CN110133578B - Seabed reflection sound ray incident angle estimation method based on semi-cylindrical volume array - Google Patents

Seabed reflection sound ray incident angle estimation method based on semi-cylindrical volume array Download PDF

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CN110133578B
CN110133578B CN201910378018.8A CN201910378018A CN110133578B CN 110133578 B CN110133578 B CN 110133578B CN 201910378018 A CN201910378018 A CN 201910378018A CN 110133578 B CN110133578 B CN 110133578B
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CN110133578A (en
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杨益新
李鋆
张亚豪
汪勇
杨龙
闫孝伟
何元安
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Northwestern Polytechnical University
CSSC Systems Engineering Research Institute
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CSSC Systems Engineering Research Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention provides a submarine reflection sound ray incident angle estimation method based on a semi-cylindrical volume array, which comprises the steps of dividing the semi-cylindrical volume array into a plurality of identical planar arrays along the axial direction, estimating sound ray azimuth angles on the planar arrays, designing a beam former according to the estimated azimuth angles, completing beam forming, outputting beams of each planar array to be equivalent to a single-dimensional array receiving signal, and estimating sound ray pitch angles by using the single-dimensional array, so that the calculation complexity is simplified, and the submarine reflection sound ray azimuth angles and the pitch angles can be efficiently and quickly estimated by the volume array. Meanwhile, the SAMV algorithm is adopted to realize the high resolution of the pitch angle of the coherent reflection sound ray.

Description

Seabed reflection sound ray incident angle estimation method based on semi-cylindrical volume array
Technical Field
The invention relates to the field of signal processing, in particular to a method for estimating a submarine reflection sound ray.
Background
The seabed reflection is a typical sound wave propagation mode, and underwater detection capability can be effectively improved by fully utilizing seabed reflection sound rays. The number of sound rays reaching a receiving end through seabed reflection is large, and four kinds of sound rays have small propagation loss and high energy reaching a receiving system, so that the sound rays are commonly used for target detection and are respectively seabed reflection sound rays for 1 time; 1 seabed reflection plus 1 sea surface reflection sound ray; 1 sea surface reflection plus 1 seabed reflection sound ray; 1 sea surface reflection, 1 seabed reflection and 1 sea surface reflection sound ray. By estimating the Direction of Arrival (DOA) of the four sound rays, effective angle information can be provided for subsequent processing such as positioning and target detection.
The Conventional Beamforming (CBF) method, as a Conventional DOA estimation algorithm, has a simple principle, is easy to implement, and is relatively robust to environmental changes. However, the algorithm is limited by the rayleigh criterion, and the resolution performance is not high. Considering that the angle difference of the four seabed reflection sound rays is small, the four sound rays are difficult to separate by adopting a CBF algorithm to carry out DOA estimation on the four seabed reflection sound rays. Conventional high resolution algorithms such as Minimum variance distortion free response (MVDR) and Multiple signal classification (MUSIC) can break through the limitations of the rayleigh criterion, but cannot process coherent signals. Because the coherence of the seabed reflected sound ray is strong, the DOA estimation of the seabed reflected sound ray can not be carried out by utilizing the traditional high-resolution algorithm.
DOA estimation based on sparse signal processing is a DOA estimation algorithm that has been developed in the last decade. Compared with the traditional direction estimation algorithm, the sparse signal processing can be used under the conditions of smaller fast beat number and lower signal-to-noise ratio, the DOA estimation problem of coherent signals can be processed, and the performance is far better than that of the traditional algorithm. The sparse algorithm is mainly divided into a regular parameter algorithm and an irregular parameter algorithm. The regular parameter algorithm generally combines a sparse term and a data fitting error by using a regular parameter to form a convex optimization problem. The regularization parameter severely impacts the performance of the algorithm and is generally harder to select. A Sparse Approximation Minimum Variance (SAMV) algorithm (H.Abeida, Q.Zhang, J.Li, et al.iterative spatial minimum variance based on approximated adaptive Processing [ J ] transformations on Signal Processing,2013,61 (4): 933-944) is a common irregular parametric DOA estimation algorithm that uses an approximate minimum variance criterion to calculate an iterative formula for Signal and noise, and iteratively reconstructs a covariance matrix. The whole solving process only needs to provide a threshold for stopping iteration and does not need any regular parameter, so that the algorithm has higher practicability than the regular parameter algorithm.
