Class Noise Interference Detection Method and System Based on Expectation Maximization and Eigenvalue Decomposition

Abstract

The present invention belongs to the technical field of sonar signal detection, and particularly relates to a method and system for detecting noise-like interference based on expectation maximization and eigenvalue decomposition. The method includes: preprocessing the echoes received by a linear array in a detection area to obtain K independent sample vectors that satisfy a zero-mean multivariate complex Gaussian distribution, forming a data matrix of the independent sample vectors; introducing independent and identically distributed discrete random variables to obtain the joint log-likelihood function of the data matrix of the independent sample vectors; using the E-step of the EM algorithm to calculate the posterior probability of the classification to which the independent sample vectors belong, and estimating the environmental noise energy and the interference covariance matrix by means of eigenvalue decomposition in the M-step; determining the category of the independent sample vectors according to the obtained maximum posterior probability. The present invention can accurately estimate the background noise energy and the covariance matrix of the NCP, and by cleverly integrating the EM clustering algorithm, makes the detection process more automated, improving the efficiency and accuracy of interference detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of sonar signal detection, and particularly relates to a method and system for detecting noise-like jamming based on expectation maximization and eigenvalue decomposition. Background Art

[0002] With the development of electronic countermeasure technology and the complication of application scenarios, sonar systems face more and more challenges in actual operation. Noise-like jammers (NLJs) are a common type of active artificial jamming, posing a significant threat to sonar detection systems. NLJs emit broadband high-power signals similar to noise, increasing the noise floor of sonar receivers, masking target information, and affecting target detection, thus interfering with the normal operation of sonar systems. Since the energy of NLJs signals usually covers the instantaneous bandwidth of sonar receivers and has no structure in the time domain, the detection method should jointly consider the spatial and frequency domain information of the interference and be able to be flexibly adjusted according to the specific environment, which is the core of the space-time adaptive detection (STAD) method.

[0003] In actual underwater acoustic countermeasure scenarios, the interference signals emitted by NLJs often take the form of noise-covered pulses (NCPs), and interference components are introduced within the unit samples corresponding to the pulse duration by emitting pulse noise signals. However, most traditional underwater NLJs information extraction methods based on STAD are based on a continuous interference model, that is, it is assumed that there are interference components with the same parameter characteristics within the unit samples, and the mismatch of the reference model makes it difficult for existing methods to work effectively. In order to achieve NCP detection and information extraction.

[0004] Regarding the problem of underwater NLJs detection and information extraction based on STAD, the existing technical solutions include: Solution 1: A two-level detection architecture proposed based on dual auxiliary datasets and the generalized information criterion, which uses multiple hypotheses to formulate the target detection problem under interferences such as NCP, and designs a two-stage algorithm to solve this problem: In the first stage, the scene is classified based on the MOS (Model Order Selection) criterion, and in the second stage, the presence and specific scene of the target are confirmed through a decision-making scheme to achieve adaptive detection of the target under multiple interferences; Solution 2: Based on the rank-one correction difference between the covariance matrix of the measured data and the covariance matrix of the reference data, and using auxiliary data and the generalized likelihood ratio test (GLRT, Generalized Likelihood Ratio Test), the detection of noise interference is realized, and this type of solution improves the estimation accuracy of the interference covariance matrix. The existing technical Solution 1 adopts a continuous interference model, assuming that all the unit samples of interest contain interference signal components with the same parameter characteristics, which will lead to a model mismatch problem between the method and the application scenario in the detection scenario where NCP exists, and it is impossible to effectively detect and extract information about the interference; the existing technical Solution 2 needs to use the reference data covariance matrix constructed from auxiliary data, and the performance will decline in an environment where the number of auxiliary data is severely lacking. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the existing technology and propose a noise-like interference detection method and system based on expectation maximization (EM, Expectation-Maximization) and eigenvalue decomposition.

