Direction of Arrival Estimation Method for Acoustic Vector Sensor Array in Non-Uniform Noise
Through the WSCMF method, the problem of deterioration in azimuth vector sensor array orientation estimation performance under non-uniform noise is solved. By reconstructing the sparse covariance matrix and estimating the signal and noise power, higher estimation accuracy and lower computational complexity are achieved.
Patent Information
- Application Number
- CN202210353033.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-04-06
- Publication Date
- 2025-04-11
- Estimated Expiration
- 2042-04-06
AI Technical Summary
In non-uniform noise environments, the azimuth estimation performance of acoustic vector sensor arrays will be severely deteriorated, and existing methods are complex in computing and difficult to meet real-time requirements.
A regularized weighted sparse covariance matrix fitting (WSCMF) method is proposed. By defining the array manifold matrix of a new acoustic vector sensor array, the sparse covariance matrix containing sparse signal power and noise power is reconstructed, and based on the sparse covariance matrix fitting criterion and sparse signal compensation mechanism, a cost function is constructed to estimate sparse signal power and noise power.
The azimuth estimation accuracy of the acoustic vector sensor array under non-uniform noise is improved, the calculation amount is reduced, the real-time requirement is met, and the estimation accuracy is shown in the low signal-to-noise ratio.
Smart Images
Figure CN114755628B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of array signal processing, and in particular to a method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise. Background Art
[0002] The acoustic vector sensor is a new type of sensor that can measure the sound pressure and vibration velocity information in the sound field in a spatially co-located and synchronous manner. Compared with the traditional sound pressure sensor, the acoustic vector sensor can not only obtain the sound pressure information in the sound field, but also obtain the sound vibration velocity information. By utilizing the additional sound vibration velocity information, the acoustic vector sensor has better signal detection and azimuth estimation performance. Compared with a single acoustic vector sensor, the acoustic vector sensor array composed of it has the advantages of high signal gain, strong interference suppression capability and high spatial resolution. It is now widely used in detection fields such as sonar and radar.
[0003] Estimating the direction of arrival (DOA) of underwater sound sources is a hot research topic in the field of passive detection. The beamforming method is a relatively classic DOA estimation method with the advantages of simple structure and low computational complexity, but it is limited by the physical aperture and has poor resolution performance. Subspace algorithms, such as the Multiple Signal Classification (MUSIC) algorithm and its improved algorithm, can achieve high-resolution estimation, but the DOA estimation performance of this type of method will be further deteriorated in low signal-to-noise ratio, few snapshots and coherent source scenarios. Sparse reconstruction methods use the sparse distribution of the incident signal relative to the entire space to grid the angle space where the signal is located, and transform the azimuth estimation problem into a sparse signal reconstruction problem. This type of algorithm makes up for the defect that the azimuth estimation performance of traditional azimuth estimation methods deteriorates in the case of coherent sources, low signal-to-noise ratio and few snapshots. The l1-norm optimization method is a relatively classic sparse signal reconstruction method. It has higher estimation accuracy and robustness than traditional methods under low signal-to-noise ratio and few snapshots. However, the l1-norm optimization method faces the problem of difficult selection of regularization parameters in complex underwater acoustic environments. The Iteration Adaptive Approach (IAA) is a sparse method that does not require setting user parameters. It not only has the advantages of sparse reconstruction algorithms, but also has a small amount of calculation. It has been widely used in radar systems. However, the above method is based on the ideal assumption that the noise power of each component of sound pressure and sound velocity is equal, and studies the azimuth estimation performance of the acoustic vector sensor array. Since the noise received by the acoustic vector sensor is mainly environmental noise rather than the noise inside the sensor, and the velocity axis of the acoustic vector sensor is directional, part of the environmental noise measured in the velocity axis direction is filtered out, resulting in the noise power of the velocity component not being equal to the noise power of the sound pressure component. In this case, the azimuth estimation performance of the above method will be seriously deteriorated.
