CN115542329B - Shallow water low-frequency sound source depth judgment method based on modal filtering - Google Patents
Shallow water low-frequency sound source depth judgment method based on modal filtering Download PDFInfo
- Publication number
- CN115542329B CN115542329B CN202211226929.7A CN202211226929A CN115542329B CN 115542329 B CN115542329 B CN 115542329B CN 202211226929 A CN202211226929 A CN 202211226929A CN 115542329 B CN115542329 B CN 115542329B
- Authority
- CN
- China
- Prior art keywords
- subspace
- matrix
- sound source
- space
- depth
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- 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
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
- G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
- G01S15/06—Systems determining the position data of a target
- G01S15/42—Simultaneous measurement of distance and other co-ordinates
-
- 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
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
- G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
- G01S15/06—Systems determining the position data of a target
- G01S15/46—Indirect determination of position data
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
- Y02A90/30—Assessment of water resources
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Mathematical Physics (AREA)
- Mathematical Optimization (AREA)
- Data Mining & Analysis (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Analysis (AREA)
- Computer Networks & Wireless Communication (AREA)
- Acoustics & Sound (AREA)
- Pure & Applied Mathematics (AREA)
- Computational Mathematics (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Computing Systems (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
Abstract
Mode-based filterA shallow water low frequency sound source depth judgment method of wave belongs to the technical field of shallow water low frequency water surface underwater target judgment. The invention aims at solving the problems that the existing water surface underwater depth resolution method based on the modal filtering technology adopted by the prior hydrophone array aperture limitation judgment sound source depth cannot simultaneously consider no subspace overlapping and complete modal space. Comprising establishing a sound field p (r, z r ,z s ) An expression for the observation matrix V and the modal amplitude matrix a; dividing the observation matrix V into notch subspaces V 0 And free subspace V 1 Singular value decomposition is carried out to obtain a rank-reduced subspace U 0 And U 1 And forming a matrix A, obtaining an orthogonal matrix beta, determining a space H and a space S, comparing the energy projected in the notch subspace with the energy projected in the whole orthogonal mode space to obtain detection statistics, comparing with a selected threshold, and judging the sound source depth. The method is used for sound source depth judgment.
Description
Technical Field
The invention relates to a shallow water low frequency sound source depth judgment method based on modal filtering, and belongs to the technical field of shallow water low frequency water surface underwater target judgment.
Background
The shallow water depth judgment technology based on modal characteristics is an important method in the classification of underwater targets on water surface, and especially when the aperture of a hydrophone array is limited, the high judgment estimation of the sound source depth cannot be carried out. The shallow water depth judgment technology based on the modal characteristics can not give the specific depth of the target, but can judge whether the target is on the water surface or under the water, and has application in aspects such as anti-submergence to marine biology.
From the adiabatic approximation theory of a simple wave, for shallow water low frequency sound sources, the sound pressure at a certain receiving location can be represented by a series of Jian Zhengbo stacks. The normal wave is influenced by various environments, and the main principle of the energy distribution of each order mode of the normal wave is the depth of a sound source and a receiving position. The vincent.e Premus simplifies the sound source localization part based on the matching field processing (Matched Field Processing, MFP) method, thereby changing the sound source localization problem into a two-classification problem of target depth decision. According to the characteristic that a shallow source is difficult to excite a low-order mode, a mode space is divided into a notch subspace and a free subspace, and the energy ratio projected in the two subspaces is used as statistics to judge a water surface and an underwater target.
In practice, however, neither horizontal nor vertical arrays of hydrophones often achieve the aperture required for normal decision making, with overlap between modal subspaces, resulting in reduced algorithm performance. In order to solve the problem, the Vincent.E Premus applies a Scharf-Friedlander matched subspace detector to a modal filtering method to obtain a matched subspace decision device (Matched Subspace Discriminator, MSD), and orthogonal non-overlapping notch and free subspaces are obtained through the Scharf and Friedlander methods, so that the performance of the decision device is improved. Ewen Conan multiplies the received sound pressure by the inverse of the observation matrix to obtain a modal amplitude vector of the notch and the free subspace, and the energy proportion projected in the notch space is calculated through the modal amplitude vector to be used as a judgment statistic. However, in the existing method, normal data of the subspace is removed at the same time when the subspace overlap is removed, so that a judgment result is affected.
In the shallow water waveguide, the mode distribution of the simple wave is closely related to the depth of the sound source, and the mode intensity of each order is difficult to directly obtain by the method, but the energy passing through the projection subspace can judge that the target is positioned under the water surface. Therefore, how to obtain a robust target decision algorithm when the aperture is limited is to be appreciated.
Disclosure of Invention
Aiming at the problem that the existing water surface underwater depth resolution method based on the modal filtering technology adopted when the aperture of the existing hydrophone array is limited can not simultaneously consider the subspace overlapping and the integrity of the modal space, the invention provides a shallow water low frequency sound source depth judgment method based on modal filtering.
The invention relates to a shallow water low-frequency sound source depth judgment method based on modal filtering, which comprises the following steps of,
setting the underwater depth of the sound source to be z s At underwater depth z r Acquisition of the sound source z through hydrophone array on the horizontal plane of the position s Sound field p (r, z) at horizontal distance r r ,z s ) The sound field p (r, z r ,z s ) Is an expression for the observation matrix V and the modal amplitude matrix a;
dividing the observation matrix V into notch subspaces V 0 And free subspace V 1 The method comprises the steps of carrying out a first treatment on the surface of the For notch subspace V 0 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 0 For free subspace V 1 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 1 The method comprises the steps of carrying out a first treatment on the surface of the Rank reduction subspace U 0 And rank reduction subspace U 1 Forming a matrix A;
processing the matrix A to obtain an orthogonal matrix beta; according to the rank reduction subspace U 0 And rank reduction subspace U 1 Dividing an orthogonal matrix beta into a space H and a space S, wherein the space H corresponds to an orthogonalized notch subspace, and the space S corresponds to an orthogonalized free subspace;
calculating a projection matrix P of the space H H Projection matrix P of sum space S S The method comprises the steps of carrying out a first treatment on the surface of the Then calculating to obtain the signal energy E of the hydrophone array received signal W projected in the space H H And projected onSignal energy E of space S S The method comprises the steps of carrying out a first treatment on the surface of the The signal energy E H For projection of energy in the notch subspace, E H +E S The sum of (2) is the energy projected in the whole orthogonal mode space; and comparing the energy projected in the notch subspace with the energy projected in the whole orthogonal mode space to obtain detection statistics, and comparing the detection statistics with a selected threshold, if the detection statistics are larger than the selected threshold, judging that the sound source is a submerged source, otherwise, judging that the sound source is a surface source.
According to the shallow water low-frequency sound source depth judgment method based on modal filtering, the underwater depth z r Greater than the underwater depth z s 。
According to the shallow water low-frequency sound source depth judgment method based on modal filtering, the sound field p (r, z) r ,z s ) The expression of (2) is:
where X (f) is the amplitude of the sound field at frequency f, j is the imaginary number, ρ (z s ) The water density of the sound source is M, the number of modes of the sound field propagating in the environment is M, and M is the ordinal number of the modes;
as a mode function of mode m with respect to depth, k rm The horizontal wavenumber for mode m.
According to the shallow water low-frequency sound source depth judgment method based on modal filtering, the horizontal wave number k of the mode m rm The method comprises the following steps:
wherein k is a constant value, and the formula is shown in the specification,
ω is the angular frequency of the sound source signal, c is the maximum sound velocity in the sound velocity gradient, ω=2pi,/and->
Is the vertical wavenumber of mode m.
