Deep sea seabed planar array target positioning method based on multipath coherent focusing

Abstract

The invention belongs to the fields of underwater acoustic array signal processing, underwater acoustic detection, underwater acoustic positioning and the like, and relates to a deep sea seabed planar array target positioning method based on multipath coherent focusing. According to the method, a physical characteristic that a sound source arrives at an array in a direct sound area mainly through a direct path and a sea surface primary reflection path is utilized, and three-dimensional grid points of possible sound source positions with different angles, distances and depths are established; further calculating propagation time and amplitude corresponding to a direct path D from each grid point to each array element and a primary reflection path S of the sea surface under the condition of a given sound velocity profile, and constructing a new guide vector for beam forming to realize coherent accumulation of multi-path sound energy; finally, the grid point position corresponding to the peak value of the ambiguity function is the position of an expected sound source; only the sound velocity profile needs to be measured, the method is suitable for azimuth angle, distance and depth estimation of broadband and narrowband targets in a direct sound area, and the calculation complexity is low.

Description

Technical Field

[0001] The present invention belongs to the fields of underwater acoustic array signal processing, underwater acoustic detection, underwater acoustic positioning, etc., and relates to a method for positioning a deep-sea seabed planar array target based on multi-path coherent focusing. Background Art

[0002] Deep-sea shore-based arrays are deployed on the seabed, with high self-safety and good concealment. At the same time, they can form arrays on a large scale and have excellent detection performance. They are one of the important means for passive detection of underwater targets at present. The target depth information is one of the important criteria for classifying surface and underwater targets known at present. However, there are many difficulties in positioning targets in the direct sound area in the actual application of deep-sea shore-based arrays. Matched field is one of the classical means to solve this problem. However, it requires full knowledge of ocean environmental parameters, and then uses an underwater acoustic model to calculate the sound field amplitude and phase of the receiving array, form a copy field vector, and match it with the acoustic data received by the array to achieve the positioning of underwater targets. This method requires the calculation of the entire sound pressure field. The computational amount is quite large in the case of a three-dimensional spatial grid of multi-frequency broadband signals. In actual applications, even if the sound pressure copy field is calculated and stored in advance, this method is very sensitive to environmental parameter mismatch, resulting in large positioning errors or even the failure of the method.

[0003] The deep-sea sound field usually has obvious and distinguishable multi-path arrival structures. For example, in the deep-sea direct sound area, the signals received by hydrophones come from the direct path, the sea surface first reflection path, the seabed first-sea surface first reflection path, etc. Existing methods make full use of multi-path information to carry out positioning research on targets. For example, the Chinese patent "A Method and Device for Detecting and Positioning an Underwater Sound Source Based on Deep-Sea Multi-Path Focusing" (Patent No. ZL 202411119049.9) discloses a method and device for detecting and positioning an underwater sound source based on deep-sea multi-path focusing. This method uses a spatial power spectrum estimation method to calculate the beam output sound field of the sound pressure signal radiated by the target sound source at different frequency points and different azimuth angles within a set frequency range; for any frequency point, the beam output sound fields at two different azimuth angles at this frequency point are phase-compensated and added according to different assumed arrival time delays to obtain a focusing result; the multi-path sound field focusing results of multiple frequency points are added to obtain a broadband multi-path three-dimensional sound field focusing result; the two angles and arrival time delays corresponding to the maximum value of the broadband focusing result are compared with the template values at different assumed target distances and depths to determine the estimated values of the target sound source distance and depth. This method realizes the coherent superposition detection of deep-sea multi-path signals and improves the detection and positioning ability of underwater weak sound sources in a multi-path environment. This method requires that the arrival elevation angles of the direct sound ray and the sea surface first reflection ray reaching the array can be distinguished. However, the equivalent vertical aperture of the seabed planar array is limited, and the arrival elevation angles of the two paths reaching the array are usually very close and difficult to distinguish.

[0004] The paper "Research on Near-field Localization of Airborne Sound Sources by Deep-sea Horizontal Arrays" (Mao Junjie, Zhang Bo, etc., Acta Acustica, Vol. 1, 2025) uses different path rays such as direct sound incident from the air to the deep sea, sea-bottom single-surface single-reflection rays, and sea-bottom double-surface double-reflection rays for near-field focusing beamforming. To solve the problem of spatial spectrum false peaks, the spatial spectra corresponding to multiple paths are weighted and summed, realizing the localization of airborne sound sources in the near-field Fresnel zone by the sea-bottom horizontal array. However, the spatial spectrum weighted summation is an incoherent summation of the energies of multi-path signals, which cannot improve the output signal-to-noise ratio, and it is difficult to improve the weak target detection ability. Summary of the Invention

[0005] To solve the problems of large computational complexity for passive target localization by deep-sea bottom plane arrays and large storage capacity of copy fields in the prior art, the present invention proposes a method for target localization of deep-sea bottom plane arrays based on multi-path coherent focusing. This method utilizes the physical characteristic that in the direct sound region, the sound source reaches the array mainly through the direct path and the single-surface reflection path from the sea surface. By establishing three-dimensional grid points of possible sound source positions at different angles, distances, and depths, and then calculating the propagation times and amplitudes corresponding to the direct path D and the single-surface reflection path S from each grid point to each array element under a given sound speed profile, a new steering vector is constructed for beamforming to achieve coherent accumulation of multi-path sound energies. Finally, the position of the grid point corresponding to the peak of the ambiguity function is the position of the expected sound source. The present invention only needs to measure the sound speed profile, is applicable to the estimation of the azimuth, distance, and depth of broadband and narrowband targets in the direct sound region, and has low computational complexity. At the same time, the present invention only needs to store the multi-path propagation times and amplitudes required as parameter templates for the steering vector, greatly reducing the storage space and significantly saving the hardware cost.

[0006] The specific steps of this method are as follows:

[0007] Step 1: Establish a three-dimensional rectangular coordinate system and obtain the sound pressure signals of the sea-bottom plane array;

[0008] Step 2: Construct three-dimensional search space grid points of all possible positions of potential targets, and use the ray model BELLHOP to calculate the propagation times and amplitudes corresponding to the direct path D and the single-surface reflection path S from each grid point to each array element;

[0009] Step 3: At each frequency point, construct a corresponding multi-path coherent focusing steering vector according to the searched sound source depth, horizontal distance, and horizontal azimuth angle and perform normalization processing;

[0010] Step 4: Perform beamforming for a given frequency point to obtain an ambiguity function, so as to achieve coherent accumulation of multipath sound energy; the value of each point in the ambiguity function represents the multipath focusing energy of the sound source propagating along two paths to the array at the corresponding grid point, and the maximum value of the ambiguity function corresponds to the depth, horizontal distance, and horizontal azimuth angle of the desired sound source.

[0011] The form of beamforming is not limited to conventional beamforming, and may also include methods such as MVDR (i.e., Minimal Variance Distortion Response). If it is a broadband signal, broadband beam energy synthesis can be further performed to obtain a broadband ambiguity function.

[0012] The specific content of the above Step 1 is as follows:

[0013] Taking an arbitrary position on the sea surface as the coordinate origin O, and the east and north directions as the x-axis and y-axis respectively to establish a rectangular coordinate system. Suppose there are M array elements in the planar array, and the coordinates of the m-th array element are , where x m is the x-axis coordinate of the m-th array element, and y m is the y-axis coordinate of the m-th array element, and H is the known sea depth. The depth of the sound source is z s , and the horizontal distance and horizontal azimuth angle to the coordinate origin are r s and θ s respectively, where the horizontal azimuth angle θ s is defined as the angle between the projection of the sound source on the xoy plane and the x-axis, and its value ranges from 0 degrees to 360 degrees.

[0014] Suppose the spectrum of the target sound source radiation signal received by the m-th array element at the frequency point f is , where , , are the lowest frequency and the highest frequency of the sound pressure signal respectively. The sound pressure signals received by the M array elements are expressed in vector form as an M×1 dimensional column vector:

[0015] (1)

[0016] The superscript T represents the transpose of the vector.

[0017] The specific content of the above Step 2 is as follows:

[0018] Suppose the depth, horizontal distance, and horizontal azimuth angle of the sound source in the search space are z, r, and θ respectively, then its coordinates in the rectangular coordinate system can be written as When the sound source is located in the direct sound area of the array, only the direct path D and the sea surface one - reflection path S are considered. Given the sound - speed profile and sea depth (the sound - speed profile and sea depth can be measured on - site during sea trials using equipment such as a sound - speed meter and a depth sounder), substituting the sound - source position and the position of the receiver (here, the m - th element of the array) into the ray model BELLHOP, the propagation times for the sound source to reach the m - th element of the array through the direct path D and the sea surface one - reflection path S are calculated. and amplitude , where correspond to the direct path D and the sea surface one - reflection path S respectively.

[0019] When not considering sound - ray bending, that is, assuming straight - line propagation, the propagation distance for the sound - pressure signal emitted by the actual sound source to reach the m - th element through the l - th path is:

[0020] (2)

[0021] where .

[0022] At this time, the propagation time and amplitude for the sound - pressure signal emitted by the actual sound source to reach the m - th element through the l - th path can be approximated by the spherical - wave propagation law, that is:

[0023]

[0024] where c is the sound speed in seawater. Subsequently, for the sake of formula simplicity, is abbreviated as , is abbreviated as ;

[0025] Since the sound speed shows a certain distribution along the depth in the real ocean environment, as the distance between the sound source and the receiver increases, equations (2) - (4) no longer hold. At this time, using the ray model BELLHOP to calculate the propagation times and amplitude for the sound source to reach the m - th element of the array through the direct path D and the sea surface one - reflection path S in the search space is more accurate, where the calculation uses the signal center frequency . Once the calculation is completed, the propagation time and amplitude Stored as a template for direct subsequent invocation. The matched field technique requires calculating the acoustic pressure copy field for each frequency point. Under deep - sea conditions, the computational load is extremely large and it is difficult to be used for real - time calculation. The present invention takes advantage of the fact that the multi - path propagation time and multi - path amplitude calculated by the ray model are insensitive to the signal frequency. For broadband signals, it can be directly invoked, greatly reducing the computational load. At the same time, the matched field needs to store the broadband complex acoustic pressure fields received by multiple element arrays as matching templates, while the present invention only stores the multi - path propagation time and amplitude , greatly reducing the storage space and significantly saving the hardware cost.

[0026] The specific steps of step 3 are as follows:

[0027] Given the acoustic signal frequency f, construct the multi - path coherent focusing steering vector according to the signal amplitude and propagation time of the direct - path D and the first - order sea - surface reflected path S under the actual sound source depth z, horizontal distance r, and horizontal azimuth angle θ : (5)

[0028] Normalize the steering vector :

[0029] (6)

[0030] denotes the normalized steering vector;

[0031] Step 4 includes:

[0032] Perform conventional beamforming processing on the acoustic pressure signal received by the planar array to obtain the beam - domain signal pointing to the target:

[0033] (7)

[0034] When the acoustic pressure signal is a narrow - band signal, then output the energy of the narrow - band signal as as the narrow - band ambiguity function. The greatest advantage of the above - mentioned processing is that it realizes the coherent synthesis of multi - path signals similar to the matched field processing, improving the signal - to - noise ratio.

[0035] The form of beamforming in formula (7) is not limited to conventional beamforming and may also include the MVDR (i.e., Minimal Variance Distortion Response) method, that is:

[0036] (8)

[0037] where is the cross-spectral density matrix of the observed data, represents the inversion of this matrix.

[0038] When the sound pressure signal is a broadband signal, broadband energy synthesis is further performed to obtain the broadband ambiguity function as follows:

[0039] (9)

[0040] The value of each point of the narrowband or broadband ambiguity function represents the multi-path focused energy of the sound source propagating along two paths to the array at the corresponding grid point. The maximum value of the ambiguity function corresponds to the depth, horizontal distance, and horizontal azimuth angle of the expected sound source.

[0041] Traverse and search for the maximum value of the ambiguity function, and its corresponding position is the estimated value of the horizontal azimuth angle of the expected sound source , the estimated value of the horizontal distance , the estimated value of the depth :

[0042] .

[0043] Compared with the prior art, the advantages of the present invention are as follows:

[0044] When using beamforming for target parameter estimation under the far-field plane wave model of a deep-sea planar array, it is affected by multi-path interference such as the direct path D of the shallow source and the sea surface first-reflected sound ray path S, making it difficult to estimate the target's elevation angle, distance, and depth. The deep-sea seafloor planar array target positioning method based on multi-path coherent focusing proposed by the present invention uses the deep-sea multi-path structure to improve the steering vector in the beamforming process: when calculating the propagation time and amplitude of the target arriving at each element of the planar array through paths D and S, three factors including the sound source depth, horizontal distance, and horizontal azimuth angle are considered. Therefore, the improved steering vector contains more target parameter information. After multi-path beam focusing, not only can the depth, horizontal distance, and horizontal azimuth angle of the sound source be estimated simultaneously by solving the position corresponding to the maximum value of the ambiguity function. Moreover, this method further realizes the energy coherent accumulation of deep-sea multi-path signals, enhances the maximum value of the ambiguity function, and is beneficial for detecting weak targets in a multi-path environment. In practical applications, the construction of the steering vector only requires calculating the multi-path propagation time and amplitude at a single frequency point, with a small amount of calculation, and at the same time, the template storage space is greatly reduced, greatly saving the hardware cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is the coordinate system adopted in the embodiment: Figure 1 (a) is a top view, in which the solid circle in the figure is a circular array, Figure 1 (b) is the sound speed profile;

[0046] Figure 2It is a flow chart of a target positioning method using a deep - sea horizontal array for multi - path coherent focusing;

[0047] Figure 3 is the three - dimensional broadband ambiguity function corresponding to the sound source: Figure 3 (a) is the three - dimensional broadband ambiguity function corresponding to sound source 1, Figure 3 (b) is the three - dimensional broadband ambiguity function corresponding to sound source 2;

[0048] Figure 4 is the slice of the broadband ambiguity function of sound source 1: Figure 4 (a) is the horizontal - distance - angle slice of the broadband ambiguity function of sound source 1, Figure 4 (b) is the depth - horizontal - distance slice of the broadband ambiguity function of sound source 1;

[0049] Figure 5 is the slice of the broadband ambiguity function of sound source 2: Figure 5 (a) is the horizontal - distance - angle slice of the broadband ambiguity function of sound source 2, Figure 5 (b) is the depth - horizontal - distance slice of the broadband ambiguity function of sound source 2;

[0050] Figure 6 Compares the results of multi - path coherent synthesis of sound source 2 using this method with the results of traditional beamforming using a single path: Figure 6 (a) is the result of the ambiguity function of this method in the distance - depth slice, Figure 6 (b) is the result of the ambiguity function considering only the direct path in the distance - depth slice, Figure 6 (c) is the result of the ambiguity function considering only the sea - surface first - reflection path in the distance - depth slice. Specific implementation manner

[0051] The present invention proposes a target positioning method applicable to multi - path energy coherent focusing of a deep - sea planar array. First, a broadband sound - pressure signal radiated by a target sound source is collected through a deep - sea planar array with horizontal and vertical apertures; then, all possible position grid points of potential targets are searched, and the propagation times and amplitudes of the direct path D and the sea - surface first - reflection path S from the sound - source grid points to each array element are calculated at different depths, target horizontal distances, and target horizontal azimuth angles, and the corresponding steering vectors are constructed and normalized; finally, beamforming is performed for each frequency point, and broadband energy synthesis is carried out to obtain a broadband ambiguity function, and the desired target is located according to the position corresponding to the maximum value of the ambiguity function.

[0052] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0053] Step 1: Establish a three - dimensional rectangular space coordinate system and obtain the sound - pressure signal of the submarine planar array:

[0054] In the embodiment, without loss of generality, consider a uniform circular array on the deep - sea floor. As Figure 1 (a) shows, the receiving array has a total of 128 elements, which are deployed on the sea floor, and the element spacing is d = 5m. The projection of the coordinate origin is at the center of the circular array, and element 1 is located on the x - axis. The array locates sound sources at two different positions respectively. The coordinates of sound source 1 and sound source 2 are (500m, 500m) and (1000m, 1000m) respectively, and the depth of both is 80m. Therefore, the horizontal distances from the two sound sources to the origin are 707m and 1414m respectively, and the horizontal azimuth angles relative to the x - axis are both 45°. Both sound sources radiate broadband continuous signals with a frequency band range of 50Hz - 160Hz. The selected ocean environment is an incomplete deep - sea sound channel environment, the sea depth is 1245m, and the sound - speed profile is as Figure 1 (b) shows. The sound speed at the sea floor is 1600m / s, the density is 1.6g / cm 3 , and the absorption attenuation is 0.6dB / λ.

[0055] Step 2: Construct a three - dimensional search - space grid of all possible positions of potential targets, and use the ray model BELLHOP to calculate the propagation times and amplitudes corresponding to the direct paths D and the single - surface - reflection paths S from each grid point to each element:

[0056] In the embodiment, assume that the distance search range of the sound source is 0.01km - 8km, and the distance search interval is 0.01km; the depth search range of the sound source is 1m - 150m, and the depth search interval is taken as 1m; the angle range of the sound source is 0 - 360°, and the angle interval is taken as 1°. The calculation frequency is the center frequency of the sound source, 105Hz. According to the ocean - environment parameters and the array position corresponding to Step 1, for each grid - point position in the search space, combined with the ray - acoustic - field calculation program BELLHOP, the propagation times and amplitudes of the potential target reaching the m - th element via paths D and S are respectively and , where correspond to paths D and S respectively. After the calculation is completed, it can be stored as a propagation - time and amplitude template. This template is applicable to broadband signals, and different frequencies can directly call this template, greatly reducing the calculation amount of this method.

[0057] Step 3: At each frequency point, construct a corresponding multi - path coherent focusing steering vector according to the searched depth, horizontal distance, and horizontal azimuth angle of the sound source and perform normalization processing;

[0058] In the embodiment, using and calculated in Step 2, select the frequency f of the signal of interest, substitute it into Formula (5) and Formula (6) to obtain the normalized steering vector 。

[0059] Step 4: Perform beamforming for a given frequency point to obtain a narrowband ambiguity function. Through this step, the coherent accumulation of multipath acoustic energy is achieved. The form of beamforming is not limited to conventional beamforming and may also include methods such as MVDR (i.e., Minimal Variance Distortion Response). If it is a broadband signal, broadband beam energy synthesis can be further performed to obtain a broadband ambiguity function. The value of each point in the narrowband or broadband ambiguity function represents the multipath focusing energy of the sound source at the corresponding grid point propagating to the array along two paths. The maximum value of the ambiguity function corresponds to the depth, horizontal distance, and horizontal azimuth angle of the desired sound source.

[0060] In the embodiment, the sound source 1 and the sound source 2 are respectively positioned, and the implementation process is as Figure 2 shown.

[0061] Figure 3 (a) is the three-dimensional broadband ambiguity function corresponding to the sound source 1, Figure 3 (b) is the three-dimensional broadband ambiguity function corresponding to the sound source 2. The depth, target horizontal distance, and target horizontal azimuth angle corresponding to the maximum value in the broadband ambiguity function are the depth, horizontal distance, and horizontal azimuth angle of the desired sound source. Figures 4(a) and (b) respectively show the horizontal distance-angle slice and the depth-horizontal distance slice of the sound source 1. The maximum values of the ambiguity functions in the two subfigures can respectively obtain the estimated results of the target's distance, depth, and horizontal azimuth angle as 700 m, 80 m, and 45°. Figure 4 (a) and Figure 5 (b) are respectively the horizontal distance-angle slice and the depth-horizontal distance slice of the sound source 2. The maximum values of the ambiguity functions in the two subfigures can respectively obtain the estimated results of the target's distance, depth, and horizontal azimuth angle as 1410 m, 80 m, and 45°. The estimated values of the sound source 1 and 2 are in good agreement with the actual values, proving that the proposed method can achieve three-dimensional underwater target positioning. To further illustrate the advantages of the proposed method, we compare the results of the ambiguity function of the proposed method in the distance-depth slice ( Figure 5 (a)) with the results of the ambiguity function in the distance-depth slice considering only the direct path ( Figure 6 (b)) or the first-order sea surface reflection path ( Figure 6 (c)). It can be seen that when only a single path is considered, there are ambiguities in both depth and distance estimations, while the proposed method can accurately estimate the distance of the sound source 2. In addition, Figure 6 (c)), and it can be seen that when only a single path is considered, there are ambiguities in both depth and distance estimations, while the proposed method can accurately estimate the distance of the sound source 2. In addition, Figure 6 the maximum value of the proposed method in (a) is -35.5 dB, Figure 6 (b) and Figure 6(c) The maximum values obtained only by using a single path are -37.6 and -37.9 dB respectively. Therefore, the maximum energy of the beam output by this method is more than 2 dB higher than that obtained only by using a single path, demonstrating the advantage of the coherent focusing of the energy of multiple paths.

Claims

1. A method for positioning targets of a deep-sea seafloor planar array based on multi-path coherent focusing, characterized in that, The specific steps of this method are as follows: Step 1: Establish a three-dimensional rectangular coordinate system and obtain the sound pressure signal of the underwater planar array; Step 2: Construct a three-dimensional search space grid of all possible positions of potential targets, and use the ray model BELLHOP to calculate the propagation time and amplitude corresponding to the direct path D and the first-order sea surface reflection path S from each grid point to each array element; Step 3: At each frequency point, construct the corresponding multi-path coherent focusing steering vector according to the searched source depth, horizontal distance, and horizontal azimuth angle and perform normalization processing; Step 4: Perform beamforming for a given frequency point to obtain an ambiguity function to achieve the coherent accumulation of multi-path sound energy; the value of each point of the ambiguity function represents the multi-path focusing energy of the sound source propagating along two paths to the array at the corresponding grid point, and the maximum value of the ambiguity function corresponds to the depth, horizontal distance, and horizontal azimuth angle of the desired sound source.

2. The method for deep-sea seafloor planar array target positioning based on multi-path coherent focusing according to claim 1, wherein The specific content of Step 1 is as follows: Taking an arbitrary position on the sea surface as the coordinate origin O, and establishing a rectangular coordinate system with the east and north directions as the x-axis and y-axis respectively. Suppose the planar array has M array elements, and the coordinates of the m-th array element are , where x m is the x-axis coordinate of the m-th array element, and y m is the y-axis coordinate of the m-th array element. H is the known sea depth; the sound source depth is z s , and the horizontal distance and horizontal azimuth angle to the coordinate origin are r s and θ s , where the horizontal azimuth angle θ s is defined as the angle between the projection of the sound source onto the xoy plane and the x-axis, and its value ranges from 0 degrees to 360 degrees; Let the spectrum of the target sound source radiation signal received by the m-th array element at the frequency point f be , where , , are the lowest frequency and the highest frequency of the sound pressure signal respectively; The sound pressure signals received by the M array elements are expressed as an M×1 dimensional column vector in vector form: (1) The superscript T represents the transpose of a vector.

3. The method for deep-sea seafloor planar array target positioning based on multi-path coherent focusing according to claim 1, wherein The specific content of Step 2 is as follows: Let the depth, horizontal distance, and horizontal azimuth angle of the sound source in the search space be \(z\), \(r\), and \(\theta\), respectively. Then its coordinates in the rectangular coordinate system can be written as ; When the sound source is in the direct sound area of the array, only consider the direct path \(D\) and the first - order sea - surface reflection path \(S\); Given the sound - speed profile and sea depth, substitute the sound - source position and receiver position into the ray - tracing model BELLHOP to calculate the propagation time and amplitude where correspond to the direct path \(D\) and the first - order sea - surface reflection path \(S\), respectively; When the sound ray bending is not considered, that is, assuming straight-line propagation, the propagation distance of the sound pressure signal emitted by the actual sound source reaching the m-th array element through the l-th path is: (2) Among them ; At this time, the propagation time and amplitude of the sound pressure signal emitted by the actual sound source reaching the m-th array element through the l-th path are approximated by the spherical wave propagation law, where c is the sound speed in seawater: 。 4. The method for deep - sea seabed planar array target positioning based on multi - path coherent focusing according to claim 1, characterized in that, The specific content of Step 3 is as follows: Given the frequency f of the acoustic signal, construct the multi-path coherent focusing steering vector according to the signal amplitudes and propagation times of the direct sound path D and the first-order sea surface reflected sound path S at the actual sound source depth z, horizontal distance r, and horizontal azimuth angle θ : (5) Normalize the steering vector as follows: (6) Indicates the normalized steering vector.

5. The method for deep-sea seafloor planar array target positioning based on multi-path coherent focusing according to claim 1, wherein Step 4 includes: For the sound pressure signal received by the planar array perform conventional beamforming processing to obtain the beam domain signal pointing to the target : (7) When the acoustic pressure signal is a narrowband signal, the output energy of the narrowband signal is used as the narrowband ambiguity function; when the acoustic pressure signal is a broadband signal, broadband energy synthesis is further performed to obtain the broadband ambiguity function as follows: (8) The value of each point of the narrowband or broadband ambiguity function represents the multi-path focusing energy of the sound source propagating along two paths to the array at the corresponding grid point; the maximum value of the ambiguity function corresponds to the depth, horizontal distance, and horizontal azimuth angle of the desired sound source; Traverse and search for the maximum value of the ambiguity function, and the corresponding position is the estimated value of the horizontal azimuth angle of the desired sound source , the estimated value of the horizontal distance , the estimated value of the depth : 。 6. The method for deep - sea seabed planar array target positioning based on multi - path coherent focusing according to claim 5, wherein The form of beamforming in formula (7) also includes the MVDR method, that is (9) wherein is the cross-spectral density matrix of the observed data, represents the inversion of this matrix.

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