[0004] In order to solve the problem of deterioration of the azimuth estimation performance of the sound pressure sensor array under non-uniform noise, Bin Liao et al. proposed an iterative subspace estimation method in the paper "Iterative Methods for Subspace and DOA Estimation in Nonuniform Noise" (IEEE Transactions on Signal Processing Volume 64, Issue 12.2016.PP3008-3020), using the maximum likelihood (ML) and least squares (LS) methods to estimate the signal subspace and noise covariance matrix. Although this method can be applied to the acoustic vector sensor array to solve the problem of deterioration of the azimuth estimation performance of the acoustic vector sensor array under non-uniform noise, both methods use an iterative method to estimate the noise covariance matrix, resulting in a high computational complexity of the algorithm, which is difficult to meet the system's real-time requirements. In order to solve this problem, Aifei Liu et al. proposed the augmented subspace MUSIC (ASMUSIC) method in the paper "Augmented subspace MUSIC method for DOA estimation using acoustic vector sensor array" (IET Radar, Sonar & Navigation Volume 13, Issue 6.2019.PP 969-975), which improves the azimuth estimation accuracy of the acoustic vector sensor array in the case of non-uniform noise by expanding the number of virtual sources to the signal subspace. However, this algorithm is only applicable to large aperture arrays and acoustic vector sensors where the noise power between the sound pressure and the vibration velocity is unequal. When the response between sensors is different, the noise received between the sound pressure and the vibration velocity between the acoustic vector sensors and the vibration velocity and the vibration velocity channels will also be different. In this case, the azimuth estimation performance of the ASMUSIC method will also be seriously deteriorated. Summary of the invention
[0005] In view of the above situation, the purpose of the present invention is to provide a regularized weighted sparse covariance matrix fitting (WSCMF) azimuth estimation method to improve the accuracy of azimuth estimation of an acoustic vector sensor array under non-uniform noise.
[0006] In order to achieve the above object, the present invention is implemented by the following technical solutions:
[0007] A method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise, the method comprising the following steps:
[0008] Step 1, receiving an output vector X output by an acoustic vector sensor array;
[0009] Step 2, based on the sparse signal model, calculate the signal covariance matrix P and the noise covariance matrix Q according to the output vector X, and construct a sparse covariance matrix R using the obtained signal covariance matrix P and the noise covariance matrix Q;
[0010] Step 3: construct a cost function based on the sparse covariance matrix R, use the cost function to estimate the sparse signal power, and obtain the signal power vector
[0011] Step 4: Signal power vector Perform a spectrum peak search, and the sound source position corresponding to the obtained spectrum peak is the estimated target azimuth.
[0012] Furthermore, in the above-mentioned method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise, step 2 includes the following sub-steps:
[0013] Step 21, construct a sparse signal model of the acoustic vector sensor array under non-uniform noise conditions:
[0014] Assume that K far-field equal-power narrowband signals with wavelength λ are incident on a uniform linear array composed of M acoustic vector sensors with an array element spacing of d. The velocity components of the narrowband signal along the x-axis and y-axis are u and x and u y , and the x-axis and y-axis are orthogonal. When the number of snapshots is L, the output vector X of the acoustic vector sensor array can be expressed as
[0015] X=A(θ)S+W
[0016] Where, X = [x(1), x(2), ..., x(L)] represents the output vector of the acoustic vector sensor array, A(θ) = [a(θ1), a(θ2), ..., a(θ K )] represents the array manifold matrix of the ideal acoustic vector sensor array, θ = [θ1, θ2, …, θ K ] represents the azimuth of the target, represents the manifold vector of the kth target, represents the Cartesian product, h(θ k )=[1 cosθ k sinθ k ] T represents the array manifold vector of the kth target incident on the acoustic vector sensor, represents the sound pressure response coefficient of the k-th target incident on the m-th sound vector sensor, W = [w(1), w(2), ..., w(L)] represents the noise vector, S = [s(1), s(2), ..., s(L)] represents the input signal waveform vector;
[0017] Assuming that the angle space (-180° to 180°) is evenly divided into N discrete grids, and the number of discrete grids N is much larger than the number of sound sources K, the incoming wave directions of all sound sources can be expressed as The sparse signal model of the acoustic vector sensor array can be expressed as
[0018]
[0019] In the formula, represents the array manifold matrix of the acoustic vector sensor array under the sparse signal model, is a row-sparse matrix, and its non-zero rows represent the location of the real signal;
[0020] Step 22, calculate the signal covariance matrix P and the noise covariance matrix Q:
[0021] The signal covariance matrix P can be expressed as
[0022]
[0023] Where E{·} represents the expected operation, diag{·} represents the diagonal matrix operation, Indicates the power of the signal corresponding to the nth grid;
[0024] The noise covariance matrix Q can be expressed as
[0025] Q = diag{q1, ..., q M}
[0026] In the formula,
[0027] Assuming that the incident signals are uncorrelated, the covariance matrix of the acoustic vector sensor array under the sparse signal model can generally be expressed as
