A sound vector array DOA estimation method based on quaternion matrix dimension reduction

Abstract

The purpose of this invention is to provide a method for DOA estimation of acoustic vector arrays based on quaternion matrix dimensionality reduction, comprising the following steps: constructing a CAACIS acoustic vector coprime array at the receiver; establishing a quaternion model of the received signal based on the array output; estimating the quaternion covariance matrix; performing dimensionality reduction on the quaternion covariance matrix to obtain a virtual array received signal model of the acoustic vector coprime array; reconstructing the Hermitian-Toeplitz matrix; performing eigenvalue decomposition on the Hermitian-Toeplitz matrix and constructing a spatial spectral function; and obtaining the DOA estimation result through spectral peak search. This invention addresses the problem of how to achieve multi-objective DOA estimation with both low complexity and good performance based on a quaternion framework under acoustic vector coprime arrays.

Description

Technical Field

[0001] This invention relates to a method for estimating the DOA of acoustic vector arrays based on quaternion matrix dimensionality reduction, belonging to the field of sonar signal processing. Background Technology

[0002] DOA estimation is an important branch of array signal processing, playing a crucial role in underwater target detection using sonar arrays. With advancements in marine industry and technology, the growing demand for deep-sea exploration is driving the miniaturization and intelligentization of various underwater platforms, placing higher demands on the design of sonar arrays mounted on these platforms. In recent years, novel array structures combining acoustic vector sensors with coprime arrays have become a research hotspot.

[0003] Because acoustic vector sensors can synchronously and pointwise acquire sound pressure and vibration velocity information of a specific point in underwater space, they exhibit higher array gain and spatial resolution with the same number of array elements compared to traditional sound pressure sensor arrays. To fully utilize the structural information and multi-channel signal components of the acoustic vector array, researchers have proposed applying quaternion theory to acoustic vector signal modeling to achieve super-resolution DOA estimation for multiple targets in large-scale sparse acoustic vector arrays. Currently, a series of super-resolution algorithms based on the quaternion framework have been proposed, demonstrating superior performance compared to traditional "long vector" methods.

[0004] However, when the quaternion model is constructed using coprime acoustic vector arrays, including CAACIS, we cannot ignore the fact that similar array structures can generate a large virtual differential array using only a small number of physical array elements. This multiplies the already considerable computational complexity of the aforementioned quaternion methods. Although a few existing algorithms simplify the computation in the quaternion domain by sacrificing some performance and using estimation methods that do not require eigenvalue decomposition, all computations in these methods are essentially still performed in the quaternion domain, and the more complex spectral peak search process cannot be avoided.

[0005] Therefore, "how to simplify the quaternion algorithm in essence and achieve good estimation performance while significantly reducing computational complexity" has become the key to further optimizing the DOA estimation algorithm based on acoustic vector coprime array. Summary of the Invention

[0006] The purpose of this invention is to provide a method for estimating the DOA of acoustic vector arrays based on quaternion matrix dimensionality reduction, which has both low complexity and good estimation performance.

[0007] The objective of this invention is achieved as follows: The steps are as follows:

[0008] Step 1: Construct a CAACIS acoustic vector coprime array at the receiving end;

[0009] Step 2: Establish a quaternion model of the received signal z based on the output of the acoustic vector coprime array. q (t):

[0010] z q (t)=[p(t)+v x (t)]+[p(t)+v y (t)]·j

[0011] =A q s(t)+n q (t),

[0012] Where p(t), v x (t), v y (t) represent the components of the array-received signal in the sound pressure channel, x-axis, and y-axis particle velocity channels, respectively; A q ∈H M×K Let n be a quaternion array manifold matrix. q s(t) is a quaternion noise vector; s(t) = [s1(t), s2(t), ..., s2(t)] K (t)] T Let θ be the incident signal vector, representing a set of K independent far-field narrowband signals originating from the horizontal direction θ = [θ1, θ2, ..., θ...]. k ] T ∈[-π,π] is incident on the array in the form of a plane wave;

[0013] The received signal quaternion model z described in step two q (t), the position of its imaginary sign j in the formula is closely related to the subsequent processing flow and cannot be arbitrarily replaced;

[0014] Step 3: Using z q (t) Estimate the quaternion covariance matrix R q :

[0015]

[0016] in, R represents the conjugate transpose of a quaternion. s R represents the signal covariance matrix. nq Represents the noise covariance matrix;

[0017] Step 4: For the quaternion covariance matrix R q Dimensionality reduction is performed; the matrix is ​​rearranged and expanded into a complex adjoint matrix. Will Block recombination yields a dimensionality-reduced array covariance matrix R. iq;

[0018] Step 5: Obtain the virtual array received signal model of the acoustic vector coprime array; vectorize R. iq Redundant rows in the resulting vector are removed and sorted in ascending order according to the indices of the virtual array elements to obtain the equivalent virtual array received signal.

