A deep sea reverberation suppression method based on generalized spatial filtering principle

Abstract

The application specifically relates to a deep-sea reverberation suppression method based on a generalized spatial filtering principle, which comprises the following steps: constructing a three-dimensional scattering function based on an incident grazing angle, a scattering grazing angle and a scattering azimuth angle; constructing seabed reverberation intensity received from a scatterer based on the three-dimensional scattering function; determining a peak moment of the reverberation intensity based on the attenuation characteristics of the seabed reverberation intensity; selecting a reverberation acoustic line at the peak moment and a target echo acoustic line, constructing an array reverberation copy vector according to the reverberation acoustic line, and constructing a target echo copy vector according to the target echo acoustic line; constructing a second-order cone programming model based on the reverberation copy vector and the echo copy vector, and solving the second-order cone programming model to obtain a generalized spatial filtering matrix; and suppressing the array reverberation signal by using the generalized spatial filtering matrix. The application considers the change of the reverberation characteristics caused by the uncertainty of the real marine environment, and has good robustness for the reverberation suppression method in the fluctuating deep-sea environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater acoustic detection, and particularly relates to a deep-sea reverberation suppression method based on a generalized spatial filtering principle. BACKGROUND

[0002] In related technologies, ocean reverberation is a phenomenon formed by the superposition of scattered waves generated by a large number of irregular scatterers at a receiving point, and is one of the main factors restricting the performance of active sonar detection. In a deep-sea environment, due to the multiple bounce effect of the transmitted sound wave between the sea bottom and the sea surface, periodic strong reverberation is generated, which causes a large number of detection blind areas in the near range when the active sonar is detected at high power. Therefore, it is of great significance to suppress the deep-sea strong periodic reverberation interference for target detection. Unlike the slow attenuation characteristics in shallow water, the deep-sea reverberation has a significant periodic characteristic due to the deep-sea transmission effect, the multiple round-trip bounce between the sea bottom and the sea surface, and a high local intensity, forming a deep-sea near-range detection blind area. Reverberation suppression has received extensive attention in the field of target acoustic detection, but current research mainly focuses on shallow water with relatively stable reverberation, and there is little research on non-stationary reverberation suppression in deep-sea environments.

[0003] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0004] The present application provides a deep-sea reverberation suppression method based on a generalized spatial filtering principle, which is used for deep-sea reverberation suppression and reduces the reverberation detection blind area, thereby overcoming the defects in the prior art to some extent.

[0005] Other characteristics and advantages of the present application will become apparent from the following detailed description, or will be learned by practice of the present application.

[0006] According to a first aspect of the present application, a deep-sea reverberation suppression method based on a generalized spatial filtering principle is provided, and the method comprises:

[0007] constructing a three-dimensional scattering function based on an incident grazing angle, a scattering grazing angle and a scattering azimuth angle;

[0008] constructing a sea bottom reverberation intensity received from the scatterer based on the three-dimensional scattering function;

[0009] determining a peak time of the reverberation intensity based on the attenuation characteristics of the sea bottom reverberation intensity;

[0010] selecting a reverberation acoustic line at the peak time and a target echo acoustic line, constructing an array reverberation copy vector according to the reverberation acoustic line, and constructing a target echo copy vector according to the target echo acoustic line;

[0011] A second-order cone programming model is constructed based on the reverberation copy vector and the echo copy vector, and a generalized spatial filtering matrix is obtained by solving the second-order cone programming model;

[0012] The array reverberation signal is suppressed using the generalized spatial filtering matrix.

[0013] In some example embodiments, the three-dimensional scattering function is constructed based on the incident grazing angle, the scattering grazing angle and the scattering azimuth angle, specifically:

[0014]

[0015] Where θ inc is the incident grazing angle, θ scatt is the scattering grazing angle, is the scattering azimuth angle, μ and v are the backscattering intensity and the lateral scattering intensity respectively, σ is the lateral scattering deviation, and ΔΩ i,j is the degree of deflection of the scattering sound ray to the mirror reflection direction.