[0006] In view of this, the present invention proposes a noise-like interference detection method based on expectation maximization and eigenvalue decomposition, including:

[0007] Step 1: Preprocess the echo received by the linear array in the detection area to obtain K independent sample vectors that satisfy the zero-mean multivariate complex Gaussian distribution, and form a data matrix of independent sample vectors ;

[0008] Step 2: Introduce independent and identically distributed discrete random variables to obtain the joint log-likelihood function of the data matrix of independent sample vectors;

[0009] Step 3: Use the E-step of the EM algorithm to calculate the posterior probability of the classification to which the independent sample vectors belong, and estimate the environmental noise energy and the interference covariance matrix through the eigenvalue decomposition method in the M-step;

[0010] Step 4: Determine the category of the independent sample vectors according to the obtained maximum posterior probability.

[0011] Preferably, the linear array in step 1 includes N array elements. After preprocessing the echoes of the N array elements, K independent sample vectors that satisfy the zero-mean multivariate complex Gaussian distribution are obtained. Furthermore, a corresponding data matrix is formed. , , where represents an N-dimensional complex number, represents dimensional complex number, represents the k-th independent sample vector that satisfies the zero-mean multivariate complex Gaussian distribution.

[0012] Preferably, step 2 includes:

[0013] Introduce independent and identically distributed discrete random variables , , used to characterize or cases; represents the subscript set where the target component exists, represents the subscript set where the NCP component does not exist; r represents the potential category of the existence of noise-like interference in the detection area, and S represents the number of NCPs in the detection scenario;

[0014] Let the probability of , then there is ; where is an unknown probability group distribution function;

[0015] Applying the total probability formula, the probability density function of the independent sample vector is:

[0016]

[0017] Among them, is the set of parameters to be estimated in the th sample unit, is the set of unknown parameters of the th unit sample under the hypothesis, is the environmental noise energy, is the interference covariance matrix, represents any variable taking when its function value's cumulative sum, represents the function;

[0018] Obtain the joint log-likelihood function of is:

[0019] Among them, represents the logarithmic operation, represents corresponding to the posterior probability under the condition, represents the set of all parameters to be estimated.

[0020] Preferably, the step 3 includes:

[0021] Apply the E-step optimization process in the EM algorithm. In the th iteration It is expressed as:

[0022] Among them, represents the estimated result of the environmental noise energy after the th cycle iteration, represents the estimated result of the interference covariance matrix after the th cycle iteration, represents the estimated result of the probability group distribution function after the th cycle iteration;

[0023] For the M-step optimization, combined with the Lagrange operator optimization method under the constraint, the estimated value of in the hth cycle optimization is as follows:

[0024] Convert the estimation problems of the environmental noise energy and the interference covariance matrix into:

[0025]

[0026] Define:

[0027]

[0028]

[0029] Among them, represents the auxiliary function in the case of no NCP, represents the auxiliary function in the case of NCP; represents the identity matrix; represents the conjugate transpose of the vector;

[0030] Combined with the method of matrix eigenvalue decomposition, then:

[0031]

[0032] Among them, is another representation of the auxiliary function in the presence of NCP, denotes the eigenvalue of the denotes the eigenvalue of the denotes the first term of

[0033] Respectively, take the partial derivatives of and and set them to zero to obtain the corresponding estimation results:

[0034]

[0035] Among them, denotes the corresponding eigenvector matrix, is the estimated value of after the h-th loop iteration; is the estimated value of after the (h - 1)-th loop iteration; , denotes the diagonal matrix generated by , is the estimated value of after the h-th loop iteration; is to find the maximum value; denotes generating a diagonal matrix with the elements in the vector as elements.

[0036] Preferably, step 4 includes:

[0037] Substitute the estimation results of the environmental noise energy and the interference covariance matrix into the GLRT detection formula to obtain:

[0038]

[0039] Among them, is the estimated value under the hypothesis, represents the no-target hypothesis, denotes the alternative hypothesis in the presence of NCP, denotes the detection threshold denotes the th estimated result of the environmental noise energy after the loop iteration, denotes the th interference covariance matrix after the loop iteration, denotes the unit sample with NCP present The probability density function represents the unit samples without NCP The probability density function.

