CN109541573B - Array element position calibration method for bending hydrophone array - Google Patents
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- 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 relates to a method for calibrating the position of an array element of a bending hydrophone array, which is based on the front M with known position c Water tinThe device uniformly divides the matrix into D sub-arrays, utilizes the first sub-array to estimate the target azimuth, eliminates the error position in the candidate position through the array element spacing information, and finally obtains the coordinate of the mth array element of the mth sub-array as
Where | | | represents the norm of vector l2, and | | represents absolute value operation. The problem of array shape calibration of mismatched arrays (such as a towed linear array and a seabed fixed array) when the array shape is seriously deformed and mismatched is solved.
Description
Technical Field
The invention belongs to the fields of array signal processing, parameter estimation and the like, and relates to a method for calibrating the array element position of a bending hydrophone array.
Background
The hydrophone array is widely applied to sensing and detecting underwater targets, a large-aperture hydrophone array is usually used for improving array gain, the common large-aperture hydrophone array comprises a towed array sonar array and a seabed fixed sonar array, and for the towed array sonar, the array shape can be bent due to the influence of environmental factors such as towing ship maneuvering and ocean currents; for a fixed-seabed sonar, the array can be bent and deformed relative to an ideal shape due to uncontrollable array arrangement. The array bending deformation can cause the serious reduction of the target azimuth estimation precision, and higher side lobes can even mask the existence of the target.
The work on the formation calibration technique began in the 80's of the 20 th century. The calibration method can be divided into a pilot-calibration method (pilot-calibration) and a self-calibration method (self-calibration). The auxiliary calibration method usually needs to prefabricate a sound source with a known position, the prefabricate sound source can be separable in time or frequency, the position of the array element is solved by utilizing the accurate position information of the prefabricate sound source, and higher estimation precision of the position of the array element can be obtained. The self-calibration method can realize the joint estimation of the array element position and the target position without a prefabricated sound source, because the target position and the array element position are coupled in the index terms of the array manifold, the direct solution of the array element position and the target position is difficult, Weiss and Friedlander (A J Weiss, B Friedlander. array shape correction using sources in unknown locations-a maximum likelihood approach [ J ]. IEEE Transactions on Acoustic, Speech and Signal Processing,1989,37(12):1958 and 1966.) firstly proposes the calculation of the alternating iteration of the target position and the array element position, and Weiss and Friedlander perform Taylor series approximation on the array manifold index terms and obtain a first-order linear expansion series solution idea. However, when the position error of the array element is large, the first-order linear approximation effect is seriously reduced. Therefore, Flanagan and Bell (B P Flanagan, K L Bell. array self-calibration with large sensor position errors [ J ]. Signal Processing,2001,81(10): 2201-.
The array calibration method assumes that the phase difference caused by the position error of the sensor is less than 2 pi, and the phase ambiguity problem is not considered. When the lineup is severely deformed and mismatched, phase ambiguity is inevitable. At present, a few array shape calibration methods considering phase ambiguity exist, and the array shape calibration problem of a severely deformed and mismatched array (such as a towed line array and a seabed fixed array) needs to be solved urgently.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides an array element position calibration method of a bending hydrophone array, which aims at a linear hydrophone array which is horizontally arranged and seriously bent and deformed.