[0016] In some example embodiments, the seabed reverberation intensity received from the scatterer is constructed based on the three-dimensional scattering function, specifically:

[0017]

[0018] Where Δs k is the area of each scattering surface element, K is the number of scattering surface elements, I0 is the intensity of the pulse signal emitted by the sound source, p inc,i and p scatt,j represent the incident and scattering sound pressures respectively, S represents the scattering function, N and M represent the total number of propagation paths of the incident sound ray and the outgoing sound ray respectively; r i represents the distance of the sound ray along the ith path from the sound source to the seabed scatterer, and r j represents the distance of the sound ray along the jth path from the seabed scatterer to the receiving position.

[0019] In some example embodiments, the peak time of the reverberation intensity is determined based on the attenuation characteristics of the seabed reverberation intensity, including:

[0020] A curve of the reverberation intensity changing with time is established according to the expression of the seabed reverberation intensity;

[0021] The time corresponding to the peak of the reverberation intensity, i.e. the peak time, is read.

[0022] In some example embodiments, the array reverberation copy vector is constructed based on the reverberation sound ray, specifically:

[0023] v k,l = S(ω) * H k,l (ω)(l = 1,...L)

[0024]

[0025] where S(ω) is the spectrum of the transmitted signal, H k,l (ω) represents the channel response of the reverberation signal, which is the product of the channel response of the sound ray from the sound source to the sea bottom scatterer and the channel response of the sound ray from the sea bottom scatterer to the receiving array, h inc,m represents the channel response of the mth sound ray from the sound source to the sea bottom scatterer, h scatt,n represents the channel response of the nth sound ray from the sea bottom scatterer to the receiving array, v r,l represents the frequency domain response of the transmitted signal to the lth array element under the channel of the sea bottom scatterer to the receiving array, and L represents the number of array elements.

[0026] In some example embodiments, the target echo copy vector is constructed according to the target echo sound ray, specifically:

[0027]

[0028] where h inc1,m represents the channel response of the mth sound ray from the sound source to the target, h scatt1,n represents the channel response of the nth sound ray from the target to the receiving array, v s,l represents the frequency domain response of the transmitted signal to the lth array element under the channel of the sound source to the target.

[0029] In some example embodiments, the second-order cone programming model is solved to obtain a generalized spatial domain filter matrix, including:

[0030] Define y = [ε, h T ] T and Let ε = b T y, where represents a zero vector of 1xL 2 ,

[0031]

[0032] where δ is a determined stopband reverberation attenuation rate, and ξ is a coefficient size limiting the spatial domain matrix filter;

[0033] The optimal solution of the vector y is obtained by solving the above using the SeDuMi optimization algorithm, and the 2~1+L 2 components of the vector y are taken out and recombined into a square matrix, i.e., a spatial domain filter matrix.

[0034] According to a second aspect of the present application, there is provided a storage medium having stored thereon a computer program which, when executed by a processor, implements the deep-sea reverberation suppression method based on the generalized spatial filtering principle of the first aspect.

[0035] According to a third aspect of the present application, there is provided a computer program product having stored thereon a computer program which, when executed by a processor, implements the deep-sea reverberation suppression method based on the generalized spatial filtering principle of the first aspect.

[0036] According to a fourth aspect of the present application, there is provided an electronic device comprising:

[0037] a processor; and

[0038] a memory for storing executable instructions of the processor;

[0039] wherein the processor is configured to implement the deep-sea reverberation suppression method based on the generalized spatial filtering principle of the first aspect via execution of the executable instructions.

[0040] The deep-sea reverberation suppression method based on the generalized spatial filtering principle provided by the embodiments of the present application, based on the established deep-sea seabed reverberation model, combines the prior information of the deep-sea environment to give the copy vector of the strong reverberation interference on the horizontal array, and through the convex optimization design of the generalized spatial filtering matrix of the line array, the array spatial response is unchanged to the expected target signal, and the strong periodic reverberation interference is suppressed. The robustness of the proposed reverberation suppression method in the deep-sea environment is analyzed. Considering the reverberation characteristic changes caused by the uncertainty of the real ocean environment, the performance and robustness of the reverberation suppression method in the fluctuating ocean environment are analyzed. The simulation results show that the method has good robustness.