[0040] On the other hand, the present invention provides a noise-like interference detection system based on expectation maximization and eigenvalue decomposition, including:

[0041] A preprocessing module for preprocessing the echo received by the linear array in the detection area to obtain K independent sample vectors that satisfy the zero-mean multivariate complex Gaussian distribution, and forming a data matrix of independent sample vectors ;

[0042] A joint log-likelihood function acquisition module for introducing independent and identically distributed discrete random variables to obtain the joint log-likelihood function of the data matrix of independent sample vectors ;

[0043] An EM algorithm module for using the E-step of the EM algorithm to calculate the posterior probability of the classification to which the independent sample vector belongs, and estimating the environmental noise energy and interference covariance matrix by the eigenvalue decomposition method in the M-step;

[0044] A class recognition module for determining the class of the independent sample vector according to the obtained maximum posterior probability.

[0045] Compared with the prior art, the advantages of the present invention are as follows:

[0046] The present invention proposes an innovative NCP detection and information acquisition technology. This technology introduces latent variables to re-model the detection scenario of NCP existence, and uses the EM algorithm and eigenvalue decomposition method for sample classification and interference parameter estimation. It can achieve interference information acquisition and accurate detection without a large amount of auxiliary data. By using the eigenvalue decomposition technology, the present invention can accurately estimate the background noise energy and the covariance matrix of NCP. In addition, the present invention also skillfully integrates the EM clustering algorithm, which can intelligently distinguish and process unit samples under various NCP existences, making the detection process more automated and improving the efficiency and accuracy of interference detection. Specifically, it includes:

[0047] 1. Based on the interference scenario of NCP, the present invention abandons the continuous interference model of the traditional method, introduces latent variables to re-model the NCP detection scenario. It no longer assumes that the interference components in the unit samples are the same, but considers them to be different and independent. This model is more in line with the actual application scenario of sonar, making the information extraction of NCP more accurate;

[0048] 2. The present invention does not rely on traditional auxiliary data sets for interference covariance matrix estimation. This means that even in real scenarios where there is a lack of sufficient auxiliary data, interference information can be accurately extracted, thereby improving the applicability and robustness of the algorithm;

[0049] 3. The method proposed by the present invention combines the EM algorithm and the eigenvalue decomposition method. By batch analyzing sample data and using the maximum a posteriori probability criterion for judgment, the identification and information estimation of NCP are achieved. This method significantly reduces the high computational load required for processing each unit sample one by one and reduces the time complexity;

[0050] 4. The NCP detection and information extraction scheme proposed by the present invention in the passive mode can help sonar perceive the noise-like interference in the scene and provide parameter basis for interference suppression in the active sonar target detection process. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is the flowchart of the method of the present invention;

[0052] Figure 2 is the classification result of NCP interference unit samples based on the first scenario (1 simulation experiment);

[0053] Figure 3 is the average classification probability of NCP interference unit samples based on the first scenario (1000 simulation experiments);

[0054] Figure 4 is the classification result of NCP interference unit samples based on the second scenario (1 simulation experiment);

[0055] Figure 5 is the average classification probability of NCP interference unit samples based on the second scenario (1000 simulation experiments);

[0056] Figure 6 is the NCP detection probability (1000 simulation experiments, the false alarm probability is ) DETAILED DESCRIPTION OF THE INVENTION

[0057] The present invention proposes a method for detecting class noise interference based on the EM and eigenvalue decomposition methods to solve the problems of detecting NCP and extracting interference information, and provides a reference basis for subsequent interference suppression work. This method remodels the passive sonar NCP detection scenario based on latent variables, and uses the EM and eigenvalue decomposition methods to realize the extraction of the interference covariance matrix and the existence judgment of NCP in the range cell dimension, getting rid of the model mismatch problem of NCP detection in the prior art and the dependence on auxiliary data, improving the applicability and robustness of the interference information extraction method, and providing a new solution for interference detection and information extraction in underwater acoustic countermeasures.