Technical scheme
A calibration method for array element positions of a bending hydrophone array is characterized by comprising the following steps: the hydrophone array to be calibrated receives K far-field target signals, the K is required to be more than or equal to 2, the array element number is M, and the interval between the M-th array element and the M + 1-th array element is known to be delta m M is 1,2, …, M-1, and pre-M is known c A hydrophone position, i.e. p m ＝[x m ,y m ] T ,m＝1,2,…,M c ，x m ,y m Coordinates of the m array element on x and y axes; the method comprises the following steps:
step 1: using the array to receive and record underwater acoustic signals, x (n) is the array output vector, calculating the array sampling covariance matrix
Step 2: to sampling covariance matrix
Performing characteristic decomposition to obtain a signal subspace E, a noise subspace V and dimensions of M × K and M × (M-K) respectively;
and step 3: the basic array is evenly divided into D sub-arrays,
(symbol)
represents the smallest integer greater than or equal to the variable in the symbol; the M is c The number of the calibrated hydrophones is;
dividing an array manifold matrix and a signal subspace according to a subarray mode:
array manifold matrix:
wherein a (θ) ═ a (θ) 1 ),…,a(θ K )]Is an array manifold matrix of theta for incident orientation k Of the hydrophone array, the array manifold vector a (theta) k )＝[exp(-j2πfτ 1k ),…,exp{-j2πfτ Mk }] T Where f is the frequency of the signal,
τ mk ＝{u k } T p m /c＝(x m cosθ k +y m sinθ k ) C, M is 1,2, … M, d is array element spacing, c is sound velocity, and the position coordinate of the array element is p m ＝[x m ,y m ] T Normalized direction vector u of the kth signal k ＝[cosθ k ,sinθ k ] T ；
Signal subspace:
the noise subspace of the first subarray isFirst M of the noise subspace matrix V c X (M-K) submatrix, denoted as V 1 ；
And 4, step 4: using the first sub-array for target orientation estimation, i.e.
Wherein
Estimation of target position by peak search
And 5: computing full rank matrices
D is 2;
step 6: the phase difference of the d-th sub-array relative to the first sub-array forms a column vector
Phase difference between array elements; then
Wherein vec { } denotes a matrix vectorization operator, Diag { } denotes arranging vectors into a diagonal matrix,
representing Kronecker product operation;
and 7: the phase ambiguity being a set of unknown integers, i.e.
And is
wherein C ═ u 1 ,…,u K ] T ，
Is a normalized direction vector, its orientation
Already calculated in step 3 is:
and 8: obtaining the coordinates of the mth array element of the mth sub-array as
Wherein | | | | represents vector l2 norm, | | | | represents absolute value operation;
and step 9: if D is less than or equal to D-1, D is D +1, and the operation returns to the step 6; if D > D-1, array position calibration is complete.
Advantageous effects
The invention provides an array element position calibration method of a bending hydrophone array, which is based on the front M with known position c The hydrophone divides the matrix into D sub-arrays uniformly, utilizes the first sub-array to estimate the target azimuth, eliminates the error position in the candidate position through the array element interval information, and finally obtains the coordinate of the mth array element of the mth sub-array as
Where | | | represents the norm of vector l2, and | | represents absolute value operation. The problem of array shape calibration of mismatched arrays (such as a towed linear array and a seabed fixed array) when the array shape is seriously deformed and mismatched is solved.
Drawings
FIG. 1: is a general flow chart of a bent hydrophone array element position calibration method;
FIG. 2: is a shape estimate of the curved array.
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
the technical scheme adopted by the invention for solving the technical problem comprises the following aspects:
1: the array element number of a linear hydrophone array horizontally placed under water is M, and the distance between the M-th array element and the M + 1-th array element is known to be delta m M is 1,2, …, M-1, and pre-M c The individual hydrophone positions are also known exactly, i.e.:
p m ＝[x m ,y m ] T ,m＝1,2,…,M c is known, x m ,y m The coordinates of the m-th array element on the x and y axes are shown.
The number of targets existing in the far field of the array is K, the K is required to be more than or equal to 2, and the incident direction is theta (theta) 1 ,…,θ K ) Wherein theta k The input direction of the kth signal is shown, and the array output vector is x (N) ═ as (N) + e (N), N ═ 1, …, N, where N is the number of data points, and s (N) ═ s (N) 1 (n),…,s K (n)] T For incident signal waveforms, where the superscript "T" denotes the vector transpose operation, e (n) is the array element receive noise, and A (θ) ([ a (θ) ] 1 ),…,a(θ K )]Is an array manifold matrix (steering matrix). For an incident orientation of theta k Incident signal of (a), array manifold vector of hydrophone array:
a(θ k )＝[exp(-j2πfτ 1k ),…,exp{-j2πfτ Mk }] T wherein f is the signal frequency;
τ mk ＝{u k } T p m /c＝(x m cosθ k +y m sinθ k ) C, M is 1,2, … M, d is array element spacing, c is sound velocity, and the position coordinate of the array element is p m ＝[x m ,y m ] T Normalized direction vector u of the kth signal k ＝[cosθ k ,sinθ k ] T . Sampling covariance for computational arraysDifference matrix
Namely, it is
To sampling covariance matrix
And performing characteristic decomposition to obtain a signal subspace E and a noise subspace V, wherein the dimensionalities of the signal subspace E and the dimensionalities of the noise subspace V are respectively MxK and Mx (M-K).
