Radar Interference Identification Method, System, Terminal and Storage Medium Based on Bispectrum Phase Angle

Abstract

The present invention relates to the technical field of radar signal, and specifically provides a radar interference identification method, system, terminal and storage medium based on bispectrum phase angle, including: acquiring 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 the numerical values of 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; 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 a true target or a false target. The present invention improves the reliability of identifying a true target and an interference signal, and solves the problem that it is difficult to distinguish a towed interference signal by traditional methods.

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 Art

[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 towed interference signals has brought great challenges to the accurate and reliable detection of real targets by radar systems.

[0003] Currently, there are mainly three spoofing interference technologies in threat tracking radars, including range gate pull-off (RGPO), velocity gate pull-off (VGPO), and range-velocity synchronized pull-off (R-VGPO). These interference technologies can generate false target signals to deceive the radar system, making it 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 acquisition period, the towing period, and the stop-towing period. During the acquisition period, the interference signal will initially interfere with the radar system and attempt to destroy its target recognition ability. During the towing period, the continuous emission of the interference signal will further deceive 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 threat during the towing period to the radar system is particularly prominent. Traditional anti-interference technology identification methods often fail to meet actual requirements, easily lead to target misjudgment, and seriously reduce 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 spoofing 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 between false target interference and 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 prior art 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 a first aspect, the present invention provides a radar interference identification method based on bispectrum phase angle, including:

[0007] Obtain the observation data received by the radar;

[0008] Calculate the bispectrum phase angle matrix of the observation data;

[0009] 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;

[0010] 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;

[0011] 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.

[0012] Further, calculating the bispectrum phase angle matrix of the observation data includes:

[0013] Take the observation data with a length of N, divide the observation data into K segments equally, with each segment having a length of M points, and let the nth segment of data be , and calculate the estimated value of the third-order cumulant of each segment of data respectively:

[0014]

[0015] Among them, = max(0, -i, -j), = min(M - 1, M - 1 - I, M - 1 - j);

[0016] [[ID=Z39]]Statistically average the third-order cumulants obtained for each segment, and the result obtained is the third-order cumulant of this data, expressed as:

[0017]

[0018] Then the bispectrum is:

[0019]

[0020] Among them, L < M - 1, represents a two-dimensional lag window function;

[0021] 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 element is represented in polar coordinates as ;

[0022] Calculate the phase angle of the element :

[0023] ;

[0024] Calculate the phase angle of each element to obtain the bispectrum phase angle matrix , where the value range is (-π, π).

[0025] Furthermore, convert the bispectrum phase angle matrix into a gray-level co-occurrence matrix, including:

[0026] Linearly map the matrix values in the bispectrum phase angle matrix to the gray-scale image . The formula is:

[0027]

[0028] where L is the number of gray levels, and the gray level range is [0, L - 1];

[0029] According to the preset discretization rule , equally discretize the gray value range of the gray-scale image into [0, 15] to obtain a new gray-scale image with 16 gray levels after discretization ;

[0030] Set the gray-level co-occurrence matrix to describe the co-occurrence relationship between pixel gray 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:

[0031]

[0032] where (m, n) represents two gray 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, and The relationship is as follows:

[0033]

[0034] Normalize the gray-level co-occurrence matrix to obtain the normalized matrix , and the normalization formula is:

[0035]

[0036] where the normalized matrix satisfies: ;

[0037] Denote the normalized gray-level co-occurrence matrix as .

[0038] Furthermore, extract the image texture features based on the gray-level co-occurrence matrix, including:

[0039] Extract the energy feature of the gray-level co-occurrence matrix, , where E is the energy, is the normalized gray-level co-occurrence matrix;

[0040] Extract the entropy value feature of the gray-level co-occurrence matrix, , where H is the entropy value;

[0041] Extract the moment of inertia feature of the gray-level co-occurrence matrix, W, where I is the moment of inertia;

[0042] Extract the correlation feature of the gray-level co-occurrence matrix, , where C is the correlation, , ; , ;

[0043] Extract the contrast difference matrix feature of the gray-level co-occurrence matrix, , where IDM is the contrast difference matrix;

[0044] 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, extract the texture features.

[0045] Further, 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:

[0046] Let the diagonal sequence be ;

[0047] Take the diagonal sequence of length N in the diagonal sequence Perform Fourier transform to obtain the spectrum , ;

[0048] Calculate the spectrum amplitude The frequency corresponding to the maximum point: , and obtain the main frequency of the spectrum;

[0049] Calculate the standard deviation of the spectrum: , and obtain the true target spectrum standard deviation interval, where represents the spectrum mean, defined as ;

[0050] Calculate the kurtosis of the spectrum: , and obtain the true target spectrum kurtosis interval;

[0051] Calculate the skewness of the spectrum: , and obtain the true target spectrum skewness interval.

