Radar interference identification method and system based on bispectrum phase angle, terminal and storage medium

Abstract

The invention relates to the technical field of radar signals, and particularly provides a radar interference identification method and system based on a bispectrum phase angle, a terminal and a storage medium, and the method comprises the steps: obtaining observation data received by a radar; calculating a bispectrum phase angle matrix of the observation data; converting the bispectrum phase angle matrix into a gray level co-occurrence matrix, and extracting image texture features based on the gray level co-occurrence matrix; extracting numerical values of main diagonals from the bispectrum phase angle matrix to obtain a diagonal sequence, and performing spectrum analysis and sequence trend characteristic analysis based on the diagonal sequence; and performing principal component analysis based on the image texture features and the sequence trend features, and inputting the features after the principal component analysis into a preset classification model to obtain a result of the identified real target or false target. According to the method, the reliability of identifying the real target and the interference signal is improved, and the problem that the dragging interference signal is difficult to distinguish by a traditional method is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signals, and particularly relates to a radar interference identification method, system, terminal and storage medium based on bispectrum phase angle. Background Technique

[0002] Radar technology plays an important role in modern military and civilian fields and is widely used in tasks such as target detection, tracking, identification, and navigation. However, with the rapid development of radar technology, various interference technologies against radar are also constantly evolving. In particular, the emergence of towing interference signals has brought great challenges to the accurate and reliable detection of real targets by radar systems.

[0003] Currently, there are mainly three deception interference technologies in threat tracking radars, including range gate pull-off (RGPO), velocity gate pull-off (VGPO), and range-velocity synchronous pull-off (R-VGPO). These interference technologies can generate false target signals to confuse the radar system, causing it to measure incorrect target distances or speeds, thus seriously interfering with the detection and tracking effects of the radar on real targets. Specifically, the implementation process of such interference usually consists of three stages: the capture period, the towing period, and the stop-towing period. During the capture period, the interference signal will initially interfere with the radar system, attempting to destroy its target recognition ability. During the towing period, the continuous emission of the interference signal will further confuse the radar, causing deviations when tracking the real target and resulting in incorrect distance and speed measurements. And during the stop-towing period, although the interference signal stops, the radar system may still be affected by the previous interference. Especially in complex electromagnetic environments and battlefield confrontations, the towing period poses a particularly prominent threat to the radar system. Traditional anti-interference technology identification methods often fail to meet actual requirements, easily leading to misjudgment of targets and seriously reducing the combat effectiveness and reliability of the radar system.

[0004] In the prior art, after the radar raw signal is preprocessed into a zero-intermediate frequency signal, the deception interference signal and the real target echo in the slow time dimension are highly similar in the time domain, frequency domain, and even time-frequency domain, making it difficult to extract subtle difference features. Existing methods have insufficient available identification features for true and false targets in the slow time dimension, and their identification performance is not stable under different interference / signal-to-noise ratios, making it difficult to stably and effectively distinguish false target interference from real targets. Especially when the false target interference overlaps with the real target in the slow time dimension, it may even cause the failure of existing algorithms, resulting in the loss of real targets and seriously affecting subsequent tracking and further identification tasks. Summary of the Invention

[0005] Aiming at the problems of insufficient extraction of characteristic information from active false target interference signals by time-domain and frequency-domain identification methods in the existing technology and poor identification ability of true and false targets, the present invention provides a radar interference identification method, system, terminal and storage medium based on bispectrum phase angle to solve the above technical problems.

[0006] In the first aspect, the present invention provides a radar interference identification method based on bispectrum phase angle, including: Obtain the observation data received by the radar; Calculate the bispectrum phase angle matrix of the observation data; Convert the bispectrum phase angle matrix into a gray-level co-occurrence matrix, and extract image texture features based on the gray-level co-occurrence matrix; Extract the numerical values on the main diagonal from the bispectrum phase angle matrix to obtain a diagonal sequence, and perform spectral analysis and sequence trend feature analysis based on the diagonal sequence; Based on the image texture features and sequence trend features, perform principal component analysis, and input the features after principal component analysis into a preset classification model to obtain the result of identifying the true target or false target.

[0007] Further, calculating the bispectrum phase angle matrix of the observation data includes: Take the observation data with a length of N, divide the observation data into K segments equally, and the length of each segment of data is M points. Let the nth segment of data be , and calculate the estimated value of the third-order cumulant of each segment of data respectively:

[0008] Among them, = max(0, -i, -j), = min(M - 1, M - 1 - I, M - 1 - j); Statistically average the third-order cumulants obtained for each segment, and the result obtained is the third-order cumulant of the data, expressed as:

[0009] Then the bispectrum is:

[0010] Among them, L < M - 1, represents a two-dimensional lag window function; Extract the phase angle information from the result matrix of the bispectrum. Let the element in the bispectrum matrix be , where , is the real part of the element , is the imaginary part of the element the element The representation in polar coordinates is ; Calculate the element phase angle of : ; The phase angle of each element is calculated , obtaining the bispectrum phase angle matrix , where the value range is (-π, π).

[0011] Furthermore, converting the bispectrum phase angle matrix into a gray-level co-occurrence matrix includes: The matrix values in the bispectrum phase angle matrix are linearly mapped to the gray-scale image by the formula:

[0012] where L is the number of gray levels, and the gray-level range is [0, L - 1]; According to the preset discretization rule , the gray-scale value range of the gray-scale image is equally discretized into [0, 15], obtaining a new gray-scale image with 16 gray levels after discretization ; Set the gray-level co-occurrence matrix , which is used to describe the co-occurrence relationship between pixel gray-scale values in the new gray-scale image . For the new gray-scale image , define the gray-level co-occurrence matrix as L×L in size. The elements in the gray-level co-occurrence matrix are calculated as:

[0013] where (m, n) represents two gray-scale values, represents the relative angle between two pixels, including four directions of 0°, 45°, 90°, and 135°, and define the displacement for calculating the gray-scale relationship, that is , respectively represent the pixel offsets in the x and y axis directions, The relationship between is as follows:

[0014] Normalize the gray-level co-occurrence matrix to obtain the normalized matrix . The normalization formula is:

[0015] Among them, the normalized matrix satisfies: ; Denote the normalized gray-level co-occurrence matrix as .

[0016] Furthermore, extract image texture features based on the gray-level co-occurrence matrix, including: Extract the energy feature of the gray-level co-occurrence matrix, , where E is the energy, is the normalized gray-level co-occurrence matrix; Extract the entropy value feature of the gray-level co-occurrence matrix, , where H is the entropy value; Extract the inertia moment feature of the gray-level co-occurrence matrix, , where I is the inertia moment; Extract the correlation feature of the gray-level co-occurrence matrix, , where C is the correlation, , ; , ; Extract the contrast difference matrix feature of the gray-level co-occurrence matrix, , where IDM is the contrast difference matrix; Based on the energy feature, entropy value feature, inertia moment feature, correlation feature and contrast difference matrix feature of the gray-level co-occurrence matrix, extract the texture features.

[0017] Furthermore, extract the values on the main diagonal from the bispectrum phase angle matrix to obtain a diagonal sequence, and perform spectral analysis based on the diagonal sequence, including: Let the diagonal sequence be ; Take the diagonal sequence with length N in the diagonal sequence Perform Fourier transform to obtain the spectrum , ; Calculate the spectrum amplitude The frequency corresponding to the maximum point: , to obtain the main frequency of the spectrum; Calculate the spectrum standard deviation: , to obtain the true target spectrum standard deviation interval, where, represents the spectrum mean, defined as ; Calculate the spectrum kurtosis: , to obtain the true target spectrum kurtosis interval; Calculate the spectrum skewness: , obtain the true target spectrum skewness interval.

[0018] Further, the sequence trend feature analysis includes: Based on the diagonal sequence being , calculate the difference between adjacent elements: ; Take the absolute value of all differences and then accumulate to calculate the cumulative sum : , obtain the true target cumulative sum interval; Define the Gaussian weight function, with the center of the Gaussian distribution being , and the standard deviation being , the weight at the th position is: ; Introduce the Gaussian weight into the absolute difference cumulative sum to obtain the Gaussian weighted cumulative sum : ; Based on the Gaussian weighted cumulative sum, obtain the sequence trend feature.

