A method and apparatus for a bayesian classifier of non-uniform backgrounds

Abstract

The embodiment of the application relates to an algorithm and a device of a Bayesian classifier of a non-uniform background, which are applied to an underwater active sonar system, the algorithm comprising: obtaining underwater data to be measured and auxiliary data through the active sonar system; the number K of the auxiliary data is greater than 0; modeling classification of the unknown covariance matrix structure into a binary hypothesis testing problem; hypotheses of the binary hypothesis testing problem comprise H i Wherein i=0, 1, H0 is a case that the unknown covariance matrix is a complex conjugate symmetric matrix; H1 is a case that the unknown covariance matrix is a real symmetric matrix; a Bayesian model is set, the Bayesian model comprising a complex inverse Wishart random matrix and a real inverse Wishart random matrix; a classifier for distinguishing the two hypotheses is obtained by using a minimum error probability criterion.

Description

Technical Field

[0001] This application relates to the field of underwater acoustic detection, and more particularly to a method and apparatus for a Bayesian classifier with a non-uniform background. Background Technology

[0002] In active sonar target detection problems where reverberation is the primary background disturbance, it is generally assumed that the background reverberation in the test data follows a complex Gaussian distribution with a mean of zero and a covariance matrix that is an unknown positive definite complex conjugate symmetric matrix. To improve the target detection capability of active sonar systems, achieve adaptive detection, and ensure a constant false alarm probability, accurate estimation of the unknown reverberation covariance matrix is ​​of paramount importance.

[0003] Underwater space-time adaptive target detection (STAD) assumes the existence of a series of auxiliary data with the same covariance matrix as the target data, used for covariance matrix estimation. When the amount of auxiliary data is sufficient, underwater STAD often achieves good target detection performance. Furthermore, to further improve detection efficiency, researchers have proposed a series of more robust and efficient target detection schemes by utilizing the property that when there is no relative motion between the sonar platform and the detection area, or when the relative motion is fully compensated, the reverberation power spectral density is symmetric about zero frequency, and the covariance matrix is ​​a real symmetric matrix.

[0004] However, due to the inherent uncertainties in active sonar systems, the unavoidable errors in compensating for relative motion will break the real symmetry of the covariance matrix. This situation will cause the target detection scheme proposed for this special structure to no longer match the actual background, resulting in a severe deterioration in the performance of active sonar target detection. Furthermore, in practical applications of active sonar, due to the highly complex underwater environment, it is highly likely that the covariance matrices of the auxiliary data and the target data will no longer be identical except for their structure (both being complex conjugate symmetric or both being real symmetric). This situation is called a non-uniform background. In non-uniform backgrounds, matching the detection scheme with the actual background is even more crucial for active sonar systems.

[0005] In summary, active sonar platforms urgently need a method and apparatus for reverberation classification under non-uniform backgrounds. This method should be able to efficiently classify the covariance matrix structure under non-uniform backgrounds, accurately determine the covariance matrix structure before target detection, and determine whether the background reverberation covariance matrix has real symmetry characteristics. This will provide a basis for active sonar to select the most suitable detection scheme under the current background and achieve efficient target detection. Summary of the Invention

[0006] The purpose of this application is to address the problem that the Model Order Selection (MOS) method is insufficient in dealing with small sample sizes when determining the reverberation covariance matrix structure for active sonar platforms.

[0007] In a first aspect, embodiments of this application propose an algorithm for a Bayesian classifier with a non-uniform background, applied to an underwater active sonar system. The algorithm includes: obtaining underwater test data and auxiliary data through the active sonar system; the number of auxiliary data K is greater than 0; the auxiliary data and the test data have the same unknown covariance matrix, and the dimension of the unknown covariance matrix is ​​N.

[0008] The classification of the unknown covariance matrix structure is modeled as a binary hypothesis testing problem; the hypothesis of the binary hypothesis testing problem is H. i Where i = 0, 1, H0 is the case where the unknown covariance matrix is ​​a complex conjugate symmetric matrix; H1 is the case where the unknown covariance matrix is ​​a real symmetric matrix; a Bayesian model is set according to the binary hypothesis testing problem, the Bayesian model includes a complex inverse Wishart random matrix and a real inverse Wishart random matrix; the binary hypothesis testing problem is solved using the minimum error probability criterion to obtain the Bayesian classifier for the non-uniform background.

