High-precision dynamic sorting method based on angle features and spatial transformation
By standardizing and spatially transforming radar signals, and combining density clustering and error compensation, the accuracy and stability issues of radar signal sorting methods in complex electromagnetic environments are solved, achieving high-precision and robust radar pulse sequence sorting.
Patent Information
- Application Number
- CN202511276053.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-08
- Publication Date
- 2025-11-11
AI Technical Summary
Existing radar signal sorting methods suffer from reduced sorting performance in complex electromagnetic environments and struggle to effectively address nonlinear errors and sparse data issues, leading to decreased accuracy and stability of sorting results.
A high-precision dynamic sorting method based on angle features and spatial transformation is adopted. By standardizing the radar pulse descriptor, combining the density clustering algorithm to separate noise points, mapping them to the slope-intercept parameter space, dynamically calculating the grid division parameters, generating a pre-sorted line parameter set, calculating the midpoint of the line, performing angle threshold determination and error compensation, and combining the first-order linear fitting distance determination to achieve accurate classification of pulse parameters.
It significantly improves the sorting accuracy in complex electromagnetic environments, adapts to the characteristics of rapid signal changes, reduces the complexity of iterative calculations, and achieves highly robust sorting of radar pulse sequences.
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Figure CN120928313A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radar signal sorting technology, specifically relating to a high-precision dynamic sorting method based on angular features and spatial transformation. Background Technology
[0002] Research on radar signal sorting technology can be traced back to the 1970s. Early methods, used in relatively simple electromagnetic environments, were quite simplistic, primarily relying on classic template-matching algorithms. With the increasing complexity of battlefield electromagnetic environments and the exponential growth in the number of radar systems, this field has undergone significant technological evolution. Currently, commonly used radar signal sorting methods based on pulse repetition intervals mainly consist of two steps: clustering pre-sorting based on inter-pulse characteristic parameters and main sorting based on pulse repetition intervals.
[0003] Traditional radar signal sorting methods primarily rely on pulse interval characteristics, but these are susceptible to interference in complex scenarios. The dynamic distribution characteristics of target angle parameters offer a new sorting approach, but also increase the dependence on the accuracy of angle estimation. Existing methods often struggle to effectively handle nonlinear errors and sparse data when processing angle parameters, leading to a decrease in the accuracy and stability of the sorting results.
[0004] In short, existing radar signal sorting methods suffer from performance degradation under complex electromagnetic environments. Summary of the Invention
[0005] To address the aforementioned problems in the existing technology, this invention provides a high-precision dynamic sorting method based on angular features and spatial transformation. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a high-precision dynamic sorting method based on angular features and spatial transformation, including: S1: The original sample dataset is subjected to standardization and density clustering noise reduction in sequence to obtain the preprocessed dataset; S2: The preprocessed dataset in S1 or the preprocessed dataset after error compensation in S5 is subjected to spatial transformation, dynamic mesh partitioning and cluster generation in sequence to obtain a pre-sorting line parameter set. The pre-sorting line parameter set is used to generate a pre-sorting cluster set through line matching. S3: Calculate the set of midpoints of the lines based on the pre-sorted line parameter set; S4: Determine whether the Euclidean distance between any two points in the set of median points of the straight line is within the angle threshold; if it deviates, proceed to S5; if it does not deviate, proceed to S6. S5: Perform angle error compensation on the preprocessed dataset to obtain the error-compensated preprocessed dataset, and return to S2; S6: Perform cluster optimization on the pre-sorting cluster set to obtain multiple sorting clusters, each sorting cluster corresponding to a set of radar pulse sequences.
[0006] Compared with the prior art, the beneficial effects of the present invention are as follows: To address the performance degradation issue in existing radar signal sorting methods under complex electromagnetic environments, this invention provides a high-precision dynamic sorting method based on angle features and spatial transformation. This method first standardizes radar pulse descriptors and separates noise points using a density clustering algorithm. It then maps the preprocessed data to a slope-intercept parameter space and dynamically calculates grid partitioning parameters based on data dispersion to construct a non-uniform super-rectangular grid. The core grid is filtered using a dual-density threshold, and a pre-sorting line parameter set is generated based on a breadth-first search algorithm, calculating the line median. Angle thresholds are used to determine the median deviation, and angle error compensation iterative optimization is implemented for the deviation data. Finally, a first-order linear fitting distance determination is used to achieve accurate pulse parameter classification, and a half-plane partitioning recursively optimizes abnormal clusters. This method significantly improves sorting accuracy under complex electromagnetic environments, effectively adapts to rapidly changing signal characteristics through parameter space transformation and dynamic error compensation mechanisms, and reduces iterative computational complexity, achieving highly robust sorting of radar pulse sequences. Attached Figure Description
[0007] Figure 1 This is a flowchart illustrating a high-precision dynamic sorting method based on angular features and spatial transformation provided in an embodiment of the present invention. Figure 2 This is an example diagram of a research scenario provided in an embodiment of the present invention; Figure 3 This is an example diagram illustrating the sorting effect of the present invention under a 15% deviation factor, as provided in an embodiment of the present invention. Figure 4 This is an example diagram of the sorting effect of DGDC under a 15% deviation factor provided in an embodiment of the present invention; Figure 5 This is an example diagram of the sorting effect of GACA under a 15% deviation factor provided in the embodiments of the present invention; Figure 6 This is an example diagram of the sorting effect of ADTC under a 15% deviation factor provided in the embodiments of the present invention; Figure 7 This is an example diagram of the sorting effect of NGBC under a 15% deviation factor provided in the embodiments of the present invention; Figure 8 This refers to the number of times each algorithm correctly identifies the target when the deviation factor is 15%, as provided in this embodiment of the invention. Figure 9 This is an example diagram of the sorting effect of the present invention under a 45% deviation factor, as provided in the embodiments of the present invention; Figure 10 This is an example diagram of the sorting effect of DGDC under a 45% deviation factor provided in the embodiments of the present invention; Figure 11 This is an example diagram of the sorting effect of GACA under a 45% deviation factor provided in the embodiments of the present invention; Figure 12 This is an example diagram of the sorting effect of ADTC under a 45% deviation factor provided in this embodiment of the invention; Figure 13 This is an example diagram of the sorting effect of NGBC under a 45% deviation factor provided in the embodiments of the present invention; Figure 14 This refers to the number of times each algorithm correctly identifies the target when the deviation factor is 45%, as provided in this embodiment of the invention. Figure 15 This is a schematic diagram of the F-values of various methods under different deviation factors provided in the embodiments of the present invention; Figure 16 This is a schematic diagram showing the purity of various methods under different deviation factors provided in the embodiments of the present invention. Detailed Implementation
[0008] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.
[0009] The high-precision dynamic sorting method based on angular features and spatial transformation proposed in this invention will now be described in detail with reference to the accompanying drawings.
[0010] Figure 1 This is a flowchart illustrating a high-precision dynamic sorting method based on angular features and spatial transformation provided in an embodiment of the present invention. Figure 1 As shown, the method includes: S1: The original sample dataset is subjected to standardization and density clustering noise reduction in sequence to obtain the preprocessed dataset; S2: Spatial transformation, dynamic mesh partitioning and cluster generation are performed sequentially on the preprocessed dataset in S1 or the preprocessed dataset after error compensation in S5 to obtain the pre-sorted line parameter set. The pre-sorted line parameter set generates a pre-sorted cluster set through line matching. S3: Calculate the set of midpoints of the line based on the pre-sorted line parameter set; S4: Determine whether the Euclidean distance between any two points in the midpoint set of the line deviates from the angle threshold; if it deviates, execute S5; if it does not deviate, execute S6. S5: Perform angle error compensation on the preprocessed dataset to obtain the error-compensated preprocessed dataset, and return to S2; S6: Perform cluster optimization on the pre-sorted cluster set to obtain multiple sorting clusters, each sorting cluster corresponding to a set of radar pulse sequences.
[0011] Specifically, S1 includes: receiving a dataset of N samples, each sample being a d-dimensional original impulse descriptor; calculating the mean and standard deviation of all samples in each dimension; standardizing each sample using the mean and standard deviation corresponding to each dimension to obtain a standardized dataset; and using a density clustering algorithm to separate noise points in the standardized dataset to obtain a preprocessed dataset.
[0012] It should be noted that the Pulse Description Word (PDW) is a core data unit in radar signal processing, used to digitally describe the set of characteristic parameters of a single radar pulse. In radar signal sorting systems, the PDW is the direct input data for algorithm processing. The core parameters of the PDW include: Time of Arrival (TOA), Pulse Width (PW), Carrier Frequency (RF), Pulse Amplitude (RF), Angle of Arrival (DOA), and Label. For example, each PDW is a d-dimensional vector; when d can take the value of 2, the PDW includes both TOA and DOA.
[0013] Here, let's assume there is indivual Dimensional sample data ,and then, The first sample The average value of dimensional data Represented as: Standard deviation Represented as: , Furthermore, utilizing The first sample 3D standardized data can be represented as: To address the potential range shift in the processed data, range normalization is performed on each data point in the standardized dataset, constraining it to the interval [0,1], resulting in the preprocessed radar dataset. The data after range normalization for the i-th data point can be represented as: , and They are The maximum and minimum values in the data are shown in Table 1. Table 1 illustrates the flow of the density clustering algorithm. Each standard data point in the standardized dataset is labeled using the flow in Table 1 to distinguish between noise and non-noise points. Multiple non-noise points are used as the preprocessed dataset.
[0014] Table 1
[0015] Here, S2 specifically includes: mapping multiple data points from the preprocessed dataset in S1 or the error-compensated preprocessed dataset in S5 to the slope-intercept parameter space to obtain a transformed point set; calculating multiple dynamic clustering parameters for each dimension of the data points in the transformed point set to determine the number of grids per dimension; using these multiple dynamic clustering parameters to partition the data distribution space of the transformed point set to obtain a hyperrectangular grid containing multiple grids; wherein each grid has a different grid side length; and using these multiple grid side lengths to calculate the grid label for each data point in the transformed point set, so as to establish a relationship between the transformed point set and the target data space. The mapping relationship of the hyperrectangular grid is determined; the number of data points in the transformation point set contained in each grid is counted to serve as the grid density of each grid; the hyperrectangular grid is divided using a grid density threshold and a core density threshold to obtain a core grid set, a first grid set, and a second grid set ordered from largest to smallest grid density; where the core density threshold is greater than the grid density threshold; each core grid in the core grid set is used as a seed point for the pre-sorted clusters, and the first grid set connected to each core grid is traversed using a breadth-first search algorithm to generate multiple pre-sorted clusters, thus obtaining the pre-sorted line parameter set.
[0016] Here, we assume the preprocessed dataset is represented as The preprocessed dataset is transformed into the slope-intercept parameter space, where the x-coordinate of each data point is: ;in, The parameter step size represents the Hough transform. Indicates rounding down to the nearest integer. Let i be a row vector, and let i be the y-coordinate of the i-th data point. Represented as: .in, To and For row vectors of the same length, the set of transformation points can be represented as: In other words, the x-coordinate of each data point in the transformation point set is: with a slope step size... exist[ , The data consists of multiple values extracted from [the data set]. It should be noted that spatial variations do not change the dimensionality of the data.
[0017] Here, calculations are performed on each dimension of the data points in the transform point set to obtain multiple dynamic clustering parameters used to determine the number of grids in each dimension. These parameters include: calculating the corresponding dispersion using the mean and standard deviation of each dimension of the data points in the transform point set to obtain multiple dispersions; calculating the standardized dispersions by combining the multiple dispersions with the dimension of the transform point set; and calculating the dimension of the transform point set with the standardized dispersions to obtain multiple dynamic clustering parameters, with each dynamic clustering parameter corresponding to one dimension.
[0018] Assumption Discreteness of data points in the c-th dimension transformation ; It is the standard deviation of the data points transformed in the c-th dimension. It is the mean of the data points transformed in the c-th dimension; thus, multiple discrete values are obtained. The expression for the standardized discreteness of the c-th dimension transformed data points is: Finally, the c-th dynamic clustering parameter can be expressed as: .
[0019] Here, dynamic clustering parameters are used. The data distribution space of the transformed point set is divided to obtain a hyperrectangular grid with multiple grids. For example, dynamic clustering parameters... Defining the spatial distribution of the first-dimensional preprocessed data, dynamic clustering parameters The spatial distribution of the second-dimensional preprocessed data is defined. The grid side length of the c-th dimension hyperrectangular grid is... It can be represented as: ;in, It refers to the maximum value in the c-th dimension of the preprocessed data. It refers to the minimum value in the c-th dimension of the preprocessed data. This represents the total number of grid divisions for the c-th dimension of the preprocessed data. Furthermore, the label representation for each grid cell in the c-th dimension hyperrectangular grid is as follows: .
[0020] In one possible implementation, the calculation expressions for each grid density threshold and each core density threshold satisfy the following: ; ; in, It is the grid density threshold. It is the core density threshold. It is the standardized dispersion. It is the number of grid cells in the super rectangular grid. It is the first The grid density of each grid.
[0021] It should be noted that the number of grids in the super-rectangular grid divided for each dimension of preprocessed data is different.
[0022] Here, based on the double threshold ( and Based on the feature similarity merging criterion, a core grid is selected to construct clusters. The cluster set is then expanded by traversing the connectivity of high-density grids using a breadth-first search algorithm, resulting in a pre-sorted set of line parameters. Pre-sorting line parameter set Pre-sorted cluster set is generated through line matching. The data in the second grid set is marked as spurious pulse data, and the data in grids that do not belong to the core grid set, the first grid set, and the second grid set are marked as unmatched datasets.
[0023] Here, the preprocessed dataset includes multiple pulse parameter pairs, each pulse parameter pair including a pulse arrival time value and a pulse arrival angle value; for example, the preprocessed dataset Pre-sorting line parameter set .
[0024] Here, the set of median points of the straight line includes multiple two-dimensional coordinates, each of which includes a first coordinate and a second coordinate; S3 specifically includes: selecting the maximum and minimum pulse arrival time values from multiple pulse arrival time values; performing a weighted summation of the maximum and minimum pulse arrival time values to obtain the median point, which is used as the first coordinate; using all the straight line parameter pairs in the pre-sorted straight line parameter set, as well as the median point, to calculate multiple straight line values, which are used as multiple second coordinates; and constructing multiple two-dimensional coordinates using the first coordinate and multiple second coordinates to obtain the set of median points of the straight line.
[0025] Here, the first coordinate can be represented as: , The i-th second coordinate is represented as Furthermore, the set of midpoints of a straight line is represented as .
[0026] Here, S4 includes: from Calculate the Euclidean distance difference between any two groups. and angle threshold Perform a size comparison. (Angle threshold) It is obtained by calculating the pulse arrival angle value in the p-th pulse parameter pair in the preprocessed dataset. And the pulse arrival angle value in the q-th pulse parameter pair. ; p and q are both random integers; calculate the pulse arrival angle value in the p-th pulse parameter pair and the distance value between the pulse arrival angle values in the q-th pulse parameter pair to obtain multiple angle distance values; filter the minimum value among the multiple angle distance values and use the minimum value of 50% as the angle threshold.
[0027] Here, S5 specifically includes: calculating multiple distance values for the i-th pulse parameter pair in the preprocessed dataset and all line parameter pairs in the pre-sorted line parameter set; 1≤i≤I; filtering multiple distance values that are less than the angle threshold to obtain multiple valid line parameter pairs; calculating the weight of each valid line parameter pair to obtain multiple weight values; using the multiple weight values, performing weighted calculation on the i-th pulse parameter pair to obtain the i-th error-compensated pulse parameter pair, continuing the calculation to obtain the (i+1)-th error-compensated pulse parameter pair, until the I-th error-compensated pulse parameter pair is obtained, thus obtaining the error-compensated preprocessed dataset.
[0028] Assume the i-th pulse parameter pair is This pulse parameter corresponds to multiple distance values. The formula for calculating each distance value is the same, where The expression is Assume that the lines that meet the conditions include At the same time, the distance from the point to each line is ,in, Then the mapping point of the i-th pulse parameter pair on each straight line is: ,in, Furthermore, the calculation formula for each weight value is the same; the i-th weight value can be expressed as... .in, This is to prevent distance values If the value is zero, resulting in a zero denominator, then a very small positive integer is added. The i-th error-compensated pulse parameter pair can then be expressed as: .
[0029] Here, S6 includes: step (1) and step (2).
[0030] (1) Preprocessing the dataset: Perform a first-order linear fit on each data point in the pre-sorted line parameter set to obtain multiple corresponding first-order fitted lines. Each first-order fitted line corresponds to a pre-sorted cluster. Calculate the distance from the i-th pulse parameter pair in the preprocessed dataset to each first-order fitted line to obtain the i-th distance set. Determine whether the minimum distance in the i-th distance set is less than a preset threshold. If so, classify the i-th pulse parameter pair into the pre-sorted cluster corresponding to the minimum distance, and continue to classify the (i+1)-th pulse parameter pair by calculating the distance from it to each first-order fitted line until all pulse parameter pairs are classified. If not, classify the i-th pulse parameter pair into the unmatched dataset, and continue to classify the (i+1)-th pulse parameter pair by calculating the distance from it to each first-order fitted line until all pulse parameter pairs are classified.
[0031] Here, the i-th distance set is represented as Each distance value is calculated in the same way, where, The preset threshold is a 20% angle threshold. .
[0032] (2) Handling of unmatched datasets: Determine whether each unmatched data point in the unmatched dataset meets the clustering criteria; the clustering criteria refer to the data point being less than a preset clustering threshold. If the conditions are met, multiple unmatched data points that meet the clustering criteria will be clustered into a temporary cluster; If the conditions are not met, multiple unmatched data points will be aggregated into multiple clusters to be fitted. The root mean square error of the linear fit is determined by using the pulse arrival time value of each cluster to be fitted. By using the root mean square error of the linear fitting of each cluster to be fitted, each cluster to be fitted is optimized, resulting in multiple optimized clusters; Multiple optimized clusters and temporary clusters are added to the pre-sorting cluster set to obtain multiple sorting clusters.
[0033] Here, the dataset is not matched. Each data point is compared with a clustering threshold. If the data points are less than a threshold, they are clustered into a temporary cluster. A first-order linear fit is then performed on the temporary cluster to obtain the corresponding fitted line.
