Singular value decomposition interference suppression method for radar signal high fidelity
Patent Information
- Application Number
- CN202611334737.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-31
- Publication Date
- 2026-10-16
AI Technical Summary
1.对全部方位向脉冲统一建立特征矩阵并执行分解，未利用干扰检测结果缩小处理范围，计算量较大，且无干扰脉冲也可能受到处理影响
一方面，本发明先确定疑似受干扰方位向脉冲集合，仅由这些脉冲的距离频谱构造特征矩阵；随后利用奇异值能量集中性提取低秩干扰主子空间，并采用累计能量阈值与最大秩上限共同确定待消除秩；最后重构并减去干扰分量，经逆变换将结果局部写回原回波矩阵，并通过再次检测评价残余干扰。因此，能够把检测结果与抑制处理联动，在确定的受干扰脉冲上构造具有可分结构的特征矩阵，提取干扰主子空间并局部消除干扰，同时保留未检测脉冲和尽可能多的目标回波成分。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of radar radio frequency interference detection technology, and in particular to a method for high-fidelity singular value decomposition interference suppression for radar signals. Background Technology
[0002] Synthetic Aperture Radar (SAR) possesses all-weather, all-day, and high-resolution imaging capabilities, and is widely used in remote sensing mapping, disaster monitoring, marine observation, and defense reconnaissance. However, with the dense deployment of wireless communication, navigation, and electronic countermeasures equipment in adjacent frequency bands, narrowband radio frequency interference, frequency sweeping interference, and other broadband modulation interference may be superimposed on the SAR received echoes. Such interference can create spikes, stripes, or continuous high-energy regions in the range spectrum, further causing streaks, artifacts, sidelobe elevation, and loss of target scattering information in the imaging results.
[0003] Existing interference detection methods can provide the location of the azimuth pulse of the interference, but simply completing the detection cannot recover the contaminated data; if filtering is applied uniformly to the entire echo, it is easy to increase the computational load and inadvertently damage the unaffected echoes.
[0004] Existing SAR radio frequency interference suppression methods mainly include notch filtering or subband cancellation, parameterized interference estimation, adaptive filtering, sparse / low-rank optimization, and eigenspace projection. Notch filtering and subband cancellation methods are simple to implement, but they can create discontinuous spectra and potentially introduce imaging artifacts. Parameterized methods require pre-assuming the interference waveform and estimating parameters such as center frequency, bandwidth, phase, or frequency modulation. Sparse and low-rank optimization methods can jointly separate the target and interference, but they typically require iterative solutions and multiple regularization parameters.
[0005] See “Mitigation of Radio Frequency Interference in Synthetic ApertureRadarData: Current Status and Future Trends” (RemoteSensing, 2019, 11(20):2438). This document lists eigenspace projection as a decomposition and reconstruction suppression method, that is, it distinguishes between large and small singular values through singular value decomposition and constructs interference subspace and signal subspace from the corresponding singular vectors. Tang et al. pointed out in “RFI Suppression for SARviaaDictionary-Based Nonconvex Low-Rank Minimization Framework and Its Adaptive Implementation” (RemoteSensing, 2022, 14(3):678) that traditional SVD subspace projection may produce interference residue or useful signal loss when the interference singular value is incorrectly divided.
[0006] Therefore, it can be found that existing technologies have the following drawbacks in the process of radar interference suppression: 1. A characteristic matrix is uniformly established for all azimuth pulses and decomposed. The interference detection results are not used to narrow the processing range, resulting in a large amount of computation. Furthermore, even pulses without interference may be affected by the processing.
[0007] 2. Relying solely on fixed singular value thresholds or preset ranks to divide the interference subspace is insufficient to adapt to changes in interference intensity, type, and quantity; excessively large ranks can weaken the target, while excessively small ranks can leave residual interference. Summary of the Invention
[0008] The purpose of this invention is to provide a singular value decomposition interference suppression method for high-fidelity radar signals, which can reduce the computational cost of full matrix decomposition, limit the modification of interference-free pulses, and reduce the risk of oversuppression caused by fixed rank.