[0028]
[0029] Generally, if the background noise is Gaussian white noise, the noise covariance matrix Q = σ 2 I 3M , σ 2 It represents the noise power output by each channel of the acoustic vector sensor array in a uniform noise environment, I 3Mrepresents a 3M×3M unit matrix. However, in practical applications, since the noise received by the acoustic vector sensor is mainly environmental noise rather than the noise inside the sensor, and the velocity axis of the acoustic vector sensor is directional, part of the environmental noise measured in the velocity axis direction is filtered out, resulting in the noise power of the acoustic velocity component not being equal to the noise power of the sound pressure component. In addition, considering the different responses between sensors, the noise power received between the sound pressure channel and the sound velocity channel of the acoustic vector sensor is different, that is, In order to solve the above problems, the present invention defines a new array manifold matrix of the acoustic vector sensor array and reconstructs the sparse covariance matrix R, so that it can simultaneously estimate the signal power on each grid and the noise power output by each channel in the acoustic vector sensor array. It should be noted that each channel of the acoustic vector sensor array refers to the sound pressure channel of each acoustic vector sensor array element and the sound velocity channel corresponding to the sound velocity component of each acoustic vector sensor array element along the x-axis and y-axis directions.
[0030] Step 23, construct the sparse covariance matrix R:
[0031] In order to estimate the sparse signal power and the noise power of each channel output in the acoustic vector sensor array, a new array manifold matrix of the acoustic vector sensor array is defined:
[0032]
[0033] Among them I 3M represents the 3M×3M unit matrix, assuming that the incident signals are uncorrelated, then the sparse covariance matrix R can be expressed as
[0034] R=DΞD H
[0035] in,
[0036]
[0037]
[0038] Wherein, the first N items of the diagonal elements represent the signal power, and the N+1 to N+3M items represent the noise power output by each channel in the acoustic vector sensor array.
[0039] Therefore, the noise covariance matrix Q can be further expressed as
[0040]
[0041] Where D n Represents the nth column data of D, D N+l =u l , l = 1, ..., 3M, ul Indicates I 3M The lth column of .
[0042] Furthermore, in the above-mentioned method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise, step 3 includes the following sub-steps:
[0043] Step 31: construct the interference plus noise covariance matrix B according to the sparse covariance matrix R n :
[0044] According to the sparse covariance matrix R constructed in step 23, the signal covariance matrix corresponding to the nth grid can be expressed as
[0045]
[0046] Then the interference plus noise covariance matrix corresponding to the signal on the nth grid is B n =RR n =DΞD H -R n
[0047] Step 32, based on the sparse covariance matrix fitting criterion, construct the following cost function:
[0048]
[0049] In the formula, the first term Represents the covariance matrix fitting term, the second term represents the sparse signal compensation term, ||·|| F Indicates the F-norm operation. represents the sample covariance matrix, q represents the user parameter used to compensate the signal, λ s represents the regularization parameter that balances the relationship between signal sparsity and fitting error, and λ s >0;
[0050] Step 33, use the iterative method to solve the sparse signal power and obtain the signal power vector
[0051] Further, in the above-mentioned method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise, step 33 includes the following sub-steps:
[0052] Step 331: In order to reduce the computational complexity and the influence of noise on the covariance matrix fitting effect in the above cost function, the sample covariance matrix Perform singular value decomposition, and we get
[0053]
[0054] In the formula, represents the signal subspace, represents the noise subspace;
[0055] Then the cost function can be expressed as
[0056]
[0057] Step 332, using the iterative method to solve the sparse signal power, setting the j+1th iteration to obtain a unique solution, the sparse signal power can be obtained
[0058]
[0059] In the formula, a n for The abbreviation of
[0060]
[0061]
[0062]
[0063]
[0064] Specifically, the process of solving the sparse signal power using the iterative method is as follows:
[0065] From the expression of the cost function, we can see that the introduction of the user parameter q makes the cost function about the variable to be determined Therefore, we can directly solve the cost function To solve this problem, assume that f(x) = x q is a concave function about the variable x. When the variable x>0, for x0>0, we can get
[0066] f(x)≤f(x0)+f′(x0)(x-x0) (1)
[0067] make The superscript j represents the number of iterations. Substituting into equation (1) we can get
[0068]
[0069] Multiply both sides of equation (2) by λ s , plus the covariance matrix fitting term Can be further transformed into
[0070]
[0071] In the formula,
[0072]
[0073] Therefore, the cost function is The minimization problem is ultimately equivalent to
[0074]
[0075] In formula (4), About The function of It can be seen that Also about Therefore, it can be considered that in formula (4), is an unknown variable. Assume that in formula (4), is estimated in the jth iteration, then formula (5) minimizes can be transformed into minimization
[0076]
[0077] In the formula,
[0078]
[0079] It is easy to see from formula (7) that About Therefore, we can directly get Calculate the sparse signal power and noise power in .
