CN109696657B - Coherent sound source positioning method based on vector hydrophone - Google Patents
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Abstract
The invention discloses a coherent sound source positioning method based on a vector hydrophone, which is characterized in that a vector hydrophone array is used for collecting sound source signals, and a covariance matrix of the collected signals is obtained; performing signal decorrelation by using a method of extracting data by non-overlapping subarrays; and estimating a signal subspace of the covariance matrix after the coherence is resolved by using a least square method, solving according to the flow pattern rotation invariant characteristic of the vector hydrophone array, and finally obtaining two-dimensional DOA estimation of a plurality of coherent sound sources. The method has high accuracy of estimating the direction of the coherent sound source, is easy to realize, and can effectively overcome the problems of direction ambiguity and mutual interference of the coherent sound sources.
Description
Technical Field
The invention relates to the field of vector hydrophone array sound source positioning under the condition of a coherent sound source, in particular to a coherent sound source positioning method based on a vector hydrophone.
Background
The vector hydrophone consists of two to three vibration velocity hydrophones which are orthogonally distributed in an underwater sound field and an acoustic pressure hydrophone. Due to its superior identification capabilities over conventional Acoustic pressure hydrophones, vector hydrophone arrays play an important role in Underwater signal processing and find wide application in the fields of Underwater identification, badie M, et al. In the past decade, many vector hydrophone-based subspace techniques have been proposed, such as MUSIC and ESPRIT, as well as the use of vector hydrophone arrays to estimate 2D underwater Signal orientation (see, e.g., he J, liu Z. Efficient underserver two-dimensional coherent source localization with linear Processing [ J ]. Signal Processing 2009,89 (9): 1715-1722.).
The above methods all use incoherent signals, i.e. the signal covariance matrix has a full rank. However, this assumption is often not applicable in the presence of coherence or high correlation due to multipath propagation or deliberate interference. The coherent signal can reduce the rank of the covariance matrix of the incident signal, thereby seriously reducing the performance of the technology and failing to correctly estimate the position of the sound source. Therefore, researchers have conducted extensive research on the problem of sound source coherence and proposed solutions such as the maximum likelihood method, the spatial smoothing technique, and the Toeplitz method.
To process coherent signals with a vector hydrophone array, the literature (Tao J, chang W, shi y.direction-definition of coherent sources via 'particle-level-field smoothing' [ J ]. Iet radio resource & Navigation,2008,2 (2): 127-134.) proposes the recovery of the rank of the signal subspace by a vector smoothing technique of a data correlation matrix. However, such vector smoothing techniques require a geometric planar array or 2D iterative search to estimate the two-dimensional direction of the incident signal. The literature (Liu S, yang L, xie Y, et al.2D DOA Estimation for Coherent Signals with Acoustic Vector-Sensor Array [ J ]. Wireless Personal Communications,2017,95 (2): 1285-1297) proposes a method for estimating the elevation of an incident signal using ESPRIT and obtaining the azimuth of the Coherent signal by modified Array pattern matching. Compared with the calculation process in the document (Gu J F, wei P, tai H M.2-D direction-of-arrival estimation of coherent signals using cross-correlation matrix [ J ]. Signal Processing,2008,88 (1): 75-85.), the method is simple and convenient to operate and more accurate in positioning.
The method comprises the step-by-step calculation, namely, a pitch angle is obtained firstly, and then the azimuth angle is obtained according to the pitch angle, so that the azimuth of the coherent sound source is obtained. Therefore, the estimation error of the pitch angle can influence the accurate estimation of the azimuth angle, and the positioning precision can be greatly influenced.
Disclosure of Invention
The invention provides a coherent sound source positioning method based on a vector hydrophone aiming at the defect of the prior vector hydrophone in positioning a coherent sound source, and aims to solve the problems of calculated amount caused by spectral peak search, errors caused by step-by-step estimation and the like. The method is suitable for vector hydrophone arrays with any structures, and can realize automatic angle estimation pairing.
In order to solve the technical problem, the invention provides a coherent sound source positioning method based on a vector hydrophone, which comprises the following steps:
step 1: collecting K sound source signals by using an M-element vector hydrophone array, and establishing a vector hydrophone array receiving data model;
step 2: obtaining a covariance matrix according to a received signal, and performing signal decorrelation by using a method of extracting data by using non-overlapping subarrays;
and 3, step 3: extracting a sound pressure vector and a vibration velocity vector in the array flow pattern after decoherence by using a transformation matrix;
and 4, step 4: estimating a signal subspace of the covariance matrix after the coherence is resolved by using a least square method;
and 5: and solving according to the flow pattern rotation invariant characteristic of the vector hydrophone array to obtain the two-dimensional DOA estimation of the coherent sound source.