[0009] As one feasible implementation, modeling the classification of the unknown covariance matrix structure as a binary hypothesis testing problem includes: obtaining a series of complex Gaussian random vectors with a mean of 0, wherein the complex Gaussian random vectors are... Where z0 is the data to be tested, z1, z2, ..., z K For auxiliary data, k = 0, ..., K For z k The unknown covariance matrix, where N is the number of channels in the active sonar system. Represents an N-dimensional complex Gaussian random distribution, where K is the number of auxiliary data points; in z0, z1, ..., z K When the data are independent of each other and the auxiliary data and the test data have the same covariance matrix structure, the classification of the structure of the covariance matrix can be modeled as the following binary hypothesis testing problem:

[0010]

[0011] As one feasible implementation, setting a Bayesian model based on the binary hypothesis testing problem includes: under the H0 hypothesis, setting the structure of the unknown covariance matrix as a complex inverse Wishart random matrix M that follows an independent distribution. 0k :

[0012]

[0013] Under the H1 hypothesis, the unknown covariance matrix is ​​assumed to have a structure of real inverse Wishart random matrix M that follows an independent distribution. 1k :

[0014]

[0015] Where M ik i = 0, 1, for z k In H i The covariance matrix is ​​assumed to be k = 1, ..., K. This represents the complex inverse Wishart distribution. Let ν represent the real inverse Wishart distribution, where ν≥N is the shape parameter, and νΣ i , i = 0, 1, are the scale parameters of the complex inverse Wishart distribution and the real inverse Wishart distribution, respectively, and i = 0, 1.

[0016] As one feasible implementation, the step of setting a Bayesian model based on the binary hypothesis testing problem includes: determining the conditional probability density function p(Mik|Hi) of Mik when the Hi hypothesis is true; and based on the M... ik The conditional probability density function determines the scaling function Σ i The scaling function Σ i Used to provide prior information, Σ i for:

[0017]

[0018] Where Σ i (m,n) is Σ i The element in the m-th row and n-th column, ρ c f is the correlation coefficient, j is the imaginary unit, and f is the correlation coefficient. d The normalized Doppler frequency; based on the scaling function Σ i Based on the provided prior information, the normalized Doppler frequency f is obtained. d Non-zero, Σ0 is a complex conjugate symmetric matrix, the normalized Doppler frequency is zero, Σ1 is a real symmetric matrix; according to the M ik The conditional probability density function p(M) ik |H i ) and H i The prior probability of H is determined i With M i1 ,…,M iK The joint distribution p(H) i M i1 ,…,M iK )for:

[0019] p(H i M i1 ,…,M iK )=p(M i1 ,…,M iK |H i )p(H i )

[0020] Where p(H i ) is H i The prior probability, p(M) i1 ,…,M iK |H i ) is a known H i When M was established i1 ,…,M iK Conditional distribution, Construct a Bayesian model for the classifier of the binary hypothesis testing problem.

[0021] As one feasible implementation, the step of solving the binary hypothesis testing problem using the minimum error probability criterion to obtain a Bayesian classifier with a non-uniform background includes: solving the binary hypothesis testing problem using the decision formula of the minimum error probability criterion; wherein the minimum error probability criterion is:

[0022]

[0023] Where p(z1,…,z) K |H i ) is H i The auxiliary data z under the assumption k The probability density function; the H i Assume the auxiliary data z k The probability density function is given by p(M) ik |H i ) and the following given M ik under z conditions k The conditional probability density function p(z) k |M ik )Sure:

[0024]

[0025] in It is the conjugate transpose. and These represent the operations of extracting the real part and the imaginary part, respectively.

[0026] As one feasible implementation, the covariance matrix structure classifier under non-uniform background is as follows:

[0027]

[0028] in:

[0029]

[0030]

[0031] Secondly, embodiments of this application propose a device for a Bayesian classifier with a non-uniform background, applied to an underwater active sonar system. The device includes: a data acquisition unit for acquiring underwater test data and auxiliary data through the active sonar system; the number of auxiliary data, K, is greater than 0; the auxiliary data and the test data have the same unknown covariance matrix, and the dimension of the unknown covariance matrix is ​​N; and a binary hypothesis unit for modeling the classification of the unknown covariance matrix structure as a binary hypothesis testing problem; the hypothesis of the binary hypothesis testing problem is H. i Where i = 0, 1, H0 is the case where the unknown covariance matrix is ​​a complex conjugate symmetric matrix; H1 is the case where the unknown covariance matrix is ​​a real symmetric matrix; the model building unit is used to set a Bayesian model according to the binary hypothesis testing problem, the Bayesian model includes a complex inverse Wishart random matrix and a real inverse Wishart random matrix; the solution unit is used to solve the binary hypothesis testing problem using the minimum error probability criterion to obtain the Bayesian classifier for the non-uniform background.

