A method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity

Abstract

The present invention relates to a method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity. Based on the interference characteristics of the direct and sea-surface reflection paths in a reliable deep-sea sound path environment, a method for estimating the depth of a near-sea-surface single-frequency moving sound source suitable for a vertical line array in this environment is proposed. The proposed method resamples the beam output intensity based on the sound speed profile information, and then performs a modified Fourier transform on the resampled beam output intensity. The peak position of the transform output is the result of the sound source depth estimation. Compared with the existing modified Fourier transform sound source depth estimation methods, the method proposed in the present invention can effectively estimate the depth of a near-sea-surface single-frequency moving sound source. In the given typical embodiments, the method proposed in the present invention (compared with the original method) can reduce the depth estimation deviation from 13.01 m to 1.23 m, and the corresponding relative estimation deviation from 16.25% to 1.54%.

Description

Technical Field

[0001] The present invention belongs to the fields of ocean engineering, underwater acoustic engineering, array signal processing, sonar technology, etc., and relates to a method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity, which is applicable to the passive estimation problem of the depth of a near-surface single-frequency moving sound source by a deep-sea large-depth vertical line array. Background Art

[0002] Estimating the depth of a deep-sea sound source is an important and challenging problem in sound source localization and has been widely concerned. In a reliable deep-sea sound path environment (the sound source is near the sea surface and the receiving array is placed near the seabed), the array received signal is mainly composed of a direct path (D) and a sea surface reflection path (SR). The interference between the two paths causes the intensity fluctuation characteristics of the beam output to be closely related to the sound source depth. Therefore, in a reliable sound path environment, the interference characteristics of the direct-sea surface reflection path (D-SR interference) are one of the effective methods for estimating the depth of a deep-sea sound source.

[0003] For a broadband sound source, the D-SR interference is reflected in the intensity fluctuation of the received signal in the frequency domain. When the vertical arrival angle of the sound source signal is known, the sound source depth can be obtained by matching the spectral amplitude fluctuation characteristics of the beamforming output signal with the theoretical spectral amplitude calculated by the model. For a narrowband / single-frequency moving sound source, the D-SR interference characteristics are reflected in the fluctuation of the beam output intensity with the vertical arrival angle (or the sound source distance) of the sound source signal. Under narrowband conditions, the sound source depth can be obtained not only by the matching method, but also by the modified Fourier transform method proposed by McCargar and Zurk [R. McCargar and L. M. Zurk, "Depth-based signal separation with vertical linear arrays in the deep ocean," J. Acoust. Soc. Am., vol. 133, no. 4, pp. EL320-EL325, 2013.]. This method is based on the Lloyd mirror theory, and performs a modified Fourier transform on the beam output intensity sequence, and the peak value of the transform output directly corresponds to the sound source depth.

[0004] Compared with the matching methods, the sound source depth estimation method based on the modified Fourier transform has the advantages of convenient practical application and fast calculation speed. However, the existing sound source depth estimation method based on the modified Fourier transform is derived under the Lloyd mirror theory (i.e., the constant sound speed hypothesis), and there may be estimation errors in the actual sound speed profile environment that varies with depth. Summary of the Invention

[0005] Technical Problems to be Solved

[0006] To avoid the deficiencies of the prior art, the present invention proposes a deep-sea sound source depth estimation method based on resampling of beam output intensity, which solves the problem of large estimation deviation of the existing deep-sea single-frequency sound source depth estimation method based on the modified Fourier transform in the actual sound speed profile environment that changes with depth. First, resample the beam output intensity based on the sound speed profile information, and then use the modified Fourier transform for sound source depth estimation. Compared with the existing modified Fourier transform sound source depth estimation method, the method proposed by the present invention has higher estimation accuracy in typical deep-sea environments.