[0041] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF DRAWINGS

[0042] The drawings incorporated into the specification and forming part of the specification, show embodiments consistent with the present application, and together with the specification, serve to explain the principles of the present application. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0043] Figure 1 The deep-sea reverberation suppression method based on the generalized spatial filtering principle of the exemplary embodiments of the present application is implemented as follows:

[0044] Figure 2A deep-sea sound speed profile for an exemplary embodiment of the present invention;

[0045] Figure 3 A reverberation intensity versus time curve for an exemplary embodiment of the present invention;

[0046] Figure 4 A scatterer contribution to reverberation intensity for an exemplary embodiment of the present invention;

[0047] Figure 5 A ray path and reverberation intensity plot for an exemplary embodiment of the present invention;

[0048] Figure 6 A detection result based on conventional and spatial filtering array processing for an exemplary embodiment of the present invention; (a) reverberation matched filter result; (b) reverberation matched filter result after spatial filtering processing; (c) (reverberation + target) matched filter result; (d) (reverberation + target) matched filter result after spatial filtering processing;

[0049] Figure 7 A reverberation suppression gain versus array spacing standard deviation trend for an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0050] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations can be implemented in any

[0051] In addition, the drawings are merely schematic and the dimensions of the various layers can be exaggerated for clarity. Like reference numerals can be used to denote like parts containing similar elements throughout the description. The drawings illustrate exemplary embodiments of the present application and, as such, should not be considered limiting in scope of the application. The illustrative drawings are intended to assist in the understanding of the present application and should not be considered limiting of the application. The exemplary embodiments of the present application can be implemented in any number of ways, and the illustrative embodiments should not be considered limiting in scope of the application.

[0052] To overcome the shortcomings and deficiencies of the prior art, the reverberation suppression method based on generalized spatial filtering is provided in the example embodiment. The time-space variation characteristics of deep sea bottom reverberation are utilized, and the prior information of the environment is combined to construct the copy vector of strong reverberation interference on the horizontal array. Through the convex optimization design of the generalized spatial filtering matrix of the line array, the strong periodic reverberation interference suppression under the condition of distortion-free target signal is realized. The simulation results show that the reverberation suppression ratio of the proposed method reaches more than 7dB. Considering the reverberation characteristic variation caused by the uncertainty of the real ocean environment, the robustness of the reverberation suppression method in the fluctuating ocean environment is analyzed. The influence of the proposed reverberation suppression method performance under the condition of deep sea environment array response mismatch is studied, and the results show that the method has good robustness.

[0053] Reference Figure 1 As shown, the method can specifically include the following steps:

[0054] Step 1: In order to more accurately describe the formation mechanism of deep sea bottom reverberation, i.e. the scattering and reflection process of sound waves in the propagation process, a scattering function is introduced to quantify the process. The scattering function represents the geometric and physical characteristics of the interaction between sound waves and obstacles, and can quantitatively analyze the scattering effect of sound waves in the underwater environment. The intensity of the bottom reverberation received by the receiver from the unit area scatterer is expressed as:

[0055]

[0056] Where p inc,i and p scatt,j represent the incident and scattered sound pressure, i and j represent the propagation modes of the incident and outgoing sound rays, S represents the scattering function, N and M represent the total number of propagation paths of the incident and outgoing sound rays, r i represents the distance of the sound ray along the i-th path from the sound source to the bottom scatterer, and r j represents the distance of the sound ray along the j-th path from the bottom scatterer to the receiving place.

