Noise-like interference detection method and system based on expectation maximization and eigenvalue decomposition

Abstract

The invention belongs to the technical field of sonar signal detection, and particularly relates to a noise-like interference detection method and system based on expectation maximization and eigenvalue decomposition. The method comprises the following steps: preprocessing echoes received by a linear array in a detection area to obtain K independent sample vectors meeting zero-mean multivariate complex Gaussian distribution, and forming a data matrix # imgabs0 # of the independent sample vectors; a # imgabs 1 # independent identically distributed discrete random variable is introduced, and a joint log-likelihood function of a data matrix # imgabs 2 # of an independent sample vector is obtained; calculating the posterior probability of the classification to which the independent sample vector belongs by using the E step of the EM algorithm, and estimating the environmental noise energy and interference covariance matrix in the M step by using the eigenvalue decomposition method; and determining the category of the independent sample vector according to the solved maximum posterior probability. According to the method, the background noise energy and the covariance matrix of the NCP can be accurately estimated, the EM clustering algorithm is ingeniously fused, so that the detection process is more automatic, and the interference detection efficiency and accuracy are improved.

Description

Technical Field

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

[0002] With the development of electronic countermeasure technology and the complexity of application scenarios, sonar systems are facing more and more challenges in actual work. Noise-Like Jammers (NLJs), as a common active artificial jammer, pose a major threat to sonar detection systems. NLJs enhance the noise floor of sonar receivers, mask target information, and affect target detection by emitting broadband high-power signals similar to noise, thereby interfering with the normal operation of sonar systems. Since the NLJs signal energy usually covers the instantaneous bandwidth of the sonar receiver 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 flexibly adjust according to the specific environment. This is the core of the Space-Time Adaptive Detection (STAD) method.

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

[0004] On the problem of underwater NLJs detection and information extraction based on STAD, existing technical solutions include: Solution 1: A two-level detection architecture proposed based on dual auxiliary data sets and generalized information criterion, using multiple assumptions to describe the target detection problem under interference such as NCP, and designing a two-stage algorithm to solve the problem: the first stage classifies the scene based on the MOS (Model Order Selection) criterion, and the second stage confirms the existence and specific scene of the target through a decision-making plan to achieve adaptive detection of the target under multiple interferences; Solution 2: Based on the rank-one corrected difference between the covariance matrix of the measured data and the covariance matrix of the reference data, auxiliary data and generalized likelihood ratio test (GLRT) are used to achieve the detection of noise interference. This type of solution improves the estimation accuracy of the interference covariance matrix. The first prior art solution adopts a continuous interference model and assumes that all unit samples of interest contain interference signal components with the same parameter characteristics. In the detection scenario where NCP exists, this will lead to a model mismatch between the method and the application scenario, making it impossible to effectively detect and extract information from the interference. The second prior art solution requires the use of a reference data covariance matrix constructed from auxiliary data, and its performance will be reduced in an environment where the amount of auxiliary data is severely lacking. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and propose a noise-like interference detection method and system based on expectation-maximization (EM) 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, comprising:

[0007] Step 1: 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, forming a data matrix of independent sample vectors ;

[0008] 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 ;

[0009] 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;

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

[0011] Preferably, the linear array in step 1 includes N array elements, and after preprocessing the echoes of the N array elements, K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution are obtained. , and then form the corresponding data matrix , ,in represents an N-dimensional complex number, express dimensional complex number, represents the kth independent sample vector satisfying the zero-mean multivariate complex Gaussian distribution.

[0012] Preferably, the step 2 comprises:

[0013] Introduction independent and identically distributed discrete random variables , , used to characterize or situation; Indicates the subscript set of the target component. represents the subscript set of the non-existent NCP components; r represents the existence potential class of noise-like interference in the detection area, and S represents the number of NCPs in the detection scene;

[0014] make Probability , then ;in is the unknown probability group distribution function;

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

[0016]

[0017] 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 Indicated function;

[0018] Conclusion The joint log-likelihood function for:

[0019] in, represents logarithmic operation, express Corresponds to The posterior probability under the condition, Represents the set of all parameters to be estimated.

[0020] Preferably, step 3 comprises:

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

[0022] 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;

[0023] For M-step optimization, combined The Lagrange operator optimization method under the restriction obtains the optimization of the hth loop Estimated value of for:

[0024] The ambient noise energy and the interference covariance matrix The estimation problem is transformed into:

[0025]

[0026] definition:

[0027]

[0028]

[0029] 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;

[0030] Combined with the matrix eigenvalue decomposition method, we can get:

[0031]

[0032] 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

[0033] Respectively , Find the partial derivative and set it to zero to get the corresponding estimate:

[0034]

[0035] in, express The corresponding eigenvector matrix, After the hth loop iteration An estimated value of After the (h-1)th loop iteration An estimated value of , indicating that The resulting diagonal matrix is, After the hth loop iteration An estimated value of To find the maximum value; This generates a diagonal matrix whose elements are in the vector.