[0007] Technical solution

[0008] A deep-sea sound source depth estimation method based on resampling of beam output intensity, characterized in that: a vertical line array is deployed on the seabed to receive single-frequency signals emitted by a radially moving sound source near the sea surface. The vertical array consists of M array elements with an element spacing of d and an array center depth of z r ; The steps for sound source depth estimation are as follows:

[0009] Step 1: At the initial moment, the horizontal distance between the sound source and the vertical array is r0, the sound source frequency is f, and the depth is z s ; The horizontal radial movement aperture of the sound source during the observation time is r SPAN , and the horizontal distance of the sound source at the end of the observation is r0 + r SPAN ;

[0010] The total observation time is T, the beam output intensity, that is, the azimuth spectrum observation interval is t intv , and during the movement of the sound source, the beam output intensity, that is, the azimuth spectrum, is observed K = ceil(T / t intv ) times, where ceil(·) represents rounding down;

[0011] Step 2: For the kth observation time point, k = 1, 2,..., K, perform conventional beamforming on the array received signal to obtain the beamforming azimuth spectrum of the sound source signal:

[0012] B k (θ) = |Y k (θ, f)| 2

[0013] where: Y k (θ, f) is the output of the beamformer pointing to the angle θ at the frequency point f;

[0014] Step 3: For the beam output azimuth spectra B k (θ) at all times, extract the sound source trajectory in the time-azimuth plane. The process is as follows: Use the L observation times with the largest normalized intensity of the peak of the beam output intensity, that is, the azimuth spectrum, at all times, denoted as L1, L2,..., L L ;

[0015] Extract the vertical arrival angles corresponding to the sound sources at L moments, i.e., the azimuth spectrum The angle corresponding to the peak is denoted as θ L1 , θ L2 , …, θ LL , corresponding to the sound source at time t L1 , t L2 , …, t LL ; the angles at these moments;

[0016] Fit the received angles of the sound source signals at all K observation time points to obtain the vertical arrival angles of the sound source signals at k = 1, 2, …, K moments, denoted as θ1, θ2, …, θ K ;

[0017] The received angles of the sound source signals at K observation time points are the sound source trajectories extracted in the time-azimuth plane;

[0018] Step 4: For k = 1, 2, …, K moments, extract the beam output intensities of the conventional beamforming in the directions of θ1, θ2, …, θ K and correspond them to sin(θ1), sin(θ2), …, sin(θ K ) to obtain the beam output intensity sequence in the sine domain of the received angle, denoted as x(u) = B k (θ k ), where u = sin(θ1), …, sin(θ K );

[0019] Step 5: Resample the beam output intensity sequence x(u);

[0020] Step 6: Perform a modified Fourier transform on the resampled beam output intensity sequence. The position of the peak of the output X rsp (z) of the resampled sequence after the modified Fourier transform is the estimated result of the sound source depth.

[0021] The calculation of the beamforming azimuth spectrum of the sound source signal in Step 2 is as follows: Perform a fast Fourier transform on the received signals of the array elements at each moment to obtain the received signals in the frequency domain, extract the received signals at frequency f. Denote the received signal of the j-th array element at the k-th moment in the frequency domain as The weights of the conventional beamformer at frequency f pointing to angle θ:

[0022]

[0023] where the superscript "T" represents the transpose operation, c is the reference sound speed for beamforming, and i is the imaginary unit; The output of the beamformer at the k-th moment, at frequency f pointing to angle θ is:

[0024]

[0025] Where the superscript "H" represents the conjugate transpose operation, and "×" represents vector multiplication;

[0026] Then the beamforming azimuth spectrum is: B k (θ) = |Y k (θ,f)| 2 .

[0027] Resampling the beam output intensity sequence x(u) in step 5: x rsp (u) = x[h(u)], where h(u) represents the resampling operator: h(u) = ξ -1 (u), and ξ -1 (u) represents the inverse function of ξ(u), and ξ(u) is as follows:

[0028]

[0029] Where: c zr is the sound speed at the depth of the center point of the vertical array, z s-orig is an initial estimated result of the sound source depth, provided by the existing modified Fourier transform method, c w is an average sound speed: Where z s-max is the maximum possible sound source depth, and c(z) is the seawater sound speed at depth z.

[0030] Performing a modified Fourier transform on the resampled beam output intensity sequence in step 6:

[0031]

[0032] Where u min-rsp = ξ(sinθ1) and u max-rsp = ξ(sinθ K ) respectively represent the lower and upper limits of the value of u in the resampled sequence x rsp (u); u n is the nth sampling point in the resampled beam intensity sequence, N is the total number of resampling points, and Δu rsp is the sampling interval of the resampled beam intensity sequence.