[0057] Since the incident and scattered sound rays of the local reverberation are always in the same vertical plane during propagation, the scattering function has a certain spatial geometric relationship with the incident grazing angle θ inc and the scattering grazing angle θ scatt In the remote reverberation, the scattering function needs to describe the scattering azimuth angle in addition to the certain geometric relationship between the incident grazing angle and the scattering grazing angle. The three-dimensional scattering function is described as:

[0058]

[0059] Where μ, v are the backscattering intensity and lateral scattering intensity, respectively, and σ is the lateral scattering deviation; ΔΩi,j The degree to which the direction of the scattered sound rays deviates from the direction of mirror reflection is determined by the following formula:

[0060]

[0061] In the deep-sea environment, due to the multipath effect, sound rays have numerous propagation paths from the sound source through the same scatterer to the receiver. A grid is used to divide the seabed scatterers into a large number of adjacent rectangular elements. The scatterer at the center of each grid is used to represent the entire element, and the paths of the incident sound rays to that element and the scattered sound rays from that element to the receiving array are statistically analyzed, along with the corresponding sound ray geometry, amplitude response, and propagation delay. The seabed reverberation intensity at time t is expressed as:

[0062]

[0063] Where τ0 is the length of the transmitted signal pulse, τ is the arrival delay, and the arrival time t = τ inc,i +τ scatt,j , τ inc,i τ represents the time it takes for a sound ray to travel from its source to the scatterer. scatt,j Let I0(τ) represent the time it takes for the scatterer to reach the receiver, I0(τ) represent the intensity of the pulse signal emitted by the sound source, and dA(t,τ) represent the area of ​​the scattering surface element. The scattering area is divided into K scattering surface elements, each with a constant area of ​​Δs. k The intensity of the scattering received by the receiver is expressed as:

[0064]

[0065] Based on this model, the reverberation intensity at the receiver at any given moment after the pulse signal is emitted can be calculated.

[0066] Step 2: Based on the established reverberation model, determine the contribution of the scatterer to the reverberation intensity at different times. According to generalized spatial filtering theory, design a specific filter based on the spatial response of the towed linear array. This filter should significantly attenuate the reverberation copy vector response at a specific time (peak time) while minimizing distortion of the target echo copy vector. Based on this principle, it is possible to eliminate the reverberation signal in certain regions (i.e., the reverberation source at the suppression time) while retaining the target echo signal in those regions, thus achieving reverberation suppression. The generalized spatial filtering reverberation suppression problem can be described as follows:

[0067]

[0068] Among them, V r V is the reverberation copy vector generated for a specific region. s R is the target echo copy vector. sS T represents the target region. However, in practical signal processing, equation (6) is too idealistic and the conditions are too strict. Assuming there is one target and K scatterers, the optimization design problem of the filter can be expressed as:

[0069]

[0070] where ε represents a non-negative variable, δ is the determined stopband reverberation decay rate, and ξ is the coefficient size limit of the spatial matrix filter.

[0071] where the reverberation copy vector V r,k of the kth scatterer can be expressed as:

[0072]

[0073] The target echo copy vector in the channel is expressed as:

[0074]

[0075] where S(ω) is the frequency spectrum of the transmitted signal, represents the three-dimensional scattering function, h inc,m represents the channel response of the mth sound line from the sound source to the seabed scatterer, h scatt,n represents the channel response of the nth sound line from the seabed scatterer to the receiving array. H k,l (ω) represents the channel response corresponding to the reverberation signal, h inc1,m represents the channel response of the mth sound line from the sound source to the target, h scatt1,n represents the channel response of the nth sound line from the target to the receiving array, v r,l , v s,l represents the frequency domain response of the transmitted signal to the lth array element under two different channels, and L represents the number of array elements.

[0076] In order to solve the matrix filter, the matrix needs to be converted into a vector, and the matrix H is decomposed into L row vectors according to the rows, that is, H T = [h1, …, h L ], and a column vector is defined as

[0077] h = [h1 T , × h L T ] T (10)

[0078] Define y = [ε, h T ] T and Let ε = b T y, where represents a 1 × L2 zero vector, formula (7) is further transformed as:

[0079]

[0080] wherein, represents L 2 ×L 2 unit matrix.

[0081] Thus, the constraint optimization problem is expressed in the form of a second-order cone programming, and after the optimal solution of the vector y is obtained by using the SeDuMi model, the 2~1+L 2 components are taken out and recombined into a square matrix, that is, the matrix filter to be solved.

[0082] Step 3: According to the reverberation field model and echo intensity calculation, the simulated array reverberation receiving signal is sequentially subjected to beam forming and matched filtering processing, the beam output BTR graph without target is obtained, the simulated array target echo signal is inserted into the reverberation, and the beam output BTR graph when the target exists can be obtained. By comparing the results before and after the spatial filtering of the reverberation receiving signal, a profile is made along the beam angle of the target, and the average value at the peak value moment is taken as the energy estimation value. The reverberation energy and target echo energy before reverberation suppression are calculated, and then the reverberation suppression ratio is obtained.

[0083] The reverberation suppression method based on the generalized spatial filtering provided by the application utilizes the reverberation model to determine the contribution of the scatterer to the reverberation intensity, suppresses the reverberation in a specific region based on the horizontal towed array spatial response characteristics of deep sea reverberation, and can reduce the short-range detection blind area.

[0084] Next, the steps of the deep sea reverberation suppression method based on the generalized spatial filtering principle in the example embodiment will be described in more details in combination with the drawings and examples.

[0085] The background information is as follows: the simulation environment is a typical deep sea area in the South China Sea, the transmitting signal is a CW pulse signal with a frequency of 500Hz and a pulse width of 1s, the sound source depth is 40m, the receiving depth is 100m, the horizontal distance between the receiving hydrophone and the sound source is 1km, the sea depth is 4000m, the target intensity is 10dB, the sound source level is 220dB, and the target with a depth of 100m is located at the 45° azimuth of the array, and the distance from the target to the center of the array is 9.2km. The sound propagation is simulated by using the sound ray model, and the reverberation intensity attenuation calculation is performed in combination with the established reverberation model.

[0086] The simulated reverberation intensity curve with time is as follows: Figure 3It can be seen that there are several obvious peaks in the bottom reverberation intensity, and there are obvious peaks at 5.3s, 10.6s and 15.9s. The peak interval is 5.3s, which is about 2H / c (H and c are the depth of seawater and the sound speed, respectively), and the deep sea reverberation intensity decays periodically with time.

[0087] Taking the reverberation arriving at 15.9s as an example, all the sound rays propagating through the sound source-scatterer-receiver are analyzed, and the scattering intensity at the position of the bottom is combined to obtain the contribution of the bottom scatterer to the reverberation intensity. Figure 4 It can be seen that the contribution of the bottom scatterer to the reverberation intensity at the peak time is in the form of an elliptical ring, and different bottom reflection times correspond to different elliptical rings. Combined with the sound propagation ray model, Figure 5 the number of sound rays propagating from the sound source to the receiver and the corresponding reverberation intensity are given. It can be seen that, due to the multipath effect, there are many types of sound ray propagation, among which the number of sound rays propagating along the path of contacting the sea surface and the sea bottom three times is the largest, that is, Figure 5 the reverberation caused by the scatterer near the origin, and the energy of this part of the reverberation is also the strongest. The distribution of the bottom scatterer contributing to the reverberation is related to the relative position of the sound source and the receiver. After the sound source transmits the signal, the propagation range of the sound ray expands, and the scattering area contributing to the reverberation gradually increases.

[0088] According to the reverberation model, the contribution of the bottom scatterer to the reverberation intensity at the peak time can be obtained, and the sound rays propagating through the bottom scatterer to the receiver array and the sound rays propagating through the target echo to the receiver array are selected respectively. Using the sound ray information, array reverberation copy vectors and target echo copy vectors are constructed respectively, and the second-order cone programming model is substituted to obtain the spatial filtering matrix. The specific process of designing the reverberation suppression spatial matrix filter is as follows:

[0089] (1) Model the entire sea area to obtain the time-space domain information of the deep sea periodic reverberation;

[0090] (2) Select the reverberation sound rays and target echo sound rays arriving at the receiver array at the suppression time respectively;

[0091] (3) Construct the copy vectors V r,k and V s of the reverberation and the target echo according to formula (8) and formula (9) respectively, k=1,...,K;

[0092] (4) Rewrite formula (7) into the form of formula (11), use the second-order cone programming method to obtain the optimal solution of y under the constraint condition, and recover the target matrix H from it.