[0080] According to the properties of the Frobenius norm, equation (7) can be further simplified to
[0081]
[0082] In the formula, Tr{·} represents the matrix trace operation. about Taking the first-order derivative, we get
[0083]
[0084] right about Taking the second-order derivative, we get
[0085]
[0086] From formula (10), we can get: Therefore, has a unique solution. Available functions The unique solution in the j+1th iteration is
[0087]
[0088] It can be seen from formula (11) that when calculating the sparse signal power corresponding to N discrete grids, it is necessary to calculate the interference plus noise covariance matrix B N times: n The inverse of , greatly increases the amount of calculation. In order to reduce the amount of calculation, according to the Woodbury formula, we can get
[0089]
[0090] Substituting formula (12) into formula (11), we can get
[0091]
[0092] In the formula,
[0093]
[0094]
[0095]
[0096] According to the definition of D, the sparse signal power can be obtained
[0097]
[0098] In the formula, a n for The abbreviation of .
[0099] The noise power
[0100]
[0101] In the formula,
[0102]
[0103]
[0104] Therefore, the noise power of the sound pressure channel and the sound velocity channel is
[0105]
[0106]
[0107]
[0108] Step 333: According to the sparse signal power obtained in step 332, the signal power vectors of the signals corresponding to the N grids are obtained as follows:
[0109] Compared with the prior art, the present invention has the following beneficial effects:
[0110] 1. The present invention defines a new array manifold matrix of an acoustic vector sensor array. According to the newly defined array manifold matrix of an acoustic vector sensor array, a sparse covariance matrix containing sparse signal power and noise power is reconstructed. Based on the sparse covariance matrix fitting criterion and the sparse signal compensation mechanism, a cost function for sparse signal power and noise power is constructed. Then, a regularized weighted covariance matrix fitting method is used to estimate noise power and signal power. In each iteration, the sparse signal power and noise power estimated by the method provided by the present invention are used to reconstruct the sparse covariance matrix, so that the sparse signal power and noise power estimated in the next iteration are more accurate. When the iteration is terminated, a spectrum peak search for the sparse signal power can achieve a more accurate azimuth estimation.
[0111] Compared with the existing DOA estimation method that only estimates the signal power, the present invention estimates the signal power and the noise power at the same time by reconstructing the sparse covariance matrix containing the sparse signal power and the noise power, so that the signal power estimated by the accurate noise power is also more accurate than the existing estimation method.
[0112] 2. Compared with the whitening process of the output vector of the acoustic vector sensor array in the existing wave direction estimation method, the wave direction estimation method provided by the present invention has less calculation amount and higher estimation accuracy. In practical applications, the method provided by the present invention can improve the azimuth estimation accuracy of the acoustic vector sensor array under non-uniform noise. BRIEF DESCRIPTION OF THE DRAWINGS
[0113] Figure 1 Flow chart of the WSCMF method proposed in the present invention;
[0114] Figure 2 is a uniform linear array model of an acoustic vector sensor array;
[0115] Figure 3 The normalized spatial spectrograms of the WSCMF method, MUSIC method, IAA method, IMLSE method and ASMUSIC method proposed in the present invention;
[0116] Figure 4 A relationship curve diagram of the root mean square error and the angle interval of the WSCMF method and the MUSIC method, the IAA method, the IMLSE method and the ASMUSIC method proposed in the present invention;
[0117] Figure 5 It is a relationship curve diagram of the root mean square error and signal-to-noise ratio of the WSCMF method and the MUSIC method, the IAA method, the IMLSE method and the ASMUSIC method proposed in the present invention;
[0118] Figure 6 This is a relationship curve diagram between the root mean square error and the worst noise power ratio of the WSCMF method proposed in the present invention and the MUSIC method, IAA method, IMLSE method and ASMUSIC method. DETAILED DESCRIPTION
[0119] The following will be combined with the drawings in this embodiment to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the protection scope of the present invention.