[0019] Step Six: Utilize Reconstructing the Hermitian-Toeplitz matrix

[0020] Step 7: Perform eigenvalue decomposition on the reconstructed Hermitian-Toeplitz matrix:

[0021]

[0022] Among them, U s and U n Representing the signal subspace and noise subspace respectively, their corresponding eigenvalue matrices are Λ s and Λ n And construct the spatial spectral function:

[0023]

[0024] Where α(θ) is the steering vector corresponding to the virtual array;

[0025] Step 8: Obtain DOA estimation results through spectral peak search; traverse θ∈[-π,π] to find the peaks of the spatial spectrum, and the angles corresponding to each peak are the final DOA estimation results.

[0026] Furthermore, the construction process of the CAACIS coprime acoustic vector array described in step one can be described as follows: An array model is constructed using several two-dimensional acoustic vector sensors, each containing one sound pressure channel and two particle velocity channels facing the x-axis and y-axis respectively; multiple of these acoustic vector sensors are linearly arranged along their y-axis direction, forming two uniform linear subarrays; the two subarrays are composed of M1 and M2 sensor elements respectively, with element spacing of M2d and (M1 / ρ)d respectively; where d is the half-wavelength of the signal, ρ is the compression factor, and... satisfy and M2 are coprime; the compression factor ρ is an integer taking the value [2, M1], and its selection affects the number of additional virtual array elements generated; finally, the first array elements of the two subarrays are aligned and superimposed into a new sparse linear acoustic vector array, namely CAACIS; the CAACIS array contains M = M1 + M2 - 1 physical array elements. If m1 and m2 represent the index of a certain array element in the two subarrays respectively, then the set p of its physical array element positions is...M for

[0027]

[0028] The received signal quaternion model described in step two: z q (t)=[p(t)+v x (t)]+[p(t)+v y The position of the imaginary sign j in the formula (t) is closely related to the subsequent processing flow and cannot be arbitrarily replaced.

[0029] The dimensionality reduction process described in step four is as follows: First, A... q Expand into A q =A1+A2j, and rearrange the quaternion covariance matrix R. q It is in the following form

[0030]

[0031] Where, A1=A(Θ) p +Θ x ), A2=A(Θ p +Θ y ), A1, A2∈C M×K A represents the original array manifold matrix; Indicates noise power; I M and 0 M Represent the M-dimensional identity matrix and the M-dimensional zero matrix, respectively; Θ p Θ x Θ y ∈R K×K Both are diagonal matrices, satisfying

[0032]

[0033] The sorted R q Represented as Expand it into complex adjoint matrix form

[0034]

[0035] For complex adjoint matrices Perform matrix partitioning

[0036]

[0037] Reorganizing the block submatrices yields a reduced-dimensional covariance matrix.

[0038]

[0039] In the formula, R iq ∈C M×MIt contains all sound pressure and vibration velocity components, as well as complete array structure information, while its dimension is only that of the original matrix R. q Half of it.

[0040] The Hermitian-Toeplitz matrix described in step six It can be obtained in the following ways:

[0041]

[0042] in For vectors The former M vc The reverse order of the elements, For vectors After M vc Elements, M vc This represents the maximum number of consecutive virtual array elements obtainable through the array.

[0043] The construction process of the spatial spectral function described in step seven is as follows: Based on the eigenvalue decomposition results, the MUSIC spatial spectral function is constructed as follows:

[0044]

[0045] Where α(θ) is the steering vector corresponding to the virtual array, satisfying

[0046]

[0047] in, λ is the signal wavelength.

[0048] Compared with the prior art, the advantages of the present invention are:

[0049] (1) This invention utilizes the inherent connection between complex-quaternion mapping and the quaternion covariance matrix structure to halve the dimension of the quaternion covariance matrix without losing the received signal information. This process significantly reduces the computational burden of the DOA estimation algorithm, and is particularly effective when processing large virtual differential co-arrays generated by CAACIS arrays.

[0050] (2) At the same time, the reasonable selection of strategies in the dimensionality reduction process enables the present invention to maintain the additional orthogonal constraints of the quaternion space while reducing the matrix dimensionality, and under the same conditions, it exhibits better spatial resolution and estimation accuracy than similar super-resolution methods.

