Frequency agility radar signal sorting and individual clustering method combining inter-pulse and intra-pulse characteristics

Abstract

The invention discloses a frequency agility radar signal sorting and individual clustering method combining inter-pulse and intra-pulse characteristics. The method comprises the following steps: screening an original pulse stream to obtain a screened pulse stream; performing frequency domain filtering on the intermediate frequency data corresponding to each pulse after screening to obtain corresponding intermediate frequency filtering data, and performing down-conversion on the intermediate frequency filtering data of all the pulses after screening to the same frequency to obtain preprocessed intermediate frequency data of each pulse after screening; sorting all pulses corresponding to the preprocessed intermediate frequency data based on the pulse description word of each type of radar to obtain a cluster of the corresponding type of radar; based on an intra-pulse fingerprint feature extraction mode, extracting a fingerprint feature vector corresponding to each cluster after sorting; and clustering the fingerprint feature vectors based on an FCM clustering algorithm of a joint parameter optimization K value to obtain an individual clustering result of the radar of the corresponding model. According to the invention, more accurate radar individual clustering can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to a frequency agile radar signal sorting and individual clustering method combining inter-pulse and intra-pulse features. Background Art

[0002] Radar signal analysis and processing is a key task in modern radio technology, of which signal sorting and individual clustering are important components. With the continuous advancement and diversification of radar technology, even the subtle differences between radar devices of the same model are becoming increasingly difficult to distinguish. Furthermore, the current electromagnetic environment is becoming increasingly complex. Traditional sorting methods based on traditional features such as pulse description words (PDWs) can effectively distinguish different types of radars, but they have difficulty effectively classifying different radars of the same model and batch produced on the same production line. Traditional radar signal sorting algorithms based on inter-pulse features have difficulty effectively mining the fingerprint differences between different individuals. Therefore, how to reasonably combine inter-pulse and intra-pulse fingerprint features to achieve radar signal sorting and individual clustering is the focus and difficulty of current research.

[0003] With the continuous development of radar systems, radar signal sorting and clustering methods have also been updated and can now be divided into three main categories. The first and most commonly used method is radar signal sorting based on PDW. PDW includes the main inter-pulse characteristics of radar signals. In the signal sorting process, the most important radar signal inter-pulse characteristic is the pulse repetition interval (PRI). In a relatively simple electromagnetic environment with a small number of radars, the PRI of multiple radar emitters is relatively stable, and this characteristic is an important basis for radar signal sorting. Classic PRI-based radar sorting algorithms include the histogram method, the Cumulative Difference Histogram Function (CDIF) method, the Sequential Difference Histogram Function (SDIF) method, and the PRI transform method. However, these methods suffer from difficulties in effectively sorting radars of the same model with similar inter-pulse parameters and inability to cluster individuals. A second type of method involves radar signal sorting based on intra-pulse modulation (IPM) information. With the advancement of radar technology, IPM patterns have become increasingly complex and diverse. Researchers have found that relying solely on PDW parameters is insufficient to adapt to the current electromagnetic spectrum environment. Consequently, sorting algorithms based on IPM features have emerged. IPM features primarily reflect the effects of different modulation parameters on radar signal frequency, phase, and amplitude. Typical IPM feature extraction methods include time-frequency analysis, time-domain autocorrelation, spectral analysis, and phase difference analysis. However, these methods are only applicable to radar signals with significant differences in IPM features and are unable to effectively sort and cluster different radars of the same model. Consequently, these methods have numerous limitations.

[0004] However, the existing radar signal sorting algorithm cannot effectively sort radars of the same model, cannot complete the task of clustering individual radars of the same model, and lacks a hierarchical progressive process from radar model classification to individual clustering, so it lacks practicality and rationality. Summary of the Invention

[0005] To address the above-mentioned problems in the prior art, the present invention provides a method for frequency-agile radar signal sorting and individual clustering that combines inter-pulse and intra-pulse features. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] An embodiment of the present invention provides a method for frequency agile radar signal sorting and individual clustering that combines inter-pulse and intra-pulse features. The method includes:

[0007] Screening the original pulse stream to obtain a screened pulse stream;

[0008] Perform frequency domain filtering on the intermediate frequency data corresponding to each pulse after screening to obtain corresponding intermediate frequency filtered data, and down-convert the intermediate frequency filtered data of all pulses after screening to the same frequency to obtain pre-processed intermediate frequency data of each pulse after screening;

[0009] Sorting all pulses corresponding to the pre-processed intermediate frequency data based on the pulse description word to obtain clusters of corresponding radar models;

[0010] Based on the intra-pulse fingerprint feature extraction method, the fingerprint feature vector corresponding to each cluster after sorting is extracted;

[0011] The fingerprint feature vectors are clustered based on the FCM clustering algorithm with joint parameter optimization K value to obtain individual clustering results of the corresponding radar model.

[0012] In one embodiment of the present invention, filtering the original pulse stream to obtain a filtered pulse stream includes:

[0013] According to the pulse width of the original pulse stream, pulses outside a specified pulse width range are removed from the original pulse stream to obtain a first screening result;

[0014] According to the carrier frequency of the original pulse stream, pulses outside a specified carrier frequency range are removed from the first screening result to obtain a second screening result;

[0015] The TOA values corresponding to the second screening results are sorted in ascending order to obtain a pulse sorting structure, and the pulse sorting result is used as the screened pulse stream.

[0016] In one embodiment of the present invention, frequency domain filtering is performed on the intermediate frequency data corresponding to each pulse after screening to obtain corresponding intermediate frequency filtered data, including:

[0017] Performing a fast Fourier transform on the intermediate frequency data corresponding to each pulse after screening, and calculating the peak frequency corresponding to each pulse after screening based on the intermediate frequency data after the fast Fourier transform;

[0018] The corresponding filtering range is calculated according to the peak frequency, and the corresponding intermediate frequency data is filtered according to the filtering range to obtain the intermediate frequency filtered data corresponding to each pulse after screening.

[0019] In one embodiment of the present invention, down-converting the filtered intermediate frequency data of all pulses to the same frequency to obtain pre-processed intermediate frequency data of each pulse after screening includes:

[0020] According to the peak frequency, the intermediate frequency filtered data of all the pulses after screening are down-converted to the same frequency to obtain the pre-processed intermediate frequency data of each pulse after screening.

[0021] In one embodiment of the present invention, the pre-processed intermediate frequency data of a certain pulse after screening is expressed as follows:

[0022]

[0023] Among them, S(t) represents the pre-processed intermediate frequency data of a pulse at time t, j represents the imaginary unit, and F max It represents the peak frequency of a pulse, and F0 represents the same frequency after down-conversion.

[0024] In one embodiment of the present invention, the pulse description word includes pulse width, carrier frequency, TOA value, and DOA value; sorting all pulses corresponding to the preprocessed intermediate frequency data based on the pulse description word to obtain clusters of corresponding radar models includes:

[0025] Using the DBSCAN algorithm, all pulses are pre-sorted based on the pulse width, the carrier frequency, and the DOA value to obtain corresponding pre-sorting results;

[0026] The PRI transformation method is used to perform main sorting on the pre-classification results to obtain corresponding main sorting results, and the main sorting results are used as clusters of corresponding radar models.

[0027] In one embodiment of the present invention, based on the intra-pulse fingerprint feature extraction method, the fingerprint feature vector corresponding to each cluster after sorting is extracted, including:

[0028] The empirical mode decomposition method is used to decompose the intermediate frequency data corresponding to each cluster after sorting into intrinsic mode components and residual components;

[0029] Using the Hilbert-Huang transform method, each intrinsic mode component is transformed into a time-frequency matrix, and all the time-frequency transform results are summed to obtain the HHT time domain matrix of the intermediate frequency signal;

[0030] Calculating the time-frequency energy entropy and marginal spectrum of the corresponding intermediate frequency signal according to the HHT time domain matrix;

[0031] Calculating the marginal spectrum distribution center of the corresponding intermediate frequency signal according to the marginal spectrum and the HHT time domain matrix;

[0032] Calculating marginal spectrum entropy, marginal spectrum kurtosis, and skewness of the corresponding intermediate frequency signal according to the marginal spectrum;

[0033] The marginal spectral entropy, the time-frequency energy entropy, the marginal spectral distribution center of gravity, the marginal spectral kurtosis, and the skewness constitute a corresponding fingerprint feature vector.

[0034] In one embodiment of the present invention, the fingerprint feature vectors are clustered based on the FCM clustering algorithm with joint parameter optimization K value to obtain individual clustering results of the corresponding radar model, including:

[0035] Using the FCM clustering algorithm, clustering the fingerprint feature vector based on the specified number of clusters to obtain a pre-clustering result of the corresponding radar model;

[0036] Calculating clustering performance indicators corresponding to the pre-clustering results; the clustering performance indicators include the sum of squared errors, silhouette coefficient, Calinski-Harabasz index, and Davies-Bouldin index;

[0037] Constructing a cluster evaluation function according to the sum of squared errors, the silhouette coefficient, the Calinski-Harabasz index, and the Davies-Bouldin index;

[0038] According to the clustering evaluation function, the clustering evaluation values of the corresponding clustering results under different clustering cluster numbers are calculated within the preset clustering cluster number optimization range, the clustering cluster number corresponding to the largest clustering evaluation value is selected as the optimal cluster, and the clustering result corresponding to the optimal cluster number is used as the individual clustering result of the corresponding radar model.

[0039] In one embodiment of the present invention, the cluster evaluation function is constructed, and the formula is expressed as follows:

[0040]

[0041] Among them, L(k) represents the clustering evaluation function, K min Indicates the minimum value of the preset cluster number optimization range, K max Indicates the maximum value of the preset cluster number optimization range, SSE k Indicates the sum of squared errors corresponding to the cluster k, SSE k ″ indicates SSE k Find the second-order difference, SC k Indicates the silhouette coefficient corresponding to the cluster k, CH k Indicates the Calinski-Harabasz index corresponding to the cluster k, DB k It represents the Davies-Bouldin index corresponding to the number of clusters k, max represents the maximum value, and λ1, λ2, λ3 and λ4 represent proportional coefficients.

[0042] Beneficial effects of the present invention:

[0043] The proposed frequency-agile radar signal sorting and clustering method, which combines both inter-pulse and intra-pulse features, addresses the existing problem of inability to effectively cluster radars of the same model. Before clustering, the original pulse stream is filtered to improve clustering efficiency. To eliminate the influence of different frequencies on the signal fingerprint, all filtered intermediate frequency signals are down-converted to the same frequency. The first clustering is then performed based on the pulse descriptor of each radar model, and the second clustering is performed based on the intra-pulse fingerprint. This radar clustering approach, which considers both inter-pulse and intra-pulse features, effectively sorts and clusters radars of different models, as well as radars of the same model. Furthermore, a radar clustering method using FCM based on joint parameter optimization of the K value is proposed, which effectively avoids the irrationality of manually setting parameters, thereby improving the performance and effectiveness of radar clustering. Overall, the present invention achieves more accurate radar clustering and a hierarchical, progressive process from radar signal sorting to clustering of same-model radars, making the clustering process design more practical and rational.

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 1 is a flow chart of a method for frequency agile radar signal sorting and individual clustering that combines inter-pulse and intra-pulse features, provided by an embodiment of the present invention;

[0046] Figure 2 1 is a schematic diagram of the process of extracting the intra-pulse fingerprint feature vector provided by an embodiment of the present invention;

[0047] Figure 3 1 is a flow chart of an FCM clustering method based on joint parameter optimization K value provided by an embodiment of the present invention;

[0048] Figure 4 (a)~ Figure 4 (d) is a diagram showing the simulation results of radar model sorting according to an embodiment of the present invention;

[0049] Figure 5 (a)~ Figure 5 (b) A distribution diagram of the extracted pulse intermediate frequency fingerprint features provided by an embodiment of the present invention;

[0050] Figure 6 (a)~ Figure 6 (b) is a schematic diagram of clustering performance curves of different radar models at the optimal K value obtained by the FCM clustering algorithm based on joint parameter optimization K value provided by an embodiment of the present invention;

[0051] Figure 7 (a)~ Figure 7 (b) is a schematic diagram of the individual clustering results of radars of the same model provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0053] See Figure 1 The embodiment of the present invention provides a method for frequency agile radar signal sorting and individual clustering based on inter-pulse and intra-pulse features, which specifically includes the following steps:

[0054] S10, screening the original pulse stream to obtain a screened pulse stream.

[0055] In an embodiment of the present invention, pulse signals transmitted by several radar models form an original pulse stream. Each pulse in the original pulse stream primarily includes four pulse descriptors: carrier frequency (RF), pulse width (PW), pulse arrival angle (DOA), and pulse arrival time (TOA). In a screening process, the embodiment of the present invention primarily uses three pulse descriptors: RF, PW, and TOA. Specifically, the original pulse stream is screened to obtain a filtered pulse stream, including: removing pulses outside a specified pulse width range from the original pulse stream based on the pulse width PW of the original pulse stream to obtain a first screening result; removing pulses outside a specified carrier frequency range from the first screening result based on the carrier frequency RF of the original pulse stream to obtain a second screening result; and sorting the TOA values corresponding to the second screening result in ascending order to obtain a pulse sorting structure, with the pulse sorting result serving as the filtered pulse stream.

[0056] S20, performing frequency domain filtering on the intermediate frequency data corresponding to each pulse after screening to obtain corresponding intermediate frequency filtered data, down-converting the intermediate frequency filtered data of all pulses after screening to the same frequency to obtain pre-processed intermediate frequency data of each pulse after screening.

[0057] In order to facilitate the extraction of the intra-pulse fingerprint feature, the intermediate frequency data corresponding to the filtered pulse stream is subjected to frequency domain filtering to eliminate the influence of the stray frequency points on the signal fingerprint feature, and the corresponding intermediate frequency filtered data is obtained. In the embodiment of the present invention, the intermediate frequency data corresponding to each pulse after filtering is subjected to frequency domain filtering to obtain the corresponding intermediate frequency filtered data, including: performing a fast Fourier transform (FFT) on the intermediate frequency data corresponding to each pulse after filtering, and calculating the peak frequency corresponding to each pulse after filtering based on the intermediate frequency data after the fast Fourier transform, which is recorded as F max ; Calculate the corresponding filtering range according to the peak frequency, recorded as [Fmax -f,F max +f], f is the bandpass frequency, usually 1MHz, and the corresponding intermediate frequency data is bandpass filtered according to the filtering range to obtain the intermediate frequency filtered data corresponding to each pulse after screening.

[0058] In order to eliminate the influence of different frequencies of the signal on the signal fingerprint characteristics, the embodiment of the present invention pre-converts the intermediate frequency filtered data of all the pulses after screening to the same frequency, more specifically according to the peak frequency F max , down-convert the intermediate frequency filtered data of all the pulses after screening to the same frequency, and obtain the pre-processed intermediate frequency data of each pulse after screening. The formula is expressed as:

[0059]

[0060] Among them, S(t) represents the pre-processed intermediate frequency data of a pulse at time t, j represents the imaginary unit, and F max It represents the peak frequency of a pulse, and F0 represents the same frequency after down-conversion.

[0061] S30. Sorting all pulses corresponding to the pre-processed intermediate frequency data based on the pulse description word to obtain clusters of corresponding radar models.

[0062] Considering that the signal density in the actual electromagnetic environment is often high, the sorting algorithm using a single pulse descriptor will cause large errors and mistakes. Therefore, the embodiment of the present invention proposes to adopt a pre-sorting + main sorting sorting strategy to complete the radar model classification.

[0063] For pre-sorting, the embodiment of the present invention uses pulse descriptors RF, PW, and DOA to perform cluster sorting to dilute the pulse flow density. More specifically, the embodiment of the present invention uses the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm to pre-sort all pulses corresponding to the pre-processed intermediate frequency data based on the pulse width PW, carrier frequency RF, and DOA value of each radar model to obtain the corresponding pre-sorting results; for example, the pulse flow after screening is recorded as D = {x1,...,x i ,...,x N}, N represents the number of pulses in the pulse stream after screening of each radar model, x i represents the pulse description word set corresponding to the i-th pulse, x i =[RF i ,PW i ,DOA i ], assuming that the neighborhood radius is Eps and the density threshold is MinPts; then: first randomly select a pulse corresponding to x from Di , and get all the values from x according to Eps and MinPts i About the points that can be reached by Eps and MinPts density; if x i Is a core point, then a new cluster is formed and all points in the cluster are labeled. If x i If it is a boundary point, the next pulse is randomly selected from D; the above steps are repeated until all pulses in D are processed. After the pre-sorting process is completed, the radar signal pre-sorting result Cluster={c1,c2,...,c n}, n represents the number of clusters after pre-sorting.

[0064] Furthermore, after the pre-sorting is completed, the pre-sorting results are further corrected using the main sorting algorithm. The embodiment of the present invention adopts the PRI-based main sorting algorithm for main sorting. Specifically, the PRI transformation method is used to perform main sorting on the pre-classification results to obtain the corresponding main sorting results, and the main sorting results are used as clusters of the corresponding radar models. More specifically:

[0065] The PRI-based primary sorting algorithm mainly includes PRI parameter estimation and corresponding sequence retrieval. When the PRI transformation method is used to realize the radar signal primary sorting function, let TOA = {t0, t1, t2, ..., t N}, simplifying each pulse after screening into an impulse function, the received pulse train can be expressed as:

[0066]

[0067] Among them, t i is the arrival time of the ith pulse. Autocorrelation processing of g(t) yields the following expression:

[0068]

[0069] Here, C(τ) represents the autocorrelation value, and τ represents the delay amount.

[0070] By adding the phase factor exp(j2πt / τ) to the autocorrelation function, the PRI transformation formula is simplified as follows:

[0071]

[0072] Where D(τ) represents the PRI transform spectrum, and a peak appears at the true PRI of the signal. Substituting formula (2) into formula (4) yields:

[0073]

[0074] The PRI transformation spectrum obtained by formula (5) is converted into a PRI spectrum in the PRI range [τ min ,τmax ] is divided into K1 equal parts to obtain PRI boxes, then the center and width of the kth PRI box are:

[0075]

[0076] in, represents the center of the kth PRI bin, τ max Indicates the upper limit of the PRI range, τ min Indicates the lower limit of the PRI range. Finally, the discretized PRI transformation formula can be expressed as:

[0077]

[0078] in, The PRI transform spectrum of the kth PRI box is shown in Figure 2. A pulse sequence with the same PRI parameters is used to generate a spectrum peak at the peak. The detection threshold is set. When the spectrum peak is greater than the detection threshold, it means that the PRI is the true value. The expression of the detection threshold is:

[0079]

[0080] in, The detection threshold value of the k1th PRI box, α, β, γ are all adjustable parameters, 0<α<1, 0<β<1, γ≥3, ρ represents the pulse flow density, represents the number of pulses in the k1th PRI box, T represents the observation period, represents the width of the k1th PRI box, and max represents the maximum value operation.

[0081] The embodiment of the present invention uses the above PRI transformation method to pre-sort the sorting result Cluster={c1,c2,...,c n} to calculate the potential PRI value of the sequence, and use the sequence detection method to extract the pulses that meet the conditions, and finally get the main sorting result Radar={r1,...,r i ,...,r n}, and the corresponding intermediate frequency signal set Sig={S1,...,S i ,...,S n}, where r i is the pulse main sorting result of the i-th radar model, S i For r i The corresponding intermediate frequency signal set.

[0082] S40. Based on the intra-pulse fingerprint feature extraction method, extract the fingerprint feature vector corresponding to each cluster after sorting.

[0083] After the main sorting is completed, it is necessary to further extract the fingerprint features of the intrapulse signal to complete the task of clustering individuals of the same model. i The intermediate frequency signal set S corresponding to the pulse i ={s1,...,s i ,...,s n}, s i Indicates S i The intermediate frequency signal corresponding to the i-th pulse in the embodiment of the present invention is the number of pulses in each cluster. The fingerprint feature vector corresponding to each cluster after sorting is extracted based on the intra-pulse fingerprint feature extraction method. Figure 2 , including the following steps:

[0084] S401 , using the empirical mode decomposition method, decomposing the intermediate frequency data corresponding to each cluster after sorting into an intrinsic mode component and a residual component.

[0085] The embodiment of the present invention uses Hilbert-Huang Transform (HHT) to transform S i Specifically, the Empirical Mode Decomposition (EMD) transform is first used to decompose the intermediate frequency signal into multiple intrinsic mode function (IMF) components and residual components. The formula is expressed as follows:

[0086]

[0087] Among them, IMF m (t) represents the mth intrinsic mode function component, t represents time, r(t) represents the residual component, and M represents the number of decomposed intrinsic mode function components.

[0088] S402 , using the Hilbert-Huang transform method, perform time-frequency transform on each intrinsic mode component, and sum all time-frequency transform results to obtain the HHT time domain matrix of the intermediate frequency signal.

[0089] The embodiment of the present invention is for each imf m (t) Obtain its Hilbert transform to obtain its analytical expression:

[0090]

[0091] in, Indicates imf m (t) is the component after Hilbert transformation. Calculate each The instantaneous frequency of the radar intermediate frequency signal is summed up and the HHT time-frequency matrix is obtained. The formula is:

[0092]

[0093] Where TF(t,f) represents the HHT time-frequency matrix, and f represents the frequency.

[0094] S403 : Calculate the time-frequency energy entropy and marginal spectrum of the corresponding intermediate frequency signal according to the HHT time-domain matrix.

[0095] Considering that the feature dimension of the time-frequency matrix TF(t,f) is high and the computational complexity of extracting fingerprint features is large, the embodiment of the present invention integrates along the time axis of TF(t,f) to obtain the HHT marginal spectrum J(f), which can clearly show the frequency composition of the radar intermediate frequency signal. The calculation formula of the HHT marginal spectrum is expressed as follows:

[0096]

[0097] At the same time, effective fingerprint features should have strong discriminability and low redundancy. Therefore, the first fingerprint feature of the signal is extracted based on the time-frequency matrix TF(t,f), that is, the time-frequency energy entropy. The calculation formula of the time-frequency energy entropy is expressed as:

[0098] E=-∑ t ∑ f TF(t,f)logTF(t,f) (13);

[0099] Where E represents the HHT time-frequency energy entropy.

[0100] S404: Calculate the marginal spectrum distribution center of the corresponding intermediate frequency signal according to the marginal spectrum and the HHT time domain matrix.

[0101] The marginal spectrum distribution center of gravity characterizes the energy distribution of the marginal spectrum. In the embodiment of the present invention, it is used as the second fingerprint feature. The calculation formula of the marginal spectrum distribution center of gravity is expressed as follows:

[0102]

[0103] Wherein, FreGravi represents the center of gravity of the marginal spectrum distribution.

[0104] S405 , calculating the marginal spectrum entropy, marginal spectrum kurtosis, and skewness of the corresponding intermediate frequency signal according to the marginal spectrum.

[0105] The marginal spectrum entropy of the signal is defined based on the marginal spectrum. It characterizes the uniformity of the marginal spectrum energy distribution. Therefore, the embodiment of the present invention uses it as the third fingerprint feature of the radar signal. The calculation formula of the marginal spectrum entropy is expressed as:

[0106]

[0107] Where Hse represents the marginal spectral entropy, and J(m) represents the mth value corresponding to the discretization of J(f).

[0108] Both marginal spectrum kurtosis and skewness can well describe the fine features of sequence distribution. Therefore, in the embodiment of the present invention, marginal spectrum kurtosis and skewness are used as the fourth and fifth fingerprint features of the radar signal, respectively.

[0109] Among them, the calculation formula of marginal spectrum kurtosis is:

[0110]

[0111] Wherein, Kurt represents the marginal spectrum kurtosis, and E() represents the expectation operation.

[0112] The calculation formula for skewness is:

[0113]

[0114] Here, Skew represents skewness.

[0115] S406 , constructing a corresponding fingerprint feature vector from the marginal spectrum entropy, the time-frequency energy entropy, the marginal spectrum distribution center of gravity, the marginal spectrum kurtosis, and the skewness.

[0116] The embodiment of the present invention constructs a corresponding fingerprint feature vector composed of marginal spectrum entropy Hse, time-frequency energy entropy E, marginal spectrum distribution center FreGravi, marginal spectrum kurtosis Kurt, and skewness Skew through S403-S405, which is recorded as v=[Hse,E n ,FreGravi,Kurt,Skew].

[0117] Traverse the set Sig={S1,...,S i ,...,S n Each subset S in i , for S i ={s1,...,s i ,...,s n}, the fingerprint feature vector of each intermediate frequency signal is calculated and recorded as V = {v1,v2,...,v n Finally, the fingerprint features corresponding to all pulses in the set Sig are obtained, which is recorded as V = [V1,...,V i ,...,V n ].

[0118] S50. Clustering the fingerprint feature vectors based on the FCM clustering algorithm with joint parameter optimization K value to obtain individual clustering results of the corresponding radar model.

[0119] The embodiment of the present invention proposes an FCM clustering algorithm based on joint parameter optimization K value to cluster fingerprint feature vectors and obtain individual clustering results of corresponding radar models. Figure 3 , including the following steps:

[0120] S501: Using the FCM clustering algorithm, cluster the fingerprint feature vector based on the specified number of clusters to obtain a pre-clustering result of the corresponding radar model.

[0121] The embodiment of the present invention specifies the number of clusters as K, and uses the FCM clustering algorithm to perform clustering on V = [V1, ..., V i ,...,V n ] to cluster each fingerprint feature vector and obtain the pre-clustering result corresponding to each radar model. How to use the FCM clustering algorithm to perform clustering under a specified number of clusters K can be referred to the existing technology and will not be repeated here.

[0122] S502 , calculating clustering performance indicators corresponding to the pre-clustering results; clustering performance indicators include the sum of squared errors, silhouette coefficient, Calinski-Harabasz index, and Davies-Bouldin index.

[0123] In order to improve the accuracy of the clustering results, the embodiment of the present invention calculates the corresponding clustering performance indicators based on the pre-clustering results; the clustering performance indicators include the sum of squared errors (SSE), silhouette coefficient (Silhouette Criterion), Calinski-Harabasz index (CH index) and Davies-Bouldin index (DB index).

[0124] Among them, the SSE index calculation expression is:

[0125]

[0126] Among them, C represents the cluster set, K represents the number of clusters, p represents a sample in the cluster, where the sample is the fingerprint feature vector, center k Represents the cluster center of the kth cluster.

[0127] The calculation expression of the silhouette coefficient is:

[0128]

[0129] Among them, a y Indicates the average distance between a sample and other samples in its cluster, b y It represents the minimum distance between a sample and other clusters, and Y represents the total number of individuals of the corresponding radar model in each cluster.

[0130] The calculation expression of CH index is:

[0131]

[0132] Among them, SS B Represents the variance among all clusters, SS W represents the variance within all clusters, K represents the number of clusters, and Y represents the total number of individuals of the corresponding radar model in each cluster.

[0133] The calculation expression of DB index is:

[0134]

[0135] Among them, d i Indicates the dispersion of sample points within the i-th cluster, d j Indicates the dispersion of sample points within the jth cluster, D ij It represents the distance between the cluster centers of the i-th cluster and the j-th cluster, and K represents the number of clusters.

[0136] S503. Construct a clustering evaluation function based on the sum of squared errors, silhouette coefficient, Calinski-Harabasz index, and Davies-Bouldin index.

[0137] Since different values of the number of clusters K have a significant impact on the clustering effect, the embodiment of the present invention uses the FCM (Fuzzy C-means) clustering algorithm that optimizes the K value with joint parameters to select the optimal K value. Specifically:

[0138] The embodiment of the present invention combines the four clustering evaluation indicators calculated in S502 to construct a clustering evaluation function, which can obtain clustering performance curves under different K values. The clustering evaluation function constructed in the embodiment of the present invention is expressed as follows:

[0139]

[0140] Among them, L(k) represents the clustering evaluation function, K min Indicates the minimum value of the preset cluster number optimization range, K max Indicates the maximum value of the preset cluster number optimization range, SSE k Indicates the sum of squared errors corresponding to the cluster k, SSE k ″ indicates SSE k Find the second-order difference, SC k Indicates the silhouette coefficient corresponding to the cluster k, CH k Indicates the Calinski-Harabasz index corresponding to the cluster k, DB kThe Davies-Bouldin index corresponding to the number of clusters k is represented by max, and λ1, λ2, λ3, and λ4 are all proportional coefficients. Since the SSE index is an empirical method, the usual judgment method is to plot its trend. Therefore, the second-order difference is calculated to facilitate combinatorial optimization. Since a lower DB index indicates a better clustering effect, its inversion is used to maximize the optimization function.

[0141] S504. Calculate, based on the clustering evaluation function, the clustering evaluation values of the corresponding clustering results under different cluster number values within the preset cluster number optimization range, select the cluster number corresponding to the largest cluster evaluation value as the optimal cluster number, and use the clustering result corresponding to the optimal cluster number as the individual clustering result of the corresponding radar model.

[0142] The embodiment of the present invention pre-sets the optimal range of cluster number, which is denoted as [K min ,K max ], K min Indicates the lower limit of the optimal range of cluster number, K max Indicates the upper limit of the optimization range of the number of clusters; traversal optimization [K min ,K max ] range, repeat the above steps to obtain the four evaluation indicators and calculate the cluster evaluation value L(k) corresponding to each k value, with [K min ,K max ] is the horizontal axis, L(k) is the vertical axis, draw the clustering performance curve, and find L(k) max The corresponding K best The value is taken as the optimal number of clusters. Finally, we get K=K best The cluster label set after FCM clustering is denoted as L i , which is the individual clustering result of the i-th radar model.

[0143] Traverse V=[V1;V2,...;V n ], the fingerprint feature vector corresponding to each radar model is obtained through S501 to S504, and the individual clustering result of each radar model is recorded as Label = [L1,...,L i ,...,L n ].

[0144] In order to verify the effectiveness of the frequency agile radar signal sorting and individual clustering method combining inter-pulse and intra-pulse features provided by the embodiment of the present invention, the following experiments were conducted for verification.

[0145] 1. Sorting experiment of different radar models

[0146] (1.1) Simulation conditions

[0147] The simulation generates the signal parameters of 6 radar radiation sources to complete the radar model sorting experiment. Specifically,

[0148] Set radiation sources 1, 2, and 3 to be radars of the same model, with DOA parameters set to 35.5°-36.5°, 35.6°-36.7°, and 35.4°-36.4°, respectively; PW parameters set to 9μs-11μs, 9.9μs-11.9μs, and 10.5μs-11.5μs, respectively; RF parameters set to 9520MHz, 9480MHz-9600MHz, and 9500MHz, respectively; PRI set to 12μs; and the number of pulses in the original pulse stream is 1000.

[0149] Set radiation sources 4, 5, and 6 to be radars of the same model, with DOA parameters set to 30.0°-31.5°, 30.1°-32.1°, and 30.01-32.0°, respectively; PW parameters to 8 μs, 7.0 μs-9.5 μs, and 8 μs-9.6 μs, respectively; RF parameters to 9700 MHz-9800 MHz, 9720 MHz, and 9680 MHz-9780 MHz, respectively; PRI to 15 μs us; and the number of pulses in the original pulse stream to 1000.

[0150] (1.2) Simulation experiment and result analysis

[0151] Step S30 is used to perform signal sorting on the pulse stream after screening, and the analysis results are as follows: Figure 4 (a)~ Figure 4 As shown in (d), Figure 4 (a) is the original PDW parameter diagram, Figure 4 (b) is the radar pre-sorting result diagram, Figure 4 (c) is the PRI transformation diagram of radar model 1, Figure 4 (d) is the PRI transformation diagram of radar model 2. Figure 4 (a) shows the pulse-to-pulse characteristic distribution of six radiation sources. It can be seen that they can be roughly divided into two categories. Radar radiation sources of the same model have similar parameters, so their characteristic distributions are close, while radiation sources of different models have farther apart characteristic distributions. Figure 4 (b) is the pre-sorting result after using the DBSCAN clustering algorithm. The experimental results show that the six radiation sources are clustered into two clusters according to the DOA, RF and PW pulse description words, that is, two radar models, which is consistent with the simulation conditions. The pre-sorting results are further corrected using the main sorting algorithm in S30 for the two clusters. The experimental results are shown in Figure 2. Figure 4 (c) Figure 4 As shown in (d), the PRIs extracted by the PRI transformation method are 12μs and 15μs respectively, which further verifies the correctness of the pre-sorting results and radar model classification.

[0152] 2. Clustering experiment of different individuals of the same radar model

[0153] (2.1) Simulation conditions

[0154] Fingerprint features were added to the intermediate frequency signals within the pulses of the six radiation sources in Experiment 1 to conduct radar individual clustering experiments, and Gaussian white noise with a signal-to-noise ratio of 15dB was added to simulate the actual environment. Finally, the intermediate frequency signals corresponding to 6000 pulses were obtained.

[0155] (2.2) Simulation experiment and result analysis

[0156] Step S40 is used to extract the intra-pulse fingerprint feature vector of each radar model, and its fingerprint feature distribution diagram is as follows: Figure 5 (a)~ Figure 5 As shown in (b), Figure 5 (a) is the fingerprint feature distribution diagram of radar model 1, Figure 5 (b) is the fingerprint feature distribution diagram of radar model 2. It can be seen that the fingerprint features of different radar models vary greatly, while the intra-pulse fingerprint features of different radar models of the same model vary more subtlely. These subtle features represent individual differences. Figure 6 (a)~ Figure 6 (b) is the clustering performance curve under different K values obtained by using the FCM algorithm based on joint parameter optimization of K value. 6(a) is the clustering performance curve under the optimal K value of radar model 1. Figure 6 (b) is the clustering performance curve of radar model 2 under the optimal K value. From the curve, we can see that the optimal number of clusters for radar models 1 and 2 is 3, that is, each model contains three radar individuals. The fingerprint features are re-clustered with the optimal K value to obtain the individual clustering results as shown below: Figure 7 (a)~ Figure 7 (b) shows the individual clustering result of radar model 1. Figure 7 (b) is the individual clustering result diagram of radar model 2. The results show that after clustering, the clusters are denser and the distance between clusters is farther, and the clustering result is better. The experiment shows that the method proposed in this invention can complete the downstream task after radar sorting, namely radar individual clustering.

[0157] In summary, the frequency-agile radar signal sorting and individual clustering method combining inter-pulse and intra-pulse features proposed in the embodiment of the present invention solves the problem that existing methods cannot effectively cluster different radars of the same model. Before clustering, the original pulse stream is first screened to improve clustering efficiency. In order to eliminate the influence of different signal frequencies on the signal fingerprint characteristics, all filtered intermediate frequency signals are down-converted to the same frequency. Then, the first clustering is achieved based on the pulse descriptor of each radar model, and the second clustering is achieved based on the intra-pulse fingerprint characteristics. Through this radar individual clustering method that simultaneously considers inter-pulse and intra-pulse, not only can effective sorting and clustering of different radar individuals be achieved, but also effective sorting and clustering of different radar individuals of the same model can be achieved. In addition, a radar individual clustering method using FCM based on joint parameter optimization K value is proposed, which effectively avoids the irrationality of manually setting parameters, thereby improving the performance and effect of radar individual clustering. In general, the embodiments of the present invention can achieve more accurate radar individual clustering tasks, and the hierarchical progressive process from radar model sorting to clustering of individuals of the same model makes the clustering process design more practical and reasonable.

[0158] In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0159] Although the present invention is described herein in conjunction with various embodiments, those skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the specification and accompanying drawings in the process of implementing the claimed invention. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple components or steps. The fact that certain measures are described in different embodiments does not mean that these measures cannot be combined to produce good results.

[0160] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for frequency agile radar signal sorting and individual clustering combining inter-pulse and intra-pulse features, characterized in that: The method comprises: Screening the original pulse stream to obtain a screened pulse stream; Perform frequency domain filtering on the intermediate frequency data corresponding to each pulse after screening to obtain corresponding intermediate frequency filtered data, and down-convert the intermediate frequency filtered data of all pulses after screening to the same frequency to obtain pre-processed intermediate frequency data of each pulse after screening; Sorting all pulses corresponding to the pre-processed intermediate frequency data based on the pulse description word to obtain clusters of corresponding radar models; Based on the intra-pulse fingerprint feature extraction method, the fingerprint feature vector corresponding to each cluster after sorting is extracted; The fingerprint feature vectors are clustered based on the FCM clustering algorithm with joint parameter optimization K value to obtain individual clustering results of the corresponding radar model.

2. The method for frequency agile radar signal sorting and individual clustering based on inter-pulse and intra-pulse features according to claim 1, characterized in that: The original pulse stream is filtered to obtain a filtered pulse stream, including: According to the pulse width of the original pulse stream, pulses outside a specified pulse width range are removed from the original pulse stream to obtain a first screening result; According to the carrier frequency of the original pulse stream, pulses outside a specified carrier frequency range are removed from the first screening result to obtain a second screening result; The TOA values corresponding to the second screening results are sorted in ascending order to obtain a pulse sorting structure, and the pulse sorting result is used as the screened pulse stream.

3. The method for frequency agile radar signal sorting and individual clustering based on inter-pulse and intra-pulse features according to claim 1, wherein: Perform frequency domain filtering on the intermediate frequency data corresponding to each pulse after screening to obtain the corresponding intermediate frequency filtered data, including: Performing a fast Fourier transform on the intermediate frequency data corresponding to each pulse after screening, and calculating the peak frequency corresponding to each pulse after screening based on the intermediate frequency data after the fast Fourier transform; The corresponding filtering range is calculated according to the peak frequency, and the corresponding intermediate frequency data is filtered according to the filtering range to obtain the intermediate frequency filtered data corresponding to each pulse after screening.

4. The method for frequency agile radar signal sorting and individual clustering based on inter-pulse and intra-pulse features according to claim 3, wherein: Down-convert the intermediate frequency filtered data of all the pulses after screening to the same frequency to obtain the pre-processed intermediate frequency data of each pulse after screening, including: According to the peak frequency, the intermediate frequency filtered data of all the pulses after screening are down-converted to the same frequency to obtain the pre-processed intermediate frequency data of each pulse after screening.

5. The method for frequency agile radar signal sorting and individual clustering based on inter-pulse and intra-pulse features according to claim 4, wherein: The pre-processed intermediate frequency data of a pulse after screening is expressed as follows: Among them, S(t) represents the pre-processed intermediate frequency data of a pulse at time t, j represents the imaginary unit, and F max It represents the peak frequency of a pulse, and F0 represents the same frequency after down-conversion.

6. The method for frequency agile radar signal sorting and individual clustering combining inter-pulse and intra-pulse features according to claim 1, characterized in that: The pulse description word includes pulse width, carrier frequency, TOA value and DOA value; All pulses corresponding to the pre-processed intermediate frequency data are sorted based on the pulse description words to obtain clusters of corresponding radar models, including: Using the DBSCAN algorithm, all pulses are pre-sorted based on the pulse width, the carrier frequency, and the DOA value to obtain corresponding pre-sorting results; The PRI transformation method is used to perform main sorting on the pre-classification results to obtain corresponding main sorting results, and the main sorting results are used as clusters of corresponding radar models.

7. The method for frequency agile radar signal sorting and individual clustering combining inter-pulse and intra-pulse features according to claim 1, characterized in that: Based on the intra-pulse fingerprint feature extraction method, the fingerprint feature vector corresponding to each cluster after sorting is extracted, including: The empirical mode decomposition method is used to decompose the intermediate frequency data corresponding to each cluster after sorting into intrinsic mode components and residual components; Using the Hilbert-Huang transform method, each intrinsic mode component is transformed into a time-frequency matrix, and all the time-frequency transform results are summed to obtain the HHT time domain matrix of the intermediate frequency signal; Calculating the time-frequency energy entropy and marginal spectrum of the corresponding intermediate frequency signal according to the HHT time domain matrix; Calculating the marginal spectrum distribution center of the corresponding intermediate frequency signal according to the marginal spectrum and the HHT time domain matrix; Calculating marginal spectrum entropy, marginal spectrum kurtosis, and skewness of the corresponding intermediate frequency signal according to the marginal spectrum; The marginal spectral entropy, the time-frequency energy entropy, the marginal spectral distribution center of gravity, the marginal spectral kurtosis, and the skewness constitute a corresponding fingerprint feature vector.

8. The method for frequency agile radar signal sorting and individual clustering combining inter-pulse and intra-pulse features according to claim 1, characterized in that: The fingerprint feature vectors are clustered based on the FCM clustering algorithm with joint parameter optimization K value to obtain the individual clustering results of the corresponding radar model, including: Using the FCM clustering algorithm, clustering the fingerprint feature vector based on the specified number of clusters to obtain a pre-clustering result of the corresponding radar model; Calculating clustering performance indicators corresponding to the pre-clustering results; the clustering performance indicators include the sum of squared errors, silhouette coefficient, Calinski-Harabasz index, and Davies-Bouldin index; Constructing a cluster evaluation function according to the sum of squared errors, the silhouette coefficient, the Calinski-Harabasz index, and the Davies-Bouldin index; According to the clustering evaluation function, the clustering evaluation values of the corresponding clustering results under different clustering number values are calculated within the preset clustering number optimization range, the clustering number corresponding to the largest clustering evaluation value is selected as the optimal clustering number, and the clustering result corresponding to the optimal clustering number is used as the individual clustering result of the corresponding radar model.

9. The method for frequency agile radar signal sorting and individual clustering combining inter-pulse and intra-pulse features according to claim 8, characterized in that: The constructed clustering evaluation function is expressed as follows: Among them, L(k) represents the clustering evaluation function, K min Indicates the minimum value of the preset cluster number optimization range, K max Indicates the maximum value of the preset cluster number optimization range, SSE k Indicates the sum of squared errors corresponding to the cluster k, SSE k ″ indicates SSE k Find the second-order difference, SC k Indicates the silhouette coefficient corresponding to the cluster k, CH k Indicates the Calinski-Harabasz index corresponding to the cluster k, DB k It represents the Davies-Bouldin index corresponding to the number of clusters k, max represents the maximum value, and λ1, λ2, λ3 and λ4 represent proportional coefficients.

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