[0120] Example
[0121] like Figure 1-6 As shown, a method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise comprises the following steps:
[0122] Step 1, receiving an output vector X output by an acoustic vector sensor array;
[0123] Step 2, based on the sparse signal model, calculate the signal covariance matrix P and the noise covariance matrix Q according to the output vector X, and construct a sparse covariance matrix R using the obtained signal covariance matrix P and the noise covariance matrix Q;
[0124] Specifically, step 2 includes the following sub-steps:
[0125] Step 21, construct a sparse signal model of the acoustic vector sensor array under non-uniform noise conditions:
[0126] Assume that K far-field equal-power narrowband signals with wavelength λ are incident on a uniform linear array composed of M acoustic vector sensors. The configuration of the acoustic vector sensor array is as follows: Figure 2 As shown, the array element spacing is d, and the velocity components of the narrowband signal along the x-axis and y-axis are u respectively. x and u y , and the x-axis and y-axis are orthogonal. When the number of snapshots is L, the output vector X of the acoustic vector sensor array can be expressed as
[0127] X=A(θ)S+W
[0128] Where, X = [x(1), x(2), ..., x(L)] represents the output vector of the acoustic vector sensor array, A(θ) = [a(θ1), a(θ2), ..., a(θ K )] represents the array manifold matrix of the ideal acoustic vector sensor array, θ = [θ1, θ2, …, θ K ] represents the azimuth of the target, represents the manifold vector of the kth target, represents the Cartesian product, h(θ k )=[1 cosθ k sinθ k ] T represents the array manifold vector of the kth target incident on the acoustic vector sensor, represents the sound pressure response coefficient of the k-th target incident on the m-th sound vector sensor, W = [w(1), w(2), ..., w(L)] represents the noise vector, S = [s(1), s(2), ..., s(L)] represents the input signal waveform vector;
[0129] Assuming that the angle space (-180° to 180°) is evenly divided into N discrete grids, and the number of discrete grids N is much larger than the number of sound sources K, the incoming wave directions of all sound sources can be expressed as The sparse signal model of the acoustic vector sensor array can be expressed as
[0130]
[0131] In the formula, represents the array manifold matrix of the acoustic vector sensor array under the sparse signal model, is a row-sparse matrix, and its non-zero rows represent the location of the real signal;
[0132] Step 22, calculate the signal covariance matrix P and the noise covariance matrix Q:
[0133] The signal covariance matrix P can be expressed as
[0134]
[0135] Where E{·} represents the expected operation, diag{·} represents the diagonal matrix operation, Indicates the power of the signal corresponding to the nth grid;
[0136] The noise covariance matrix Q can be expressed as
[0137] Q = diag{q1, ..., q M}
[0138] In the formula,
[0139] Step 23, construct the sparse covariance matrix R:
[0140] Define a new array manifold matrix for an acoustic vector sensor array
[0141]
[0142] Among them I 3M represents the 3M×3M identity matrix, then the sparse covariance matrix R can be expressed as
[0143] R=DΞD H
[0144] in,
[0145]
[0146] Wherein, the first N items of the diagonal elements of Ξ represent the signal power, and the N+1 to N+3M items represent the noise power output by each channel in the acoustic vector sensor array. Thus, the noise covariance matrix Q can be further expressed as
[0147]
[0148] Where D n Indicates the nth column data of D, DN +l =u l , l = 1, ..., 3M, u l Indicates I 3M The lth column of .
[0149] Step 3: construct a cost function based on the sparse covariance matrix R, use the cost function to estimate the sparse signal power, and obtain the signal power vector
[0150] Specifically, step 3 includes the following sub-steps:
[0151] Step 31: construct the interference plus noise covariance matrix B according to the sparse covariance matrix R n :
[0152] According to the sparse covariance matrix R constructed in step 23, the signal covariance matrix corresponding to the nth grid can be expressed as
[0153]
[0154] Then the interference plus noise covariance matrix corresponding to the signal on the nth grid is B n =RR n =DΞD H -R n
[0155] Step 32, based on the sparse covariance matrix fitting criterion, construct the following cost function:
[0156]
[0157] In the formula, ||·||F Indicates the F-norm operation. represents the sample covariance matrix, q represents the user parameter used to compensate the signal, and λ s represents the regularization parameter that balances the relationship between signal sparsity and fitting error, and λ s >0;
[0158] Step 33, use the iterative method to solve the sparse signal power and obtain the signal power vector
[0159] Specifically, step 33 includes the following sub-steps:
[0160] Step 331, perform singular value decomposition on the sample covariance matrix to obtain
[0161]
[0162] In the formula, represents the signal subspace, represents the noise subspace;
[0163] Then the cost function can be expressed as
[0164]
[0165] Step 332, using the iterative method to solve the sparse signal power, setting the j+1th iteration to obtain a unique solution, the sparse signal power can be obtained
[0166]
[0167] In the formula, a n for The abbreviation of
[0168]
[0169]
[0170]
[0171] Step 333: According to the sparse signal power obtained in step 332, the signal power vectors of the signals corresponding to the N grids are obtained as follows:
[0172] Step 4: Signal power vector Perform a spectrum peak search, and the sound source position corresponding to the obtained spectrum peak is the estimated target azimuth.
[0173] Compared with the existing non-uniform noise power estimation method, the method designed by the present invention has less calculation amount and higher estimation accuracy. At the same time, the signal power estimated by using accurate noise power is also more accurate than the existing estimation method.
[0174] The effect of the present invention can be compared and illustrated with the existing MUSIC method, IAA method, iterative maximum likelihood subspace estimation (Iterative ML Subspace Estimation, IMLSE) method and ASMUSIC method through simulation experiments:
[0175] Comparative Example 1
[0176] The resolution performance of the WSCMF method proposed in the present invention is compared with the existing MUSIC method, IAA method, IMLSE method and ASMUSIC method from the perspective of normalized spatial spectrum.
[0177] In this comparative example, the acoustic vector sensor array is set to be a uniform linear array consisting of M=4 acoustic vector sensors, the background noise of the acoustic vector sensor array is non-uniform noise, and the noise covariance matrix is
[0178] Q=diag{3, 1.5, 2, 5, 2, 1.5, 4, 2, 5, 2, 30, 2, 1.5}
[0179] Therefore, the worst noise power ratio (WNPR) is
[0180]
[0181] In the formula, represents the maximum value in Q, represents the minimum value in Q. The signal-to-noise ratio (SNR) is defined as
[0182]
[0183] In the formula, Indicates the signal power.
[0184] In this comparative example, three far-field narrowband signals with a signal-to-noise ratio of 10 dB are incident on the acoustic vector sensor array from azimuths θ1 = -15°, θ2 = 38°, and θ3 = 50°, respectively. The sound velocity is 1500 m / s, the system sampling frequency is 5 kHz, the center frequency of the signal is 700 Hz, and the number of snapshots is 300. In the WSCMF method proposed in the present invention, the number of iterations is 30, and the convergence threshold is 10 -3 .
[0185] The resolution performance of the WSCMF method proposed in this invention is compared with the existing MUSIC method, IAA method, IMLSE method and ASMUSIC method in terms of normalized spatial spectrum. The simulation results are as follows: Figure 3 shown.
[0186] from Figure 3 It can be seen from the normalized spatial spectrum shown that the MUSIC method, the IAA method and the IMLSE method cannot distinguish the target azimuth at θ2 = 38°. Although the ASMUSIC method can distinguish the target with an azimuth angle at θ2 = 38°, the estimated result is obviously deviated from the actual target azimuth angle. The WSCMF method proposed in the present invention can distinguish the three targets, and the estimated result is closest to the azimuth angle of the actual target, showing that the method of the present invention has good resolution performance.
[0187] Comparative Example 2
[0188] Taking the root mean square error (RMSE) as the evaluation criterion of the bearing estimation performance, the estimation accuracy of the WSCMF method proposed in the present invention is compared with the existing MUSIC method, IAA method, IMLSE method and ASMUSIC method.
[0189] Generally, the smaller the RMS error, the more accurate the estimation, and the larger the RMS error, the lower the estimation accuracy. The RMS error can be expressed as
[0190]
[0191] In the formula, θ k is the true horizontal azimuth angle of the kth target, The horizontal azimuth of the kth target estimated in the uth Monte Carlo experiment, U = 3000 is the number of independent Monte Carlo trials performed in the experiment.
[0192] In this comparative example, the estimation performance of several azimuth estimation methods is studied from the relationship curves of the root mean square error and the angle interval, the relationship curves of the root mean square error and the signal-to-noise ratio, and the relationship curves of the root mean square error and the worst noise power ratio. The specific simulation experimental conditions are set as follows:
[0193] (1) Two far-field narrowband signals of equal power with a signal-to-noise ratio of 5 dB are incident on the acoustic vector sensor array. The angles of the two incident signals are θ1 = -14° and θ2 = -14° + Δ, respectively. Δ represents the azimuth angle interval of the two incident signals, which varies from 15° to 55° in increments of 5°. The relationship between the root mean square error and the angle interval of the estimation results obtained by applying the WSCMF method proposed in the present invention and the existing MUSIC method, IAA method, IMLSE method and ASMUSIC method is compared. The results are as follows: Figure 4 As shown;
[0194] (2) Two far-field narrowband signals of equal power are incident on the acoustic vector sensor array from θ1 = -14° and θ2 = 38°, respectively. The signal-to-noise ratio varies from -15 dB to 15 dB. The relationship between the root mean square error and the signal-to-noise ratio of the estimation results obtained by applying the WSCMF method proposed in the present invention and the existing MUSIC method, IAA method, IMLSE method and ASMUSIC method is compared. The results are as follows: Figure 5 As shown;
[0195] (3) Two far-field narrowband signals of equal power are incident on the acoustic vector sensor array from azimuth angles θ1 = -14° and θ2 = 38°, respectively. The signal-to-noise ratio is 5 dB, and the worst noise power ratio is varied from 10 to 80 in increments of 10. The relationship between the root mean square error and the worst noise power ratio of the estimation results obtained by applying the WSCMF method proposed in the present invention and the existing MUSIC method, IAA method, IMLSE method and ASMUSIC method is compared. The results are shown in FIG. Figure 6 shown.
[0196] from Figure 4 It can be seen that the IMLSE method and the ASMUSIC method cannot distinguish two targets whose azimuth angle intervals are less than 45° and 35° respectively. The IAA method cannot distinguish two targets whose angular intervals are less than 30°. The MUSIC method cannot distinguish two targets whose angular intervals are less than 25°. The WSCMF method proposed in the present invention can distinguish two targets whose angular intervals are not less than 20°. Although the root mean square error of the method of the present invention increases when the azimuth angle interval is less than 25°, the estimation accuracy of the method of the present invention is still the highest compared with the IMLSE method, the ASMUSIC method, the IAA method and the MUSIC method. In addition, it is easy to see that when the azimuth angle interval is greater than 50°, the azimuth estimation accuracy of the WSCMF method proposed in the present invention is within an acceptable range compared with the IMLSE method, the ASMUSIC method, the IAA method and the MUSIC method, but the azimuth estimation accuracy of the WSCMF method proposed in the present invention is the highest.
[0197] from Figure 5It can be found that with the increase of signal-to-noise ratio, the estimation performance of the MUSIC method improves less. Although the performance of the IAA method, the IMLSE method, and the ASMUSIC method has been improved, their azimuth estimation accuracy is not high enough when the signal-to-noise ratio is low. The WSCMF method proposed in the present invention uses a regularized weighted sparse covariance matrix fitting method to estimate noise power and signal power, and balances the relationship between the sparsity of the signal in the spatial domain and the fitting error through user parameters, so that the azimuth estimation accuracy of the acoustic vector sensor array of the WSCMF method proposed in the present invention is improved at low signal-to-noise ratios.
[0198] from Figure 6 It can be seen that the azimuth estimation performance of the MUSIC method and the IAA method without considering the non-uniform noise seriously deteriorates with the increase of the worst noise power ratio. Although the root mean square error of the IMLSE method, the ASMUSIC method and the method proposed in the present invention is less affected with the increase of the worst noise power ratio, the root mean square error of the method proposed in the present invention is the smallest compared with the IMLSE method and the ASMUSIC method, which shows that the method proposed in the present invention has better azimuth estimation performance in the non-uniform noise scene.
[0199] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.