[0093] According to the reverberation field model and echo intensity calculation, the array received signal mixing ratio obtained by simulation is about -4.9dB. The simulated 64-element reverberation receiving signal sequentially passes through beam forming and matched filtering processing, and the beam output BTR graph without target is obtained, as shown in Figure 6 (a). The 64-element target echo signal obtained by simulation is inserted into the reverberation, and the beam output BTR graph with target is obtained, as shown in Figure 6 (b). It can be seen from the comparison of the two graphs that the target echo signal has been 'annihilated' in the reverberation. According to the designed generalized spatial filter, the matched filtering result is obtained through spatial filtering processing under the conditions of with and without target. The comparison of Figure 6 (a) and Figure 6 (c) can see that Figure 6 (d) appears a bright spot at about 45° azimuth at 15.9s, which is the target. Comparing the results of the reverberation receiving signal before spatial filtering Figure 6 (a) and after spatial filtering Figure 7 (c), a profile along the target located beam angle 45° is made, and the average value of 15.8-16.0s is taken as the energy estimation value. The reverberation energy is about 85.6dB before reverberation suppression, and the target echo energy is about 80.7dB. After the generalized spatial filtering processing, the reverberation energy is about 77.2dB, and the target echo energy remains basically unchanged. The reverberation suppression gain is 8.4dB.

[0094] In order to further analyze the robustness of the reverberation suppression method based on the generalized spatial filtering principle, it is assumed that the disturbance obeys the Gaussian distribution with mean value of 0 and standard deviation of 1-5m (interval of 0.5m). 50 groups of samples are taken for each standard deviation, the reverberation suppression gain obtained by 50 groups of samples is averaged as the reverberation suppression gain under the standard deviation, and the change trend of the simulation reverberation suppression gain with the array spacing standard deviation is simulated. As shown in ​ , it can be seen that as the disturbance standard deviation becomes larger, the reverberation suppression gain decreases, but in the range of standard deviation of 0-3m, the reverberation suppression gain reaches more than 6.3dB, and the reverberation suppression effect is good. The suppression method has good robustness.

[0095] This embodiment shows that for the problem of strong periodic reverberation interference existing in deep sea active detection, the present application proposes a deep sea seabed strong periodic reverberation suppression method based on the generalized spatial filtering principle from the aspects of reverberation characteristic research and reverberation suppression. The reverberation suppression ratio of the proposed method reaches more than 7dB, and the strong periodic reverberation interference suppression under the condition of undistorted target signal is realized.

[0096] It should be noted that, as another aspect, the present application also provides a storage medium, which can be included in an electronic device, or exist independently without being assembled into the electronic device. The storage medium carries one or more programs, which, when executed by an electronic device, cause the electronic device to implement the methods described in the following embodiments.

[0097] In one embodiment, the present application provides a computer program product, including a computer program which, when executed by a processor, implements the steps in the above method embodiments.

[0098] In addition, the above-described drawings are only schematic illustrations of the processes included in the method according to the exemplary embodiments of the present application, and are not intended for limiting purposes. It is easy to understand that the processes shown in the above-described drawings do not indicate or limit the time sequence of the processes. In addition, it is also easy to understand that the processes can be executed synchronously or asynchronously, for example, in multiple modules.

[0099] Other embodiments of the present application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. It is intended that the present application cover any and all variations of the application that come within the scope of the present application, including custom and practice of the art known to those skilled in the art. It is intended that the specification and examples be considered exemplary only, with the true scope and spirit of the application being indicated by the following claims.

[0100] It should be understood that the present application is not limited to the precise construction that has been described above and illustrated in the accompanying drawings, and that various modifications and changes can be made by those skilled in the art without departing from the scope of the present application. The scope of the present application is limited only by the appended claims.

Claims

1. A deep-sea reverberation suppression method based on generalized spatial filtering principle, characterized in that, The method comprises: constructing a three-dimensional scattering function based on an incident grazing angle, a scattering grazing angle and a scattering azimuth angle; constructing seabed reverberation intensity received from a scatterer based on the three-dimensional scattering function; determining a peak time of the reverberation intensity based on an attenuation characteristic of the seabed reverberation intensity; selecting a reverberation ray of the peak time and a target echo ray, constructing an array reverberation copy vector according to the reverberation ray, and constructing a target echo copy vector according to the target echo ray; constructing a second-order cone programming model based on the reverberation copy vector and the echo copy vector, and solving the second-order cone programming model to obtain a generalized spatial domain filtering matrix; suppressing an array reverberation signal using the generalized spatial domain filtering matrix.

2. The method of claim 1, wherein, The three-dimensional scattering function is constructed based on the incident grazing angle, the scattering grazing angle and the scattering azimuth angle, and specifically: wherein is the backscattering azimuth, , are the backscattering intensity and side scattering intensity, respectively, is the side scattering deviation, is the degree of deviation of the direction of the scattered sound ray from the direction of the specular reflection.

3. The method of claim 2, wherein, The seabed reverberation intensity received from the scatterer is constructed based on the three-dimensional scattering function, and specifically: in, The area of ​​each scattering surface element, K The number of scattering surface elements. The intensity of the pulse signal emitted by the sound source. and These represent the incident and scattered sound pressures, respectively. Represents the scattering function. and These represent the total number of propagation paths for the incident and emitted sound rays, respectively. Representing the vocal tract along the first The distance from the sound source to the seabed scatterer along the path. Representing the vocal tract along the first The distance from the seabed scatterer to the receiver.

4. The method of claim 3, wherein, The peak time of the reverberation intensity is determined based on the attenuation characteristic of the seabed reverberation intensity, and includes: establishing a curve of the reverberation intensity changing with time according to an expression of the seabed reverberation intensity; reading a time corresponding to a peak point of the reverberation intensity, i.e. the peak time.

5. The method of claim 3, wherein, The array reverberation copy vector is constructed according to the reverberation ray, and specifically: wherein, is the frequency spectrum of the transmitted signal, represents the channel response corresponding to the reverberation signal, which is the product of the channel response from the sound source to the sea bottom scatterer and the channel response from the sea bottom scatterer to the receiving array, represents the channel response of the first sound line from the sound source to the sea bottom scatterer, represents the channel response of the first sound line from the sea bottom scatterer to the receiving array, represents the number of array elements.

6. The method of claim 5, wherein, The target echo copy vector is constructed according to the target echo ray, and specifically: wherein, a channel response representing the first order acoustic ray from the source to the target, a channel response representing the first order acoustic ray from the target to the receiving array, a frequency domain response representing the transmitted signal at the first array element in the channel from the source to the target.

7. The method of claim 6, wherein, The generalized spatial domain filtering matrix is obtained by solving the second-order cone programming model, and includes: Definitions and , let where represents the zero vector, wherein, to determine the stopband reverberation decay rate, to limit the coefficient size of the spatial domain matrix filter; The vector is obtained by solving the above problem using the SeDuMi optimization algorithm. Find the optimal solution and extract the vector. No. The components are recombined into a square matrix, which is the spatial filtering matrix.

8. A storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to implement the deep sea reverberation suppression method based on the generalized spatial domain filtering principle as claimed in any one of claims 1 to 7.

9. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to implement the deep sea reverberation suppression method based on the generalized spatial domain filtering principle as claimed in any one of claims 1 to 7.

10. An electronic device, comprising: comprise: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to execute the deep sea reverberation suppression method based on the generalized spatial domain filtering principle as claimed in any one of claims 1 to 7 by executing the executable instructions.

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