A method for suppressing direct wave based on fractional fourier transform in bistatic sonar

Abstract

Aiming at the problem of detection blind area caused by strong direct wave interference in bistatic imaging sonar system, a narrow-band filtering method based on fractional Fourier transform domain is proposed. The characteristic of linear frequency modulation signal is that it appears as an impulse in the fractional Fourier transform domain at its best transform order. The fractional Fourier transform of the best order is performed on the element domain signal to separate the direct wave from the echo. Then the direct wave is eliminated in the fractional Fourier transform domain. Finally, the forward scattering time domain signal of the seabed is reconstructed by fractional inverse Fourier transform. Further, the acoustic imaging processing is performed on the signal processed by fractional filtering, and the acoustic imaging result after direct wave suppression is obtained. Compared with the traditional bistatic sonar imaging, the method can effectively suppress the direct wave, reduce the direct wave masking area in the bistatic acoustic imaging, and improve the detection blind area problem caused by the direct wave in the traditional bistatic sonar imaging.

Description

A method for suppressing direct waves from bistatic sonar based on fractional Fourier transform Technical Field

[0001] This invention relates to a bistatic sonar direct wave suppression method based on fractional Fourier transform, applicable to seabed mapping and seabed target detection, and belongs to the field of sonar imaging. Background Technology

[0002] Currently, monostatic sonar systems with both transmitter and receiver are commonly used for seabed topography and geomorphology measurements, such as multibeam echo sounders, side-scan sonars, and geotomometers. These systems acquire acoustic images of seabed topography and geomorphology by receiving backscattered signals from the seabed. However, their detection range and scope are limited, making them inefficient and time-consuming for large-scale seabed topography and geomorphology measurements. Against this backdrop, bistatic sonar systems utilize more powerful forward-scattered signals, significantly improving sonar range and anti-interference capabilities (Edwards JR, Schmidt H, Lepage KD. Bistatic synthetic aperture target detection and imaging with an AUV[J].IEEE Journal of Oceanic Engineering, 2001, 26(4): 690-699.). The bistatic sonar imaging system proposed by Zhang Ting et al. in "A Bistatic Acoustic Imaging Method for Large-Scale Seafloor Geomorphological Remote Sensing" (Zhejiang Province: CN110456361A, 2019-11-15) uses a fixed vertical transmitting array as the transmitter. The vertical array controls the transmission pointing angle to illuminate a predetermined seafloor area. Simultaneously, a moving horizontal receiving array travels along a predetermined route centered on the transmitting array to receive forward-scattered signals from the seafloor. Acoustic imaging post-processing of the scattered signals yields a seafloor scattering intensity distribution map. However, in this bistatic sonar imaging system, within an elliptical direct wave masking area centered on both the transmitter and receiver, the direct wave signal amplitude is much larger than the target or seafloor scattering signal amplitude. This causes the seafloor scattering echo from the direct sound zone to be submerged by the direct wave, severely affecting the bistatic sonar imaging quality and failing to accurately reflect seafloor geomorphological features, resulting in a detection blind zone for bistatic imaging sonar. Summary of the Invention

[0003] Technical problems to be solved

[0004] To overcome the problem of direct wave detection blind zone in existing bistatic imaging sonar systems, this invention proposes a bistatic direct wave suppression method based on fractional Fourier transform.

[0005] Technical solution

[0006] A method for suppressing direct waves from bistatic sonar based on fractional Fourier transform, characterized by the following steps:

[0007] Step 1: Model the sonar echo based on the application scenario where the transmitter and receiver are separate. The transmitted signal uses a linear frequency modulated (LFM) signal. The seabed area to be detected is divided into k rectangular grids. According to ray theory, assuming the sound source is located at (0, z0), the sound wave excited by this source will be located at (r...). t The sound pressure of the scattering body at (z) can be expressed as

[0008]

[0009] Where r t Let z be the horizontal position of the scatterer, z be the ocean depth, N be the total number of incident sound rays, and A be the horizontal position of the scatterer. n (s) represents the amplitude of the nth vocal ray. τ is a function of the amplitude of the sound beam, ω is the angular frequency of the emitted sound source, and τ is the frequency of the emitted sound source. n (s) represents the propagation time of the sound ray from the sound source to the scattering point, and s represents the distance the sound ray travels.

[0010] According to the reciprocity principle, the scattered sound pressure received by a hydrophone at a horizontal distance r from the sound source from a unit area of ​​scattering surface can be expressed as:

[0011]

[0012] In the formula, N and M are the total number of incident and emitted sound rays, respectively, and p inc,n Let p be the incident sound wave transfer function. scatt,m Let r be the transfer function of the emitted sound wave. n Let r be the horizontal distance from the sound source to the scattering body for the nth sound ray. m g(a) represents the horizontal distance of the m-th sound ray from the scatterer to the receiver. inc,n ,a scatt,m (θ) is a three-dimensional scattering function, representing the amplitude of the plane wave scattered per unit area of ​​the seabed under the action of a plane wave, a inc,n and a scatt,m θ represents the incident grazing angle and the exit grazing angle of the sound ray, respectively, where θ is the exit azimuth angle.

