A phase modal domain unknown source number characteristic subspace direction estimation method

Abstract

The application discloses a phase modal domain unknown source number characteristic subspace direction estimation method, device and equipment, which comprises the following steps: receiving sound pressure signals emitted by sources in space by using a uniform circular ring sensor array; decomposing the sound pressure signals based on a phase modal decomposition theory to obtain multi-order modal signals and phase modal domain directional vectors; constructing a phase modal domain signal covariance matrix by using the multi-order modal signals, performing characteristic decomposition on the phase modal domain signal covariance matrix, and extracting the minimum characteristic value as an approximate noise power estimation value; based on the noise power and a limited larger integer, approximately solving signal subspace and noise subspace related parameters to obtain a characteristic subspace MUSIC scanning vector under the unknown source number; and calculating a direction spectrum according to the characteristic subspace MUSIC scanning vector under the unknown source number and the phase modal domain signal covariance matrix, so that the characteristic subspace direction estimation of the unknown source number is realized. The method does not need to know the source number in advance, and the direction estimation performance is improved.

Description

Technical Field

[0001] This application relates to fields such as acoustics, array signal processing, and sonar technology, and in particular to a method, apparatus, and device for estimating the eigenspace orientation of unknown source numbers in the phase mode domain. Background Technology

[0002] Sensor arrays, due to their high flexibility, are widely used in radar, sonar, communications, and medical imaging. Target direction-of-arrival (DOA) estimation is a major research area in array signal processing. Effective tracking and localization of underwater acoustic targets can be achieved through DOA estimation; therefore, improving DOA estimation performance is of great significance for enhancing the detection capabilities of sensor arrays.

[0003] Circular arrays are widely used in underwater acoustics, airborne acoustics, and antennas due to their advantages such as simple structure, absence of port-side ambiguity, and ability to form beams with essentially constant main lobe width across the horizontal range. Phase mode (PM) domain array signal processing is a type of signal processing method based on circular or spherical arrays. Phase mode theory is based on spatial Fourier analysis of the incident plane wave of the array. Through Fourier series expansion, the weighting coefficients of the sound pressure sensor are obtained, thus yielding orthogonal harmonic components. This process is called phase mode decomposition. Phase mode decomposition theory is generally applied to uniformly distributed circular or spherical arrays of sensors. It can convert sound pressure signals into orthogonal circular harmonics, which are characteristic solutions of the wave equation in spherical or cylindrical coordinates, representing some characteristics of the sound field. Based on the harmonic components obtained from the decomposition, beamforming methods in the phase mode domain of circular / spherical arrays can provide high directivity, good azimuth resolution, and excellent broadband frequency invariance performance using a smaller array aperture.

[0004] In recent years, researchers have proposed the Eigenspace algorithm, which utilizes the eigenstructure of the correlation matrix for azimuth estimation. This algorithm projects the scan vector from the Minimum Variance Distortionless Response (MVDR) algorithm onto the signal subspace to obtain the algorithm's scan vector, which is then substituted into the azimuth spectrum estimation formula to yield the azimuth estimate. This algorithm has been widely applied in ultrasound, not only simultaneously improving the resolution and contrast of ultrasound imaging but also exhibiting strong robustness. Furthermore, compared to classic methods such as MUSIC, this algorithm has lower sidelobes and higher azimuth estimation accuracy. However, existing Eigenspace methods require eigenvalue decomposition and the division of the signal and noise subspaces, necessitating the accurate determination of the number of known signal sources. However, many practical applications face scenarios where the exact number of signal sources cannot be obtained. Therefore, a high-resolution azimuth estimation method using the eigenspace with an unknown number of signal sources is urgently needed to address these practical application scenarios. Summary of the Invention

[0005] The main objective of this application is to provide a method, apparatus, and device for estimating the eigenspace orientation of unknown source numbers in the phase mode domain, aiming to solve the technical problems of eigenspace orientation estimation methods for unknown source numbers in the phase mode domain.

[0006] To achieve the above objectives, this application provides a method for estimating the eigenspace orientation of unknown sources in the phase mode domain, comprising: A uniform circular sensor array is used to receive sound pressure signals emitted by a source in space; Based on the phase mode decomposition theory, the sound pressure signal received by the uniform circular sensor array is decomposed to obtain multi-mode signals and phase mode domain steering vectors. The covariance matrix of the phase mode domain received signal is constructed using multi-mode signals, and the covariance matrix is ​​approximated by the correlation matrix of a segment of received data; the covariance matrix is ​​subjected to eigenvalue decomposition to extract the minimum eigenvalue, and the minimum eigenvalue is used as an approximate estimate of the noise power. Based on the approximate estimate of the noise power, the relevant parameters of the signal subspace and noise subspace are solved by finite large integers to obtain the MUSIC scan vector of the phase mode domain feature subspace under the condition of unknown number of sources; Based on the MUSIC scan vector and phase mode domain covariance matrix of the phase mode domain feature subspace under the scenario of unknown source number, the azimuth spectrum estimation result is calculated to realize the azimuth estimation of unknown source number.

[0007] Optionally, the uniform circular sensor array includes M Each array element, multiple array elements are placed in xoyThe array is planar with its center at the origin, and element 0 is located at... x On the axis; The radius of the uniform circular sensor array is r The central angle between two adjacent array elements is twice pi divided by the number of array elements. M ; No. m In the spherical coordinates of the first array element, the vertical elevation angle is 0, and the horizontal azimuth angle is the first... m Multiply the array element by the central angle, where m The value ranges from 1 to M Positive integers; Based on the transformation relationship from spherical coordinates to rectangular coordinates, we obtain the first... m Cartesian coordinates of the array element; The transformation relationships include: Rectangular coordinates x The component is the array radius. r Multiply by the sine of the vertical pitch angle and then multiply by the cosine of the horizontal azimuth angle; Rectangular coordinates y The component is the array radius. r Multiply by the sine of the vertical pitch angle and then multiply by the sine of the horizontal azimuth angle; Rectangular coordinates z The component is the array radius. r Multiply by the cosine of the vertical pitch angle.