[0051] (3) In addition, in view of the rank loss problem of the covariance matrix of the equivalent virtual array, this invention draws on the idea of ​​using single snapshot data to realize coherent target estimation, reconstructs a Hermitian-Toeplitz matrix, and then realizes multi-target robust DOA estimation under coprime acoustic vector array without sacrificing the array aperture. Attached Figure Description

[0052] Figure 1 For the CAACIS acoustic vector coprime array system: M1 and M2 are the number of elements in subarray 1 and subarray 2, respectively, d is the element spacing, and ρ is the compression factor;

[0053] Figure 2 This is a flowchart of the DOA estimation process of the present invention;

[0054] Figure 3 Spatial spectra of each method (in the figure, ICQ-MUSIC is the method proposed in this invention, CLV-MUSIC and ACQ-MUSIC are existing methods, the same below): SNR = 0dB, number of snapshots L = 300, 9 independent targets;

[0055] Figure 4 The target resolution probabilities of each method with angular interval as the variable are: SNR = 0 dB, number of snapshots L = 300, 1000 Monte Carlo trials;

[0056] Figure 5 The computational complexity of each method is given by the number of physical array elements: number of snapshots L = 500, number of spectral peak search points N = 2000. Detailed Implementation

[0057] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0058] Combination Figure 1-5 The steps of this invention are as follows:

[0059] (1) As Figure 1 As shown, a CAACIS acoustic vector coprime array is constructed at the receiving end using M = M1 + M2 - 1 two-dimensional acoustic vector sensors;

[0060] (2) Establishing a quaternion model of the received signal z based on the output of the coprime acoustic vector array q (t):

[0061] z q (t)=[p(t)+v x (t)]+[p(t)+v y (t)]·j

[0062] =A q s(t)+n q(t), where p(t) and v x (t), v y (t) are all i-complex vectors, representing the components of the array-received signal in the sound pressure channel, x-axis, and y-axis particle velocity channels, respectively; j is an imaginary number, and i and j are orthogonal to each other; A q ∈H M×K Let n be a quaternion array manifold matrix. q s(t) is a quaternion noise vector; s(t) = [s1(t), s2(t), ..., s2(t)] K (t)] T Let θ be the incident signal vector, representing a set of K independent far-field narrowband signals originating from the horizontal direction θ = [θ1, θ2, ..., θ...]. k ] T ∈[-π,π] is incident on the array in the form of a plane wave;

[0063] (3) Using z q (t) Estimate the quaternion covariance matrix R q :

[0064]

[0065] in, R represents the conjugate transpose of a quaternion. s R represents the signal covariance matrix. nq Represents the noise covariance matrix;

[0066] (4) For the quaternion covariance matrix R q Perform dimensionality reduction; first, A q Expand into A q =A1+A2j, and rearrange the quaternion covariance matrix R. q It is in the following form

[0067]

[0068] Among them, I M Describes an M-dimensional identity matrix, 0 M Represents an M-dimensional zero matrix; This represents the noise power; and we have A1 = A(Θ). p +Θ x ), A2=A(Θ p +Θ y ), A1, A2∈C M×K A represents the original array manifold matrix; Θ p Θ x Θ y ∈R K×K Both are diagonal matrices, satisfying

[0069]

[0070] The sorted R q Represented as Expand it into complex adjoint matrix form

[0071]

[0072] For complex adjoint matrices Perform matrix partitioning

[0073]

[0074] Reorganizing the block submatrices yields a reduced-dimensional covariance matrix.

[0075]

[0076] In the formula, R iq ∈C M×M It contains all sound pressure and vibration velocity components, as well as complete array structure information, while its dimension is only that of the original matrix R. q Half of;

[0077] (5) Obtain the virtual array received signal model of the acoustic vector coprime array; first, vectorize R iq :

[0078]

[0079] in, ⊙ denotes the Kronecker product, and ⊙ denotes the Khatri-Rao product; h = vec{I M}, vec{·} denotes vectorization operation; g is the equivalent received signal vector for a single snapshot; vector r is extracted based on the index information of the virtual array element positions. iq The corresponding elements in the array are processed, redundant rows are removed, and the array is rearranged in ascending order according to the virtual array element numbers to obtain the equivalent virtual array received signal.