[0036] Preferably, step 4 comprises:

[0037] The ambient noise energy and the interference covariance matrix Substituting the estimated result into the GLRT detection formula, we get:

[0038]

[0039] 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 .

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

[0041] The preprocessing module is used to 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 a data matrix of independent sample vectors. ;

[0042] 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 ;

[0043] 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;

[0044] The category recognition module is used to determine the category of the independent sample vector according to the required maximum posterior probability.

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

[0046] The present invention proposes an innovative NCP detection and information acquisition technology, which introduces latent variables to remodel the detection scene where NCP exists, and uses the EM algorithm and eigenvalue decomposition method to perform sample classification and interference parameter estimation, so that interference information acquisition and accurate detection can be achieved 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 cleverly integrates the EM clustering algorithm, which can intelligently distinguish and process unit samples in the presence of multiple NCPs, 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 and introduces latent variables to remodel the NCP detection scenario. It is no longer assumed that the interference components in the unit sample are the same, but that they are different and independent of each other. 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 to estimate the interference covariance matrix. This means that even in the absence of sufficient auxiliary data in real scenarios, interference information can be accurately extracted, thereby improving the applicability and robustness of the algorithm;

[0049] 3. The method proposed in this invention combines the EM algorithm and the eigenvalue decomposition method, analyzes the sample data in batches, and uses the maximum a posteriori probability criterion for judgment, thus realizing the identification and information estimation of NCP. This method significantly reduces the high computational load required to process each unit sample one by one, and reduces the time complexity;

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

[0051] Figure 1 is a flow chart of the method of the present invention;

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

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

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

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

[0056] Figure 6 is the NCP detection probability (1000 simulation tests, the false alarm probability is ). DETAILED DESCRIPTION

[0057] The present invention proposes a noise-like interference detection method based on EM and eigenvalue decomposition method to solve the problem of NCP detection and interference information extraction, and provide a reference for subsequent interference suppression work. This method remodels the passive sonar NCP detection scene based on latent variables, and uses EM and eigenvalue decomposition methods to realize the interference covariance matrix extraction and existence judgment of NCP in the distance unit 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 confrontation.

[0058] The core principle of the present invention is to jointly utilize EM and matrix eigenvalue decomposition methods under the latent variable model. First, latent variables are introduced to construct a classification identification framework to characterize the existence of NCP components and their signal characteristics (arrival angle and interference intensity). The posterior probability of the classification to which the sample unit belongs is calculated using the E step of the EM algorithm. In the M step, the environmental noise energy and the interference covariance matrix are estimated by the eigenvalue decomposition method. Finally, the category of the sample unit is determined based on the maximum a posteriori probability required. The detailed design process of the present invention is as follows: Figure 1 As shown:

[0059] 1. Scenario Statistical Modeling

[0060] Consider a passive sonar detection system used only for signal reception. Assume that the echo in the detection area is The linear array reception composed of array elements is obtained after preprocessing. independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution ( express There are multiple active noise-like interferences in the detection scene. Assuming that the interference exists in the form of NCP, noise-like interference may be introduced into all sample units corresponding to its pulse duration. In order to determine the existence of NCP in the sample unit, the following binary hypothesis test problem is established:

[0061]

[0062] in:

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

[0064] express is a mean value , the covariance matrix is of Gaussian complex vector;

[0065] represents the ambient noise component, Indicates The interference covariance matrix of NCPs is is the number of NCPs in the detection scene, As the The energy of the NCP is determined by the interference-to-noise ratio (JNR) and the ambient noise energy Sure: , It is The signal incident angle of each NCP is express The corresponding normalized spatial steering vector, represents conjugate transpose;

[0066] Represents the sample vector , The subscript set of ; let Indicates that The number of sample units contaminated by NCP signals, then the subscript set of the target component can be further expressed as , Indicates that there is no subscript set for the NCP component.

[0067] definition For the The unit samples are Assume that the unknown parameter set, For the The unit samples are The unknown parameter set under the assumption is Assume The probability density function (PDF) of is:

[0068]

[0069] Assume The PDF expression of

[0070]

[0071] in, represents the conjugate transpose, represents exponential operation, represents the matrix trace, represents the matrix inversion. Therefore, in Assume that the sample data matrix received is The joint PDF expression of is:

[0072]

[0073] 2. Algorithm Design

[0074] First introduce independent and identically distributed discrete random variables , , used to characterize or The situation. Probability , then . Applying the total probability formula, the unit sample can be The probability density function of is rewritten as:

[0075]

[0076] in, , . Combined , The formula can be obtained The joint log-likelihood function of is:

[0077]

[0078] in, represents logarithmic operation, express Corresponds to The posterior probability under the condition, Represents the set of parameters to be estimated. Apply the E-step optimization process in the EM algorithm. In iteration It can be expressed as:

[0079] in, Indicates After loop iteration The M-step optimization process needs to solve the following problems:

[0080]

[0081] Only consider The second item is related, and combined with The Lagrange operator optimization method under the restriction can obtain the optimization of the hth loop The estimated value of is:

[0082]

[0083] according to Mode, and The estimation problem 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 This breaks down into: , .in , They are respectively , The eigenvalue of , Note that the diagonal matrix of a single NCP The corresponding eigenvalue The number is 1. As the corresponding eigenvector matrix, ;but Can be further transformed into:

[0089] Will Substitution After finishing, we can get:

[0090]

[0091] Respectively , By taking partial derivatives and setting them to zero, we can get the estimated results of the two:

[0092]

[0093] After finishing, we can get:

[0094]

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

[0096]

[0097] is equivalent to:

[0098]

[0099] in, for exist The estimated value under the assumption that represents the detection threshold, Sure, is the false alarm probability.

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

[0101] Example 1

[0102] like Figure 1 As shown, embodiment 1 of the present invention proposes a noise-like interference detection method 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, forming a data matrix of independent sample vectors. ;

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

[0105] The posterior probability of the classification to which the independent sample vector belongs is calculated using the E step of the EM algorithm, and the environmental noise energy and interference covariance matrix are estimated by the eigenvalue decomposition method in the M step;

[0106] Determine the category of the independent sample vector based on the required maximum posterior probability.

[0107] Simulation Analysis

[0108] We use Monte Carlo simulation method to verify the accuracy of sample classification in the NCP interference scenario. Uniform linear array with the number of array elements, number of received signal samples In order to verify the algorithm's ability to identify NCPs with different energy sizes and incident angles, two different NCP existence scenarios were constructed. In both scenarios, there are three NCPs with different energies or signal incident angles, and their specific parameter information is shown in Tables 1 and 2.

[0109] In the first scenario, NCP follows the parameter information shown in Table 1. The three NCPs have the same energy and all obey , with an interval of Radiation at different incident angles enters the detection array. Figure 2The algorithm's classification of noise-like interference scenarios in one experiment is shown. Assume that the unit sample without NCP belongs to the first category, and the sample units with the first, second, and third NCPs belong to the second, third, and fourth categories respectively. As can be seen from the content of the figure, the classification results are consistent with the actual results, and the proposed algorithm can correctly identify NCP pulses based on different incident angles. Figure 3 The figure shows the average correct classification probability of each channel in 1000 Monte Carlo experiments. It can be seen that the classification accuracy is above 98%, and the classification effect is satisfactory.

[0110] In the second scenario, the basic information of NCP is shown in Table 2. The incident angles of the three NCPs are the same, but the energies are different. . Figure 4 The algorithm's classification of scenes in one experiment is shown, and the classification results are basically correct. Figure 5 The figure shows the average correct classification ratio of each unit sample in 1000 Monte Carlo experiments. It can be seen that the algorithm is slightly less sensitive to different NCP energies than to angles, and the classification accuracy is about 85%. Figure 6 The curves of NCP detection probability and JNR (interference-to-noise ratio) under different numbers of array elements in 1000 Monte Carlo experiments are given. Except for JNR, the NCP parameters are the same as those in Table 1. It can be seen that when SINR The NCP detection probability can reach above 0.9, with excellent performance.

[0111] Table 1

[0112]

[0113] Table 2

[0114]

[0115] Example 2

[0116] Embodiment 2 of the present invention proposes a noise-like 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] The preprocessing module is used to 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 a data matrix of independent sample vectors. ;

[0118] 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 ;

[0119] 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;

[0120] The category recognition module is used to determine the category of the independent sample vector according to the required 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 and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art 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 should be included in 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 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, forming 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 based on the obtained maximum posterior probability.

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 are obtained. , and then form the corresponding data matrix , ,in represents an N-dimensional complex number, express dimensional complex number, represents the kth independent sample vector satisfying the 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. represents the subscript set of target components; 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 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 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; For M-step optimization, combined The Lagrange operator optimization method under the restriction obtains the optimization of the hth loop 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, After the hth loop iteration An estimated value of After the (h-1)th loop iteration An estimated value of , indicating that The resulting diagonal matrix is, After the hth loop iteration An estimated value of To find the maximum value; This generates a diagonal matrix whose elements are in the vector.

5. The noise-like interference detection method based on expectation maximization and eigenvalue decomposition according to claim 4 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 .

6. A noise-like interference detection system based on expectation maximization and eigenvalue decomposition, characterized in that: include: The preprocessing module is used to 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 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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