[0033] The sound source depth is not less than 10m.

[0034] The radial motion aperture r SPAN of the sound source is not less than 3km.

[0035] The sound source frequency is not less than 100Hz.

[0036] Beneficial effects

[0037] A method for estimating the depth of a deep - sea sound source based on resampling of beam output intensity is proposed in the present invention. Based on the interference characteristics of the direct and sea - surface reflection paths in a reliable deep - sea acoustic path environment, a method for estimating the depth of a near - sea - surface single - frequency moving sound source applicable to a vertical linear array in this environment is proposed. The proposed method resamples the beam output intensity based on the sound - speed profile information, and then performs a modified Fourier transform on the resampled beam output intensity. The peak position of the transform output is the estimated result of the sound - source depth. Compared with the existing modified Fourier transform method for sound - source depth estimation.

[0038] The method proposed in the present invention has higher estimation accuracy, and at the same time retains the advantages of fast calculation speed and convenient practical application. The basic principle and implementation scheme of the method proposed in the present invention have been verified by computer numerical simulation. The results show that in a typical deep - sea environment, the method proposed in the present invention can effectively estimate the depth of a near - sea - surface single - frequency moving sound source. In the given typical embodiment, the method proposed in the present invention (compared with the original method) can reduce the depth - estimation deviation from 13.01 m to 1.23 m, and the corresponding relative estimation deviation from 16.25% to 1.54%. Brief Description of the Drawings

[0039] Figure 1 It is a schematic diagram of the sound - speed profile of the simulation scenario.

[0040] Figure 2 It is a simulation example of the sound - source signal and the array - received signal. Sub - figure (a) is the time - domain waveform and time - frequency analysis result of the sound - source signal, and sub - figure (b) is the array - received signal when the sound - source distance is 6 km.

[0041] Figure 3 It is a flow chart of a method for estimating the depth of a deep - sea sound source based on resampling of beam output intensity proposed in the present invention.

[0042] Figure 4 It is the conventional beam - forming azimuth spectrum (normalized result) of the array - received signal at all times. The black circles in the figure represent the peak positions of the beam outputs with a normalized intensity greater than - 3 dB, and the black dashed line represents the extracted sound - source trajectory.

[0043] Figure 5 It is from Figure 4 The normalized result of the beam output intensity in the sine domain of the received angle extracted in.

[0044] Figure 6 It is the normalized result of the beam output intensity in the sine domain of the received angle after resampling.

[0045] Figure 7 It is the result of the original modified Fourier transform method for sound - source depth estimation.

[0046] Figure 8The sound source depth estimation result of the method proposed by the present invention. Detailed implementation manners

[0047] The present invention will be further described below in conjunction with embodiments and the accompanying drawings:

[0048] The technical solution adopted by the present invention to solve its technical problems: A deep-sea sound source depth estimation method based on resampling of beam output intensity, which is characterized by including the following steps:

[0049] Step 1: In a typical deep-sea environment, deploy a vertical line array near the seabed to receive the single-frequency signal emitted by a radially moving sound source near the sea surface. The vertical array consists of M array elements, the element interval is d, and the center depth of the array is z r . The sound source depth is z s , the frequency is f, the horizontal distance between the sound source and the vertical array at the initial moment is r0, the horizontal radial movement aperture of the sound source during the observation time is r SPAN , and the horizontal distance of the sound source at the end of the observation is r0 + r SPAN . The total observation time is T, the beam output intensity observation interval is t intv , and the beam output intensity is observed K = ceil(T / t intv ) times during the movement of the sound source, where ceil(·) represents rounding down.

[0050] Step 2: For the k-th observation time point, k = 1, 2,..., K, perform conventional beamforming on the array received signal to obtain the beam output intensity of the sound source signal. The specific process is as follows:

[0051] For each moment, perform a fast Fourier transform on the element received signal to obtain the frequency-domain received signal, and extract the received signal at frequency f. Denote the frequency-domain received signal of the j-th element at the k-th moment as The weight of the conventional beamformer at frequency f pointing to the angle θ is

[0052]

[0053] where the superscript "T" represents the transpose operation, c is the beamforming reference sound speed, and i is the imaginary unit. The output of the beamformer at the k-th moment, at the frequency point f pointing to the angle θ, is

[0054]

[0055] where the superscript "H" represents the conjugate transpose operation, and "×" represents vector multiplication.

[0056] The beamforming azimuth spectrum is calculated by the following formula:

[0057] B k (θ) = |Y k(θ,f)| 2 (3)

[0058] Step 3: Combine the beam output azimuth spectra B k (θ) at all times, and extract the sound source trajectory in the time-azimuth plane. The specific process is as follows:

[0059] Since the beam intensity of the sound source signal fluctuates with time, L observation times with relatively large beam output intensities (the normalized intensity of the azimuth spectrum peak) can be found, denoted as L1, L2, …, L L . Extract the vertical arrival angles of the sound source corresponding to these L times [i.e., the angles corresponding to the azimuth spectrum peaks], denoted as θ L1 , θ L2 , …, θ LL , corresponding to the angles of the sound source at times t L1 , t L2 , …, t LL . According to the sound source angles at the above L times, fit the sound source signal reception angles at all K times to obtain the vertical arrival angles of the sound source signal at k = 1, 2, …, K times, denoted as θ1, θ2, …, θ K .

[0060] Step 4: For k = 1, 2, …, K times, extract the beam output intensities of the conventional beamforming in the directions of θ1, θ2, …, θ K , and correspond them to sin(θ1), sin(θ2), …, sin(θ K ) to obtain the beam output intensity sequence in the sine domain of the reception angle, denoted as x(u) = B k (θ k ), u = sin(θ1), …, sin(θ K ).

[0061] Step 5: Resample the beam output intensity sequence x(u) according to the following formula:

[0062] x rsp (u) = x[h(u)] (4)

[0063] where h(u) represents the resampling operator, which is determined by the following formula

[0064] h(u) = ξ -1 (u) (5)

[0065] where ξ -1 (u) represents the inverse function of ξ(u)

[0066]

[0067] In the above formula, czr is the sound speed at the depth of the center point of the vertical array, z s-orig is an estimated result of the initial sound source depth, which can be provided by the existing modified Fourier transform method, c w is an average sound speed, calculated by the following formula:

[0068]

[0069] where z s-max is the maximum possible sound source depth, and c(z) is the seawater sound speed at depth z.

[0070] Step Six: Perform a modified Fourier transform on the resampled beam output intensity sequence according to the following formula:

[0071]

[0072] where u min -rsp = ξ(sinθ1) and u max -rsp = ξ(sinθ K ) respectively represent the lower and upper limits of the value of u in the resampled sequence x rsp (u). u n is the nth sampling point in the resampled beam intensity sequence, N is the total number of resampling points, and Δu rsp is the sampling interval of the resampled beam intensity sequence.

[0073] Finally, the position of the peak of the output X rsp (z) of the modified Fourier transform of the resampled sequence is the estimated result of the sound source depth.

[0074] It is applicable to narrowband / single-frequency sound sources with radial motion, and the radial motion of the sound source can be from far to near or from near to far. Specific embodiments:

[0076] 1. Deep-sea waveguide environment, sound source, and receiving vertical array configuration

[0077] To verify the effectiveness of the method of the present invention, a computer simulation experiment is carried out. This embodiment considers a typical deep-sea environment with a sea depth of 3950 m, and the seawater sound speed profile is as shown in the appendix Figure 1 shown, the seawater density is 1.0 g / cm 3 ; the sound speed of the seabed half-space is 1600 m / s, the density is 1.5 g / cm 3 , and the compression wave attenuation coefficient of the seabed sediment is 0.14 dB / λ. The vertical line array used for reception consists of 16 elements, the element interval is 2 m, and the center depth of the array is 3716 m. The sound source depth is 80 m, radiating a single-frequency signal with a radiation frequency f = 535 Hz, the initial horizontal distance is r0 = 6 km, and the horizontal radial motion aperture is rSPAN = 5 km, the radial velocity of the sound source is 5 m / s. During the movement of the sound source, the vertical array makes 1000 observations on the beam output intensity of the sound source signal, and the observation interval is t intv = 1 s, and the horizontal distance interval of the observation is 5 m.

