CN109557526B - Vector hydrophone sparse array arrangement method based on compressed sensing theory - Google Patents

Vector hydrophone sparse array arrangement method based on compressed sensing theory Download PDF

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CN109557526B
CN109557526B CN201811451175.9A CN201811451175A CN109557526B CN 109557526 B CN109557526 B CN 109557526B CN 201811451175 A CN201811451175 A CN 201811451175A CN 109557526 B CN109557526 B CN 109557526B
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罗再磊
沈同圣
赵德鑫
黎松
郭少军
刘峰
孟路稳
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National Defense Technology Innovation Institute PLA Academy of Military Science
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    • G—PHYSICS
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    • 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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    • 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 vector hydrophone sparse arraying method based on a compressive sensing theory, which comprises the following steps of: (1) the method comprises the steps of determining a vector hydrophone combination directivity and composite array directivity function, (2) constructing a vector hydrophone array target directivity wave beam, (3) constructing a sparse vector hydrophone array problem model, and (4) performing sparse reconstruction on the vector hydrophone array. The method is based on a vector hydrophone array sparse array mechanism, combines convex optimization and compressive sensing theories, utilizes the sensing relation between sparse array positions and target array beams, adopts a non-uniform spacing array mode to reconstruct the target beams, and can obtain an accurate sparse array result. The vector sparse array arrangement method provided by the invention can automatically set the number of hydrophones in an expected sparse vector array according to the performance requirement of the system, and can accurately control the complexity of the system. The vector sparse array arrangement method provided by the invention adopts the orthogonal matching pursuit algorithm, the obtained sparse approximation result is fixed, multiple times of debugging are not needed, a large amount of algorithm adjusting time can be saved, and the method is more suitable for the practical application of engineering.

Description

Vector hydrophone sparse array arrangement method based on compressed sensing theory
Technical Field
The invention belongs to the technical field of sonar, and particularly relates to a vector hydrophone sparse arraying method based on a compressed sensing theory.
Background
The vector hydrophone is used as a novel underwater sound measuring sensor, is structurally formed by compounding a traditional nondirectional sound pressure sensor and a dipole directional vibration velocity sensor, can synchronously and jointly measure sound pressure and vibration velocity information, fundamentally solves the problem of port and starboard fuzzy, and is widely applied to the fields of underwater sound warning sonar, towed line array sonar, shipboard array conformal sonar, multi-base sonar and the like.
The sparse array is an array with array elements distributed in a sparse form obtained by removing part of array elements from a traditional densely-arranged full array on the basis of meeting array performance constraint, and can reduce the number of sensors and reduce the system hardware cost on the premise of obtaining higher resolution. The vector hydrophone sparse array distribution technology is beneficial to solving the problems of invalid array element repair and distributed multi-base sonar array distribution in the actual sonar array, and has important engineering value.
The aim of sparse array design is to find an array arrangement form of the minimum array element number meeting the array performance requirement, and the sparse array design is essentially to find the sparsest expression mode of signals. The compressive sensing theory is a theory developed aiming at the accurate reconstruction of sparse signals, and the fundamental purpose of the compressive sensing theory is to approximate signals in a highly nonlinear form in an over-complete dictionary and search the most sparse solution in a redundant state.
The existing sparse array technology usually adopts a random optimization algorithm to search a global optimal solution of the problems, the global optimal solution is easy to approach, but a large amount of time is needed for adjustment in the algorithm implementation process, and the actual engineering application is not facilitated.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention discloses a vector hydrophone sparse arraying method based on a compressive sensing theory, which mainly comprises the following steps:
(1) determining a vector hydrophone combination directivity and composite array directivity function:
in the ocean waveguide, since a vertical direction is a standing wave, two-dimensional directivity in a horizontal direction is generally considered. The sound pressure and vibration speed channel output signals of a single vector hydrophone are utilized to obtain and combine to form a directivity function R (f, theta), wherein f is the center frequency of the hydrophone, and theta is the horizontal azimuth angle. The sound pressure signal is recorded as p, the vibration velocity signal is recorded as v, and the vibration velocity sensors can form dipole directivity in a three-dimensional space. According to a single vector hydrophoneCombining the directivity functions R (F, theta) to determine a composite array directivity function F consisting of a plurality of vector hydrophonesm(f, θ) expressed by
Fm(f，θ)＝R(f，θ)·F(f，θ)
Wherein F (F, theta) is a directivity function of the sound pressure scalar array.