[0032] Thirdly, embodiments of this application provide an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in any of the first aspects above.

[0033] Fourthly, embodiments of this application propose a storage medium storing instructions that, when executed on a terminal, cause the first terminal to perform the method described in any of the first aspects.

[0034] Compared with existing MOS methods, which cannot function properly in extremely complex underwater environments due to insufficient auxiliary data, the Bayesian classifier algorithm with non-uniform background proposed in this application can not only function normally but also guarantee extremely excellent classification performance. It can accurately determine the structure of the covariance matrix of reverberation, providing a very reliable basis for selecting the optimal scheme for target detection in active sonar systems.

[0035] The proposed Bayesian classifier algorithm for non-uniform backgrounds in this application incorporates Bayesian theory, modeling the unknown covariance matrix of the auxiliary data as an independently distributed complex inverse Wishart or real inverse Wishart random matrix. It also employs the minimum error probability criterion to solve the classification problem. The proposed method not only functions correctly when the amount of auxiliary data is smaller than the data dimensionality, but also guarantees excellent classification performance.

[0036] The Bayesian classifier algorithm for non-uniform backgrounds proposed in this application presents a Bayesian-based reverberation covariance matrix structure classification algorithm for non-uniform backgrounds. This algorithm effectively improves the ability of active sonar platforms to identify reverberation covariance matrix structures when auxiliary data is insufficient. It can provide a more reliable basis for selecting the most suitable target detection scheme and further improving target detection performance.

[0037] The algorithm for the Bayesian classifier with non-uniform background proposed in this application model the classification of the reverberation covariance matrix structure as a binary hypothesis testing problem and solves it using the minimum error probability criterion.

[0038] The algorithm for the Bayesian classifier with non-uniform background proposed in this application model the unknown covariance matrix of the data as a random matrix. It assumes that the covariance matrix of the data with non-uniform background is independent and identically distributed, and that it follows a complex inverse Wishart distribution under the assumption of complex conjugate symmetry, and a real inverse Wishart distribution under the assumption of real symmetry.

[0039] The algorithm for the Bayesian classifier with non-uniform background proposed in this application overcomes the problem that existing technologies cannot work when the amount of auxiliary data is small. It can not only work normally when K < N, but also guarantee extremely superior performance. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the various embodiments disclosed in this specification, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only a few embodiments disclosed in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 A flowchart of the algorithm for a Bayesian classifier with a non-uniform background proposed in an embodiment of this application;

[0042] Figure 2 This is a graph showing the correct classification probability of each classification algorithm when the H0 assumption holds in the embodiments of this application.

[0043] Figure 3This is a graph showing the correct classification probability of each classification algorithm when the H1 assumption holds in the embodiments of this application;

[0044] Figure 4 This is a schematic diagram of a Bayesian classifier with a non-uniform background proposed in an embodiment of this application.

[0045] Figure 5 This is a schematic diagram of an electronic device proposed in an embodiment of this application. Detailed Implementation

[0046] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0047] In the following description, the terms “first, second, third, etc.” or module A, module B, module C, etc. are used only to distinguish similar objects and do not represent a specific ordering of objects. It is understood that a specific order or sequence may be interchanged where permitted so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0048] In the following description, the labels of the steps, such as S110, S120, etc., do not necessarily mean that the steps will be executed in this way. The order of the steps can be interchanged or executed simultaneously if permitted.

[0049] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0050] The following describes the implementation scheme most similar to the embodiments of this application.

[0051] Existing classification techniques for covariance matrix structures primarily employ the Model Order Selection (MOS) method. In non-uniform contexts, the MOS method uses auxiliary data to classify the covariance matrix structure. The MOS method leverages the varying number of unknowns across different models, using a penalized likelihood function to determine the specific model to which the covariance matrix structure belongs. This method exhibits good performance when sufficient auxiliary data is available, and different criteria can be selected based on computational and performance requirements.

