A radar signal sorting method based on BIC Gaussian mixture model

Abstract

The present invention provides a radar signal sorting method based on a BIC Gaussian mixture model, comprising: S1, parameter definition and initialization; S2, calculation of probability density Psi and probability Gamma; S3, parameter updating based on the calculated probability density Psi and probability Gamma; S4, recalculation of probability density Psi and probability Gamma using the updated parameters; repeating steps S3 and S4 until iterative convergence and an optimal solution for the parameters is obtained; S5, calculation of probability Gamma corresponding to the optimal solution; S6, calculation of the complexity BIC of the Gaussian model based on the maximum value of probability Gamma, selecting the Gaussian model with the maximum complexity BIC as the radar signal sorting model, and thus performing radar signal sorting using the radar signal sorting model. The present invention solves the problem that radar signals are difficult to model due to complex parameter variations, and achieves automatic output of sorting results.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal sorting, and in particular to a radar signal sorting method based on a BIC Gaussian mixture model. Background Art

[0002] In modern electronic warfare, radar reconnaissance receivers face unprecedented challenges due to the increasingly complex electromagnetic environment on the battlefield and the increasing threat level of modern radar systems. The complexity of the current radar signal sorting environment is primarily reflected in three key factors: signal density, complex waveforms, and pulse loss. Radar signal density has increased from approximately 200,000 pulses per second a decade ago to approximately 2 million pulses per second today. In just a decade, the pulse density in electronic warfare environments has increased tenfold. Early pulse sorting methods primarily utilized pulse repetition period (PRI) histograms, such as cumulative difference histograms and sequence difference histograms. These methods perform extensive calculations on PRI multiples, sums, and differences, making threshold determination difficult. While effective for sorting pulses with a fixed PRI, they can result in errors or even failure when used to sort dense signals. To address this difficulty in sorting dense signals, clustering methods based on K-means have emerged, gradually classifying aliased pulses into multiple categories for sorting.

[0003] The core idea of ​​the K-means algorithm is to randomly select k points as the initial cluster centers. By calculating the distance between the data object being studied and each point, it is assigned to the cluster with the closest cluster center. The center of the adjusted cluster is then recalculated. If the cluster center does not change after two consecutive calculations, it means that the clustering criterion function has converged and the adjustment of the data object is complete. The algorithm examines whether the classification of the data object is correct during each iteration. If not, it needs to be adjusted. After the adjustment of the data object is completed, the cluster center is modified and the next iteration is entered. If all data objects have been correctly classified in one iteration, no further adjustments will be made, the cluster center is determined, and the algorithm ends.

[0004] The K-means algorithm can roughly cluster data, but it has two disadvantages. First, K-means is a discriminant model, which means it can only determine whether a sample belongs to a certain class, but cannot give the probability of the sample belonging to each class, and cannot provide more information for subsequent signal processing. Second, for classes with non-circular distributions, it will produce incorrect classification results. Radar pulse parameters are often not a standard normal distribution, so using K-means clustering is more prone to errors. Summary of the Invention

[0005] The present invention aims to provide a radar signal sorting method based on the BIC Gaussian mixture model to solve the problems existing in the radar signal sorting based on the K-means algorithm.

[0006] The present invention provides a radar signal sorting method based on the BIC Gaussian mixture model, comprising the following steps:

[0007] S1, parameter definition and initialization; the parameters include: the mean Mu and covariance Sigma of K Gaussian models, the weight Pi of each Gaussian model, the probability density Psi of a sample belonging to a certain Gaussian model calculated by the Gaussian distribution, and the probability Gamma of each sample belonging to each Gaussian model;

[0008] S2, calculate the probability density Psi and probability Gamma;

[0009] S3, based on the calculated probability density Psi and probability Gamma, update the mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model;

[0010] S4, using the updated mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model to recalculate the probability density Psi and probability Gamma; repeatedly perform steps S3 to S4 until the iteration converges, and obtain the optimal solution for the mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model;

[0011] S5, calculate the probability Gamma corresponding to the optimal solution, and the sample belongs to the Gaussian model corresponding to the maximum value of probability Gamma, thereby dividing the sample into K clusters;

[0012] S6, calculates the complexity BIC of the Gaussian model based on the maximum value of probability Gamma, selects the Gaussian model with the largest complexity BIC as the radar signal sorting model, and then uses the radar signal sorting model to perform radar signal sorting.

[0013] Furthermore, the size of the parameters in step S1 is:

[0014] Gamma=zeros(N,K)

[0015] Psi=zeros(N,K)

[0016] Mu=zeros(K,D)

[0017] Sigma=zeros(D,D,K)

[0018] Pi=zeros(1,K)

[0019] Wherein, N represents the total number of samples in the sample set X of the two-dimensional radar signal data; D represents the dimension; and K represents the number of Gaussian models.

[0020] Furthermore, in step S1, the initial values ​​of the parameters are as follows:

[0021] (1) Randomly select K samples and calculate the initial mean of K Gaussian models;

[0022] (2) The initial weights of each Gaussian model are equal;

[0023] (3) Calculate the covariance of all samples as the initial covariance.

[0024] Furthermore, the method for calculating the probability density Psi in step S2 is:

[0025] Traverse K Gaussian models and calculate the probability density Psi of each sample for Gaussian model k based on the high-dimensional Gaussian distribution probability:

[0026]

[0027] *(Y k ′))

[0028] where Y k =X-Mu(k,:).

[0029] Furthermore, the method for calculating the probability Gamma in step S2 is:

[0030] After considering the Gaussian model weights, traverse each Gaussian model and each sample to calculate the probability Gamma:

[0031] Gamma(j,k)=Pi(1,k)*Psi(j,k) / sum(Psi(j,:)*Pi′).

[0032] Furthermore, the method for updating the mean Mu of the K Gaussian models in step S3 is:

[0033] The weighted center values ​​of all sample points (L(:,:)) are used as the mean value Mu of each Gaussian model. For a given Gaussian model, the probability of each sample belonging to the Gaussian model (Gamma(j,k)) multiplied by the product of the sample and the X-coordinate (L(j,0)) is added together and divided by the sum of the probabilities of all samples in the Gaussian model (Sum(Gamma(:,k))). This yields the mean value Mu(k,0) of the Gaussian model on the X-axis. Similarly, the mean value Mu(k,1) of the Gaussian model on the Y-axis can be obtained.

[0034] Furthermore, the method for updating the covariance Sigma of the K Gaussian models in step S3 is:

[0035] The covariance of all sample points and the mean of the center point is weighted and used as the covariance of each Gaussian model. The calculation process is the same as that of the mean.

[0036] Furthermore, in step S3, the method for updating the weight Pi of each Gaussian model is:

[0037] The sum of the probabilities of all sample points contained in each Gaussian model is divided by the sum of the probabilities of all Gaussian models as the weight of each Gaussian model.

[0038] Furthermore, in step S4, iterative convergence means:

[0039] The iteration converges when the difference between the updated parameters and the parameters before the update is less than the difference threshold.

[0040] Furthermore, in step S6, the calculation formula of Bayesian accuracy BIC is as follows:

[0041]

[0042] Among them, k max Indicates the Gaussian model number corresponding to the maximum value of probability Gamma. When calculating the Bayesian accuracy BIC, it is necessary to pre-set the value range of K. The Bayesian accuracy BIC corresponding to each value of K is calculated, and the K value with the largest Bayesian accuracy BIC is selected as the optimal number of radar signal sorting.

[0043] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are as follows: the present invention utilizes the characteristics of the Gaussian mixture model that can fit arbitrary distributions and output membership probabilities, combined with the Bayesian Information Criterion (BIC), to solve the problem that radar signals are difficult to model due to complex parameter changes, and realizes automatic output of sorting results. Compared with K-means and density-based DBSCAN clustering algorithms, the Gaussian mixture model can calculate the probability that each sample belongs to each cluster. Therefore, it can be combined with the BIC algorithm to quantitatively evaluate the performance of different numbers of clusters. By traversing within a certain range, the optimal number of clusters can be automatically selected. Summary:

[0044] (1) Compared with the K-means clustering algorithm, the Gaussian mixture model can fit the complex radar signal distribution;

[0045] (2) Compared with the DBSCAN algorithm, the Gaussian mixture model can output membership probabilities;

[0046] (3) Compared with simple clustering algorithms, the BIC algorithm solves the problem of automatically finding the optimal number of clusters, which is the most difficult problem among all types of clustering algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings in the embodiments will be briefly introduced below. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0048] Figure 1 Flowchart of a radar signal sorting method based on the BIC Gaussian mixture model in an embodiment of the present invention.

[0049] Figure 2 This is a pulse distribution diagram of radar data simulation in an embodiment of the present invention.

[0050] Figure 3 This is a distribution diagram of clustering results of the radar signal sorting method based on the BIC Gaussian mixture model in an embodiment of the present invention.

[0051] Figure 4 This is a distribution diagram of clustering results of the radar signal sorting method based on K-means in an embodiment of the present invention.

[0052] Figure 5 This is a diagram showing the changes in Bayesian accuracy BIC in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0054] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0055] Example

[0056] Design idea: The so-called Gaussian mixture model refers to the estimation of the probability density distribution of the sample set, and each Gaussian model represents a cluster. GMM is a soft clustering process. This clustering method divides samples into clusters according to the size of the probability, rather than completely belonging to a certain cluster. The training model used for estimation is the weighted sum of several Gaussian models, and then the samples are projected on several Gaussian models respectively to obtain the probability of these samples being divided into each cluster. Finally, the cluster with the largest probability is selected as the final classification result of the samples. Therefore, Figure 1 As shown, this embodiment proposes a radar signal sorting method based on the BIC Gaussian mixture model, including the following steps:

[0057] S1, parameter definition and initialization; the parameters include: the mean Mu and covariance Sigma of K Gaussian models, the weight Pi of each Gaussian model, the probability density Psi of a sample belonging to a Gaussian model calculated by the Gaussian distribution, and the probability Gamma of each sample belonging to each Gaussian model; specifically:

[0058] Let X be the sample set of two-dimensional radar signal data, X j is the jth sample in the sample set X, j = 1, 2, ..., N, N is the total number of samples in the sample set X of the two-dimensional radar signal data, and D is the dimension; the Gaussian model is numbered k, k = 1, 2, ..., K, and K is the number of Gaussian models; therefore, the size of the above parameters is:

[0059] Gamma=zeros(N,K)

[0060] Psi=zeros(N,K)

[0061] Mu=zeros(K,D)

[0062] Sigma=zeros(D,D,K)

[0063] Pi=zeros(1,K)

[0064] Randomly select K samples to calculate the initial means of K Gaussian models; calculate the covariance of all samples as the initial covariance; the initial weight of each Gaussian model is equal, as shown below:

[0065] Mu(k,:)=X(random,:)

[0066] Pi(k)=1 / K

[0067] Sigma(:,:,k)=cov(X)

[0068] S2, calculate the probability density Psi and probability Gamma; specifically:

[0069] Traverse K Gaussian models and calculate the probability density Psi of each sample for Gaussian model k based on the high-dimensional Gaussian distribution probability:

[0070]

[0071] in:

[0072] Y k =X-Mu(k,:)

[0073] After considering the Gaussian model weights, traverse each Gaussian model and each sample to calculate the probability Gamma:

[0074] Gamma(j,k)=Pi(1,k)*Psi(j,k) / sum(Psi(j,:)*Pi′)

[0075] S3, based on the calculated probability density Psi and probability Gamma, updates the mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model; specifically:

[0076] (1) In this embodiment, the center values ​​of all sample points (L(:,:)) are weighted and used as the mean Mu of each Gaussian model. For a certain Gaussian model, the probability that each sample belongs to the Gaussian model (Gamma(j,k)) multiplied by the product of the sample and the X coordinate (L(j,0)) is added and then divided by the sum of the probabilities of all samples of the Gaussian model (Sum(Gamma(:,k))). The mean Mu(k,0) of the X axis of the Gaussian model can be obtained. Similarly, the mean Mu(k,1) of the Y axis of the Gaussian model can be obtained. The specific algorithm is expressed as follows:

[0077]

[0078] (2) In this embodiment, the covariance of all sample points and the center point (mean) is (L(j,:)-Mu(k,:)) ′ *(L(j,:)-Mu(k,:))) is weighted as the covariance of each Gaussian model. The calculation process is the same as the mean. The specific algorithm is expressed as follows:

[0079]

[0080] (3) In this embodiment, the sum of the probabilities of all sample points contained in each Gaussian model is divided by the sum of the probabilities of all Gaussian models (Gamma(:,:)) as the weight of each Gaussian model. The specific algorithm is expressed as follows:

[0081]

[0082] S4, using the updated mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model to recalculate the probability density Psi and probability Gamma (the calculation method is the same as step S2); repeatedly perform steps S3 to S4 until the iteration converges, that is, the iteration converges when the difference between the updated parameters and the parameters before the update is less than the difference threshold, and stop the loop, thereby obtaining the optimal solution of the mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model;

[0083] S5, calculate the probability Gamma corresponding to the optimal solution, and the sample belongs to the Gaussian model corresponding to the maximum value of probability Gamma, thereby dividing the sample into K clusters;

[0084] S6, calculating the Bayesian accuracy BIC of the Gaussian model based on the maximum value of probability Gamma, selecting the Gaussian model with the largest Bayesian accuracy BIC as the radar signal sorting model, and then using the radar signal sorting model to perform radar signal sorting;

[0085] The Bayesian Information Criterion (BIC) originates from Bayesian theory and primarily addresses the problem of Gaussian model selection. Its approach is to find the optimal balance between the complexity of the Gaussian model and its ability to describe the sample set. In this method, the logarithm of the maximum probability that each sample belongs to each Gaussian model is used to represent the Gaussian model's ability to describe the sample set, and the product of the number of Gaussian models K and the logarithm of the number of samples is used to represent the complexity of the Gaussian model. Therefore, the Bayesian accuracy BIC is calculated as follows:

[0086]

[0087] Among them, k max Indicates the Gaussian model number corresponding to the maximum value of probability Gamma. When calculating the Bayesian accuracy BIC, it is necessary to pre-set the value range of K. The Bayesian accuracy BIC corresponding to each value of K is calculated, and the K value with the largest Bayesian accuracy BIC is selected as the optimal number of radar signal sorting.

[0088] As can be seen from the above, the present invention utilizes the Gaussian mixture model's ability to fit arbitrary distributions and output membership probabilities. Combined with the Bayesian Information Criterion (BIC), this solves the difficulty of modeling radar signals due to complex parameter variations, enabling automatic output of sorting results. Compared to the K-means and density-based DBSCAN clustering algorithms, the Gaussian mixture model can calculate the probability that each sample belongs to each cluster. Therefore, it can be combined with the BIC algorithm to quantitatively evaluate the performance of different numbers of clusters, automatically selecting the optimal number of clusters within a certain range.

[0089] Summary:

[0090] (1) Compared with the K-means clustering algorithm, the Gaussian mixture model can fit the complex radar signal distribution;

[0091] (2) Compared with the DBSCAN algorithm, the Gaussian mixture model can output membership probabilities;

[0092] (3) Compared with simple clustering algorithms, the BIC algorithm solves the problem of automatically finding the optimal number of clusters, which is the most difficult problem among all types of clustering algorithms.

[0093] In order to prove the effectiveness of the present invention, a simulation test was conducted on the proposed radar signal sorting method based on the BIC Gaussian mixture model. Figure 1 First, the number of clusters is set to a range of 2 to 10, and then the parameters of the Gaussian model are calculated for each selected number of clusters to select the optimal number of clusters.

[0094] Pulse width and repetition frequency are selected as input features for radar signal sorting. After summarizing the basic distribution of measured radar data, four sets of parameters are simulated, such as Figure 2 As shown, the horizontal axis is the repetition rate and the vertical axis is the pulse width.

[0095] Figure 3 and Figure 4 These are the clustering results of the BIC Gaussian mixture model and the K-means algorithm, where different color depths represent different clusters. It can be seen that the clustering results of the BIC Gaussian mixture model are consistent with the subjective results. The K-means algorithm will stagger some pulses, as shown in the box in the figure, because the principle of the K-means algorithm determines that each cluster can only be distributed in a circular shape.

[0096] Figure 5 The BIC values ​​corresponding to different numbers of clusters show that BIC is the largest when K=4, which is consistent with the most appropriate number of clusters. On other data sets, the number of clusters corresponding to the maximum BIC value is also the most appropriate number of clusters, indicating that the BIC Gaussian mixture model can achieve the goal of automatically determining the number of clusters.

[0097] In summary, the method proposed in the present invention can achieve sorting in a complex radar signal environment, which proves the effectiveness of the invention.

[0098] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A radar signal sorting method based on the BIC Gaussian mixture model, characterized in that: The steps include: S1, parameter definition and initialization; the parameters include: the mean Mu and covariance Sigma of K Gaussian models, the weight Pi of each Gaussian model, the probability density Psi of a sample belonging to a certain Gaussian model calculated by the Gaussian distribution, and the probability Gamma of each sample belonging to each Gaussian model; S2, calculate the probability density Psi and probability Gamma; S3, based on the calculated probability density Psi and probability Gamma, update the mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model; S4, using the updated mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model to recalculate the probability density Psi and probability Gamma; repeatedly perform steps S3 to S4 until the iteration converges, and obtain the optimal solution for the mean Mu and covariance Sigma of the K Gaussian models and the weight Pi of each Gaussian model; S5, calculate the probability Gamma corresponding to the optimal solution, and the sample belongs to the Gaussian model corresponding to the maximum value of probability Gamma, thereby dividing the sample into K clusters; S6, calculates the complexity BIC of the Gaussian model based on the maximum value of probability Gamma, selects the Gaussian model with the largest complexity BIC as the radar signal sorting model, and then uses the radar signal sorting model to perform radar signal sorting.

2. The radar signal sorting method based on the BIC Gaussian mixture model according to claim 1, characterized in that: The size of the parameters in step S1 is: Gamma=zeros(N,K) Psi=zeros(N,K) Mu=zeros(K,D) Sigma=zeros(D,D,K) Pi=zeros(1,K) Wherein, N represents the total number of samples in the sample set X of the two-dimensional radar signal data; D represents the dimension; and K represents the number of Gaussian models.

3. The radar signal sorting method based on the BIC Gaussian mixture model according to claim 2, characterized in that: In step S1, the initial values ​​of the parameters are as follows: (1) Randomly select K samples and calculate the initial mean of K Gaussian models; (2) The initial weights of each Gaussian model are equal; (3) Calculate the covariance of all samples as the initial covariance.

4. The radar signal sorting method based on the BIC Gaussian mixture model according to claim 3, characterized in that: The method for calculating the probability density Psi in step S2 is: Traverse K Gaussian models and calculate the probability density Psi of each sample for Gaussian model k based on the high-dimensional Gaussian distribution probability: where Y k =X-Mu(k,:).

5. The radar signal sorting method based on the BIC Gaussian mixture model according to claim 4, characterized in that: The method for calculating the probability Gamma in step S2 is: After considering the Gaussian model weights, traverse each Gaussian model and each sample to calculate the probability Gamma: Gamma(j,k)=Pi(1,k)*Psi(j,k) / sum(Psi(j,:)*Pi′).

6. The radar signal sorting method based on the BIC Gaussian mixture model according to claim 5, characterized in that: The method for updating the mean Mu of the K Gaussian models in step S3 is: The weighted center values ​​of all sample points are used as the mean Mu of each Gaussian model. For a certain Gaussian model, the probability that each sample belongs to the Gaussian model (Gamma(j,k)) is multiplied by the product of the sample and the X-coordinate, and then divided by the sum of the probabilities of all samples of the Gaussian model to obtain the mean Mu(k,0) of the X-axis of the Gaussian model. Similarly, the mean Mu(k,1) of the Y-axis of the Gaussian model is obtained.

7. The radar signal sorting method based on the BIC Gaussian mixture model according to claim 5, characterized in that: The method for updating the covariance Sigma of the K Gaussian models in step S3 is: The covariance of all sample points and the mean of the center point is weighted as the covariance of each Gaussian model.

8. The radar signal sorting method based on the BIC Gaussian mixture model according to claim 5, characterized in that: In step S3, the method for updating the weight Pi of each Gaussian model is: The sum of the probabilities of all sample points contained in each Gaussian model is divided by the sum of the probabilities of all Gaussian models as the weight of each Gaussian model.

9. The radar signal sorting method based on the BIC Gaussian mixture model according to any one of claims 5 to 8, characterized in that: In step S4, iterative convergence means: The iteration converges when the difference between the updated parameters and the parameters before the update is less than the difference threshold.

10. The radar signal sorting method based on the BIC Gaussian mixture model according to claim 9, characterized in that: In step S6, the calculation formula of Bayesian accuracy BIC is as follows: Among them, k max Indicates the Gaussian model number corresponding to the maximum value of probability Gamma. When calculating the Bayesian accuracy BIC, it is necessary to pre-set the value range of K. The Bayesian accuracy BIC corresponding to each value of K is calculated, and the K value with the largest Bayesian accuracy BIC is selected as the optimal number of radar signal sorting.

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