[0009] The technical solution adopted by this invention to solve its technical problem is as follows: This invention provides a singular value decomposition interference suppression method for high-fidelity radar signals, comprising the following steps: Obtain the radar echo matrix, extract the suspected jammed pulse index set, and construct the range frequency domain feature matrix using the range spectrum of the suspected jammed pulse index set; Singular value decomposition is performed on the distance frequency domain feature matrix, and the square of the singular value is used as the energy of the corresponding singular mode. The rank of the interference subspace is determined based on the cumulative energy ratio of the singular mode and the maximum allowable rank. The interference components of the range frequency domain feature matrix are reconstructed and the interference components are subtracted, or the interference subspace is positively interactively projected to obtain the clean feature matrix. Perform inverse spectrum center shifting and inverse fast Fourier transform processing on the clean feature matrix to obtain the processed local echo, and write it back to the position corresponding to the suspected interfered pulse index set to obtain the complete output matrix; An interference suppression index is constructed to evaluate the effectiveness of interference suppression for the complete output matrix.
[0010] In some embodiments, the acquired radar echo matrix includes useful target echoes, radio frequency interference, and additive noise, and is expressed as follows: ; in, , For radar echo matrix, For useful target echo, For radio frequency interference, Additive noise, This refers to the azimuth pulse count. This represents the number of sampling points in the single-pulse distance direction.
[0011] In some embodiments, the set of suspected interfered pulse indices is denoted as ,like If so, the original echo is output directly. If so, only pulses from the suspected interference pulse index set will be extracted for subsequent decomposition.
[0012] In some embodiments, when extracting the index set of suspected interfered pulses, the index extraction process is written as a derivable linear operator, and a row selection matrix is defined. It is represented as: ; in, for dimensional standard basis vectors, , , , For pulse-level interference decision; In some embodiments, when extracting the suspected interfered pulse index set, the local echo submatrix satisfies: ,and ; in, Describes an m-order identity matrix, matrix For a diagonal selection operator defined on the full orientation dimension, its diagonal is... The index is set to 1, and the rest are set to 0.
[0013] In some embodiments, constructing a range-frequency domain feature matrix using the range spectrum of the suspected interfered pulse index set refers to: Using row selection matrix Constructing the local echo submatrix Then, a normalized fast Fourier transform and spectral center shift are performed along the range direction to obtain the range-frequency domain feature matrix. .
[0014] In some embodiments, the singular value decomposition of the distance frequency domain feature matrix includes the following steps: make For the distance frequency domain feature matrix Perform singular value decomposition, represented as: ; in, It is a left singular vector matrix. , It is a right singular vector matrix. , It is a singular value matrix. and satisfy ; Define the left and right covariance matrices as follows: ; ; in, and They are and The eigenvectors of are and the corresponding eigenvalues are respectively and .
[0015] In some embodiments, the step of using the square of the singular value as the energy of the corresponding singular mode, and determining the rank of the interference subspace based on the cumulative energy ratio of the singular modes and the maximum permissible rank, includes the following steps: Before definition The cumulative energy ratio of each singular mode is expressed as: ; in, It is the first The contribution of each singular mode to the total energy; Given an energy threshold The candidate rank is defined as: ; Set the maximum allowed rank And determine the rank of the interference subspace, which is expressed as: .
[0016] In some embodiments, the processed local echo is represented as: ; The complete output matrix is represented as follows: .
[0017] In some embodiments, the complement of an undetected index is represented as The complement of the undetected index ,have Therefore: .
[0018] The beneficial effects of this invention are: On one hand, this invention first identifies a set of suspected interference azimuth pulses, constructing a feature matrix solely from the range spectrum of these pulses. Then, it extracts the low-rank interference principal subspace using singular value energy concentration, and determines the rank to be eliminated using a cumulative energy threshold and a maximum rank upper limit. Finally, it reconstructs and subtracts the interference components, performs an inverse transformation, locally writes the result back to the original echo matrix, and evaluates the residual interference through re-detection. Therefore, it can link the detection results with suppression processing, constructing a separable feature matrix on the identified interference pulses, extracting the interference principal subspace and locally eliminating interference, while retaining undetected pulses and as many target echo components as possible.
[0019] On the other hand, this invention does not require precise prior estimation of the interference center frequency, initial phase, and modulation frequency. Instead, it utilizes the correlation and approximate low-rank nature of the interference among multiple pulses to uniformly process narrowband, frequency sweep, and partially structured broadband interference. The cumulative energy threshold makes the candidate rank change with the singular energy distribution, and the maximum rank limits the false deletion of targets. It suppresses the error of subsequent re-detection and unprocessed areas to form a closed loop, which is beneficial for parameter adjustment, engineering acceptance, and batch processing. Attached Figure Description
[0020] Figure 1 This is a flowchart of a singular value decomposition interference suppression method for high-fidelity radar signals, implemented in one example. Figure 2 A schematic diagram of a two-dimensional time-domain echo after interference is added to the original sentinel echo in an example implementation. Figure 3 This is a schematic diagram of the time-domain anomaly occupancy rate detection results after adding interference to the original sentinel echo in an example implementation. Figure 4 This is a schematic diagram illustrating the abnormal energy percentage detection results of the original sentinel echo after interference has been added in an example implementation. Figure 5A schematic diagram of the overall detection results after interference is added to the original sentry echo in an example implementation; Figure 6 A schematic diagram illustrating the accumulation of spatial energy and the selection of the disturbance spatial rank in an example implementation. Figure 7 This is a schematic diagram of the two-dimensional time-domain echo after SVD suppression in an example implementation. Figure 8 This is a schematic diagram of the re-inspection results of time-frequency anomaly occupancy rate after suppression in an example implementation; Figure 9 This is a schematic diagram showing the results of a re-examination of the percentage of abnormal energy after suppression in an example implementation. Figure 10 This is a schematic diagram of the results of a re-examination after suppressing interference in one example implementation. Figure 11 To illustrate the addition of narrowband and broadband interference in an example implementation, the time-domain plot before suppression is shown. Figure 12 In an example implementation, with Figure 11 After the corresponding suppression, the temporal map of the video feature matrix after SVD is obtained. Detailed Implementation
[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0022] In one example implementation, see Figure 1 This embodiment provides a singular value decomposition interference suppression method for high-fidelity radar signals, which may include the following steps: S1. Obtain the radar echo matrix, extract the suspected jammed pulse index set, and construct the range frequency domain feature matrix using the range spectrum of the suspected jammed pulse index set. S2. Perform singular value decomposition on the distance frequency domain feature matrix, use the square of the singular value as the energy of the corresponding singular mode, and determine the rank of the interference subspace based on the cumulative energy ratio of the singular mode and the maximum allowable rank. S3. Reconstruct the interference components of the distance frequency domain feature matrix and subtract the interference components, or perform positive interactive complement projection of the interference subspace to obtain the clean feature matrix. S4. Perform inverse spectrum center shifting and inverse fast Fourier transform processing on the clean feature matrix to obtain the processed local echo, and write it back to the position corresponding to the suspected interfered pulse index set to obtain the complete output matrix. S5. Construct an interference suppression index to evaluate the effectiveness of interference suppression for the complete output matrix.
[0023] It should be noted that in this embodiment, the radar echo signal needs to be received first. Here, it is assumed that the radar echo consists of three parts: useful target echo, radio frequency interference, and additive noise. ; in, , For radar echo matrix, For useful target echo, For radio frequency interference, Additive noise, This refers to the azimuth pulse count. This represents the number of sampling points in the single-pulse distance direction.
[0024] If the matrix's th The line represents the first If the range-direction complex sampling sequence of the azimuth pulses is used, then the front-stage detector will output a set of suspected interference pulse indices. ,like If so, the original echo is output directly. Then, only pulses from the suspected interference pulse index set are extracted for subsequent decomposition. To make "index extraction" a derivable linear operator, a row selection matrix can be defined in this embodiment. It can be represented as:
[0025] in, for dimensional standard basis vectors, , , , For pulse-level interference determination, the local echo satisfies: ,and ; in, Describes an m-order identity matrix, matrix For a diagonal selection operator defined on the full orientation dimension, its diagonal is... The index is set to 1, and the rest are set to 0.
[0026] During the process of receiving radar echo signals, invalid values, dimensions, sampling rates, and pulse sequences can be standardized.
[0027] Furthermore, a range-frequency domain feature matrix can be constructed. In one example implementation, in this embodiment, constructing the range-frequency domain feature matrix using the range spectrum of the suspected interfered pulse index set can refer to using a row selection matrix. Constructing the local echo submatrix Then, a normalized fast Fourier transform and spectral center shift are performed along the range direction to obtain the range-frequency domain feature matrix. .
[0028] Specifically, in the above-mentioned distance frequency domain feature matrix... In the specific process, firstly, it is necessary to define 1-th order discrete Fourier matrix Its elements can be represented as: ; The matrix satisfies Since each row is a distance-direction sequence, the discrete Fourier transform along the distance direction can be expressed as a right multiplication. Combining amplitude normalization and spectrum center shifting operators in the program It can be defined as: .
[0029] therefore: ; in, , and These are the characteristic matrices of the target, interference, and noise in the range-frequency domain, respectively. If multiple interfered pulses have the same or slowly varying center frequency, frequency modulation pattern, or amplitude-phase envelope, then these row vectors are not independent but can be approximated as a linear combination of a few basis vectors, i.e.: ; In the formula, This represents the complex weights of different pulses on each interference mode. Represents the range-frequency domain interference base , For the model mismatch term, we can obtain the following from the matrix rank inequality: .
[0030] This indicates that interference with cross-pulse correlation exists in In contrast, thermal noise is typically dispersed in more singular directions; while target echoes may also have a structure, the probability that their energy completely coincides with the main direction of interference is usually low. Therefore, target loss can be reduced by limiting the removal of rank.
[0031] It should be noted that, in one exemplary implementation, in this embodiment, step S2 can be executed to perform singular value decomposition on the distance frequency domain feature matrix, using the squared singular values as the energy of the corresponding singular mode, and determining the rank of the interference subspace based on the cumulative energy ratio of the singular modes and the maximum permissible rank. First, let... For the distance frequency domain feature matrix Singular value decomposition can be represented as: ; in, It is a left singular vector matrix. , It is a right singular vector matrix. , It is a singular value matrix. and satisfy ; Then, define the left and right covariance matrices as follows: ; ; in, and They are and The eigenvectors of are and the corresponding eigenvalues are respectively and .
[0032] At this point, the Frobenius energy of the matrix satisfies: ; Therefore, It is the first The contribution of each singular mode to the total energy.
[0033] Furthermore, according to the Eckart–Young–Mirsky optimal low-rank approximation theorem, for all ranks not exceeding... In the matrix, the matrix given by truncated singular value decomposition has the smallest Frobenius reconstruction error: ; ; ; Therefore, when the interference energy is mainly concentrated in the first few singular modes, It is the optimal squared reconstruction of the dominant correlated component under given rank conditions, which constitutes the theoretical basis for using SVD to reconstruct the disturbance.
[0034] In one example implementation, the adaptive selection of the rank of the interference subspace can then be performed. Here, firstly, the pre-defined... The cumulative energy ratio of each singular mode can be expressed as: ; in, It is the first The contribution of each singular mode to the total energy; Secondly, given an energy threshold The candidate rank can be defined as: ; If only the cumulative energy condition is used, an excessively large rank may be selected when a single strong target or broadband background occupies a large number of modes. Therefore, this embodiment can set a maximum allowable rank. And determine the rank of the interference subspace, which can be expressed as: .
[0035] Preferably, , Both can be adjusted according to radar system, interference intensity, and target retention requirements.
[0036] At this point, step S2 has been completed. Next, step S3 can be executed. Specifically, in an example implementation, the interference components of the range frequency domain feature matrix can be reconstructed and the interference components can be subtracted, or a positive interactive complement projection of the interference subspace can be performed to obtain a clean feature matrix.
[0037] Specifically, firstly, take the previous one. Singular vectors and singular values: ; Secondly, the interference estimate is obtained from the truncated singular value decomposition: .
[0038] In one example implementation, because ,so: ; Then, define the projection matrix of the interference subspace and its orthogonal complement projection matrix: ; Both conditions are met: ; Therefore, the clean feature matrix can be written as:
[0039] The above equation shows that "subtraction after reconstruction" and "orthogonal complement of projection onto the interference subspace" are mathematically equivalent. Since the two projection components are orthogonal, we have: ; This satisfies the energy decomposition relationship: .
[0040] In one example implementation, in this embodiment, the proportion of energy removed can be:
[0041] This equation establishes a direct correspondence between "cumulative singular energy rank selection" and "actual energy removed".
[0042] To analyze the target loss, this embodiment can make If we represent the target frequency domain component in the detection pulse, then the proportion of target energy that is projected onto the interference subspace and removed can be defined as: ; If the orthogonal basis of the target subspace is ,and Then we have: ; in, This represents the maximum overlap between the target subspace and the interference subspace. When they are nearly orthogonal, this value is small, and target loss is suppressed; when they are highly overlapping, any pure subspace elimination method may simultaneously weaken the target. Therefore, this embodiment can utilize detection guidance, maximum rank constraint, and optional target protection conditions to jointly control oversuppression.
[0043] Next, step S4 can be executed, which involves performing inverse spectrum center shifting and inverse fast Fourier transform processing on the clean feature matrix to obtain the processed local echo, and writing it back to the position corresponding to the suspected interfered pulse index set to obtain the complete output matrix.
[0044] In one example implementation, the normalization method mentioned in the above steps can be used, and the processed local time-domain echo can be expressed as: ; The complete output can be written as: ; complement of undetected indexes ,have Therefore: .
[0045] In this embodiment, the azimuth pulses that are not detected as interference remain strictly unchanged in theory. This local write-back relationship not only reduces the risk of irrelevant data being misprocessed, but also facilitates the review of data consistency before and after processing.
[0046] Finally, an interference suppression index can be constructed to evaluate the effectiveness of interference suppression for the complete output matrix. To evaluate the effectiveness of suppression, it is necessary to simultaneously examine whether "interference components are removed" and "target echoes are destroyed." Therefore, it is not sufficient to simply observe whether the image becomes darker after suppression; rather, an index system constrained by residual interference, signal distortion, and re-detection results must be established. In this embodiment, the interference suppression index can be constructed from the following four aspects: First, residual interference power is used to measure the interference and additional error that remain after suppression. If the true value of interference-free data is known in the simulation experiment... Then the error before suppression and the error after suppression are respectively:
[0047] in, The interference region is defined as the additional distortion caused by the suppression process to the useful echo. The average residual power on is: ; ; The residual power reduction is defined as:
[0048] The larger the value, the lower the residual interference energy after suppression. However, this indicator only reflects the degree of interference reduction and cannot be used as the sole criterion for optimal performance.
[0049] Second, the echo distortion index is used to measure whether the useful signal is excessively attenuated. If the true value without interference is known, the normalized mean square error can be defined as follows: ; The smaller the value, the closer the suppressed echo is to the true useful echo. If the measured data does not contain an interference-free true value, the change in total energy before and after suppression can be used as a substitute constraint. ; ;
[0050] like If the value is too high, it indicates that while the suppression algorithm reduces energy, it may also be removing true SAR echoes; if... If the signal is close to zero but residual interference is still significant, it indicates insufficient suppression strength. Therefore, this index is used to constrain the echo retention capability during the suppression process.
[0051] Third, the signal-to-interference ratio (SIR) improvement is used to comprehensively describe the degree of improvement in useful echo relative to interference error. In simulation experiments, it can be defined as follows: ; ; ; The larger the value, the more significant the advantage of the suppressed useful echo over the residual interference, indicating that the suppression algorithm improves the echo quality at the signal level.
[0052] Fourth, the residual interference rate upon redetection is used to evaluate whether the suppression result will still be judged as interference by the detection model. Let the number of interference azimuth directions detected before suppression be... The number of interference azimuth directions that were redetected after suppression was ,but:
[0053] The larger the value, the fewer pulses that still meet the interference decision criteria after suppression. In the measured data, since there is no interference-free true value, the JS divergence, the number of outlier points in the Z-test, and the number of redetections before and after suppression can be further compared as indirect evidence of whether the residual RFI has decreased.
[0054] In summary, the interference suppression evaluation using the interference suppression index in this embodiment should simultaneously satisfy two constraints: on the one hand, It should be as close as possible to real interference. ,make , and Increase; on the other hand, It should not contain too many useful echo components, otherwise or Increase. Therefore, the comprehensive compromise criterion adopted in this embodiment can be written as: in and These are the weighting coefficients, which can be obtained by scanning the feature matrix decomposition in actual experiments. and Parameters, observation and The relationship between the changes in interference suppression intensity and echo distortion is investigated to find the compromise between these two factors.
[0055] In one example implementation, this embodiment uses Sentinel-1 IW mode burst-level complex echoes to verify the method. The program reads the echo matrix with specified polarization and burst number, and constructs interference signals along the range direction. The narrowband interference center frequency is 10MHz, and approximately 90 azimuth pulses are randomly injected. The linear frequency modulated broadband interference sweeps from 10MHz to 13MHz with an amplitude factor of 10, and approximately 90 azimuth pulses are randomly injected.
[0056] During the verification process, the interference detection module is first invoked to obtain the set of indices before suppression. ; then construct and Execute SVD, and by , Determine the actual rank removed ; obtained through orthogonal projection, inverse transformation, and local write-back The set was then detected. .
[0057] To quantify the overall energy decay in the characteristic domain, we can define the interference suppression gain, which can be expressed as: ; in, For numerically stable terms, The larger the value, the more fully the energy in the selected master subspace is removed; however, this index itself cannot distinguish whether the removed energy is interference or the target, so it must be interpreted in conjunction with the target index.
[0058] Furthermore, this embodiment defines the residual detection ratio after suppression: ; in, The smaller the value, the lower the proportion of pulses that are still identified as interference by the preceding detector after suppression. When the detector has a fixed false alarm rate, It doesn't necessarily reduce to zero; it's advisable to interpret it in conjunction with the detection threshold and false alarm probability. To verify the rigor of the local write-back, define the unprocessed region error. .
[0059] Based on the aforementioned derivation, without considering numerical rounding, we should have: If the program outputs a clearly non-zero value, it usually indicates an error in the index mapping, matrix dimension, or write-back location, and this metric can be used as an implementation verification measure. If the residual ratio is still high but the target retention rate has decreased, then blindly increasing it is no longer advisable. Instead, the cumulative energy threshold should be lowered, the processing window narrowed, and re-detection or a block feature matrix should be used.
[0060] This embodiment also outputs , , These quantities respectively reflect the energy removed, the degree of suppression, and the residual interference forming a verifiable chain of results.
[0061] In one example implementation, see Figures 2-5 The results of semi-blind interference detection before suppression are presented. There are 90 narrowband and 90 wideband interference detections, with a pulse detection rate of 0.956 and an F1 score of 0.977. The F1 score is used to comprehensively evaluate the interference pulse detection performance and is defined as the harmonic mean of precision and recall. Precision represents the proportion of actual interference pulses among the detected interference pulses, and recall represents the proportion of correctly detected actual interference pulses. In this embodiment, the pulse detection rate is 0.956 and the F1 score is 0.977, indicating that the interference detection method maintains a high detection rate while having a low false alarm rate. The F1 score is only used for detection performance evaluation and is not included in subsequent SVD interference suppression calculations.
[0062] Figure 2 For the two-dimensional time-domain echo after interference is added, Figure 3 and Figure 4 The time-frequency anomaly occupancy rate and the percentage of anomaly energy are given respectively. Figure 5 The overall detection score is given; pulses with an overall score exceeding 0dB are marked with a red "×". The abnormal statistics mainly exceed the threshold in the first half of the azimuth pulses, while the second half generally remains below the threshold. This is consistent with the fact that the interference is concentrated in the first half of this embodiment, indicating that the adjacent pulse background and RadarPara prior constraints can suppress large-scale false alarms. The pulse detection rate in the figure is 0.956, meaning a small amount of weak broadband interference was not detected initially. This is because the broadband random energy is distributed across multiple time-frequency cells, and the power-background ratio of a single cell is lower than that of narrowband interference.
[0063] See Figure 6 It presents the relationship between cumulative singular energy and rank selection, where the curve rises rapidly at lower ranks, indicating that the dominant component in the detected pulse has a low-rank concentration; the curve reaches... When to obtain candidate rank Then by In this embodiment, the threshold of 85% is reached when r=3, and the maximum allowable rankCap of the interference subspace rank is satisfied as rankCap=4. If the curve rises slowly without a clear inflection point, it usually corresponds to broadband noise interference, multiple incoherent interference sources, or the target background jointly occupying a large number of modes. In this case, the separability of a single SVD decreases, and it is not advisable to increase it without an upper limit. To achieve higher energy coverage, this embodiment can employ block SVD, sliding window, time-frequency feature matrix, or target protection constraints to improve local low rank and subspace separation.
[0064] See Figures 7-10 It presents the retest results obtained after suppression using the same half-blind detector and the same set of decision thresholds, where, Figure 7 The high-energy anomaly texture in the Central Plains is significantly weakened. Figure 8 Mid-frequency anomaly occupancy rate and Figure 9 Most pulses in the abnormal energy range have dropped below the original threshold. Figure 10 The overall detection score still has 11 red "×", corresponding to 11 residuals out of 180 injected interferences. The interference elimination rate is 93.89%, and no new false alarms were generated. This indicates that the suppression effect comes from the actual reduction of abnormal time-frequency energy.
[0065] Figure 11 and Figure 12 Use the same color scale to display the time-domain echo before and after suppression, see [link / reference]. Figure 11 Before suppression, multiple high-amplitude horizontal stripes extending along the range direction correspond to the disturbed azimuth pulses. These pulses have strong inter-row correlation in the local frequency domain matrix, thus their energy is concentrated in the first few singular values, performing... Reconstructed and by After subtraction, see Figure 12 The high-amplitude bands are significantly weakened, indicating that the dominant correlation interference has been eliminated by projection. The texture of the unprocessed areas remains continuous, consistent with... This is consistent with theoretical conclusions. If light-colored stripes still exist locally, it usually means that broadband interference energy is dispersed across multiple modes and the selected... The pulses are too small or the preceding stage detection missed some of the interference pulses; if both the target and the background darken significantly at the same time, it indicates... If the target subspace is too large or overlaps with the interference subspace, it is necessary to strengthen the rank upper limit or target protection. In this study, the same robust amplitude reference of the original echo was used for normalization before and after processing. Therefore, the brightness difference between the two images can be directly interpreted as changes in echo amplitude and interference energy. Figure 12 The small amount of still visible abnormal texture corresponds to the 11 residual pulses re-examined in Figure 0.
[0066] In summary, this embodiment allows interference detection results to be directly used for suppression range selection, only affecting... The suspected interfered pulses in the data are used to construct a feature matrix and perform SVD. The processing scale is from Reduced to ;when At that time, the proportion of the main decomposition complexity is approximately Meanwhile, the complete output uses... Perform a partial write-back to ensure that undetected pulses remain unchanged.
[0067] Furthermore, this embodiment does not require precise pre-estimation of the interference center frequency, initial phase, and modulation frequency. Instead, it utilizes the correlation and approximate low-rank nature of the interference across multiple pulses to uniformly handle narrowband, swept-frequency, and partially structured broadband interference. (Cumulative energy threshold) The candidate rank varies with the distribution of singular energy, and the maximum rank is obtained. Limiting accidental deletion of targets; suppressing re-detection and , The target retention rate and the unprocessed area error form a closed loop, which is beneficial for parameter adjustment, project acceptance and batch processing.
[0068] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A singular value decomposition interference suppression method for high-fidelity radar signals, characterized in that, Includes the following steps: Obtain the radar echo matrix, extract the suspected jammed pulse index set, and construct the range frequency domain feature matrix using the range spectrum of the suspected jammed pulse index set; Singular value decomposition is performed on the distance frequency domain feature matrix, and the square of the singular value is used as the energy of the corresponding singular mode. The rank of the interference subspace is determined based on the cumulative energy ratio of the singular mode and the maximum allowable rank. The interference components of the range frequency domain feature matrix are reconstructed and the interference components are subtracted, or the interference subspace is positively interactively projected to obtain the clean feature matrix. Perform inverse spectrum center shifting and inverse fast Fourier transform processing on the clean feature matrix to obtain the processed local echo, and write it back to the position corresponding to the suspected interfered pulse index set to obtain the complete output matrix; An interference suppression index is constructed to evaluate the effectiveness of interference suppression for the complete output matrix.
2. The singular value decomposition interference suppression method for high-fidelity radar signals according to claim 1, characterized in that, The acquired radar echo matrix, including useful target echoes, radio frequency interference, and additive noise, is expressed as: ； in, , For radar echo matrix, For useful target echo, For radio frequency interference, Additive noise, This refers to the azimuth pulse count. This represents the number of sampling points in the single-pulse distance direction.
3. The singular value decomposition interference suppression method for high-fidelity radar signals according to claim 1, characterized in that, The set of suspected interfered pulse indices is denoted as ,like If so, the original echo is output directly. If so, only pulses from the suspected interference pulse index set will be extracted for subsequent decomposition.
4. The singular value decomposition interference suppression method for high-fidelity radar signals according to claim 3, characterized in that, When extracting the index set of suspected interfered pulses, the index extraction process is written as a derivable linear operator, and a row selection matrix is defined. It is represented as: ； in, for dimensional standard basis vectors, , , , This is a pulse-level interference decision.
5. The singular value decomposition interference suppression method for high-fidelity radar signals according to claim 3, characterized in that, When extracting the suspected interfered pulse index set, the local echo submatrix satisfies: ,and ; in, Denotes an m-order identity matrix, matrix For a diagonal selection operator defined on the full orientation dimension, its diagonal is... The index is set to 1, and the rest are set to 0.
6. The singular value decomposition interference suppression method for high-fidelity radar signals according to claim 5, characterized in that, The construction of a range-frequency domain feature matrix using the range spectrum of the suspected interfered pulse index set refers to: Using row selection matrix Constructing the local echo submatrix Then, a normalized fast Fourier transform and spectral center shift are performed along the range direction to obtain the range-frequency domain feature matrix. .
7. The singular value decomposition interference suppression method for high-fidelity radar signals according to claim 6, characterized in that, The singular value decomposition of the distance frequency domain feature matrix includes the following steps: make For the distance frequency domain feature matrix Perform singular value decomposition, represented as: ； in, It is a left singular vector matrix. , It is a right singular vector matrix. , It is a singular value matrix. and satisfy ; Define the left and right covariance matrices as follows: ； ； in, and They are and The eigenvectors of are and the corresponding eigenvalues are respectively and .
8. The singular value decomposition interference suppression method for high-fidelity radar signals according to claim 7, characterized in that, The step of using the square of the singular value as the energy of the corresponding singular mode, and determining the rank of the interference subspace based on the cumulative energy ratio of the singular modes and the maximum permissible rank, includes the following steps: Before definition The cumulative energy ratio of each singular mode is expressed as: ； in, It is the first The contribution of each singular mode to the total energy; Given an energy threshold The candidate rank is defined as: ； Set the maximum allowed rank And determine the rank of the interference subspace, which is expressed as: 。 9. The singular value decomposition interference suppression method for high-fidelity radar signals according to any one of claims 1-8, characterized in that, The processed local echo is represented as follows: ； The complete output matrix is represented as follows: 。 10. The singular value decomposition interference suppression method for high-fidelity radar signals according to claim 9, characterized in that, The complement of the undetected index is represented as The complement of the undetected index ,have Therefore: 。