[0052] In practical applications of active sonar, the underwater environment is complex and variable, and the quantity of auxiliary data with the same covariance matrix structure as the target data is often difficult to guarantee. The MOS method suffers significant performance degradation when the amount of auxiliary data is small. More importantly, the MOS method fails completely when the amount of auxiliary data is less than the data dimensionality, which severely limits its application in underwater environments. In summary, existing technologies struggle to guarantee efficient covariance matrix structure classification with small sample sizes, and cannot provide reliable information for selecting active sonar target detection schemes.

[0053] The technical solution of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0054] This application proposes an algorithm for a Bayesian classifier with a non-uniform background. Based on Bayesian theory, it obtains underwater target data and auxiliary data through an active sonar system. The number of auxiliary data, K, is greater than 0. The auxiliary data and the target data have the same unknown covariance matrix, with the dimension of the unknown covariance matrix being N. The classification of the unknown covariance matrix structure is modeled as a binary hypothesis testing problem. The hypothesis of the binary hypothesis testing problem is Hi, where i = 0, 1, H0 is the case where the unknown covariance matrix is ​​a complex conjugate symmetric matrix, and H1 is the case where the unknown covariance matrix is ​​a real symmetric matrix. A Bayesian model is set according to the binary hypothesis testing problem, which includes a complex inverse Wishart random matrix and a real inverse Wishart random matrix. The binary hypothesis testing problem is solved using the minimum error probability criterion to obtain a Bayesian classifier with a non-uniform background. This can effectively improve the ability of the covariance matrix structure classification algorithm to handle small sample situations and further optimize the performance of active sonar target detection.

[0055] Figure 1 This is a flowchart of the algorithm for a Bayesian classifier with a non-uniform background proposed in an embodiment of this application. Figure 1 As shown, the algorithm for the non-uniform background Bayesian classifier proposed in this application embodiment is implemented through the following steps S1-S4.

[0056] S1 acquires underwater test data and auxiliary data through an active sonar system.

[0057] In one embodiment, underwater test data and auxiliary data are obtained through an active sonar system; wherein the number of auxiliary data K is greater than 0; the auxiliary data and the test data have the same unknown covariance matrix, and the dimension of the unknown covariance matrix is ​​N.

[0058] In one embodiment, assuming that against a non-uniform background, the active sonar system receives data as a series of complex Gaussian random vectors with a mean of 0, using... Indicates, that is k = 0, ..., K, where z0 is the data to be measured, z1, z2, ..., z K For auxiliary data, For z k The covariance matrix, where N is the number of channels in the active sonar system. Let represent an N-dimensional complex Gaussian random distribution, where K is the number of auxiliary data points. Assume z0, z1, ..., zn. K The data are independent of each other, and the auxiliary data and the data to be tested have the same covariance matrix structure.

[0059] S2, modeling the classification of unknown covariance matrix structures as a binary hypothesis testing problem; the hypothesis of the binary hypothesis testing problem is H. i , where i = 0, 1, H0 is the case where the unknown covariance matrix is ​​a complex conjugate symmetric matrix; H1 is the case where the unknown covariance matrix is ​​a real symmetric matrix.

[0060] In one embodiment, when the active sonar platform has no relative motion with the detection area or the relative motion can be fully compensated, M1, M2, ..., M K Both M0 and M1 are real symmetric matrices; otherwise, they are complex conjugate symmetric matrices. Based on this, the classification of covariance matrix structures can be modeled as a classifier for the following binary hypothesis testing problem:

[0061]

[0062] S3. Based on the binary hypothesis testing problem, a Bayesian model is set up. The Bayesian model includes the complex inverse Wishart random matrix and the real inverse Wishart random matrix.

[0063] In one embodiment, to solve for M1,…,M, Bayesian theory is introduced, assuming M1,…,M K Given independent and identically distributed random matrices, under the H0 assumption, the structure of the unknown covariance matrix is ​​assumed to be a complex inverse Wishart random matrix M that follows an independent distribution. 0k Under the H1 hypothesis, the unknown covariance matrix is ​​assumed to be a real inverse Wishart random matrix M that follows an independent distribution. 1k .