[0008] Optionally, the decomposition of the sound pressure signal received by the uniform circular sensor array based on phase mode decomposition theory to obtain multi-mode signals includes: Based on the spatial Fourier analysis of the incident plane wave of the array, the weighting coefficients of the sound pressure sensor are obtained by performing Fourier series expansion on the sound pressure signal. The orthogonal harmonic components are determined based on the weighting coefficients, and the multi-mode signals are determined based on the orthogonal harmonic components to decompose the received sound pressure signal. In the process of decomposing the received sound pressure signal, the highest order of the multi-mode signal is controlled according to the spatial sampling theorem. Nmax satisfy M≥2Nmax And the dimension is Nc = 2Nmax + 1 , M The number of array elements.

[0009] Optionally, the information source is P narrowband sound sources that are incoherent, and each source emits a single-frequency signal of a different frequency; The sound pressure signal is obtained by superimposing Gaussian white noise onto a single-frequency signal.

[0010] Optionally, the approximate expression for the covariance matrix is:

[0011] Among them, the definition , The covariance matrix R PM The first P largest eigenvalues ​​correspond to the signal term ( ), It is the matrix formed by the eigenvectors corresponding to the largest eigenvalue, that is, the eigenvector matrix of the signal subspace. ; , For R PM Smaller eigenvalues ​​correspond to noise terms ( ), This is the matrix formed by the eigenvectors corresponding to the smaller eigenvalues, i.e., the eigenvector matrix of the noise subspace. Let be the conjugate transpose of the eigenvector matrix of the signal subspace. Let be the conjugate transpose of the eigenvectors of the noise subspace. This represents noise power.

[0012] Optionally, the step of obtaining the MVDR scan vector of the phase mode domain feature subspace under the condition of unknown source number by approximating the signal subspace correlation parameters through a finite number of large integers based on the approximate estimate of the noise power includes: Based on the approximate expression of the covariance matrix, the covariance matrix features of the phase mode signal are decomposed into a mode domain signal subspace and a mode noise subspace, and the inverse of the covariance matrix is ​​determined based on the decomposed covariance matrix. Based on the approximate expression for the covariance matrix, a first approximate expression for characterizing the inverse of the covariance matrix is ​​determined, where the first approximate expression is: ; By using the approximate expression of left-multiplying the noise power by the inverse of the covariance matrix, we obtain the second approximate expression, which is:

[0013] Given a finite integer, raise the second approximation to the nearest integer power. As the integer approaches infinity, we obtain the third approximation, which is:

[0014] Based on the fact that as integers approach infinity, diagonal matrices approach zero, a fourth approximation expression is determined, which is:

[0015] Based on the fourth and first approximation expressions, the fifth approximation expression is determined, whereby the fifth approximation expression is:

[0016] In the formula, This represents the minimum value of the noise term; Substituting the fifth approximation expression into the MVDR scan vector expression of the modal domain feature subspace, we obtain the MVDR scan vector of the phase modal domain feature subspace under the scenario of unknown source number. The expression for the MVDR scan vector of the phase modal domain feature subspace under the scenario of unknown source number is as follows:

[0017] In the formula, Indicates the scan vector parameters. The phase mode domain of the circular array with respect to direction The guiding vector The conjugate transpose of .

[0018] Optionally, the MVDR scan vector and phase mode domain covariance matrix based on the phase mode domain feature subspace under the scenario of unknown source number can be used to calculate the azimuth spectrum estimation result, including: Based on the expression for the MVDR scan vector of the phase mode domain feature subspace under the scenario of unknown source number, considering the orthogonality between the feature vector matrix of the signal subspace and the noise subspace, the signal model of the steering vector is mainly related to the signal subspace. That is, it can be considered that the steering vector and the feature vector of the noise subspace are spatially orthogonal. In order to make Minimize the factors in the denominator, and reduce the parameters. Replace with The specific expression is:

[0019] Based on the approximate expression of the scan vector parameters and the fourth approximation expression, the expression for the scan vector parameters in the case of an unknown number of sources is determined, where the expression for the scan vector parameters in the case of an unknown number of sources is:

[0020] Based on the expression of the MVDR scan vector of the phase mode domain feature subspace under the scenario with unknown number of sources and the expression of the scan vector parameter under the scenario with unknown number of sources, the final scan vector of the phase mode domain feature subspace MUSIC under the scenario with unknown number of sources is determined. The azimuth spectrum estimation result is calculated according to the relationship between the feature subspace MUSIC scan vector and the azimuth spectrum expression.

[0021] Optionally, the final expression for the MUSIC scan vector is:

[0022] The corresponding azimuth spectrum expression is obtained as follows: .

[0023] Furthermore, to achieve the above objectives, this application also provides a feature subspace orientation estimation device for unknown sources in the phase mode domain, comprising: The signal receiving module is used to receive sound pressure signals emitted by a signal source in space using a uniform circular sensor array; The signal decomposition module is used to decompose the sound pressure signal received by the uniform circular sensor array based on the phase mode decomposition theory to obtain multi-mode signals and phase mode domain steering vectors. The noise power estimation module is used to construct the covariance matrix of the phase mode domain received signal using multi-mode signals, and to approximate the covariance matrix using the correlation matrix of a segment of received data; to perform eigenvalue decomposition on the covariance matrix, extract the minimum eigenvalue, and use the minimum eigenvalue as an approximate estimate of the noise power; The scanning vector calculation module is used to solve the relevant parameters of the signal subspace and the noise subspace by using finite large integers based on the approximate estimate of the noise power, so as to obtain the MUSIC scanning vector of the phase mode domain feature subspace under the condition of unknown number of signal sources; The source azimuth calculation module is used to calculate the azimuth spectrum estimation results based on the MUSIC scan vector and phase mode domain covariance matrix of the phase mode domain feature subspace under the scenario of unknown source number, so as to realize the azimuth estimation of unknown source number.