Considering that the receiving array is generally a semi-cylinder volume array and has more array elements, the SAMV algorithm is adopted to estimate the azimuth angle and the pitch angle of the reflected sound ray at the same time, the calculation amount is larger, and the calculation speed is slower. Therefore, an appropriate manner is selected to estimate the azimuth angle and the elevation angle of the sound ray arrival, so as to improve the calculation efficiency.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for estimating the incident angle of the seabed reflection sound ray based on a semi-cylindrical volume array. In order to simplify the calculation complexity of the algorithm, the semi-cylindrical volume array is divided into a plurality of identical semicircular annular planar arrays along the axis direction, and the azimuth angle of the sound ray is estimated on any one planar array by adopting an SAMV algorithm; designing a beam former according to the estimated azimuth angle, and respectively forming beams of each planar array, wherein the beam output can be equivalent to a receiving signal of a vertical linear array; on the equivalent vertical line array, the sound ray pitch angle estimation is carried out by adopting an SAMV algorithm, so that the high-efficiency estimation of the azimuth angles and the pitch angles of the four seabed reflection sound rays is completed.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: reflected sound ray azimuth estimation
Dividing the semi-cylindrical array into L planar arrays along the axis direction, wherein the L planar arrays are the same semi-circular arrays, the number of the array elements is M, for any planar array, a two-dimensional coordinate system is established by taking the circle center as the origin, and the coordinate of the No. M array element on the array is marked as (x) m ,y m ) Wherein, M = 1.. M, a plane on which the planar array is located is uniformly divided into Q discrete grid points, and a vector composed of azimuth angles represented by each grid point is recorded as Θ = [ θ ] 1 ,θ 2 ,…,θ Q ]Assuming that the signals are distributed on the divided grid, the signals received by the array are expressed as:
y(t)＝A(Θ)s(t)+n(t),t＝1,2,…,T (1)
where y (T) is the array received signal, s (T) and n (T) are the signal and noise data vectors, respectively, the fast beat number is T, and a (Θ) is the array manifold matrix, denoted as a (Θ) = [ a (θ) ] 1 ),a(θ 2 ),…a(θ q ),…,a(θ Q )]Whose column is represented as
Figure GDA0003953662880000021
k is the wave number, the superscript "T" is the transposition operation, θ q Representing the azimuth represented by the q-th grid point;
assuming that the noisy data is white gaussian noise with independent co-distribution, the corresponding covariance matrix is E [ n (t) n ] H (t)]＝σ 2 I, where E (-) is the mathematical expectation operator, superscript "H" is the conjugate transpose operation, σ 2 For noise power, I is the identity matrix, and the signal and noise are considered uncorrelated, then the array output covariance matrix R is expressed as:
Figure GDA0003953662880000031
wherein P = diag (P) 1 ,p 2 ,…,p q ,…p Q )，p q For signal power, Q = 1., Q, diag (·) represents a diagonal matrix, and the array output covariance matrix R is determined by sampling the covariance matrix R
Figure GDA0003953662880000032
Is estimated to be, wherein
Figure GDA0003953662880000033
T is the total fast beat number;
vectorizing the formula (2) to obtain:
Figure GDA0003953662880000034
where vec (-) represents the matrix vectorization operator,
Figure GDA0003953662880000035
representing the Kronecker product, the prime symbol is conjugate operation, matrix
Figure GDA0003953662880000036
Is composed of
Figure GDA0003953662880000037
(Vector)
Figure GDA0003953662880000038
Is composed of
Figure GDA0003953662880000039
According to the SAMV algorithm, the signal power and the noise power are calculated in an iterative mode, and the iterative formula of the signal power and the noise power is as follows:
Figure GDA00039536628800000310
wherein
Figure GDA00039536628800000311
And
Figure GDA00039536628800000312