(2) Constructing a directional beam of a vector hydrophone array target:
according to the performance requirements of the sonar system, a vector hydrophone array target directive beam convex optimization problem model meeting performance constraints is constructed
Figure GSB0000186322680000021
In the formula [ theta ]0Indicating the main beam pointing position, U indicating the desired side lobe peak of the predetermined region, and the optimization objective τ indicating the maximum response amplitude of the remaining unconstrained region. w represents the vector acoustic array weight excitation matrix and A represents the vector acoustic array manifold vector.
Solving method of convex optimization problem to obtain target directional beam F of vector acoustic arraym(f, theta), and the corresponding array excitation weight is w0。
(3) Constructing a sparse vector hydrophone array problem model:
according to the array spacing requirement of the sonar vector acoustic array, a virtual spacing d is constructed0The corresponding vector acoustic array manifold is A0Flow shape and virtual spacing d of vector acoustic array0Is expressed as
Figure GSB0000186322680000031
M represents the number of hydrophones of the virtual vector acoustic array, and lambda represents the wavelength corresponding to the central operating frequency of the acoustic array.
According to the vector sound array directional beam F obtained in the step (2)m(f, theta), constructing a sparse vector hydrophone array constraint equation, and further utilizing sparse vector waterThe hydrophone array manifold A is used as a sensing matrix, and a minimum 0 norm problem model of a sparse vector hydrophone array can be obtained
Figure GSB0000186322680000032
(4) Sparse reconstruction of the vector hydrophone array:
solving a constraint equation of the sparse vector hydrophone array by using an orthogonal matching pursuit algorithm, and performing sparse reconstruction on the vector hydrophone array, wherein the sparse reconstruction mainly comprises the following steps:
(4.1) initialization: residual r0＝Fm(f, θ), index set
Figure GSB0000186322680000033
Incremental matrix phi0For an empty matrix, the number of iterations gen is 1, and the desired sparsity is set to K.
(4.2) finding residual error r and sensing matrix AjThe index t corresponding to the maximum projection coefficient, i.e. t ═ argmaxj＝1，2，L，N|<rgen-1，Aj>And | N represents the number of virtual hydrophones.
(4.3) updating index set Λgen＝Λgen-1∪ { t }, records the reconstructed set of atoms Φ in the indexed sensing matrixgen＝[Φgen-1，At]And deleting the column corresponding to the subscript t of the sensing matrix.
(4.4) obtaining a sparse approximation solution by least squares
Figure GSB0000186322680000034
(4.5) updating residual
Figure GSB0000186322680000035
(4.6) judging whether the iteration times meet the condition that gen is larger than K, if so, stopping iteration and outputting the final index set position and the sparse approximation solution, otherwise, turning to the step (4.2).
Compared with the prior art, the invention has the following advantages:
(1) the method is based on a vector hydrophone array sparse array mechanism, combines convex optimization and compressive sensing theories, utilizes the sensing relation between sparse array positions and target array beams, adopts a non-uniform spacing array mode to reconstruct the target beams, and can obtain an accurate sparse array result.
(2) The vector sparse array arrangement method provided by the invention can automatically set the number of hydrophones in an expected sparse vector array according to the performance requirement of the system, and can accurately control the complexity of the system.
(3) The vector sparse array arrangement method provided by the invention adopts the orthogonal matching pursuit algorithm, the obtained sparse approximation result is fixed, multiple times of debugging are not needed, a large amount of algorithm adjusting time can be saved, and the method is more suitable for the practical application of engineering.
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FIG. 1 is a flow chart of the sparse arraying method of vector hydrophones according to the present invention;
FIG. 2 is a convex optimized beam pattern for a conventional dense vector hydrophone array;
FIG. 3 is a diagram showing a vector hydrophone array excitation weight distribution after sparse arrangement;
fig. 4 is a sparse vector hydrophone array directional beam pattern.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 is a flow chart of a sparse arraying method for vector hydrophones based on teaching and learning optimization, based on which, the sparse arraying is performed on the most common linear arrays in the sonar field, and the main steps are as follows:
(1) determining a vector hydrophone combination directivity and composite array directivity function:
obtaining a directional function R (f, theta) formed by combining sound pressure and vibration speed channel output signals of a single vector hydrophone, wherein f is the center frequency of the vector hydrophone, theta is the horizontal azimuth angle, the sound pressure signal is recorded as p, the vibration speed signal is recorded as v, and the combined directivity is
Figure GSB0000186322680000041
In the formula
Figure GSB0000186322680000042
To guide orientation, vcFor combining the vibration velocities, from two orthogonal vibration velocity components vxAnd vyIs formed by combining the following formula
Figure GSB0000186322680000051
In the example, the most common half-wavelength uniform linear array in the sonar field is considered, the number of array elements is 32, the central frequency of the vector hydrophone array is 7.5kHz, the focusing direction of the main beam is 90 degrees, and the spacing between the array elements is
Figure GSB0000186322680000052
Determining a composite array directivity function F consisting of a plurality of vector hydrophones according to the combined directivity function R (F, theta) of the single vector hydrophonem(f, θ) expressed by
Fm(f，θ)＝R(f，θ)·F(f，θ)
Wherein F (F, theta) is a directivity function of a sound pressure scalar array and is expressed as
Figure GSB0000186322680000053
(2) Constructing a directional beam of a vector hydrophone array target:
according to the performance requirements of the sonar system, a vector hydrophone array target directive beam convex optimization problem model meeting performance constraints is constructed
Figure GSB0000186322680000054
In the formula [ theta ]0Indicating the main beam pointing position, U indicating the desired side lobe peak of the predetermined region, and the optimization objective τ indicating the maximum response amplitude of the remaining unconstrained region. w represents the vector acoustic array weight excitation matrix and A represents the vector acoustic array manifold vector. The side lobe region is set to [0, 85 ° ] in this example]∪[95°，360°]。
Solving method of convex optimization problem to obtain target directional beam F of vector acoustic arraym(f, theta), and the corresponding array excitation weight is w0. The comparison between the convex optimized vector acoustic array directional beam pattern and the original array directional beam pattern is shown in fig. 2, the side lobe peak value of the original array is-13.3 dB, and the side lobe peak value after optimization is-26.13 dB.
(3) Constructing a sparse vector hydrophone array problem model:
according to the array spacing requirement of the sonar vector acoustic array, a virtual spacing d is constructed0The corresponding vector acoustic array manifold is A0Flow shape and virtual spacing d of vector acoustic array0Is expressed as
Figure GSB0000186322680000061
M represents the number of hydrophones of the virtual vector acoustic array, and lambda represents the wavelength corresponding to the central operating frequency of the acoustic array. The virtual pitch of the vector acoustic array in this example is set to d0λ/40 is 0.05cm, and the corresponding number of virtual array elements is 621.
According to the vector sound array directional beam F obtained in the step (2)m(f, theta), constructing a constraint equation of the sparse vector hydrophone array, and further, obtaining a minimum 0 norm problem model of the sparse vector hydrophone array by using the manifold A of the sparse vector hydrophone array as a sensing matrix
Figure GSB0000186322680000062
(4) Sparse reconstruction of the vector hydrophone array:
solving a constraint equation of the sparse vector hydrophone array by using an orthogonal matching pursuit algorithm, and performing sparse reconstruction on the vector hydrophone array, wherein the sparse reconstruction mainly comprises the following steps:
(4.1) initialization: residual r0＝Fm(f, θ), index set
Figure GSB0000186322680000063
Incremental matrix phi0For an empty matrix, the iteration number gen is 1, and the desired sparsity is set to K24, that is, the number of hydrophones in the desired sparse vector acoustic array is 24.
(4.2) finding residual error r and sensing matrix AjThe index t corresponding to the maximum projection coefficient, i.e. t ═ argmaxj＝1，2，L，N|<rgen-1，Aj>And | N represents the number of virtual hydrophones.
(4.3) updating index set Λgen＝Λgen-1∪ { t }, records the reconstructed set of atoms Φ in the indexed sensing matrixgen＝[Φgen-1，At]And deleting the column corresponding to the subscript t of the sensing matrix.
(4.4) obtaining a sparse approximation solution by least squares
Figure GSB0000186322680000064
(4.5) updating residual
Figure GSB0000186322680000065
(4.6) judging whether the iteration times meet the condition that gen is larger than K, if so, stopping iteration and outputting the final index set position and the sparse approximation solution, otherwise, turning to the step (4.2).