[0013] By traversing all seabed scattering points that need to be calculated within the imaging area, the superposition of all scattered sound waves in the time domain by the receiving hydrophone is obtained, ultimately yielding the seabed scattering signal in the time domain with separate transmission and reception. Let the transmitted signal be S(t). Without considering interference, the echo signal of the Lth element at the receiving end can be expressed as:

[0014]

[0015] In the formula, K is the number of seabed grids, and τ n Let τ be the propagation time of the nth sound ray from the sound source to the scattering body. m Let θ be the propagation time of the m-th sound ray from the scatterer to the receiver. k Let be the incident angle of the k-th grid ray in the receiving array, d be the element spacing, and f be the distance between the array elements. d This refers to the Doppler frequency shift caused by the relative motion between the receiving array platform and the seabed scattering body. This refers to the random phase perturbation of the signal scattered by the seabed scatterer;

[0016] Step 2: Eliminate direct waves in the u-domain using fractional Fourier transform;

[0017] Sub-step 1: Calculate the optimal FrFT transform order p based on α = -arccotk. opt =2α opt / π, where k is the frequency modulation slope of the LFM signal;

[0018] Sub-step two: Perform p on the single-channel received signal opt The FrFT of order 1 yields a series of impulse signals of the received signal in the u-domain, where the maximum peak point u0 corresponds to the direct wave position;

[0019] For signal X l (t), its fractional Fourier transform can be defined as

[0020]

[0021] Where p is the order of the fractional Fourier transform, α = pπ / 2 is the transform angle, and K p (t,u) is the kernel function of FrFT:

[0022]

[0023] Sub-step 3: Set the transformed signal to zero in the interval after u0-Δu in the u-domain;

[0024] Sub-step four: Perform an order-p transformation on the signal processed in sub-step three. opt The fractional Fourier transform yields the single-channel time-domain signal after direct wave suppression.

[0025]

[0026] Step 3: Receive signals from K array elements. Repeat step 2 for the signals from the K array elements.

[0027] Step 4: After processing the above steps to obtain the array element signal after direct wave suppression, perform beamforming processing to estimate the angle of arrival of the seabed scattered signal; perform matched filtering processing on the output signal of each beam at each angle to estimate the arrival time delay of the seabed scattered signal.

[0028] Step 5: Use imaging algorithms to image the seabed topography and obtain the seabed scattering intensity distribution map after direct wave suppression.

[0029] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0030] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0031] Beneficial effects

[0032] This invention provides a bistatic direct wave suppression method based on fractional Fourier transform. It utilizes the characteristic that a linear frequency modulated signal exhibits an impulse in its optimal fractional Fourier transform domain. An optimal-order fractional Fourier transform is performed on the pairwise domain signal to separate the direct wave from the echo. Then, the direct wave is eliminated in the fractional Fourier transform domain. Finally, the inverse fractional Fourier transform is used to reconstruct the seabed forward scattering time-domain signal. Further acoustic imaging processing is applied to the fractionally filtered signal to obtain the acoustic imaging result after direct wave suppression. Compared with traditional bistatic sonar imaging, this method can effectively suppress direct waves, reduce the direct wave masking area in the bistatic acoustic imaging map, and improve the detection blind zone problem caused by direct waves in traditional bistatic sonar imaging. The beneficial effects are reflected in:

[0033] 1. The bistatic mode, consisting of a fixed vertical transmitting array and a mobile receiving horizontal array, overcomes the problems of short detection range and insufficient resolution in the traditional monostatic acoustic imaging mode.

[0034] 2. Utilizing the separability of direct waves and seabed scattered echoes in the fractional-order transform domain, direct wave suppression is performed on the array element received signal in the fractional-order transform domain, and the preprocessed array element signal is then imaged. The imaging results can reveal the topographic features of the area where the direct wave is masked. Attached Figure Description

[0035] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0036] Figure 1 is a flowchart illustrating the method of the present invention.

[0037] Figure 2 is a schematic diagram of the bistatic sonar imaging system of the present invention.

[0038] Figure 3 is a schematic diagram of the blind zone of direct wave detection by bistatic sonar.

[0039] Figure 4 is a schematic diagram of the seabed feature region constructed in the invention example.

[0040] Figure 5 is an acoustic imaging diagram of the bistatic sonar of the invention example.

[0041] Figure 6 is an acoustic imaging diagram of the invention example when direct wave interference exists.

