Multi-level radar signal sorting method and equipment based on pulse parameter cascading

Abstract

The invention discloses a multilevel radar signal sorting method and equipment based on pulse parameter cascading. The method comprises the steps of receiving radar pulse signals, constructing corresponding three-dimensional pulse description words, performing normalization processing, mapping the radar pulse signals into data points in a three-dimensional feature space, and calculating Euclidean distances to establish a distance matrix; calculating the local density of each pulse data point based on K neighbor and natural neighbor, introducing a relative local abnormal factor, and identifying and eliminating false alarm pulses; k-nearest neighbor search is executed again, the DBSCAN algorithm is adopted for primary pulse sorting, the neighborhood radius is constructed based on the third quartile and the quartile distance of the K-nearest neighbor distance, and the minimum point number threshold value is K value; based on inter-cluster K neighbor correlation and boundary natural neighbor connectivity, verification merging is carried out; and according to a preset PRI search range and step length, carrying out two-dimensional plane mapping on the arrival time sequence of each cluster pulse after combination, constructing a comprehensive judgment criterion to identify a real PRI and extract a pulse sequence, and obtaining a sorting result.

Description

A multi-level radar signal sorting method and device based on pulse parameter cascading Technical Field

[0001] This invention belongs to the field of electronic reconnaissance and signal processing technology, and specifically relates to a multi-level radar signal sorting method and device based on pulse parameter cascading. Background Technology

[0002] Radar signal sorting technology is a key component of Electronic Support Measures (ESM) systems. Its main task is to accurately separate pulse sequences belonging to the same radar source from a mixed pulse stream intercepted by the receiver, providing reliable foundational data for subsequent radar signal identification, threat assessment, and electronic countermeasures decision-making. With the continuous increase in electromagnetic environment complexity and the diversification of radar systems, the performance of the signal sorting stage has become a crucial factor affecting the overall effectiveness of electronic reconnaissance systems.

[0003] In the development of radar signal sorting technology, sorting methods based on Pulse Repetition Interval (PRI) constituted an early established technical system and have been widely used in engineering practice. These methods typically use the Time of Arrival (TOA) sequence as input and estimate the PRI value and its modulation pattern using algorithms such as Difference Histogram (CDIF), Sequential Difference Histogram (SDIF), and Cumulative Difference Histogram (CDIF). Then, the pulse sequence is assigned based on the PRI consistency criterion. Since PRI is an inherent time-domain characteristic parameter of the radar radiation source and exhibits relative stability under specific operating modes, this method can usually achieve high sorting accuracy in low-density, single-mode radar environments.

[0004] However, PRI-based sorting methods have certain limitations in complex scenarios: First, under conditions of dense multi-radiation sources, the probability of overlapping or similar PRI values ​​from different radars increases, easily leading to a decrease in sorting performance; second, for non-stationary modulation schemes such as agile PRI, staggered PRI, and jittery PRI, traditional PRI analysis algorithms have high computational complexity and poor separability; third, when the pulse stream contains false alarm pulses, pulse loss, or incomplete intercept sequences, the accuracy of PRI estimation relying solely on the TOA sequence is easily affected, thus reducing sorting reliability. Therefore, in electromagnetic environments with multiple schemes, high density, and non-stationary modulation, sorting strategies relying solely on PRI characteristics are difficult to maintain stable performance.

[0005] On the other hand, sorting methods based on Pulse Description Words (PDWs) have received considerable research and application in recent years. A PDW is a comprehensive description of the multidimensional characteristic parameters of a radar pulse, typically including parameters such as radio frequency (RF), pulse width (PW), direction of arrival (DOA), and pulse amplitude (PA). This type of method achieves the separation and merging of radar pulse sequences by performing clustering or pattern matching in a multidimensional feature space. Its main advantages are: no need for complex PRI modulation analysis, resulting in a relatively simple processing flow; the ability to utilize multidimensional information for joint decision-making, thereby improving anti-jamming capabilities; and a certain degree of adaptability to radars with agile parameters or diverse systems. With the development of machine learning and deep learning, PDW sorting schemes based on intelligent algorithms such as neural networks, support vector machines, and fuzzy clustering have been continuously proposed, improving the overall sorting performance to a certain extent.

[0006] However, PDW-based sorting methods still face several problems in engineering applications: First, these methods typically require preset input parameters such as the number of clusters, distance threshold, and membership degree. These parameters are significantly affected by signal conditions and noise levels, making it difficult to achieve uniform and adaptive settings in different environments, resulting in insufficient algorithm robustness. Second, in complex electromagnetic environments, the PDW parameters of different radars may overlap or partially aliased. For example, radars with similar operating frequencies, pulse widths, and adjacent azimuths of arrival may be difficult to distinguish effectively using only PDW. Furthermore, for multi-functional radars, the switching of their operating modes causes significant temporal changes in PDW parameters, inevitably leading to different modes of the same radar being mistakenly classified as multiple radiation sources (over-batching) or multiple radars with similar parameters being incorrectly merged into the same radiation source (missed batching), thus affecting sorting accuracy and the reliability of subsequent threat assessment.