The number of hydrophones in the sparse vector array finally obtained in the present example is 24, the excitation weight distribution is shown in fig. 3, and fig. 4 is a directional beam pattern of the sparse vector hydrophone array. According to the final sparse array arrangement result, the sparse vector array has the advantages that the number of hydrophones is reduced by 25% compared with the original array, the maximum side lobe peak value is reduced to-24.33 dB from the original-13.3 dB, and the better side lobe suppression effect is achieved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (2)

1. A vector hydrophone sparse arraying method based on a compressed sensing theory is characterized by comprising the following steps:
(1) determining a vector hydrophone combination directivity and composite array directivity function:
in the ocean waveguide, since the vertical direction is a standing wave, the two-dimensional directivity in the horizontal direction is generally considered; utilizing the sound pressure and vibration speed channel output signals of a single vector hydrophone to obtain and combine to form a directivity function R (f, theta), wherein f is the hydrophone center frequency, and theta is a horizontal azimuth angle; the sound pressure signal is marked as p, the vibration velocity signal is marked as v, and the vibration velocity sensors can form dipole directivity in a three-dimensional space; determining a composite array directivity function F consisting of a plurality of vector hydrophones according to the combined directivity function R (F, theta) of the single vector hydrophonem(f, θ) expressed by
Fm(f，θ)＝R(f，θ)·F(f，θ)
Wherein F (F, theta) is a directivity function of the sound pressure scalar array;
(2) constructing a directional beam of a vector hydrophone array target:
according to the performance requirements of the sonar system, a vector hydrophone array target directive beam convex optimization problem model meeting performance constraints is constructed
Figure FSB0000186322670000011
s.t|wA(θ0)|＝＝1
||wA(θ)||≤U，{θ}∈SL
In the formula [ theta ]0Indicating the main beam pointing position, U indicating the period of the predetermined zoneThe peak value of the expectation sidelobe, and the optimization target tau represents the maximum response amplitude of the rest unconstrained region; w represents a vector acoustic array weight excitation matrix, and A represents a vector acoustic array manifold vector;
solving method of convex optimization problem to obtain target directional beam F of vector acoustic arraym(f, theta), and the corresponding array excitation weight is w0；
(3) Constructing a sparse vector hydrophone array problem model:
according to the array spacing requirement of the sonar vector acoustic array, a virtual spacing d is constructed0The corresponding vector acoustic array manifold is A0Flow shape and virtual spacing d of vector acoustic array0Is expressed as
Figure FSB0000186322670000021
M represents the number of hydrophones of the virtual vector acoustic array, and lambda represents the wavelength corresponding to the central working frequency of the acoustic array;
according to the vector sound array directional beam F obtained in the step (2)m(f, theta), constructing a constraint equation of the sparse vector hydrophone array, and further, obtaining a minimum 0 norm problem model of the sparse vector hydrophone array by using the manifold A of the sparse vector hydrophone array as a sensing matrix
Figure FSB0000186322670000022
(4) Sparse reconstruction of the vector hydrophone array:
and solving a constraint equation of the sparse vector hydrophone array by using an orthogonal matching pursuit algorithm, and performing sparse reconstruction on the vector hydrophone array.
2. The sparse vector hydrophone arraying method based on the compressed sensing theory as claimed in claim 1, wherein the sparse reconstruction mainly comprises the following steps:
(4.1) initialization: residual r0＝Fm(f, θ), index set
Figure FSB0000186322670000023
Incremental matrix phi0For an empty matrix, the iteration number gen is 1, and the desired sparsity is set to be K;
(4.2) finding residual error r and sensing matrix AjThe index t corresponding to the maximum projection coefficient, i.e. t ═ argmaxj＝1，2，L，N|<rgen-1，Aj>L, N represents the number of virtual hydrophones;
(4.3) updating index set Λgen＝Λgen-1∪ { t }, records the reconstructed set of atoms Φ in the indexed sensing matrixgen＝[Φgen-1，At]Deleting the column corresponding to the subscript t of the sensing matrix;
(4.4) obtaining a sparse approximation solution by least squares
Figure FSB0000186322670000024
(4.5) updating residual
Figure FSB0000186322670000025
(4.6) judging whether the iteration times meet the condition that gen is larger than K, if so, stopping iteration and outputting the final index set position and the sparse approximation solution, otherwise, turning to the step (4.2).
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