2: and dividing the subarray.
From front M whose position is known c The hydrophone divides the matrix into D sub-arrays,
(symbol)
representing the smallest integer greater than or equal to the variable in the symbol. Whereupon the array manifold matrix and the signal subspace are also subdivided in a subarray manner, i.e.
And
wherein A is d (theta) and E d D is 1. ltoreq. d.ltoreq.D-1 is M c xK submatrix, A D (theta) and E D Is M D Sub-matrix of xK, M D ＝M-(D-1)M c 。
3: and (4) calculating the phase difference.
The noise subspace of the first sub-array is the first M of the entire array noise subspace matrix V c X (M-K) sub-matrix, denoted as V 1 . Using the first sub-array for target orientation estimation, i.e.
Wherein
Estimation of target position by peak search
Computing full rank matrices
The phase difference of the d-th sub-array relative to the first sub-array forms a column vector
Wherein
λ is the signal wavelength.
Then
Wherein vec { } denotes a matrix vectorization operator, Diag { } denotes arranging vectors into a diagonal matrix,
representing the Kronecker product operation.
4: and (5) phase solution fuzzy calculation.
Considering the phase ambiguity problem, the phase ambiguity quantity is assumed to be a set of unknown integers, i.e.
And is
N c Is an integer, usually the value is M/pi, then for the mth array element of the mth sub-array, the candidate position of the array element position is
Wherein C ═ u1, …, u K ] T ，
Is a normalized direction vector, its orientation
Having been calculated in step 3 already and,
as phase difference, it has already been calculated in step 3. Rejecting error positions in the candidate positions through array element spacing information to finally obtain the coordinates of the mth array element of the mth sub-array
Where | | | represents the norm of vector l2, and | | represents absolute value operation.
The steps of the embodiment are as follows:
(1) receiving K far-field signals by using a hydrophone array to be calibrated, wherein K is required to be more than or equal to 2, the array element number is M, and the interval between the M-th array element and the M + 1-th array element is known to be delta m M is 1,2, …, M-1, and pre-M c A hydrophone position, i.e. p m ＝[x m ,y m ] T ,m＝1,2,…,M c Is known, x m ,y m The coordinates of the m-th array element on the x and y axes are shown. Receiving and recording the underwater acoustic signals by using the array, wherein x (n) is an array output vector;
(2) computing array sampling covariance matrix
(3) To sampling covariance matrix
And performing characteristic decomposition to obtain a signal subspace E and a noise subspace V, wherein the dimensionalities of the signal subspace E and the noise subspace V are respectively MxK and Mx (M-K).
(4) From front M whose position is known c The hydrophone divides the basic array into D sub-arrays,
(symbol)
representing the smallest integer greater than or equal to the variable in the symbol. Whereupon the array manifold matrix and the signal subspace are also subdivided in a subarray manner, i.e.
And
meanwhile, the noise subspace of the first sub-matrix is the first M of the noise subspace matrix V c X (M-K) submatrix, denoted as V 1 。
(5) Using the first sub-array for target orientation estimation, i.e.
Wherein
Estimation of target position by peak search
(6) Computing full rank matrices
Let d be 2.
(7) The phase difference of the d-th sub-array relative to the first sub-array forms a column vector
Then
Wherein vec { } denotes a matrix vectorization operator, Diag { } denotes arranging vectors into a diagonal matrix,
representing the Kronecker product operation.
(8) Considering the phase ambiguity problem, the phase ambiguity quantity is assumed to be a set of unknown integers, i.e.