[0080]

[0081] in, λ represents the position of the array elements in the rearranged continuous virtual array, and λ represents the half wavelength of the signal. M vc This represents the maximum number of consecutive virtual array elements obtainable through this array;

[0082] (6)Use Reconstructing the Hermitian-Toeplitz matrix

[0083]

[0084] in For vectors The former M vc The reverse order of the elements, For vectors After M vc Elements, M vc =M1M2-M1(M2-1) / ρ, where M1 and M2 are the number of subarray elements, and ρ is the compression factor;

[0085] (7) Perform eigenvalue decomposition on the reconstructed Hermitian-Toeplitz matrix:

[0086]

[0087] Among them, U s and U n Representing the signal subspace and noise subspace respectively, their corresponding eigenvalue matrices are Λ s and Λ n And construct the spatial spectral function:

[0088]

[0089] Where α(θ) is the steering vector corresponding to the virtual array, satisfying

[0090]

[0091] in,

[0092] (8) Obtain the DOA estimation result by searching for spectral peaks; traverse θ∈[-π,π] to find the peaks of the spatial spectrum, and the angles corresponding to each peak are the final DOA estimation results.

[0093] Figure 2 The process of DOA estimation is described. Because this invention reduces the dimensionality of the quaternion covariance matrix based on the complex-quaternion mapping property, it reduces the matrix dimension to half of its original size without losing received signal information. Furthermore, it restores the rank of the virtual covariance matrix using Hermitian-Toeplitz matrix reconstruction technology. Therefore, it can achieve multi-objective DOA estimation with both low complexity and good estimation performance in coprime acoustic vector arrays such as CAACIS.

[0094] It should be noted that the method of "reducing the dimensionality of the quaternion covariance matrix using the complex-quaternion mapping property" proposed in this invention has a certain degree of universality and can be considered as part of the data modeling process. Therefore, this method is applicable to various types of acoustic vector linear arrays (this invention takes the CAACIS acoustic vector coprime array as an example), and can also be combined with various DOA estimation methods (this paper takes MUSIC as an example) to expand the application scenarios or improve the performance of the method. Without departing from the technical principles of this invention, those skilled in the art can make several modifications to this method (for example, applying this method to other similar common acoustic vector arrays, or combining this method with other existing algorithms), and these modifications should also be within the protection scope of this invention.

[0095] Application examples of this invention:

[0096] Figure 3 , Figure 4 , Figure 5 This paper demonstrates the advantages and disadvantages of the proposed method (ICQ-MUSIC) compared to existing methods (CLV-MUSIC, ACQ-MUSIC) in terms of performance and computational complexity. In the simulations described above, it is assumed that: signals from different directions arrive at the array simultaneously as plane waves, remaining independent of each other; each receiving element has the same sensitivity and does not interfere with the others, possessing an equal signal-to-noise ratio for any signal; and the sound pressure and particle velocity components within the array elements are uncorrelated. Unless otherwise specified, all methods are compared under identical conditions.

[0097] Figure 3 The spatial spectra of nine independent targets estimated by various methods under the conditions of SNR=0dB and snapshot number L=300 are shown. Although all three methods can accurately estimate the azimuth angles of all preset targets, the ICQ-MUSIC method proposed in this invention has the sharpest spectral peak.

[0098] Figure 4 The target resolution probabilities of each method based on 1000 Monte Carlo trials are presented, where SNR = 0 dB and the number of snapshots L = 300. At different angular intervals, the ICQ-MUSIC method exhibits the highest target resolution probability.

[0099] Figure 5 The computational complexity of each method is shown with the number of physical array elements as the variable, given the number of snapshots L=500 and the number of spectral peak search points N=2000. It can be observed that the ICQ-MUSIC method proposed in this invention has a significant advantage in terms of computational complexity.

[0100] In summary, the simulation results show that, compared with existing similar methods, the method proposed in this invention not only significantly reduces computational complexity but also achieves certain advantages in estimation accuracy and spatial resolution, thus realizing efficient multi-target DOA estimation under acoustic vector arrays.