[0024] To achieve the above objectives, this application also provides an electronic device, which includes: at least one processor, a memory, and an input / output unit; wherein the memory is used to store a computer program, and the processor is used to call the computer program stored in the memory to execute the feature subspace orientation estimation method for unknown number of phase mode domain sources provided in any of the foregoing embodiments.

[0025] This application proposes a method, apparatus, and device for estimating the azimuth of a feature subspace in the phase-mode domain with an unknown number of sources. The method involves using a uniform circular sensor array to receive sound pressure signals emitted by sources in space. Based on phase-mode decomposition theory, the sound pressure signals received by the uniform circular sensor array are decomposed to obtain multi-mode signals and a phase-mode domain steering vector. A covariance matrix of the received phase-mode domain signal is constructed using the multi-mode signals, and the covariance matrix is ​​approximated by a correlation matrix of a segment of received data. The covariance matrix is ​​eigenvalued, and the minimum eigenvalue is extracted and used as an approximate estimate of the noise power. Based on the approximate estimate of the noise power, the correlation parameters of the signal subspace and noise subspace are solved using finite large integers to obtain the MUSIC scan vector of the feature subspace in the phase-mode domain under the condition of an unknown number of sources. Based on the MUSIC scan vector and the phase-mode domain covariance matrix in the scenario of an unknown number of sources, the azimuth spectrum estimation result is calculated, thus achieving azimuth estimation of the unknown number of sources. The method proposed in this application does not require prior knowledge of the number of sound sources in the space. It uses the covariance matrix of existing modal signals to approximate the closed-form expression of the relevant parameters of the modal domain signal subspace and noise subspace, realizing the solution of the phase modal domain feature subspace MUSIC scan vector for cases with unknown number of sources. This effectively improves the practicality of the Eigenspace method in real-world scenarios. This application can further enhance the azimuth estimation capability with a smaller array aperture. Attached Figure Description

[0026] Figure 1 A flowchart illustrating an embodiment of the characteristic subspace orientation estimation method for unknown number of sources in the phase mode domain of this application; Figure 2 A schematic diagram of the coordinates of a uniform circular array provided in an embodiment of the characteristic subspace orientation estimation method for unknown number of sources in the phase mode domain of this application; Figure 3 This is a schematic diagram of the azimuth spectrum estimation results of the MUSIC, EMUSIC, and PM-EMUSIC methods provided in an embodiment of the characteristic subspace azimuth estimation method for unknown number of sources in the phase mode domain of this application, where SNR=5dB; Figure 4 This diagram illustrates the azimuth spectrum estimation results of the MUSIC, EMUSIC, and PM-EMUSIC methods provided in an embodiment of the characteristic subspace azimuth estimation method for unknown sources in the phase mode domain of this application, where SNR=0dB.

[0027] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0028] It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit this application.

[0029] Existing technologies, designed for circular arrays, can achieve good azimuth estimation capabilities with relatively small array apertures using phase mode decomposition (PMD) theory. However, as underwater acoustic detection continues to advance towards lower frequency bands, achieving effective estimation of underwater acoustic targets with limited array apertures is a pressing issue. The Eigenspace algorithm projects the scan vector onto the signal subspace, reducing the norm of the weight vector through projection transformation, thus improving the algorithm's convergence and robustness. Simultaneously, this algorithm fully utilizes the signal subspace, resulting in better azimuth resolution. However, existing Eigenspace methods require a known number of sound sources, significantly limiting their applicability in practical scenarios. To overcome the shortcomings of existing technologies, this invention proposes an Eigenspace azimuth estimation method with an unknown number of source sources in the phase mode domain. For uniform circular arrays, PMD theory is used to convert the sound pressure signals acquired by the circular array into a series of high-order mode signals, providing good azimuth resolution for low-frequency signals even with a small array aperture. This invention introduces the Eigenspace method into the phase mode domain. Addressing the shortcomings of existing Eigenspace methods, it approximates the signal and noise subspaces using the covariance matrix of the array-received signals, thus proposing a high-resolution azimuth estimation method for the characteristic subspace with unknown source numbers in the phase mode domain. This invention offers significant performance advantages in resolution compared to traditional azimuth estimation methods, and it does not require prior knowledge of the number of sound sources, making it promising for practical applications.

[0030] Reference Figure 1 The first embodiment of this application provides a method for estimating the directional location of the feature subspace of unknown sources in the phase mode domain. This method can be executed by a processor of a server or a terminal. Taking a processor as an example, the process of estimating the directional location of the feature subspace of unknown sources in the phase mode domain may include the following: S101. A uniform circular sensor array is used to receive the sound pressure signal emitted by the source in space.

[0031] In one embodiment of this application, the uniform circular sensor array includes M Each array element, multiple array elements are placed in xoy The array is planar with its center at the origin, and element 0 is located at... x On the axis.

[0032] The radius of the uniform circular sensor array is r The central angle between two adjacent array elements is twice pi divided by the number of array elements. M .

[0033] No. m In the spherical coordinates of the first array element, the vertical elevation angle is 0, and the horizontal azimuth angle is the first... m The number of array elements is multiplied by the central angle, where m takes values ​​from 1 to... M Positive integers.

[0034] Based on the transformation relationship from spherical coordinates to rectangular coordinates, we obtain the first... m The rectangular coordinates of the array element.

[0035] The transformation relationships include: Rectangular coordinates x The component is the array radius. r Multiply by the sine of the vertical pitch angle and then multiply by the cosine of the horizontal azimuth angle.

[0036] Rectangular coordinates y The component is the array radius. r Multiply by the sine of the vertical pitch angle and then multiply by the sine of the horizontal azimuth angle.

[0037] Rectangular coordinates z The component is the array radius. r Multiply by the cosine of the vertical pitch angle.

[0038] In one embodiment of this application, the information source is P Each narrowband sound source is an incoherent sound source, and each source emits a single-frequency signal of a different frequency.

[0039] The sound pressure signal is obtained by superimposing Gaussian white noise onto a single-frequency signal.