[0078] 2. Signal received by the vertical line array

[0079] In this embodiment, it is assumed that the sound source signal is a single-frequency CW pulse signal, the pulse length is 0.5 s, the amplitude is 1, and its time-domain waveform and time-frequency analysis results are as shown in the appendix Figure 2 (a). The array sampling frequency is f s = 10 kHz, and the array starts to collect data at the same time as the sound source signal is emitted. The receiver startup time is 20 s.

[0080] The simulation method for the signal received by the array is as follows: For the sound source distance at a certain moment, use the Bellhop sound field model to calculate the arrival time and amplitude of the sound rays between the sound source and the receiving array (all sensors). For a certain sensor, use the arrival structure of these sound rays to form the channel impulse response, and perform time-domain convolution on the sound source signal and the channel impulse response to obtain the signal received by this sensor. Finally, add noise to the simulated received signal according to the signal-to-noise ratio. It is assumed that the received signal-to-noise ratio of each sensor within T R is SNR = 0 dB. Perform the above simulation operations on all receiving elements at all receiving times in sequence to obtain the simulated array received signal. The received signals of all elements when the sound source distance is 6 km are as shown in the appendix Figure 2 (b).

[0081] 3. A method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity

[0082] As shown in the appendix Figure 3 , the specific implementation process of the method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity proposed by the present invention is as follows:

[0083] Step 1: In a typical deep-sea environment, deploy a set of vertical line arrays near the seabed to receive narrowband single-frequency signals emitted by a radially moving sound source near the sea surface. The vertical array consists of M = 16 elements, the element interval is d = 2 m, and the center depth of the array is z r = 3716 m. The depth of the sound source is z s = 80 m, the frequency is f = 535 Hz, the horizontal distance between the sound source and the vertical array at the initial moment is r0 = 6 km, the horizontal radial movement aperture of the sound source during the observation time is r SPAN = 5 km, and the horizontal distance of the sound source at the end of the observation is r0 + r SPAN = 11 km. The total observation time is T = 1000 s, and the beam output intensity observation interval is tintv = 1 s, a total of K = ceil(T / t intv ) = 1000 times are observed during the movement of the sound source, where ceil(·) represents rounding down. In this embodiment, this step has been completed through the sound field model simulation of the Bellhop model, and finally 1000 groups of array reception signals corresponding to different positions of the sound source are obtained. The number of sampling points of each group of array reception signals is 2×10 5 .

[0084] Step 2: For the k-th observation time point, k = 1, 2, …, 1000, perform conventional beamforming on the array reception signal to obtain the beam output intensity of the sound source signal. The specific process is as follows:

[0085] For each moment, perform a fast Fourier transform on the element reception signal to obtain the frequency-domain reception signal, and extract the reception signal at the frequency f = 535 Hz. The specific operation method is: perform a fast Fourier transform on the element reception signal with a length of 2×10 5 to obtain a transform result with a length of 2×10 5 , and extract the value of the 10701st point as the reception signal at 535 Hz. Denote the frequency-domain reception signal of the j-th element at the k-th moment as

[0086] The weight of the conventional beamformer at the frequency f and the pointing angle θ is

[0087]

[0088] where the superscript "T" represents the transpose operation, c = 1521.4 m / s is the beamforming reference sound speed, and i is the imaginary unit. The output of the beamformer at the k-th moment, at the frequency point f and the pointing angle θ, is

[0089]

[0090] where the superscript "H" represents the conjugate transpose operation, and "×" represents vector multiplication.

[0091] The beamforming azimuth spectrum is calculated by the following formula:

[0092] B k (θ) = |Y k (θ, f)| 2 (11)

[0093] Through the above steps, the time-azimuth plane composed of the beamforming azimuth spectra at all observation moments is as shown in the appendix Figure 4 .

[0094] Step 3: Combine the beam output azimuth spectra B k(θ), extract the sound source trajectory on the time-azimuth plane. The specific process is as follows:

[0095] As shown in the appendix Figure 4 , the beam intensity of the sound source signal fluctuates with time. Therefore, 212 observation times with relatively large beam output intensity (normalized intensity greater than -3 dB) can be found and denoted as L1, L2, …, L 212 . Extract the vertical arrival angle of the sound source corresponding to these 212 times [i.e., the angle corresponding to the peak of the azimuth spectrum , denoted as θ L1 , θ L2 , …, θ L212 , corresponding to the angles of the sound source at times t L1 , t L2 , …, t L212 (as shown by the black circles in the appendix Figure 4 ). According to the sound source angles at the above 212 times, fit the received angles of the sound source signals at all 1000 times to obtain the vertical arrival angles of the sound source signals at times k = 1, 2, …, 1000, denoted as θ1, θ2, …, θ 1000 , as shown by the black dashed line in the appendix Figure 4 .

[0096] Step 4: For k = 1, 2, …, 1000 times, respectively extract the beam output intensities of the conventional beamforming in the directions of θ1, θ2, …, θ 1000 , and correspond them to sin(θ1), sin(θ2), …, sin(θ 1000 ) to obtain the beam output intensity sequence in the sine domain of the received angle, denoted as x(u) = B k (θ k ), u = sin(θ1), …, sin(θ 1000 ). For this embodiment, the normalized result of the beam output intensity sequence in the sine domain of the received angle is as shown in the appendix Figure 5 , and the value range of u is 0.2804~0.5079.

[0097] Step 5: Resample the beam output intensity sequence x(u) according to the following formula:

[0098] x rsp (u) = x[h(u)] (12)

[0099] where h(u) represents the resampling operator, which is determined by the following formula

[0100] h(u) = ξ -1 (u) (13)

[0101] where

[0102]

[0103] In the above formula, c zr is the sound speed at the depth of the center point of the vertical array, which is 1521.4 m / s, and z s-orig = 93.01 m is an estimated result of the initial sound source depth, provided by the existing modified Fourier transform method (the result is as shown in the appendix Figure 7 ), c w is an average value of the sound speed, calculated by the following formula:

[0104]

[0105] where z s-max = 300 m is the maximum possible sound source depth, and c(z) is the seawater sound speed at the depth z.

[0106] The beam output intensity sequence after resampling is as shown in the appendix Figure 6 . After resampling, the value range of u is 0.2119 - 0.4732. The resampling interval in the u domain is 3×10 -4 , and the number of resampling points is 1000 points.

[0107] Step Six: Perform a modified Fourier transform on the beam output intensity sequence after resampling according to the following formula:

[0108]

[0109] where u min-rsp = ξ(sinθ1) = 0.211 and u max-rsp = ξ(sinθ K ) = 0.4732 respectively represent the lower limit and the upper limit of the value of u in the resampled sequence x rsp (u). u n is the nth sampling point in the resampled beam intensity sequence, and Δu rsp = 3×10 -4 is the sampling interval of the resampled beam intensity sequence.

[0110] The output X rsp (z) of the modified Fourier transform of the resampled sequence is as shown in the appendix Figure 8 . The peak position thereof is the estimated result of the sound source depth, which is 81.23 m. It has a higher estimation accuracy compared with the original method (the estimated result is 93.01 m). It can be seen that compared with the original method, the method proposed by the present invention can reduce the estimation deviation from 13.01 m to 1.23 m, and the corresponding relative estimation deviation from 16.25% to 1.54%.

Claims

1. A method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity, characterized in that: A vertical line array is deployed on the seabed to receive single-frequency signals emitted by a radial motion sound source near the sea surface. The vertical line array consists of M array elements with an element spacing of d and the center depth of the array is z r The steps for estimating the sound source depth are as follows: Step 1: At the initial moment, the horizontal distance between the sound source and the vertical array is r0, the frequency of the sound source is f, and the depth is z s ; During the observation time, the horizontal radial movement aperture of the sound source is r SPAN , and at the end of the observation, the horizontal distance of the sound source is r0 + r SPAN ; The total observation time is T, and the beam output intensity, i.e., the azimuth spectrum observation interval, is t intv , and during the movement of the sound source, a total of K = ceil(T / t intv ) times of beam output intensity, i.e., azimuth spectra, are observed, where ceil(·) represents rounding down; Step 2: For the k-th observation time point, where k = 1, 2, …, K, perform conventional beamforming on the array received signals to obtain the beamforming azimuth spectrum of the sound source signal: B k (θ) = |Y k (θ, f)| 2 Where: Y k (θ,f) is the output of the beamformer at the pointing angle θ at the frequency point f; Step 3: For the beam output azimuth spectrum B k (θ) at all times, extract the sound source trajectory in the time-azimuth plane. The process is as follows: Denote the L observation times with the largest normalized intensity of the beam output intensity at all times, i.e., the azimuth spectrum peak, as L1, L2, …, L L ; Extract the vertical arrival angles corresponding to the sound sources at L moments, that is, the azimuth spectrum The angle corresponding to the peak is denoted as θ L1 , θ L2 , …, θ LL , corresponding to the angles of the sound sources at t L1 , t L2 , …, t LL moments; Fit the received angles of the sound source signals at all K observation time points to obtain the vertical arrival angles of the sound source signals at times k = 1, 2, …, K, denoted as θ1, θ2, …, θ K ; The received angles of the sound source signals at the K observation time points are the sound source trajectories extracted on the time-azimuth plane of the sound source; Step 4: At moments \(k = 1, 2, \ldots, K\), extract the beam output intensities of the conventional beamforming in the directions of \(\theta_1, \theta_2, \ldots, \theta\) K and correspond them to \(\sin(\theta_1), \sin(\theta_2), \ldots, \sin(\theta\) K ), to obtain a beam output intensity sequence in the sine domain of the reception angle, denoted as \(x(u)=B\) k (\theta k ), where \(u = \sin(\theta_1), \ldots, \sin(\theta\) K ); Step 5: Resample the beam output intensity sequence x(u); Step 6: Perform a modified Fourier transform on the resampled beam output intensity sequence. The output X of the modified Fourier transform of the resampled sequence rsp (z) at the peak position is the estimated result of the sound source depth.

2. The method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity according to claim 1, characterized in that: The calculation of the beamforming azimuth spectrum of the sound source signal in step 2 is as follows: perform a fast Fourier transform on the received signals of each array element at each moment to obtain the received signals in the frequency domain, extract the received signals at frequency f, and denote the received signal in the frequency domain of the j-th array element at time k as The weights of the conventional beamformer at the pointing angle θ at frequency f: where the superscript "T" represents the transpose operation, c is the beamforming reference sound speed, and i is the imaginary unit; at the k-th moment, the output of the beamformer with a pointing angle θ at the frequency point f is: where the superscript "H" represents the conjugate transpose operation, and "×" represents the vector multiplication; Then the beamforming azimuth spectrum is: B k (θ) = |Y k (θ, f)| 2 .

3. The method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity according to claim 1, wherein: Resampling the beam output intensity sequence x(u) in step 5: x rsp (u) = x[h(u)], where h(u) represents the resampling operator: h(u) = ξ -1 (u), ξ -1 (u) represents the inverse function of ξ(u), and ξ(u) is as follows: where: c zr is the sound speed at the depth of the center point of the vertical array, z s-orig is an estimated result of the initial sound source depth, provided by the existing modified Fourier transform method, c w is an average sound speed: where, z s-max is the maximum possible sound source depth, and c(z) is the seawater sound speed at depth z.

4. The method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity according to claim 1, wherein: Step 6 performs a modified Fourier transform on the resampled beam output intensity sequence; where u min-rsp = ξ(sinθ1) and u max-rsp = ξ(sinθ K ) represent the lower and upper limits of the value of u in the resampled sequence x rsp (u), respectively; u n is the nth sampling point in the resampled beam intensity sequence, N is the total number of resampling points, and Δu rsp is the sampling interval of the resampled beam intensity sequence.

5. The method for estimating the depth of a deep-sea sound source based on beam output intensity resampling according to claim 1, wherein: The depth of the sound source is not less than 10 m.

6. The method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity according to claim 1, wherein: The radial motion aperture r of the sound source SPAN is not less than 3 km.

7. The method for estimating the depth of a deep-sea sound source based on resampling of beam output intensity according to claim 1, wherein: The frequency of the sound source is not less than 100 Hz.

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