Claims

1. A method for estimating the DOA of acoustic vector arrays based on quaternion matrix dimensionality reduction, characterized in that: It includes the following steps: Step 1: Construct a CAACIS acoustic vector coprime array at the receiving end; Step 2: Establish a quaternion model of the received signal z based on the output of the acoustic vector coprime array. q (t): z q (t)=[p(t)+v x (t)]+[p(t)+v y (t)]·j =A q s(t)+n q (t), Where p(t), v x (t), v y (t) represent the components of the array-received signal in the sound pressure channel, x-axis, and y-axis particle velocity channels, respectively; A q ∈H M×K Let n be a quaternion array manifold matrix. q s(t) is a quaternion noise vector; s(t) = [s1(t), s2(t), ..., s2(t)] K (t)] T Let θ be the incident signal vector, representing a set of K independent far-field narrowband signals originating from the horizontal direction θ = [θ1, θ2, ..., θ...]. K ] T ∈[-π,π] is incident on the array in the form of a plane wave; Step 3: Using z q (t) Estimate the quaternion covariance matrix R q : in, R represents the conjugate transpose of a quaternion. s R represents the signal covariance matrix. nq Represents the noise covariance matrix; Step 4: For the quaternion covariance matrix R q Dimensionality reduction is performed; the matrix is ​​rearranged and expanded into a complex adjoint matrix. Will Block recombination yields a dimensionality-reduced array covariance matrix R. iq ; Step 5: Obtain the virtual array received signal model of the acoustic vector coprime array; vectorize R. iq Redundant rows in the resulting vector are removed and sorted in ascending order according to the indices of the virtual array elements to obtain the equivalent virtual array received signal. Step Six: Utilize Reconstructing the Hermitian-Toeplitz matrix Step 7: Perform eigenvalue decomposition on the reconstructed Hermitian-Toeplitz matrix: Among them, U s and U n Representing the signal subspace and noise subspace respectively, their corresponding eigenvalue matrices are Λ s and Λ n And construct the spatial spectral function: Where α(θ) is the steering vector corresponding to the virtual array; Step 8: Obtain DOA estimation results through spectral peak search; traverse θ∈[-π,π] to find the peaks of the spatial spectrum, and the angles corresponding to each peak are the final DOA estimation results.

2. The method for estimating the DOA of acoustic vector arrays based on quaternion matrix dimensionality reduction according to claim 1, characterized in that: The specific method for step one is as follows: An array model is constructed using several two-dimensional acoustic vector sensors, each containing a sound pressure channel and two particle velocity channels facing the x-axis and y-axis respectively. Multiple acoustic vector sensors described above are arranged linearly along their y-axis to form two uniform linear subarrays. Each subarray consists of M1 and M2 sensor elements, with element spacing of M2d and (M1 / ρ)d, respectively; where d is the half-wavelength of the signal, and ρ is the compression factor. satisfy and M2 are coprime; the compression factor ρ is an integer taking the value [2, M1], and its selection affects the number of additional virtual array elements generated; Finally, the first elements of the two subarrays are aligned and superimposed to form a new sparse linear acoustic vector array, i.e., an acoustic vector coprime array with compressed element spacing. This array contains M = M1 + M2 - 1 physical elements. If m1 and m2 represent the indexes of a certain element in the two subarrays, then the set p of its physical element positions... M for:

3. The method for estimating the DOA of acoustic vector arrays based on quaternion matrix dimensionality reduction according to claim 1, characterized in that: The received signal quaternion model z described in step two q The position of the imaginary sign j in the formula (t) is closely related to the subsequent processing flow and cannot be arbitrarily replaced.

4. The method for estimating the DOA of acoustic vector arrays based on quaternion matrix dimensionality reduction according to claim 1, characterized in that: The dimensionality reduction process described in step four is as follows: First, A... q Expand into A q =A1+A2j, and rearrange the quaternion covariance matrix R. q It is in the following form: Where, A1=A(Θ) p +Θ x ), A2=A(Θ p +Θ y ), A1, A2∈C M×K A represents the original array manifold matrix; Indicates noise power; I M and 0 M Represent the M-dimensional identity matrix and the M-dimensional zero matrix, respectively; Θ p Θ x Θ y ∈R K×K Both are diagonal matrices, satisfying: The sorted R q Represented as And expand it into a complex adjoint matrix form: For complex adjoint matrices Perform matrix partitioning: Reorganizing the submatrices yields a reduced-dimensional covariance matrix: In the formula, R iq ∈C M×M It contains all sound pressure and vibration velocity components, as well as complete array structure information, while its dimension is only that of the original matrix R. q Half of it.

5. The method for estimating the DOA of acoustic vector arrays based on quaternion matrix dimensionality reduction according to claim 1, characterized in that: The Hermitian-Toeplitz matrix described in step six Obtained in the following ways: in For vectors The former M vc The reverse order of the elements, For vectors After M vc elements, M vc M is the maximum number of consecutive virtual array elements obtainable by the array. vc =M1M2-M1(M2-1) / ρ, where M1 and M2 are the number of subarray elements, and ρ is the compression factor.

6. The method for estimating the DOA of acoustic vector arrays based on quaternion matrix dimensionality reduction according to claim 5, characterized in that: The construction process of the spatial spectral function described in step seven is as follows: Based on the eigenvalue decomposition results, the MUSIC spatial spectral function is constructed as follows: Where α(θ) is the steering vector corresponding to the virtual array, satisfying: in, λ is the signal wavelength.

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