[0040] Specifically, refer to Figure 2 Consider a uniform circular sensor array placed in space, the array consisting of... M Composed of individual array elements, Figure 2 This illustrates the array and its spherical coordinate representation, with the array placed... xoy Plane, with the center of the circle located at the origin of the coordinate system, and the 0th element located at... x On the axis. The first m The coordinates of the array element in the spherical coordinate system can be represented as follows: Then, the corresponding coordinates in the rectangular coordinate system can be represented as follows: (1) In the formula, and They represent the first m The vertical elevation and horizontal azimuth angles of each array element , The central angle between two adjacent array elements. Indicates transpose. r Let be the radius of the annular array. For example, the number of array elements is selected. M =12, Array radius r =0.5 meters, at this time the central angle of the adjacent array element is 2π / 12=π / 6 (i.e. 30°), the horizontal azimuth angle of the first array element (m=1) is 1×π / 6=30°, and the vertical elevation angle is 0 (because the array is placed on xoy A plane (considering only the horizontal orientation estimation) has its rectangular coordinates. x The component is 0.5 × sin0 × cos30° = 0. y The z component is 0.5 × sin0 × sin30° = 0, and the z component is 0.5 × cos0 = 0.5 meters.

[0041] Assuming that there exists in the space P A narrowband sound source emits single-frequency signals of different frequencies. The sound sources are distributed in In the direction, the first p The unit vector in the direction of sound pressure signal propagation is defined as: (2) The negative sign is due to the signal propagation direction being opposite to the direction of the sound source relative to the array. Assuming the analytical form of the real signal received at the origin is... Then the array's first m The signal received at the location of the array element can be represented as: (3) In the formula, The imaginary unit, Indicates signal frequency, For the first p The sound pressure signal arrived at the first m The time delay of the array element relative to the origin c For the speed of sound wave propagation, T For the number of snapshots, For the first m The noise received by sensor number 1.

[0042] Define the array receive signal vector as The incident signal vector is noise vector According to formula (3), the array received signal can be re-expressed as: (4) in For array manifold matrix, Given a relative time delay vector, the array manifold matrix can be represented as: (5) This is defined as an array manifold vector. This invention considers the orientation estimation case in a two-dimensional plane, where... , Therefore, the time delay can be expressed as: (6) Therefore, the array manifold matrix can be viewed as an angle. The function, that is:

[0043] in, , For wave number.

[0044] Clearly, by combining a uniform circular array, a narrowband incoherent signal source, and Gaussian white noise, the signal environment in actual underwater acoustic detection scenarios can be simulated: the circular array adapts to the installation requirements of underwater sensors, the narrowband signal conforms to the narrowband characteristics of underwater acoustic target (such as submarine) radiated noise, and the Gaussian white noise corresponds to the statistical characteristics of ocean background noise, providing a realistic signal input basis for subsequent azimuth estimation.

[0045] S102. Based on the phase mode decomposition theory, the sound pressure signal received by the uniform circular sensor array is decomposed to obtain multi-mode signals and phase mode domain steering vectors.

[0046] In one embodiment of this application, based on phase mode decomposition theory, the sound pressure signal received by a uniform circular sensor array is decomposed to obtain multi-mode signals, which may include the following: Based on the spatial Fourier analysis of the incident plane wave of the array, the weighting coefficients of the sound pressure sensor are obtained by performing Fourier series expansion on the sound pressure signal. The orthogonal harmonic components are determined based on the weighting coefficients, and the multi-mode signals are determined based on the orthogonal harmonic components to decompose the received sound pressure signal.

[0047] In the process of decomposing the received sound pressure signal, the highest order Nmax of the multi-mode signal is controlled according to the spatial sampling theorem to satisfy... M≥2Nmax And the dimension is Nc = 2Nmax + 1 , M The number of array elements.

[0048] Specifically, phase-mode domain array signal processing is a type of signal processing method based on circular or spherical arrays. Phase-mode theory is based on spatial Fourier analysis of incident plane waves on the array. Through Fourier series expansion, the weighting coefficients of the sound pressure sensor are obtained, thus acquiring orthogonal harmonic components. This process is called phase-mode decomposition. Phase-mode decomposition theory is generally applied to uniformly distributed circular or spherical arrays of sensors. It can convert sound pressure signals into orthogonal circular harmonics, which are characteristic solutions of the wave equation in spherical or cylindrical coordinates, representing some characteristics of the sound field. Based on phase-mode decomposition theory, utilizing... M By decomposing the received signals from each sensor, different modal signals can be obtained as outputs. Taking the first... n Taking the output of a first-order signal as an example: (7) According to the spatial sampling theorem, the highest order of a phase mode signal is... Nmax Subject to the number of sound pressure sensors M The limitations, and satisfy M≥2Nmax Therefore, the dimension of the maximum output signal is Nc = 2Nmax+1 For example, when the number of array elements... M When =12, according to M≥2Nmax The highest order can be obtained Nmax≤6 Theoretically, this can be decomposed into a maximum of 6 orders, resulting in 13 modal signals (Nc = 2 × 6 + 1 = 13). This embodiment employs a reduction-order processing method, retaining the highest order of modal information down to 3 orders, resulting in 7 channel modal signals (Nc = 7). This processing can ensure the integrity of modal information while avoiding the problem of low signal-to-noise ratio in higher-order modes. The different order modal signals obtained after phase mode decomposition can be represented as follows: Based on this, the covariance matrix of the received signal of the phase mode domain sensor array can be obtained.

[0049] It should be noted that the introduction of phase mode decomposition solves the problem of low-frequency signal azimuth estimation under finite array aperture: traditional array signal processing requires a larger aperture to ensure resolution in the low-frequency band, while the mode signals obtained by decomposition in this application can be used for... M =12、 r The application enables effective processing of low-frequency signals on a small aperture array of 0.5 meters, significantly improving its applicability in miniaturized sonar devices.

[0050] S103. Construct the covariance matrix of the phase-mode domain received signal using multi-mode signals, and approximate the covariance matrix using the correlation matrix of a segment of received data. Perform eigenvalue decomposition on the covariance matrix, extract the minimum eigenvalue, and use the minimum eigenvalue as an approximate estimate of the noise power.

[0051] In one embodiment of this application, the approximate expression for the covariance matrix is:

[0052] Among them, the definition , The covariance matrix R PM The former P The largest eigenvalues, corresponding to the signal term ( ), It is the matrix formed by the eigenvectors corresponding to the largest eigenvalue, that is, the eigenvector matrix of the signal subspace. . , For R PM Smaller eigenvalues ​​correspond to noise terms ( ), This is the matrix formed by the eigenvectors corresponding to the smaller eigenvalues, i.e., the eigenvector matrix of the noise subspace. Let be the conjugate transpose of the eigenvector matrix of the signal subspace. Let be the conjugate transpose of the eigenvectors of the noise subspace. This represents noise power.

[0053] In practice, the correlation matrix of a segment of received data is usually used to approximate the covariance matrix R of the received signal. PM ,Right now: (8) The Eigenspace algorithm projects the weight vectors of the minimum variance distortionless response (MVDR) algorithm onto the signal subspace to obtain the weight vectors for this algorithm. This projection transformation reduces the norm of the weight vectors, improving the algorithm's convergence and robustness. Simultaneously, this algorithm fully utilizes the signal subspace, resulting in better spatial resolution. Based on phase mode decomposition theory, the phase mode domain Eigenspace algorithm can be derived.

[0054] In the phase-mode domain Eigenspace algorithm, at the desired frequency... f and The guide angle is Then, the guiding vector of the circular array can be obtained as: (9) Among them, the elements of the guiding vector .

[0055] Using phase mode decomposition theory, the first phase mode of a circular array can be obtained. n The first-order phase modal domain steering vector is as follows: (10) in, It is an nth-order first-class cylindrical Bessel function.

[0056] Will Defined as the phase mode domain of a circular array with respect to direction The guiding vector, i.e. .

[0057] Based on the existing MVDR calculation expression, the scan vector expression for the phase mode domain MVDR algorithm is obtained as follows: (11) The covariance matrix R of the phase mode signal PM By performing eigenvalue decomposition, we can obtain the modal domain signal subspace and the modal domain noise subspace, and use the modal domain signal subspace and the modal domain noise subspace to represent R. PM : (12) definition ,in, For R PM forward P The large eigenvalues ​​correspond to the signal term ( ), It is a matrix composed of eigenvectors corresponding to the large eigenvalues. . , For R PM Smaller eigenvalues ​​correspond to noise terms ( ), This is the matrix formed by the eigenvectors corresponding to the smaller eigenvalues. .

[0058] Based on the expression for the scan vector in the phase modal domain MVDR algorithm, the guide angle can be obtained as follows: The scan vector expression for the phase mode domain eigenspace MVDR algorithm is: (13) in, .

[0059] From formula (12), we can obtain: (14) Substituting formula (14) into formula (13), and considering the orthogonality between the eigenvector matrix of the signal subspace and the eigenvectors of the noise subspace, i.e. Since the steering vector model is based on the signal subspace, the eigenvectors of the steering vector and the noise subspace are also orthogonal, i.e. In this way, we can further obtain the simplified form of the scan vector for the phase mode domain eigenspace MVDR method: (15) It should be noted that the information source in this application refers to a sound source, and the number of information sources is the same as the number of sound sources. Since in practical applications, it is impossible to obtain the number of sound sources existing in a known space, i.e. P It is unknown. Therefore, it is necessary to... Approximate calculations are performed to achieve high-resolution azimuth estimation even with an unknown number of signal sources. This application assumes that the circular array is located in a Gaussian white noise field, and the noise power of the Gaussian white noise field is set as follows: This allows formula (12) to be reformulated as: (16) Clearly, this step not only solves the problem of the finiteness of actual data, but also realizes the noise power quantization under the unknown number of signal sources, providing a key noise benchmark for the subsequent solution of signal subspace parameters. It is one of the core steps of this application to achieve unknown number of signal sources.

[0060] S104. Based on the approximate estimate of noise power, the relevant parameters of the signal subspace are solved by approximation using finite large integers to obtain the MUSIC scan vector of the phase mode domain feature subspace under the condition of unknown number of sources.

[0061] In one embodiment of this application, the process of obtaining the scan vector of the phase mode domain feature subspace MVDR under unknown source number conditions by approximating the signal subspace correlation parameters through a finite number of large integers based on an approximate estimate of the noise power can include the following: Based on the approximate expression of the covariance matrix, the covariance matrix features of the phase mode signal are decomposed into a mode domain signal subspace and a mode noise subspace, and the inverse of the covariance matrix is ​​determined based on the decomposed covariance matrix.

[0062] Based on the approximate expression for the covariance matrix, a first approximate expression for characterizing the inverse of the covariance matrix is ​​determined, where the first approximate expression is: .

[0063] By using the approximate expression of left-multiplying the noise power by the inverse of the covariance matrix, we obtain the second approximate expression, which is:

[0064] Given a finite integer, raise the second approximation to the nearest integer power. As the integer approaches infinity, we obtain the third approximation, which is:

[0065] Based on the fact that as integers approach infinity, diagonal matrices approach zero, a fourth approximation expression is determined, which is:

[0066] Based on the fourth and first approximation expressions, the fifth approximation expression is determined, whereby the fifth approximation expression is:

[0067] In the formula, Represents the covariance matrix R PM The minimum value of the eigenvalue.

[0068] Substituting the fifth approximation expression into the scan vector expression of the modal domain feature subspace MVDR, we obtain the phase modal domain feature subscan vector under the scenario of unknown source number. The expression for the MVDR scan vector of the phase modal domain feature subspace under the scenario of unknown source number is as follows:

[0069] In the formula, Indicates the scan vector parameters. The phase mode domain of the circular array with respect to direction The guiding vector The conjugate transpose of .