According to the shallow water low-frequency sound source depth judgment method based on modal filtering, a hydrophone array is set to be an N-element horizontal array, and a sound source r is distant from the hydrophone array 1 ,r 2 ,…,r N The position samples the sound field, and the hydrophone array receives a signal W as a vector of the sound field p:
W＝Va；
r i ＝r 1 +(i-1)d cosθ,i＝1,2,…,N，
wherein d is the array element spacing, and θ is the included angle between the sound source and the hydrophone array in the horizontal direction;
dividing the observation matrix V into notch subspaces V 0 And free subspace V 1 And the modal amplitude matrix a is divided into a notch subspace V 0 Corresponding modal amplitude a 0 And with free subspace V 1 Corresponding modal amplitude a 1 The method comprises the following steps of:
wherein the column vector V of the matrix V is observed m The method comprises the following steps:
wherein R is R i A vector of components;
the modal amplitude matrix a is:
a＝[a 1 ,a 2 ,…,a M ] T ,
wherein κ is a constant:
according to the shallow water low-frequency sound source depth judgment method based on modal filtering, a hydrophone array receiving signal W is regarded as a corresponding to each mode m The weight vector of each mode is the column vector V of the observation matrix V m The method comprises the steps of carrying out a first treatment on the surface of the Let us assume a notch subspace V 0 The number of modes is M 0 Then:
in the middle of
To correspond to notch subspace V 0 M of (2) 0 Individual column vectors>
To correspond to the modal amplitude a 0 M of (2) 0 An element; />
To correspond to the free subspace V 1 M-M of (2) 0 Individual column vectors>
To correspond to the modal amplitude a 1 M-M of (2) 0 An element;
for notch subspace V 0 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 0 ：
U 0 ∈C N×q ，
Wherein C is complex matrix set, q is reduced rank subspace U 0 The number of columns of (a);
for free subspace V 1 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 1 ：
U 1 ∈C N×t ，
Wherein t is a rank reduction subspace U 1 The number of columns of (a);
and then obtaining a matrix A:
A＝[U 0 U 1 ]。
the shallow water low-frequency sound source depth judgment method based on modal filtering is used for eliminating a rank reduction subspace U 0 And rank reduction subspace U 1 Is orthogonal processed to two rank reduction subspaces, so that rank reduction subspace U 0 And rank reduction subspace U 1 Is spread out as a set of orthogonal basis of observation space:
according to matrix a= [ U ] 0 U 1 ]，
Matrix A εC N×(q+t) Column vector [ u ] 1 ,…,u q+t ]For a set of linearly independent vectors of the observation space, then there is an orthogonal matrix β:
β＝[β 1 ,…,β q+t ]，
let A= [ beta ] 1 ,…,β q+t ]B A ，
In B of A The unit is a triangular array:
B A ∈C (q+t)×(q+t) ；
column vector [ u ] 1 ,…,u q+t ]The relationship with the orthogonal matrix β is as follows:
according to the shallow water low-frequency sound source depth judgment method based on modal filtering, according to the rank reduction subspace U 0 And rank reduction subspace U 1 Dividing the orthogonal matrix β into space H and space S:
this gives:
the space formed by column vectors of span (·) expression in the formula.
According to the shallow water low-frequency sound source depth judgment method based on modal filtering, the projection y of the hydrophone array receiving signal W on the space H H And projection y onto space S S The method comprises the following steps:
the hydrophone array receives signal energy E projected in space H from signal W H And signal energy E projected in space S S The method comprises the following steps of:
E H ＝tr(W H P H W)
E S ＝tr(W H P S W)
wherein tr (. Cndot.) represents the trace of the matrix, W H Is the conjugate transpose of W.
According to the shallow water low-frequency sound source depth judgment method based on modal filtering, the detection statistic is L (z) s )：
The selected threshold is η:
if L (z) s ) If eta is less than or equal to eta, the sound source is a surface source;
if L (z) s )>η, the sound source is a inundation source.
The invention has the beneficial effects that: the method of the invention divides the mode space into a notch and a free subspace according to the fact that a shallow source is difficult to excite a low-order mode in the sound velocity profile environment with a negative jump layer. The non-overlapping notch mode subspace and free mode subspace are obtained through a Schmidt orthogonal method, so that the subspace overlapping caused by insufficient array aperture is eliminated, and meanwhile, the integrity of the mode space is maintained. A decision is made as to whether the sound source is on the water surface or under water by the energy ratio projected in the notch subspace and the free subspace.
Drawings
FIG. 1 is a schematic diagram of a shallow water low frequency sound source depth decision method based on modal filtering according to the invention; SVD in the figure represents singular value decomposition; schmidt represents the Schmidt orthometric method;
FIG. 2 is a cross-sectional view of sound velocity at 160m of simulated ambient water depth;
fig. 3 is a graph of detection statistics as a function of sound source depth.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
The invention provides a shallow water low frequency sound source depth judging method based on modal filtering, which comprises the following steps of,
setting the underwater depth of the sound source to be z s At underwater depth z r Acquisition of the sound source z through hydrophone array on the horizontal plane of the position s Sound field p (r, z) at horizontal distance r r ,z s ) The sound field p (r, z r ,z s ) Is an expression for the observation matrix V and the modal amplitude matrix a;
dividing the observation matrix V into notch subspaces V 0 And free subspace V 1 The method comprises the steps of carrying out a first treatment on the surface of the For notch subspace V 0 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 0 For free subspace V 1 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 1 The method comprises the steps of carrying out a first treatment on the surface of the Rank reduction subspace U 0 And rank reduction subspace U 1 Forming a matrix A;
processing the matrix A to obtain an orthogonal matrix beta; according to the rank reduction subspace U 0 And rank reduction subspace U 1 Dividing an orthogonal matrix beta into a space H and a space S, wherein the space H corresponds to an orthogonalized notch subspace, and the space S corresponds to an orthogonalized free subspace;
calculating a projection matrix P of the space H H Projection matrix P of sum space S S The method comprises the steps of carrying out a first treatment on the surface of the Then calculating to obtain the signal energy E of the hydrophone array received signal W projected in the space H H And signal energy E projected in space S S The method comprises the steps of carrying out a first treatment on the surface of the The signal energy E H For projection of energy in the notch subspace, E H +E S The sum of (2) is the energy projected in the whole orthogonal mode space; and comparing the energy projected in the notch subspace with the energy projected in the whole orthogonal mode space to obtain detection statistics, and comparing the detection statistics with a selected threshold, if the detection statistics are larger than the selected threshold, judging that the sound source is a submerged source, otherwise, judging that the sound source is a surface source.
As an example, the underwater depth z r Greater than the underwater depth z s 。
Further, according to the adiabatic approximation theory of a simple wave, in a shallow water waveguide, at a depth z s Is at depth z r Excitation sound field p (r, z r ,z s ) The expression of (2) is:
where X (f) is the amplitude of the sound field at frequency f, j is the imaginary number, ρ (z s ) The water density of the sound source is M, the number of modes of the sound field propagating in the environment is M, and M is the ordinal number of the modes;
as a mode function of mode m with respect to depth, k rm The horizontal wavenumber for mode m.
Horizontal wavenumber k of mode m rm The method comprises the following steps:
wherein k is a constant value, and the formula is shown in the specification,
ω is the angular frequency of the sound source signal, c is the maximum sound velocity in the sound velocity gradient, ω=2pi,/and->
Is the vertical wavenumber of mode m.
In view of the simplified model, a single frequency signal is used in the derivation, so X (f),
k rm m these frequency-dependent parameters can be regarded as constants.
Setting hydrophone array as N-element horizontal array and depth as z r At a distance from the sound source r 1 ,r 2 ,…,r N The position samples the sound field, and under the condition of not considering noise, the hydrophone array received signal W is a vector of the sound field p, expressed as:
W＝Va；
r i ＝r 1 +(i-1)d cosθ,i＝1,2,…,N，
wherein d is the array element spacing, and θ is the included angle between the sound source and the hydrophone array in the horizontal direction;
in shallow water environments with negative transitions, low-order modes that are difficult to excite by shallow sources are called notch modes (trap modes), and modes with phase velocities less than the maximum speed of sound in water are defined as notch modes. Dividing the observation matrix V into notch subspaces V 0 And free subspace V 1 And the modal amplitude matrix a is divided into a notch subspace V 0 Corresponding modal amplitude a 0 And with free subspace V 1 Corresponding modal amplitude a 1 The method comprises the following steps of:
wherein the column vector V of the matrix V is observed m The method comprises the following steps:
wherein R is R i A vector of components;
the modal amplitude matrix a is:
a＝[a 1 ,a 2 ,…,a M ] T ,
wherein κ is a constant:
still further, the hydrophone array received signal W is regarded as a corresponding to each mode m The weight vector of each mode is the column vector V of the observation matrix V m The method comprises the steps of carrying out a first treatment on the surface of the From the expression of the modal amplitude matrix a, a is known when the depth and aperture of the horizontal receiving array are known m The size of (2) depends on the sound source depth z s 。
Let us assume a notch subspace V 0 The number of modes is M 0 Then:
in the middle of
To correspond to notch subspace V 0 M of (2) 0 Individual column vectors>
To correspond to the modal amplitude a 0 M of (2) 0 An element; />
To correspond to the free subspace V 1 M-M of (2) 0 Individual column vectors>
To correspond to the modal amplitude a 1 M-M of (2) 0 An element;
for notch subspace V 0 Singular value decomposition is carried out, and a main eigenvalue vector is taken to obtain a linear independent rank reduction subspace U 0 ：
U 0 ∈C N×q ，
Wherein C is complex matrix set, q is reduced rank subspace U 0 The number of columns of (a);
for free subspace V 1 Singular value decomposition is carried out, and a main eigenvalue vector is taken to obtain a linear independent rank reduction subspace U 1 ：
U 1 ∈C N×t ，
Wherein t is a rank reduction subspace U 1 The number of columns of (a);
in U 0 And U 1 Is the column vector direction of (1), subspace V 0 And V 1 With the greatest energy.
And then obtaining a matrix A:
A＝[U 0 U 1 ]。
to eliminate rank reduction subspace U 0 And rank reduction subspace U 1 Is orthogonal processed to two rank reduction subspaces, so that rank reduction subspace U 0 And rank reduction subspace U 1 Is spread out as a set of orthogonal basis of observation space:
according to matrix a= [ U ] 0 U 1 ]，
Matrix A εC N×(q+t) Column vector [ u ] 1 ,…,u q+t ]For a set of linearly independent vectors of the observation space, then there is an orthogonal matrix β:
β＝[β 1 ,…,β q+t ]，
let A= [ beta ] 1 ,…,β q+t ]B A ，
In B of A The diagonal elements of the triangular matrix on the unit are all 1:
B A ∈C (q+t)×(q+t) ；
column vector [ u ] 1 ,…,u q+t ]The relationship with the orthogonal matrix β is as follows:
based on the above formula, a set of orthogonal basis [ beta ] that is tensed into space A can be obtained 1 ,…,β q+t ]。
According to the rank reduction subspace U 0 And rank reduction subspace U 1 Dividing the orthogonal matrix beta into a space H and a space S, and respectively corresponding to the orthogonalized notch and the free subspace:
thus two orthogonal subspaces are obtained which are non-overlapping and constitute the whole modal space:
the space formed by column vectors of span (·) expression in the formula.
The array received signal is projected onto the processed notch subspace H and the free subspace S. Projection matrix P of space Y Y Can be calculated by the following formula:
P Y ＝Y(Y H Y) -1 Y H and has P Y ＝P Y *P Y 。
Thereby obtaining projection y of hydrophone array received signal W on space H H And projection y onto space S S The method comprises the following steps:
the hydrophone array receives signal energy E projected in space H from signal W H And signal energy E projected in space S S The method comprises the following steps of:
E H ＝tr(W H P H W)
E S ＝tr(W H P S W)
wherein tr (. Cndot.) represents the trace of the matrix, W H Is the conjugate transpose of W.
The depth decision problem is reduced to a binary hypothesis problem, hypothesis H 0 Indicating that the sound source is near the water surface, which is a surface source, assuming H 1 For the sound source to be under water, for the submerged source. As shown below
Z in lim For the judgment depth, generally 5-10 m is taken. From the expression of the modal amplitude matrix a, it is known that the energy distribution in modal space is mainly affected by the sound source depth when the target is in the far field. Because the surface source is difficult to couple to the low order modes, if more energy is detected in the high order mode subspace, the sound source is the surface source, whereas the sound source is the submerged source. From this, the ratio of the projected energy into the notch subspace and the free subspace can be established as a detection statistic
The detection statistic is L (z) s )：
The selected threshold is η:
if L (z) s ) If eta is less than or equal to eta, the sound source is a surface source;
if L (z) s )>η, the sound source is a inundation source.
Because the two orthogonal subspaces in the method form a complete modal space, almost no energy is lost; in the conventional VE method, the subspace projection is used, and the overlapping part of the two subspaces is finally discarded, so that the received signal energy projected on the overlapping part is discarded theoretically. Therefore, the method of the invention obtains more accurate detection results.
At a certain energy of the received signal, z s ≤z lim When the sound source is difficult to couple to the low-order mode, the energy is concentrated in the free subspace S of the high-order mode, L (z) s ) Should be small in this sound source depth range. The sound velocity profile at 160m of simulated ambient water depth is shown in fig. 2. The sound source frequency is 353Hz, a 20-element uniform linear array is fixed on the water bottom, the array element spacing is 15m, and the sound source is positioned in the array end-fire direction for the convenience of analysis.