[0007] In summary, existing radar signal sorting methods mostly employ a single-level processing architecture. When faced with overlapping parameters, false alarm pulses, multi-functional radars, and non-stationary modulation schemes, single-level sorting strategies struggle to balance accuracy and robustness. Therefore, combining the complementary advantages of PRI and PDW features to construct a hierarchical, collaborative, and information-cascaded comprehensive sorting framework has clear engineering application significance and research value. Summary of the Invention

[0008] To overcome the problems of insufficient sorting stability, limited robustness, and decreased adaptability of existing radar signal sorting methods in complex electromagnetic environments such as dense multi-radiation sources, parameter overlap, non-stationary PRI modulation, false alarms and lost pulses, and multi-functional radar mode switching, and to improve the accuracy, stability, and environmental adaptability of signal sorting, this invention proposes a multi-level radar signal sorting method based on pulse parameter cascading. This method achieves effective separation and merging of homogeneous pulse sequences in a mixed pulse stream by hierarchically fusing and cascading constraints on multi-dimensional parameters of the pulse descriptor word (PDW) and pulse timing characteristic parameters.

[0009] In view of this, the present invention proposes a multi-level radar signal sorting method based on pulse parameter cascading, comprising: Step 1: receiving radar pulse signals within a set time period, constructing a corresponding three-dimensional pulse descriptor based on the carrier frequency, pulse width, and angle of arrival of each pulse signal, and performing normalization processing to map it into data points in a three-dimensional feature space, and calculating the Euclidean distance between any two points to establish a distance matrix; Step 2: calculating the local density of each pulse data point based on K-nearest neighbors and natural nearest neighbors, introducing a relative local anomaly factor, and identifying and eliminating false alarm pulses; Step 3: re-executing the pulse data after eliminating false alarms. K-nearest neighbor search is used, and the DBSCAN algorithm is used for initial pulse sorting. The neighborhood radius is constructed based on the third quartile and interquartile range of the K-nearest neighbor distance, and the minimum number of points threshold is taken as the value of K. Step 4: Based on the K-nearest neighbor correlation between clusters and the natural nearest neighbor connectivity of the boundary, the clusters are verified and merged. Step 5: According to the preset PRI search range and step size, the arrival time series of pulses of each merged cluster are mapped in two-dimensional plane. By constructing a comprehensive decision criterion by statistical histogram counting sequence features, the real PRI is identified and the corresponding pulse sequence is extracted to obtain the complete radar pulse sorting results.

[0010] Preferably, the distance matrix established in step 1 for dimension, where n represents the total number of received pulse signals. It is symmetrical and its diagonal elements are 0.

[0011] Preferably, step 2 calculates the local density of each pulse data point based on K-nearest neighbors and natural nearest neighbors, including: initialization For the first pulse signal Calculate its K nearest neighbor set and natural neighbors Determine whether all pulses have at least one natural nearest neighbor. If not, then let... And continue iterating; if the judgment is yes, then the current value of K is determined, and at the same time, the result is obtained. The K-nearest neighbor set and the natural nearest neighbor set; where For each set of natural nearest neighbors It employs a Gaussian kernel function as the weighting function and is based on a global adaptive bandwidth strategy, with bandwidth parameters... Take the minimum distance from all data points to their Kth nearest neighbor, and calculate the result. Local density :

[0012] in, Distance matrix The Okay, number The elements of the column.

[0013] Preferably, the relative local anomaly factor in step 2 for:

[0014] for The average density of K-nearest neighbors:

[0015] when At that time, the corresponding Mark as a false alarm and remove.

[0016] Preferably, the setting of the neighborhood radius and minimum number of points threshold in step 3 includes the following steps: for the pulse set after removing false alarms, the number of pulses is m, Collect K-nearest neighbor distances to form a distance sequence ,in Given the m-th pulse in the pulse set, calculate the first quartile of this distance sequence. Third and quartiles The interquartile range is obtained. Set the neighborhood radius parameter according to the following formula. :

[0017] in, For adjustment coefficients, Minimum number of points threshold .

[0018] Preferably, step 3 re-executes the K-nearest neighbor search on the pulse data after removing false alarms, and uses the DBSCAN algorithm for initial pulse sorting, including: Step 3-1: Initialize the m pulse data after removing false alarms, and mark them all as unvisited; Step 3-2: Traverse each unvisited pulse data. Calculate its - Neighborhood Step 3-3: If Then Mark as the core point, create a new cluster and All points are added to the cluster; Step 3-4: For each point in the cluster, if it is also a core point, its neighboring points are added to the cluster to achieve density-reachable cluster expansion; Step 3-5: When all points have been visited, points not assigned to any cluster are marked as false alarm pulses, thus obtaining the preliminary sorting results, denoted as ,in Indicates pulse Cluster label; if The corresponding pulse and Belonging to the same radar radiation source; when When, it means It was determined to be a residual false alarm pulse; when When, it means The pulse sequence belonging to the k-th cluster and corresponding to the k-th radar radiation source is denoted as the effective cluster set obtained from the initial sorting. ,in The total number of clusters, each cluster A corresponding set of tag values Data points.

[0019] Preferably, step 5 includes: for any two clusters and If the following conditions are met simultaneously, the two clusters are determined to originate from the same radar radiation source and a merging operation is performed:

[0020] in, This represents the set of points that are both natural neighbors of two clusters and are clustered together. Cluster and The correlation index between them satisfies the following formula:

[0021] in, For data points The set of K nearest neighbors, Representing data points K-nearest neighbors belong to cluster The point set, Let be the cardinality of the point set.

[0022] Preferably, the feature quantity in step 5 includes: skewness. kurtosis Ratio of mean to median They respectively satisfy the following formulas:

[0023] in, The mean of the histogram counts. The central moment is the third order. Standard deviation The number of equal-width bins used to divide the relative position intervals after mapping the two-dimensional plane; Indicates the first Each box;

[0024] in, It is the fourth-order central moment;

[0025] in, Let be the median of the histogram counting sequence; the constructed comprehensive decision criterion is: like If the corresponding histogram counting sequence simultaneously satisfies the comprehensive judgment criterion, then it is determined that... This is the true PRI.

[0026] On the other hand, the present invention provides an electronic reconnaissance device, comprising: a processor and a memory, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described multi-level radar signal sorting method based on pulse parameter cascading.

[0027] Compared with existing technologies, the advantages of this invention are as follows: 1. Addressing the problem of difficulty in adaptively determining input parameters in PDW-based sorting technology, this invention proposes an adaptive parameter determination mechanism that combines natural nearest neighbor metric and bit statistics. This mechanism can automatically estimate clustering scale parameters and decision thresholds based on the distribution characteristics of pulse parameters, thereby achieving effective dilution processing of mixed pulse streams and providing stable and reliable input conditions for subsequent hierarchical sorting processes.

[0028] 2. To address the challenges of PRI estimation and simultaneous pulse extraction in non-stationary PRI modulation modes and dense radiation source scenarios, this invention employs a joint search strategy based on a two-dimensional PRI plane. This strategy can simultaneously extract and merge the corresponding radiation source pulse sequences while determining the PRI value, achieving integrated processing of PRI analysis and pulse attribution determination, effectively improving PRI sorting capabilities under complex conditions.

[0029] 3. To address the sorting failures, batch additions, and missed batches caused by pulse parameter aliasing between different radiation sources, this invention constructs a comprehensive multi-level sorting model based on the cascaded constraint of "pulse descriptor – pulse repetition interval". This model establishes a multi-feature collaborative decision mechanism, enabling complementary decision relationships between different feature dimensions, effectively reducing the risk of misclassification under single feature failure conditions, and improving distinguishability and sorting stability under pulse parameter overlap conditions.

[0030] 4. To address the decline in sorting robustness caused by the coexistence of multiple non-ideal factors such as false alarm pulses and pulse loss, this invention constructs an anomaly identification model in the PDW three-dimensional feature space. False alarm rejection is implemented in both the PDW clustering sorting and PRI extraction stages, forming a multi-layered denoising mechanism. Furthermore, the method of this invention exhibits strong insensitivity to pulse loss, maintaining high sorting accuracy and robustness even in complex environments where false alarm pulses and lost pulses coexist. Attached Figure Description

[0031] Figure 1 is a schematic diagram of the PDW three-dimensional feature space; Figure 2 is a schematic diagram of pulse sorting based on density clustering algorithm; Figure 3 is a flowchart of a multi-level radar signal sorting method based on pulse parameter cascading. Detailed Implementation

[0032] Based on a radar radiation source reconnaissance system, radar radiation source pulse signals within a designated reconnaissance area are intercepted and detected. The received radar electromagnetic pulse signals are preprocessed to obtain corresponding pulse parameters. The method includes: Step 1) Constructing a corresponding three-dimensional pulse descriptor (PDW) based on the pulse signal's carrier frequency, pulse width, and angle of arrival, and normalizing each dimension. Based on the normalized feature data, the three-dimensional PDW of each pulse signal is mapped to data points in a three-dimensional feature space. The data points corresponding to all pulse signals together constitute the PDW's three-dimensional feature space. On this basis, the Euclidean distance between any two data points in the feature space is calculated, and a distance matrix is ​​formed accordingly.

[0033] Step 2) Set up a K-nearest neighbor search mechanism. While determining the K value, calculate the K-nearest neighbor and natural nearest neighbor for each radar pulse. Based on the K-nearest neighbor distance and natural nearest neighbor, use a weighting function to calculate the local density of each pulse data point. To avoid instability caused by the absolute density threshold, a relative local anomaly factor is introduced as a discrimination index. When the local density of a pulse is significantly lower than the average level of its K-nearest neighbor data points, that is, its relative local anomaly factor is significantly greater than 1, the data point is judged as a false alarm pulse and is removed.

[0034] Step 3) After the initial false alarm pulse removal, the K-nearest neighbor search is re-executed to update the K value and the corresponding nearest neighbor relationships. Based on this, the DBSCAN algorithm is used for initial pulse sorting. The parameter Eps is constructed based on the third quartile and interquartile range of the K-nearest neighbor distance of the data points to reflect the local distribution of the pulse feature space; the parameter minPts uses the K value as the point threshold. DBSCAN clustering is performed using the determined parameters to achieve pulse sorting and further remove residual false alarm pulses.

[0035] Step 4) Based on the initial pulse sorting obtained in Step 3), to avoid the "batch increase" phenomenon of radar radiation sources caused by factors such as multi-function radar mode switching and PDW parameter changes, the existing clusters are verified for correlation and boundary connectivity based on the inter-cluster K-nearest neighbor and natural nearest neighbor sets. When any cluster satisfies both the inter-cluster correlation criterion and the boundary connectivity requirement with other clusters, the two clusters are determined to have the same source and cluster merging is performed to complete the cluster integration process.

[0036] Step 5) Based on the cluster merging results obtained in Step 4), to address the "missed batch" problem caused by pulses from different radiation sources being mistakenly merged into the same cluster due to similar PDW parameters, a PRI search and verification mechanism is introduced. According to the preset PRI search range and step size, the TOA sequences of pulses in each cluster are mapped in a two-dimensional plane, and the number of histogram bins is determined by the mapping width. For each searched PRI value, its histogram bin count sequence is statistically analyzed. The bin counts corresponding to the true PRI exhibit a strong right-skewed long-tail distribution characteristic, with a few significantly large values ​​and most values ​​close to zero. Based on this statistical characteristic, the skewness, kurtosis, and mean-median ratio of the bin count sequence are calculated, and a comprehensive decision criterion is constructed to identify the true PRI and extract the TOA sequences of the corresponding histogram bins. Subsequently, only the TOA sequences of the bins corresponding to the maximum values ​​of the true PRI are extracted to further clean up residual false alarm pulses. The above PRI determination and sequence extraction process is sequentially performed on each cluster obtained in Step 4), ultimately obtaining the complete pulse sorting results for each radar radiation source.

[0037] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0038] Example 1, as shown in Figure 3, provides a highly fault-tolerant radar signal sorting method based on improved planar transformation, comprising the following steps: 1. Constructing a PDW three-dimensional feature space, assuming the radar reconnaissance system receives during the reconnaissance period... A pulse signal, denoted as Its corresponding pulse descriptor set is For the first pulse signal Its pulse description word is , , , They represent the first The original pulse width, angle of arrival, and carrier frequency of each pulse signal. Correspondingly, the TOA sequence includes the arrival times of the pulse sequence as follows: .

[0039] To eliminate the influence of different physical dimensions on the feature space construction, a min-max normalization method is used to normalize the pulse width, carrier frequency, and angle of arrival dimensions separately: For the pulse width dimension: (1) For the carrier frequency dimension: (2) For the angle of arrival dimension: (3) Among them, , , They represent the first The normalized eigenvalues ​​of a pulse signal in the dimensions of carrier frequency, pulse width, and angle of arrival, where the normalized eigenvalues ​​are all in the range [0,1], then the normalized pulse descriptor is: It can be mapped to data points in a three-dimensional feature space. Its coordinates are represented as: (4) All Data points corresponding to each pulse signal Together they constitute the PDW three-dimensional feature space Figure 1 shows a schematic diagram of the PDW three-dimensional feature space. To quantify the similarity between pulse signals within the feature space, the similarity between any two pulse data points is calculated. and The Euclidean distance between them is defined as follows: (5) Based on the above Euclidean distance calculation, construct 3D distance matrix Its elements Indicates the first The pulse signal and the first The distance between pulse signals: (6) The distance matrix is ​​symmetric, that is... diagonal elements The three-dimensional spatial features and distance matrix provide a quantitative basis for subsequent analysis.

[0040] 2. False Alarm Impulse Removal Based on Local Density: Based on the distance matrix obtained in the preceding steps... ,for Its K-nearest neighbor set Defined as distance The most recent K pulses (excluding) itself): (7) express According to distance The rank after ascending order. The K-nearest neighbor relation establishes a one-way proximity relationship between data points, i.e., if... , only indicates yes Neighbors, but not guaranteed Too The neighbors. To more accurately characterize the proximity relationships between data points, this invention introduces the concept of natural nearest neighbors. If yes K nearest neighbor, at the same time Too The K nearest neighbors are called for The natural nearest neighbor, mathematically expressed as: (8) Natural neighbors embody a two-way proximity relationship, that is, "I treat you as my neighbor, and you treat me as your neighbor." for The number of natural neighbors, i.e. Obviously And when it is in a sparse region or at the boundary of a cluster, It may be significantly smaller than K.

[0041] To determine a suitable K value and simultaneously obtain the K nearest neighbors and natural nearest neighbors for each radar pulse, the following iterative search mechanism is adopted: Initialization For each radar pulse data point Calculate its K-nearest neighbor set and natural neighbors Check whether all pulses have at least one natural nearest neighbor, i.e. If this condition is not met, then let The process continues iterating; if the condition is met, the current K value is determined, and the K-nearest neighbor set and natural nearest neighbor set for each pulse are obtained. This search mechanism ensures that each pulse can find at least one neighbor with a bidirectional proximity relationship, thus providing a reliable basis for subsequent local density calculations.

[0042] Traditional density estimation methods typically rely on K-nearest neighbors for calculation. However, since K-nearest neighbors may include one-way neighbors with weak connections to the center point, density estimation can be biased. This invention employs a density estimation method based on natural nearest neighbors. The fundamental idea is that only points with bidirectional proximity to the current point truly represent the density characteristics of the region where that point is located. The local density is defined as: (9) of which This is the weighting function, used to weight the contribution of neighbors based on distance; closer neighbors contribute more to the density. The weighting function uses a Gaussian kernel function. (10) of which The bandwidth parameter controls the local scale of density estimation. This invention employs a global adaptive bandwidth strategy, denoted as... for The bandwidth parameter h is defined as the distance to its Kth nearest neighbor, i.e., the point farthest from the K nearest neighbors. (11) The minimum distance from all data points to their Kth nearest neighbor is taken as the global bandwidth, ensuring sufficient resolution in dense regions while avoiding excessive noise in sparse regions. Therefore, The formula for calculating the integrity of local density is: (12) Among them, Distance matrix The Okay, number The elements of the column.

[0043] Considering that absolute density values ​​may vary by orders of magnitude in different regions, it is difficult to set a uniform absolute density threshold for false alarm detection. To address this issue, this invention draws on the relative comparison concept of the Local Outlier Factor (LOF) and defines the Relative Local Outlier Factor (RLOF): (13) of which for The average density of K-nearest neighbors: (14) RLOF provides a relative measure of anomaly by comparing the density relationship between data points and their neighbors. When When, it means The density of the pulse is comparable to the average density of its natural neighbors, consistent with the surrounding environment, and is considered a normal radar pulse; when When, it means The density of a point is significantly lower than the average density of its natural neighbors, indicating that the point is exceptionally sparse relative to its neighborhood. Therefore, it is marked as a false alarm and removed from subsequent processing. When, it means A point whose density is higher than the average density of its natural neighbors is located in a relatively dense area, typically the core region of a cluster. Let the set of pulses after removing false alarms be denoted as . The number of pulses is ,in Accordingly, from the original distance matrix Extract the rows and columns corresponding to the retained pulses and reconstruct a new distance matrix. This provides high-quality input data for subsequent signal sorting and parameter estimation.

[0044] 3. After the initial false alarm pulse removal, the distribution structure of the pulse signal changes, and the original K-nearest neighbor relationships are no longer fully applicable. Therefore, it is necessary to re-execute the K-nearest neighbor search mechanism on the retained radar pulse data to update the K value and the corresponding nearest neighbor relationships. After determining the K value and the nearest neighbor relationships, the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm is applied to perform the initial pulse sorting. DBSCAN is a density-based clustering algorithm that can discover clusters of arbitrary shapes and automatically identify noise points, making it very suitable for radar pulse sorting scenarios. It relies on two key parameters: neighborhood radius. (Eps) and the minimum number of points minPts.

[0045] The neighborhood radius Eps defines the neighborhood range of a data point, that is, a range with a radius of 10 ... All points within the hypersphere constitute its neighborhood. This parameter controls the spatial scale of density determination: too small a scale results in most points being labeled as noise, forming too many small clusters; too large a scale leads to the merging of different clusters, reducing sorting accuracy. Therefore, The settings need to reflect the local distribution characteristics of the dataset. The minimum number of points, minPts, defines the minimum number of neighboring points required for a point to become a core point. If a point's hypersphere neighborhood contains at least minPts points, then that point is considered a core point and can be used as the center of a cluster for outward expansion; otherwise, the point may be a boundary point or a noise point. Therefore, the setting of minPts affects the cluster density threshold: a value that is too small will treat sparse regions as valid clusters, leading to false alarms; a value that is too large may miss real but smaller clusters.

[0046] To reasonably determine the parameters mentioned above, this invention constructs them based on the statistical characteristics of the K-nearest neighbor distance of data points. The K-nearest neighbor distances of all data points are collected to form a distance sequence. Calculate the third quartile of this distance sequence. and interquartile range ,in The first quartile is the first quartile. The third quartile reflects the local neighborhood scale of 75% of the points in the dataset, while the interquartile range measures the dispersion of the distance distribution. Based on these two statistics, the neighborhood radius parameter is set as follows: (15) of which This is the adjustment coefficient, typically taking the value of... In this embodiment, the standard value is 1. As a benchmark value, It can cover most of the local neighborhood of a normal pulse; As an extension variable, it adapts to the discreteness of the data distribution. This method is robust to outliers and is not easily affected by extreme distance values.

[0047] Regarding the determination of the parameter minPts, this invention directly uses the updated K value as the minimum number of points threshold, that is: (16) The principle behind this setting is that the K value is determined through a natural nearest neighbor search mechanism, ensuring that each data point has at least one bidirectional neighbor, reflecting the inherent neighborhood structure of the dataset. Setting minPts to K means that the neighborhood of a core point must contain at least K points, which is consistent with the concept of K-nearest neighbors, ensuring sufficient density support around the core point. At the same time, since the K value is determined adaptively by data, minPts can also automatically adapt to the characteristics of different datasets without manual parameter tuning. This setting ensures the density requirements of the clusters while avoiding the subjectivity of parameter selection.

[0048] Based on the parameters determined above And minPts, execute the DBSCAN clustering algorithm, as shown in Figure 2, which is a schematic diagram of pulse sorting based on this density algorithm. The execution process of the algorithm is as follows: (1) Initialize all points to an unvisited state; (2) Traverse each unvisited point Calculate its - Neighborhood (3) If Then Mark as the core point, create a new cluster and (4) For each point in the cluster, if it is also a core point, add the points in its neighborhood to the cluster to achieve density-reachable cluster expansion; (5) Repeat the above process until all points are visited; (6) Points not assigned to any cluster are marked as false alarm pulses.

[0049] This led to preliminary sorting results. (Note: The original text contains a note about the process.) For the set of sorting labels, where Indicates pulse Cluster labels. Data points with the same label indicate that they come from the same cluster class, i.e., if... ,but and They belong to the same radar radiation source. The meanings of the label values ​​are as follows: When When, it means It was determined to be a residual false alarm pulse; when When, it means The pulse sequence belonging to the k-th cluster and corresponding to the k-th radar radiation source is denoted as the effective cluster set obtained from the initial sorting. ,in The total number of clusters, each cluster A corresponding set of tag values The data points. It should be noted that false alarm pulses with a label of -1 do not constitute a valid cluster and are not included in the subsequent cluster merging process.

[0050] 4. Cluster merging based on inter-cluster correlation and boundary connectivity: In actual radar signal environments, multi-functional radars often have multiple operating modes. Such parameter changes may cause the same radar radiation source to be identified as multiple independent clusters at different times, resulting in the so-called "batch addition" phenomenon, that is, a radar radiation source is incorrectly divided into multiple batches.

[0051] To address this issue, this invention proposes a cluster merging strategy based on inter-cluster correlation and boundary connectivity. The core idea of ​​this strategy is that if two clusters should belong to the same radar radiation source, they should exhibit correlation characteristics in both statistical properties and topological structure. Therefore, for any two clusters... and This invention determines whether clusters should be merged by calculating inter-cluster correlation and boundary connectivity.

[0052] Inter-cluster correlation reflects the degree of statistical association between two clusters in the K-nearest neighbor structure. If two clusters do indeed originate from the same radar radiation source, then when searching for K-nearest neighbors, a significant proportion of the data points in one cluster should fall into the other cluster. Define a cluster. and The correlation index between them is: (17) of which For data points The set of K nearest neighbors, Representing data points K-nearest neighbors belong to cluster The point set, This is the cardinality of the point set. This index is normalized by summing the cross-cluster nearest neighbor counts of all points in both clusters and dividing by K to obtain the average association strength between clusters. When When the K nearest neighbors of at least some data points cross the cluster boundary, it indicates that the two clusters are statistically correlated in the feature space.

[0053] Boundary connectivity verifies whether two clusters should be merged from a topological perspective. If two clusters share a natural nearest neighbor relationship in the feature space, meaning some boundary points are each other's natural nearest neighbors, then the two clusters are spatially connected and may belong to the same larger cluster. Defining a cluster. and The set of boundary connected points is: (18) of which For data points The natural neighborhood set, Cluster The union of the natural neighbors of all points. This represents the set of points that appear simultaneously in the natural nearest neighbors of two clusters and are clustered together; that is, data points that are considered natural nearest neighbors by both clusters. These points are located in the boundary region between the two clusters, acting as a bridge connecting them. When the condition is met, it indicates that there is at least one data point that has a bidirectional proximity relationship with points in two clusters, indicating that the two clusters are topologically connected.

[0054] Based on the above two indicators, this invention adopts the following merging criterion: for any two clusters and If the following conditions are met simultaneously, the two clusters are determined to originate from the same radar radiation source and a merging operation is performed: (19) This criterion requires both inter-cluster correlation and boundary connectivity to be satisfied simultaneously, ensuring the reliability of the merging decision. The rationale for this design is that inter-cluster correlation reflects the consistency of statistical characteristics, and the similarity of the two clusters in feature distribution is verified through the cross-validation of the K-nearest neighbor structure; boundary connectivity reflects the continuity of the topological structure, and the spatial connectivity of the two clusters is verified through natural nearest neighbor connections. Only when both conditions are met simultaneously can it be fully confirmed that the two clusters do indeed originate from the same radar radiation source. This avoids both the erroneous merging of clusters from different radiation sources due to accidental similarity in statistical characteristics and the merging of essentially different clusters due to accidental topological connectivity, effectively avoiding the "batch addition" phenomenon.

[0055] When performing cluster merging, an iterative merging strategy is used: traversing all cluster pairs. ,calculate and If the merging criterion is met, then the cluster will be merged. All data points are relabeled as clusters The labels are updated, and the cluster label set is updated. Repeat this process until no more cluster pairs meet the merging criteria, at which point the initial merging process is complete. To ensure the continuity and standardization of labels, all valid cluster classes after merging are re-encoded sequentially, and the labels are updated accordingly. ,in The total number of clusters after batching is obviously The updated set of sorting labels is denoted as . The set of clusters is denoted as It should be noted that the sorting label set and cluster set have been updated at this point, and their labels... and clusters The difference from the above and The tags and clusters are now complete, thus consolidating the cluster integration process.

[0056] 5. Cluster Sorting and Pulse Extraction Based on PRI Search: Based on the cluster merging results obtained in step 4, the updated cluster label set is as follows. Although the PDW parameter-based sorting and batch processing has largely achieved pulse sorting of different radar radiation sources, in actual electromagnetic environments, multiple radar radiation sources with similar PDW parameters (such as carrier frequency, pulse width, angle of arrival, etc.) may still be misclassified as the same radiation source, resulting in the so-called "missed batch" phenomenon, where pulses from different radiation sources that should be separated are incorrectly merged into the same cluster. To solve this problem, this invention introduces PRI (Pulse Repetition Interval)-based search and verification to implement a second-layer sorting mechanism. By performing PRI search and statistical analysis on the pulse arrival time (TOA) sequence in the time domain, pulses from different radiation sources are further distinguished, thereby achieving re-sorting after the initial PDW parameter-based sorting.

[0057] For each cluster Extract the TOA sequence of all pulses in the cluster. Preset PRI search range. and search step size The search space is discretized into a series of candidate PRI values. For each candidate PRI value... A two-dimensional planar mapping is performed on the TOA sequence. The principle of this mapping method is as follows: if a candidate PRI is close to the real PRI, then the arrival time of the pulses should exhibit a periodic pattern. If the candidate PRI is the real PRI, then most of the relative positions should be concentrated near a few positions; if the candidate PRI is not the real PRI, then the relative positions will be approximately uniformly distributed.

[0058] To quantify this distribution characteristic, the mapped relative position intervals are divided into: Divide the data into equal-width bins. Count the pulses within each bin to form a histogram counting sequence. .when When approaching the true PRI (Radar Pulse Response), the histogram counting sequence exhibits a typical strong right-skewed long-tailed distribution: a few bins (usually corresponding to the arrival location of the true pulse) have significantly large count values, while the count values ​​of most bins (false alarm pulses and other radar pulse emission sources of the PRI) are close to zero or very small. This distribution can be quantitatively described as follows: Suppose the histogram counting sequence has... The count value of this bin is significantly greater than that of the other bins. Record this value as... The maximum value is Its average value is Remaining The minimum value is Its average value is .

[0059] Based on the aforementioned distribution characteristics, this invention employs three statistical features to distinguish candidate PRIs: skewness, kurtosis, and mean-median ratio. These features characterize the degree of right skewness and concentration of the distribution from different perspectives.

[0060] Skewness is an indicator of the symmetry of a distribution, defined as the standardized third central moment: (20) of which The mean of the histogram counts. The central moment is the third order. The standard deviation is given. For a strongly right-skewed distribution, the skewness is significantly greater than 0. Through theoretical derivation, when the histogram counts show... Largest values ​​and When dealing with a binary distribution of small values, the skewness threshold is set as follows: (21) When the calculated skewness When the value exceeds this threshold, it indicates that the histogram count exhibits a significant right-skewed characteristic, and the candidate PRI may be the true PRI.

[0061] Kurtosis is a measure of the sharpness and thickness of the tails of a distribution, defined as the normalized fourth central moment minus 3: (22) of which Let be the fourth-order central moment. For a strongly right-skewed, long-tailed distribution, the kurtosis is significantly greater than 0, reflecting the "heavy-tailed" characteristic of the distribution caused by the existence of a few maxima. Through similar theoretical derivation, the kurtosis discrimination threshold is set as: (23) When the calculated kurtosis When the value exceeds this threshold, it indicates that the histogram count has significant heavy-tailed characteristics, further verifying that the candidate PRI may be the real PRI.

[0062] The mean-median ratio is another simple and effective indicator of the degree of distribution skewness. For right-skewed distributions, a few maxima can significantly inflate the mean, while the median, as a location statistic, is unaffected by extreme values; therefore, the mean is usually much larger than the median. The mean-median ratio is defined as: (24) of which This is the median of the histogram counting sequence. For a severely right-skewed distribution, this ratio should be greater than 1. The discrimination criterion is set as follows: (25) When this condition is met, it indicates that there is a significant right-skewed feature in the histogram count, supporting the hypothesis that the candidate PRI is the true PRI.

[0063] Based on the above three statistical characteristics, a comprehensive judgment criterion is set: if The corresponding histogram counting sequence simultaneously satisfies the following three conditions: (26) Then determine The candidate PRI is considered a true PRI. This comprehensive discrimination criterion performs multiple verifications on the candidate PRI from three dimensions: symmetry, sharpness, and concentration of the distribution, ensuring the reliability of the discrimination results and effectively avoiding misjudgments.

[0064] Once the true PRI is determined, the TOA sequence corresponding to the bin with the maximum count value in the histogram is further extracted. Specifically, the histogram count sequence is identified. Maximum binning is performed. For each maximum bin, its corresponding sequence pulse and TOA value are extracted. The remaining unextracted pulse data points are considered residual false alarm pulses and are discarded.

[0065] For each cluster class obtained in step 4 The PRI determination and sequence extraction processes described above are executed sequentially. If multiple true PRIs are identified in a cluster, it indicates that the cluster indeed contains pulses from multiple different radiation sources (i.e., "missed batches"). In this case, the cluster is further divided into multiple sub-clusters based on the TOA sequences corresponding to different PRIs. After iterative processing, the complete pulse sorting results for each radar radiation source are finally obtained. The updated final cluster label set is denoted as... The final set of clusters is denoted as ,in This represents the final number of radar radiation source clusters. At this point, the two-stage sorting based on PDW parameters and PRI information was completed, achieving high-precision separation of multiple radar radiation source pulses and providing a reliable data foundation for subsequent radiation source identification and threat assessment.

[0066] Example 2 An electronic reconnaissance device provided in Example 2 of the present invention includes: at least one processor, a memory, at least one network interface, and a user interface. The various components of the device are coupled together via a bus system. It is understood that the bus system is used to enable communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0067] The user interface may include a display, keyboard, or clicking device (e.g., mouse, trackball, touchpad, or touchscreen).

[0068] It is understood that the memory in the embodiments disclosed in this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0069] In some implementations, the memory stores elements such as executable modules or data structures, or subsets thereof, or extended sets thereof: operating systems and applications.

[0070] The operating system includes various system programs, such as the framework layer, core library layer, and driver layer, used to implement various basic business functions and handle hardware-based tasks. The application programs include various applications, such as media players and browsers, used to implement various application functions. Programs implementing the methods of the embodiments of this disclosure can be included in the application programs.

[0071] In the above embodiments, the processor can also execute the steps of the method of embodiment 1 by calling a program or instruction stored in the memory, specifically a program or instruction stored in an application program.

[0072] The method of Embodiment 1 can be applied to a processor or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in Embodiment 1. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in Embodiment 1 can be directly implemented by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0073] It is understood that the embodiments described in this invention can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0074] For software implementation, the technology of this invention can be implemented by executing the functional modules (e.g., procedures, functions, etc.) of this invention. The software code can be stored in memory and executed by a processor. The memory can be implemented in the processor or externally.

[0075] Simulation Example: The effectiveness of this invention can be verified using the following simulation data: Nine radar radiation sources are set up, and their radiation source parameters are shown in Table 1. To simulate a real-world scenario, the radar clusters are similar in certain dimensions and the number of pulses is uneven, with overlapping parameters in the PDW and PRI dimensions of each radar. Based on the parameter information provided in Table 1, radar pulse descriptor word (PDW) data received by the receiving station is generated. A random false alarm rate of 5-30% is set for this sequence, and a 10% pulse loss rate is also set.

[0076] Table 1 Radar radiation source parameters

[0077] Using the accuracy ACC, adjusted mutual information (AMI), adjusted Rand index (ARI), and Fowlkes-Mallows index (FMI), the specific sorting results of the examples are shown in Table 2.

[0078] Table 2 Sorting Results of Simulation Examples

[0079] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-level radar signal sorting method based on pulse parameter cascading, comprising: Step 1: Receive radar pulse signals within a set time period. Construct a corresponding 3D pulse descriptor based on the carrier frequency, pulse width, and angle of arrival of each pulse signal, and perform normalization processing to map it into data points in a 3D feature space. Calculate the Euclidean distance between any two points to establish a distance matrix. Step 2: Calculate the local density of each pulse data point based on K-nearest neighbors and natural neighbors. Introduce a relative local anomaly factor to identify and remove false alarm pulses. Step 3: Re-execute K-nearest neighbor search on the pulse data after removing false alarms. Use the DBSCAN algorithm for initial pulse sorting. The neighborhood radius is constructed based on the third quartile and interquartile range of the K-nearest neighbor distance, and the minimum number of points threshold is set to K. Step 4: Verify and merge clusters based on the K-nearest neighbor correlation between clusters and the natural neighbor connectivity at the boundary. Step 5: Based on the preset PRI search range and step size, perform 2D plane mapping on the arrival time series of the merged cluster pulses. Construct a comprehensive decision criterion by statistical histogram counting sequence features, identify the real PRI, extract the corresponding pulse sequence, and obtain the complete radar pulse sorting result.

2. The multi-level radar signal sorting method based on pulse parameter cascading according to claim 1, characterized in that, The distance matrix established in step 1 for dimension, where n represents the total number of received pulse signals. It is symmetrical and its diagonal elements are 0.

3. The multi-level radar signal sorting method based on pulse parameter cascading according to claim 2, characterized in that, Step 2 calculates the local density of each pulse data point based on K-nearest neighbors and natural nearest neighbors, including: initialization For the first pulse signal Calculate its K nearest neighbor set and natural neighbors Determine whether all pulses have at least one natural nearest neighbor. If not, then let... And continue iterating; if the judgment is yes, then the current value of K is determined, and at the same time, the result is obtained. The K-nearest neighbor set and the natural nearest neighbor set; where For each set of natural nearest neighbors It employs a Gaussian kernel function as the weighting function and is based on a global adaptive bandwidth strategy, with bandwidth parameters... Take the minimum distance from all data points to their Kth nearest neighbor, and calculate the result. Local density ： ;in, Distance matrix The Okay, number The elements of the column.

4. The multi-level radar signal sorting method based on pulse parameter cascading according to claim 3, characterized in that, The relative local anomaly factor in step 2 for: ； for The average density of K-nearest neighbors: ;when At that time, the corresponding Mark as a false alarm and remove.

5. The multi-level radar signal sorting method based on pulse parameter cascading according to claim 3, characterized in that, The setting of the neighborhood radius and minimum number of points threshold in step 3 includes the following steps: for the pulse set after removing false alarms, the number of pulses is m. Collect K-nearest neighbor distances to form a distance sequence ,in Given the m-th pulse in the pulse set, calculate the first quartile of this distance sequence. Third and quartiles The interquartile range is obtained. Set the neighborhood radius parameter according to the following formula. ： ;in, For adjustment coefficients, Minimum number of points threshold 。 6. The multi-level radar signal sorting method based on pulse parameter cascading according to claim 5, characterized in that, Step 3 involves re-performing the K-nearest neighbor search on the pulse data after removing false alarms, and using the DBSCAN algorithm for initial pulse sorting. This includes: Step 3-1: Initializing the m pulse data after removing false alarms, marking them all as unvisited; Step 3-2: Traversing each unvisited pulse data. Calculate its - Neighborhood Step 3-3: If Then Mark as the core point, create a new cluster and All points are added to the cluster; Step 3-4: For each point in the cluster, if it is also a core point, its neighboring points are added to the cluster to achieve density-reachable cluster expansion; Step 3-5: When all points have been visited, points not assigned to any cluster are marked as false alarm pulses, thus obtaining the preliminary sorting results, denoted as ,in Indicates pulse Cluster label; if The corresponding pulse and Belonging to the same radar radiation source; when When, it means It was determined to be a residual false alarm pulse; when When, it means The pulse sequence belonging to the k-th cluster and corresponding to the k-th radar radiation source is denoted as the effective cluster set obtained from the initial sorting. ,in The total number of clusters, each cluster A corresponding set of tag values Data points.

7. The multi-level radar signal sorting method based on pulse parameter cascading according to claim 1, characterized in that, Step 5 includes: for any two clusters and If the following conditions are met simultaneously, the two clusters are determined to originate from the same radar radiation source and a merging operation is performed: ;in, This represents the set of points that are both natural neighbors of two clusters and are clustered together. Cluster and The correlation index between them satisfies the following formula: ;in, For data points The set of K nearest neighbors, Representing data points K-nearest neighbors belong to cluster The point set, Let be the cardinality of the point set.

8. The multi-level radar signal sorting method based on pulse parameter cascading according to claim 1, characterized in that, The feature quantities in step 5 include: skewness. kurtosis Ratio of mean to median They respectively satisfy the following formulas: ;in, The mean of the histogram counts. The central moment is the third order. Standard deviation, The number of equal-width bins used to divide the relative position intervals after mapping the two-dimensional plane; Indicates the first Each box; ;in, It is the fourth-order central moment; ;in, Let be the median of the histogram counting sequence; the constructed comprehensive decision criterion is: ;like If the corresponding histogram counting sequence simultaneously satisfies the comprehensive judgment criterion, then it is determined that... This is the true PRI.

9. An electronic reconnaissance device, characterized in that, include: A processor and a memory, the memory storing a computer program, the processor executing the computer program to implement the multi-level radar signal sorting method based on pulse parameter cascading as described in any one of claims 1 to 8.

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