[0070] Specifically, formula (14) can also be reformulated as: (17) This application addresses the covariance matrix R of the phase mode signal. PM进行 The minimum eigenvalue obtained from eigenvalue decomposition is used as an approximate estimate of the noise power, thus: (18) That is, the third approximate expression, which is applied to formula (18). Calculations show that when j When approaching infinity: (19) because ,when j When it approaches infinity, Therefore, when j When the value is infinite, formula (19) can be approximated as: (20) According to formula (17), we can see ,and It can be obtained by solving formula (20), therefore The approximate solution expression can be written as: (twenty one) That is, the fifth approximation expression. Substituting formula (21) into formula (15), we can obtain the scan vector expression for the phase mode domain eigenspace MVDR in the case of unknown source number: (twenty two) Comparing formulas (22) and (15), it can be found that the method proposed in this application does not require prior knowledge of the number of sound sources in the space. It uses the covariance matrix of the existing modal signal to approximate the closed expression of the relevant parameters of the modal domain signal subspace and noise subspace, realizing the solution of the phase modal domain feature subspace MVDR scanning vector for unknown source numbers, thus improving the practicality of the Eigenspace algorithm in real-world scenarios.

[0071] It should be noted that, as shown above, the first to fifth approximate expressions correspond to formulas (17), (18), (19), (20), and (21), respectively, and will not be explained in detail here.

[0072] It should be noted that the traditional Eigenspace method first requires eigenvalue decomposition of the covariance matrix of the array received signal, and then uses the number of sound sources... P The signal / noise subspace is divided to compute the scan vector of the MVDR method for the feature subspace, while this embodiment will use the unknown... P Implicit in the limit operation, it does not require prior knowledge of the number of sound sources in the space. It uses the covariance matrix of the existing modal signal to approximate the closed-form expression of the relevant parameters of the modal domain signal subspace and noise subspace, thus realizing the solution of the MVDR scan vector of the phase modal domain feature subspace for cases with unknown number of signal sources.

[0073] S105. Based on the MVDR scanning vector and phase mode domain steering vector of the phase mode domain feature subspace under the condition of unknown source number, the MUSIC scanning vector of the phase mode domain feature subspace under the condition of unknown source number is further proposed. The azimuth spectrum estimation result is calculated, and high-resolution azimuth estimation is performed under the condition of unknown source number.

[0074] In one embodiment of this application, based on the MVDR scan vector and the phase mode domain steering vector for the case of unknown source number, a MUSIC scan vector for the phase mode domain feature subspace for the case of unknown source number is proposed, and the process of calculating the azimuth spectrum estimation result may include the following: Considering the orthogonality between the eigenvector matrix of the signal subspace and the noise subspace, the signal model of the steering vector is mainly related to the signal subspace. Based on the expression of the scan vector parameters and the MUSIC algorithm, the expression for minimizing the denominator of the scan vector parameters is obtained as follows: .

[0075] Based on the expression for minimizing the scan vector parameters in the denominator and the fourth approximation expression, the expression for minimizing the scan vector parameters in the case of an unknown number of sources is determined. The expression for the scan vector parameters in the case of an unknown number of sources is: .

[0076] Based on the expression for the scan vector of the phase mode domain feature subspace MVDR under the scenario of unknown source number and the expression for the scan vector parameter with denominator minimization under the scenario of unknown source number, the scan vector of the phase mode domain feature subspace MUSIC under the scenario of unknown source number is determined. The azimuth spectrum estimation result is calculated according to the relationship between the MUSIC scan vector and the azimuth spectrum expression.

[0077] In one embodiment of this application, the expression for the final scan vector is: .

[0078] The expression for the azimuth spectrum obtained from the scan vector is as follows: .

[0079] because Substituting formula (14) into the previous expression, we can... Represented as: (twenty three) Since the eigenvector matrix of the signal subspace is orthogonal to the noise subspace, and the signal model of the steering vector is based on the signal subspace, this invention will... Represented as: (twenty four) Because formula (24) contains elements related to the noise subspace Item. Combining formula (20), we can obtain the result when the number of unknown sources is unknown. Approximate calculation expression: (25) In practical applications, for parameters j By taking a finite number of relatively large integers, a good approximation can be obtained. Finally, the scan vector calculation expression for the eigenspace of the MUSIC algorithm for the unknown number of sources in the phase mode domain is obtained: (26) Based on the above formula (26), the formula for estimating its azimuth spectrum can be obtained as follows: (27) It should be noted that this method inherits the advantages of the Eigenspace algorithm and expands its application scenarios by adapting to the number of unknown sources. Simulation results show that in real-world scenarios with small apertures, low signal-to-noise ratios, and unknown sources, the estimation performance of this application is significantly better than traditional methods, effectively improving the underwater target detection and localization capabilities of sonar equipment.

[0080] For example, the performance of the high-resolution azimuth estimation method for the feature subspace of unknown source numbers in the phase mode domain proposed in this application is compared with that of existing azimuth estimation methods using computer simulation.