In fig. 2, p1, p6, and p16 are phase velocities corresponding to modes 1, 6, and 16, respectively. Only the mode phase velocity is greater than the depth of sound velocity, the mode will propagate normally. In this environment, L (z s ) As shown in fig. 3, the energy ratio L (z s ) Minimum; in a depth range where the sound source depth is larger than the decision depth, the energy ratio L (z s ) Continuously changing, the energy ratio of the surface source is larger than that of the surface source at the position close to the water bottom and gradually decreases along with the depth. Similar features exist in other frequencies and environments with negative gradients of sound velocity. Thus, in the process of the invention L (z) s ) As detection statistics are possible. In choosing the decision depth, reference may be made to L (z s ) A curve that varies with the depth of the sound source.
The performance of the algorithm is evaluated using the receiver operating characteristic ROC, where detection refers to the detection of a submerged source. Then, the probability P of detection d To determine the submerged source as the probability of submerged source, the false alarm probability P f Refers to the probability of determining a surface source as a submerged source. In other words, the detection probability P d Can be used as a measure of the judgment capability of the submerged source by an algorithm, and the judgment capability of the submerged source can be 1-P f As an evaluation index. When the threshold is selected, the ROC curve can be referred to, and the corresponding threshold can be selected according to the preset false alarm probability. Sound source depth by decision index and thresholdAnd (5) judging.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (9)
1. A shallow water low frequency sound source depth judging method based on modal filtering is characterized by comprising the following steps,
setting the underwater depth of the sound source to be z s At underwater depth z r Acquisition of the sound source z through hydrophone array on the horizontal plane of the position s Sound field p (r, z) at horizontal distance r r ,z s ) The sound field p (r, z r ,z s ) Is an expression for the observation matrix V and the modal amplitude matrix a;
dividing the observation matrix V into notch subspaces V 0 And free subspace V 1 The method comprises the steps of carrying out a first treatment on the surface of the For notch subspace V 0 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 0 For free subspace V 1 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 1 The method comprises the steps of carrying out a first treatment on the surface of the Rank reduction subspace U 0 And rank reduction subspace U 1 Forming a matrix A;
processing the matrix A to obtain an orthogonal matrix beta; according to the rank reduction subspace U 0 And rank reduction subspace U 1 Dividing an orthogonal matrix beta into a space H and a space S, wherein the space H corresponds to an orthogonalized notch subspace, and the space S corresponds to an orthogonalized free subspace;
calculating a projection matrix P of the space H H Projection matrix P of sum space S S The method comprises the steps of carrying out a first treatment on the surface of the Then the hydrophone array receiving signal W is obtained through calculation and projected in the space HSignal energy E of (2) H And signal energy E projected in space S S The method comprises the steps of carrying out a first treatment on the surface of the The signal energy E H For projection of energy in the notch subspace, E H +E S The sum of (2) is the energy projected in the whole orthogonal mode space; the energy projected in the notch subspace is compared with the energy projected in the whole orthogonal mode space to obtain detection statistics, the detection statistics are compared with a selected threshold, if the detection statistics are larger than the selected threshold, the sound source is judged to be a submerged source, and otherwise, the sound source is judged to be a surface source;
depth z under water r Greater than the underwater depth z s 。
2. The method for determining the depth of a shallow water low frequency sound source based on modal filtering as claimed in claim 1, wherein,
sound field p (r, z) r ,z s ) The expression of (2) is:
where X (f) is the amplitude of the sound field at frequency f, j is the imaginary number, ρ (z s ) The water density of the sound source is M, the number of modes of the sound field propagating in the environment is M, and M is the ordinal number of the modes;
as a mode function of mode m with respect to depth, k rm The horizontal wavenumber for mode m.
3. The method for determining the depth of a shallow water low frequency sound source based on modal filtering as claimed in claim 2, wherein,
horizontal wavenumber k of mode m rm The method comprises the following steps:
wherein k is a constant value, and the formula is shown in the specification,
ω is the angular frequency of the sound source signal, c is the maximum sound velocity in the sound velocity gradient, ω=2pi,/and->
Is the vertical wavenumber of mode m.
4. A shallow water low frequency sound source depth decision method based on modal filtering as claimed in claim 3, wherein,
setting hydrophone array as N-element horizontal array, and setting the hydrophone array to be distant from sound source r 1 ,r 2 ,…,r N The position samples the sound field, and the hydrophone array receives a signal W as a vector of the sound field p:
W＝Va；
r i ＝r 1 +(i-1)dcosθ,i＝1,2,…,N，
wherein d is the array element spacing, and θ is the included angle between the sound source and the hydrophone array in the horizontal direction;
dividing the observation matrix V into notch subspaces V 0 And free subspace V 1 And the modal amplitude matrix a is divided into a notch subspace V 0 Corresponding modal amplitude a 0 And with free subspace V 1 Corresponding modal amplitude a 1 The method comprises the following steps of:
wherein the column vector V of the matrix V is observed m The method comprises the following steps:
wherein R is R i A vector of components;
the modal amplitude matrix a is:
a＝[a 1 ,a 2 ,…,a M ] T ,
wherein κ is a constant:
5. the method for determining the depth of a shallow water low frequency sound source based on modal filtering as claimed in claim 4, wherein,
the hydrophone array received signal W is regarded as a corresponding to each mode m The weight vector of each mode is the column vector V of the observation matrix V m The method comprises the steps of carrying out a first treatment on the surface of the Let us assume a notch subspace V 0 The number of modes is M 0 Then:
in the middle of
To correspond to notch subspace V 0 M of (2) 0 Individual column vectors>
To correspond to the modal amplitude a 0 M of (2) 0 An element; />
To correspond to the free subspace V 1 M-M of (2) 0 Individual column vectors>
To correspond to the modal amplitude a 1 M-M of (2) 0 An element;
for notch subspace V 0 Singular value decompositionSolving to obtain a linearly independent rank reduction subspace U 0 ：
U 0 ∈C N×q ，
Wherein C is complex matrix set, q is reduced rank subspace U 0 The number of columns of (a);
for free subspace V 1 Singular value decomposition is carried out to obtain a linear independent rank reduction subspace U 1 ：
U 1 ∈C N×t ，
Wherein t is a rank reduction subspace U 1 The number of columns of (a);
and then obtaining a matrix A:
A＝[U 0 U 1 ]。
6. the method for determining the depth of a shallow water low frequency sound source based on modal filtering as claimed in claim 5, wherein,
to eliminate rank reduction subspace U 0 And rank reduction subspace U 1 Is orthogonal processed to two rank reduction subspaces, so that rank reduction subspace U 0 And rank reduction subspace U 1 Is spread out as a set of orthogonal basis of observation space:
according to matrix a= [ U ] 0 U 1 ]，
Matrix A εC N×(q+t) Column vector [ u ] 1 ,…,u q+t ]For a set of linearly independent vectors of the observation space, then there is an orthogonal matrix β:
β＝[β 1 ,…,β q+t ]，
let A= [ beta ] 1 ,…,β q+t ]B A ，
In B of A The unit is a triangular array:
B A ∈C (q+t)×(q+t) ；
column vector [ u ] 1 ,…,u q+t ]The relationship with the orthogonal matrix β is as follows:
7. the method for determining the depth of a shallow water low frequency sound source based on modal filtering as claimed in claim 6, wherein,
according to the rank reduction subspace U 0 And rank reduction subspace U 1 Dividing the orthogonal matrix β into space H and space S:
this gives:
the space formed by column vectors of span (·) expression in the formula.
8. The method for determining the depth of a shallow water low frequency sound source based on modal filtering as claimed in claim 7,
projection y of hydrophone array received signal W onto space H H And projection y onto space S S The method comprises the following steps:
the hydrophone array receives signal energy E projected in space H from signal W H And signal energy E projected in space S S The method comprises the following steps of:
E H ＝tr(W H P H W)
E S ＝tr(W H P S W)
wherein tr (. Cndot.) represents the trace of the matrix, W H Is the conjugate transpose of W.
