radar scattering data into a power spectrum image, generates a global candidate point set with a level label through log power spectrum construction, sub-aperture decomposition, hierarchical candidate point extraction, consistency voting and density clustering deduplication, and further forms a closed loop through translation and combination prediction and bidirectional matching verification, and the original multi-target array structure is inferred from geometric evidence, which has good robustness, engineering feasibility and identification accuracy; and the present application does not depend on phase compensation, is suitable for observation scenes under multi-target, and meets the application requirements of complex target structure identification, multi-target imaging identification and target classification.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing and target recognition technology, and specifically provides a method for inverting the structure of a multi-target array based on two-dimensional power spectrum imaging. The aim is to reconstruct the dot matrix structure layout of the target from radar scattering data in a multi-scattering target scenario through power spectrum imaging. Background Technology

[0002] As the application demands of radar continue to expand in various scenarios such as unmanned reconnaissance, formation identification, port security, and low-altitude traffic management, the operational side has placed higher requirements on the acquisition of the spatial arrangement, mutual geometric relationships, and structural features of multiple targets. However, when multiple targets coexist and channel conditions are complex, echo superposition and coherent interference can produce phenomena such as aliasing, fringe artifacts, speckle fusion, and phase center drift in the imaging domain. This makes it difficult to directly separate the contributions of each target in a single image, further affecting the reliability of situational awareness, structure recognition, and subsequent decision-making. Therefore, how to recover the relative arrangement of multiple scattering centers from radar scattering data under suboptimal phase conditions has become a key challenge in engineering applications.

[0003] Currently, multi-target processing strategies mainly include three types. The first method adopts the idea of ​​image domain segmentation after global imaging. It divides the mixed image into several sub-regions through threshold detection, window segmentation, clustering, or morphological operators, and then reconstructs them separately. This type of method has a certain effect in scenarios where the targets are relatively far apart and the interference is relatively light. However, when the targets are dense, the side lobes are significant, or the motion state is complex, the segmentation boundary is not accurate enough, and false peaks and leakage will cause the loss of structural information. The second method is the iterative stripping and parameter estimation method, which can extract scattering points stepwise from strong to weak energy and remove them. One approach is to perform parameter fitting based on geometric trajectories on the feature plane to distinguish different targets. However, as noise and sidelobe proportions increase, these methods become more sensitive to parameters such as step size, gain, and stopping criteria, making it difficult to guarantee convergence stability and result consistency. The third approach is model-driven or data-driven methods, represented by sparse reconstruction, which rely on the sparsity of the target in the distance-Doppler or higher-dimensional representation space to achieve reconstruction. This approach is highly dependent on phase quality, prior models, and computational resources, and faces implementation obstacles in application scenarios with insufficient sampling, model mismatch, or limited real-time performance.

[0004] As can be seen from the above, in scenarios with dense targets, strong aliasing, and unsatisfactory phase conditions, existing multi-target radar imaging and recognition methods still generally suffer from problems such as incomplete structure recovery, unstable separation results, strong dependence on prior and phase quality, and high computational cost, making it difficult to meet the accuracy, reliability, and efficiency requirements of complex engineering applications. Therefore, there is an urgent need for a multi-target imaging and recognition method that can achieve statistical robustness and computational efficiency under strong aliasing, noise, and coherent interference conditions in order to complete the multi-target structure recognition in complex scenarios. Summary of the Invention

[0005] The purpose of this invention is to provide a method for inverting the structure of a multi-target array based on two-dimensional power spectrum imaging, in order to solve the problem of the difficulty in stably recovering the array structure in multi-target scattering images under background conditions of strong aliasing, strong speckle, and strong coherence interference. This invention converts the acquired radar scattering data into a power spectrum image, and generates a global candidate point set with hierarchical labels through logarithmic power spectrum construction, sub-aperture decomposition, hierarchical candidate point extraction, consensus voting, and density clustering deduplication. Furthermore, it forms a closed loop by using translational merging prediction and bidirectional matching verification, and derives the original multi-target array structure from geometric evidence. This method has good robustness, engineering feasibility, and recognition accuracy. Moreover, this invention does not rely on phase compensation, is applicable to observation scenarios with multiple targets, and meets the application requirements of complex target structure recognition, multi-target imaging recognition, and target classification.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for inverting the structure of a multi-target array based on two-dimensional power spectrum imaging includes the following steps:

[0008] Step 1: Obtain the two-dimensional intensity spectrum data of the far-field electromagnetic field scattering of the target scene, and calculate the square of its amplitude value as the input of the two-dimensional power spectrum for imaging;

[0009] Step 2: Perform logarithmic processing on the two-dimensional power spectrum input to obtain the two-dimensional logarithmic power spectrum;

[0010] Step 3: Divide the two-dimensional logarithmic power spectrum into multiple sub-apertures according to the frequency domain and / or observation angle domain to obtain several sub-aperture two-dimensional logarithmic power spectra;

[0011] Step 4: Perform a two-dimensional inverse Fourier transform on the two-dimensional logarithmic power spectrum of each sub-aperture to obtain the imaging results of the corresponding two-dimensional logarithmic power spectrum of several sub-apertures.

[0012] Step 5: Perform threshold segmentation and local maximum detection on the two-dimensional log power spectrum imaging results of each sub-aperture to obtain all scattering peaks on the two-dimensional log power spectrum imaging results of each sub-aperture, forming a candidate point set; then perform unsupervised clustering and classification on the members of the candidate point set according to the intensity of the scattering peaks to obtain the level labels.

[0013] Step 6: Map all candidate points detected in the two-dimensional logarithmic power spectrum imaging results of all sub-apertures to the same two-dimensional physical coordinate plane, and record each candidate point as an information unit containing location coordinates, grade label and sub-aperture number; extract the location coordinates of all candidate points to form a candidate point coordinate set, set the tolerance distance as the spatial neighborhood radius, and use the DBSCAN density clustering algorithm to uniformly cluster the candidate point coordinate set to form several clusters, each cluster corresponding to a candidate spatial location; for each cluster, count the sub-aperture numbers corresponding to the candidate points in the cluster, use the number of sub-apertures as the number of supporting sub-apertures for the candidate spatial location, set the voting ratio threshold, calculate the minimum support threshold, for each cluster, when the number of supporting sub-apertures is not less than the minimum support threshold, the candidate spatial location corresponding to the cluster is determined to be a valid spatial location, otherwise, it is determined to be an invalid spatial location and discarded;

[0014] Step 7: For each valid spatial location, calculate the arithmetic mean of the coordinates of all candidate points within the corresponding cluster, and use it as the global candidate point coordinates for that valid spatial location; at the same time, count the occurrence frequency of each level label within the cluster, and use the level label with the most occurrence frequency as the final level label of the scattering center point corresponding to that valid spatial location; record the global candidate point coordinates and final level labels for all valid spatial locations to obtain the global candidate point set;

[0015] Step 8: Select any non-empty proper subset from the global candidate point set as the candidate basis structure, and perform translation and union operations on the candidate basis structure with each of its reference points as the center according to the agreed coordinate system to obtain the predicted point set;

[0016] Step 9: Perform bidirectional matching verification between the predicted point set and the global candidate point set within the tolerance distance. When the bidirectional matching verification is satisfied, determine that the candidate basis structure is the multi-target array structure obtained by identification; otherwise, backtrack and change the candidate basis structure until the identification is completed.

[0017] Furthermore, in step 1, the two-dimensional intensity spectrum data of far-field electromagnetic field scattering uses cross-polarization channel data.

[0018] Furthermore, in step 2, the logarithmic processing is specifically expressed as: log(I+C), where I is the two-dimensional power spectrum input and C is a preset constant to avoid numerical underflow. After logarithmic processing, multiplicative speckle can be suppressed and the dynamic range can be compressed.

[0019] Furthermore, in step 4, the imaging result of the sub-aperture two-dimensional logarithmic power spectrum includes the following features: a zero-order bright spot at the center of the image, and one or more groups of first-order bright spots symmetrically distributed on both sides of the center.

[0020] Furthermore, in step 5, the number of clusters for unsupervised clustering is preferably 3, and they are defined as level 0, level 1 and level 2 respectively according to their strength from large to small.

[0021] Furthermore, in step 6, the tolerance distance satisfies: , , , , Tolerance distance, The speed of electromagnetic wave propagation. For sub-aperture bandwidth, The center frequency of the sub-aperture The sampling width is in the angular direction. To observe the pitch angle, It is a dimensionless proportionality coefficient.

[0022] Furthermore, in step 6, the minimum support threshold is: m = τ × M, where m is the minimum support threshold, τ is the vote counting ratio threshold, M is the total number of sub-apertures, and the vote counting ratio threshold τ is set to 70%~80%.

[0023] Furthermore, in step 8, the specific process of the translation and union operation is as follows: For the candidate basis structure Q, for any reference point b in the candidate basis structure, construct a translation mapping: , Represents the position vector of the reference point. Indicates the initial position vector. Let represent the translation vector; through this translation mapping, each candidate point in the candidate basis structure Q is translated to form the translation mapping set of the reference point b; traverse all reference points in the candidate basis structure Q to obtain the translation mapping set of each reference point, and take the union of the sets to obtain the prediction point set of the candidate basis structure Q.

[0024] Furthermore, the specific process of bidirectional matching verification is as follows: for the predicted point set and the global candidate point set, when each predicted point in the predicted point set has a matching point in the global candidate point set that does not exceed the tolerance distance, and each candidate point in the global candidate point set also has a matching point in the predicted point set that does not exceed the tolerance distance, it is determined that the bidirectional matching verification is satisfied.

[0025] Based on the above technical solution, the beneficial effect of the present invention is that it provides a multi-target array structure inversion method based on two-dimensional power spectrum imaging, which has significant progress compared with existing methods that rely on coherent phase recovery, motion compensation, or highly complex sparse reconstruction; specifically as follows:

[0026] Firstly, the input conditions of this invention are more relaxed. It only takes the power spectrum composed of the far-field scattering amplitude domain as input, without relying on coherent phase and motion compensation. It can still work stably in common amplitude-level data scenarios or phase instability scenarios, significantly reducing the cost of acquisition and calibration.

[0027] Secondly, the present invention has stronger noise resistance and separability. It obtains a two-dimensional logarithmic power spectrum through logarithmic processing, and then directly carries the relative geometric relationship of the scattering center in the difference vector domain through the two-dimensional inverse Fourier transform (IFFT) of the logarithmic power spectrum, which plays a dynamic range compression and suppression role against multiplicative speckle and background. At the same time, with the cooperation of cross-polarization (|HV|×|HV|) channels, the contrast of the first-order / second-order peaks is significantly improved, and the separability of weak targets and close-range multiple targets is better than that of amplitude spectrum or single-polarization schemes.

[0028] Thirdly, this invention has the advantages of high robustness and high accuracy. By using consensus voting across multiple apertures, it retains only the peak values ​​that recur stably across apertures within the spatial tolerance distance. Then, through DBSCAN density clustering adaptive deduplication and merging, it systematically suppresses occasional peaks, sidelobe peaks and spurious peaks, reducing ambiguity and false detections in subsequent geometric verification.

[0029] Fourth, the criteria of this invention are more rigorous, with translational merger prediction and bidirectional matching verification as the core, automatically verifying the sufficiency of candidate basis structures;

[0030] Fifth, the computational burden of the present invention is controllable. Compared with traditional methods that require repeated solutions to large-scale sparse optimization or phase retrieval, the complexity and storage requirements of the present invention are significantly reduced, making it more suitable for embedded and near real-time scenarios.

[0031] Sixth, the present invention has better robustness and scalability. It adopts a fixed order of sub-aperture consistency voting, density clustering deduplication, hierarchical constraint base structure selection, merger prediction, and bidirectional matching, which not only improves the purity of candidate lattices, but also ensures the stability and interpretability of geometric inversion.

[0032] In summary, this invention provides a multi-target array structure inversion method based on two-dimensional power spectrum imaging. Under conditions of dense multi-target arrays, phase instability, and strong aliasing, it can achieve more stable, interpretable, and engineering-friendly identification and extraction of multi-target array structures. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the process for the multi-target array structure inversion method based on two-dimensional power spectrum imaging provided by the present invention.

[0034] Figure 2 This is a schematic diagram of the distribution of the three-point target array with right-angled distribution in Embodiment 1 of the present invention.

[0035] Figure 3 This is a power spectrum imaging result of a three-point target array distributed at a right right angle in Embodiment 1 of the present invention.

[0036] Figure 4 This is a logarithmic power spectrum imaging result of a three-point target array distributed at a right right angle in Embodiment 1 of the present invention; wherein, Figure 4 In the middle (a), the spectrum is a single copolarization spectrum (|HH|×|HH|). Figure 4 In the middle (b), the product spectrum of copolarization × crosspolarization (|HH|×|HV|) is shown. Figure 4 (c) shows the cross-polarization spectrum (|HV|×|HV|). Figure 4 In the middle (d), the spectrum is the double copolarization spectrum (|HH|×|VV|).

[0037] Figure 5 This is a theoretical distribution diagram of the scattering centers obtained by inverse Fourier transform of the power spectrum of the three-point target array distributed at a right right angle in Embodiment 1 of the present invention.

[0038] Figure 6 This is a distribution map of the predicted point set of the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 1 of the present invention.

[0039] Figure 7 This is a schematic diagram of the identification results of the hierarchical array in the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 1 of the present invention. Figure 7 (a) is a schematic diagram of the sub-aperture imaging results. Figure 7 (b) shows the candidate point set identification results.

[0040] Figure 8 This is an image of the imaging spatial lattice obtained by the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 1 of the present invention.

[0041] Figure 9 This is a diagram showing the identification result of the original target array obtained by the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 1 of the present invention.

[0042] Figure 10 This is a schematic diagram of the distribution of the irregularly arranged three-point target array in Embodiment 2 of the present invention.

[0043] Figure 11 This is a schematic diagram of the hierarchical point array identification results in the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 2 of the present invention. Figure 11 (a) is a schematic diagram of the sub-aperture imaging results. Figure 11 (b) shows the candidate point set identification results.

[0044] Figure 12 This is an image of the imaging spatial lattice obtained by the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 2 of the present invention.

[0045] Figure 13 This is a diagram showing the identification result of the original target array obtained by the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 2 of the present invention.

[0046] Figure 14 This is a schematic diagram of the distribution of the irregularly arranged four-point target array in Embodiment 3 of the present invention.

[0047] Figure 15 This is a schematic diagram of the identification results of the hierarchical array in the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 3 of the present invention. Figure 15 (a) is a schematic diagram of the sub-aperture imaging results. Figure 15 (b) shows the candidate point set identification results.

[0048] Figure 16 This is an image of the imaging spatial lattice obtained by the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 3 of the present invention.

[0049] Figure 17 This is a diagram showing the identification result of the original target array obtained by the multi-target array structure inversion method based on two-dimensional power spectrum imaging in Embodiment 3 of the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0051] Example 1

[0052] This embodiment provides a method for inverting the structure of a multi-target array based on two-dimensional power spectrum imaging, the process of which is as follows: Figure 1 As shown, the specific steps include:

[0053] Step 1: Obtain the two-dimensional intensity spectrum data of the far-field electromagnetic field scattering of the target scene, and calculate the square of its amplitude value as the two-dimensional power spectrum input I for imaging;

[0054] Step 2: Logarithmize the two-dimensional power spectrum input I to obtain the two-dimensional logarithmized power spectrum. The logarithmization is specifically expressed as: log(I+C), where C is a preset constant to avoid numerical underflow. Logarithmization can suppress multiplicative speckle and compress the dynamic range.

[0055] Step 3: Divide the two-dimensional logarithmic power spectrum into multiple sub-apertures according to the frequency domain and / or observation angle domain to obtain several sub-aperture two-dimensional logarithmic power spectra;

[0056] Step 4: Perform a two-dimensional inverse Fourier transform (IFFT) on the two-dimensional logarithmic power spectrum of each sub-aperture to obtain the imaging results of the corresponding two-dimensional logarithmic power spectrum of several sub-apertures, which include the following features: a zero-order bright spot in the center of the image and one or more groups of first-order bright spots symmetrically distributed on both sides of the center.

[0057] Step 5: Perform threshold segmentation and local maximum detection on the two-dimensional logarithmic power spectrum imaging result map of each sub-aperture to obtain all scattering peaks on the two-dimensional logarithmic power spectrum imaging result map of each sub-aperture, forming a candidate point set Si, where i is the sub-aperture index, i=1,…,N, and N is the number of sub-apertures; then, perform unsupervised clustering to classify the members of the candidate point set Si according to the intensity of the scattering peaks to obtain level labels; in this embodiment, the number of unsupervised clusters is preferably 3, and they are defined as level 0, level 1 and level 2 respectively according to the intensity from large to small.

[0058] Step 6: Map all candidate points detected in the two-dimensional logarithmic power spectrum imaging results of all sub-apertures onto the same two-dimensional physical coordinate plane, and record each candidate point as an information unit containing position coordinates, grade label, and sub-aperture number. The sub-aperture number is the number of the two-dimensional logarithmic power spectrum of the sub-aperture to which the candidate point belongs. Then, extract the position coordinates of all candidate points to form a candidate point coordinate set; set the tolerance distance ε as the spatial neighborhood radius, and use DBSCAN. The density clustering algorithm performs unified clustering on the set of candidate point coordinates, grouping candidate points that are spatially close to each other into several clusters. Each cluster corresponds to a candidate spatial location. For each cluster, the sub-aperture numbers corresponding to the candidate points within the cluster are counted, and the number of sub-apertures is taken as the number of supporting sub-apertures for that candidate spatial location. A voting ratio threshold τ is set, and the minimum support threshold m is calculated, where m = τ × M, and M is the total number of sub-apertures. For each cluster, if the number of supporting sub-apertures is not less than the minimum support threshold, the candidate spatial location corresponding to the cluster is determined to be a valid spatial location; otherwise, it is determined to be an invalid spatial location and discarded.

[0059] The tolerance distance ε is determined by the physical sampling interval of sub-aperture imaging, satisfying: , , , , The speed of electromagnetic wave propagation. For sub-aperture bandwidth, The center frequency of the sub-aperture The sampling width is in the angular direction. To observe the pitch angle, It is a dimensionless proportionality coefficient (with a value range of 1.0 to 1.5).

[0060] Vote counting ratio threshold Set to 70%~80%;

[0061] In this embodiment, the tolerance distance ε is set to 4 meters, and the vote counting ratio threshold τ is set to 75%.

[0062] Step 7: For each valid spatial location, calculate the arithmetic mean of the coordinates of all candidate points within the cluster and use it as the global candidate point coordinates for that valid spatial location; at the same time, count the occurrence frequency of each level label within the cluster and determine the level label with the most occurrence frequency as the final level label of the scattering center point corresponding to that valid spatial location; finally, record the global candidate point coordinates and final level labels corresponding to each valid spatial location to obtain the global candidate point set P;

[0063] Step 8: Select any non-empty proper subset from the global candidate point set P as the candidate basis structure Q. Perform translation and union operations on the candidate basis structure Q with each of its reference points as the center according to the agreed coordinate system. The specific process is as follows: For any reference point b in the candidate basis structure, construct the translation mapping: , Represents the position vector of the reference point. Indicates the initial position vector. Let represent the translation vector; through this translation mapping, each candidate point in the candidate basis structure Q is translated to form the translation mapping set of the reference point b; traverse all reference points in the candidate basis structure Q to obtain the translation mapping set of each reference point, and take the union to obtain the prediction point set U(Q) of the candidate basis structure Q;

[0064] Step 9: Perform bidirectional matching verification between the predicted point set U(Q) and the global candidate point set P within the tolerance distance ε. The specific process is as follows: when each predicted point in U(Q) has a matching point in P that does not exceed ε and each candidate point in P also has a matching point in U(Q) that does not exceed ε, it is determined that the bidirectional matching verification is satisfied. When the bidirectional matching verification is satisfied, the candidate basis structure Q is determined to be the identified multi-target array structure, which is the set of relative positions of the scattering centers. Otherwise, backtrack and replace the candidate basis structure Q until the identification is completed.

[0065] The following explanation uses a three-point target array distributed at a right right angle as an example for further detail. Figure 2 As shown, scattering centers A, B, and C form a right-angled relationship on the imaging plane; under conventional conditions without logarithmic noise reduction or polarization optimization, direct power spectrum imaging yields the following results: Figure 3As shown in the figure, the background speckle and stripe artifacts raise the noise floor, weak peaks are buried, and the contrast between the first-order peak and the artifacts is insufficient, making it difficult to form a clear structural dot pattern. This indicates that unenhanced linear power spectrum imaging cannot meet the requirements for the clarity and stability of the difference vector dot pattern in multi-target scenes. It also effectively illustrates the necessity and effectiveness of using logarithmic processing, which is beneficial to improving imaging quality and increasing the accuracy and stability of dot pattern recognition.

[0066] like Figure 4 The image shown is the logarithmic power spectrum imaging result of the three-point target array with right-angled distribution in this embodiment. Figure 4 In the middle (a), the spectrum is a single copolarization spectrum (|HH|×|HH|). Figure 4 In the middle (b), the product spectrum of copolarization × crosspolarization (|HH|×|HV|) is shown. Figure 4 (c) shows the cross-polarization spectrum (|HV|×|HV|). Figure 4 The middle (d) spectrum is the double copolarization spectrum (|HH|×|VV|); as can be seen from the figure, compared to Figure 3 The imaging results in the logarithmic domain all showed better noise suppression. Logarithmic processing compressed the dynamic range and transformed multiplicative speckle into more easily suppressed additive perturbations, reducing the background without shifting the geometric peak position. Furthermore, among the four polarization structures, the logarithmic power spectrum of cross-polarization was more stable, with significant attenuation of background and clutter, improved structural peak contrast, clear first-order peak boundaries, and fewer residual artifacts. In other words, under the same scene, the logarithmic power spectrum imaging results of cross-polarization performed better in terms of background suppression and peak contrast.

[0067] like Figure 5 The figure shows the theoretical distribution of scattering centers obtained by inverse Fourier transform of the power spectrum of a three-point target array with a right-angled distribution, where r A r B r C Let A, B, and C represent the position vectors of the original targets A, B, and C, respectively. As shown in the figure, a zero-order bright spot is formed at the image center, contributed by scattering from all targets. There are also several first-order bright spots distributed in pairs and perfectly symmetrical about the image center. The relative position vector of each pair of first-order bright spots relative to the image center is equal to the relative position vector between the two scattering centers in the original multi-target lattice. For example... Figure 6 The diagram shown is a distribution map of the predicted point set in this embodiment. When the original target C is placed at the center, the positions of the original targets A and B are A. C With B C When the original target B is placed in the center position, the positions of the original targets A and C are A. B With C B When the original target A is placed in the center position, the positions of the original targets B and C are B. A With CA As shown in the figure, by sequentially translating the original target point array so that each scattering center is placed at the center of the image, the points that appeared during all the translation processes converge into a union, which is the predicted point set. Figure 5 Theoretical distribution shown Figure 1 This demonstrates that the bidirectional matching verification proposed in this invention conforms to the theoretical derivation.

[0068] like Figure 7 The diagram shown is a schematic representation of the recognition results of the hierarchical dot matrix in this embodiment. Figure 7 (a) is a schematic diagram of the sub-aperture imaging results of the logarithmic power spectrum of a three-point target array distributed at a right angle. Figure 7 Image (b) shows the corresponding candidate point set identification results; further, consensus voting is performed on the identification results of each sub-aperture within a spatial neighborhood with radius ε, and the candidate points that pass the vote are sent to DBSCAN for density clustering merging and deduplication to obtain the global candidate point set P, as shown in Figure 1. Figure 8 As shown; a subset satisfying the ranking priority strategy is selected from the global candidate point set P as the candidate basis structure Q. The candidate basis structure Q is then translated and merged to form the prediction point set U(Q). Within a tolerance distance ε, the prediction point set U(Q) and the global candidate point set P are bidirectionally matched and verified. If the verification passes, the target array determined by the candidate basis structure Q is output, as shown. Figure 9 As shown, its geometric topology is similar to Figure 2 Consistency demonstrates the effectiveness of this invention.

[0069] Example 2

[0070] This embodiment provides a method for inverting the structure of a multi-target array based on two-dimensional power spectrum imaging. The process is the same as in Embodiment 1. This embodiment uses an irregularly arranged three-point target array as an example for further detailed explanation. Figure 10 As shown, the scattering centers A, B, and C are arranged irregularly.

[0071] Following the same procedure as in Example 1, the original data underwent logarithmic power spectrum construction, sub-aperture segmentation, and two-dimensional inverse transform processing. Peak detection and three-class intensity grading were performed on each sub-aperture image to obtain the sub-aperture grading dot matrix recognition results, such as... Figure 11 As shown, Figure 11 (a) is a schematic diagram of the sub-aperture imaging results. Figure 11 Image (b) shows the identification results of the corresponding candidate point set; further, after cross-sub-aperture consensus voting and DBSCAN density clustering merging, the global candidate point set P is obtained, as shown in Figure 1. Figure 12 As shown; candidate basis structures Q are generated from the global candidate point set P, and translational merging and bidirectional matching verification are performed to obtain the final recognition result as shown. Figure 13 As shown, its geometric topology is similar to Figure 10 Consistency. In this embodiment, for cases of asymmetric geometry and local weak peaks, the consistency voting threshold τ and the DBSCAN neighborhood radius are adaptively set based on the voting frequency and local density to avoid excessive merging or false positives and false negatives.

[0072] Example 3

[0073] This embodiment provides a method for inverting the structure of a multi-target array based on two-dimensional power spectrum imaging. The process is the same as in Embodiment 1. This embodiment uses an irregularly arranged four-point target array as an example for further detailed explanation. Figure 14 As shown, the scattering centers A, B, C, and D are arranged irregularly.

[0074] Following the same procedure as in Example 1, the original data underwent logarithmic power spectrum construction, sub-aperture segmentation, and two-dimensional inverse transform processing. Peak detection and three-class intensity grading were performed on each sub-aperture image to obtain the sub-aperture grading dot matrix recognition results, such as... Figure 15 As shown, Figure 15 (a) is a schematic diagram of the sub-aperture imaging results. Figure 15 Image (b) shows the identification results of the corresponding candidate point set; further, after cross-sub-aperture consensus voting and DBSCAN density clustering merging, the global candidate point set P is obtained, as shown in Figure 1. Figure 16 As shown; candidate basis structures Q are generated from the global candidate point set P, and translational merging and bidirectional matching verification are performed to obtain the final recognition result as shown. Figure 17 As shown, its geometric topology is similar to Figure 14 Consistent.

[0075] In summary, this invention provides a method for inverting the structure of a multi-target array based on two-dimensional power spectrum imaging. This method can stably identify and extract the structure of a multi-target array by relying solely on amplitude domain data. First, the relative geometric relationships between targets are preserved in the difference vector domain through logarithmic power spectrum and two-dimensional inverse transform. Then, occasional peaks and sidelobe interference are significantly suppressed through sub-aperture consistency voting and density clustering, and a global candidate point set with hierarchical labels is output. Finally, a geometric closed loop is constructed using translational merging prediction and bidirectional matching verification, providing a clear correctness criterion and completing the identification. Examples 1 to 3 verify the applicability and robustness of this invention under conditions of regular target arrays, irregular target arrays, different numbers of targets, and different polarization structures.

[0076] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A method for inverting the structure of a multi-target array based on two-dimensional power spectrum imaging, characterized in that, Includes the following steps: Step 1: Obtain the two-dimensional intensity spectrum data of the far-field electromagnetic field scattering of the target scene, and calculate the square of its amplitude value as the input of the two-dimensional power spectrum for imaging; Step 2: Perform logarithmic processing on the two-dimensional power spectrum input to obtain the two-dimensional logarithmic power spectrum; Step 3: Divide the two-dimensional logarithmic power spectrum into multiple sub-apertures according to the frequency domain and / or observation angle domain to obtain several sub-aperture two-dimensional logarithmic power spectra; Step 4: Perform a two-dimensional inverse Fourier transform on the two-dimensional logarithmic power spectrum of each sub-aperture to obtain the imaging results of the corresponding two-dimensional logarithmic power spectrum of several sub-apertures. Step 5: Perform threshold segmentation and local maximum detection on the two-dimensional log power spectrum imaging results of each sub-aperture to obtain all scattering peaks on the two-dimensional log power spectrum imaging results of each sub-aperture, forming a candidate point set; then perform unsupervised clustering and classification on the members of the candidate point set according to the intensity of the scattering peaks to obtain the level labels. Step 6: Map all candidate points detected in the two-dimensional logarithmic power spectrum imaging results of all sub-apertures to the same two-dimensional physical coordinate plane, and record each candidate point as an information unit containing location coordinates, grade label and sub-aperture number; extract the location coordinates of all candidate points to form a candidate point coordinate set, set the tolerance distance as the spatial neighborhood radius, and use the DBSCAN density clustering algorithm to uniformly cluster the candidate point coordinate set to form several clusters, each cluster corresponding to a candidate spatial location; for each cluster, count the sub-aperture numbers corresponding to the candidate points in the cluster, use the number of sub-apertures as the number of supporting sub-apertures for the candidate spatial location, set the voting ratio threshold, calculate the minimum support threshold, for each cluster, when the number of supporting sub-apertures is not less than the minimum support threshold, the candidate spatial location corresponding to the cluster is determined to be a valid spatial location, otherwise, it is determined to be an invalid spatial location and discarded; Step 7: For each valid spatial location, calculate the arithmetic mean of the coordinates of all candidate points within the corresponding cluster, and use it as the global candidate point coordinates for that valid spatial location; at the same time, count the occurrence frequency of each level label within the cluster, and use the level label with the most occurrence frequency as the final level label of the scattering center point corresponding to that valid spatial location; record the global candidate point coordinates and final level labels for all valid spatial locations to obtain the global candidate point set; Step 8: Select any non-empty proper subset from the global candidate point set as the candidate basis structure, and perform translation and union operations on the candidate basis structure with each of its reference points as the center according to the agreed coordinate system to obtain the predicted point set; Step 9: Perform bidirectional matching verification between the predicted point set and the global candidate point set within the tolerance distance. When the bidirectional matching verification is satisfied, determine that the candidate basis structure is the multi-target array structure obtained by identification; otherwise, backtrack and change the candidate basis structure until the identification is completed.

2. The multi-target array structure inversion method based on two-dimensional power spectrum imaging according to claim 1, characterized in that, In step 1, the two-dimensional intensity spectrum data of far-field electromagnetic field scattering are obtained using cross-polarization channel data.

3. The multi-target array structure inversion method based on two-dimensional power spectrum imaging according to claim 1, characterized in that, In step 2, the logarithmic processing is specifically represented as: log(I+C), where I is the two-dimensional power spectrum input and C is a preset constant to avoid numerical underflow.

4. The multi-target array structure inversion method based on two-dimensional power spectrum imaging according to claim 1, characterized in that, In step 4, the imaging result of the sub-aperture two-dimensional logarithmic power spectrum includes the following features: a zero-order bright spot at the center of the image, and one or more groups of first-order bright spots symmetrically distributed on both sides of the center.

5. The multi-target array structure inversion method based on two-dimensional power spectrum imaging according to claim 1, characterized in that, In step 5, the number of unsupervised clusters is 3, and they are defined as level 0, level 1 and level 2 respectively according to their strength from large to small.

6. The multi-target array structure inversion method based on two-dimensional power spectrum imaging according to claim 1, characterized in that, In step 6, the tolerance distance satisfies: , , , , Tolerance distance, The speed of electromagnetic wave propagation. For sub-aperture bandwidth, The center frequency of the sub-aperture The sampling width is in the angular direction. To observe the pitch angle, It is a dimensionless proportionality coefficient.

7. The multi-target array structure inversion method based on two-dimensional power spectrum imaging according to claim 1, characterized in that, In step 6, the minimum support threshold is: m = τ × M, where m is the minimum support threshold, τ is the vote counting ratio threshold, M is the total number of sub-apertures, and the vote counting ratio threshold τ is set to 70%~80%.

8. The multi-target array structure inversion method based on two-dimensional power spectrum imaging according to claim 1, characterized in that, In step 8, the specific process of the translation and union operation is as follows: For the candidate basis structure Q, for any reference point b in the candidate basis structure, construct the translation mapping: , Represents the position vector of the reference point. Indicates the initial position vector. Let represent the translation vector; through this translation mapping, each candidate point in the candidate basis structure Q is translated to form the translation mapping set of the reference point b; traverse all reference points in the candidate basis structure Q to obtain the translation mapping set of each reference point, and take the union of the sets to obtain the prediction point set of the candidate basis structure Q.

9. The multi-target array structure inversion method based on two-dimensional power spectrum imaging according to claim 1, characterized in that, In step 9, the specific process of bidirectional matching verification is as follows: For the predicted point set and the global candidate point set, when each predicted point in the predicted point set has a matching point in the global candidate point set that does not exceed the tolerance distance, and each candidate point in the global candidate point set also has a matching point in the predicted point set that does not exceed the tolerance distance, it is determined that the bidirectional matching verification is satisfied.

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