The specific steps of establishing a data receiving module of the vector hydrophone array in the step 1 are as follows:
assuming K narrow-band plane wave signals s with wavelength lambda i (t), i =1,2.. K is incident on the M-element vector hydrophone array from a far field, and noises and signals in the sound field are not correlated, and L is provided in the K signals max Coherent sound source with pitch angle of sound source
Azimuth angle phi i I =1,2,.. K, then the array flow pattern vector for the vector hydrophone is:
in the formula (I), the compound is shown in the specification,
each vector hydrophone array receives a data model as follows:
in the formula (I), the compound is shown in the specification,
array flow pattern vector, n, representing the m-th array element m (t) represents the noise received by the mth array element, m =1,2, · M, t =1,2., N, ψ i ＝(2πd/λ)γ i I =1,2.. K, where M denotes the number of array elements, N denotes the number of fast beats of the signal, and K denotes the number of sound sources.
The step 2 is as follows:
the array received signal is obtained from equation (2):
x(t)＝As(t)+n(t)，t＝1,2,...,N (3)
in the formula (I), the compound is shown in the specification,
the correlation matrix of the array received signals is:
in the formula (I), the compound is shown in the specification,
a correlation matrix representing the signal;
dividing the correlation matrix into L max Individual sub-array, L max Representing the number of coherent sound sources, each subarray having a dimension of 4 (M-L) max + 1) x 4M, the first subarray being denoted R l ，l＝1,2,…l max From R x Lines 4 (L-1) +1 to 4 (M-L) max + 1) lineAnd constructing a new matrix R through the sub-matrices:
in the formula, the dimension of the matrix R is 4 (M-L) max +1)×4ML max ；
According to the correlation matrix of the array received signals:
substituting into the matrix R, one can get: :
in the formula (I), the compound is shown in the specification,
due to the fact that
Therefore, the decorrelated data covariance matrix R is full rank when the number of subarray elements is greater than or equal to K.
The step 3 is specifically as follows:
extracting sound pressure vector and vibration velocity vector in matrix R array flow pattern by using conversion matrix J to obtain a new matrix
Can be expressed as
In the formula (I), the compound is shown in the specification,
J＝[J 1 J 2 J 3 J 4 ]，
e i is that the ith component is 1 and the others are all zero 4 (M = L) max + 1) × 1 unit vector;
array flow pattern matrix after segmented representation conversion
Can be written in segments as:
in the formula (I), the compound is shown in the specification,
thereby obtaining A j And A 4 The relationship of (1):
A j ＝A 4 Γ j ，j＝1,2,3 (10)
in the formula, gamma 1 ＝diag{α 1 ,α 2 ,…α K }，Γ 2 ＝diag{β 1 ,β 2 ,…β K }，Γ 3 ＝diag{γ 1 ,γ 2 ,…γ K All three matrixes are K multiplied by K diagonal matrixes;
by estimating the matrix f j The value of the middle element obtains the azimuth of the ith sound source
The step 4 is as follows:
matrix array
The feature vector corresponding to the K maximum feature vectors is in a linear relationship with the array flow pattern vectors of the K sound sources, so that:
in the formula
U j ＝A j T，j＝1,2,3,4 (14)
Slave U 4 ＝A 4 T can deduce A 4 ＝U 4 T -1 . By U 1 ＝A 1 T＝A 4 Γ 1 T can obtain U 1 ＝U 4 T -1 Γ 1 T, similarly obtainable, U 2 ＝U 4 T -1 Γ 2 T，U 3 ＝U 4 T -1 Γ 3 T；
We define
Λ j ＝T -1 Γ j T，j＝1,2,3 (15)
Then Λ j Is the matrix Γ i The diagonal elements of (a). So construct the matrix Λ i Calculating its characteristic value to obtain the azimuth of the signal
Equation (14) can be written as
U j ＝U 4 Λ j (16)
Can be pushed out from the above way
Matrix array
Forming a signal subspace characteristic vector by the characteristic vectors corresponding to the K maximum characteristic values;
suppose U j And Λ j Are respectively estimated as
And
estimating the signal subspace using a least squares method:
to obtain
The estimated values of (c) are:
the step 5 specifically comprises the following steps:
first, obtain
Can be obtained from the characteristic value of
Order:
obtaining the azimuth angle and the pitch angle of each sound source:
has the beneficial effects that: compared with the prior art, the invention has the following advantages:
(1) The invention adopts the linear vector hydrophone array, and compared with the common L-shaped array, the array structure is simpler and more convenient.
(2) The invention adopts a mutually non-overlapping subarray extraction method to solve the coherence, and reduces the influence of coherent sound sources on positioning estimation while keeping a larger array aperture.
(3) The invention fully utilizes the array flow pattern structure of the vector hydrophone and the rotation invariant characteristic thereof to ensure that the positioning estimation effect is more stable.
(4) The implementation case of the invention shows that the invention has better positioning effect than the traditional method.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a diagram of the array architecture of the present invention.
FIG. 3 is a simulation of the results of coherent sound source localization at three different azimuths according to the present invention.
FIG. 4 is a comparison of SNR versus RMSE for the PM and ESPRIT-AMM methods of the present invention.
FIG. 5 is a comparison of the RMSE versus fast beat number for the PM and ESPRIT-AMM methods of the present invention.
Fig. 6 is a graph of the present invention's SNR versus RMSE for different array element numbers.
Detailed Description
The invention is further illustrated below with reference to the figures and examples.
As shown in fig. 1, the present invention comprises the steps of:
step 1: collecting K sound source signals by using an M-element vector hydrophone array, and establishing a vector hydrophone array receiving data model;
assuming K narrow-band plane wave signals s with wavelength lambda i (t), i =1,2.., K is incident on the M-element vector hydrophone array from the far field, and noise and signal in the sound field are not correlated, as shown in fig. 2. Among K signals, has L max Coherent signals, given the pitch angle of the signals
An azimuth angle phi i I =1,2, K, then an array of vector hydrophonesFlow pattern vector of
In the formula (I), the compound is shown in the specification,
the received data model for each vector hydrophone is:
in the formula (I), the compound is shown in the specification,
array flow pattern vector, n, representing the m-th array element m (t) represents the noise received by the mth array element, m =1,2, · M, t =1,2., N, ψ i ＝(2πd/λ)γ i I =1,2.. K, where M denotes the number of array elements, N denotes the number of fast beats of the signal, and K denotes the number of sound sources.
Step 2: obtaining a covariance matrix according to a received signal, and performing signal decorrelation by using a method of extracting data by using non-overlapping subarrays;
the array received signal is obtained from equation (2):
x(t)＝As(t)+n(t)t＝1,2,...,N (3)
in the formula (I), the compound is shown in the specification,
the correlation matrix of the array received signal is:
in the formula (I), the compound is shown in the specification,
a correlation matrix representing the signal;
to enable decoherence of coherent signals, the correlation matrix is first divided into L max A plurality of sub-arrays, each sub-array having a dimension of 4 (M-L) max + 1). Times.4M. The first sub-array is marked R l ,l＝1,2,…l max From R x Lines 4 (L-1) +1 to 4 (M-L) max + 1) line. From these sub-matrices, we construct a new matrix R:
wherein the dimension of the matrix R is 4 (M-L) max +1)×4ML max 。
Using matrices R of equations (4) and (5) can be written in segmented form as follows:
in the formula (I), the compound is shown in the specification,
due to the fact that
Therefore, the decorrelated data covariance matrix R is full rank when the number of subarray elements is greater than or equal to K.
And step 3: extracting a sound pressure vector and a vibration velocity vector in the array flow pattern after decoherence by using a conversion matrix;
extracting the sound pressure vector and the vibration velocity vector in the matrix R array flow pattern by using the conversion matrix J to obtain a new matrix
Can be expressed as
In the formula (I), the compound is shown in the specification,
J＝[J 1 J 2 J 3 J 4 ]，
e i is 4 (M-L) with the ith component being 1 and the others being zero max + 1) × 1 unit vector. Since each column of matrix J is orthogonal to the other columns, the rank of matrix J is equal to 4 (M-L) max + 1), the matrix can be derived directly from equation (7)
Is equal to K. By means of a pair matrix
Can obtain K orthogonal vectors to form a signal subspace, namely
Linear space of column vectors.
Array flow pattern matrix
Can be written into by segments
In the formula，
Thus, A can be obtained j And A 4 The relationship of (1):
A j ＝A 4 Γ j ，j＝1,2,3 (10)
in the formula, gamma 1 ＝diag{α 1 ,α 2 ,…α K }，Γ 2 ＝diag{β 1 ,β 2 ,…β K }，Γ 3 ＝diag{γ 1 ,γ 2 ,…γ K And all three matrixes are K multiplied by K diagonal matrixes. Equation (10) indicates that each matrix pair (A) j ,A 4 ) Can be estimated by estimating the matrix Γ i The value of the middle element obtains the azimuth of the ith sound source
And 4, step 4: estimating a signal subspace of the covariance matrix after the coherence is resolved by using a least square method;
Therefore, the signal is emptyInter U s Can be expressed as
T is a K nonsingular matrix. As can be seen from equation (12), the matrix
The feature vectors corresponding to the K maximum feature vectors are in a linear relationship with the array flow pattern vectors of the K sound sources. From the formulae (9) and (12) can be obtained
In the formula
U j ＝A j T，j＝1,2,3,4 (14)
Slave U 4 ＝A 4 T can deduce A 4 ＝U 4 T -1 . By U 1 ＝A 1 T＝A 4 Γ 1 T can obtain U 1 ＝U 4 T -1 Γ 1 T, similarly obtainable, U 2 ＝U 4 T -1 Γ 2 T，U 3 ＝U 4 T -1 Γ 3 T。
We define
Λ j ＝T -1 Γ j T，j＝1,2,3 (15)
Then Λ j Is the matrix Γ i The diagonal elements of (a). So construct the matrix Λ i Computing its characteristic value, the azimuth of the signal can be obtained
Equation (14) can be written as
U j ＝U 4 Λ j (16)
Can be pushed out from the above way
Matrix of
The eigenvectors corresponding to the K largest eigenvalues form the signal subspace eigenvector. Suppose U j And Λ j Are respectively estimated as
And
u obtained by signal subspace eigenvector estimation 4 Is not accurate, so LS-ESPRIT is used to estimate equation (16)
To obtain
Is estimated as
And 5: and solving according to the flow pattern rotation invariance characteristic of the vector hydrophone array to obtain the two-dimensional DOA estimation of the coherent sound source.
From
Can be obtained from the characteristic value of
Thus, α i ,β i ,γ i Can be expressed as
Finally, the azimuth angle and the pitch angle of each sound source are obtained
The results were performed as shown in FIGS. 3-6:
the parameters used in the following examples are as follows:
FIG. 3 is a simulation of the results of coherent sound source localization at three different orientations. The number of the vector hydrophone arrays is 10, the array element interval is d = lambda/2, wherein lambda represents the wavelength of sound waves, and 3 coherent information sources respectively come from
100 times simulation results for SNR =0dB and SNR =20dB, respectively.
FIG. 4 is a comparison of SNR versus RMSE for the PM and ESPRIT-AMM methods of the present invention. The number of the vector hydrophone arrays is 10, the array element interval is d = lambda/2, wherein lambda represents the wavelength of the sound wave. The root mean square error of the angle estimate is
J represents the number of Monte Carlo tests, K represents the number of sound sources,
and
the angle of arrival estimate for the kth target in j trials is shown. Taking the fast beat number as 500, the signal-to-noise ratio range as 0dB to 20dB, and the Monte Carlo experiment times as 200Mean square error of positioning results of all methods and positioning estimation performance of the verification method.
FIG. 5 is a comparison of the RMSE versus fast beat number for the PM and ESPRIT-AMM methods of the present invention. The number of the vector hydrophone arrays is 10, the array element interval is d = lambda/2, wherein lambda represents the wavelength of the sound wave. And when the signal-to-noise ratio is 20dB, the fast beat number is 100-1000, and the Monte Carlo experiment frequency is 200, the mean square error of the positioning result of each method is obtained, and the positioning estimation performance of each method is verified.
Fig. 6 is a graph of the present invention's SNR versus RMSE for different array element numbers. The number of the vector hydrophone arrays is 10, the array element interval is d = lambda/2, wherein lambda represents the wavelength of the sound wave. And when the snapshot number is 500, the signal-to-noise ratio is 20dB, the Monte Carlo experiment times are 200, and the array element numbers are 5, 8 and 10 respectively, performing simulation comparison on the positioning results of the two coherent sound sources.
Claims (5)
1. A coherent sound source positioning method based on a vector hydrophone is characterized in that: the method comprises the following steps:
step 1: collecting K sound source signals by using an M-element vector hydrophone array, and establishing a vector hydrophone array receiving data model;
and 2, step: obtaining a covariance matrix according to a received signal, and performing signal decorrelation by using a method of extracting data by using non-overlapping subarrays;
and step 3: extracting a sound pressure vector and a vibration velocity vector in the array flow pattern after decoherence by using a transformation matrix;
and 4, step 4: estimating a signal subspace of the covariance matrix after the coherence is resolved by using a least square method;
and 5: solving according to the flow pattern rotation invariant characteristic of the vector hydrophone array to obtain two-dimensional DOA estimation of a coherent sound source;
the specific steps of establishing a data receiving module of the vector hydrophone array in the step 1 are as follows:
assuming K narrow-band plane wave signals s with wavelength lambda i (t), i =1,2, K is incident on the M-element vector hydrophone array from the far field, and noise and signal in the sound field are not correlated with each other, and K are independentIn the signal has L max Coherent sound source with pitch angle of sound source
Azimuth angle phi i I =1,2,.. K, then the array flow pattern vector for the vector hydrophone is:
in the formula (I), the compound is shown in the specification,
each vector hydrophone array receives a data model as follows:
in the formula (I), the compound is shown in the specification,
array flow pattern vector, n, representing the m-th array element m (t) represents the noise received by the mth array element, m =1,2, · M, t =1,2., N, ψ i ＝(2πd/λ)γ i I =1,2.. K, where M denotes the number of array elements, N denotes the number of fast beats of the signal, and K denotes the number of sound sources.
2. The method according to claim 1, wherein the step 2 specifically comprises the following steps:
the array received signal is obtained from equation (2):
x(t)＝As(t)+n(t)，t＝1,2,...,N (3)
in the formula (I), the compound is shown in the specification,
the correlation matrix of the array received signals is:
in the formula (I), the compound is shown in the specification,
a correlation matrix representing the signal;
dividing the correlation matrix into L max Individual sub-array, L max The dimension of each subarray is 4 (M-L) representing the number of coherent sound sources max + 1) x 4M, the first subarray being denoted R l ,l＝1,2,…l max From R x Lines 4 (L-1) +1 to 4 (M-L) max + 1) rows, from which a new matrix R is constructed:
wherein the dimension of the matrix R is 4 (M-L) max +1)×4ML max ；
According to the correlation matrix of the array received signals:
substituting into the matrix R, one can get:
in the formula (I), the compound is shown in the specification,
due to the fact that
Therefore, the decorrelated data covariance matrix R is full rank when the number of subarray elements is greater than or equal to K.
3. The method according to claim 2, wherein the step 3 is as follows:
extracting the sound pressure vector and the vibration velocity vector in the matrix R array flow pattern by using the conversion matrix J to obtain a new matrix
Can be expressed as
In the formula (I), the compound is shown in the specification,
J＝[J 1 J 2 J 3 J 4 ]，
e i is the ith component is 1 and the other components are all zero 4 (M-L) max + 1) × 1 unit vector;
array flow pattern matrix after segmented representation conversion
Can be written in segments as:
in the formula (I), the compound is shown in the specification,
thus, A can be obtained j And A 4 The relationship of (1):
A j ＝A 4 Γ j ，j＝1,2,3 (10)
in the formula, gamma 1 ＝diag{α 1 ,α 2 ,…α K }，Γ 2 ＝diag{β 1 ,β 2 ,…β K }，Γ 3 ＝diag{γ 1 ,γ 2 ,…γ K }, the three matrices are K × K diagonal matrices;
by estimating the matrix Γ j The value of the middle element obtains the azimuth of the ith sound source
4. The method according to claim 3, wherein the step 4 is as follows:
matrix array
The feature vector corresponding to the K maximum feature vectors is in a linear relation with the array flow pattern vector of the K sound sources, so that the following can be obtained:
in the formula
U j ＝A j T，j＝1,2,3,4 (14)
Slave U 4 ＝A 4 T can deduce A 4 ＝U 4 T -1 From U 1 ＝A 1 T＝A 4 Γ 1 T can be converted into U 1 ＝U 4 T -1 Γ 1 T, similarly obtainable, U 2 ＝U 4 T -1 Γ 2 T，U 3 ＝U 4 T -1 Γ 3 T；
We define
Λ j ＝T -1 Γ j T，j＝1,2,3 (15)
Then Λ j Is the matrix Γ i So that a matrix Λ is constructed i Calculating its characteristic value to obtain the azimuth of the signal
Equation (14) can be written as
U j ＝U 4 Λ j (16)
Can be pushed out from the above way
Matrix array
Forming a signal subspace characteristic vector by the characteristic vectors corresponding to the K maximum characteristic values;
suppose U j And Λ j Are each U j And Λ j Estimating the signal subspace by using a least square method:
to obtain
The estimated value of (c) is:
5. the method according to claim 4, wherein the method comprises:
the step 5 specifically comprises the following steps:
first, obtain
Can be obtained from the characteristic value of
Order:
obtaining the azimuth angle and the pitch angle of each sound source:
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