[0064] The above model can be represented as: k = 1, ..., K, where M ik i = 0, 1, for z k In H i The covariance matrix under the assumption, This represents the complex inverse Wishart distribution. Let ν represent the real inverse Wishart distribution, where ν≥N is the shape parameter, and νΣ i, i = 0, 1, are the scale parameters of the complex inverse Wishart distribution and the real inverse Wishart distribution, respectively, and i = 0, 1.

[0065] In one embodiment, step S3 can be implemented by the following steps S31-S35.

[0066] S31, Determine H i When the assumption holds true, M ik The conditional probability density function p(M) ik |H i ).

[0067] In one embodiment, H is known i When the assumption holds true, M ik The conditional probability density function is:

[0068]

[0069]

[0070] Where det(·) is the determinant of the matrix, Tr(·) is the trace of the matrix, and:

[0071]

[0072]

[0073] In equations (4) and (5), I i (.) is the normalization factor, and Γ(·) is the Gamma function.

[0074] S32, according to M ik The conditional probability density function determines the scaling function Σ i , scaling function Σ i Used to provide prior information, Σ i for:

[0075]

[0076] Where Σ i (m,n) is Σ i The element in the m-th row and n-th column, ρ c f is the correlation coefficient, j is the imaginary unit, and f is the correlation coefficient. d This is the normalized Doppler frequency.

[0077] S33, according to the scaling function Σ i The normalized Doppler frequency f can be obtained from the provided prior information. d Non-zero, Σ0 is a complex conjugate symmetric matrix, and the normalized Doppler frequency f d The value is zero, and Σ1 is a real symmetric matrix.

[0078] For example, from equation (6), when the H0 assumption holds, the normalized Doppler frequency f d The frequency is not zero. Σ0 is a complex conjugate symmetric matrix. When the H1 hypothesis holds, the normalized Doppler frequency is zero. Σ1 is a real symmetric matrix.

[0079] S34, according to M ik The conditional probability density function p(M) ik |H i ) and H i The prior probability of H is determined i With M i1 ,…,M iK The joint distribution p(H) i M i1 ,…,M iK ).

[0080] In one embodiment, let p(H) i M i1 ,…,M iK ) represents Hi and M i1 ,…,M iK The joint distribution of p(H) is then: i M i1 ,…,M iK )=p(M i1 ,…,M iK |H i )p(H i ), i = 0, 1, where p(H i ) is H i The prior probability, p(M) i1 ,…,M iK |H i ) is a known H i When the assumption holds true, M i1 ,…,M iK The conditional distribution, due to M i1 ,…,M iK Independent and identically distributed, with

[0081] S35. Construct a Bayesian model for a classifier of a binary hypothesis testing problem based on the above parameters.

[0082] S4 uses the minimum error probability criterion to solve the binary hypothesis testing problem and obtains a Bayesian classifier for non-uniform backgrounds.

[0083] In one embodiment, step S4 is implemented through the following steps S41-S42.

[0084] S41, Solve the binary hypothesis testing problem using the decision formula of the minimum error probability criterion; Based on the Bayesian model of the above binary hypothesis testing, solve the binary hypothesis testing problem using the decision formula of the following minimum error probability criterion (1):

[0085]

[0086] Where p(z1,…,z) K |H i ) is H i Assume the probability density function of the auxiliary data.

[0087] S42, Auxiliary data z k The probability density function p(z1,…,z) K |H i ) by p(M ik |H i ) and given M ik under z conditions k The conditional probability density function p(z) k |M ik )Sure.

[0088] In one embodiment, step S42 is implemented through the following steps S421-S424.

[0089] S421, Equation (7) is transformed as follows:

[0090]

[0091] Equation (8) is the equivalent form of the minimum error probability criterion. From the law of total probability, we know that in equation (8):

[0092]

[0093] Where Ω0 is the set of all positive definite complex conjugate symmetric matrices, and Ω1 is the set of all positive definite real symmetric matrices.

[0094] S422, by Bayes' theorem, the integrand in equation (9) is p(z1,…,z…). K M i1 ,…,M iK |H i It can be written as:

[0095]

[0096] Equation (10) uses the result p(H) i |z1,…,z K M i1 ,…,M iK ) = 1.

[0097] Meanwhile, since the data follows the independent distribution assumption, and p(H) i |M i1 ,…,M iK ) = 1, equation (10) is equivalent to:

[0098]

[0099] Where p(z) k |M ik ) is given M ik time z k The conditional probability density function.

[0100] S423, regarding H i When the prior information is unknown, let it follow a uniform distribution, that is... If i = 0, 1, then substituting (11) into (8) yields:

[0101]

[0102] S424, determine the conditional probability density function of the data.

[0103] When the H1 hypothesis holds, the power density spectrum of the reverberation is symmetric about zero frequency, z k covariance matrix M 1k Let z be a real symmetric matrix. k The real and imaginary parts are covariance matrices of M. 1k / 2 is an independent and identically distributed real Gaussian random vector. Therefore, given M ik Under the condition of z k The conditional probability density function can be expressed as:

[0104]

[0105] in It is the conjugate transpose. and These represent the operations of extracting the real part and the imaginary part, respectively.

[0106] S5, obtain the covariance matrix structure classifier under non-uniform background.

[0107] According to the previous embodiment, substituting equations (2), (3), and (13) into (12) yields:

[0108]

[0109] as well as

[0110]

[0111] From the above results, the final form of the Bayesian covariance matrix structure classifier under non-uniform background is:

[0112]

[0113] In the following performance analysis, the classification algorithm proposed in this application embodiment, namely the formula, is called the Bayesian classifier for heterogeneous environment (BCHE). AIC, AICc, and GIC4 represent the classification algorithms in the MOS method that use the Akaike information criterion, the corrected Akaike information criterion, and the extended information criterion (parameter 4), respectively. Other parameter settings are as follows: N = 12, ν = 12, ρ c =0.95, f d =0.2, and the covariance matrix of the actual data. k = 1, ..., K.

[0114] Figure 2 This is a graph showing the probability of correct classification (Pcc) of each classification algorithm when the H0 hypothesis holds in the embodiments of this application. Figure 3 This is a graph showing the correct classification probability of each classification algorithm when the H1 assumption holds in the embodiments of this application.

[0115] Depend on Figure 2 and Figure 3 It can be intuitively seen that, regardless of whether H0 or H1 is assumed, only the BCHE proposed in the embodiments of this application can work under the condition that K < N, and P can also be achieved even when K is extremely small. cc =1; Furthermore, when K≥N, under the H0 assumption, BCHE and AIC can guarantee P cc =1, and both are superior to GIC4 and AICc. Under the H1 assumption, BCHE and AICc can guarantee P. cc =1, GIC4 and AICc can only reach P when K>N+1 and K>N+3 respectively. cc =1.

[0116] In summary, the Bayesian classifier algorithm with non-uniform background proposed in this application can guarantee excellent classification performance with a very small amount of auxiliary data. In contrast, various MOS-based methods not only cannot work when K < N, but also perform worse than BCHE when K ≥ N.

[0117] Compared with existing MOS methods, which cannot function properly in extremely complex underwater environments due to insufficient auxiliary data, the Bayesian-based classification method proposed in this application not only functions normally but also guarantees extremely excellent classification performance. It accurately determines the structure of the reverberation covariance matrix, providing a highly reliable basis for selecting the optimal target detection scheme for active sonar systems.

[0118] The proposed Bayesian classifier algorithm for non-uniform backgrounds in this application incorporates Bayesian theory, modeling the unknown covariance matrix of the auxiliary data as an independently distributed complex inverse Wishart or real inverse Wishart random matrix. It also employs the minimum error probability criterion to solve the classification problem. The proposed method not only functions correctly when the amount of auxiliary data is smaller than the data dimensionality, but also guarantees excellent classification performance.

[0119] The Bayesian classifier algorithm for non-uniform backgrounds proposed in this application presents a Bayesian-based reverberation covariance matrix structure classification algorithm for non-uniform backgrounds. This algorithm effectively improves the ability of active sonar platforms to identify reverberation covariance matrix structures when auxiliary data is insufficient. It can provide a more reliable basis for selecting the most suitable target detection scheme and further improving target detection performance.

[0120] The algorithm for the Bayesian classifier with non-uniform background proposed in this application model the classification of the reverberation covariance matrix structure as a binary hypothesis testing problem and solves it using the minimum error probability criterion.

[0121] The algorithm for the Bayesian classifier with non-uniform background proposed in this application model the unknown covariance matrix of the data as a random matrix. It assumes that the covariance matrix of the data with non-uniform background is independent and identically distributed, and that it follows a complex inverse Wishart distribution under the assumption of complex conjugate symmetry, and a real inverse Wishart distribution under the assumption of real symmetry.

[0122] The algorithm for the Bayesian classifier with non-uniform background proposed in this application overcomes the problem that existing technologies cannot work when the amount of auxiliary data is small. It can not only work normally when K < N, but also guarantee extremely superior performance.

[0123] Figure 4 A schematic diagram of a Bayesian classifier with a non-uniform background provided for embodiments of this application. This device is applied to underwater active sonar systems, such as... Figure 4As shown, in this device, the data acquisition unit 41 acquires underwater test data and auxiliary data through an active sonar system; the number of auxiliary data, K, is greater than 0; the auxiliary data and the test data have the same unknown covariance matrix, and the dimension of the unknown covariance matrix is ​​N; the binary hypothesis unit 42 models the classification of the unknown covariance matrix structure as a binary hypothesis testing problem; the hypothesis of the binary hypothesis testing problem is H. i Where i = 0, 1, H0 is the case where the unknown covariance matrix is ​​a complex conjugate symmetric matrix; H1 is the case where the unknown covariance matrix is ​​a real symmetric matrix; the model building unit 43 sets up a Bayesian model based on the binary hypothesis testing problem, the Bayesian model includes a complex inverse Wishart random matrix and a real inverse Wishart random matrix; the solution unit 44 solves the binary hypothesis testing problem using the minimum error probability criterion to obtain a Bayesian classifier with a non-uniform background.

[0124] Figure 5 A schematic diagram of an electronic device provided for an embodiment of this application. (As shown) Figure 5 As shown, it includes: at least one memory 1102 for storing a program; and at least one processor 1101 for executing the program stored in the memory. When the program stored in the memory 1102 is executed, the processor 1101 is used to execute the method of any of the above embodiments.

[0125] This application provides a storage medium storing instructions that, when executed on a terminal, cause the first terminal to perform the method described in any of the above embodiments.

[0126] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0127] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented in hardware, processor-executed software modules, or a combination of both. The software modules can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disks, removable disks, CD-ROMs, or any other form of storage medium known in the art.

[0128] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the embodiments of this application. It should be understood that the above descriptions are merely specific embodiments of the embodiments of this application and are not intended to limit the protection scope of the embodiments of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of this application should be included within the protection scope of the embodiments of this application.

Claims

1. A method for a Bayesian classifier with a non-uniform background, applied to an underwater active sonar system, characterized in that, The method includes: Underwater test data and auxiliary data are acquired through an active sonar system; the quantity of auxiliary data... Greater than 0; the auxiliary data and the data to be tested have the same unknown covariance matrix, and the dimension of the unknown covariance matrix is... ; The classification of the unknown covariance matrix structure is modeled as a binary hypothesis testing problem, including: Against a non-uniform background, a series of complex Gaussian random vectors with a mean of 0 are obtained, wherein the complex Gaussian random vectors are... ; in For the data to be tested, For auxiliary data, , for The unknown covariance matrix, The number of channels in an active sonar system. represent A complex Gaussian random distribution. The amount of auxiliary data; exist When the data are independent of each other and the auxiliary data and the test data have the same covariance matrix structure, the classification of the structure of the covariance matrix can be modeled as the following binary hypothesis testing problem: ； The assumption of the binary hypothesis testing problem is: ,in =0,1 This is the case where the unknown covariance matrix is ​​a complex conjugate symmetric matrix; This is the case where the unknown covariance matrix is ​​a real symmetric matrix; A Bayesian model is defined based on the binary hypothesis testing problem. This Bayesian model includes a complex inverse Wishart random matrix and a real inverse Wishart random matrix, comprising: exist Assume that the structure of the unknown covariance matrix is ​​a complex inverse Wishart random matrix that follows an independent distribution. : ； exist Under the assumption that the unknown covariance matrix has a structure of real inverse Wishart random matrices following independent distributions. : ； in for exist The covariance matrix under the assumption, , This represents the complex inverse Wishart distribution. This represents the real inverse Wishart distribution. For shape parameters, These are the scale parameters of the complex inverse Wishart distribution and the real inverse Wishart distribution, respectively. ; The binary hypothesis testing problem is solved using the minimum error probability criterion, which is: in, ; Let be the set of all positive definite complex conjugate symmetric matrices. Let be the set of all positive definite real symmetric matrices; Obtain the Bayesian classifier for the non-uniform background; the covariance matrix structure classifier for the non-uniform background is: in: in, yes The sample covariance matrix under the assumptions, yes The sample covariance matrix under the assumptions, , , , , This is the conjugate transpose. and These represent the operations of extracting the real part and the imaginary part, respectively. The step of setting a Bayesian model based on the binary hypothesis testing problem includes: Sure When the assumption is true conditional probability density function ; According to the above The conditional probability density function determines the scaling function. The scaling function Used to provide prior information, for: ； in for The Middle OK Column elements, The correlation coefficient, The imaginary unit, Normalized Doppler frequency; based on the scaling function Based on the provided prior information, the normalized Doppler frequency is obtained. Not zero, The matrix is ​​a complex conjugate symmetric matrix, and the normalized Doppler frequency is zero. It is a real symmetric matrix; According to the above conditional probability density function and Prior probability determination and joint distribution for: in for The prior probability, Known When it was established Conditional distribution; ; Construct a Bayesian model for the classifier of the binary hypothesis testing problem.

