Multi-radar radiation source sorting identification method based on hierarchical clustering and time-frequency convolution

Abstract

The invention discloses a multi-radar radiation source sorting and identifying method based on hierarchical clustering and time-frequency convolution, which can solve intra-class clustering and inter-class aliasing phenomena and efficiently complete multi-class sorting and identifying. Compared with a traditional sorting algorithm, the problems of intra-class feature distribution and inter-class feature aliasing can be effectively solved, and the processing speed of the sorting algorithm is increased; aiming at the problems of high inter-class feature distribution range overlapping degree and poor separability of original PDW features, periodic features between different classes are extracted based on slow time dimension TFA, and the recognition effect is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar countermeasures, and in particular relates to a multi-radar radiation source sorting and identification method based on hierarchical clustering and time-frequency convolution. Background Art

[0002] Radar emitter identification is an important part of the electronic attack and defense system. Its key task is to sort and identify various information of the emitter from the aliased pulse stream. Pulse Descriptor Word (PDW) is a very easy-to-obtain feature and is often used for sorting and identification.

[0003] Successful sorting is a prerequisite for accurate identification of radiation sources. Especially for complex electromagnetic scenarios with multi-category signal aliasing, PDWs with adjacent arrival times may belong to different radiation sources, making it difficult to extract the statistical features and multi-processing domain features of PDWs, which seriously restricts the optional range of feature extraction methods and identification methods. Clustering is a common method for sorting radiation sources. It can complete the clustering of various categories according to certain rules, so as to achieve the extraction and splicing of single-category time series samples. However, as the electromagnetic environment becomes more complex, the number of pulses increases sharply, and the intra-class clustering and inter-class aliasing phenomena are serious. Common clustering algorithms are difficult to solve the above problems.

[0004] With the rapid development of artificial intelligence, the recognition method based on PDW has transitioned from template matching method to machine learning classifier, and has completed the transition to deep learning classifier. Deep learning can further extract deep features for classification and recognition through neural networks based on raw data or manually extracted features. Time-frequency analysis (TFA) is a common non-stationary signal analysis technology. Many scholars have proved that it has great advantages in the field of radiation source identification when combined with convolutional neural networks. However, the discussion on the combination of PDW and TFA is still insufficient. Summary of the invention

[0005] In response to the above problems and current research trends, this paper proposes a multi-radar radiation source sorting and identification method based on hierarchical clustering and time-frequency convolution, which can solve the intra-class clustering and inter-class aliasing phenomena, and efficiently complete multi-category sorting and identification.

[0006] 1. A method for sorting and identifying multiple radar radiation sources, comprising:

[0007] Step S1, performing initial clustering based on the feature probability distribution function, includes:

[0008] Step S1.1, do N on the pulse flow s times uniform downsampling;

[0009] Step S1.2, fitting the characteristic distribution of the pulse stream after downsampling;

[0010] Step S1.3, set the density threshold h p Divide the feature distribution, and set it above the density threshold h p The sample points are clustered according to continuity;

[0011] Step S1.4: Calculate the posterior probability P of the remaining sample point i belonging to cluster c c,i , select cluster c with the largest feature probability density as the cluster to which sample point i belongs, and obtain the initial cluster set C0;

[0012] Step S2, merging clusters of the same type based on the similarity of feature distribution between clusters, includes:

[0013] Step S2.1, traverse the cluster set C0, and determine whether the PRI samples of the cth cluster are the same type of clusters to be merged according to whether they have periodicity: if they have periodicity, proceed to step S5, otherwise proceed to the next step;

[0014] Step S2.2, calculating the feature distribution similarity matrix D between each cluster in the cluster set C0;

[0015] Step S2.3: merge the similarity matrices that are smaller than the threshold h s The merged cluster set C2 is obtained;

[0016] Step S3, performing anti-aliasing based on TOA period extraction and template matching, includes:

[0017] Step S3.1, calculate the TOA feature density r of each cluster in the merged cluster C2 c2,w , by checking whether a mutation occurs, it is determined whether the cluster is aliased. If it is an aliased cluster, the next step is executed. If it is not aliased, step S5 is directly executed;

[0018] Step S3.2, select a pure sample segment from the aliasing cluster and extract the periodic template of each component from it; then perform steps S3.2.1 and S3.2.2 on each aliasing sample segment in the aliasing cluster in turn:

[0019] Step S3.2.1, determining a matching starting sample point k of the aliased sample segment;

[0020] Step S3.2.2, starting from the matching starting sample point k, the aliased sample segment is matched with the periodic template of each component in the forward and reverse directions. A successful match indicates that the periodic template of the current component belongs to the same category, and so on, until the periodic template matching of all components in the current aliased segment is completed, and the anti-aliasing cluster set C3 is obtained;

[0021] Step S4, constructing a training data set and training the EfficientNet network;

[0022] Step S5: For the data to be identified, the methods of steps S1 to S3 are used to sort them and the trained EfficientNet network is used to identify the sorted data set to obtain the radiation source type identification results of each sample.

[0023] Preferably, in step S1.2, a KDE Gaussian kernel density function is used to fit the probability density of the DOA-RF joint features of the downsampled pulse stream.

[0024] Preferably, in step S2.1, the method of judging whether the c-th cluster is a cluster of the same type to be merged according to whether the PRI samples of the c-th cluster have periodicity includes:

[0025] First, set the mutation point screening threshold Select |{Δ 2 TOA c,i}|>h cp,c of As a sequence of mutation points, periodicity discrimination is equivalent to {Δ 2 TOA c,i} Arithmetic sequence judgment:

[0026]

[0027] Among them, N cp,c is the number of mutation point samples, h c is the periodicity discrimination threshold, modenum(·) is the number of mode samples:

[0028]

[0029] Where [·] is an indicator function, which takes the value of 1 when the internal condition is met and 0 otherwise.

[0030] Preferably, in step S3.1, the method of determining whether the cluster is aliased by checking whether a mutation occurs comprises:

[0031] First, each cluster is divided into multiple overlapping windows, and the feature density of adjacent windows is and And set a threshold h d , determine whether the cluster meets the following conditions. If so, aliasing occurs, otherwise no aliasing occurs:

[0032]

[0033] The sample density is calculated by setting the window length W in the TOA dimension. r , using unit step sliding window calculation:

[0034]

[0035] Among them, N c,w is the total number of samples in the wth window of the cth cluster, TOA c,i is the i-th sample point in the c-th cluster.

[0036] Preferably, the step S4 specifically includes:

[0037] Step S4.1, firstly, segment the data set consisting of the pure pulse stream, perform time-frequency transformation on each segment, obtain a time-frequency graph, and set its category as a label;

[0038] In step S4.2, the data set is divided into a training set and a validation set in a ratio of 8:2. The training set is sent to the EfficientNet network for training, and the validation set is used to evaluate the training results until the requirements are met.

[0039] The present invention has the following beneficial effects:

[0040] 1. The present invention proposes a hierarchical clustering sorting method. Compared with the traditional sorting algorithm, it can effectively solve the problem of intra-class feature distribution and inter-class feature aliasing, and the sorting algorithm processing speed is improved.

[0041] 2. The present invention proposes a recognition method based on time-frequency convolution. Aiming at the problem that the original PDW features have high overlap in the distribution range of features between categories and poor separability, the periodic features between different categories are extracted based on the slow time dimension TFA, which improves the recognition effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is the overall framework diagram of the radiation source sorting and identification method based on hierarchical clustering and time-frequency convolution;

[0043] Figure 2 (a) Figure 2 (b) Figure 2 (c) Figure 2 (d) Figure 2 (e) Distribution diagrams of the five characteristics of data: PRI, RF, PW, PA and DOA;

[0044] Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 3 (d) Figure 3 (e) Figure 3 (f) Figure 3 (g) Figure 3 (h) Figure 3 (i) Figure 3 (j) Figure 3 (k) Figure 3 (l) Figure 3 (m), Figure 3 (n) Figure 3 (o), Figure 3 (p) Figure 3 (q), Figure 3 (r) Figure 3 (s), Figure 3 (t) are the PRI cycle remainder diagrams of each category in the training set and the test set respectively;

[0045] Figures 4(a), 4(b), 4(c), 4(d), 4(e), and 4(f) are the DOA-RF distribution, t-sne of 5-dimensional features, density clustering diagram, clustering, merging, and anti-aliasing results, respectively;

[0046] Figure 5 It is the time-frequency diagram of PRI of each category in the training set and the test set;

[0047] Figure 6 Identify the confusion matrix of the training set results;

[0048] Figure 7(a), Figure 7(b), and Figure 7(c) are the confusion matrices of the recognition results after initial clustering, merging, and de-aliasing, respectively;

[0049] Figure 8 The following is a graph showing the changes in accuracy, Rand index, and time required for clustering at different downsampling multiples. DETAILED DESCRIPTION

[0050] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is clearly and completely described below in conjunction with the embodiments of the present application and the accompanying drawings.

[0051] Sorting part:

[0052] Applicable data: multi-category aliased pulse stream (multi-category aliased pulse sequence), each pulse includes five characteristics: carrier frequency (Radio Frequency, RF), pulse width (Pulse Width, PW), amplitude (Pulse Amplitude, PA), time of arrival (Time of Arrival, TOA), and direction of arrival (Direction of Arrival, DOA).

[0053] Figure 1 This is the overall framework diagram of the radiation source sorting and identification method based on hierarchical clustering and time-frequency convolution. The overall method is divided into two parts: sorting and identification, in which sorting is further divided into three sub-parts: initial clustering, merging, and anti-aliasing:

[0054] Step S1, use KDE (Kernel Density Estimation) method to perform initial clustering:

[0055] Step S1.1, do N to the pulse flow s Multiple uniform downsampling to reduce the amount of data to be processed;

[0056] Step S1.2, use the KDE Gaussian kernel density function to fit the probability density of the DOA-RF joint feature of the downsampled pulse flow, formula

[0057] as follows

[0058]

[0059] Where N' is the total number of samples after downsampling in the test set, h1 and h2 are the window lengths used to smooth DOA and RF, respectively. i and RF i is the DOA and RF of the ith sample, K(·) is the kernel function, and the Gaussian kernel function is usually selected:

[0060]

[0061] in,

[0062] Step S1.3, set the density threshold h based on experience p Divide the feature distribution, cluster the sample points above the threshold according to continuity, and use the KDE method to calculate the 2D feature joint probability density f of each central cluster c , the formula is as follows

[0063]

[0064] Among them, N c is the number of samples in cluster c, DOA c,i and RF c,i are the DOA and RF of the i-th sample in the c-th cluster.

[0065] Step S1.4: Calculate the posterior probability P of the remaining sample point i in the test set belonging to cluster c c,i , select the cluster c with the largest posterior probability as the cluster to which the sample point i belongs, and obtain the initial cluster set C1;

[0066] The formula for calculating the posterior probability is as follows:

[0067]

[0068] Step S2: Merge similar clusters based on KL divergence (KLD):

[0069] Step S2.1, traverse the cluster set C1, and determine whether the PRI samples of the cth cluster are of the same type to be merged according to whether there is periodicity. First, set the mutation point screening threshold Select |{Δ 2 TOA c,i}|>h cp,c The point set is taken as the mutation point sequence, and then the mutation sequence is used to determine whether it has periodicity. The specific judgment formula is as follows:

[0070] Periodicity determination is equivalent to {Δ 2 TOA c,i} Arithmetic sequence judgment:

[0071]

[0072] Where Δ represents the differential operation; TOA c,i represents the TOA of the i-th sample of the c-th cluster; Δ 2 TOA c,i Indicates TOA c,i The second-order difference of cp,c is the number of mutation point samples, h c is the periodicity discrimination threshold, modenum(·) is the number of mode samples: Indicates the index of the first sampling point of the cp segment in the c cluster in the original sequence; Represents an index The point set consisting of the difference of ;

[0073]

[0074] Where [·] is an indicator function, which takes the value 1 when the internal condition is met, otherwise it takes the value 0. mode(·) represents the mode;

[0075] If equation (6) is satisfied, PRI has periodicity and step S5 is executed. Otherwise, the following steps are executed.

[0076] Step S2.2, calculate the DOA-PW joint distribution similarity matrix D between clusters C1 pairwise;

[0077]

[0078] in,

[0079]

[0080] Step S2.3, the similarity matrix is ​​less than the threshold h s The categories will be merged to obtain the merged cluster set C2;

[0081] Step S3, performing anti-aliasing based on TOA period extraction and template matching:

[0082] Step S3.1, perform density mutation check on each merged cluster set C2. First, each cluster is divided into multiple overlapping windows, and the characteristic density of adjacent windows is and And set a threshold h d , determine whether the cluster is aliased:

[0083]

[0084] The sample density is calculated by setting the window length W in the TOA dimension. r , using unit step sliding window calculation:

[0085]

[0086] Among them, N c,w is the total number of samples in the wth window of the cth cluster, TOA c,i is the i-th sample point in the c-th cluster.

[0087] If equation (9) is satisfied, aliasing occurs. The pure segment and the aliasing segment can be divided by density. The low-density segment is the pure segment and the high-density segment is the aliasing segment. The following steps are performed. If there is no aliasing, directly proceed to step S5;

[0088] Step S3.2, extracting each component periodic template from each pure sample segment

[0089]

[0090] in, represents the period of the pth pure segment of the cth cluster, is the number of cycles.

[0091] Step S3.3, perform the following processing steps on each aliasing segment in turn.

[0092] Step S3.3.1 determines the matching starting sample point. Traverse the current aliasing segment and use each TOA value as the starting point to match along the TOA forward template. The sample corresponding to the point with the minimum loss is the forward matching starting position k:

[0093]

[0094] in, N c,a Indicates the total number of samples in the ath aliasing segment in the cth cluster.

[0095] Step S3.3.2, from TOA c,a,k Start forward and reverse matching, and repeat steps S3.3.1-S3.3.2 until all categories of periodic template matching in the current aliasing segment are completed, and the anti-aliasing cluster set C3 is obtained;

[0096] Identification section:

[0097] Step S4, construct a training data set and train the network.

[0098] Step S4.1, construct a clean data set containing 5-dimensional pulse description words for network training. First, perform N rec After point sliding window processing, STFT is performed to obtain a time-frequency diagram with the label as its category;

[0099] The STFT formula is as follows:

[0100]

[0101] Among them, x(n) is the discrete sample to be processed, w(n) is the window function, W stft is the window length, N fft is the number of Fourier transform points, T and F are time and frequency sampling units respectively. The window function used in this paper is the Hanning window, and the window length is adjusted according to the periodicity of PRI.

[0102] Step S4.2, divide the data set into a training set and a validation set in a ratio of 8:2, send the training set to the EfficientNet network for training, and use the validation set to evaluate the training results;

[0103] Step S5: The test set has the same category as the training data, but there is aliasing. After sorting, a nearly pure pulse cluster set C3 is obtained, which is input into the trained EfficientNet network for testing to obtain the radiation source category of each sample.

[0104] Example:

[0105] In this embodiment, a total of 10 radiation source signals are set, and sorting and identification are performed in sequence:

[0106] The sample distribution of the training data set and the test set is as follows Figure 2 shown.

[0107] Among them, each type of radiation source sample in the training set is collected separately, without aliasing, loss, error and interference. Each type of radiation source sample is sorted by arrival time and collected for a total of 10 seconds. The sample size of each category is about 120,000 to 220,000, and the total sample size is about 1.4 million. The test set aliases the samples of 10 types of radiation sources according to different arrival times, and collects a total of 16 seconds. The sample size of each category is about 180,000 to 350,000, and the total sample size is about 2.06 million. Note that there is only one type of radiation source per TOA, corresponding to one category label.

[0108] from Figure 2It can be seen intuitively that for the above five features, except for category 4, there is a lot of overlap in the features of various radiation sources in the training set and the test set, making it difficult to distinguish one of the radiation source categories from all other categories. However, DOA and RF can achieve at least two categories of distinction in both the training set and the test set, and have local separability, so these two features are selected for sorting.

[0109] The periodic difference of PRI makes it possible to purify aliased samples. The PRI period comparison of the training data set and the test set is as follows: Figure 3 shown.

[0110] The test set is sorted and identified. The algorithm simulation parameters are shown in Table 1

[0111] Table 1

[0112]

[0113] Sorting part:

[0114] The sorting accuracy is evaluated using the Rand Index, which represents the degree of overlap between two category clusters:

[0115]

[0116] Among them, TP represents the number of cases where two sample points of the same type are in the same cluster, TN represents the number of cases where two sample points of different types are in two clusters respectively, FP represents the number of cases where two sample points of different types are in the same cluster, and FN represents the number of cases where two sample points of the same type are in two clusters respectively.

[0117] Figure 4 shows the DOA-RF distribution, t-sne of 5-dimensional features, density cluster diagram, clustering, merging and anti-aliasing results. Since the RF distribution range of category 4 is significantly different from other categories and is easy to sort, the clustering results of this category are not shown for the sake of beautiful feature visualization. Figure 4 (a) shows the original DOA-RF distribution. The 2-dimensional features of all categories are distributed in horizontal strips. Except for category 7, the feature distributions of each category overlap to a certain extent. Among them, the overlapping ranges of categories 3 and 6 and categories 2 and 10 are relatively large, and there is feature clustering in categories 1, 2, 8 and 9.

[0118] Figure 4(c) is a density clustering diagram after executing step S1.2, which intuitively presents the changes in the 2D feature probability density of the test set samples. Among them, the background color represents the density change, the blue dots represent the sample points after downsampling, and the red dotted line represents the probability threshold. According to the probability threshold, the clusters are divided in the probability density contour map, and then the posterior probability of the sample points belonging to each cluster is calculated, and the cluster with the maximum posterior probability is selected to complete the clustering of the sample points. The clustering result after executing step S1.4 is shown in Figure 4(d), which is divided into 11 clusters in total. Categories 1, 2, 8 and 9 with feature clustering are all mistakenly divided into two clusters, and categories 2, 3, 6 and 10 with feature aliasing are all mistakenly merged into 1 cluster, with a Rand index of 70.89%.

[0119] After executing the merging process of step S2.3, 11 clusters are merged into 7 clusters, and the Rand index is increased to 82%, achieving the intra-class cluster merging of 4 categories, as shown in Figure 4(e). After executing the anti-aliasing process of step S3.4, 7 clusters are transformed into 9 clusters, and the Rand index is further increased to 92.24%, basically achieving the anti-aliasing of 4 categories. The sorting error mainly comes from the inaccurate classification of edge aliasing samples.

[0120] Identification section:

[0121] Without loss of generality, the confusion matrix and accuracy indicators are used to evaluate the recognition performance.

[0122] The time-frequency diagram obtained after executing step S4.1 is as follows Figure 5 As shown, there are obvious differences between the categories.

[0123] First, without considering the wrong sorting, the confusion matrix after executing step S4.2 is as follows Figure 6 As shown in the figure, the recognition accuracy of time-frequency convolution is 99.21%. For category 3 and category 10 without periodicity, the recognition accuracy of the proposed method is 98.42% and 94.47% respectively, and the recognition accuracy of the remaining categories can reach 100%, which proves that the proposed method has excellent recognition performance for periodic sequences and also has certain recognition potential for categories without periodicity.

[0124] Combined with the proposed sorting method, the recognition result is shown in Figure 7. When only KDE clustering is performed, the confusion matrix is ​​shown in Figure 7(a), and the recognition accuracy is 37.42%. Focus on the impact of inter-class feature aliasing and intra-class feature clustering on the recognition effect:

[0125] For categories 3 and 6, as well as categories 2 and 10, where aliasing is more serious, the recall rates are all less than 10%, which are 5.19%, 9.77%, 6.02%, and 6.77%, respectively;

[0126] For categories 1, 2, 8, and 9 where feature clustering occurs, except for category 8, the recall rates are all less than 10%, namely 0%, 6.02%, 69.62%, and 1.36%, respectively.

[0127] It can be seen that both feature aliasing and feature clustering will seriously deteriorate the recognition performance.

[0128] After adding the merging process, the recognition accuracy rate increased by 33.94% to 71.36%, as shown in Figure 7(b). For categories 1, 2, 8, and 9 with feature clustering, the recall rate increased to 99.45%, 48.92%, 77.77%, and 85.31%, respectively, an increase of 39.15% to 94.26%, proving that the merging process can effectively improve the recognition performance. Among them, the recall rate of category 2 has limited improvement due to the existence of aliasing.

[0129] After further adding anti-aliasing processing, the recognition accuracy is further improved by 20.22% to 91.58%, as shown in Figure 7(c). For categories 3, 6, 2, and 10 with aliasing, the recall rate is increased to 76.22%, 97.22%, 89.21%, and 93.16%, respectively, an increase of 40.29% to 87.45%, proving that the anti-aliasing algorithm can also effectively improve the recognition performance.

[0130] Figure 8 The effects of different downsampling multiples on accuracy, Rand index, and clustering time are shown. It can be seen that when the downsampling is 2 to 100 times, the recognition accuracy can be maintained at about 90%, and the processing time reaches a low of about 58s when the downsampling is 50 to 100 times. As the downsampling multiple continues to increase, the recognition accuracy deteriorates rapidly to about 40%. This is because when the downsampling is too much, most of the sample points are lost and an effective central cluster cannot be formed, which makes the attribution of all samples very unreliable, resulting in more complex intra-class clustering and inter-class aliasing. This brings greater difficulty to the subsequent merging and anti-aliasing processing, and ultimately deteriorates the recognition performance. At the same time, the processing time may increase due to the need for frequent anti-aliasing. Therefore, the downsampling multiple should not be too large, so as to reduce the processing time while ensuring the recognition performance.

[0131] In summary, the multi-radar radiation source sorting and identification method based on hierarchical clustering and time-frequency convolution proposed in the present invention can effectively solve the intra-class clustering and inter-class aliasing phenomena, and can efficiently complete the sorting and identification of multiple categories.

Claims

1. A method for sorting and identifying multiple radar radiation sources, characterized in that: include: Step S1, performing initial clustering based on the feature probability distribution function, includes: Step S1.1, do N on the pulse flow s times uniform downsampling; Step S1.2, fitting the characteristic distribution of the pulse stream after downsampling; Step S1.3, set the density threshold h p Divide the feature distribution, and set it above the density threshold h p The sample points are clustered according to continuity; Step S1.4: Calculate the posterior probability P of the remaining sample point i belonging to cluster c c,i , select cluster c with the largest feature probability density as the cluster to which sample point i belongs, and obtain the initial cluster set C0; Step S2, merging clusters of the same type based on the similarity of feature distribution between clusters, includes: Step S2.1, traverse the cluster set C0, and determine whether the PRI samples of the cth cluster are the same type of clusters to be merged according to whether they have periodicity: if they have periodicity, proceed to step S5, otherwise proceed to the next step; Step S2.2, calculating the feature distribution similarity matrix D between each cluster in the cluster set C0; Step S2.3: merge the similarity matrices that are smaller than the threshold h s The merged cluster set C2 is obtained; Step S3, performing anti-aliasing based on TOA period extraction and template matching, includes: Step S3.1, calculate the TOA feature density of each cluster in the merged cluster C2 Determine whether the cluster is aliased by checking whether a mutation occurs. If it is an aliased cluster, proceed to the next step. If it is not aliased, proceed directly to step S5. Step S3.2, select a pure sample segment from the aliasing cluster and extract the periodic template of each component from it; then perform steps S3.2.1 and S3.2.2 on each aliasing sample segment in the aliasing cluster in turn: Step S3.2.1, determining a matching starting sample point k of the aliased sample segment; Step S3.2.2, starting from the matching starting sample point k, the aliased sample segment is matched with the periodic template of each component in the forward and reverse directions. A successful match indicates that the periodic template of the current component belongs to the same category, and so on, until the periodic template matching of all components in the current aliased segment is completed, and the anti-aliasing cluster set C3 is obtained; Step S4, constructing a training data set and training the EfficientNet network; Step S5: For the data to be identified, the methods of steps S1 to S3 are used to sort them and the trained EfficientNet network is used to identify the sorted data set to obtain the radiation source type identification results of each sample.

2. The multi-radar radiation source sorting and identification method according to claim 1, characterized in that: In the step S1.2, the KDE Gaussian kernel density function is used to fit the probability density of the DOA-RF joint features of the downsampled pulse flow.

3. The multi-radar radiation source sorting and identification method according to claim 1, characterized in that: In step S2.1, the method of judging whether the PRI samples of the cth cluster are clusters of the same type to be merged according to whether there is periodicity includes: First, set the mutation point screening threshold Select |{Δ 2 TOA c,i }|>h cp,c of As a sequence of mutation points, periodicity discrimination is equivalent to {Δ 2 TOA c,i } Arithmetic sequence judgment: Among them, N cp,c is the number of mutation point samples, h c is the periodicity discrimination threshold, modenum(·) is the number of mode samples: Where [·] is an indicator function, which takes the value of 1 when the internal condition is met and 0 otherwise.

4. The multi-radar radiation source sorting and identification method according to claim 1, characterized in that: In step S3.1, the method of determining whether the cluster is aliased by checking whether a mutation occurs includes: First, each cluster is divided into multiple overlapping windows, and the feature density of adjacent windows is and And set a threshold h d , determine whether the cluster meets the following conditions. If so, aliasing occurs, otherwise no aliasing occurs: The sample density is calculated by setting the window length W in the TOA dimension. r , using unit step sliding window calculation: Among them, N c,w is the total number of samples in the wth window of the cth cluster, TOA c,i is the i-th sample point in the c-th cluster.

5. The method for sorting and identifying multiple radar radiation sources according to claim 1, characterized in that: The step S4 specifically includes: Step S4.1, firstly, segment the data set consisting of the pure pulse stream, perform time-frequency transformation on each segment, obtain a time-frequency graph, and set its category as a label; In step S4.2, the data set is divided into a training set and a validation set in a ratio of 8:

2. The training set is sent to the EfficientNet network for training, and the validation set is used to evaluate the training results until the requirements are met.

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