[0034] Using the root mean square error of the linear fitting of each cluster to be fitted, each cluster is optimized to obtain multiple optimized clusters, including: For the r-th cluster to be fitted: Determine whether the root mean square error of the linear fitting of the r-th cluster to be fitted is greater than the r-th error threshold; 1≤r≤R; If yes, divide the r-th cluster to be fitted into two sub-clusters according to the half-plane, using the fitted line corresponding to the temporary cluster as the boundary, and recursively optimize the two sub-clusters until the root mean square error of the linear fitting of each sub-cluster is less than or equal to the r-th error threshold, thus obtaining the corresponding set of the r-th optimized clusters and completing the optimization of the r-th cluster to be fitted; If no, use the r-th cluster to be fitted as the r-th optimized cluster, and continue to optimize the (r+1)-th cluster to be fitted until the optimization of the R-th cluster to be fitted is completed, thus obtaining multiple optimized clusters.
[0035] In one possible implementation, the expression for each error threshold is the same; the expression for the r-th error threshold satisfies: ; in, It is the r-th error threshold. It is the maximum pulse arrival time value in the r-th cluster to be fitted. It is the minimum pulse arrival time value in the r-th cluster to be fitted. It is the slope of the fitted line corresponding to the temporary cluster. It is the intercept of the fitted line corresponding to the temporary cluster. It is the number of the r-th cluster to be fitted.
[0036] In one possible implementation, the first The expression for calculating the root mean square error of linear fitting for each cluster to be fitted satisfies: ; in, It refers to the first The root mean square error of linear fitting for each cluster to be fitted. It is the first The total amount of data for each cluster to be fitted. It is a first-order fitting function. It is the first The arrival time values of each pulse parameter pair It is the first The actual pulse arrival angle of each pulse parameter pair Indicates the first Fitted pulse arrival angle and actual pulse arrival angle at each time point The Euclidean distance between them.
[0037] Here, two sub-clusters It can be represented as .
[0038] It should be noted that recursively optimizing two sub-clusters means that the root mean square error of linear fitting for each sub-cluster is calculated, and it is determined whether the corresponding root mean square error of linear fitting is greater than the error threshold. If it is greater, the sub-cluster is further split into three sub-cluster sets. The root mean square error of linear fitting for each sub-cluster in the three sub-cluster sets is then determined whether it is greater than the error threshold. This process of recursively optimizing continues until the root mean square error of linear fitting for each cluster is less than or equal to the error threshold, thus completing the optimization.
[0039] To address the performance degradation issue in existing radar signal sorting methods under complex electromagnetic environments, this invention provides a high-precision dynamic sorting method based on angle features and spatial transformation. This method first standardizes radar pulse descriptors and separates noise points using a density clustering algorithm. It then maps the preprocessed data to a slope-intercept parameter space and dynamically calculates grid partitioning parameters based on data dispersion to construct a non-uniform super-rectangular grid. The core grid is filtered using a dual-density threshold, and a pre-sorting line parameter set is generated based on a breadth-first search algorithm, calculating the line median. Angle thresholds are used to determine the median deviation, and angle error compensation iterative optimization is implemented for the deviation data. Finally, a first-order linear fitting distance determination is used to achieve accurate pulse parameter classification, and a half-plane partitioning recursively optimizes abnormal clusters. This method significantly improves sorting accuracy under complex electromagnetic environments, effectively adapts to rapidly changing signal characteristics through parameter space transformation and dynamic error compensation mechanisms, and reduces iterative computational complexity, achieving highly robust sorting of radar pulse sequences.
[0040] To verify the technical effects of this invention, a simulation study is conducted. The study scenario is as follows: Figure 2 As shown, where, This indicates the location of each launch station. This represents the velocity vector of the airborne receiving station. Indicates the movement of the airborne receiving station. Indicates the elevation angle from the transmitting station to the receiving station. It is the relative azimuth angle, which is the launch station. to receiving station The line connecting the projected positions on the horizontal plane and The angle along the positive direction of the axis. This represents the angle of arrival of the signal received by the receiving station. In this experimental scenario, the trajectory of the airborne receiving station is known. The trajectory can be divided into three uniform linear motion phases and two maneuvering turning phases, with the uniform linear motion phases connected by maneuvering turning phases. Table 2 shows the simulation parameters involved in the experimental scenario.
[0041] Table 2
[0042] In the actual simulation process, based on the given receiver location and target trajectory, the above parameters are simulated under a specific spatial scenario. The specific dataset simulation process is shown in Table 3. Through simulation, the Pulse Sequence Descriptor (PDW) for each radar can be obtained, which includes information such as Time of Arrival (TOA), Pulse Width (PW), Carrier Frequency (RF), Pulse Amplitude (PA), Angle of Arrival (DOA), and label (LAB) for identification. Finally, the Pulse Sequence Descriptors of all radars are mixed to form an input dataset suitable for radar signal sorting algorithms. Here, the error range of the pulse width and pulse repetition period of the simulated mixed PDW data is 1% of the actual value, the error range of the carrier frequency is 5MHz, and the standard deviation of the angle of arrival is 0.1°. At the same time, spurious pulses with a 1% pulse count are added, i.e., pulse parameters that do not belong to any actual radar target.
[0043] Here, the proposed solution of this invention is compared with similar solutions mentioned above. The high-precision dynamic sorting method based on angular features and spatial transformation provided by this invention is called High Accuracy-DOA Hough Dynamic Compensation, abbreviated as HA-DHDC. The following references are: [1]: PRI sorting algorithm based on grid clustering optimization, abbreviated as DGDC (Dynamic Grid Density Clustering); [2]: sorting method based on TDOA parameter, abbreviated as GACA (Clustering Algorithm based on Grid Density); [3]: dynamic sorting method based on adaptive density threshold, abbreviated as ADTC (Adaptive density threshold Clustering); [4]: grid clustering algorithm based on K-Dist function, abbreviated as NGBC (Novel Grid-Based Clustering).
[0044] Table 3
[0045] Here, we compare the methods of this invention and those in references [1][2][3][4] by simulating different estimation error deviation factors. Table 4 shows the parameter settings of the radar transmitting station. The DOA estimation error index deviation factor of this invention is defined as the minimum absolute value of the difference between the angle of DOA deviation from the true value and the DOA change of different targets at the same time. When the deviation factor is 50% or above, it indicates that the DOA parameter distributions of the two radars will overlap.
[0046] Figure 3 This is an example diagram of the sorting effect of the present invention under a 15% deviation factor, as provided in the embodiments of the present invention. Figure 4 This is an example diagram of the sorting effect of DGDC under a 15% deviation factor provided in an embodiment of the present invention. Figure 5 This is an example diagram of the sorting effect of GACA under a 15% deviation factor provided in the embodiments of the present invention. Figure 6 This is an example diagram of the sorting effect of ADTC under a 15% deviation factor provided in the embodiments of the present invention. Figure 7 This is an example diagram of the sorting effect of NGBC under a 15% deviation factor provided in this embodiment of the invention. The vertical axis represents the number of clusters, and the horizontal axis represents the batch size. Figure 8 This refers to the number of times each algorithm correctly selects the target when the deviation factor is 15%, as provided in the embodiments of the present invention. Figure 9 This is an example diagram of the sorting effect of the present invention under a 45% deviation factor, as provided in the embodiments of the present invention. Figure 10 This is an example diagram of the sorting effect of DGDC under a 45% deviation factor provided in the embodiments of the present invention. Figure 11 This is an example diagram of the sorting effect of GACA under a 45% deviation factor provided in the embodiments of the present invention. Figure 12 This is an example diagram of the sorting effect of ADTC under a 45% deviation factor provided in the embodiments of the present invention. Figure 13 This is an example diagram of the sorting effect of NGBC under a 45% deviation factor provided in this embodiment of the invention. The vertical axis represents the number of clusters, and the horizontal axis represents the batch size. Figure 14 This refers to the number of times each algorithm correctly selects the target when the deviation factor is 45%, as provided in this embodiment of the invention. Figure 3-14 It can be seen that the present invention is significantly superior to references [1]-[4].
[0047] Table 4
[0048] Under complex parameter perturbations in the experimental scenario, the performance of different sorting strategies exhibits significant differences. Algorithms based on pulse repetition intervals (DGDC, ADTC, NGBC) show stable convergence characteristics in the low number of classifications (1-6), but their effective sorting ability shows a gradient decay as the target completeness requirement increases (7-9), especially in the scenario of completely correct classification, where they only reach a low performance threshold. In contrast, the sorting scheme based on angle features shows better adaptability in the scenario of complete target recognition: HA-DHDC's correct number of sortings for nine targets is close to the maximum value on the vertical axis, significantly higher than other methods. With the complexity of the electromagnetic environment, the HA-DHDC algorithm still maintains a high sorting accuracy. The sorting performance of each algorithm is analyzed, and the results are shown in Table 5.
[0049] When the deviation factor is less than 50%, the present invention exhibits a parameter matching accuracy of over 98.2%, which is 15%-25% higher than the methods in other literature. Moreover, it maintains optimal stability even as the deviation factor continues to increase, which shows that the present invention significantly enhances the robustness of sorting performance in complex electromagnetic environments.
[0050] Figure 15 This is a schematic diagram showing the F-values of various methods under different deviation factors provided in the embodiments of the present invention. Figure 16 This is a schematic diagram showing the purity of various methods under different deviation factors provided in the embodiments of the present invention.
[0051] Experimental verification shows that the nonlinear compensation optimization theory proposed in this invention can effectively suppress the degradation of sorting performance caused by the deterioration of linear characteristics. When the deviation factor reaches the critical threshold of 50%, the proposed method still maintains an F-value and purity of over 95%, confirming its high robustness. Furthermore, when the deviation factor varies within the range of 20-50%, the comprehensive performance indicators F-index and purity of this invention consistently remain at a high level of over 97%, and these quantitative analysis results fully verify the applicability advantages of this invention under non-ideal observation conditions.
[0052] Table 5
[0053] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.
Claims
1. A high-precision dynamic sorting method based on angular features and spatial transformation, characterized in that, include: S1: The original sample dataset is subjected to standardization and density clustering noise reduction in sequence to obtain the preprocessed dataset; S2: The preprocessed dataset in S1 or the error-compensated preprocessed dataset in S5 is sequentially subjected to spatial transformation, dynamic mesh partitioning and cluster generation to obtain a pre-sorted line parameter set. The pre-sorted line parameter set can generate a pre-sorted cluster set through line matching. S3: Calculate the set of midpoints of the lines based on the pre-sorted line parameter set; S4: Determine whether the Euclidean distance between any two points in the set of median points of the straight line deviates from the angle threshold; If the deviation is found, execute S5; if the deviation is not found, execute S6. S5: Perform angle error compensation on the preprocessed dataset to obtain the error-compensated preprocessed dataset, and return to S2; S6: The preprocessed dataset is optimized using the pre-sorted line parameter set to obtain multiple sorting clusters, each sorting cluster corresponding to a set of radar pulse sequences.
2. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 1, characterized in that, S1 includes: Receive a dataset of N samples, each sample being a d-dimensional raw pulse descriptor; Calculate the mean and standard deviation of all samples in each dimension; Each sample is standardized using the mean and standard deviation corresponding to each dimension to obtain a standardized dataset; The noise points in the standardized dataset are separated using a density clustering algorithm to obtain the preprocessed dataset.
3. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 2, characterized in that, S2 includes: Map multiple data points from the preprocessed dataset in S1 or the error-compensated preprocessed dataset in S5 to the slope-intercept parameter space to obtain the transform point set. Calculate the data points in each dimension of the transformed point set to obtain multiple dynamic clustering parameters used to determine the number of grids in each dimension; Using the multiple dynamic clustering parameters, the data distribution space of the transformation point set is divided to obtain a super-rectangular grid containing multiple grids; wherein, the grid side length of each grid is different; Using multiple grid side lengths, calculate the grid label for each data point in the transformation point set, and use multiple grid labels to establish a mapping relationship between the transformation point set and the hyperrectangular grid; The number of data points in the transformation point set contained in each grid is counted, and this number is used as the grid density of each grid. The super-rectangular mesh is divided using a mesh density threshold and a core density threshold to obtain a core mesh set, a first mesh set, and a second mesh set, ordered from largest to smallest mesh density; wherein, the core density threshold is greater than the mesh density threshold. Using each core grid in the core grid set as the seed point of the pre-sorted cluster, the first grid set connected to each core grid is traversed by a breadth-first search algorithm to generate multiple pre-sorted clusters, thus obtaining the pre-sorted line parameter set.
4. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 3, characterized in that, The calculation of each dimension of the data points in the transformed point set yields multiple dynamic clustering parameters used to determine the number of grid cells per dimension, including: Using the mean and standard deviation of each dimension of data points in the transformation point set, the corresponding dispersion is calculated to obtain multiple dispersions; The standardized discreteness is obtained by calculating the multiple discretenesses and the dimension of the transformation point set; The dimension of the transformed point set and the standardized dispersion are calculated to obtain the multiple dynamic clustering parameters, with each dynamic clustering parameter corresponding to one dimension.
5. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 3, characterized in that, The preprocessed dataset includes multiple pulse parameter pairs, each pulse parameter pair including pulse arrival time value and pulse arrival angle value; The set of median points of the straight line includes multiple two-dimensional coordinates, and each two-dimensional coordinate includes a first coordinate and a second coordinate. S3 includes: Filter the maximum and minimum pulse arrival time values from multiple pulse arrival time values; The maximum pulse arrival time value and the minimum pulse arrival time value are weighted and summed to obtain the median time point, which is used as the first coordinate. Using all the line parameter pairs in the pre-sorted line parameter set, and the median point in time, multiple line values are calculated and used as multiple second coordinates; The multiple two-dimensional coordinates are constructed using the first coordinate and the multiple second coordinates to obtain the set of median points of the line.
6. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 5, characterized in that, The angle threshold is obtained by calculation in the following way: Obtain the pulse arrival angle value in the p-th pulse parameter pair and the pulse arrival angle value in the q-th pulse parameter pair in the preprocessed dataset; p and q are both random integers; Calculate the pulse arrival angle value in the p-th pulse parameter pair and the distance value between the pulse arrival angle values in the q-th pulse parameter pair to obtain multiple angle distance values; The minimum value among the plurality of angular distance values is selected, and 50% of the minimum value is used as the angular threshold.
7. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 5, characterized in that, S5 includes: Multiple distance values are calculated for the i-th pulse parameter pair in the preprocessed dataset and all line parameter pairs in the pre-sorted line parameter set; 1≤i≤1; Filter multiple distance values that are less than the angle threshold to obtain multiple corresponding valid line parameter pairs; Calculate the weight of each valid line parameter pair to obtain multiple weight values; Using multiple weight values, the i-th pulse parameter pair is weighted to obtain the i-th error-compensated pulse parameter pair. The calculation continues to obtain the (i+1)-th error-compensated pulse parameter pair, until the I-th error-compensated pulse parameter pair is obtained, thus obtaining the error-compensated preprocessed dataset.
8. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 5, characterized in that, All data within the second grid set are marked as spurious pulse data, and data in grids that do not belong to the core grid set, the first grid set, and the second grid set are aggregated into an unmatched dataset; S6 includes: (1) Preprocessing the dataset: Perform a first-order linear fit on each data point in the pre-sorting line parameter set to obtain multiple corresponding first-order fitted lines. Each first-order fitted line corresponds to a pre-sorting cluster. Calculate the distance from the i-th impulse parameter pair in the preprocessed dataset to each first-order fitted line to obtain the i-th set of distances; Determine whether the minimum distance in the i-th distance set is less than a preset threshold; If so, classify the i-th pulse parameter pair into the pre-sorted cluster corresponding to the minimum distance, and continue to classify the i+1 pulse parameter pair by the distance from the (i+1)-th pulse parameter pair to each first-order fitted line in the preprocessed dataset, until the classification of all pulse parameter pairs is completed. If not, classify the i-th pulse parameter pair into the unmatched dataset, and continue to classify the i+1 pulse parameter pair by measuring the distance from the (i+1)-th pulse parameter pair to each first-order fitted line in the preprocessed dataset, until all pulse parameter pairs are classified. (2) Handling of unmatched datasets: Each unmatched data point in the unmatched dataset is individually determined to meet the clustering condition; the clustering condition refers to the data point being less than a preset clustering threshold. If the conditions are met, multiple unmatched data points that satisfy the clustering conditions will be clustered into temporary clusters. If the conditions are not met, multiple unmatched data points will be aggregated into multiple clusters to be fitted. The root mean square error of the linear fit is determined by using the pulse arrival time value of each cluster to be fitted. By using the root mean square error of the linear fitting of each cluster to be fitted, each cluster to be fitted is optimized to obtain multiple optimized clusters. The multiple optimized clusters and the temporary clusters are added to the pre-sorting cluster set to obtain the multiple sorting clusters.
9. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 8, characterized in that, A first-order linear fit is performed on the temporary cluster to obtain the corresponding fitted line; The method utilizes the root mean square error of the linear fit of each cluster to be fitted to optimize each cluster, resulting in multiple optimized clusters, including: For the r-th cluster to be fitted: determine whether the root mean square error of the linear fitting of the r-th cluster to be fitted is greater than the r-th error threshold; 1≤r≤R; If so, using the fitted line corresponding to the temporary cluster as the boundary, the r-th cluster to be fitted is divided into two sub-clusters according to the half-plane. The two sub-clusters are recursively optimized until the root mean square error of the linear fitting of each sub-cluster is less than or equal to the r-th error threshold, thus obtaining the corresponding r-th optimized cluster set and completing the optimization of the r-th cluster to be fitted. If not, the r-th cluster to be fitted is taken as the r-th optimized cluster, and the (r+1)-th cluster to be fitted is optimized until the optimization of the R-th cluster to be fitted is completed, thus obtaining the plurality of optimized clusters.
10. The high-precision dynamic sorting method based on angular features and spatial transformation according to claim 9, characterized in that, The expression for each error threshold is the same; the expression for the r-th error threshold satisfies: ； in, It is the r-th error threshold. It is the maximum pulse arrival time value in the r-th cluster to be fitted. It is the minimum pulse arrival time value in the r-th cluster to be fitted. It is the slope of the fitted line corresponding to the temporary cluster. It is the intercept of the fitted line corresponding to the temporary cluster. It is the number of the r-th cluster to be fitted.