[0042] Figure 7 shows an acoustic imaging diagram of the array signal after processing using fractional Fourier transform in an example of the invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0044] As shown in Figure 1, the present invention provides a method for suppressing direct waves from bistatic sonar based on fractional Fourier transform, comprising the following steps:

[0045] Step 1: Establish a seabed imaging scene with separate transmitter and receiver as shown in Figure 4, and perform sonar echo modeling; the transmitted signal uses a linear frequency modulated signal, and the seabed area to be detected is divided into k rectangular grids. According to ray theory, if the sound source is located at (0, z0), then the sound wave excited by the sound source will be located at (r... t The sound pressure of the scattering body at (z) can be expressed as

[0046]

[0047] Where r t Let z be the horizontal position of the scatterer, z be the ocean depth, N be the total number of incident sound rays, and A be the horizontal position of the scatterer. n (s) represents the amplitude of the nth vocal ray. τ is a function of the amplitude of the sound beam, ω is the angular frequency of the emitted sound source, and τ is the frequency of the emitted sound source. n (s) represents the propagation time of the sound ray from the sound source to the scattering point, and s represents the distance the sound ray travels.

[0048] According to the reciprocity principle, the scattered sound pressure received by a hydrophone at a horizontal distance r from the sound source from a unit area of ​​scattering surface can be expressed as:

[0049]

[0050] In the formula, N and M are the total number of incident and emitted sound rays, respectively, and p inc,n Let p be the incident sound wave transfer function. scatt,m Let r be the transfer function of the emitted sound wave. n Let r be the horizontal distance from the sound source to the scattering body for the nth sound ray. m Let g(a) be the horizontal distance from the scatterer to the receiver for the m-th sound ray. inc,n ,a scatt,m ,θ) is a three-dimensional scattering function, representing the plane wave amplitude scattered per unit area of ​​the seabed under the action of a plane wave. inc,n and a scatt,m θ represents the incident grazing angle and the exit grazing angle of the sound ray, respectively, and θ is the exit azimuth angle.

[0051] By traversing all seabed scattering points within the imaging area that need to be calculated, the superposition of all scattered sound waves in the time domain by the receiving hydrophone is obtained, ultimately yielding the seabed scattering signal in the time domain with separate transmission and reception. Let the transmitted signal be S(t). Without considering noise, reverberation, and other interference factors, the echo signal of the l-th element at the receiving end can be expressed as:

[0052]

[0053] In the formula, K is the number of seabed grids, and τ n Let τ be the propagation time of the nth sound ray from the sound source to the scattering body. m Let θ be the propagation time of the m-th sound ray from the scatterer to the receiver. k Let be the incident angle of the k-th grid ray in the receiving array, d be the element spacing, and f be the distance between the array elements. d This refers to the Doppler frequency shift caused by the relative motion between the receiving array platform and the seabed scattering body. This represents the random phase perturbation of the scattered signal from the seabed scatterer.

[0054] Step 2: Eliminate direct waves in the u-domain using fractional Fourier transform;

[0055] Sub-step 1: Based on α opt = -arccotk calculates the optimal FrFT transform order p opt =2α opt / π, where k is the frequency modulation slope of the LFM signal;

[0056] Sub-step two: Perform p on the single-channel received signal opt The FrFT of order 1 yields a series of impulse signals of the received signal in the u-domain, where the maximum peak point u0 corresponds to the direct wave position.

[0057] For signal Xl (t), its fractional Fourier transform can be defined as

[0058]

[0059] Where p is the order of the fractional Fourier transform, α = pπ / 2 is the transform angle, and K p (t,u) is the kernel function of FrFT:

[0060]

[0061] Sub-step 3: Set the transformed signal to zero in the interval after u0-Δu in the u-domain;

[0062] Sub-step four: Perform an order-p transformation on the signal processed in sub-step three. opt The fractional Fourier transform yields the single-channel time-domain signal after direct wave suppression.

[0063]

[0064] Step 3: Receive signals from a total of L array elements. Repeat step 2 for the signals from the L array elements.

[0065] Step 4: After processing the above steps to obtain the array element signal with suppressed direct wave, perform beamforming processing to estimate the angle of arrival of the seabed scattered signal. Perform matched filtering processing on the beam output signals at each angle to estimate the arrival time delay of the seabed scattered signal;

[0066] Step 5: Use imaging algorithms to image the seabed topography and obtain the seabed scattering intensity distribution map after direct wave suppression.

[0067] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0068] To verify the feasibility of the method of this invention and to illustrate its characteristics, simulation analysis was conducted. The imaging region was constructed in the simulation as shown in Figure 4. Two seabed feature regions were set inside and outside the direct sound zone to simulate strong seabed scatterers. Feature region 1 was set to the range [-2.5:-1.5,-0.5:0.5], and feature region 2 was set to the range [-0.5:0.5,-0.5:0.5]. The scattering coefficient of the feature regions was set to 1, and the scattering coefficients of other regions were set to 0. The transmitted signal was a linear frequency modulated signal with a center frequency f0 = 1800 Hz, a bandwidth of B = 200 Hz, and a pulse width T = 1 s. Figure 5 shows the image without the addition of a direct wave, where the strong seabed target scatterer can be clearly seen. Figure 6 shows the image after the addition of a direct wave to the simulated signal. At this time, due to the interference of the strong direct wave, a direct wave masking area as shown in Figure 3 is generated in the image, and the seabed scatterer cannot be observed in this area. Figure 7 shows the imaging result after using fractional Fourier transform to suppress the direct wave in the array element signal. At this time, the seabed scatterer in the direct wave masking area can be observed in the imaging result.

[0069] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for suppressing direct waves from bistatic sonar based on fractional Fourier transform, characterized in that... The steps are as follows: Step 1: Model the sonar echo according to the application scenario where the transmitting and receiving ends are set separately; the transmitted signal uses a linear frequency modulated signal, and the seabed to be detected is divided into k rectangular grids. According to ray theory, if the sound source is located at (0, z0), then the sound wave excited by the sound source will be located at (r). t The sound pressure of the scattering body at (z) can be expressed as Where r t Let z be the horizontal position of the scatterer, z be the ocean depth, N be the total number of incident sound rays, and A be the horizontal position of the scatterer. n (s) represents the amplitude of the nth vocal ray. τ is a function of the amplitude of the sound beam, ω is the angular frequency of the emitted sound source, and τ is the frequency of the emitted sound source. n (s) represents the propagation time of the sound ray from the sound source to the scattering point, and s represents the path traveled by the sound ray; according to the reciprocity principle, the scattered sound pressure received by a hydrophone at a horizontal distance r from the sound source, corresponding to a unit area of ​​scattering body, can be expressed as: In the formula, N and M are the total number of incident and emitted sound rays, respectively, and p inc,n Let p be the incident sound wave transfer function. scatt,m Let r be the transfer function of the emitted sound wave. n Let r be the horizontal distance from the sound source to the scattering body for the nth sound ray. m g(a) represents the horizontal distance of the m-th sound ray from the scatterer to the receiver. inc,n ,a scatt,m (θ) is a three-dimensional scattering function, representing the amplitude of the plane wave scattered per unit area of ​​the seabed under the action of a plane wave, a inc,n and a scatt,m θ represents the incident grazing angle and the exit grazing angle of the sound ray, respectively, where θ is the exit azimuth angle. By traversing all seabed scattering points that need to be calculated within the imaging area, the superposition of all scattered sound waves in the time domain by the receiving hydrophone is obtained, ultimately yielding the seabed scattering signal in the time domain with separate transmission and reception. Let the transmitted signal be S(t). Without considering interference, the echo signal of the Lth element at the receiving end can be expressed as: In the formula, K is the number of seabed grids, and τ n Let τ be the propagation time of the nth sound ray from the sound source to the scattering body. m Let θ be the propagation time of the m-th sound ray from the scatterer to the receiver. k Let be the incident angle of the k-th grid ray in the receiving array, d be the element spacing, and f be the distance between the array elements. d This refers to the Doppler frequency shift caused by the relative motion between the receiving array platform and the seabed scattering body. Step 2: Eliminate direct waves in the u-domain using fractional Fourier transform; Sub-step 1: Calculate the optimal FrFT transform order p based on α = -arccotk. opt =2α opt / π, where k is the frequency modulation slope of the LFM signal; Sub-step two: Perform p on the single-channel received signal. opt A first-order FrFT yields a series of impulse signals in the u-domain from the received signal, where the maximum peak point u0 corresponds to the direct wave position; for signal X l (t), its fractional Fourier transform can be defined as Where p is the order of the fractional Fourier transform, α = pπ / 2 is the transform angle, and K p (t,u) is the kernel function of FrFT: Sub-step 3: Set the transformed signal to zero in the u-domain after u0-Δu; Sub-step 4: Perform a transformation on the signal processed in sub-step 3 with order -p. opt The fractional Fourier transform yields the single-channel time-domain signal after direct wave suppression. Step 3: Receive signals from K array elements, and repeat Step 2 for the K array element signals; Step 4: After processing the above steps, obtain the array element signals after direct wave suppression, perform beamforming processing, and estimate the angle of arrival of the seabed scattered signal; perform matched filtering processing on the beam output signals at each angle, and estimate the arrival time delay of the seabed scattered signal; Step 5: Use imaging algorithms to perform seabed topographic imaging, and obtain the seabed scattered intensity distribution map after direct wave suppression.

2. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

3. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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