the q signal power and noise power, a, of the (i) th iteration, respectively q ＝a(θ q ) An array manifold vector representing the azimuth angle corresponding to the qth grid point,
Figure GDA00039536628800000313
Figure GDA00039536628800000314
tr (-) is a matrix trace operator, and an iteration initial value is determined by the following formula:
Figure GDA00039536628800000315
wherein | · | | represents a vector norm of 2, when two adjacent iterations satisfy the following equation:
Figure GDA00039536628800000316
wherein eta 1 For the selected iteration termination threshold, when the iteration condition of formula (6) is satisfied, the iteration is terminated, and the position corresponding to the peak value in the estimated power spectrum
Figure GDA0003953662880000041
The azimuth angle of the reflected sound ray is obtained;
step 2: beam forming
According to the sound ray azimuth angle estimated in the step 1
Figure GDA0003953662880000042
Filtering by adopting a CBF algorithm, and calculating the beam output of each planar array on the azimuth;
the weighting vector corresponding to the CBF algorithm is:
Figure GDA0003953662880000043
the beam output corresponding to the ith planar array is:
Figure GDA0003953662880000044
Figure GDA0003953662880000045
receiving signals of the equivalent array elements of the first planar array at the circle center;
and 3, step 3: reflected sound line pitch angle estimation
According to the step 2, each layer of plane array is equivalent to an array element at the circle center, the volume array is equivalent to an L-element vertical linear array, the array element interval is d, and the array elements are arranged in a matrix modeThe sound source closest to the water surface is used as a reference point, and the array manifold vector corresponding to the equivalent vertical linear array is
Figure GDA0003953662880000046
Uniformly dividing the space into U grids along the direction vertical to the equivalent linear array, and recording the vector formed by the angles represented by each grid point as
Figure GDA0003953662880000047
Based on the grid, the model of the signal received by the vertical array is represented as:
Figure GDA0003953662880000048
wherein
Figure GDA0003953662880000049
And
Figure GDA00039536628800000410
respectively, are the signal and noise data vectors,
Figure GDA00039536628800000411
is an array manifold matrix expressed as
Figure GDA00039536628800000412
Estimating the pitch angle by adopting an SAMV algorithm, wherein the iterative formula of the signal power and the noise power is as follows:
Figure GDA00039536628800000413
wherein,
Figure GDA00039536628800000414
and
Figure GDA00039536628800000415
respectively the (i) th sub-stackThe u-th signal power and noise power of the generation,
Figure GDA00039536628800000416
an array manifold vector representing the azimuth angle corresponding to the u-th grid point,
Figure GDA00039536628800000417
indicating the azimuth angle corresponding to the u-th grid point,
Figure GDA00039536628800000418
is a sampling covariance matrix; the iteration initial value is composed of
Figure GDA0003953662880000051
Calculating to obtain; when two adjacent iterations satisfy
Figure GDA0003953662880000052
The iteration terminates, where 2 For the selected iteration termination threshold, the position corresponding to the peak in the estimated power spectrum
Figure GDA0003953662880000053
I.e. the pitch angle of the reflected sound ray.
The method has the advantages that the semi-cylinder volume array is divided into a plurality of identical plane arrays along the axial direction, the sound ray azimuth angle is estimated by utilizing the plane arrays, the beam former is designed according to the estimated azimuth angle to complete beam forming, the beam output of each plane array is equivalent to a single-dimensional array receiving signal, the single-dimensional array is utilized to estimate the sound ray pitch angle, the calculation complexity is simplified, and the volume arrays can efficiently and quickly estimate the seabed reflection sound ray azimuth angle and the seabed reflection sound ray pitch angle. Meanwhile, the SAMV algorithm is adopted to realize the high resolution of the coherent reflection sound ray pitch angle.
Drawings
FIG. 1 is a general flow diagram of the seafloor reflection sound line azimuth and elevation estimation of the present invention.
FIG. 2 is a schematic diagram of a semi-cylindrical volumetric array of the present invention.
FIG. 3 (a) is a schematic plan view of the array, and FIG. 3 (b) is a schematic equivalent vertical line array.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The invention discloses a method for estimating azimuth angles and pitch angles of submarine reflection sound rays based on a semi-cylindrical volume array, which mainly comprises the steps of successively and equivalently estimating the azimuth angles and the pitch angles by using the volume array as a plane array and a linear array, respectively, and realizing the effective estimation of the pitch angles and the azimuth angles of the submarine reflection sound rays by using the high resolution of sparse approximate minimum variance on coherent signals, thereby providing effective submarine reflection sound ray angle information for the subsequent processing of target positioning and the like, and mainly relates to the field of signal processing and the like.
Step 1: reflected sound ray azimuth estimation
Dividing the semi-cylindrical array into L planar arrays along the axis direction, wherein the L planar arrays are the same semi-circular arrays, the number of the array elements is M, for any planar array, a two-dimensional coordinate system is established by taking the circle center as the origin, and the coordinate of the No. M array element on the array is marked as (x) m ,y m ) Wherein, M = 1.. M, a plane where the planar array is located is uniformly divided into Q discrete grid points, and a vector formed by azimuth angles represented by the grid points is recorded as Θ = [ θ = ] 1 ,θ 2 ,…,θ Q ]Assuming that the signals are distributed on the divided grid, the signals received by the array are expressed as:
y(t)＝A(Θ)s(t)+n(t),t＝1,2,…,T (1)
where y (T) is the array received signal, s (T) and n (T) are the signal and noise data vectors, respectively, the fast beat number is T, and a (Θ) is the array manifold matrix, denoted as a (Θ) = [ a (θ) ] 1 ),a(θ 2 ),…a(θ q ),…,a(θ Q )]Whose column is represented as
Figure GDA0003953662880000061
k is the wave number, the superscript "T" is the transposition, θ q Representing the azimuth represented by the q-th grid point;
suppose that the noisy data isIndependent and identically distributed white Gaussian noise, and the corresponding covariance matrix is E [ n (t) n H (t)]＝σ 2 I, where E (-) is the mathematical expectation operator, superscript "H" is the conjugate transpose operation, σ 2 For noise power, I is the identity matrix, and the signal and noise are considered uncorrelated, then the array output covariance matrix R is expressed as:
Figure GDA0003953662880000062
wherein P = diag (P) 1 ,p 2 ,…,p q ,…p Q )，p q For signal power, Q = 1., Q, diag (·) represents a diagonal matrix, and the array output covariance matrix R is determined by sampling the covariance matrix R
Figure GDA0003953662880000063
Is estimated to be wherein
Figure GDA0003953662880000064
T is the total number of rapid beats;
vectorization operation is performed on the formula (2) to obtain:
Figure GDA0003953662880000065
where vec (-) represents the matrix vectorization operator,
Figure GDA0003953662880000066
representing the Kronecker product, the superscript is a conjugate operation, the matrix
Figure GDA0003953662880000067
Is composed of
Figure GDA0003953662880000068
(Vector)
Figure GDA0003953662880000069
Is composed of
Figure GDA00039536628800000610
According to the SAMV algorithm, the signal power and the noise power are calculated in an iterative mode, and the iterative formulas of the signal power and the noise power are as follows:
Figure GDA00039536628800000611
wherein
Figure GDA00039536628800000612
And
Figure GDA00039536628800000613
the q signal power and noise power, a, of the (i) th iteration, respectively q ＝a(θ q ) An array manifold vector representing the azimuth angle corresponding to the qth grid point,
Figure GDA00039536628800000614
Figure GDA00039536628800000615
tr (-) is a matrix tracing operator, and an iteration initial value is determined by the following formula:
Figure GDA0003953662880000071
wherein | · | | represents a vector norm of 2, when two adjacent iterations satisfy the following equation:
Figure GDA0003953662880000072
wherein eta 1 For the selected iteration termination threshold, the invention takes eta 1 Is 10 -4 As an iteration termination threshold; when the iteration condition of the formula (6) is met, the iteration is terminated, and the position corresponding to the peak value in the estimated power spectrum
Figure GDA0003953662880000073
The azimuth angle of the reflected sound ray is obtained;
and 2, step: beamforming
According to the sound ray azimuth angle estimated in the step 1
Figure GDA0003953662880000074
Filtering by adopting a CBF algorithm, and calculating the beam output of each planar array on the azimuth;
the weighting vector corresponding to the CBF algorithm is:
Figure GDA0003953662880000075
the beam output corresponding to the ith planar array is:
Figure GDA0003953662880000076
Figure GDA0003953662880000077
receiving signals of the equivalent array elements of the first planar array at the circle center;
and step 3: reflected sound line pitch angle estimation
According to the step 2, each layer of planar array is equivalent to an array element at the center of a circle, the volume array is equivalent to an L-element vertical linear array, the distance between the array elements is d, a sound source closest to the water surface is used as a reference point, and the array manifold vector corresponding to the equivalent vertical linear array is
Figure GDA0003953662880000078
Uniformly dividing the space into U grids along the direction vertical to the equivalent linear array, and recording the vector formed by the angles represented by each grid point as
Figure GDA0003953662880000079
Based on the grid, the model of the signal received by the vertical array is represented as:
Figure GDA00039536628800000710
wherein
Figure GDA00039536628800000711
And
Figure GDA00039536628800000712
respectively, a signal and a noisy data vector,
Figure GDA00039536628800000713
is an array manifold matrix expressed as
Figure GDA00039536628800000714
Estimating the pitch angle by adopting an SAMV algorithm, wherein the iterative formula of the signal power and the noise power is as follows:
Figure GDA0003953662880000081
wherein,
Figure GDA0003953662880000082
and
Figure GDA0003953662880000083
respectively the u-th signal power and the noise power of the (i) -th iteration,
Figure GDA0003953662880000084
an array manifold vector representing the azimuth angle corresponding to the u-th grid point,
Figure GDA0003953662880000085
indicating the azimuth angle corresponding to the u-th grid point,
Figure GDA0003953662880000086
as a sampling covarianceA matrix; the iteration initial value is composed of
Figure GDA0003953662880000087
Calculating to obtain; when two adjacent iterations satisfy
Figure GDA0003953662880000088
The iteration terminates, where η 2 For selected iteration termination thresholds, the invention eta 2 Get 10 -4 As an iteration termination threshold, the position corresponding to the peak in the estimated power spectrum
Figure GDA00039536628800000820
I.e. the pitch angle of the reflected sound ray.