2. The method for a Bayesian classifier with a non-uniform background according to claim 1, characterized in that, The method of solving the binary hypothesis testing problem using the minimum error probability criterion to obtain a Bayesian classifier with a non-uniform background includes: Solve the binary hypothesis testing problem using the decision formula of the minimum error probability criterion; wherein the minimum error probability criterion is: in, for The auxiliary data under the assumption The probability density function; The Assuming auxiliary data The probability density function is derived from With the following given under conditions conditional probability density function Sure: in , , , , This is the conjugate transpose. and These represent the operations of extracting the real part and the imaginary part, respectively.

3. A method and apparatus for a Bayesian classifier with a non-uniform background, applied to an underwater active sonar system, characterized in that... The device includes: The data acquisition unit is used to acquire underwater test data and auxiliary data through an active sonar system; the number of auxiliary data... Greater than 0; the auxiliary data and the data to be tested have the same unknown covariance matrix, and the dimension of the unknown covariance matrix is... ; The binary hypothesis unit is used to model the classification of the unknown covariance matrix structure as a binary hypothesis testing problem, including: Against a non-uniform background, a series of complex Gaussian random vectors with a mean of 0 are obtained, wherein the complex Gaussian random vectors are... ; in For the data to be tested, For auxiliary data, , for The unknown covariance matrix, The number of channels in an active sonar system. represent A complex Gaussian random distribution. The amount of auxiliary data; exist When the data are independent of each other and the auxiliary data and the test data have the same covariance matrix structure, the classification of the structure of the covariance matrix can be modeled as the following binary hypothesis testing problem: ； The assumption of the binary hypothesis testing problem is: ,in =0,1 This is the case where the unknown covariance matrix is ​​a complex conjugate symmetric matrix; This is the case where the unknown covariance matrix is ​​a real symmetric matrix; The model building unit is used to set a Bayesian model based on the binary hypothesis testing problem. The Bayesian model includes a complex inverse Wishart random matrix and a real inverse Wishart random matrix, comprising: exist Assume that the structure of the unknown covariance matrix is ​​a complex inverse Wishart random matrix that follows an independent distribution. : ； exist Under the assumption that the unknown covariance matrix has a structure of real inverse Wishart random matrices following independent distributions. : ； in for exist The covariance matrix under the assumption, , This represents the complex inverse Wishart distribution. This represents the real inverse Wishart distribution. For shape parameters, These are the scale parameters of the complex inverse Wishart distribution and the real inverse Wishart distribution, respectively. ; The solution unit is used to solve the binary hypothesis testing problem using the minimum error probability criterion, which is: in, ; Let be the set of all positive definite complex conjugate symmetric matrices. Let be the set of all positive definite real symmetric matrices; Obtain the Bayesian classifier for the non-uniform background; the covariance matrix structure classifier for the non-uniform background is: in: in, yes The sample covariance matrix under the assumptions, yes The sample covariance matrix under the assumptions, , , , , It is the conjugate transpose. and These represent the operations of extracting the real part and the imaginary part, respectively.

4. An electronic device, characterized in that, include: At least one memory for storing programs; and At least one processor is configured to execute a program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to perform the method as described in any one of claims 1-2.

5. A storage medium storing instructions that, when executed on a terminal, cause a first terminal to perform the method as described in any one of claims 1-2.

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