[0081] The simulation conditions are set as follows: the sensor array is a uniform circular array with 12 elements and a radius of 0.5 meters. Two incoherent single-frequency sound sources exist in space, with signal frequencies of 1010Hz and 1020Hz, and incident directions of 55° and 95° respectively. The background noise is Gaussian white noise. Phase mode decomposition (PMD) is performed on the received signal from the circular array, extracting mode signals from orders 0 to 6. Studies show that the output noise power is consistent across all order modes obtained from PMD under Gaussian white noise conditions, while the signal power varies according to… This leads to a decrease in the signal-to-noise ratio of the modal signal as the order increases, and higher-order terms exhibit poor robustness, which has a more significant impact on the orientation estimation results. Therefore, this application utilizes a computer processor to employ order reduction processing during simulation, i.e., discarding higher-order terms with insufficient robustness. The simulation selects 0-3 order modal signals as the optimal processing method, yielding... Figure 3 and Figure 4 The simulation results are shown. Figure 3 The azimuth spectrum results of different methods, namely MUSIC, EMUSIC and PM-EMUSIC, are shown respectively. The signal-to-noise ratio of each method is set to 5dB. It should be noted that "EMUSIC" represents the Eigenspace-MUSIC method when the number of sound sources is known, and PM-EMUSIC represents the characteristic subspace MUSIC method of the phase mode domain with unknown number of sound sources proposed in this invention. Figure 4The azimuth spectrum results of different methods, MUSIC, EMUSIC, and PM-EMUSIC, are presented, with their respective signal-to-noise ratios set to 0dB. It can be seen that the present invention has a narrower main lobe width and lower side lobes compared to the MUSIC and EMUSIC methods, indicating that the present invention has better resolution of nearby multiple targets and superior azimuth estimation performance. Furthermore, traditional MUSIC and EMUSIC methods require prior knowledge of the number of sound sources in space, thus dividing the corresponding signal and noise subspaces based on eigenvalue magnitudes. The method proposed in this invention can achieve effective azimuth estimation even when the number of sound sources is unknown, and it exhibits better performance advantages in processing low-frequency signals in the phase mode domain for small-aperture annular arrays, improving the practicality of the method in real-world scenarios.

[0082] Based on the above method embodiments, this application also provides a feature subspace orientation estimation device for unknown sources in the phase mode domain, to solve the same technical problem as the method embodiments. The device may include the following modules: The signal receiving module is used to receive sound pressure signals emitted by a signal source in space using a uniform circular sensor array; The signal decomposition module is used to decompose the sound pressure signal received by the uniform circular sensor array based on the phase mode decomposition theory to obtain multi-mode signals and phase mode domain steering vectors. The noise power estimation module is used to construct the covariance matrix of the phase mode domain received signal using multi-mode signals. The covariance matrix is ​​approximated by the correlation matrix of a segment of received data. The covariance matrix is ​​then subjected to eigenvalue decomposition to extract the minimum eigenvalue, which is used as an approximate estimate of the noise power. The scanning vector calculation module is used to approximate the parameters of the signal subspace and noise subspace based on the approximate estimate of the noise power, and obtain the MUSIC scanning vector of the phase mode domain feature subspace under the condition of unknown number of sources by using finite large integers to solve the relevant parameters of the signal subspace and noise subspace. The source azimuth calculation module is used to calculate the azimuth spectrum estimation results based on the MUSIC scan vector and phase mode domain covariance matrix of the phase mode domain feature subspace under the scenario of unknown source number, so as to realize the azimuth estimation of unknown source number.

[0083] Based on the above method embodiments, this application also provides an electronic device, which includes: at least one processor, a memory, and an input / output unit; wherein, the memory is used to store a computer program, and the processor is used to call the computer program stored in the memory to execute the feature subspace orientation estimation method for unknown number of phase mode domain sources provided in any of the foregoing embodiments.

[0084] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for estimating the eigenspace orientation of unknown source numbers in the phase mode domain, characterized in that, include: A uniform circular sensor array is used to receive sound pressure signals emitted by a source in space; Based on the phase mode decomposition theory, the sound pressure signal received by the uniform circular sensor array is decomposed to obtain multi-mode signals; The covariance matrix of the phase mode domain received signal is constructed using multi-mode signals, and the covariance matrix is ​​approximated by the correlation matrix of a segment of received data. The covariance matrix after approximation is decomposed into eigenvalues, the minimum eigenvalue is extracted, and the minimum eigenvalue is used as an approximate estimate of the noise power. Based on the approximate estimate of noise power and the covariance matrix of the received signal in the phase mode domain, the correlation parameters of the signal subspace are solved by finite large integers to obtain the scanning vector of the MVDR of the phase mode domain feature subspace under the scenario of unknown source number. Based on the scan vector and phase mode domain covariance matrix of the MVDR feature subspace in the scenario with unknown source numbers, the azimuth spectrum estimation results are calculated to estimate the azimuth of unknown source numbers.

2. The method for estimating the eigenspace orientation of unknown source numbers in the phase mode domain as described in claim 1, characterized in that, Uniform circular sensor array includes M Each array element, multiple array elements are placed in xoy The array is planar with its center at the origin, and element 0 is located at... x On the axis; The radius of the uniform circular sensor array is r The central angle between two adjacent array elements is twice pi divided by the number of array elements. M ; No. m In the spherical coordinates of the array element, the vertical elevation angle is 0, and the horizontal azimuth angle is... m Multiply the array element by the central angle, where m The value ranges from 1 to M Positive integers; Based on the transformation relationship from spherical coordinates to rectangular coordinates, we obtain the first... m Cartesian coordinates of the array element; The transformation relationships include: Rectangular coordinates x The component is the array radius. r Multiply by the sine of the vertical pitch angle and then multiply by the cosine of the horizontal azimuth angle; Rectangular coordinates y The component is the array radius. r Multiply by the sine of the vertical pitch angle and then multiply by the sine of the horizontal azimuth angle; Rectangular coordinates z The component is the array radius. r Multiply by the cosine of the vertical pitch angle.

3. The method for estimating the eigenspace orientation of unknown source numbers in the phase mode domain as described in claim 1, characterized in that, The sound pressure signal received by the uniform circular sensor array is decomposed based on phase mode decomposition theory to obtain multi-mode signals, including: Based on the spatial Fourier analysis of the incident plane wave of the array, the weighting coefficients of the sound pressure sensor are obtained by performing Fourier series expansion on the sound pressure signal. The orthogonal harmonic components are determined based on the weighting coefficients, and the multi-mode signals are determined based on the orthogonal harmonic components to decompose the received sound pressure signal. In the process of decomposing the received sound pressure signal, the highest order of the multi-mode signal is controlled according to the spatial sampling theorem. Nmax satisfy M≥2Nmax And the dimension is Nc = 2Nmax + 1 , M The number of array elements.

4. The method for estimating the eigenspace orientation of unknown source numbers in the phase mode domain as described in claim 1, characterized in that, The information source consists of P incoherent narrowband sound sources, each emitting a single-frequency signal of a different frequency; The sound pressure signal is obtained by superimposing Gaussian white noise onto a single-frequency signal.

5. The method for estimating the eigenspace orientation of unknown source numbers in the phase mode domain as described in claim 1, characterized in that, The approximate expression for the covariance matrix of the received signal is: Among them, the definition And there are , It is the matrix formed by the eigenvectors corresponding to the first P largest eigenvalues, that is, the eigenvector matrix of the signal subspace. ; This is the matrix formed by the eigenvectors corresponding to the smaller eigenvalues, i.e., the eigenvector matrix of the noise subspace. ; Let be the conjugate transpose of the eigenvector matrix of the signal subspace. Let be the conjugate transpose of the eigenvectors of the noise subspace. For noise power, This is the covariance matrix of the received signal from the phase mode domain array.

6. The method for estimating the eigenspace orientation of unknown source numbers in the phase mode domain as described in claim 5, characterized in that, The approximate estimate based on noise power is used to solve for the correlation parameters of the signal subspace using finite large integers, resulting in the scan vector of the phase mode domain feature subspace MVDR in scenarios with unknown number of sources, including: Based on the approximate expression of the covariance matrix, the covariance matrix features of the phase mode signal are decomposed into a mode domain signal subspace and a mode noise subspace, and the inverse of the covariance matrix is ​​determined based on the decomposed covariance matrix. Based on the approximate expression for the covariance matrix, a first approximate expression for characterizing the inverse of the covariance matrix is ​​determined, where the first approximate expression is: , The eigenvector matrix of the signal subspace. Let be the eigenvector matrix of the noise subspace. For noise power, And there are ; By using the approximate expression of left-multiplying the noise power by the inverse of the covariance matrix, we obtain the second approximate expression, which is: Get a finite integer j Taking the second approximate expression to the power of an integer, as the integer approaches infinity, yields the third approximate expression, which is: Based on the fact that as integers approach infinity, diagonal matrices approach zero, a fourth approximation expression is determined, which is: Based on the fourth and first approximation expressions, the fifth approximation expression is determined, whereby the fifth approximation expression is: In the formula, This represents the smallest eigenvalue of the covariance matrix; Substituting the fifth approximation expression into the MVDR scan vector expression of the modal domain feature subspace, we obtain the scan vector expression of the phase modal domain feature subspace MVDR in the scenario with an unknown number of sources. The expression for the MVDR scan vector of the phase modal domain feature subspace in the scenario with an unknown number of sources is as follows: In the formula, Indicates the scan vector parameters. The phase mode domain of the circular array with respect to direction The guiding vector The conjugate transpose of .

7. The method for estimating the eigenspace orientation of unknown source numbers in the phase mode domain as described in claim 6, characterized in that, The azimuth spectrum estimation results are calculated based on the scan vector and phase mode domain covariance matrix of the phase mode domain feature subspace MVDR in scenarios with unknown source numbers, including: Based on the expression for the MVDR scan vector in the phase mode domain feature subspace under the scenario of unknown source number, and considering the orthogonality between the feature vector matrix of the signal subspace and the noise subspace, as well as the correlation between the signal model of the steering vector and the signal subspace, the scan vector parameters are... Replace with scan vector parameters So that the scan vector parameters Minimize the factors in the denominator, where the scan vector parameters An approximate expression is: Based on the approximate expression of the source parameters and the fourth approximation expression, the expression for the scan vector parameters in the case of an unknown number of sources is determined. The expression for the scan vector parameters in the case of an unknown number of sources is: Based on the expression of the scan vector of the phase mode domain feature subspace MVDR under the scenario with unknown number of sources and the expression of the scan vector parameter under the scenario with unknown number of sources, the final scan vector of the phase mode domain feature subspace MUSIC under the scenario with unknown number of sources is determined. The azimuth spectrum estimation result is calculated according to the relationship between the expression of the feature subspace MUSIC scan vector and the azimuth spectrum.

8. The method for estimating the eigenspace orientation of unknown source numbers in the phase mode domain as described in claim 7, characterized in that, The scanning vector and phase mode domain covariance matrix of the phase mode domain feature subspace MVDR under the scenario of unknown source number are used to calculate the azimuth spectrum estimation result. The final expression of the scanning vector is as follows: The expression for the final azimuth spectrum is as follows: In the formula, The covariance matrix of the received signal from the phase mode domain array. For the phase modal domain of the array with respect to direction The guiding vector, The covariance matrix R PM Corresponding to the smallest eigenvalue, For noise power, and The two are approximately equal.

9. A device for estimating the eigenspace orientation of an unknown number of sources in the phase mode domain, characterized in that, include: The signal receiving module is used to receive sound pressure signals emitted by a signal source in space using a uniform circular sensor array; The signal decomposition module is used to decompose the sound pressure signal received by the uniform circular sensor array based on the phase mode decomposition theory to obtain multi-mode signals. The noise power estimation module is used to construct the covariance matrix of the phase mode domain received signal using multi-mode signals, and the covariance matrix is ​​approximated by the correlation matrix of a segment of received data. The covariance matrix after approximation is decomposed into eigenvalues, the minimum eigenvalue is extracted, and the minimum eigenvalue is used as an approximate estimate of the noise power. The scanning vector calculation module is used to obtain the scanning vector of the phase mode domain feature subspace MVDR under the scenario of unknown source number by approximating the signal subspace correlation parameters with finite large integers based on the approximate estimate of noise power and the covariance matrix of the received signal in the phase mode domain. The source azimuth calculation module is used to calculate the azimuth spectrum estimation results based on the scan vector and phase mode domain covariance matrix of the phase mode domain feature subspace MVDR in scenarios with unknown source numbers, so as to perform azimuth estimation for unknown source numbers.

10. An electronic device, characterized in that, The electronic device includes: At least one processor, memory, and input / output unit; The memory is used to store computer programs, and the processor is used to call the computer programs stored in the memory to execute the feature subspace orientation estimation method for unknown number of phase mode domain sources according to any one of claims 1 to 8.

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