Fig. 1 of the present invention is a flow chart of a method for estimating the azimuth angle and the pitch angle of a submarine reflection sound ray by using a volume array, and the method is specifically implemented as follows:
assuming that the noise is white Gaussian noise, the covariance matrix of the array output signals can be expressed as
Figure GDA0003953662880000089
Is the signal power, σ 2 Noise power, I is unit matrix, array output covariance matrix R is formed by sampling covariance matrix
Figure GDA00039536628800000810
And (6) obtaining the estimation. The covariance matrix is vectorized to obtain
Figure GDA00039536628800000811
Wherein
Figure GDA00039536628800000812
vec (-) represents a matrix vectorization operator,
Figure GDA00039536628800000813
representing the Kronecker product, the superscript is a conjugate operation,
Figure GDA00039536628800000814
according to the SAMV algorithm, the iterative relationship between the signal and the noise is:
Figure GDA00039536628800000815
Figure GDA00039536628800000816
wherein
Figure GDA00039536628800000817
And
Figure GDA00039536628800000818
the q signal power and noise power, a, of the (i) th iteration, respectively q ＝a(θ q ) An array manifold vector representing the azimuth angle corresponding to the qth grid point,
Figure GDA00039536628800000819
diag (·) denotes a diagonal matrix. Tr (-) is a matrix trace operator. The iteration initial value may be determined by
Figure GDA0003953662880000091
And (4) calculating. When two adjacent iterations satisfy
Figure GDA0003953662880000092
The iteration terminates, where η 1 For the selected iteration termination threshold, 10 is selected -4 As an iteration termination threshold, the position corresponding to the peak in the estimated power spectrum
Figure GDA0003953662880000093
I.e. the azimuth angle of the reflected sound ray.
2) According to the sound ray azimuth angle estimated in the step 1)
Figure GDA0003953662880000094
Filtering by CBF algorithm with weight vector of
Figure GDA0003953662880000095
And calculating the beam output of each planar array at the azimuth angle. The first planar array corresponds to a beam output of
Figure GDA0003953662880000096
Can be regarded as the receiving signal of the equivalent array element at the centre of a circle.
3) And (3) each layer of planar array is equivalent to an array element at the center of a circle, the volume array is equivalent to an L-element vertical linear array, and the array element interval is d. Vertical line array As shown in FIG. 3 (b), when the array element No. 1 is taken as the reference point, the array manifold vector is expressed as
Figure GDA0003953662880000097
Uniformly dividing the space into U grids along the direction vertical to the equivalent linear array, and recording the vector formed by the angles represented by each grid point as
Figure GDA0003953662880000098
Based on the grid, the signal model received by the vertical array can be expressed as
Figure GDA0003953662880000099
Wherein
Figure GDA00039536628800000910
And
Figure GDA00039536628800000911
respectively, signal and noise data vectors, with a fast beat number T,
Figure GDA00039536628800000912
is an array manifold matrix, which can be expressed as
Figure GDA00039536628800000913
As can be seen from the SAMV algorithm, the iterative relationship between the signal power and the noise power at this time is:
Figure GDA00039536628800000914
Figure GDA00039536628800000915
wherein
Figure GDA00039536628800000916
And
Figure GDA00039536628800000917
respectively the u-th signal power and the noise power of the (i) -th iteration,
Figure GDA00039536628800000918
an array manifold vector representing the azimuth angle corresponding to the u-th grid point,
Figure GDA00039536628800000919
indicating the azimuth angle corresponding to the u-th grid point,
Figure GDA00039536628800000920
is a sampled covariance matrix. The iteration initial value may be determined by
Figure GDA00039536628800000921
And (4) calculating. When two adjacent iterations satisfy
Figure GDA00039536628800000922
The iteration terminates, where 2 For the selected iteration termination threshold, the invention selects 10 -4 As an iteration termination threshold. When the iteration is terminated, the position corresponding to the peak in the estimated power spectrum
Figure GDA00039536628800000923
I.e. the pitch angle of the reflected sound ray.

Claims (1)

1. A seabed reflection sound ray incident angle estimation method based on a semi-cylindrical volume array is characterized by comprising the following steps:
step 1: reflected sound ray azimuth estimation
Dividing the semi-cylindrical array into L planar arrays along the axial direction, wherein the L planar arrays are the same semi-circular arrays, the number of the array elements is M, for any planar array, taking the circle center as the origin, establishing a two-dimensional coordinate system, and recording the coordinate of the No. M array element on the array as (x) m ,y m ) Wherein, M = 1.. M, a plane where the planar array is located is uniformly divided into Q discrete grid points, and a vector formed by azimuth angles represented by the grid points is recorded as Θ = [ θ = ] 1 ,θ 2 ,…,θ Q ]Assuming that the signals are distributed on the divided grids, the signals received by the array are expressed as:
y(t)＝A(Θ)s(t)+n(t),t＝1,2,…,T (1)
where y (T) is the array received signal, s (T) and n (T) are the signal and noise data vectors, respectively, the total fast beat number is T, and a (Θ) is the array manifold matrix, denoted as a (Θ) = [ a (θ) ] 1 ),a(θ 2 ),…a(θ q ),…,a(θ Q )]The column of which is represented as
Figure FDA0003953662870000011
k is the wave number, the superscript "T" is the transposition, θ q Representing the azimuth represented by the q-th grid point;
assuming that the noisy data is white gaussian noise with independent co-distribution, the corresponding covariance matrix is E [ n (t) n ] H (t)]＝σ 2 I, where E (-) is the mathematical expectation operator, superscript "H" is the conjugate transpose operation, σ 2 For noise power, I is the identity matrix, and the signal and noise are considered uncorrelated, then the array output covariance matrix R is expressed as:
Figure FDA0003953662870000012
wherein P = diag (P) 1 ,p 2 ,…,p q ,…p Q )，p q For signal power, Q = 1., Q, diag (·) represents a diagonal matrix, and the array output covariance matrix R is formed by sampling the covariance matrix R
Figure FDA0003953662870000013
Is estimated to be, wherein
Figure FDA0003953662870000014
T is the total fast beat number;
vectorization operation is performed on the formula (2) to obtain:
Figure FDA0003953662870000015
where vec (-) represents the matrix vectorization operator,
Figure FDA0003953662870000016
representing the Kronecker product, the superscript is a conjugate operation, the matrix
Figure FDA0003953662870000021
Is composed of
Figure FDA0003953662870000022
(Vector)
Figure FDA0003953662870000023
Is composed of
Figure FDA0003953662870000024
According to the SAMV algorithm, the signal power and the noise power are calculated in an iterative mode, and the iterative formulas of the signal power and the noise power are as follows:
Figure FDA0003953662870000025
wherein
Figure FDA0003953662870000026
And
Figure FDA0003953662870000027
the q signal power and noise power, a, of the (i) th iteration, respectively q ＝a(θ q ) An array manifold vector representing the azimuth angle corresponding to the qth grid point,
Figure FDA0003953662870000028
Figure FDA0003953662870000029
tr (-) is a matrix trace operator, and an iteration initial value is determined by the following formula:
Figure FDA00039536628700000210
wherein | · | | represents a vector 2 norm, when two adjacent iterations satisfy the following equation:
Figure FDA00039536628700000211
wherein eta 1 For the selected iteration termination threshold, when the iteration condition of formula (6) is satisfied, the iteration is terminated, and the position corresponding to the peak value in the estimated power spectrum
Figure FDA00039536628700000212
The azimuth angle of the reflected sound ray is obtained;
and 2, step: beamforming
According to the sound ray azimuth angle estimated in the step 1
Figure FDA00039536628700000213
Filtering by adopting a CBF algorithm, and calculating the beam output of each planar array on the azimuth;
the weighting vector corresponding to the CBF algorithm is:
Figure FDA00039536628700000214
the beam output corresponding to the ith planar array is:
Figure FDA00039536628700000215
Figure FDA00039536628700000216
receiving signals of the equivalent array elements of the first planar array at the circle center;
and step 3: reflected sound ray pitch angle estimation
According to the step 2, each layer of planar array is equivalent to an array element at the center of a circle, the volume array is equivalent to an L-element vertical linear array, the distance between the array elements is d, a sound source closest to the water surface is used as a reference point, and the array manifold vector corresponding to the equivalent vertical linear array is
Figure FDA0003953662870000031
Uniformly dividing the space into U grids along the direction vertical to the equivalent linear array, and recording the vector formed by the angles represented by each grid point as
Figure FDA0003953662870000032
Based on the grid, the signal model received by the vertical array is represented as:
Figure FDA0003953662870000033
wherein
Figure FDA0003953662870000034
Figure FDA0003953662870000035
And
Figure FDA0003953662870000036
respectively, are the signal and noise data vectors,
Figure FDA0003953662870000037
is an array manifold matrix expressed as
Figure FDA0003953662870000038
Estimating the pitch angle by adopting an SAMV algorithm, wherein the iterative formula of the signal power and the noise power is as follows:
Figure FDA0003953662870000039
wherein,
Figure FDA00039536628700000310
and
Figure FDA00039536628700000311
respectively the u-th signal power and the noise power of the (i) -th iteration,
Figure FDA00039536628700000312
an array manifold vector representing the azimuth angle corresponding to the u-th grid point,
Figure FDA00039536628700000313
indicating the azimuth angle corresponding to the u-th grid point,
Figure FDA00039536628700000314
is a sampling covariance matrix; the iteration initial value is composed of
Figure FDA00039536628700000315
Calculating to obtain; when two adjacent iterations satisfy
Figure FDA00039536628700000316
The iteration terminates, where η 2 For the selected iteration termination threshold, the position corresponding to the peak in the estimated power spectrum
Figure FDA00039536628700000317
I.e. the pitch angle of the reflected sound ray.
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CN113673158B (en) * 2021-08-19 2023-05-26 西北工业大学 Beam domain variation Bayesian azimuth estimation method suitable for strong interference environment
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102809742A (en) * 2011-06-01 2012-12-05 杜比实验室特许公司 Sound source localization equipment and method
CN107561486A (en) * 2017-07-03 2018-01-09 西北工业大学 It is a kind of based on active when anti-Shallow Water Target Wave arrival direction estimating method
CN108694957A (en) * 2018-04-08 2018-10-23 湖北工业大学 The echo cancelltion design method formed based on circular microphone array beams
CN108845309A (en) * 2018-08-28 2018-11-20 西北工业大学 A kind of submarine target DOA estimation method based on active negative side's method when virtual
CN109116337A (en) * 2018-07-30 2019-01-01 西北工业大学 A kind of sparse approximate minimum variance direction estimation method based on matrix filtering
CN109307855A (en) * 2018-08-02 2019-02-05 西北工业大学 The sparse approximate minimum variance DOA estimation method of mesh free based on mesh error model
CN109521392A (en) * 2018-10-24 2019-03-26 华南理工大学 Underwater one-dimensional DOA estimation method and device based on non-circular signal and L-type linear array

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102809742A (en) * 2011-06-01 2012-12-05 杜比实验室特许公司 Sound source localization equipment and method
CN107561486A (en) * 2017-07-03 2018-01-09 西北工业大学 It is a kind of based on active when anti-Shallow Water Target Wave arrival direction estimating method
CN108694957A (en) * 2018-04-08 2018-10-23 湖北工业大学 The echo cancelltion design method formed based on circular microphone array beams
CN109116337A (en) * 2018-07-30 2019-01-01 西北工业大学 A kind of sparse approximate minimum variance direction estimation method based on matrix filtering
CN109307855A (en) * 2018-08-02 2019-02-05 西北工业大学 The sparse approximate minimum variance DOA estimation method of mesh free based on mesh error model
CN108845309A (en) * 2018-08-28 2018-11-20 西北工业大学 A kind of submarine target DOA estimation method based on active negative side's method when virtual
CN109521392A (en) * 2018-10-24 2019-03-26 华南理工大学 Underwater one-dimensional DOA estimation method and device based on non-circular signal and L-type linear array

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
基于主动时反的浅海目标DOA估计优化算法;荆海霞等;《西北工业大学学报》;20180430;第36卷(第2期);第270-275页 *
基于协方差矩阵降维稀疏表示的二维波达方向估计;李文杰等;《计算机应用》;20160810(第08期);第2197-2201页 *

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