Radar signal sorting algorithm, equipment and storage device based on improved FCM algorithm

Abstract

The present invention provides an improved radar signal sorting algorithm, device, and storage device based on the FCM algorithm, relating to the field of radar signal sorting. The method extracts pulse width, carrier frequency, and angle of arrival from pulse descriptor data received by the radar and performs normalization processing; calculates the field strength function and the potential value of each point based on data field theory; calculates the change of potential entropy with radiation factor, and selects the optimal radiation factor based on the minimum value of potential entropy; calculates the potential value based on the optimal radiation factor and eliminates noise points; adaptively determines the number of class centroids based on the distribution of potential values ​​of data points; calculates weight coefficients based on the correlation between data points and potential values; and calculates an improved objective function based on the weight coefficients and the adaptive number of clusters, iteratively obtaining the optimal clustering result. The present invention has the beneficial effects of significantly improving the noise resistance of the FCM algorithm and ensuring classification effectiveness.

Description

Technical Field

[0001] The present invention relates to the field of radar signal sorting, and in particular to an improved radar signal sorting algorithm, device and storage device based on an FCM algorithm. Background Art

[0002] As the electromagnetic environment becomes increasingly complex, electronic reconnaissance technology faces increasing challenges. Radar receivers typically receive multiple radar signals, which are mixed together in their arrival time order. To obtain the parameter information of each radar signal, de-aliasing is required. This process is called radar signal sorting. Clustering algorithms play an important role in this area, helping to discover correlations between unknown data.

[0003] The fuzzy C-means (FCM) algorithm is a clustering algorithm that partitions data points into distinct clusters, where each data point has a degree of membership, representing its likelihood of belonging to a particular cluster. The general steps for using FCM for radar signal sorting are: First, preprocessing steps such as normalization and feature extraction are required to ensure that the data is suitable for cluster analysis. Next, the number of clusters is determined, typically using cluster evaluation metrics such as the silhouette coefficient and DB index to assist in determining the optimal number of clusters. Finally, the FCM algorithm is applied to calculate the degree of membership of each data point with the cluster center by minimizing an objective function, thereby determining the data point's class.

[0004] However, traditional FCM algorithms have two drawbacks: 1. The number of clusters must be determined in advance, and the clustering effect depends on the number of initial cluster centers; 2. They are sensitive to noise, which can lead to unstable clustering results. Noise and outliers are a common problem when processing data such as radar signals. Summary of the Invention

[0005] In order to solve the problem that the clustering effect depends on the selection of the initial number of cluster centers and the clustering results are unstable, the present invention provides a radar signal sorting algorithm, device and storage device improved based on the FCM algorithm. The radar signal sorting algorithm improved based on the FCM algorithm mainly includes:

[0006] S1: Extract pulse width, carrier frequency, and arrival angle from the pulse descriptor data received by the radar to form three-dimensional coordinate data, and perform normalization on the three-dimensional coordinate data;

[0007] S2: Obtain the field intensity function and the potential value formula of each point based on the data field theory;

[0008] S3: Calculate the change of potential entropy with radiation factor based on the normalized data, and select the optimal radiation factor based on the minimum value of potential entropy;

[0009] S4: Calculate the potential value according to the optimal radiation factor and remove noise points;

[0010] S5: Adaptively determine the number of class centers based on the distribution of potential values ​​of data points;

[0011] S6: Calculate the weight coefficient based on the correlation and potential value between data points;

[0012] S7: Calculate the improved objective function based on the weight coefficient and the adaptive number of clusters, and iterate to obtain the best clustering result.

[0013] A storage device stores instructions and data for implementing an improved radar signal sorting algorithm based on an FCM algorithm.

[0014] A radar signal sorting device improved based on the FCM algorithm comprises: a processor and a storage device; the processor loads and executes instructions and data in the storage device to implement a radar signal sorting algorithm improved based on the FCM algorithm.

[0015] The beneficial effects of the technical solution provided by the present invention are as follows: the present invention combines the FCM algorithm and data field theory, and overcomes the shortcoming of traditional FCM being easily affected by noise by eliminating noise and outliers. According to the data field theory and the idea of ​​the region growing algorithm, in the absence of prior information, the number of clusters can be accurately obtained, thereby improving the clustering effect. The weight coefficient is constructed in combination with the potential value, and the objective function is improved, thereby solving the problem that the traditional FCM algorithm cannot accurately sort when the amount of data between classes is very different. The present invention utilizes data field theory to significantly improve the noise resistance of the FCM algorithm and ensure the classification effect. The number of class centers is adaptively determined, overcoming the shortcoming that the traditional FCM algorithm needs to give the number of class centers in advance. It effectively handles unbalanced data sets that the traditional FCM algorithm cannot handle, thereby improving the accuracy and robustness of classification. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0017] Figure 1 This is a flowchart of a radar signal sorting algorithm improved based on the FCM algorithm in an embodiment of the present invention.

[0018] Figure 2 1 and 2 are graphs of noisy data and sorted results in an embodiment of the present invention, wherein (a) is a graph of the original data without sorting and containing noise, and (b) is a graph of the sorting result using the improved FCM algorithm.

[0019] Figure 3It is a schematic diagram of the sorting results of different data sets (three radars, four radars, and five radars) using the three algorithms DF-FCM, SC-KMEANS, and RI-FCM in an embodiment of the present invention.

[0020] Figure 4 Schematic diagram of the sorting results of the three algorithms DF-FCM, SC-KMEANS, and RI-FCM on an unbalanced data set in an embodiment of the present invention.

[0021] Figure 5 It is a schematic diagram of the operation of the hardware device in the embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0023] Please refer to Figure 1 , Figure 1 This is a flowchart of an improved radar signal sorting algorithm based on the FCM algorithm in an embodiment of the present invention. The DF-FCM algorithm provided by the present invention realizes the adaptation of the initial number of classes by introducing data field theory, and eliminates noise and outliers at the same time. Specifically, it includes:

[0024] S1: Based on the PDW (Pulse Descriptor Word) data received by the radar, the pulse width, carrier frequency, and arrival angle are obtained and analyzed and processed to ensure data accuracy and consistency. These parameters are then normalized to ensure that the values ​​of different parameters are comparable.

[0025] S2: Based on the data field theory, we can get the formula for calculating the field strength function and the potential value of each point. The field strength function represents the interaction force between data points. The field strength function is:

[0026]

[0027] Among them, d(x a ,x b ) represents the data object x a with x b The Euclidean distance is σ, and σ is the radiation factor.

[0028] The potential value is the midpoint of the data field x a The generated field strength function and is used to measure the influence of the position and characteristics of the data point in the data set on the overall data. The potential value function is:

[0029]

[0030] The denser the data points, the larger the potential value, which can eliminate free noise points.

[0031] S3: Use potential entropy to represent the uncertainty between data objects in the data field, calculate the change of potential entropy with radiation factor, and select the optimal radiation factor σ based on the minimum value of potential entropy. Assume that the potential value of the i-th data point is The expression of potential entropy is as follows:

[0032]

[0033] In the formula is the normalization factor.

[0034] From the above formula, we can conclude that When the radiation factor σ is infinitely close to 0, The potential entropy is logn. When the radiation factor is very large, If there is no correlation between data points, potential cannot be used for sorting. Only when the radiation factor σ is appropriately chosen will the potential of each sample change significantly, minimizing the uncertainty between samples and minimizing the potential entropy. This optimal radiation factor results in the best data classification and the clearest grouping.

[0035] S4: Determine the potential value of each data point based on the optimal radiation factor and eliminate data points with low potential values. Generally speaking, noise points will deviate from the cluster center of the pulse signal, and the distance will exceed the radiation range of the cluster center, that is, greater than 3σ. Therefore, the formula of the field strength function can be modified to set the interaction force between data points greater than 3σ to 0. The field strength function is as follows:

[0036]

[0037] Recalculate the potential value for each data point. Remove data points with low potential values, as these may be noise or unrepresentative information. By retaining data points with high potential values, subsequent classification and analysis can be more accurate.

[0038] S5: Adaptively determine the number of class centers based on the distribution of the potential values ​​of the data points. The specific process is:

[0039] First, the initial class center is selected: the point with the largest potential value is taken as the first class center.

[0040] Then, the region is expanded: for the selected cluster centroid, the nearest point is found and its potential value is determined to be less than that of the cluster centroid. If so, it is assigned to that cluster. The next step is to find the point closest to any point in that cluster (point a) and determine whether the potential value of point a is less than the potential value of the point closest to point a in the current cluster (point b). If the condition is met, point a is assigned to the current cluster. Repeat the above expansion process until no points meet the condition within a certain distance of the cluster centroid.

[0041] New centroid selection: From the remaining unclassified data points, select the point with the largest potential value as the new centroid, and repeat the above steps. When the number of remaining unclassified data points is less than a certain proportion of the total number of data points, the new centroid selection is stopped. The number of centroids at this time is the estimated number of clusters.

[0042] S6: Obtain weight coefficients based on the correlation between data points. The weight coefficients describe the similarity or degree of association between data points. For a data point, the denser the surrounding data points, the greater the average similarity, and the greater the influence on the clustering results. Therefore, it is necessary to give this data point a greater weight. The calculation formula for the correlation between data points is:

[0043]

[0044] where d(x j ,x i ) represents the distance between the jth data point and the i-th data point, represents the potential value of the j-th data point.

[0045] Weight coefficient V j The expression is as follows:

[0046]

[0047] From the above formula, we can know that when the distance d(x j ,x i ) is closer, the weight w j The larger it is, the more weights the core points will have and the less weights the edge points will have, which further enhances the noise resistance of the algorithm and can also handle imbalanced data sets well.

[0048] S7: Use the improved objective function based on the weight coefficient to iterate and obtain the membership matrix and classification results.

[0049] The improved objective function is:

[0050] Both

[0051] According to the Lagrange multiplier method, the membership matrix and cluster center that minimize J can be obtained. The cluster center c i for:

[0052]

[0053] Membership matrix u ij for:

[0054]

[0055] Iteration stopping condition:

[0056] mx ij {|J (t+1) -J (t) |}<ε (10)

[0057] Among them, C represents the number of clusters, N represents the number of data points, and v j represents the weight coefficient of the jth data point, represents the mth power of the membership matrix, c k represents the kth cluster center, c i represents the i-th cluster center, m represents the fuzzy weight coefficient, ε represents the error threshold, J (t+1) represents the objective function value of the t+1th iteration, J (t) Represents the objective function value at the tth iteration.

[0058] When the iteration stops, the effective classification of the original data set is completed and accurate classification results are obtained.

[0059] In this specific embodiment, to evaluate the performance of the proposed algorithm, detailed experiments were conducted on different radar datasets, and multiple algorithms were compared. The research focused on three key areas: noise immunity, dataset sorting performance for different radars, and performance on imbalanced datasets.

[0060] Noise Immunity Study:

[0061] We simulated a dataset containing four radars and added varying degrees of Gaussian noise to each parameter during the simulation to make the data distribution more similar to actual radar data. We then compared the performance of our proposed algorithm with other algorithms under varying noise levels to assess its noise resistance.

[0062] Figure 2 (a) is the original data without sorting and with noise, and (b) is the sorting result after the improved FCM algorithm.

[0063] Table 1 shows the corresponding evaluation metrics for different algorithms under different noise ratios. This paper uses four evaluation metrics to assess algorithm performance: accuracy, F1 value, Rand coefficient, and silhouette coefficient. For each of these metrics, higher values ​​indicate better clustering results.

[0064] Table 1 Clustering results of different algorithms

[0065]

[0066] Table 1 shows that the improved algorithm achieves a good classification effect on noisy data. As the proportion of noisy data increases, the fluctuations in accuracy, F1 value, Rand coefficient, and silhouette coefficient are relatively small, indicating that the algorithm's overall noise resistance is strong. Judging from the values ​​of various evaluation indicators, the clustering effect of the other two algorithms is lower than that of the DF-FCM algorithm. When the proportion of noise is high, two spatially close radar data sets may be grouped together, resulting in a significant decrease in all evaluation indicators. The silhouette coefficient values ​​of the various algorithms are all below 0.5. This is mainly due to the fact that Gaussian noise is added to the radar parameters during data generation to simulate real-world conditions, making the data relatively loose overall, resulting in relatively low silhouette coefficient values.

[0067] Algorithm performance experiment:

[0068] To test the accuracy of the algorithm's adaptive cluster count and compare its performance with other algorithms, three radar datasets were generated, containing data from three, four, and five radars, respectively. These datasets simulate different radar signal scenarios likely to be encountered in the real world, ensuring the algorithm's robustness and effectiveness in diverse data settings. The improved DF-FCM algorithm was then compared with the SC-KMEANS algorithm (an adaptive KMEANS algorithm that incorporates the silhouette coefficient) and the RI-FCM algorithm (a fuzzy C-means algorithm that incorporates the Rand coefficient to implement an adaptive C value).

[0069] Figure 3 The following are the sorting results of DF-FCM, SC-KMEANS and RI-FCM algorithms on three data sets. DF-FCM-1 (Figure a), SC-KMEANS-1 (Figure b) and RI-FCM-1 (Figure c) are the sorting results of the three algorithms on three radar data sets. DF-FCM-2 (Figure d), SC-KMEANS-2 (Figure e) and RI-FCM-2 (Figure f) are the sorting results of the three algorithms on four radar data sets. DF-FCM-3 (Figure g), SC-KMEANS-3 (Figure h) and RI-FCM-3 (Figure i) are the sorting results of the three algorithms on five radar data sets. The same color and shape represent the same category. Figure 3 It can be seen that the DF-FCM algorithm can accurately classify the three data sets, while the SC-KMEANS algorithm incorrectly classifies the four-radar and five-radar data sets into three categories, and the RI-FCM algorithm classifies the four-radar data set into five categories and the five-radar data set into six categories.

[0070] Table 2 is the corresponding result data table:

[0071] Table 2 Clustering results of different algorithms

[0072]

[0073] As shown in Table 2, for the three-radar dataset, all three algorithms accurately identified the correct number of classes and performed well in classification. However, for the four-radar and five-radar datasets, the RI-FCM and SC-KMEANS algorithms failed to correctly identify the correct number of classes, resulting in poor results. This is primarily due to the large separation of radar data points and the dense concentration of core points. This prevented the adaptive process from accurately determining the correct number of classes, ultimately leading to incorrect classification.

[0074] Research on Imbalanced Datasets:

[0075] The traditional fuzzy C-means clustering algorithm has a poor sorting effect on unbalanced data sets, while the DF-FCM algorithm improves the objective function of the traditional FCM algorithm by combining the weight factor of the potential value, and can better handle this situation. Figure 4 Table 3 shows the classification results of the data set by DF-FCM, SC-KMEANS, and RI-FCM algorithms. Table 3 shows the corresponding clustering result evaluation index values:

[0076] Table 3 Clustering results of different algorithms under unbalanced datasets

[0077]

[0078] Figure 4 (a) shows the results of the improved DF-FCM algorithm based on the data field, (b) shows the results using the adaptive KMEANS algorithm, and (c) shows the results of adaptive fuzzy C-means clustering using the Rand coefficient. In an unbalanced dataset with eight radars, only the DF-FCM algorithm correctly sorts the three radars with fewer pulses. The SC-KMEANS and RI-FCM algorithms mistakenly classify two radars as one, or even classify radar pulses from a larger dataset as two radars. The SC-KMEANS algorithm misclassifies because the data points between classes are relatively close, resulting in the data from two closely spaced radars being grouped together. The RI-FCM algorithm misclassifies because it assumes that each data point has the same influence on the clustering result. In this case, if the number of radars in the dataset varies significantly, radars with fewer data points will be considered to be on the edge of adjacent classes and thus grouped together. The improved algorithm proposed in this paper combines the concept of potential value proposed in the data field and the average similarity between data points to construct weight coefficients and improve the objective function, so that the algorithm can handle this kind of data set well.

[0079] See Figure 5 , Figure 54 is a schematic diagram of the working of the hardware device of an embodiment of the present invention, wherein the hardware device specifically comprises: an improved radar signal sorting device 401 based on the FCM algorithm, a processor 402 and a storage device 403.

[0080] An improved radar signal sorting device 401 based on the FCM algorithm: The improved radar signal sorting device 401 based on the FCM algorithm implements the improved radar signal sorting algorithm based on the FCM algorithm.

[0081] Processor 402: The processor 402 loads and executes instructions and data in the storage device 403 to implement the radar signal sorting algorithm improved based on the FCM algorithm.

[0082] Storage device 403: The storage device 403 stores instructions and data; the storage device 403 is used to implement the radar signal sorting algorithm improved based on the FCM algorithm.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A radar signal sorting algorithm improved based on the FCM algorithm, characterized by: include: S1: Extract pulse width, carrier frequency, and arrival angle from the pulse descriptor data received by the radar to form three-dimensional coordinate data, and perform normalization on the three-dimensional coordinate data; S2: Obtain the field intensity function and the potential value formula of each point based on the data field theory; S3: Calculate the change of potential entropy with radiation factor based on the normalized data, and select the optimal radiation factor based on the minimum value of potential entropy; S4: Calculate the potential value according to the optimal radiation factor and remove noise points; S5: Adaptively determine the number of class centers based on the distribution of potential values ​​of data points; The specific process of S5 is as follows: (1) Initial centroid selection: the point with the largest potential value is selected as the first centroid; (2) Region expansion: For the selected cluster center, find the nearest point around it and determine whether the potential value of the point is less than the potential value of the cluster center. If so, classify it into the cluster and continue to find the point a that is closest to any point in the cluster. Determine whether the potential value of point a is less than the potential value of point b that is closest to point a in the current cluster. If the condition is met, classify point a into the current cluster. Repeat the above expansion process until there are no points that meet the condition within a certain distance from the cluster center. (3) New centroid selection: From the remaining unclassified data points, select the point with the largest potential value as the new centroid. Repeat the above operation. When the number of remaining unclassified data points is less than a certain proportion of the total number of data points, stop selecting new centroids. The number of centroids at this time is the estimated number of clusters. S6: Calculate the weight coefficient based on the correlation and potential value between data points; S7: Calculate the improved objective function based on the weight coefficient and the adaptive number of clusters, and iterate to obtain the best clustering result.

2. The radar signal sorting algorithm improved based on the FCM algorithm according to claim 1, characterized in that: In S2, the field strength function is: in, Represents a data object and The Euclidean distance, σ is the radiation factor, m represents the fuzzy weighting coefficient The potential value is the point pair in the data field The generated field strength function and is used to measure the influence of the position and characteristics of the data point in the data set on the overall data; the potential value function is: in, represents the potential value, represents the field strength function, Represents a data object and The Euclidean distance, Represents the i-th data object.

3. The radar signal sorting algorithm improved based on the FCM algorithm according to claim 1, characterized in that: In S3, the expression of potential entropy is as follows: in, represents potential entropy, is the normalization factor, The potential value of the i-th data point, n represents the number of data points.

4. The radar signal sorting algorithm improved based on the FCM algorithm according to claim 1, characterized in that: In S6, the calculation formula for the correlation between data points is: in, Indicates the j Data points and i The correlation between the data points, Indicates the j Data points and i The distance between data points, Indicates the j The potential value of the data point, Indicates the i The potential value of the data point, n represents the number of data points.

5. The radar signal sorting algorithm improved based on the FCM algorithm as claimed in claim 4, characterized in that: In S6, the expression of the weight coefficient is: in, Represents the weight coefficient.

6. The radar signal sorting algorithm improved based on the FCM algorithm according to claim 1, characterized in that: In S7, the improved objective function is: According to the Lagrange multiplier method, the membership matrix and cluster center that minimize the objective function J are obtained. for: Membership matrix for: Iteration stopping condition: in, C represents the number of clusters, N Indicates the number of data points, represents the weight coefficient of the jth data point, represents the mth power of the membership matrix, represents the kth cluster center, represents the i-th cluster center, represents the fuzzy weighting coefficient, represents the error threshold, represents the objective function value of the t+1th iteration, Represents the objective function value at the tth iteration.

7. A storage device, characterized in that: The storage device stores instructions and data for implementing the radar signal sorting algorithm improved based on the FCM algorithm as described in any one of claims 1 to 6.

8. A radar signal sorting device based on an improved FCM algorithm, characterized by: include: A processor and a storage device; the processor loads and executes instructions and data in the storage device to implement the radar signal sorting algorithm improved based on the FCM algorithm as described in any one of claims 1 to 6.

Images