Claims
1. A method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise, characterized in that: The method comprises the following steps: Step 1, receiving an output vector X output by an acoustic vector sensor array; Step 2, based on the sparse signal model, calculate the signal covariance matrix P and the noise covariance matrix Q according to the output vector X, and use the obtained signal covariance matrix P and the noise covariance matrix Q to construct a sparse covariance matrix R, further comprising the following sub-steps: Step 21, constructing a sparse signal model of the acoustic vector sensor array under non-uniform noise conditions; Step 22, calculating the signal covariance matrix P and the noise covariance matrix Q; Step 23, construct the sparse covariance matrix R: Define a new array manifold matrix for an acoustic vector sensor array Among them I 3M represents the identity matrix of 3M×3M, then the sparse covariance matrix R can be expressed as R=DΞD H in, Wherein, the first N items of the diagonal elements of Ξ represent the signal power, and the N+1 to N+3M items represent the noise power output by each channel in the acoustic vector sensor array; thus, the noise covariance matrix Q can be further expressed as Where D n Represents the nth column data of D, D N+l =u l ,l=1,…,3M,u l Indicates I 3M The lth column of Step 3: construct a cost function based on the sparse covariance matrix R, use the cost function to estimate the sparse signal power, and obtain the signal power vector It also includes the following sub-steps: Step 31: construct the interference plus noise covariance matrix B according to the sparse covariance matrix R n : According to the sparse covariance matrix R constructed in step 23, the signal covariance matrix corresponding to the nth grid can be expressed as Then the interference plus noise covariance matrix corresponding to the signal on the nth grid is B n =R-R n =DΞD H -R n Step 32, based on the sparse covariance matrix fitting criterion, construct the following cost function: In the formula, ||·|| F Indicates the F-norm operation. represents the sample covariance matrix, q represents the user parameter used to compensate the signal, and λ s represents the regularization parameter that balances the relationship between signal sparsity and fitting error, and λ s >0; Step 33, use the iterative method to solve the sparse signal power and obtain the signal power vector Step 4: Signal power vector Perform a spectrum peak search, and the sound source position corresponding to the obtained spectrum peak is the estimated target azimuth.
2. The method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise according to claim 1, characterized in that: In step 21, it is assumed that K far-field equal-power narrowband signals with a wavelength of λ are incident on a uniform linear array composed of M acoustic vector sensors, with an array element spacing of d, and the velocity components of the narrowband signals along the x-axis and y-axis are u and x and u y , and the x-axis and y-axis are orthogonal. When the number of snapshots is L, the output vector X of the acoustic vector sensor array can be expressed as X=A(θ)S+W Where X = [x(1), x(2), …, x(L)] represents the output vector of the acoustic vector sensor array, A(θ) = [a(θ1), a(θ2), …, a(θ K )] represents the array manifold matrix of the ideal acoustic vector sensor array, θ = [θ1, θ2, …, θ K ] represents the azimuth of the target, represents the manifold vector of the kth target, represents the Cartesian product, h(θ k )=[1 cosθ k sinθ k ] T represents the array manifold vector of the kth target incident on the acoustic vector sensor, represents the sound pressure response coefficient of the kth target incident on the mth acoustic vector sensor, W = [w(1), w(2), ..., w(L)] represents the noise vector, S = [s(1), s(2), ..., s(L)] represents the input signal waveform vector; Assuming that the angle space [-180°~180°] is evenly divided into N discrete grids, and the number of discrete grids N is much larger than the number of sound sources K, the incoming wave directions of all sound sources can be expressed as The sparse signal model of the acoustic vector sensor array can be expressed as In the formula, represents the array manifold matrix of the acoustic vector sensor array under the sparse signal model, is a row-sparse matrix, and its non-zero rows represent the location of the real signal; In step 22, the signal covariance matrix P can be expressed as Where E{·} represents the expected operation, diag{·} represents the diagonal matrix operation, Indicates the power of the signal corresponding to the nth grid; The noise covariance matrix Q can be expressed as Q = diag{q1,…,q M } In the formula, 3. The method for estimating the direction of arrival of an acoustic vector sensor array under non-uniform noise according to claim 2, characterized in that: Step 33 includes the following sub-steps: Step 331, perform singular value decomposition on the sample covariance matrix to obtain In the formula, represents the signal subspace, represents the noise subspace; Then the cost function can be expressed as Step 332, using the iterative method to solve the sparse signal power, setting the j+1th iteration to obtain a unique solution, the sparse signal power can be obtained In the formula, a n for The abbreviation of Step 333: According to the sparse signal power obtained in step 332, the signal power vectors of the signals corresponding to the N grids are obtained as follows: