A radar pulse sorting method based on inverse distance weighting online clustering

Abstract

The application discloses a radar pulse sorting method based on inverse distance weighting online clustering and belongs to the field of radar signal sorting, and comprises the following steps: step one, according to the characteristics of modern radar signals, a large number of pulse samples with typical radar signal diversity are generated by using python; step two, the first 1000 full quantities of the generated pulse data set are pre-clustered; step three, real-time signal sorting of single-sample inverse distance weighting similarity is carried out on the remaining pulse data; step four, the sorting result is verified in real time; step five, steps three and four are repeated until all data are sorted; step six, steps three and four are repeated by using the incremental Leader algorithm and the non-incremental DBSCAN and BGMM algorithms, and comparison test verification is carried out on the application; the application carries out pulse clustering association based on the weighted sum discriminant criterion, overcomes the predicament of prior knowledge dependence, dynamically updates the cluster center through the sliding average technology, and realizes higher sorting accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal sorting, and in particular to a radar pulse sorting method based on inverse distance weighted online clustering. Background Art

[0002] Radar pulse sorting algorithms are technologies that extract individual radar pulse sequences from a randomly interwoven pulse stream. They are a crucial technical foundation for radar signal parameter analysis and extraction, radar type identification, and a core step in sensing the electronic battlefield situation. They are also a key component in current radar countermeasures. However, with the increasing complexity of the electromagnetic signal environment, radar signals are becoming increasingly dense, diverse, and concealed, presenting unprecedented challenges for radar signal sorting.

[0003] Existing radar pulse sorting algorithms are mainly developed from two directions:

[0004] One approach is to classify signals based on intrapulse features. This approach converts the radar signal sorting problem into a supervised classification problem by extracting combined features across multiple domains (time, frequency, and time-frequency domains). However, this approach ignores the complex nature of the electromagnetic environment. For example, the massive number of signal samples cannot be manually labeled. Furthermore, it is difficult to identify features that generalize well and are highly separable for signals with complex modulation, variable parameters, agile changes, or even randomness. Furthermore, the time cost of feature extraction and classifier training is prohibitive given the high real-time requirements, making it difficult to adapt to the demands of modern radar signal sorting.

[0005] The second method is based on pulse-to-pulse features, typically described using pulse descriptor words (PDWs). Template matching is an early classification method that rapidly separates signals by building a database containing characteristic parameters of radar emitters and comparing the received signal against templates in the database. However, with the advancement of radar technology and the increase in signal types, template matching faces challenges in database completeness and updating in practical applications.

[0006] Sorting methods based on the pulse repetition interval (PRI) are another major category of inter-pulse modulation feature sorting techniques. PRI describes the time interval between adjacent pulses in a pulse sequence and is relatively stable, making it the key to sorting algorithms. Techniques such as PRI search, PRI histogram, PRI transform, and plane transform are effective in processing scenarios with low pulse density, few radiation sources, and fixed PRI parameters. However, with the advancement of radar signal modulation technology, the non-constant characteristics of PRI (such as PRI agility and random modulation) and the increase in pulse density have challenged traditional PRI-based sorting methods, resulting in reduced processing performance.

[0007] Unsupervised clustering methods have become an important research direction due to the difficulty in obtaining prior information about target radiation sources. Traditional clustering methods, such as K-Means and Fuzzy C-Means clustering, while capable of processing clusters of arbitrary shapes, require prior information such as the number of clusters to be set, limiting their scope of application. Density-based clustering algorithms can mine clusters of arbitrary shapes, but they are highly parameter-sensitive and may degrade or even fail in dynamic scenarios. Furthermore, these clustering algorithms process data in batches, failing to meet real-time requirements and ignoring temporal variations in the underlying data points.

[0008] In recent years, incremental algorithms have begun to be used for radar emitter signal sorting, processing each pulse sequentially to achieve real-time sorting. Improved incremental DBSCAN and incremental Leader algorithms significantly reduce computational complexity and optimize the processing of noisy pulses through real-time clustering of single-sample increments. However, the performance of these algorithms is severely affected when radar emitter data distributions overlap. Summary of the Invention

[0009] In view of the shortcomings of the existing technology, the present invention discloses a radar pulse sorting method based on inverse distance weighted online clustering, which solves the problems of insufficient real-time performance and insufficient prior information in the existing radar sorting technology.

[0010] To achieve the above object, the present invention provides the following technical solution: a radar pulse sorting method based on inverse distance weighted online clustering, comprising the following steps:

[0011] Step 1: Construct radar signal samples. Based on the characteristics of modern radar signals, use Python to generate several pulse sequence samples with typical radar signal diversity.

[0012] Step 2: Perform full clustering on the first 1000 pulse trains to obtain the initial cluster center list and category number;

[0013] Step 3: Based on the pre-obtained initial cluster center list and category serial number, the remaining data is sorted in real time using single-sample inverse distance weighted similarity according to the time beat;

[0014] Step 4: Real-time verification of the sorting results of step 3;

[0015] Step 5: Repeat steps 3 and 4 until all data are sorted;

[0016] Step 6: Repeat steps 3, 4, and 5 using the incremental Leader algorithm and the non-incremental DBSCAN and BGMM algorithms for comparative experimental verification.

[0017] Preferably, in step 1, the five-dimensional features of the radar signal sample including the radar pulse description word are first determined:

[0018] TOA: Time of arrival, which indicates the time it takes for the pulse to reach the receiver, in seconds;

[0019] CF: Center frequency, indicating the frequency center of the pulse, in megahertz;

[0020] PW: Pulse width, which indicates the duration of the pulse in microseconds;

[0021] PA: Amplitude, which indicates the intensity of the pulse, in volts;

[0022] DOA: Angle of arrival, indicating the direction of the pulse, in degrees;

[0023] 1) Determine the arrival time based on the three modulation modes of radar,

[0024] For a simple pulse radar, the first-order difference of arrival times is a constant:

[0025] ΔTOA(t)=C;

[0026] For frequency modulated continuous wave radar, the first-order difference of arrival time is a linear function of time:

[0027] ΔTOA(t)=t;

[0028] For nonlinear frequency modulation radar, the first-order difference of arrival time is a complex function of time:

[0029] ΔTOA(t)=f(t);

[0030] 2) Arrival angle varies from 0 degrees to 360 degrees

[0031] The continuously varying angle of arrival is simulated by combining intercepted sine, cosine, polynomial, exponential, and linear functions:

[0032]

[0033] By giving different value thresholds of a, b, c, d, e, f, g and DOA(t), we can simulate the changes in the arrival angles of different radar signals in the real electromagnetic world.

[0034] 3) The center frequency range is from 1 GHz to 15 GHz, and the stable center frequency is described by a combination of a constant function and Gaussian noise:

[0035]

[0036] 4) The pulse width ranges from 0.05 microseconds to 35 microseconds, and the stable center frequency is described by a combination of a constant function and Gaussian noise:

[0037]

[0038] 5) The variation range of the pulse amplitude. According to the definition of the pulse amplitude, P is specified as a random number within a certain range:

[0039]

[0040] According to the above rules, 12 radar signal sources with different pulse quantity scales are simulated. The arrival times of the pulse width, center frequency, arrival angle, and amplitude are plotted on a plane, and each point represents a pulse.

[0041] Preferably, in step 2, the full - scale pre - clustering using the first 1000 radar signal samples specifically includes the following:

[0042] For the first 1000 pulse sequences x

[0046] , j , j , ,

[0048] ,

[0047] , , , j , j , i ,

[0049] , , (n = 1, 2, …, K), perform full - scale clustering to obtain the initial cluster center list x i and the class serial number i(1, 2, …, C).

[0043] Preferably, in step 3, according to the pre - obtained initial cluster center list and class serial number, the remaining data is sorted for real - time signals by single - sample inverse - distance weighted similarity according to the time beat, specifically including the following steps:

[0044] Given a pulse query point x j , the known - class cluster center list x i , i = 1, 2, …, C, where C is the maximum index of the known classes in the full - scale clustering and a pulse stream T:

[0045] T = {(CF1, DOA1), (CF2, DOA2), …, (DF N , DOA N )},

[0046] where X j =(CF j , DOA j ) is the feature vector of the instance, j = 1, 2, …, N;

[0047] Step 3.1: Calculate the CF and DOA distances between x j and the current known - class cluster center x i :

[0048]

[0049] Step 3.2: Select the k cluster centers closest to each pulse feature, where k is n / 2 and n is the current number of clusters, recorded as:

[0050] N k1 (CF j )=min k distance CF ;

[0051] N k2 (DOA j )=min k distance DOA ;

[0052] Step 3.3: Based on the inverse distance weighted similarity, calculate each x i In N k (x q ) in the reciprocal s(x j , x i ),

[0053]

[0054] Where ∈ is a small positive number to avoid the denominator being zero. The calculated distance is converted into a reliable probability threshold. i In N k (x j ) is normalized so that the probability of each set of features is 1, which is provided for subsequent sorting, that is,

[0055]

[0056] Step 3.4: Get each x i The weight w(x j , x i ) after N k1 (CF j )∩N k2 (DOA j ) Perform similarity weighted sum to obtain the total weight W K =W(N k1 (CF j )∩N k2 (DOA j )), according to W K Make a judgment and get x j Category y q ,Right now

[0057]

[0058] n represents the current number of categories, and threshold represents the threshold set by the similarity function.

[0059] Preferably, in the step 4, the sorting results in the step 3 are verified in real time, and the experimental results are measured from three aspects: ARI, AMI, and ACC;

[0060] 1) ARI algorithm. The value range of ARI is -1 to 1. The larger the value, the better the clustering result. The calculation formula of ARI is:

[0061]

[0062] in, Indicates the number of combinations of selecting k elements from n elements, n ij Indicates the number of samples contained in the i-th category in the clustering result and the j-th category in the true category, a i Indicates the number of samples in the i-th category in the clustering results, b j represents the number of samples of the jth class in the true category, and n represents the total number of samples;

[0063] 2) AMI algorithm. The value range of AMI is 0 to 1. The larger the value, the better the clustering result. The calculation formula of AMI is:

[0064]

[0065] Among them, MI represents the mutual information between the clustering results and the true categories, H(U) and H(V) represent the entropy of the clustering results and the true categories respectively, and E[MI] represents the expected mutual information between the clustering results and the true categories when randomly assigned;

[0066] 3) The ACC algorithm is based on the Hungarian algorithm and is used to solve the maximum weight matching problem in bipartite graphs. The idea of ​​the ACC algorithm is to find a maximum weight matching so that each class in the clustering result corresponds to a class in the real class:

[0067]

[0068] Where w is a D×D matrix, D=max(max(y),max(Y))+1, and L is the Hungarian matching algorithm;

[0069] Finally, we get y for each time step in step 3. q Compare with the actual label and calculate the ARI, AMI, and ACC scores, and take their average as the metric, as follows:

[0070]

[0071] The above score represents the average of ARI, AMI and ACC scores.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] 1. This invention proposes a similarity measurement algorithm based on inverse distance and designs a weighted sum-based criterion for pulse clustering and association. This algorithm does not require a preset number of clusters, is independent of the selection of sensitive parameters, and can adapt to overlapping data distributions, overcoming the reliance on prior knowledge. Furthermore, the algorithm utilizes incremental processing, storing only a small amount of data in memory, enabling real-time pulse deinterleaving, meeting the real-time data processing requirements of modern electromagnetic environments. Simulation results on simulated data sets demonstrate that this invention achieves high sorting accuracy.

[0074] 2. The present invention proposes a radar pulse sorting method based on inverse distance weighted online clustering. In order to dynamically learn the representation of pulses, the present invention adopts a sliding average technology to dynamically update the cluster center. The cluster center is represented as the average value of nearly one hundred pulse data streams and is continuously updated dynamically, so as to better track the changing patterns of pulses, automatically learn the pulse feature representation, and achieve higher sorting accuracy.

[0075] 3. In order to mitigate the pulse clustering phenomenon of different radars caused by overlapping pulse features, the present invention introduces the concept of k-nearest neighbors to calculate the similarity of each pulse feature. By selecting the k cluster centers closest to the pulse feature, the algorithm can more accurately evaluate the similarity between the pulse and each cluster center. Using the inverse distance weighted method, the algorithm converts the similarity into a probability form, avoiding complex threshold selection and ensuring the rationality of the similarity probability. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0077] In the attached figure:

[0078] Figure 1 is a distribution diagram of the simulated data set of the present invention;

[0079] Figure 2 It is a flow chart of the algorithm of the present invention. DETAILED DESCRIPTION

[0080] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0081] A radar pulse sorting method based on inverse distance weighted online clustering comprises the following steps:

[0082] Step 1: Construct a radar signal sample. First, determine the five-dimensional features of the radar signal sample, including the radar pulse descriptor:

[0083] TOA: Time of arrival, which indicates the time it takes for the pulse to reach the receiver, in seconds;

[0084] CF: Center frequency, indicating the frequency center of the pulse, in megahertz;

[0085] PW: Pulse width, which indicates the duration of the pulse in microseconds;

[0086] PA: Amplitude, which indicates the intensity of the pulse, in volts;

[0087] DOA: Angle of arrival, indicating the direction of the pulse, in degrees;

[0088] The time of arrival (TOA) of the radar signal ranges from 0 to 6×10^11s;

[0089] 1) Determine the time of arrival (TOA) based on three radar modulation methods,

[0090] For a simple pulse radar, the first-order difference of arrival times is a constant:

[0091] ΔTOA(t)=C

[0092] For frequency modulated continuous wave radar, the first-order difference of arrival time is a linear function of time:

[0093] ΔTOA(t)=t

[0094] For nonlinear frequency modulation radar, the first-order difference of arrival time is a complex function of time:

[0095] ΔTOA(t)=f(t)

[0096] 2) Angle of arrival (DOA) varies from 0 degrees to 360 degrees

[0097] The continuously varying angle of arrival is simulated by a combination of intercepted sine, cosine, polynomial, exponential and linear functions:

[0098]

[0099] By giving different value threshold ranges of a, b, c, d, e, f, g and DOA(t), the changes in the arrival angles of different radar signals in the real electromagnetic world are simulated.

[0100] 3) Center frequency (CF) range from 1GHz to 15GHz

[0101] The stable center frequency is described by a combination of a constant function and Gaussian noise:

[0102]

[0103] 4) Pulse width (PW) ranges from 0.05 microseconds to 35 microseconds

[0104] The stable center frequency is described by a combination of a constant function and Gaussian noise:

[0105]

[0106] 5) The pulse amplitude (PA) has a large range of variation. According to the definition of pulse amplitude, P is specified as a random number within a certain range.

[0107]

[0108] like Figure 1 As shown in the figure, according to the above rules, 12 radar signal sources with different pulse numbers (ranging from 54722 pulses to more than 976575 pulses) are simulated. The pulse width (PW), center frequency (CF), angle of arrival (DOA) and amplitude (PA) are plotted on the arrival time (TOA) plane, and each point represents a pulse.

[0109] Step 2: Use the first 1000 radar signal samples for full pre-clustering:

[0110] For the first 1000 pulse trains x n (n=1,2,…,K), perform full clustering and obtain the initial cluster center list x i And category number i (1, 2,…, C).

[0111] Step 3: Based on the pre-obtained initial cluster center list and category serial number, the remaining data is sorted according to the time beat using single-sample inverse distance weighted similarity in real-time signal sorting:

[0112] Given a pulse query point x j , a list of cluster centers of known classes x i , i = 1, 2, ..., C, where C is the maximum index of all known clusters and a pulse stream T;

[0113] T={(CF1, DOA1), (CF2, DOA2),…, (DF N , DOA N )},

[0114] where X j =(CF j , DOA j ) is the feature vector of the instance, j = 1, 2, …, N.

[0115] Step 3.1: Calculate x j and the currently known cluster center x i The CF and DOA distance between:

[0116]

[0117] Step 3.2: Since different radiation sources may have very similar distributions in certain features, overlapping data distributions may lead to misjudgment of clustering results. To make the similarity probability more reliable, the algorithm introduces the idea of ​​k-nearest neighbors, selecting the k cluster centers closest to each pulse feature (k is usually n / 2, where n is the current number of clusters), recorded as:

[0118] N k1 (CF j )=min k distance CF

[0119] N k2 (DOA j )=min k distance DOA

[0120] Step 3.3: This invention proposes an inverse distance weighted similarity to calculate each x i In N k (x q ) in the reciprocal s(x j , x i ),

[0121]

[0122] Where ∈ is a small positive number to avoid the situation where the denominator is zero. The calculated distance is converted into a reliable probability threshold, avoiding the threshold selection of complex distance parameters. For each x i In N k (x j ) is normalized so that the probability of each set of features is 1, which is provided for subsequent sorting, that is,

[0123]

[0124] Step 3.4: Get each x i The weight w(x j , x i ), the final judgment is to select from the intersection of the similarity of each group of pulse features, avoiding the pulse misclassification caused by the similarity of a certain feature. k1 (CF j )∩N k2 (DOA j) Perform similarity weighted sum to obtain the total weight W K =W(N k1 (CF j )∩N k2 (DOA j )), according to W K Make a judgment and get x j Category y q ,Right now;

[0125]

[0126] n represents the current number of categories, and threshold represents the threshold set by the similarity function.

[0127] Step 4: Real-time verification of the sorting results in step 3:

[0128] In order to compare the advantages and disadvantages of different algorithms, the present invention measures the experimental results from three aspects: ARI, AMI, and ACC.

[0129] 1) ARI (Adjusted Rand Index) is an indicator used to measure the similarity between clustering results and true categories. It takes into account the influence of random assignment. The larger the value, the more similar the clustering results are to the true categories. The value range of ARI is -1 to 1. The larger the value, the better the clustering result. The calculation formula of ARI is:

[0130]

[0131] in, Indicates the number of combinations of selecting k elements from n elements, n ij Indicates the number of samples contained in the i-th category in the clustering result and the j-th category in the true category, a i Indicates the number of samples in the i-th category in the clustering results, b j represents the number of samples of the jth category in the true category, and n represents the total number of samples.

[0132] 2) AMI (Adjusted Mutual Information) is an indicator used to measure the similarity between clustering results and true categories. It takes into account the effects of random assignment and class imbalance. A larger value indicates that the clustering results are more similar to the true categories. The value range of AMI is 0 to 1, and a larger value indicates a better clustering result. The calculation formula of AMI is:

[0133]

[0134] Among them, MI represents the mutual information between the clustering results and the true categories, H(U) and H(V) represent the entropy of the clustering results and the true categories respectively, and E[MI] represents the expected mutual information between the clustering results and the true categories when randomly assigned.

[0135] 3) Accuracy (ACC) is a metric used to measure the proportion of correctly classified samples in the clustering results to the total number of samples. It only considers whether the sample classification is correct, and does not consider the classification precision and recall. Unlike the general ACC, the ACC algorithm of this invention is based on the Hungarian algorithm (also known as the Kuhn-Munkres algorithm), which is an algorithm for solving the maximum weight matching problem in bipartite graphs. The idea of ​​the ACC algorithm is to find a maximum weight matching so that each class in the clustering result corresponds as closely as possible to a class in the true class.

[0136]

[0137] Where w is a D×D matrix, D=max(max(y),max(Y))+1, and L is the Hungarian matching algorithm.

[0138] Get y for each time step in step 3 q Compared with the actual label, the ARI, AMI, and ACC scores are calculated and their average is taken as the metric, as follows:

[0139]

[0140] Step 5: Repeat step 3 and step 4 until the data is finished. The algorithm flow chart is as follows: Figure 2 shown.

[0141] Step 6. Repeat steps 3, 4, and 5 using the incremental Leader algorithm and the non-incremental DBSCAN and BGMM algorithms to conduct comparative experiments.

[0142] Examples are given below to illustrate the present invention:

[0143] Example 1:

[0144] The first 1000 pulses of the pulse stream are clustered (DBSCAN), and a total of 6 types of pulses appear. These 6 types of pulses are regarded as known radars, and their center points, CF mean and DOA mean are calculated, which are recorded as X i Starting from the 1001th pulse, pulse-by-pulse online clustering is performed to sort the remaining pulses. According to the pulse characteristics (center frequency, arrival angle), the pulses are processed in non-incremental and incremental ways respectively.

[0145] In order to evaluate the performance of the present invention (IDP algorithm) and its comparative algorithm, three indicators were used: ARI (Adjusted Rand Index), AMI (Adjusted Mutual Information), and ACC (Accuracy). ARI and AMI can more comprehensively measure the degree of fit between the clustering results and the true category labels, and have been widely used in clustering algorithm evaluation; ACC directly reflects the proportion of cluster labels given by the algorithm that are the same as the true labels. The value range of the three is 0 to 1, and the closer to 1, the better the performance. Since the non-incremental algorithm is sensitive to initialization, that is, different initial cluster centers will affect the final clustering results, in order to ensure the uniqueness of the experiment, the random seed is fixed to 42, that is, the same initial cluster center is used each time the non-incremental algorithm is run. The experimental results show that under complex conditions of signal interweaving, overlap, parameter changes and noise, the IDP algorithm is significantly better than other algorithms in the above three indicators. The ARI, AMI, and ACC values ​​presented are the average values ​​of 10 scenarios, as shown in Table 1.

[0146] Table 1 Comparison results of algorithms

[0147]

[0148] As can be seen, the IDP algorithm's ARI value of 0.924 is significantly higher than that of other algorithms; its AMI value of 0.935 is also the highest; and its ACC value of 0.948, compared to other algorithms, which are all around 0.9, fully demonstrates that IDP has superior clustering accuracy and robustness. Static DBSCAN and BGMM, as non-incremental algorithms, require all data to be loaded at once, ignoring the influence of time parameters. The DBSCAN algorithm has good discrimination capabilities for noise pulses, but requires a reasonable choice of parameters such as the neighborhood radius, otherwise it can easily merge different clusters or split the same cluster. The clustering quality of BGMM depends largely on the number of Gaussian distributions estimated in advance.

[0149] Algorithms usually have some user parameters that may affect the results and need to be fine-tuned. These parameters usually involve aspects such as the sensitivity, accuracy, and efficiency of the algorithm. As shown in Table 2, different algorithms have different parameters, for example:

[0150] IDP: threshold. As mentioned above, this is the similarity threshold used to determine whether two data points belong to the same class. If the distance between two data points is less than or equal to the threshold, they are considered to belong to the same class. A smaller threshold value makes the algorithm more sensitive and produces more clusters, but it may also lead to overfitting or noise.

[0151] Leader: Feature distance, a metric used to calculate the similarity between data points. Feature distances can be Euclidean, Manhattan, or cosine distances. The choice of feature distance depends on the data distribution and the type of features. Larger feature distances make it easier for the algorithm to group different data points into a single category, resulting in fewer clusters. However, this may also lead to underfitting or information loss.

[0152] DBSCAN: eps radius, which is a radius used to define a neighborhood. If a data point has a sufficiently large number of data points within its neighborhood (greater than or equal to min_samples), it is considered a core point; otherwise, it is a boundary point or a noise point. A larger eps radius makes it easier for the algorithm to group distant data points into one category, resulting in fewer clusters. However, this may also lead to overfitting or noise.

[0153] BGMM: n_components specifies the number of components used in the Gaussian mixture model. Each component represents a Gaussian distribution that describes a subset of the data. Larger values ​​for n_components allow the algorithm to capture more detail in the data and produce more clusters, but this can also lead to overfitting or increased computational complexity.

[0154] The average values ​​of ARI, AMI, and ACC are used to observe these effects. In this validation set, there are 11 categories in total;

[0155] Table 2 User parameter impact

[0156]

[0157] The IDP algorithm consistently achieved clustering results close to 11 categories at various threshold values, demonstrating that the algorithm is not sensitive to parameter selection. Furthermore, the number of clusters matches the actual number of categories, indicating that the algorithm effectively partitions the data. The algorithm's average evaluation index (ARI, AMI, and ACC) reached a maximum of 0.942 at a threshold of 0.6, indicating that the algorithm effectively maintains internal similarity and external diversity in the data, while also achieving high clustering accuracy.

[0158] The Leader algorithm obtains clustering results with more than 11 categories under different EPS values, indicating that the algorithm is sensitive to parameter selection. In addition, the number of clusters is different from the actual number of categories, indicating that the algorithm may separate some data points that belong to the same category.

[0159] The DBSCAN algorithm obtains clustering results with more than 11 categories under different EPS values. The algorithm is also sensitive to parameter selection. The number of clusters does not match the actual number of categories, and there is a more obvious batch phenomenon in this dataset.

[0160] The BGMM algorithm has relatively good results under different n_components values. However, the BGMM algorithm requires specifying the number of clusters. When the number of clusters is greater than the actual number of categories, the evaluation index will drop significantly. The BGMM computational complexity is also high because it needs to estimate the parameters of the Gaussian distribution of each component, and it assumes that the data follows a Gaussian distribution, which may not be true in reality.

[0161] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A radar pulse sorting method based on inverse distance weighted online clustering, characterized in that: The following steps are involved: Step 1: Construct radar signal samples. Based on the characteristics of modern radar signals, use Python to generate several pulse sequence samples with typical radar signal diversity. Step 2: Perform full clustering on the first 1000 pulse trains to obtain the initial cluster center list and category number; Step 3: Based on the pre-obtained initial cluster center list and category serial number, the remaining data is sorted in real time using single-sample inverse distance weighted similarity according to the time beat; Step 4: Real-time verification of the sorting results of step 3; Step 5: Repeat steps 3 and 4 until all data are sorted; Step 6: Repeat steps 3, 4, and 5 using the incremental Leader algorithm and the non-incremental DBSCAN and BGMM algorithms for comparative experimental verification; In step 3, based on the pre-obtained initial cluster center list and category serial number, the remaining data is sorted according to the time beat using single-sample inverse distance weighted similarity real-time signal sorting, specifically including the following steps: Given a pulse query point , a list of cluster centers of known classes , ,in The maximum index of the known class for full clustering and a pulse stream : ， in is the feature vector of the instance, ; Step 3.1: Calculation Compared with the currently known cluster centers The CF and DOA distance between: ； ； Step 3.2: Select the k cluster centers closest to each pulse feature, where k is n / 2 and n is the current number of clusters, recorded as: ； ； Step 3.3: Based on the inverse distance weighted similarity, calculate each exist The reciprocal of , ； in Is a small positive number used to avoid the denominator being zero. The calculated distance is converted into a reliable probability threshold. exist Normalize the similarity in the feature vector so that the probability of each set of features is 1, which is provided for subsequent sorting. ； Step 3.4: Get each Weight Afterwards, Perform weighted sum of similarities to obtain the total weight = ,according to Make a judgment and get Category ,Right now ； Among them, n represents the number of current categories, and threshold represents the threshold set by the similarity function.

2. The radar pulse sorting method based on inverse distance weighted online clustering according to claim 1, characterized in that: In step 1, the five-dimensional features of the radar signal sample including the radar pulse descriptor are first determined: : Arrival time, which indicates the time it takes for the pulse to reach the receiver, in seconds; : Center frequency, indicating the frequency center of the pulse, the unit is MHz; : Pulse width, which indicates the duration of the pulse in microseconds; : Amplitude, indicating the strength of the pulse, in volts; : Angle of arrival, indicating the direction of the pulse, in degrees; 1) Determine the arrival time based on the three modulation modes of radar, For a simple pulse radar, the first-order difference of arrival times is a constant: ； For frequency modulated continuous wave radar, the first-order difference of arrival time is a linear function of time: ； For nonlinear frequency modulation radar, the first-order difference of arrival time is a complex function of time: ； 2) Arrival angle varies from 0 degrees to 360 degrees The continuously varying angle of arrival is simulated by combining intercepted sine, cosine, polynomial, exponential, and linear functions: ； By giving different as well as The threshold range is used to simulate the changes in the arrival angles of different radar signals in the real electromagnetic world; 3) The center frequency range is from 1 GHz to 15 GHz, and the stable center frequency is described by a combination of a constant function and Gaussian noise: ； 4) Pulse width ranges from 0.05 μs to 35 μs, and the stable center frequency is described by a combination of a constant function and Gaussian noise: ； 5) The range of pulse amplitude variation. According to the definition of pulse amplitude, P is specified as a random number within a certain range: ； According to the rules, radar signal sources with different pulse number scales are simulated, and the arrival time of pulse width, center frequency, arrival angle and amplitude are plotted on the plane, with each point representing a pulse.

3. The radar pulse sorting method based on inverse distance weighted online clustering according to claim 1, characterized in that: In step 2, full pre-clustering is performed using the first 1000 radar signal samples. the following: For the first 1000 pulse trains ( ), perform full clustering and obtain the initial cluster center list and category number .

4. The radar pulse sorting method based on inverse distance weighted online clustering according to claim 1, characterized in that: In step 4, the sorting results in step 3 are verified in real time, and the experimental results are measured from three aspects: ARI, AMI, and ACC; 1) ARI algorithm. The value range of ARI is -1 to 1. The larger the value, the better the clustering result. The calculation formula for ARI is: ； in, It represents the number of combinations of selecting k elements from n elements. Indicates the clustering result Class and real class The number of samples that the class contains, Indicates the clustering result The number of samples of the class, Indicates the true category The number of samples of the class, represents the total number of samples; 2) AMI algorithm. The value range of AMI is 0 to 1. The larger the value, the better the clustering result. The calculation formula of AMI is: ； in, Represents the mutual information between the clustering results and the true category, and Represent the entropy of clustering results and true categories respectively, Represents the expected mutual information between the clustering results and the true category when randomly assigned; 3) The ACC algorithm is based on the Hungarian algorithm and is used to solve the maximum weight matching problem of bipartite graphs. The idea of ​​the ACC algorithm is to find a maximum weight matching so that each class in the clustering result corresponds to a class in the real class: ； in, is a The matrix, , It is the Hungarian matching algorithm; Finally, each time beat in step 3 is obtained Compare with the actual label and calculate the ARI, AMI, and ACC scores, and take their average as the metric, as follows: ； Here, score represents the average of ARI, AMI, and ACC scores.

Images