And is
Then for the m-th element of the d-th sub-array,
the candidate position of the array element position is
Wherein C ═ u 1 ,…,u K ] T ，
Is a normalized direction vector, its orientation
Having been calculated in step 7 already and,
as phase difference, it has already been calculated in step 3.
(9) Rejecting error positions in the candidate positions through array element spacing information to finally obtain the coordinates of the mth array element of the mth sub-array
Where | | | represents the norm of vector l2, and | | represents absolute value operation.
(10) If D is less than or equal to D-1, D is D +1, and the operation returns to the step (7); if D > D-1, array position calibration is complete.
The specific embodiment is as follows: consider a 14-element array of curved deformations to the line array, the actual array being shown as a black circle in figure 2, with the array being heavily curved with respect to the x-axis, and receiving 2 far-field targets.Let the positions of the first 5 array elements be known exactly, i.e. M c 5. By using the algorithm provided by the invention, the position of the array element can be accurately estimated.
Claims (1)
1. A calibration method for array element positions of a bending hydrophone array is characterized by comprising the following steps: the hydrophone array to be calibrated receives K far-field target signals, K is required to be more than or equal to 2, the number of array elements is M, and the distance between the M-th array element and the M + 1-th array element is known to be delta m M is 1,2, …, M-1, and pre-M is known c A hydrophone position, i.e. p m ＝[x m ,y m ] T ,m＝1,2,…,M c ，x m ,y m Coordinates of the m array element on x and y axes; the method comprises the following steps:
step 1: using the array to receive and record underwater acoustic signals, x (n) is the array output vector, calculating the array sampling covariance matrix
Step 2: to sampling covariance matrix
Performing characteristic decomposition to obtain a signal subspace E with dimension of M multiplied by K; the noise subspace is V, with dimensions M × (M-K);
and step 3: the basic array is evenly divided into D sub-arrays,
(symbol)
represents the smallest integer greater than or equal to the variable in the symbol; the M is c The number of the calibrated hydrophones is;
dividing an array manifold matrix and a signal subspace according to a subarray mode:
array manifold matrix:
wherein a (θ) ═ a (θ) 1 ),…,a(θ K )]Is an array manifold matrix of theta for incident orientation k Of the hydrophone array, the array manifold vector a (theta) k )＝[exp(-j2πfτ 1k ),…,exp{-j2πfτ Mk }] T Wherein f is the signal frequency;
τ mk ＝{u k } T p m /c＝(x m cosθ k +y m sinθ k ) C, M is 1,2, … M, d is array element spacing, c is sound velocity, and the position coordinate of the array element is p m ＝[x m ,y m ] T Normalized direction vector u of the kth signal k ＝[cosθ k ,sinθ k ] T ；
Signal subspace:
wherein E d D is more than or equal to 1 and less than or equal to D-1 is the D-th dimension M c Sub-matrix of xK, E D For D dimension as M D A sub-matrix of xK, wherein M D ＝M-(D-1)M c ；
The noise subspace of the first sub-matrix is the first M of the noise subspace matrix V c X (M-K) submatrix, denoted as V 1 ；
And 4, step 4: using the first sub-array for target orientation estimation, i.e.
Wherein
Estimation of target position by peak search
And 5: computing full rank matrices
D is 2;
step 6: the phase difference of the d-th sub-array relative to the first sub-array forms a column vector
Phase difference between array elements; then
Wherein vec { } denotes a matrix vectorization operator, Diag { } denotes arranging vectors into a diagonal matrix,
representing Kronecker product operation;
and 7: the phase ambiguity being a set of unknown integers, i.e.
And is
N c Is an integer and takes the value of M/pi; then for the m-th array element of the d-th sub-array, the candidate position of the array element position is
Wherein C ═ u 1 ,…,u K ] T ，
Is a normalized direction vector, its orientation
Has been calculated in step 3;
and 8: to obtainThe coordinate of the mth array element of the mth sub-array is
Wherein | | | | represents vector l2 norm, | | | | represents absolute value operation;
and step 9: if D is less than or equal to D-1, D is D +1, and the operation returns to the step 6; if D > D-1, array position calibration is complete.
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