[0058] The core principle of the present invention lies in jointly using the EM under the latent variable model and the matrix eigenvalue decomposition method. First, latent variables are introduced to construct a classification identification framework to characterize the existence of NCP components and their signal characteristics (angle of arrival and interference intensity). The E-step of the EM algorithm is used to calculate the posterior probability of the sample unit belonging to the classification, and in the M-step, the eigenvalue decomposition method is used to estimate the environmental noise energy and the interference covariance matrix. Finally, the category of the sample unit is determined according to the obtained maximum posterior probability. The detailed design process of the present invention is as Figure 1 shown:

[0059] 1. Scene statistical modeling

[0060] Consider a passive sonar detection system only for signal reception. Assume that the echoes in the detection area are received by a linear array composed of array elements, and after preprocessing, independent sample vectors that satisfy the zero-mean multivariate complex Gaussian distribution are obtained ( represents dimensional complex numbers). There are multiple active class noise interferences in the detection scene. Assume that this interference exists in the form of NCP, and class noise interference may be introduced in all sample units corresponding to its pulse duration. To determine the existence of NCP in the sample unit, the following binary hypothesis testing problem is established:

[0061]

[0062] where:

[0063] represents the no-target hypothesis, represents the alternative hypothesis under the existence of NCP;

[0064] represents is a mean of and the covariance matrix is dimensional Gaussian complex vector;

[0065] represents the environmental noise component, represents the interference covariance matrix of the th NCP, is the number of NCPs in the detection scenario, as the energy of the th NCP, determined by the interference-to-noise ratio (JNR) and the environmental noise energy , is the signal incident angle of the th NCP, represents the corresponding normalized spatial domain steering vector, represents conjugate transpose;

[0066] represents the sample vector , is the subscript set of ; let represent the number of sample units contaminated by the signal of the th NCP, then the subscript set where the target component exists can be further expressed as ,

[0067] Define as the set of unknown parameters of the th unit sample under the hypothesis, is the set of unknown parameters of the th unit sample under the hypothesis. Under the hypothesis the expression of the probability density function (PDF) is:

[0068]

[0069] Under the hypothesis, the PDF expression is

[0070]

[0071] where, represents conjugate transpose, represents exponentiation, represents matrix trace, represents matrix inversion. Therefore, under the hypothesis, the joint PDF expression of the received sample data matrix is:

[0072]

[0073] 2. Algorithm Design

[0074] First, introduce independent and identically distributed discrete random variables , , to represent or conditions. Let the probability of , then there is . Applying the total probability formula, the probability density function of the unit sample can be rewritten as:

[0075]

[0076] where, , . Combining , formulas, the joint log-likelihood function of can be obtained:

[0077]

[0078] where, represents the logarithmic operation, represents the posterior probability corresponding to under the condition, represents the set of parameters to be estimated. Applying the E-step optimization process in the EM algorithm, in the th iteration, can be expressed as:

[0079] where, represents the estimation result of after the th loop iteration. The M-step optimization process needs to solve the following problem:

[0080]

[0081] Only considering the second term related to , and combining the Lagrange operator optimization method under the constraint of , the estimated value of in the hth loop optimization can be obtained as:

[0082]

[0083] According to formula, the estimation problems of and can be transformed into:

[0084]

[0085] To simplify the problem, we define:

[0086]

[0087]

[0088] Considering the method of matrix eigenvalue decomposition, the matrix and can be decomposed as: , . Among them, , are respectively the diagonal matrices composed of the eigenvalues , of , . Note that the number of eigenvalues corresponding to a single NCP is 1. As the corresponding eigenvector matrix, it satisfies ; then can be further transformed into:

[0089] Substitute into and after arrangement, we can get:

[0090]

[0091] Take the partial derivatives of , respectively and set them to zero, then the estimation results of the two can be obtained:

[0092]

[0093] After arrangement, we can get:

[0094]

[0095] Substitute the above estimation results into the GLRT detection formula, and we get:

[0096]

[0097] which is equivalent to:

[0098]

[0099] Among them, is the estimated value of under the hypothesis, denotes the detection threshold, which is determined by and is the false alarm probability.