[0052] Further, the sequence trend feature analysis includes:

[0053] Based on the diagonal sequence being , calculate the difference between adjacent elements:

[0054] ;

[0055] Take the absolute value of all differences and then accumulate to calculate the cumulative sum : , and obtain the true target cumulative sum interval;

[0056] Define the Gaussian weight function, with the center of the Gaussian distribution being , the standard deviation being , and the weight at the th position being: ;

[0057] Introduce the Gaussian weight into the absolute difference cumulative sum to obtain the Gaussian weighted cumulative sum :

[0058] ;

[0059] Based on the Gaussian weighted cumulative sum, obtain the sequence trend feature.

[0060] Further, based on the image texture features and sequence trend features, principal component analysis is performed, and the features after principal component analysis are input into a preset classification model to obtain the result of identifying the true target or false target, including:

[0061] 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;

[0062] Use principal component analysis to reduce the dimension of the normalized eigenvalue to obtain the dimensionality-reduced data;

[0063] Input each dimensionality-reduced data into a preset classification model to obtain the result of identifying the true target or false target.

[0064] In a second aspect, the present invention provides a radar interference identification system based on bispectrum phase angle, including:

[0065] A data acquisition module for acquiring the observed data received by the radar;

[0066] A matrix calculation module for calculating the bispectrum phase angle matrix of the observed data;

[0067] 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;

[0068] A feature analysis module for extracting the numerical values on the main diagonal from the bispectrum phase angle matrix to obtain a diagonal sequence, and performing spectral analysis and sequence trend feature analysis based on the diagonal sequence;

[0069] 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 true target or false target.

[0070] In a third aspect, a terminal is provided, including:

[0071] A processor and a memory, wherein,

[0072] The memory is used to store a computer program,

[0073] The processor is used to call and run the computer program from the memory, so that the terminal executes the method of the above terminal.

[0074] In a fourth aspect, a computer storage medium is provided, and instructions are stored in the computer-readable storage medium. When it runs on a computer, the computer is made to execute the methods described in the above aspects.

[0075] The beneficial effects of the present invention are as follows. The radar interference identification method, system, terminal, and storage medium based on bispectrum phase angle provided by the present invention highlight the hidden non-linear relationships and subtle feature differences within radar signals through bispectrum phase angle analysis, significantly improving the reliability of real target and interference signal identification and solving the problem that traditional methods are difficult to distinguish towed interference signals. By extracting the gray-level co-occurrence matrix and texture features from the gray-scale image converted from the bispectrum phase angle, the spatial texture differences of the signals are deeply explored, further enhancing the ability to distinguish real targets from interference signals. By combining two analysis dimensions of sequence trend features and sequence frequency domain features, a more comprehensive and complementary feature system is constructed, enabling the present method to have excellent recognition effects on different types of towed interference signals and significantly enhancing the robustness and generalization performance of the algorithm. This application uses principal component analysis (PCA) to effectively reduce the dimensionality of features, reducing computational complexity. At the same time, the CatBoost classification algorithm is used to efficiently achieve accurate identification of interference signals. Through experimental verification, the recognition accuracy rate reaches more than 97%, showing a significant improvement compared with the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0077] Figure 1 It is a schematic flowchart of the method according to an embodiment of the present invention.

[0078] Figure 2 It is a schematic block diagram of the system according to an embodiment of the present invention.

[0079] Figure 3 It is a schematic structural diagram of a terminal provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0080] In order to enable those skilled in the art 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 in conjunction with the 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 of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0081] Unless otherwise defined, all technical and scientific terms used in this application have the same meaning as commonly understood by those of ordinary skill in the technical field to which this invention belongs. The terms used in the specification of this invention in this application are only for the purpose of describing specific embodiments and are not intended to limit the invention.

[0082] Radar deception jamming is a technical means of interfering with or confusing a radar system by transmitting or relaying 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 increasingly widespread, 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 gate pull-off jamming, and range-velocity synchronous pull-off jamming, among which R-VGPO jamming is mostly used in actual combat.

[0083] 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 conduct preliminary interference on the radar system, attempting 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. And 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 in this stage to improve the jamming identification ability of the radar system.

[0084] Let the radar transmitted signal be:

[0085] (1)

[0086] Where: 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; , When it is RGPO jamming; When it is VGPO jamming; When it is R-VGPO jamming.

[0087] Among them, for the detection of range gate pull-off or range-velocity synchronous jamming signals during the pull-off 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 jamming signal.

[0088] 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:

[0089] Now assume a random sequence whose third-order cumulant is absolutely summable, that is , then there exists its nth-order cumulant spectrum , and it is defined as the (n - 1)-dimensional Fourier transform of the nth-order cumulant.

[0090] (2)

[0091] When n = 3 in Equation (2), it is defined as the third-order spectrum, that is, the bispectrum, usually denoted as

[0092] (3)

[0093] where the domain is: .

[0094] 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.

[0095] 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.

[0096] 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 a radar based on the bispectrum phase angle in the embodiments.

[0097] Specifically, as Figure 1 shown, the radar interference identification method based on the bispectrum phase angle includes:

[0098] S1. Obtain the observed data received by the radar.

[0099] Specifically, after the jammer is started, 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.

[0100] S2. Calculate the bispectrum phase angle matrix of the observed data.

[0101] Take the observed data of length N, divide the observed data into K equal segments, each segment has a length of M points, and let the nth segment of data be , and calculate the estimated value of the third-order cumulant of each segment of data respectively:

[0102]

[0103] 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 the data, denoted as:

[0104]

[0105] Then the bispectrum is:

[0106]

[0107] 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 elements in the bispectrum matrix be , where , is the real part of the element , is the imaginary part of the element , and the element is represented in polar coordinates as . Calculate the phase angle of the element :

[0108] ;

[0109] Calculate the phase angle of each element to obtain the bispectrum phase angle matrix where the value range is (-π, π).

[0110] Specifically, in the actual measurement environment, for the false target interference and the real target received by the radar in the slow time dimension, after calculating the bispectrum result and extracting the result of the bispectrum phase angle matrix, there are significant differences in the phase relationship between the two types of signals in the bispectrum estimation.

[0111] The matrix formed after extracting the phase angle information of the bispectrum of the real signal has a relatively regular overall texture, 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 movement 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.

[0112] 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 appears 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 non-linear relationship resulting from the superposition of the characteristics of the false target interference signal and the sea clutter signal.

[0113] 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 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 non-linear 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 non-linear 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.

[0114] S3. Transform 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.

[0115] The matrix values in the bispectrum phase angle matrix are linearly mapped to a grayscale image by the formula:

[0116]

[0117] 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 . Set the gray-level co-occurrence matrix to describe the co-occurrence relationship between pixel gray values in the new grayscale image . For the new grayscale 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:

[0118]

[0119] where (m, n) represents two gray values, represents the relative angle between two pixels, includes four directions: 0°, 45°, 90°, and 135°, and define the displacement for calculating the gray relationship, that is, , represent the pixel offsets in the x and y axis directions respectively, and are related as follows:

[0120]

[0121] Normalize the gray-level co-occurrence matrix to obtain the normalized matrix . The normalization formula is:

[0122]

[0123] where the normalized matrix satisfies: . Denote the normalized gray-level co-occurrence matrix as .

[0124] Extract the energy feature of the gray-level co-occurrence matrix, , where E is 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 moment of inertia feature of the gray-level co-occurrence matrix, , where I is the moment of inertia. 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, moment of inertia feature, correlation feature and contrast difference matrix feature of the gray-level co-occurrence matrix, texture features are extracted.

[0125] Specifically, since there are significant differences in the texture structures of the false target interference and the real echo in the bispectrum phase angle matrix, the phase angle matrix of the real target signal usually exhibits regular and structured texture features, while the false target signal is more random and disordered. Combining this characteristic, from the perspective of image texture features, this application can effectively distinguish real signals from false signals and at the same time enhance the robustness to noise. In addition, the bispectrum phase angle matrix contains high-order statistical information of the signal, and this information is often intuitively displayed 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.

[0126] There are significant differences in the texture structures of the false target interference and the real echo in the bispectrum phase angle matrix. By analyzing the image texture features, the spatial distribution law of pixel gray values can be captured, and the deep characteristics of the signal can be intuitively revealed. In texture analysis, the gray-level co-occurrence matrix (Gray Level Cooccurrence Matrix, GLCM), as a classic method, 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 phase angle matrix of the real signal but also effectively distinguish the random texture features of the false signal.

[0127] 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:

[0128] 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 discretize the value of

[0129] (1.3)

[0130] After calculation, the matrix value can be linearly mapped to the grayscale image .

[0131] During 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 grayscale image into [0, 15], and obtain a new grayscale image with 16 gray levels after discretization . The discretization rule is:

[0132] (1.4)

[0133] The gray-level co-occurrence matrix is used to describe the co-occurrence relationship between pixel gray-level values in the grayscale image. For the discrete grayscale image , the gray-level co-occurrence matrix is defined as a matrix of size L×L , and its elements are calculated as follows:

[0134] (1.5)

[0135] 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: 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:

[0136] (1.6)

[0137] To facilitate subsequent feature extraction, the gray-level co-occurrence matrix usually needs to be normalized to a probability form. The specific normalization formula is:

[0138] (1.7)

[0139] Normalized matrix Satisfy: .

[0140] Finally, the normalized is the gray-level co-occurrence matrix, which represents the joint distribution probability of different gray-level pairs and provides a basis for subsequent texture analysis.

[0141] Statistical feature extraction

[0142] The gray-level co-occurrence matrix intuitively reflects the texture characteristics of an image by statistically analyzing the spatial relationship between pixel gray-level values. However, relying solely on the gray-level co-occurrence matrix itself is not sufficient 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 contrast difference matrix, are selected. These features deeply analyze the gray-level co-occurrence matrix from different perspectives and can provide rich information for distinguishing different image signals.

[0143] 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:

[0144] (1.8)

[0145] where is the normalized gray-level co-occurrence matrix in the above text.

[0146] Entropy: Entropy is an important indicator to describe information uncertainty or complexity. The higher the entropy value, the more random the probability distribution of two pixels with a specific spatial position relationship and their respective gray-level values in the gray-level co-occurrence matrix, and the more complex the texture; the lower the entropy value, the more certain the gray-level distribution, and the simpler or more regular the texture. The entropy value is denoted as , and the specific calculation process is as follows:

[0147] (1.9)

[0148] Inertia moment: The inertia moment reflects the degree of difference between gray-level values. The higher the value, the greater the difference in the spatial correlation between pixel gray-level values in the image, and the stronger the texture contrast; the lower the value, the smaller the gray-level difference, and the more uniform or smooth the image. The inertia moment is denoted as , and the specific calculation process is as follows:

[0149] (1.10)

[0150] 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. The correlation is denoted as , and the specific calculation process is as follows:

[0151] (1.11)

[0152] Where: , ; , .

[0153] 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:

[0154] (1.12)

[0155] 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, avoid the excessive influence of the eigenvalue in a single direction on the result, but also sensitively capture the change law between different directions.

[0156] 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.

[0157] (1)Analysis of the separability of energy features

[0158] 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.

[0159] From the perspective of the distribution of energy variance, the energy variance of the false target interference signal is relatively low and the distribution is narrow, while the energy variance of the real target signal is relatively high and the distribution range is wider. Moreover, 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 different directions, thus leading to a low energy variance and a narrower distribution range.

[0160] The histogram results reflect the significant differences in energy characteristics 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 energy means and variances in different directions have a certain degree of separability and can be used as one of the identification features of the false target interference signal.

[0161] (2)Analysis of the separability of entropy

[0162] In the distribution of entropy means, the real 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 the distribution is very concentrated. This indicates that the gray-level co-occurrence matrix of the real 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 distribution of the standard deviation of entropy, the real target signal shows a relatively uniform bell-shaped distribution, which shows that the texture of the real target signal shows an orderly change in different directions, and there are significant differences in the gray-level co-occurrence matrices in different directions. This difference causes fluctuations in the entropy values, resulting in a larger 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.

[0163] The real target signal image 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 relatively low and the distribution is wider, reflecting a relatively large change in the gray-level complexity between different image regions. Since the gray-level co-occurrence matrices in different directions of the false target interference signal are similar in distribution and lack directional features, the entropy value changes very little in different directions and the standard deviation is close to zero. In summary, the histogram results can show that the entropy means and variances in different directions have a certain degree of separability and can be used as one of the identification features of the false target interference signal.

[0164] (3)Analysis of the separability of the inertia moment feature

[0165] In the mean distribution of the moment of inertia, the true target signals are concentrated in the low-value range, mainly distributed between 0 and 10, and show a long-tailed distribution. The false target interference signals are concentrated in the high-value range and have a relatively narrow distribution. The reason is that the texture structure of the true target signals is relatively smooth and directional, the gray-level difference in the gray-level co-occurrence matrix is small, so the mean moment of inertia is low. While the gray-level distribution of the false target interference signals is random, the texture is irregular, the gray-level difference in the gray-level co-occurrence matrix is large, and the mean moment of inertia is on the high side. In the mean distribution of the moment of inertia, the true target signals are widely distributed, mainly concentrated between 0.5 and 3, showing a certain degree of discreteness. The false target interference signals are concentrated in the low-value range (close to 0 to 1), with a relatively narrow distribution, but there is a serious overlap in the distribution of some of them with the true target signals. This is because the differences in the spatial correlation between the gray-level values of the gray-level co-occurrence matrix of the false target interference signals in each direction are very similar.

[0166] 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 true target signals and the false target interference signals in this feature dimension. There is a large overlap in the standard deviation distributions of the true and false signals in the histogram of the moment of inertia standard deviation, and its individual classification ability is limited. The comprehensive histogram results show that the mean moment of inertia in different directions has a certain degree of separability and can be used as one of the identification features of the false target interference signals.

[0167] (4)Analysis of the separability of correlation features

[0168] In the mean distribution of correlation, the true 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 and have a very concentrated distribution. The reason is that the gray-level co-occurrence matrix of the true target signals has a significant texture structure, there is a strong linear correlation between different pixels, and the mean correlation in the gray-level co-occurrence matrix is high. While for the false target interference signals, due to the random gray-level distribution and almost no correlation between pixels, the mean correlation is close to zero. In the mean distribution of correlation, the changes in the correlation in the gray-level co-occurrence matrix in different directions of the true target signals and the false target interference signals are both small, both show a right-skewed distribution, and are distributed in the low-value range.

[0169] From the perspective of the separability of the feature space, since the mean correlation of the true target signals is high while the mean correlation of the false target interference signals is 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 true target signals and the false target interference signals in the correlation standard deviation, and the separability is poor. It is difficult to achieve effective classification by using this feature alone. Through the analysis of the comprehensive histogram results, the mean correlation in different directions has a certain degree of separability and can be used as one of the identification features of the false target interference signals.

[0170] (5)Analysis of the Separability of the Contrast Difference Matrix Features

[0171] In the mean distribution of the contrast difference matrix, the real target signals are mainly distributed in the range of 0.4 - 0.9, showing a right-skewed distribution with 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 real target signals. The reason is that the texture structure of real target signals is relatively smooth and regular, with a high local similarity of gray levels, resulting in a relatively high mean value of the contrast difference matrix. However, the bispectral phase angle matrix of false target interference signals shows randomness and high-frequency noise characteristics, with large local texture variations, making its mean value relatively 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 amount of overlap in the interval near the value of 0.01.

[0172] 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.

[0173] In the roughness distribution, the real target signals are mainly distributed in the higher range (9 - 11) and show a certain width of distribution. This indicates that the texture of real target signals is smooth, with slow gray level changes, 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 false target interference signals is relatively delicate, with rapid and random gray level changes, and lacks obvious large-scale texture structures.

[0174] The image texture of real target signals has a certain directionality and regularity. Since the gray level changes slowly in most areas, the calculated optimal window size is relatively large, and the overall roughness is relatively high. The image texture of false target interference signals is similar to high-frequency noise, without obvious directionality and regularity, and the gray level changes frequently and randomly. This texture characteristic of rapid change makes the image roughness of this type of signal concentrated in the lower range. This matches the histogram distribution result. Therefore, due to the regular texture and large-scale structure of real signals and the randomness and rapid gray level changes of the image of false target signals, the roughness feature can effectively distinguish real target signals from false target interference signals. The roughness value distributions of true and false target signals in the histogram hardly overlap, which more directly shows that the roughness feature has significant classification ability.

[0175] Linearity

[0176] In the linearity distribution, the true target signals are mainly distributed between 0.05 and 0.25, showing a relatively wide distribution range. This is because the images of true target signals usually have regular line-like textures, with certain directionality and linearity. In the co-occurrence matrix of directions, there is a strong cosine similarity between the gradients in different directions. While 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 textures of false target interference signals are basically non-directional and lack line structures, and the correlation between gradient directions is weak. Therefore, the linearity value is very low and the distribution range is narrow.

[0177] Generally speaking, true signals are due to the directionality and line structures of the textures; while false signals are due to the characteristics of random noise. The feature of linearity has a strong quantification ability for such differences. Therefore, linearity can effectively distinguish true target signals from false target interference signals.

[0178] 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.

[0179] Let the diagonal sequence be . Take the diagonal sequence with length N in the diagonal sequence and perform Fourier transform to obtain the spectrum , . Calculate the amplitude of the spectrum The frequency corresponding to the maximum point: , to obtain the main frequency of the spectrum. Calculate the standard deviation of the spectrum: , to obtain the standard deviation interval of the true target spectrum, where represents the spectrum mean, defined as . Calculate the kurtosis of the spectrum: , to obtain the kurtosis interval of the true target spectrum. Calculate the skewness of the spectrum: , to obtain the skewness interval of the true target spectrum.

[0180] Based on the diagonal sequence being , calculate the difference between adjacent elements:

[0181] . Take the absolute value of all differences and then accumulate them to calculate the cumulative sum : , to obtain the cumulative sum interval of the true target. Define the Gaussian weight function, with the center of the Gaussian distribution being , the standard deviation being , and the weight at the th position being: . Introduce the Gaussian weight into the absolute difference cumulative sum to obtain the Gaussian weighted cumulative sum :

[0182] Based on the Gaussian weighted cumulative sum, the sequence trend feature is obtained.

[0183] 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 representation of the important texture information in the original image, and can reflect the global structural features and local change trends of the image.

[0184] The overall change trend of the diagonal sequence of the real target signal is relatively gentle. 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 features. 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 frequency domain, are extracted, and the separability of the features for real and false target signals is verified.

[0185] Verification of the sequence frequency domain features

[0186] (1) Verification of the main frequency index of the spectrum

[0187] In the distribution of the main frequency of the frequency domain, most of the main frequency values of the real target sequence are concentrated in the lower (close to 0 Hz) frequency region, and the distribution range is relatively narrow, indicating that the main frequency component of the real target signal is stable and the low frequency is dominant. The main frequency values of the false target interference sequence are distributed in a wider frequency range. Compared with the real target, the main frequency values of the false target interference sequence are not concentrated, and the spectrum distribution is relatively dispersed.

[0188] 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 spectrum 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, the frequency components are complex, its spectrum energy distribution is relatively dispersed, and there are more high-frequency components, so that the main frequency is distributed in a wider frequency range. The degree of fluctuation in the sequence enables the main frequency feature of the sequence frequency domain to effectively distinguish the real target signal and the false target interference signal. Therefore, the main frequency feature is an important index for distinguishing the two types of signals, with strong separability and classification ability.

[0189] (2) Verification of the spectrum standard deviation

[0190] In the frequency-domain standard deviation distribution, the sequence standard deviation values of real targets have a relatively wide distribution range, mainly concentrated between 14 and 18, indicating that the spectral amplitude changes of real target signals have a certain degree of volatility but are overall relatively stable. The sequence standard deviation values of false target interference signals have a relatively narrow distribution range, indicating that the amplitude changes of the false target signal spectrum are relatively small and the spectral distribution is more concentrated.

[0191] 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 exhibits 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. As can be seen from the histogram, 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 algorithm's ability to identify false target interference.

[0192] (3)Spectrum kurtosis verification

[0193] In the frequency-domain kurtosis distribution, the sequence kurtosis values of real targets have a relatively wide distribution range, concentrated between 20 and 45, indicating that the spectra of real target signals have high sharpness and concentration. The sequence kurtosis values of false target interference are mainly concentrated between 0 and 10, with a relatively narrow distribution range. This indicates that the spectral distribution of false target signals is flatter and lacks sharp energy concentration points.

[0194] The sequence of real target signals has a smooth low-frequency change trend. Such a signal shows energy concentration in a few low-frequency bands in the frequency domain, forming relatively high peaks. The peak characteristics of the spectrum result in higher kurtosis values and a more concentrated distribution. The sequence of false target signals is more like random high-frequency oscillations, and the spectral energy is distributed over a wide range of frequencies. Due to the lack of obvious energy concentration points, the spectral kurtosis is low, showing a flat spectral distribution. The spectral kurtosis feature can clearly reflect the concentration and sharpness of 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.

[0195] (4)Spectrum skewness verification

[0196] In the frequency-domain skewness distribution, the sequence skewness values of real targets have a relatively wide distribution range, indicating that the spectral amplitude distribution of real target signals has strong positive skewness (spectral energy is concentrated in the low-frequency region). The sequence skewness values of false target interference have a relatively narrow distribution, with low skewness values and no significant high-value regions, indicating that the spectral distribution of false target signals is relatively symmetric and there is no obvious energy concentration trend.

[0197] The sequence of true target signals exhibits a smooth variation trend, with spectral energy primarily concentrated in low-frequency bands and relatively weak high-frequency components. This concentration of spectral energy in low frequencies results in a positively skewed spectral distribution and a high skewness value. The sequence of false target interference signals exhibits high-frequency random fluctuations, with spectral energy evenly distributed across all frequency bands. The symmetry of the spectral distribution results in a low skewness value. The spectral kurtosis feature clearly reflects the symmetry of spectral energy in true and false target sequences. This property has strong discriminatory power and can be used as a classification feature for identifying false target interference.

[0198] The sequence of the real target presents a smooth trend change as a whole, usually containing slow transitions or obvious directional changes. Although there are local mutation points, the overall trend is relatively stable and the direction of change is relatively small. The sequence of false target interference presents drastic changes and no direction. The trend is manifested as a noise-type signal with strong randomness and no obvious smooth trend. For this difference in trend, the difference between the real target signal and 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 true and false target signals.

[0199] Sequence trend feature analysis

[0200] (1) Cumulative sum of absolute differences

[0201] In the distribution of the cumulative sum of absolute differences (CSADs), the CSADs of the true target sequence are primarily concentrated in the range of 20 to 200, with a significant peak near 40. The overall distribution is relatively concentrated, indicating that the true target signal sequence changes smoothly and the difference fluctuations are small. This is because the grayscale values of the true target signal sequence change slowly and smoothly, with small differences between adjacent grayscale values. In contrast, the CSADs of the false target interference sequence have a narrow distribution range and high differences, mainly concentrated in the range of 250 to 320, reflecting the frequent high-frequency fluctuations and dramatic changes in the false target signal sequence. This is because the diagonal sequence of the false target signal exhibits significant high-frequency random fluctuations, resulting in large differences between adjacent grayscale values. This frequent change results in high CSADs and their concentration in a larger interval.

[0202] The Cumulative Sum of Absolute Differences (CSADs) feature shows almost no overlap between true target signals and false target jammers, with completely separate distribution intervals. The CSAD feature effectively reflects the smoothness and volatility of a sequence. True target signals have low CSADs due to their gradual variations, while false target jammers have high CSADs due to their random and drastic variations. This demonstrates the strong separability of the CSAD feature, making it an important basis for distinguishing true target signals from false target jammers.

[0203] (2) Gaussian weighted cumulative sum of absolute differences

[0204] The weighted absolute difference cumulative sum distribution is similar to the absolute difference cumulative sum distribution. The distribution of the true target signal has a smaller tail and higher concentration. However, the formation reasons of the two feature histograms are different. The Gaussian weighted absolute difference cumulative sum assigns a larger weight to the central region of the sequence, which can more prominently show the fluctuation characteristics of the key region (center) in the sequence and is insensitive to the fluctuations in the edge part. While the absolute difference cumulative sum focuses on the overall gray-scale change amplitude of the sequence and 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). By jointly using the two features, the global and local features of the sequence can be comprehensively analyzed, and the robustness and accuracy of classification can be improved.

[0205] Therefore, the Gaussian weighted absolute difference cumulative sum feature can effectively distinguish the true target signal from the false target interference signal, and its joint use with the absolute difference cumulative sum feature can play a greater role in the classification task. The absolute difference cumulative sum 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.

[0206] In the process of extracting the Gaussian weighted absolute difference cumulative sum, it is necessary to first construct a Gaussian weighted function. Since there is a hyperparameter of the 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 selecting an appropriate standard deviation can the weights of the global trend and local changes be balanced, thereby improving the discrimination ability of the feature and ensuring that the feature performs optimally when distinguishing the true target signal from the false target interference signal.

[0207] This application selects two optimization methods, the Mahalanobis distance method and the Fisher discriminant coefficient method, to select the best standard deviation. The Mahalanobis distance method can judge the separation effect of the Gaussian weighted cumulative sum feature between the true target signal and the false target signal by measuring the projection of the mean difference between two groups of data in the covariance matrix. The Fisher discriminant coefficient method can evaluate the discrimination ability of the feature 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 best standard deviation by combining the results of the two types of optimization methods. The specific optimization process is as follows:

[0208] Mahalanobis distance calculation formula: Let the Gaussian weighted absolute difference cumulative sum features of two types of sequences be and , the mean vectors be and , and the covariance matrix be .

[0209] (1.31)

[0210] Fisher discriminant coefficient method: Let the cumulative sum of Gaussian weighted absolute differences of two types of sequences be and , the mean vectors be and , and the variances be and .

[0211] (1.32)

[0212] The experimental results of using two optimization methods, the Mahalanobis distance method and the Fisher discriminant coefficient method, to select the best standard deviation. The experimental data shows 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 groups 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 it can better distinguish the two groups of data. Considering the experimental results comprehensively, this application selects a standard deviation value of 18.

[0213] 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 real target or false target.

[0214] 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 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.

[0215] Specifically, to verify the effectiveness and practicality of the algorithm of this 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 this 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 set on the sea vessel 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.

[0216] According to the above content, a total of 16 available features are summarized into four categories. Although the calculation methods of each feature 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 a high-dimensional feature space, the distribution of data may become sparse, making it difficult for classification algorithms to work effectively. However, projecting high-dimensional features into a low-dimensional space can reduce the influence of irrelevant or weakly relevant features while retaining the main information of the data. Since the true and false target identification task is realistic, it is also necessary to consider the increase in the complexity of the classification model caused by high-dimensional features, which may lead to overfitting problems. For the above reasons, this 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, and reduce the dimension, so as to improve the classification efficiency and the generalization ability of the model.

[0217] To further illustrate the necessity of reducing the dimension of feature data, this application uses a random forest as the benchmark classification model to analyze the importance of 16 original features in the actual classification task. Through the comprehensive analysis of the correlation between each feature before PCA dimensionality reduction and the importance results of each feature 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, PCA is needed to screen the main feature directions, ignore the directions corresponding to low-importance features, and reduce the interference of irrelevant or weakly relevant features on the model.

[0218] Selection of the Optimal Dimension of PCA

[0219] 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, and 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:

[0220] First, normalize the data, compress the feature values into the interval [0, 1], and improve the efficiency of PCA and the classification model. Then perform PCA dimensionality reduction to extract different numbers of principal components (from 1 to the maximum number of features 16) in turn, generating a data matrix after dimensionality reduction. After each reduction of the data dimension, the new low-dimensional data is passed to the classifier. This application uses 10-fold cross-validation during cross-validation. In each fold of cross-validation, 70% of the data is used to train the classifier (still using the random forest as the benchmark 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, find the dimension number with the highest classification accuracy and the corresponding classification accuracy.

[0221] During the process of increasing the number of principal components from 1 to 6, the classification accuracy rate increased rapidly; after exceeding 6 principal components, the accuracy rate tended to be stable, indicating that redundant features had little impact on the classification results. When the number of principal components was 6, the classification accuracy rate reached the highest value of 0.99786, indicating that the feature information retained after dimensionality reduction at this time could effectively describe the samples and avoid the interference of redundant features. Therefore, selecting 6 principal components after PCA dimensionality reduction could maintain a classification accuracy rate close to 100%, and the stable trend of the classification accuracy rate in the figure also verified the effectiveness of PCA and the rationality of selecting dimensions through cross-validation.

[0222] Analysis of PCA Dimensionality Reduction Results

[0223] By adjusting the parameter of the feature dimension after PCA with the best PCA dimension determined in the above text, the original feature dataset was reprocessed by PCA dimensionality reduction, and the independence and variance contribution rate of each component after dimensionality reduction were analyzed.

[0224] In the PCA feature correlation matrix after selecting the best 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 indicates that selecting 6 principal components can well balance the data fidelity and computational complexity after dimensionality reduction.

[0225] 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 been processed by 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 well in processing 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:

[0226] According to the confusion matrix results of the test set of the CatBoost model, 5 samples in each of the two categories were 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 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.

[0227] Table 1 shows the classification report of the trained CatBoost model. It can be seen from the table 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 reaches 0.9732, indicating that the overall performance of the model is relatively excellent.

[0228] Table 1

[0229]

[0230] It can be seen that the macro-average in the table represents the average of the precision, recall rate, and comprehensive score for each category; the weighted average is based on the macro-average and uses weighted averaging according to the number of samples in each category. Both the macro-average and weighted average indicators 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.

[0231] 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 a 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).

[0232] 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, such as Figure 2As shown in the figure. The functional modules of the 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 modules referred to in the present invention refer 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 a memory. In this embodiment, the functions of each module will be described in detail in subsequent embodiments.

[0233] The data acquisition module is used to acquire the observation data received by the radar;

[0234] The matrix calculation module is used to calculate the bispectrum phase angle matrix of the observation data;

[0235] The feature extraction module is used to 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;

[0236] The feature analysis module is used to extract the numerical 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;

[0237] The result identification module is used to perform principal component analysis based on the image texture features and sequence trend features, input the features after principal component analysis into a preset classification model, and obtain the result of identifying the true target or false target.

[0238] Figure 3 It is a schematic structural diagram of a terminal 300 provided by an embodiment of the present invention. 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.

[0239] 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 to 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 certain components, or different component arrangements.

[0240] 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 solutions 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. This 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., various media that can store program codes, including several instructions for causing 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 the various embodiments of the present invention.

[0241] 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 for the relevant parts, reference can be made to the descriptions in the method embodiments.

[0242] In the 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 only 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 couplings or direct couplings or communication connections to each other can be through some interfaces. The indirect couplings or communication connections of the systems or modules can be in electrical, mechanical or other forms.

[0243] The modules described as separate components may or may not be physically separated. The components displayed as modules may or may not be physical modules, that is, they can be located in one place or distributed to 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.

[0244] In addition, in each embodiment of the present invention, the various functional modules 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.

[0245] Although the present invention has been described in detail by reference to the accompanying drawings and in conjunction 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 within 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 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; Calculating the bispectrum phase angle matrix of the observation data includes: Take the observed data of length N, divide the observed data into K equal segments, with each segment having a data length of M points. Let the nth segment of data be , and calculate the estimated values of the third-order cumulants for 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 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 ; Calculation element of the phase angle : ； Calculate the phase angle of each element , and obtain the bispectrum phase angle matrix , where the value range is (-π, π); 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 rule , the gray value range of the gray-scale image is evenly discretized into [0, 15] to obtain a new gray-scale image with 16 gray levels after discretization ; Set the gray-level co-occurrence matrix , which is used to describe the new grayscale image The co-occurrence relationship between the pixel gray-level values in the new grayscale image , define the gray-level co-occurrence matrix as of size L×L. The elements in the gray-level co-occurrence matrix are calculated as follows: where (m, n) represent 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, and represent the pixel offsets in the x and y axis directions respectively, The relationship between is as follows: Normalize the gray-level co-occurrence matrix to obtain the normalized matrix , and the normalization formula is: Among them, the normalized matrix satisfies: ; Denote the normalized gray-level co-occurrence matrix as ; 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 ; 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: , to obtain the true target spectral skewness interval; 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 sum of absolute differences to obtain the Gaussian weighted sum : ； Based on the Gaussian weighted cumulative sum, obtain the sequence trend feature.

2. The method according to claim 1, characterized in that, 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 gray-level co-occurrence matrix after normalization; 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.

3. The method according to claim 1, characterized in that 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, including: Normalize the image texture features and sequence trend features, compress the image texture features and sequence trend features into the [0, 1] interval to obtain 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 true target or false target.

4. 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 spectral 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 true target or false target; ​ Take the observed data with length N, divide the observed data into K equal segments, each segment has a 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); ​ ​ 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 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 ; 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); ​ Map the matrix values in the bispectrum phase angle matrix linearly to a grayscale image with the formula: ​ According to the preset discretization rule , 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 new gray-scale image The co-occurrence relationship between the pixel gray-level values in it. For the new gray-scale image , define the gray-level co-occurrence matrix as of size L×L. The elements in the gray-level co-occurrence matrix are calculated as follows: where (m, n) represent two gray values, represents the relative angle between two pixels, including four directions: 0°, 45°, 90°, and 135°, and defines the displacement for calculating the gray relationship, that is, and represent the pixel offsets in the x and y axis directions respectively, The relationship between is as follows: Normalize the gray-level co-occurrence matrix to obtain the normalized matrix , and the normalization formula is: Among them, the normalized matrix satisfies: ; Let the normalized gray-level co-occurrence matrix be denoted as ; 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 ; 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: to obtain the true target spectral kurtosis interval; Calculate the spectral skewness: , and obtain the true target spectral skewness interval; 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 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 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.

5. A terminal, characterized in that, Including: A memory for storing a 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 1-3 when executing the radar interference identification program based on the bispectrum phase angle.

6. A computer-readable storage medium storing a computer program, characterized in that, A radar interference identification program based on the bispectrum phase angle is stored on the readable storage medium, and when the radar interference identification program based on the bispectrum phase angle is executed by the processor, the steps of the radar interference identification method based on the bispectrum phase angle as described in any one of claims 1-3 are implemented.

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