[0019] Further, based on the image texture feature and the sequence trend feature, perform principal component analysis, and input the features after principal component analysis into a preset classification model to obtain the result of identifying the true target or false target, including: Normalize the image texture feature and the sequence trend feature, compress the image texture feature and the sequence trend feature into the interval [0, 1] to obtain the normalized eigenvalue; Use principal component analysis to reduce the dimension of the normalized eigenvalue to obtain the reduced-dimensional data; Input each reduced-dimensional data into the preset classification model to obtain the result of identifying the true target or false target.

[0020] In a second aspect, the present invention provides a radar interference identification system based on the bispectrum phase angle, including: A data acquisition module for acquiring the observation data received by the radar; A matrix calculation module for calculating the bispectrum phase angle matrix of the observation data; A feature extraction module for converting the bispectrum phase angle matrix into a gray-level co-occurrence matrix and extracting the image texture feature based on the gray-level co-occurrence matrix; A feature analysis module for extracting the numerical values on the main diagonal from the bispectrum phase angle matrix to obtain the diagonal sequence, and performing spectrum analysis and sequence trend feature analysis based on the diagonal sequence; The result recognition module is used to perform principal component analysis based on image texture features and sequence trend features, input the features after principal component analysis into a preset classification model, and obtain the results of the recognized real target or false target.

[0021] In a third aspect, a terminal is provided, including: processor, memory, wherein: The memory is used to store computer programs. The processor is used to call and run the computer program from the memory, so that the terminal executes the above-mentioned terminal method.

[0022] According to a fourth aspect, a computer storage medium is provided, wherein the computer-readable storage medium stores instructions, and when the instructions are executed on a computer, the computer executes the methods described in the above aspects.

[0023] The beneficial effect of the present invention is that the radar interference identification method, system, terminal and storage medium based on the dual spectrum phase angle provided by the present invention highlight the nonlinear relationship and small feature differences hidden in the radar signal through the dual spectrum phase angle analysis, significantly improve the reliability of the identification of the real target and the interference signal, and solve the problem that the traditional method is difficult to distinguish the towing interference signal. By extracting the grayscale co-occurrence matrix and texture features from the grayscale image after the dual spectrum phase angle conversion, the spatial texture difference of the signal is deeply excavated, and the ability to distinguish the real target from the interference signal is further enhanced. By combining the two analysis dimensions of sequence trend features and sequence frequency domain features, a more comprehensive and complementary feature system is constructed, so that the method has excellent recognition effect on different types of towing interference signals, and significantly enhances the robustness and generalization performance of the algorithm. The present application uses principal component analysis (PCA) to effectively reduce the dimension of the features, reduce the computational complexity, and use the CatBoost classification algorithm to efficiently realize the accurate identification of the interference signal. The recognition accuracy rate is more than 97% verified by experiments, which is significantly improved compared with the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0025] Figure 1 is a schematic flow chart of a method according to an embodiment of the present invention.

[0026] Figure 2 is a schematic block diagram of a system according to an embodiment of the present invention.

[0027] Figure 3 The structural schematic diagram of a terminal provided by an embodiment of the present invention. Specific implementation manners

[0028] In order to enable those skilled in the art of the present technology to better understand the technical solutions in the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

[0029] Unless otherwise defined, all technical and scientific terms used in this application have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the specification of the present invention in this application are only for the purpose of describing specific embodiments, and are not intended to limit the present invention.

[0030] Radar deceptive jamming is a technical means of interfering with or confusing a radar system by sending or forwarding signals with deceptive information, so that it cannot accurately identify real targets or obtain target parameters. In modern electronic warfare, the application of this technology is becoming more and more extensive, especially in complex battlefield environments. This application takes the slow-time dimension sequence after preprocessing of the linear frequency modulation signal (LFM) as the research object, and focuses on the detection and identification of three main types of jamming: range gate pull-off jamming, velocity pull-off jamming, and range-velocity synchronous pull-off jamming, among which R-VGPO jamming is mostly used in actual combat.

[0031] The implementation process of such jamming is usually divided into three stages: the capture period, the pull-off period, and the stop-pull period. In the capture period, the jamming signal will initially interfere with the radar system and attempt to destroy its target recognition ability. In the pull-off period, the continuous emission of the jamming signal will further confuse the radar, causing deviations when tracking the real target and resulting in incorrect range and velocity measurements. In the stop-pull period, although the jamming signal stops, the radar system may still be affected by the previous jamming. The research focus of this application is on the analysis of specific signals during the pull-off period, aiming to reveal how to effectively identify and suppress these jamming signals during this stage to improve the jamming identification ability of the radar system.

[0032] Let the radar transmitted signal be: (1) In the formula: A is the amplitude of the jamming signal; k is the frequency modulation slope; is the inherent delay of the jammer; is the modulation time delay; is the modulation frequency shift; , It is RGPO interference when...; It is VGPO interference when...; It is R-VGPO interference when...

[0033] Among them, by detecting the range towing or range-velocity synchronization interference signal during the towing period within a short time, it can be regarded as a range false target, and the sequence can be directly intercepted in the slow-time dimension as the interference signal.

[0034] The bispectrum, that is, the third-order cumulative spectrum, is defined by the two-dimensional discrete Fourier transform of the third-order cumulant of the sequence. The specific derivation is as follows: Now assume a random sequence whose third-order cumulant is is absolutely summable, that is , then there exists its nth-order cumulative spectrum , and it is defined as the (n - 1)-dimensional Fourier transform of the nth-order cumulant.

[0035] (2) When n = 3 in formula (2), it is defined as the third-order spectrum, that is, the bispectrum, usually denoted as (3) where the domain is: .

[0036] The radar interference identification method based on the bispectrum phase angle provided by the embodiments of the present invention is executed by a computer device. Correspondingly, the radar interference identification system based on the bispectrum phase angle runs in the computer device.

[0037] Figure 1 is a schematic flowchart of the method of an embodiment of the present invention. Among them, Figure 1 The execution subject can be a radar interference identification system based on the bispectrum phase angle. According to different requirements, the order of the steps in this flowchart can be changed, and some can be omitted.

[0038] For the convenience of understanding the present invention, the principle of the radar interference identification method based on the bispectrum phase angle of the present invention will be further described below in combination with the process of interfering with and identifying the radar based on the bispectrum phase angle in the embodiments.

[0039] Specifically, as Figure 1 shown, the radar interference identification method based on the bispectrum phase angle includes: S1. Obtain the observation data received by the radar.

[0040] Specifically, after the jammer is activated, the radar receives the signal after the false target interference is superimposed on the sea clutter signal. Since the superimposed signal contains two signal sources with different characteristics: the false target interference usually has a relatively regular phase coupling characteristic, and the design of the false target interference often focuses on the signal form close to the characteristics of the real target, but its phase relationship still retains the artificial characteristic; while the characteristics of the sea clutter signal are affected by environmental factors such as wind speed, wave height, and scattering mechanisms (Bragg scattering, higher-order scattering, etc.), and usually show strong randomness and non-Gaussianity. Moreover, the multipath effect and noise in the sea clutter will further increase the complexity of the signal, making its phase relationship difficult to form a regular pattern in the frequency space. The superposition of the two makes the phase relationship between the frequency components more complex.

[0041] S2. Calculate the bispectrum phase angle matrix of the observed data.

[0042] Take the observed data of length N, divide the observed data into K segments equally, with the length of each segment being M points. Let the nth segment of data be , and calculate the estimated value of the third-order cumulant of each segment of data respectively:

[0043] where = max(0, -i, -j), = min(M - 1, M - 1 - I, M - 1 - j). Statistically average the third-order cumulants obtained for each segment, and the result obtained is the third-order cumulant of this data, denoted as:

[0044] Then the bispectrum is:

[0045] where L < M - 1, represents the two-dimensional lag window function. Extract the phase angle information from the result matrix of the bispectrum. Let the element in the bispectrum matrix be , where , is the real part of the element , is the imaginary part of the element . The representation of the element in polar coordinates is . Calculate the phase angle of the element : ; Calculate the phase angle of each element, and obtain the bispectrum phase angle matrix , where the value range is (-π, π).

[0046] Specifically, in the measured environment, there are significant differences in the phase relationships of the two types of signals in the bispectrum estimation between the false target interference received by the radar and the real target in the slow time dimension after calculating the bispectrum result and extracting the bispectrum phase angle matrix result.

[0047] After extracting the phase angle information of the bispectrum of the real signal to form a matrix form, the overall texture is relatively regular, showing clear symmetry and structured distribution characteristics. The color change is relatively smooth and orderly, reflecting that the phase coupling relationship between frequency components is relatively consistent. The phase angle matrix of the real signal shows regularity mainly because the signal comes from a single target, and the coupling relationship between its frequency components is dominated by the linear motion characteristics or stable scattering characteristics of the target. For example, the motion of a real target usually causes a consistent Doppler frequency shift, and the amplitude and phase distribution of its echo signal are relatively stable. This regularity makes the color distribution in the phase angle matrix orderly, and the frequency coupling characteristics are manifested as symmetry and clear structure.

[0048] In contrast, the matrix after extracting the bispectrum phase angle information of the false target interference has an obviously chaotic texture, disordered color distribution, lack of symmetry and regularity, showing highly random characteristics. This contrast indicates the significant difference in the phase coupling of the frequency components of the two signals. This difference occurs mainly because in the real environment, when the radar receives false target interference, it also receives sea clutter information in the same range cell. The chaotic and disordered distribution of the phase angle matrix of the false target interference signal is caused by the complex nonlinear relationship resulting from the superposition of the characteristics of the false target interference signal and the sea clutter signal.

[0049] False target interference is usually artificially generated and has significant harmonic characteristics or specific modulation frequencies. There may be regular phase coupling between frequency components. Sea clutter, on the other hand, is the result of the combined action of random scattering, multipath effects, and environmental noise. The phase relationship between its frequency components lacks regularity and shows randomness. When the false target interference is superimposed on the sea clutter signal, the regular harmonic characteristics interact with the random scattering characteristics, which may trigger new frequency coupling and complex phase modulation. This nonlinear mixing effect further exacerbates the complexity of the signal, making the phase angle matrix of the superimposed signal show a high degree of disorder and randomness. This chaotic phase distribution reflects the nonlinear relationship between the false target interference and the sea clutter, providing an important basis for analyzing and distinguishing interference signals. Therefore, this application uses the structural difference between the false target interference and the real echo in the bispectrum phase angle matrix to further extract relevant available features to quantify this difference, so as to realize the identification of false target interference.

[0050] S3. Convert the bispectrum phase angle matrix into a gray-level co-occurrence matrix, and extract image texture features based on the gray-level co-occurrence matrix.

[0051] The matrix values in the bispectrum phase angle matrix are linearly mapped to a grayscale image using the formula:

[0052] where L is the number of gray levels, and the gray level range is [0, L - 1]. According to the preset discretization rule , the gray level range of the grayscale image is equally discretized into [0, 15] to obtain a new grayscale image with 16 gray levels after discretization . A gray level co - occurrence matrix is set up to describe the co - occurrence relationship between pixel gray values in the new grayscale image . For the new grayscale image , the gray level co - occurrence matrix is defined as having a size of L×L. The elements in the gray level co - occurrence matrix are calculated as:

[0053] where (m, n) represents two gray values, represents the relative angle between two pixels, including four directions: 0°, 45°, 90°, and 135°, and define the displacement for calculating the gray level relationship, that is , represent the pixel offsets in the x and y axis directions respectively, and are related as follows:

[0054] The gray level co - occurrence matrix is normalized to obtain the normalized matrix , and the normalization formula is:

[0055] where the normalized matrix satisfies: . Denote the normalized gray level co - occurrence matrix as .

[0056] Extract the energy feature of the gray level co - occurrence matrix , where E is the energy, is the normalized gray level co - occurrence matrix. Extract the entropy value feature of the gray level co - occurrence matrix , where H is the entropy value. Extract the inertia moment feature of the gray level co - occurrence matrix , where I is the inertia moment. Extract the correlation feature of the gray level co - occurrence matrix , where C is the correlation, , ; , . Extract the contrast difference matrix features of the gray-level co-occurrence matrix, , where IDM is the contrast difference matrix. Based on the energy feature, entropy value feature, moment of inertia feature, correlation feature, and contrast difference matrix feature of the gray-level co-occurrence matrix, texture features are extracted.

[0057] Specifically, since the false target interference and the real echo show great differences in the texture structure of the bispectrum phase angle matrix, the phase angle matrix of the real target signal usually shows regular and structured texture features, while the false target signal is more random and disordered. Combining this feature, the present application can effectively distinguish real signals from false signals from the perspective of image texture features, while enhancing the robustness to noise. In addition, the bispectrum phase angle matrix contains high-order statistical information of the signal, and these information are often intuitively presented through texture patterns. Extracting texture features using image processing technology not only improves the analysis efficiency, but also provides an intuitive basis for target recognition and classification, thus better understanding the essential characteristics of the signal.

[0058] The false target interference and the real echo show great differences in the texture structure of the bispectrum phase angle matrix. The spatial distribution law of pixel gray values can be captured by analyzing the image texture features, and the deep characteristics of the signal can be intuitively revealed. In texture analysis, the gray-level co-occurrence matrix (GLCM) is a classic method that can quantify the texture features of an image, such as directionality, contrast, roughness, etc., by statistically analyzing the co-occurrence relationship of pixel gray values in a specific direction and distance. It can not only reveal the potential regular texture in the real signal phase angle matrix, but also effectively distinguish the random texture features of false signals.

[0059] The role of the gray-level co-occurrence matrix is reflected in the in-depth description of texture features. By calculating its eigenvalues (such as energy, correlation, entropy, moment of inertia, and contrast difference matrix), the high-order statistical characteristics of the image can be comprehensively reflected. These characteristics provide an important basis for the classification and recognition of target signals and false signals. Therefore, combining image texture feature extraction with the solution of the gray-level co-occurrence matrix can not only improve the accuracy of feature extraction, but also lay a foundation for subsequent target detection and classification. The specific extraction process of the gray-level co-occurrence matrix is as follows: The bispectrum phase angle information of the sequence to be measured is in the form of an N*N matrix, and its value range is (-π, π). To calculate the gray-level co-occurrence matrix, it is necessary to The value is discretized into the gray level range [0, L - 1]. Here, L is the number of gray levels, and in the actual application of this application, L = 255. The discretization formula is as follows: (1.3) After calculation, the matrix value can be linearly mapped to the gray scale image .

[0060] In the process of extracting the gray level co-occurrence matrix, to reduce the computational complexity, it is necessary to equally discretize the gray level value range of the gray scale image into [0, 15], and a new gray scale image with 16 gray levels after discretization is obtained . The discretization rule is: (1.4) The gray level co-occurrence matrix is used to describe the co-occurrence relationship between the pixel gray level values in the gray scale image. For the discrete gray scale image , the gray level co-occurrence matrix is defined as a matrix of size L×L , and its element calculation is as follows: (1.5) where (m, n) represents two gray level values; represents the relative angle between two pixels. In this application, a total of four directions of the gray level co-occurrence matrix are calculated, namely 0°, 45°, 90°, and 135°; and define the displacement for calculating the gray level relationship, that is , respectively represent the pixel offset amounts in the x and y axis directions. The relationship between is as follows: (1.6) To facilitate subsequent feature extraction, the gray level co-occurrence matrix usually needs to be normalized into a probability form. The specific normalization formula is: (1.7) The normalized matrix satisfies: .

[0061] Finally, the normalized is the gray level co-occurrence matrix, representing the joint distribution probability of different gray level pairs, providing a basis for subsequent texture analysis.

[0062] Statistical feature extraction The gray-level co-occurrence matrix reflects the texture characteristics of an image intuitively by statistically analyzing the spatial relationships between pixel gray values. However, relying solely on the gray-level co-occurrence matrix itself is insufficient to comprehensively describe the texture features of an image. Therefore, it is necessary to further extract statistical features that can quantify these relationships. In this application, five features, namely energy, entropy, inertia moment, correlation, and inverse difference moment, are selected. These features deeply analyze the gray-level co-occurrence matrix from different perspectives and can provide rich information for differentiating different image signals.

[0063] Energy: Energy reflects the uniformity or consistency of the gray-level co-occurrence matrix. The higher the energy value, the higher the occurrence frequency of certain gray-level pairs in the gray-level co-occurrence matrix, and the more concentrated the probability distribution. That is, a high energy value indicates that the image texture is smoother and more regular, while a low energy value indicates that the texture is more random or complex. Energy is denoted as , and the specific calculation process is as follows: (1.8) where is the normalized gray-level co-occurrence matrix in the above text.

[0064] Entropy: Entropy is an important indicator to describe the uncertainty or complexity of information. The higher the entropy value, the more random the probability distribution of two pixels with a specific spatial position relationship and their respective gray values in the gray-level co-occurrence matrix, and the more complex the texture; the lower the entropy value, the more certain the gray distribution, and the simpler or more regular the texture. The entropy value is denoted as , and the specific calculation process is as follows: (1.9) Inertia moment: The inertia moment reflects the degree of difference between gray values. The higher the value, the greater the difference in the spatial correlation between pixel gray values in the image, and the stronger the texture contrast; the lower the value, the smaller the gray difference, and the more uniform or smoother the image. The inertia moment is denoted as , and the specific calculation process is as follows: (1.10) Correlation: Correlation describes the linear dependence or mutual relationship between gray values. The higher the value, the stronger the correlation between gray values, and the more ordered the texture; the lower the value, the weaker the correlation between gray values, and the more random the texture. Correlation is denoted as , and the specific calculation process is as follows: (1.11) where: , ; , .

[0065] Contrast difference matrix: The contrast difference matrix reflects the local similarity of gray values. The higher the value, the smaller the change in gray values and the smoother the local texture; the lower the value, the greater the difference in gray values and the more drastic the local change. The contrast difference matrix is denoted as , and the specific calculation process is as follows: (1.12) Since four independent gray-level co-occurrence matrices are calculated in four directions (0°, 45°, 90°, 135°) in the previous text, each eigenvalue has four results in different directions. In order to obtain a more representative final eigenvalue, this application uses the mean value to comprehensively describe the global texture characteristics of the image, and the standard deviation to analyze the consistency of the image texture in different directions. Finally, the statistical method of the mean value and the standard deviation is used to calculate the final eigenvalue. Such a statistical method can not only balance the information in different directions and avoid the excessive influence of the eigenvalue in a single direction on the result, but also keenly capture the change law between different directions.

[0066] According to the above feature extraction method, this application extracts features from the measured interference and real target data, and uses the histogram results to observe the separability of false target interference and real targets in different feature spaces.

[0067] (1)Analysis of the separability of energy features The mean energy distribution of the gray-level co-occurrence matrix of false target interference in four directions is in the low-value area and is very concentrated. The mean energy distribution of the real target signal is more dispersed. This is because the texture of the gray-level co-occurrence matrix of the real target signal has a certain regularity, and the combination of pixel values and the probability of their frequencies are concentrated on several specific values, reflecting the consistency of the texture, while the texture distribution of the false target signal is more random, and the change of pixel values is dispersed and lacks concentration.

[0068] From the distribution of energy variance, the energy variance of the false target interference signal is low and the distribution is narrow, while the energy variance of the real target signal is relatively high and the distribution range is wider. The energy variance distribution of the real target signal is wider and more dispersed. This is because the overall texture of the bispectrum phase angle matrix of the false target interference signal is random and uniform, without obvious structure or directionality. The randomness and disorder of the texture in different directions are also very similar, resulting in very small differences in the energy values of the gray-level co-occurrence matrices in each direction, thus making the energy variance low and the distribution range narrower.

[0069] The histogram results reflect the significant differences in energy features between the real target signal and the false target interference signal, and this difference corresponds closely to the texture characteristics. In summary, it can be shown that the mean energy and variance in different directions have a certain degree of separability and can be used as one of the identification features of false target interference signals.

[0070] (2)Divisibility analysis of entropy In the entropy mean distribution, the true target signal is in the lower range (1.5 - 4.0) and shows a relatively wide distribution. The false target interference signal is concentrated near the maximum value (about 5.5) and has a very concentrated distribution. This indicates that the gray-level co-occurrence matrix of the true target signal has a certain degree of complexity but still maintains a certain regularity, while the gray-level distribution of the false target interference signal is close to completely random, lacking obvious texture features and gray-level correlation. In the standard deviation distribution of entropy, the true target signal shows a relatively uniform bell-shaped distribution, which shows that the texture of the true target signal exhibits orderly changes in different directions, and there are significant differences in the gray-level co-occurrence matrix in different directions. This difference causes fluctuations in the entropy value, resulting in a relatively large standard deviation. The standard deviation of the entropy value on the gray-level co-occurrence matrix of the false target interference signal is almost 0 and the distribution is highly concentrated. This is because the texture of the false target interference signal is completely disordered in space, and the gray-level co-occurrence matrices in the four directions are almost indistinguishable.

[0071] The image of the true target signal usually has obvious texture or structural features. This regularity makes there be more coherence information in the gray-level co-occurrence matrix of the bispectrum phase angle. Therefore, the mean value of entropy is lower and the distribution is wider, reflecting a relatively large change in the gray-level complexity between different image regions. Due to the similar distribution of the gray-level co-occurrence matrices in all directions of the false target interference signal and the lack of directional features, the entropy value changes very little in all directions, and the standard deviation is close to zero. In summary, the histogram results can show that the mean value and variance of entropy in different directions have a certain degree of divisibility and can be used as one of the identification features of the false target interference signal.

[0072] (3)Divisibility analysis of moment of inertia features In the mean distribution of the moment of inertia, the true target signal is concentrated in the low value range, mainly distributed between 0 and 10, and shows a long-tailed distribution. The false target interference signal is concentrated in the high value range and has a relatively narrow distribution. The reason is that the texture structure of the true target signal is relatively smooth and directional, and the gray-level difference in the gray-level co-occurrence matrix is small, so the mean value of the moment of inertia is low. The gray-level distribution of the false target interference signal is random, the texture is irregular, and the gray-level difference in the gray-level co-occurrence matrix is large, so the mean value of the moment of inertia is relatively high. In the mean distribution of the moment of inertia, the distribution of the true target signal is relatively wide, mainly concentrated between 0.5 and 3, showing a certain degree of discreteness. The false target interference signal is concentrated in the low value range (close to 0 - 1) and has a relatively narrow distribution, but there is a serious overlap in part of the distribution with the true target signal. This is because the differences in the spatial correlation between gray-level values in the gray-level co-occurrence matrix of the false target interference signal in all directions are very similar.

[0073] From the perspective of the separability of the feature space, the mean distribution of the moment of inertia is completely separated, with stronger separability, making it easy to distinguish the real target signal and the false target interference signal in this feature dimension. In the standard deviation histogram of the moment of inertia, there is a large overlap in the standard deviation distributions of the real and false signals, and its individual classification ability is limited. The comprehensive histogram results show that the mean values of the moment of inertia in different directions have a certain degree of separability and can be used as one of the identification features of false target interference signals.

[0074] (4)Analysis of the separability of correlation features In the correlation mean distribution, the real target signals are concentrated between 0.03 and 0.07, showing a right-skewed distribution and a relatively wide distribution. The false target interference signals are concentrated in the low-value range close to 0 to 0.005, with a very concentrated distribution. The reason is that the gray-level co-occurrence matrix of the real target signal has a significant texture structure, and there is a strong linear correlation between different pixels, resulting in a relatively high correlation mean in the gray-level co-occurrence matrix. For the false target interference signal, due to the random gray-level distribution and almost no correlation between pixels, the correlation mean is close to zero. In the correlation mean distribution, the changes in the correlation of the real target signal and the false target interference signal in the gray-level co-occurrence matrix in different directions are all relatively small. Both show a right-skewed distribution and are distributed in the low-value range.

[0075] From the perspective of the separability of the feature space, due to the relatively high correlation mean of the real target signal and the correlation mean of the false target interference signal being close to zero, the distribution overlap between the two is small, and they have strong separability. However, there is a large overlap in the distributions of the real target signal and the false target interference signal in the correlation standard deviation, and the separability is poor. It is difficult to achieve effective classification by using this feature alone. Through comprehensive histogram result analysis, the correlation means in different directions have a certain degree of separability and can be used as one of the identification features of false target interference signals.

[0076] (5)Analysis of the separability of the contrast difference matrix features In the mean distribution of the contrast difference matrix, the real target signals are mainly distributed in the range of 0.4 to 0.9, showing a right-skewed distribution and a relatively wide overall distribution. The false target interference signals are distributed in the low-value area, with a narrow range and almost no overlap with the distribution of the real target signals. The reason is that the texture structure of the real target signal is relatively smooth and regular, and the local similarity of the gray level is relatively high, resulting in a relatively high mean of the contrast difference matrix. For the false target interference signal, the bispectrum phase angle matrix shows randomness and high-frequency noise characteristics, with large local texture changes, making its mean value low. The distribution of the standard deviation of the contrast difference matrix is similar to the distribution result of the mean of the contrast difference matrix, except for a small overlap in the interval near the value of 0.01.

[0077] This application extracts features from the measured interference and real target data and uses the histogram results to observe the separability of false target interference and real targets in the Tamura texture feature space. In the roughness distribution, the real target signals are mainly distributed in the higher range (9 - 11), and the distribution shows a certain width. This indicates that the texture of the real target signals is smooth, the gray-scale changes slowly, and the overall texture has large-scale structural features. The false target interference signals are concentrated in the lower range (6 - 7), with a narrow distribution range and obvious peaks. This reflects that the texture of the false target interference signals is relatively delicate, the gray-scale changes rapidly and randomly, and there is a lack of obvious large-scale texture structures.

[0078] The image texture of the real target signals has a certain directionality and regularity. Since the gray-scale changes slowly in most areas, the calculated optimal window size is relatively large, and the overall roughness is relatively high. The image texture of the false target interference signals is similar to high-frequency noise, without obvious directionality and regularity, and the gray-scale changes frequently and randomly. This fast-changing texture characteristic makes the image roughness of this type of signal concentrated in the lower range. This matches the histogram distribution results. Therefore, due to the regularity and large-scale structure of the image texture of the real signals and the randomness and rapid gray-scale changes of the false target signal images, the roughness feature can effectively distinguish the real target signals from the false target interference signals. The roughness value distributions of the true and false target signals in the histogram hardly overlap, which more directly shows that the roughness feature has significant classification ability.

[0079] Linearity In the linearity distribution, the real target signals are mainly distributed between 0.05 and 0.25, showing a relatively wide distribution range. This is because the real target signal images usually have regular linear textures, with a certain directionality and linearity. In the co-occurrence matrix of directions, there is a strong cosine similarity between the gradients in different directions. The false target interference signals are concentrated in the lower range (0 - 0.05), with a narrow and highly concentrated distribution. This reflects that the texture of the false target interference signals has basically no directionality and linear structure, and the correlation between the gradient directions is weak. Therefore, the linearity value is very low and the distribution range is narrow.

[0080] Generally speaking, real signals are due to the directionality and linear structure of the texture; while false signals are due to the characteristics of random noise. The linearity feature has a strong quantification ability for such differences. Therefore, linearity can effectively distinguish real target signals from false target interference signals.

[0081] S4. Extract the values on the main diagonal from the bispectrum phase angle matrix to obtain a diagonal sequence, and perform spectral analysis and sequence trend feature analysis based on the diagonal sequence.

[0082] Let the diagonal sequence be . Take the diagonal sequence with a length of N in the diagonal sequence for Fourier transform to obtain the spectrum , . Calculate the spectral amplitude The frequency corresponding to the maximum point: , and obtain the main frequency of the spectrum. Calculate the standard deviation of the spectrum: , and obtain the true target spectrum standard deviation interval, where represents the spectrum mean, defined as . Calculate the kurtosis of the spectrum: , and obtain the true target spectrum kurtosis interval. Calculate the skewness of the spectrum: , and obtain the true target spectrum skewness interval.

[0083] Based on the diagonal sequence being , calculate the difference between adjacent elements: . Take the absolute value of all differences and then accumulate to calculate the cumulative sum : , and obtain the true target cumulative sum interval. Define the Gaussian weight function, with the center of the Gaussian distribution being , and the standard deviation being , and the weight at the th position is: . Introduce the Gaussian weight into the absolute difference cumulative sum to obtain the Gaussian weighted cumulative sum : . Based on the Gaussian weighted cumulative sum, obtain the sequence trend feature.

[0084] Specifically, in addition to extracting information from the grayscale image of the bispectrum phase angle matrix, the present application extracts the matrix diagonal sequence for analysis. The diagonal sequence can be regarded as a concentrated expression of the important texture information in the original image, and can reflect the global structure characteristics and local change trends of the image.

[0085] The overall change trend of the diagonal sequence of the true target signal is relatively flat. There are mutation points or large gradient changes in such sequences, but most of the signals show a stable trend and have a certain periodicity. In the false target interference sequence, there are frequent and rapid high-frequency fluctuations, and there is no obvious stable part in the signal. Its frequency distribution is relatively wide, the high-frequency components are significant, showing strong randomness and lacking prominent low-frequency characteristics. These two types of signals can be effectively distinguished through frequency domain features, and their essential differences can be captured. In the present application, four frequency domain features, namely the main frequency, standard deviation, kurtosis, and skewness of the spectrum, are extracted, and the separability of the features for true and false target signals is verified.

[0086] Verification of the frequency domain features of the sequence (1) Verification of the spectral main frequency index In the main frequency distribution in the frequency domain, the main frequency values of the sequences of real targets mostly concentrate in the lower (close to 0 Hz) frequency region, and the distribution range is relatively narrow, indicating that the main frequency components of real target signals are stable and the low frequencies are dominant. The main frequency values of the sequences of false target interferences are distributed in a relatively wide frequency range. Compared with real targets, the main frequency values of the sequences of false target interferences are not concentrated, and the frequency spectrum distribution is relatively dispersed.

[0087] The main reason is that the real target signal shows slow change and low-frequency characteristics in the sequence. After the fast Fourier transform (FFT), the spectral energy of the signal is concentrated in the low-frequency band, and the main frequency value is usually close to zero. While the false target interference signal shows high-frequency oscillation and fast change in the sequence, with complex frequency components, its spectral energy distribution is relatively dispersed, and there are more high-frequency components, making the main frequency distributed in a wider frequency range. The degree of fluctuation intensity in the sequence enables the main frequency characteristics in the sequence frequency domain to effectively distinguish real target signals and false target interference signals. Therefore, the main frequency characteristic is an important index for distinguishing the two types of signals, with strong separability and classification ability.

[0088] (2)Verification of spectral standard deviation In the spectral standard deviation distribution in the frequency domain, the distribution range of the sequence standard deviation values of real targets is relatively wide, mainly concentrated between 14 and 18, indicating that the spectral amplitude change of real target signals has certain fluctuations, but is relatively stable as a whole. The distribution range of the sequence standard deviation values of false target interference signals is relatively narrow, indicating that the amplitude change range of the false target signal spectrum is smaller and the spectrum distribution is more concentrated.

[0089] The diagonal sequence of real targets has obvious regularity and low-frequency characteristics, which results in higher spectral amplitudes in the low-frequency band and gradual attenuation in the high-frequency band. This non-uniform amplitude distribution leads to a higher spectral standard deviation. The example diagram of the diagonal sequence of false target interference shows that the false target signal presents high-frequency random fluctuations and has no obvious low-frequency dominant characteristics. Its spectral amplitudes are relatively evenly distributed in each frequency band with small fluctuations, so the spectral standard deviation is low. It can be seen from the histogram that the spectral standard deviation distribution of real target signals is significantly higher than that of false target interference signals. As a feature, the spectral standard deviation can effectively capture the differences in the fluctuations of signal spectral amplitudes and can effectively improve the recognition ability of the algorithm for false target interference.

[0090] (3)Verification of spectral kurtosis In the spectral kurtosis distribution in the frequency domain, the distribution range of the sequence kurtosis values of real targets is relatively wide, concentrated between 20 and 45, indicating that the spectrum of real target signals has higher sharpness and concentration. The sequence kurtosis values of false target interferences are mainly concentrated between 0 and 10, and the distribution range is relatively narrow. It indicates that the spectrum distribution of false target signals is flatter and lacks sharp energy concentration points.

[0091] The sequence of the true target signal has a smooth low-frequency variation trend. Such a signal shows that the energy is concentrated in a few low-frequency bands in the frequency domain, forming relatively high spikes. The spike characteristics of the spectrum result in a higher kurtosis value and a more concentrated distribution. In contrast, the sequence of the false target signal is more like random high-frequency oscillations, and the spectral energy is distributed over a wide frequency range. Since there is no obvious concentration point of energy, the spectral kurtosis is low, presenting a flat spectral distribution. The spectral kurtosis feature can clearly reflect the concentration and sharpness of the spectral energy in the true and false target sequences. This property has strong discrimination ability and can be used as a classification feature for identifying false target interference.

[0092] (4)Spectrum skewness verification In the frequency-domain skewness distribution, the skewness value distribution range of the true target sequence is relatively wide, indicating that the spectral amplitude distribution of the true target signal has strong positive skewness (the spectral energy is concentrated in the low-frequency region). The skewness value distribution of the false target interference sequence is relatively narrow, with a low skewness value and no significant high-value region, indicating that the spectral distribution of the false target signal is relatively symmetric and there is no obvious concentration trend of energy.

[0093] The sequence of the true target signal has a smooth variation trend, and its spectral energy is mainly concentrated in the low-frequency band, while the high-frequency component is weak. This characteristic of spectral energy concentration in the low-frequency band results in a positive skew in the spectral distribution and a higher skewness value. The false target signal of the false target interference sequence shows high-frequency random fluctuations, and its spectral energy is evenly distributed in each frequency band. The symmetry of the spectral distribution leads to a lower skewness value. The spectral kurtosis feature can clearly reflect the symmetry property of the spectral energy in the true and false target sequences. This property has strong discrimination ability and can be used as a classification feature for identifying false target interference.

[0094] The sequence of the true target as a whole shows a smooth trend change, usually including slow transitions or obvious directional changes. Although there are local mutation points, the overall trend is relatively stable and the change direction is less. The sequence of the false target interference shows violent and non-directional changes, and the trend is a noise-like signal with strong randomness and no obvious smooth trend. For such differences in trends, the difference between the true target signal and the smoothness and the random fluctuations of the false target can be captured by extracting trend features. Therefore, this application extracts two trend features, the cumulative sum of absolute differences and the Gaussian-weighted cumulative sum of absolute differences, and verifies the separability of the features for the true and false target signals.

[0095] Analysis of sequence trend features (1)Cumulative sum of absolute differences In the cumulative sum distribution of absolute differences, the cumulative sum of absolute differences of the sequence of the true target is mainly concentrated in the range of 20 to 200, and a significant peak is formed near 40. The overall distribution is relatively concentrated, indicating that the sequence change of the true target signal is smooth and the difference fluctuation is small. The reason is that the sequence gray value of the true target signal changes slowly and the trend is smooth, and the difference between adjacent gray values is small. While the cumulative sum value distribution range of the sequence of false target interference is narrow and the difference is high, mainly concentrated in the range of 250 to 320, reflecting the frequent high-frequency fluctuations and drastic changes in the false target signal sequence. The reason is that the diagonal sequence of the false target signal shows obvious high-frequency random fluctuations, resulting in a large difference between adjacent gray values. This frequent change leads to a higher cumulative sum value of absolute differences and is concentrated in a larger interval.

[0096] The true target signal and the false target interference signal hardly overlap at all in terms of the cumulative sum of absolute differences feature, and the distribution intervals are completely separated. The cumulative sum of absolute differences feature can effectively reflect the smoothness and volatility of the sequence. The cumulative sum of the true target signal is lower due to its gentle change, while the cumulative sum of the false target interference signal is higher due to its random drastic change. The above proves that the cumulative sum of absolute differences feature has extremely strong separability and can be used as an important basis for distinguishing the true target signal from the false target interference signal.

[0097] (2)Gaussian weighted cumulative sum of absolute differences The distribution of the weighted cumulative sum of absolute differences is similar to the distribution of the cumulative sum of absolute differences. The distribution of the true target signal has a smaller tail and higher concentration. However, the formation reasons for the results of the two feature histograms are different. The Gaussian weighted cumulative sum of absolute differences assigns a larger weight to the central region of the sequence. It can more prominently show the fluctuation characteristics of the key region (center) in the sequence and is not sensitive to the fluctuations in the edge part. While it focuses on the overall gray change amplitude of the sequence. It is more sensitive to the global trend change of the sequence but may ignore the characteristics of some key regions (such as the central part). Using the two features jointly can comprehensively analyze the global and local features of the sequence and improve the robustness and accuracy of classification.

[0098] Therefore, the Gaussian weighted cumulative sum of absolute differences feature can effectively distinguish the true target signal from the false target interference signal, and its joint use with the cumulative sum of absolute differences feature can play a greater role in the classification task. The cumulative sum of absolute differences focuses on global changes, while the Gaussian weighted cumulative sum focuses on changes in the local central region. The two complement each other, providing a more comprehensive signal description and improving the classification effect.

[0099] In the process of extracting the cumulative sum of Gaussian weighted absolute differences, it is necessary to first construct a Gaussian weighting function. Since there is a hyperparameter of standard deviation, and the standard deviation can directly affect the feature extraction result. Therefore, it is particularly important to select the standard deviation value. Only by choosing an appropriate standard deviation can the weights of the global trend and local changes be balanced, thereby improving the discrimination ability of features and ensuring that the features perform optimally when distinguishing between real target signals and false target interference signals.

[0100] This application selects two optimization methods, the Mahalanobis distance method and the Fisher discriminant coefficient method, to select the optimal standard deviation. The Mahalanobis distance method can judge the separation effect of the Gaussian weighted cumulative sum features between real target signals and false target signals by measuring the projection of the mean difference between two sets of data in the covariance matrix. The Fisher discriminant coefficient method can evaluate the discrimination ability of features under different standard deviations by analyzing the ratio of the mean difference of each feature dimension to the within-group variance. This application selects the optimal standard deviation by combining the results of the two types of optimization methods. The specific optimization process is as follows: Mahalanobis distance calculation formula: Let the Gaussian weighted absolute difference cumulative sum features of two types of sequences be and , the mean vectors are and , and the covariance matrix is .

[0101] (1.31) Fisher discriminant coefficient method: Let the Gaussian weighted absolute difference cumulative sum features of two types of sequences be and , the mean vectors are and , and the variances are and .

[0102] (1.32) The experimental results of using the Mahalanobis distance method and the Fisher discriminant coefficient method, two optimization methods, to select the optimal standard deviation. The experimental data show that when the standard deviation is in the range of 15 to 25, the Mahalanobis distance is relatively stable and at a high level, and the Fisher discriminant coefficient is also in a high range, indicating that the mean difference between the two sets of data is relatively larger than the variance in this range, and the separability is stronger. This shows that within this standard deviation range, the discrimination ability of each feature is relatively good, and the two sets of data can be better distinguished. Considering the experimental results comprehensively, this application selects the standard deviation value of 18.

[0103] S5. Based on the image texture features and sequence trend features, perform principal component analysis, and input the features after principal component analysis into a preset classification model to obtain the result of identifying the true target or false target.

[0104] Normalize the image texture features and sequence trend features, compress the image texture features and sequence trend features into the interval [0, 1] to obtain normalized eigenvalue. Use principal component analysis to reduce the dimension of the normalized eigenvalue to obtain the dimensionality-reduced data. Input each dimensionality-reduced data into a preset classification model to obtain the result of identifying the true target or false target.

[0105] Specifically, to verify the effectiveness and practicality of the algorithm of the present application, radar measured data is used for verification. The test data all come from the radar sea detection data sharing plan initiated by the Naval Aviation University. The test environment of the measured data is under sea state 4. The shore-based radar is used for circular scanning to receive echo signals, and the interference machine is installed on the sea ship to interfere with the shore-based radar. According to the B-display intention of the radar echo data, the following principal component analysis is carried out.

[0106] According to the above content, a total of 16 available features in four categories are summarized. Although the calculation methods of the features are different, due to the possible homogenization of the physical meanings expressed among multiple features of the same type, this redundancy will increase the computational complexity and reduce the efficiency of the classification task. In addition, in the high-dimensional feature space, the distribution of data may become sparse, resulting in the difficulty for the classification algorithm to work effectively. However, by projecting the high-dimensional features into a low-dimensional space, the influence of irrelevant or weakly relevant features can be reduced while retaining the main information of the data. Since the task of identifying true and false targets has practicality, it is also necessary to consider the increase in the complexity of the classification model caused by high-dimensional features, which may lead to the overfitting problem. For the above reasons, the present application believes that it is necessary to use principal component analysis (PCA) to reduce the dimension of the feature data, optimize the feature space structure by analyzing the contributions of each feature, reduce the dimension, and thus improve the classification efficiency and the generalization ability of the model.

[0107] To further illustrate the necessity of reducing the dimension of the feature data, the present application takes the random forest as the benchmark classification model and analyzes the importance of the 16 original features in the actual classification task. Through the comprehensive analysis of the correlation between the features before PCA dimensionality reduction and the importance of the features before PCA, among the 16 original features, there is a high correlation between some features, and there is a significant redundancy problem in the overall features. In addition, there are some features with low importance. Retaining these features may increase noise and reduce the performance of the classification model. Therefore, it is necessary to use PCA to screen the main feature directions, ignore the directions corresponding to the low-importance features, and reduce the interference of irrelevant or weakly relevant features on the model.

[0108] Selection of the Optimal Dimension of PCA During the PCA dimensionality reduction process, it is necessary to first determine the size of the dimension after dimensionality reduction. The method used in this application is to combine PCA and cross-validation. By gradually increasing the number of principal components, the classification accuracy of each number of principal components in the classification task is tested. Finally, the number of principal components that can achieve the highest classification accuracy is selected as the optimal dimension. The specific processing process is as follows: First, the data is normalized to compress the feature values into the interval [0, 1] to improve the efficiency of PCA and the classification model. Then, PCA dimensionality reduction is performed to sequentially extract different numbers of principal components (from 1 to the maximum number of features, 16), generating a data matrix after dimensionality reduction. After each reduction of the data dimension, the new low-dimensional data is passed to the classifier. In this application, 10-fold cross-validation is used during cross-validation. In each fold of cross-validation, 70% of the data is used to train the classifier (the random forest is still used as the baseline classification model here), 30% of the data is used to test the classifier, and the average classification accuracy of all folds at each dimension is recorded. Finally, the dimension number with the highest classification accuracy and the corresponding classification accuracy are found.

[0109] During the process of increasing the number of principal components from 1 to 6, the classification accuracy increases rapidly; while after more than 6 principal components, the accuracy tends to be stable, indicating that redundant features have little impact on the classification results. When the number of principal components is 6, the classification accuracy reaches the highest value of 0.99786, indicating that the feature information retained after dimensionality reduction at this time can effectively describe the samples and avoid the interference of redundant features. Therefore, selecting 6 principal components after PCA dimensionality reduction can maintain a classification accuracy close to 100%, and the stable trend of the classification accuracy in the figure also verifies the effectiveness of PCA and the rationality of selecting the dimension by cross-validation.

[0110] Analysis of PCA Dimensionality Reduction Results Based on the optimal PCA dimension determined in the above text, the parameter of the feature dimension after PCA is adjusted, and the original feature dataset is reprocessed by PCA dimensionality reduction to analyze the independence and variance contribution rate of each component after dimensionality reduction.

[0111] In the PCA feature correlation matrix after selecting the optimal PCA dimension, it shows that the principal components are independent of each other. This proves that PCA dimensionality reduction reduces redundant information and avoids the interference of feature correlation on subsequent analysis, thereby improving the stability of the classifier or regression model. The variance contribution rate of each principal component demonstrates the explanatory ability of each principal component to the total data variance. According to the cumulative variance contribution rate, it can be seen that the cumulative contribution rate of the first 6 principal components has reached 98.32%, indicating that most of the information of the original data can be well retained through 6 principal components. It can be concluded that the principal components after PCA dimensionality reduction explain most of the data variance, and only a small number of principal components are required to achieve a high cumulative variance contribution rate, indicating that the dimensionality reduction process is reasonable and effective. At the same time, the cumulative variance contribution rate shows that selecting 6 principal components can well balance the data fidelity and computational complexity after dimensionality reduction.

[0112] This application uses the CatBoost model for multi-feature joint classification to achieve the identification of real targets and false target interferences. The specific reasons for selecting the CatBoost model are as follows: First, the feature data for training the model has undergone PCA dimensionality reduction, but the principal components after dimensionality reduction may have non-linear relationships, and the built-in gradient boosting algorithm of CatBoost can capture the complex relationships between features, which is particularly important for the principal component features extracted by PCA; Second, the CatBoost model performs excellently in dealing with data with small samples and complex features. After PCA dimensionality reduction, the redundancy of the data is reduced and the information is concentrated, making the classification task more effective. The specific test results are as follows: According to the confusion matrix results of the test set of the CatBoost model, 5 samples in each of the two categories are misclassified. Generally speaking, the classification error rate is very low, indicating that the model has strong classification ability for real targets and false targets, and the classification balance is very good. Through the analysis of the ROC curve and AUC value of the training model, the ROC curve reflects the classification ability of the model at different thresholds. The curve is close to the upper left corner and the AUC value approaches 1, indicating that the model can correctly classify real targets and false target interferences in most cases. Such a performance shows that the model not only performs well in classifying known data, but also has strong discrimination ability for new samples. Combining the analysis of the confusion matrix and the ROC curve, it can be seen that this classification model has high precision and recall rate and can effectively distinguish real targets and false targets.

[0113] Table 1 is the classification report of the trained CatBoost model. From the table, it can be seen that the precision and recall rates of both categories are close to 0.97 or above, indicating that the model has high accuracy and detection rate in predicting the two types of samples. The overall accuracy rate has reached 0.9732, indicating that the overall performance of the model is relatively excellent.

[0114] Table 1

[0115] It can be seen that the macro-average in the table represents the average of the precision, recall, and comprehensive score for each category; the weighted average is based on the macro-average and uses weighted averaging according to the sample size of the category. Both the macro-average and the weighted average reach 0.97. This further proves the stability and balance of the model's classification performance. This indicates that the model has no obvious bias when classifying different categories and has good generalization ability. This ensures that when this method performs classification tasks in diverse real-world environments, it can reduce false alarms and missed detections, thereby improving the reliability and practicality of the system.

[0116] In some embodiments, the radar interference identification system based on bispectral phase angle may include multiple functional modules composed of computer program segments. The computer programs of each program segment in the radar interference identification system based on bispectral phase angle can be stored in the memory of the computer device and executed by at least one processor to perform the functions of radar interference identification based on bispectral phase angle (see Figure 1 description).

[0117] In this embodiment, the radar interference identification system based on bispectral phase angle can be divided into multiple functional modules according to the functions it performs, as Figure 2 shown. The functional modules of system 200 may include: a data acquisition module 210, a matrix calculation module 220, a feature extraction module 230, a feature analysis module 240, and a result identification module 250. The module referred to in the present invention refers to a series of computer program segments that can be executed by at least one processor and can complete fixed functions, and are stored in the memory. In this embodiment, the functions of each module will be described in detail in subsequent embodiments.

[0118] The data acquisition module is used to acquire the observation data received by the radar; The matrix calculation module is used to calculate the bispectral phase angle matrix of the observation data; The feature extraction module is used to convert the bispectral phase angle matrix into a gray-level co-occurrence matrix and extract image texture features based on the gray-level co-occurrence matrix; The feature analysis module is used to extract the values on the main diagonal from the bispectral phase angle matrix to obtain a diagonal sequence, and perform spectral analysis and sequence trend feature analysis based on the diagonal sequence; The result identification module is used to perform principal component analysis based on the image texture features and sequence trend features, and input the features after principal component analysis into a preset classification model to obtain the result of identifying real targets or false targets.

[0119] Figure 3FIG. 0 is a schematic structural diagram of a terminal 300 provided by an embodiment of the present invention, and the terminal 300 can be used to execute the radar interference identification method based on the bispectrum phase angle provided by the embodiment of the present invention.

[0120] Among them, the terminal 300 may include: a processor 310, a memory 320, and a communication unit 330. These components communicate through one or more buses. Those skilled in the art can understand that the structure of the server shown in the figure does not constitute a limitation on the present invention. It can be a bus structure, a star structure, and may also include more or fewer components than shown in the figure, or combine some components, or have different component arrangements.

[0121] Those skilled in the art can clearly understand that the technology in the embodiments of the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution in the embodiments of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product is stored in a storage medium such as a USB flash drive, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk, or an optical disc, etc., which can store program codes, and includes several instructions to enable a computer terminal (which can be a personal computer, a server, or a second terminal, a network terminal, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention.

[0122] For the same or similar parts among the various embodiments in this specification, reference can be made to each other. In particular, for the terminal embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the description in the method embodiments.

[0123] In several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the system embodiments described above are merely illustrative. For example, the division of the modules is only a logical function division. In actual implementation, there may be other division methods. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection to each other can be through some interfaces. The indirect coupling or communication connection of the system or module can be in an electrical, mechanical, or other form.

[0124] The module described as a separation component may or may not be physically separated. The component shown as a module may or may not be a physical module, that is, it may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0125] In addition, in each embodiment of the present invention, each functional module can be integrated in a processing module, or each module can exist physically alone, or two or more modules can be integrated in one module.

[0126] Although the present invention has been described in detail by referring to the accompanying drawings and in combination with the preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, those of ordinary skill in the art can make various equivalent modifications or substitutions to the embodiments of the present invention, and these modifications or substitutions should all be within the scope of the present invention. / Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A radar interference identification method based on bispectrum phase angle, characterized in that Including: Obtain the observation data received by the radar; Calculate the bispectrum phase angle matrix of the observation data; Convert the bispectrum phase angle matrix into a gray-level co-occurrence matrix, and extract image texture features based on the gray-level co-occurrence matrix; Extract the values on the main diagonal from the bispectrum phase angle matrix to obtain a diagonal sequence, and perform spectrum analysis and sequence trend feature analysis based on the diagonal sequence; Based on the image texture features and sequence trend features, perform principal component analysis, and input the features after principal component analysis into a preset classification model to obtain the result of identifying the real target or false target.

2. The method according to claim 1, wherein Calculating the bispectrum phase angle matrix of the observation data includes: Take the observation data of length N, divide the observation data into K equal segments, each segment has a data length of M points, and let the nth segment of data be , and calculate the estimated values of the third-order cumulants of each segment of data respectively: wherein, = max(0, -i, -j), = min(M - 1, M - 1 - I, M - 1 - j); Statistically average the third-order cumulants obtained for each segment, and the result is the third-order cumulant of the data, expressed as: Then the bispectrum is: where L < M - 1, is expressed as a two-dimensional lag window function; Extract the phase angle information from the result matrix of the bispectrum. Let the elements in the bispectrum matrix be , where , is the real part of the element , is the imaginary part of the element . The representation of the element in polar coordinates is ; Calculation element phase angle of : ； Calculate the phase angle of each element , and obtain the bispectrum phase angle matrix , where the value range is (-π, π).

3. The method according to claim 1, wherein Converting the bispectrum phase angle matrix into a gray-level co-occurrence matrix includes: The matrix values in the bispectrum phase angle matrix are linearly mapped to a grayscale image with the formula: Where L is the number of gray levels, and the gray level range is [0, L - 1]; According to the preset discretization rules , the gray value range of the grayscale image is evenly discretized into [0, 15], and a new grayscale image with 16 gray levels after discretization is obtained ; Set the gray-level co-occurrence matrix , which is used to describe the co-occurrence relationship between the pixel gray-level values in the new gray-scale image . For the new gray-scale image , define the gray-level co-occurrence matrix as having a size of L×L. The elements in the gray-level co-occurrence matrix are calculated as follows: Among them, (m, n) represents two grayscale values, represents the relative angle between two pixels, including four directions: 0°, 45°, 90°, and 135°, and defines the displacement for calculating the grayscale relationship, that is, 、 respectively represent the pixel offsets in the x and y axis directions, The relationship between is as follows: Normalize the gray-level co-occurrence matrix to obtain the normalized matrix . The normalization formula is as follows: Among them, the normalized matrix satisfies: ; Let the normalized gray-level co-occurrence matrix be denoted as .

4. The method according to claim 3, wherein Extracting image texture features based on the gray-level co-occurrence matrix includes: Extract the energy feature of the gray-level co-occurrence matrix, , where E is the energy, is the normalized gray-level co-occurrence matrix; Extract the entropy value feature of the gray-level co-occurrence matrix, , where H is the entropy value; Extract the inertia moment feature of the gray-level co-occurrence matrix, , where I is the inertia moment; Extract the correlation features of the gray-level co-occurrence matrix, , where C is the correlation, , ; , ; Extract the contrast difference matrix features of the gray-level co-occurrence matrix, , where IDM is the contrast difference matrix; Based on the energy feature, entropy value feature, inertia moment feature, correlation feature, and contrast difference matrix feature of the gray-level co-occurrence matrix, extract the texture features.

5. The method according to claim 1, characterized in that Extracting the values on the main diagonal from the bispectrum phase angle matrix to obtain a diagonal sequence, and performing spectrum analysis based on the diagonal sequence includes: Let the diagonal sequence be ; Extract the diagonal sequence with length N from the diagonal sequences Perform Fourier transform to obtain the frequency spectrum , ; Calculate the spectral amplitude Frequency corresponding to the maximum point: , to obtain the main frequency of the spectrum; Calculate the standard deviation of the spectrum: , to obtain the true target spectrum standard deviation interval, where represents the spectrum mean, defined as ; Calculate the spectral kurtosis: , and obtain the true target spectral kurtosis interval; Calculate the spectral skewness: , and obtain the true target spectral skewness interval.

6. The method according to claim 1, characterized in that, The sequence trend feature analysis includes: Based on the diagonal sequence being , calculate the difference between adjacent elements: ； Take the absolute value of all differences and then accumulate them to calculate the cumulative sum : , to obtain the true target cumulative sum range; Define the Gaussian weight function, with the center of the Gaussian distribution being , and the standard deviation being , the weight at the -th position is: ; Introduce Gaussian weights into the cumulative sum of absolute differences to obtain the Gaussian weighted cumulative sum : ； Based on the Gaussian weighted cumulative sum, obtain the sequence trend feature.

7. The method according to claim 1, wherein Based on the image texture features and sequence trend features, perform principal component analysis, and input the features after principal component analysis into a preset classification model to obtain the result of identifying the real target or false target, including: Normalize the image texture features and sequence trend features, compress the image texture features and sequence trend features into the interval [0, 1], and obtain the normalized eigenvalue; Use principal component analysis to reduce the dimension of the normalized eigenvalue to obtain the reduced-dimensional data; Input each reduced-dimensional data into a preset classification model to obtain the result of identifying the real target or false target.

8. A radar interference identification system based on bispectrum phase angle, characterized in that, Including: A data acquisition module for obtaining the observation data received by the radar; A matrix calculation module for calculating the bispectrum phase angle matrix of the observation data; A feature extraction module for converting the bispectrum phase angle matrix into a gray-level co-occurrence matrix and extracting image texture features based on the gray-level co-occurrence matrix; A feature analysis module for extracting the values on the main diagonal from the bispectrum phase angle matrix to obtain a diagonal sequence, and performing spectrum analysis and sequence trend feature analysis based on the diagonal sequence; A result identification module for performing principal component analysis based on the image texture features and sequence trend features, and inputting the features after principal component analysis into a preset classification model to obtain the result of identifying the real target or false target.

9. A terminal, characterized in that, Including: A memory for storing the radar interference identification program based on the bispectrum phase angle; A processor for implementing the steps of the radar interference identification method based on the bispectrum phase angle as described in any one of claims 1 - 7 when executing the radar interference identification program based on the bispectrum phase angle.

10. A computer-readable storage medium storing a computer program, characterized in that, The readable storage medium stores a radar interference identification program based on bispectrum phase angle. When the radar interference identification program based on bispectrum phase angle is executed by a processor, the steps of the radar interference identification method based on bispectrum phase angle according to any one of claims 1-7 are implemented.

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