[0100] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0101] Embodiment 1

[0102] As Figure 1 shown, Embodiment 1 of the present invention proposes a method for detecting noise-like interference based on expectation maximization and eigenvalue decomposition, including:

[0103] Preprocess the echoes received by the linear array in the detection area to obtain K independent sample vectors that satisfy the zero-mean multivariate complex Gaussian distribution, and form the data matrix of the independent sample vectors ;

[0104] Introduce independent and identically distributed discrete random variables to obtain the joint log-likelihood function of the data matrix of the independent sample vectors;

[0105] Use the E-step of the EM algorithm to calculate the posterior probability of the classification to which the independent sample vectors belong, and estimate the environmental noise energy and interference covariance matrix by the eigenvalue decomposition method in the M-step;

[0106] Determine the category of the independent sample vectors according to the obtained maximum posterior probability.

[0107] Simulation analysis

[0108] We use the Monte Carlo simulation method to verify the sample classification accuracy of the present invention in the NCP interference scenario. The passive detection sonar is equipped with a uniform linear array with the number of array elements, and the number of received signal samples is . To verify the recognition ability of the algorithm for NCPs with different energy levels and incident angles, two different NCP presence scenarios are constructed. There are 3 NCPs with different energies or signal incident angles in both scenarios, and their specific parameter information is shown in Tables 1 and 2.

[0109] In the first scenario, the NCPs follow the parameter information shown in Table 1. The energies of the three NCPs are the same, all following , and radiate into the detection array at different incident angles with an interval of . Figure 2Shows the classification of the algorithm for the class noise interference scenario in 1 experiment. Assume that the unit samples without NCP belong to the first class, and the sample units with the first, second, and third types of NCP are the second, third, and fourth classes respectively. It can be seen from the content of the figure that the classification result is consistent with the true result, and the proposed algorithm can correctly identify the NCP pulses based on different incident angles. Figure 3 Shows the average correct classification probability of each channel in 1000 Monte Carlo experiments. It can be seen that the classification accuracy rate is above 98%, and the classification effect is satisfactory.

[0110] In the second scenario, the basic information of the NCP is shown in Table 2. The incident angles of the three NCPs are the same, but the energies differ by . Figure 4 Shows the classification of the algorithm for the scenario in 1 experiment, and the classification result is basically correct. Figure 5 Shows the average correct classification ratio of each unit sample in 1000 Monte Carlo experiments. It can be seen that the sensitivity of the algorithm to different NCP energies is slightly lower than that to angles, and the classification accuracy rate is about above 85%. Figure 6 Gives the change curve of the NCP detection probability with the JNR (interference-to-noise ratio) under different array element numbers in 1000 Monte Carlo experiments. Except for the JNR, the NCP parameters are the same as those in Table 1, and the false alarm rate . It can be seen that when SINR , the NCP detection probability can reach above 0.9, and the performance is excellent.

[0111] Table 1

[0112]

[0113] Table 2

[0114]

[0115] Embodiment 2

[0116] Embodiment 2 of the present invention proposes a class noise interference detection method system based on expectation maximization and eigenvalue decomposition, which is implemented based on the method of Embodiment 1. The system includes:

[0117] A preprocessing module for preprocessing the echo received by the linear array in the detection area to obtain K independent sample vectors that satisfy the zero-mean multivariate complex Gaussian distribution, and forming a data matrix of the independent sample vectors ;

[0118] A joint log-likelihood function acquisition module for introducing independent and identically distributed discrete random variables to obtain the joint log-likelihood function of the data matrix of the independent sample vectors;

[0119] The EM algorithm module is used to calculate the posterior probability of the classification to which the independent sample vector belongs by using the E-step of the EM algorithm, and estimate the environmental noise energy and the interference covariance matrix by means of eigenvalue decomposition in the M-step;

[0120] The class recognition module is used to determine the class of the independent sample vector according to the obtained maximum posterior probability.

[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit them. Although the present invention has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A noise-like interference detection method based on expectation maximization and eigenvalue decomposition, comprising: Step 1: Preprocess the echo received by the linear array in the detection area to obtain K Independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution form a data matrix of independent sample vectors ; Step 2: Import independent and identically distributed discrete random variables, and obtain the data matrix of independent sample vectors The joint log-likelihood function of ; Step 3: Use the E step of the EM algorithm to calculate the posterior probability of the category to which the independent sample vector belongs, and in the M step, use the eigenvalue decomposition method to estimate the environmental noise energy and interference covariance matrix; Step 4: Determine the category of the independent sample vector according to the obtained maximum posterior probability; The step 3 comprises: Apply the E-step optimization process in the EM algorithm, In iteration It is expressed as: in, Indicates The estimated result of the ambient noise energy after the iteration of the loop is: Indicates The estimated result of the interference covariance matrix after the iteration is: Indicates The estimated result of the probability group distribution function after the iteration of the cycle; Indicates k independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution, are independent and identically distributed discrete random variables, r represents the existence of noise-like interference potential in the detection area, S Indicates the number of NCPs in the detection scene; For M-step optimization, combined The Lagrange operator optimization method under the restriction obtains the h Second cycle optimization Estimated value of for: The ambient noise energy and the interference covariance matrix The estimation problem is transformed into: definition: in, Represents the auxiliary function when no NCP exists. Indicates the auxiliary function in the presence of NCP; represents the identity matrix; Represents the conjugate transpose of a vector; Combined with the matrix eigenvalue decomposition method, we can get: in, is another representation of the auxiliary function in the presence of NCP, express The eigenvalues ​​of the terms, express The eigenvalues ​​of the terms, express The first item of Respectively , Find the partial derivative and set it to zero to get the corresponding estimate: in, express The corresponding eigenvector matrix, For the h After loop iteration An estimated value of For the first ( h -1) After the loop iteration An estimated value of , indicating that The resulting diagonal matrix is, For the h After loop iteration An estimated value of To find the maximum value; This generates a diagonal matrix whose elements are in the vector.

2. The noise-like interference detection method based on expectation maximization and eigenvalue decomposition according to claim 1 is characterized in that: The linear array in step 1 includes N array elements. After preprocessing the echoes of the N array elements, K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution , and then form the corresponding data matrix , ,in represents an N-dimensional complex number, express dimensional complex number, Indicates k independent sample vectors that satisfy a zero-mean multivariate complex Gaussian distribution.

3. The noise-like interference detection method based on expectation maximization and eigenvalue decomposition according to claim 2 is characterized in that: The step 2 comprises: Introduction independent and identically distributed discrete random variables , , used to characterize or situation; Indicates that there is no subscript set for the NCP component. A subscript set indicating the existence of the target component; r represents the existence of noise-like interference potential in the detection area, S Indicates the number of NCPs in the detection scene; make Probability , then ;in is the unknown probability group distribution function; Applying the total probability formula, the independent sample vector The probability density function of for: in, For the The set of parameters to be estimated within the sample units, For the The unit samples are Assume that the unknown parameter set, is the ambient noise energy, is the interference covariance matrix, Represents any variable Pick When its function The cumulative sum of the values ​​of express Function of Conclusion The joint log-likelihood function for: in, represents logarithmic operation, express Corresponds to The posterior probability under the condition, Represents the set of all parameters to be estimated.

4. The noise-like interference detection method based on expectation maximization and eigenvalue decomposition according to claim 3 is characterized in that: The step 4 comprises: The ambient noise energy and the interference covariance matrix Substituting the estimated result into the GLRT detection formula, we get: in, for exist The estimated value under the assumption that represents the no-target hypothesis, represents the alternative hypothesis under the existence of NCP, Indicates the detection threshold Indicates The estimated result of the ambient noise energy after the iteration of the loop is: Indicates The interference covariance matrix after the iteration is: Indicates the unit sample with NCP The probability density function of Indicates that there is no NCP in the unit sample The probability density function of .

5. A system for detecting noise-like interference based on the expectation maximization and eigenvalue decomposition method of claim 1, characterized in that: include: The preprocessing module is used to preprocess the echo received by the linear array in the detection area to obtain K Independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution form a data matrix of independent sample vectors ; Joint log-likelihood function acquisition module, used to introduce independent and identically distributed discrete random variables, and obtain the data matrix of independent sample vectors The joint log-likelihood function of ; EM algorithm module, used to calculate the posterior probability of the classification to which the independent sample vector belongs by using the E step of the EM algorithm, and to estimate the environmental noise energy and interference covariance matrix by using the eigenvalue decomposition method in the M step; and The category recognition module is used to determine the category of the independent sample vector according to the required maximum posterior probability.

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