9. The method for determining the depth of a shallow water low frequency sound source based on modal filtering as claimed in claim 8,
the detection statistic is L (z) s )：
The selected threshold is η:
if L (z) s ) If eta is less than or equal to eta, the sound source is a surface source;
if L (z) s ) > η, the sound source is a inundation source.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211226929.7A CN115542329B (en) | 2022-10-09 | 2022-10-09 | Shallow water low-frequency sound source depth judgment method based on modal filtering |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211226929.7A CN115542329B (en) | 2022-10-09 | 2022-10-09 | Shallow water low-frequency sound source depth judgment method based on modal filtering |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115542329A CN115542329A (en) | 2022-12-30 |
| CN115542329B true CN115542329B (en) | 2023-07-07 |
Family
ID=84732506
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211226929.7A Active CN115542329B (en) | 2022-10-09 | 2022-10-09 | Shallow water low-frequency sound source depth judgment method based on modal filtering |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115542329B (en) |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111914641A (en) * | 2020-06-30 | 2020-11-10 | 中国科学院声学研究所 | Target depth identification method and system based on modal intensity matching analysis |
Family Cites Families (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7471592B2 (en) * | 2005-05-10 | 2008-12-30 | The United States Of America As Represented By The Secretary Of The Navy | Method and apparatus for passive acoustic ranging |
| CN111273229B (en) * | 2020-02-18 | 2021-06-08 | 华南理工大学 | Underwater sound broadband scattering source positioning method based on low-rank matrix reconstruction |
| CN111273230B (en) * | 2020-03-02 | 2022-06-07 | 开放智能机器（上海）有限公司 | Sound source positioning method |
| CN111580078B (en) * | 2020-04-14 | 2022-09-09 | 哈尔滨工程大学 | Single hydrophone target identification method based on fusion modal flicker index |
| CN112965053B (en) * | 2020-12-04 | 2023-03-21 | 中国船舶重工集团公司第七一五研究所 | Shallow sea sound source depth resolution method based on matching of vertical array beam intensity |
| CN112946732B (en) * | 2021-02-02 | 2022-09-30 | 中国海洋大学 | Processing method and system for jointly suppressing multiple single cable of offshore stereo observation system |
| CN113411278A (en) * | 2021-07-07 | 2021-09-17 | 哈尔滨工程大学 | Equalization processing method of low-frequency underwater acoustic communication based on receiving array |
| CN114019452A (en) * | 2021-10-25 | 2022-02-08 | 中国船舶重工集团公司第七一五研究所 | Shallow sea target depth resolution method based on vertical beam spectrum space difference factor |
-
2022
- 2022-10-09 CN CN202211226929.7A patent/CN115542329B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111914641A (en) * | 2020-06-30 | 2020-11-10 | 中国科学院声学研究所 | Target depth identification method and system based on modal intensity matching analysis |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115542329A (en) | 2022-12-30 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110764053B (en) | Multi-target passive positioning method based on underwater sensor network | |
| Dosso et al. | Uncertainty estimation in simultaneous Bayesian tracking and environmental inversion | |
| Schmidt et al. | Environmentally tolerant beamforming for high‐resolution matched field processing: Deterministic mismatch | |
| US8428897B2 (en) | Method and apparatus for spectral cross coherence | |
| CN109188019B (en) | Three-dimensional wind speed and direction measuring method based on multiple signal classification algorithm | |
| CN102645265A (en) | Ship radiated noise level measuring method based on virtual time reversal mirror | |
| Li et al. | Time-reversal detection of multidimensional signals in underwater acoustics | |
| CN102692620A (en) | Underwater noise source high-robustness focusing positioning process suitable for shallow sea multipath environments | |
| Conan et al. | Using the trapped energy ratio for source depth discrimination with a horizontal line array: Theory and experimental results | |
| CN113030979B (en) | Method and device for detecting position depth of target object | |
| CN109001297B (en) | Method for measuring acoustic reflection coefficient of large-sample underwater acoustic material based on single-vector hydrophone | |
| US6424596B1 (en) | Method and apparatus for reducing noise from near ocean surface sources | |
| Zhou et al. | 2-D deconvolved conventional beamforming for a planar array | |
| JP7056212B2 (en) | Direction estimation method and equipment | |
| CN115542329B (en) | Shallow water low-frequency sound source depth judgment method based on modal filtering | |
| CN110320492B (en) | Low-complexity DOA estimation method based on symmetric characteristics of steering vectors | |
| US6525994B2 (en) | Tracking system and method of operation thereof | |
| Blanford et al. | Measurements and models of the correlation of redundant spatial coherence measurements for the incoherently scattered field | |
| CN115201821B (en) | Small target detection method based on strong target imaging cancellation | |
| CN113721184B (en) | Near-field signal source positioning method based on improved MUSIC algorithm | |
| CN115993591A (en) | Self-adaptive interference suppression method based on characteristic subspace judgment | |
| Bo et al. | Sequential inversion of self-noise using adaptive particle filter in shallow water | |
| Soares et al. | Environmental inversion using high-resolution matched-field processing | |
| Lu et al. | A simple method for depth estimation of a sound source at known range in the deep sea | |
| RU2650830C1 (en) | Device for obtaining information on noisy object in sea |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |