A passive ranging method and system for horizontal linear array based on surface waveguide leakage effect

By using a method based on the surface waveguide leakage effect and leveraging Fourier transform and ray geometry, the problem of inaccurate sound source distance estimation in the deep-sea acoustic shadow zone was solved, achieving higher robustness and computational efficiency.

CN120993423BActive Publication Date: 2026-03-06INST OF ACOUSTICS CHINESE ACAD OF SCI
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-08-11
Publication Date
2026-03-06

AI Technical Summary

Technical Problem

Under deep-sea waveguide conditions, horizontal arrays cannot accurately estimate the angle of arrival of a single seabed reflection signal in the acoustic shadow zone, resulting in inaccurate sound source distance estimation. Furthermore, they are sensitive to prior environmental knowledge and involve a large amount of computation.

Method used

By utilizing the surface waveguide leakage effect, and through Fourier transform, beamforming, and incoherent accumulation, combined with diffraction ray theory and ray geometry, the azimuth and distance of the target sound source can be estimated.

Benefits of technology

It achieves greater robustness and computational efficiency in deep-sea acoustic shadow zones, reduces reliance on prior environmental knowledge, and improves the accuracy of sound source distance estimation.

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Abstract

This application provides a passive ranging method and system for horizontal linear arrays based on surface waveguide leakage effects. The method includes: transforming the time-domain signal received by the horizontal array to the frequency domain, and then performing beamforming to obtain a spatial spectrum; incoherently accumulating the spatial spectrum on the frequency axis to obtain a broadband spatial spectrum, and extracting the angular positions corresponding to the spectral peaks in the broadband spatial spectrum; selecting the minimum angle corresponding to the peak, and correcting the formula using diffraction ray theory to obtain the azimuth angle of the sound source relative to the horizontal array; correcting the angle corresponding to the spectral peak of the seabed reflected wave in the broadband spatial spectrum using the relationship between the spatial angle and the azimuth angle to obtain the angle of arrival of the first seabed reflected signal; and using the estimated angle of arrival of the first seabed reflected signal and the ray geometry formula to obtain an estimated distance to the sound source. This invention eliminates the distance-azimuth coupling problem that occurs when using horizontal linear arrays for sound source localization, and can provide an accurate estimate of the sound source distance.
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Description

Technical Field

[0001] This application belongs to the fields of underwater acoustic array signal processing, underwater acoustic detection, underwater acoustic positioning and sonar technology, specifically relating to a passive ranging method and system for horizontal linear arrays based on surface waveguide leakage effect. Background Technology

[0002] In deep-sea waveguide conditions, when the sound source is located within a few hundred meters of the sea surface, the direct sound zone can only extend to a small area near the surface. Therefore, towed horizontal arrays often need to operate in the shadow zone. In the shadow zone, there are no direct signals or sea surface reflected signals. The primary seabed reflection signal and the surface waveguide leakage signal are the main components of the received signal. Methods for sound source localization using the multipath arrival delay and angle of arrival characteristics of the primary seabed reflection signal have been proposed. However, the correlation between multipath signals reflected from the real seabed is very poor, the time delay estimation error is large, and the multipath features used for matching require a sound field model, which also brings problems of sensitivity to prior environmental knowledge and high computational cost. The angle of arrival of the primary seabed reflection signal is easier to extract than the multipath arrival delay, is less affected by the real seabed reflection, and has a simple geometric relationship with the sound source distance based on ray geometry. However, for horizontal arrays, there is an azimuth-angle of arrival coupling problem, making it impossible to accurately estimate the angle of arrival of the primary seabed reflection signal. Summary of the Invention

[0003] The purpose of this application is to overcome the problem of azimuth-angle of arrival coupling in the prior art, which makes it impossible to accurately estimate the angle of arrival of a first seabed reflected signal, and thus impossible to accurately estimate the distance to the sound source.

[0004] To achieve the above objectives, this application proposes a passive ranging method for a horizontal linear array based on the surface waveguide leakage effect, comprising:

[0005] Step 1: Obtain the time-domain sound pressure signal of the target sound source using a horizontal linear array, and perform a Fourier transform on the time-domain sound pressure signal to obtain the frequency-domain signal;

[0006] Step 2: Perform beamforming on the frequency domain signal to obtain the spatial spectrum of the target sound source;

[0007] Step 3: Incoherently accumulate the obtained spatial spectrum on the frequency axis to obtain a broadband spatial spectrum; extract the angle value corresponding to the peak value from the amplitude of the broadband spatial spectrum, and take the smallest angle among them;

[0008] Step 4: Correct the minimum angle using diffraction theory to obtain an estimated value of the target sound source azimuth angle;

[0009] Step 5: Using the spectral peak position of the corresponding first seabed reflection signal extracted from the spatial spectrum, and based on the relationship between the angle of arrival and the azimuth, obtain the estimated value of the angle of arrival of the first seabed reflection signal.

[0010] Step 6: Using the estimated angle of arrival of the first seabed reflection signal, and based on the ray geometry, obtain the estimated distance to the target sound source.

[0011] As an improvement to the above method, the frequency domain signal obtained by performing a Fourier transform on the time-domain sound pressure signal is expressed as:

[0012] ;

[0013] in, This represents the frequency domain signal on each array element; Represents the time-domain sound pressure signal of the target sound source; Indicates frequency; The imaginary unit; The number of array elements; Indicates the first The distance between each array element and the sound source; Indicates time.

[0014] As an improvement to the above method, the beamforming of the frequency domain signal to obtain the spatial spectrum of the target sound source is expressed as follows:

[0015] ;

[0016] in, Represents the spatial spectrum; Indicates the speed of sound at the array location; Indicates the spacing between elements of a horizontal linear array; Indicates the search angle; Indicates frequency; The imaginary unit; The number of array elements; This represents the frequency domain signal on each array element.

[0017] As an improvement to the above method, the obtained spatial spectrum is incoherently accumulated along the frequency axis to obtain a broadband spatial spectrum, which is expressed as:

[0018] ;

[0019] in, Represents the broadband spatial spectrum; Represents the spatial spectrum; Indicates the search angle; Indicates frequency.

[0020] As an improvement to the above method, the minimum angle is corrected using diffraction theory to obtain an estimated value of the target sound source azimuth angle, expressed as:

[0021] ;

[0022] in, This represents an estimated value of the azimuth angle of the target sound source; This represents the sound velocity at the interface between the surface waveguide and the thermocline. Indicates the speed of sound at the array location; This represents the minimum angle from which the peak value corresponding to the amplitude of the broadband spatial spectrum is extracted.

[0023] As an improvement to the above method, the estimated angle of arrival of the first seabed reflection signal is obtained based on the relationship between the angle of arrival and the azimuth, expressed as:

[0024] ;

[0025] in, This represents the estimated angle of arrival of a single seabed reflected signal; This indicates the position of the spectral peak of the corresponding first seabed reflection signal extracted from the spatial spectrum; This represents the estimated azimuth angle of the target sound source.

[0026] As an improvement to the above method, the distance estimate of the target sound source is obtained by using the estimated angle of arrival of the primary seabed reflection signal and based on the ray geometry, expressed as:

[0027] ;

[0028] in, This represents the estimated distance to the target sound source; Indicates seawater depth; This represents the estimated angle of arrival of a single seabed reflected signal.

[0029] This application also provides a horizontal linear array passive ranging system based on the surface waveguide leakage effect, implemented using the above method, the system comprising:

[0030] The detection and conversion module is used to obtain the time-domain sound pressure signal of the target sound source using a horizontal linear array, and to perform a Fourier transform on the time-domain sound pressure signal to obtain a frequency-domain signal.

[0031] A spatial spectrum acquisition module is used to perform beamforming on the frequency domain signal to obtain the spatial spectrum of the target sound source.

[0032] The minimum angle acquisition module is used to incoherently accumulate the obtained spatial spectrum on the frequency axis to obtain a broadband spatial spectrum; extract the angle value corresponding to the peak value from the amplitude of the broadband spatial spectrum, and take the minimum angle among them;

[0033] An azimuth estimation module is used to correct the minimum angle using diffraction theory to obtain an estimated value of the azimuth angle of the target sound source.

[0034] The angle of arrival estimation module is used to obtain the estimated angle of arrival of the first seabed reflection signal by using the spectral peak position of the corresponding first seabed reflection signal extracted from the spatial spectrum and the relationship between the angle of arrival and the azimuth.

[0035] The sound source distance estimation module is used to obtain the distance estimate of the target sound source by using the estimated angle of arrival of the seabed reflection signal and the ray geometry.

[0036] Compared with existing technologies, the advantages of this application are:

[0037] 1. Compared with the multipath delay matching method, the method of the present invention does not need to extract multipath delay features that are greatly affected by the actual seabed from the signal, thus having stronger robustness;

[0038] 2. Apart from needing to know the sound velocity at the lower boundary of the surface waveguide and the sound velocity at the horizontal array deployment depth, there are no other requirements for prior environmental knowledge;

[0039] 3. No need to use a sound field calculation model to calculate the matching sound field, greatly reducing the amount of computation. Attached Figure Description

[0040] Figure 1 The diagram shows a flowchart of a passive ranging method for horizontal linear arrays based on the leakage effect of surface waveguides.

[0041] Figure 2 The diagram shows the geometric relationship between the sound source and the array position.

[0042] Figure 3 The image shown is a deep-sea sound velocity profile used in the simulation example.

[0043] Figure 4 The image shows the energy distribution of the signal received on the horizontal array in the frequency-angle domain after Fourier transform and beamforming, as well as the broadband spatial spectrum obtained by incoherent accumulation on the frequency axis.

[0044] Figure 5 The figure shows the distance estimation results under different azimuth angles and distances of the sound source. Detailed Implementation

[0045] The technical solution of this application will be described in detail below with reference to the accompanying drawings.

[0046] To provide a clearer picture of the invention, the technical terms used in the invention will be described below.

[0047] Sound shadow zone: refers to the area where sound rays cannot reach due to obstacles or refraction, that is, the area with almost no sound.

[0048] Ocean surface waveguide mode: This is a special type of atmospheric waveguide that occurs over the ocean. This waveguide mode typically occurs in relatively stable atmospheric environments, with a stable temperature inversion layer in the lower atmosphere and atmospheric humidity decreasing with altitude. These conditions cause the atmospheric corrected refractive index to decrease upwards, thus forming a surface waveguide.

[0049] Surface waveguide leakage signal: The signal emitted by the target sound source is diffracted on the ocean surface beneath the surface waveguide, thus forming a surface waveguide leakage signal. Studies have shown that this surface waveguide leakage signal is more stable in terms of propagation angle characteristics, and therefore has stronger robustness.

[0050] Deep sea: Sea areas with a depth of 200m or more.

[0051] Thermocline: Located about 100-200 m below the sea surface, this layer exhibits significant temperature and density variations. It is a layer where the water temperature drops sharply between the upper thin warm water layer and the lower thick cold water layer.

[0052] Example 1

[0053] This invention utilizes the surface waveguide leakage effect and, based on diffraction ray theory, estimates the azimuth angle of the sound source to resolve the azimuth-angle-arrival coupling problem of the horizontal array, providing an accurate estimate of the angle of arrival of the first seabed reflected signal. Finally, using ray geometry formulas, the distance estimate of the sound source is given. Specifically, the method first transforms the time-domain signal received by the horizontal array to the frequency domain; secondly, beamforming is performed on the obtained frequency-domain signal to obtain a spatial spectrum; then, the obtained spatial spectrum is incoherently accumulated on the frequency axis to obtain a broadband spatial spectrum, and the angle values ​​corresponding to the peak values ​​in the broadband spatial spectrum are extracted; then, the minimum angle corresponding to the peak value is selected as the spectral peak position corresponding to the surface waveguide leakage signal, and the azimuth angle estimate of the sound source relative to the horizontal array is obtained by correcting the formula using diffraction ray theory. Then, based on the relationship between the spatial angle and the azimuth angle, the estimated angle of arrival of the first seabed reflected signal is given. Finally, based on ray geometry relationships, the estimated distance of the sound source can be given using the angle of arrival of the first seabed reflected signal. This invention is applicable to horizontal arrays operating in the acoustic shadow zone in deep-sea environments with surface waveguides. Compared to multipath delay matching methods, the method of this invention has higher robustness and requires no prior environmental knowledge other than knowing the sound velocity at the lower boundary of the surface waveguide and the sound velocity at the horizontal array deployment depth. Furthermore, it eliminates the need for a sound field calculation model, significantly reducing computational complexity.

[0054] like Figure 1 As shown, this application provides a passive ranging method for horizontal linear arrays based on surface waveguide leakage effect, which includes the following steps:

[0055] Step 1: Obtain the time-domain sound pressure signal of the sound source using a horizontal linear array pre-deployed in an underwater environment with surface waveguides and operating in the sound shadow region. ,in Represents time, and Representing the The distance between each array element and the sound source is used to perform a Fourier transform with formula (1) to obtain the frequency domain signal on each array element. .

[0056] (1)

[0057] in, Represents the time-domain sound pressure signal of the target sound source; Represents frequency, It is the imaginary unit. It refers to the number of array elements.

[0058] Preferably, the distance from the target sound source to the horizontal linear array is ~ The drag depth of the horizontal linear array is 50~200m. Furthermore, the element aperture of the horizontal linear array is unlimited, and the element spacing can be set to half the wavelength of the target sound source frequency until no fan lobes appear.

[0059] Step 2: Use formula (2) to analyze the frequency domain signal in the pairwise domain. Beamforming is performed to obtain the spatial spectrum. .

[0060] (2)

[0061] in, It is the speed of sound at the array. It is the spacing between the elements of the horizontal linear array. It's a search perspective.

[0062] Step 3: Use formula (3) to obtain the spatial spectrum Incoherent accumulation along the frequency axis yields a broadband spatial spectrum. Then, the angle values ​​corresponding to the peak values ​​are extracted from the amplitude of the obtained broadband spatial spectrum, and the smallest angle is selected. The corresponding surface waveguide leakage signal.

[0063] (3)

[0064] Step 4: Using formula (4) derived from the theory of diffraction rays, for... After making corrections, an estimate of the target's bearing can be obtained. .

[0065] (4)

[0066] in, It is the sound velocity at the interface between the surface waveguide and the thermocline. It is an inverse cosine function.

[0067] Step 5: Use the target azimuth estimate obtained in Step 4. and the spectral peak positions of the corresponding first seabed reflection signal extracted from the spatial spectrum. Based on the relationship between the angle of arrival and the azimuth, an estimated value of the angle of arrival of a single seabed reflected signal can be obtained.

[0068] (5)

[0069] Step 6: Use the estimated angle of arrival of the first seabed reflection signal obtained in Step 5. Based on the geometric relationship of the rays, the distance estimate of the sound source can be obtained. .

[0070] (6)

[0071] in, It refers to the depth of the seawater.

[0072] Simulation Example

[0073] Simulation parameters: Waveguide environment is depth is A deep-sea acoustic waveguide with surface waveguides is shown in Figure 3, with a seawater sound velocity profile and a density of [missing information]. The sound velocity in the lower sediment layer is The density is The seabed attenuation coefficient is ,in Represents the wavelength of the sound wave. The thickness of the surface waveguide is... The sound speed gradient is The sound source signal frequency band is 400-450 Hz, the frequency sampling interval is 1 Hz, and the distance from the sound source to the array is from... Change to The array drag depth is fixed at 50 m, and the array aperture is [missing information]. The array elements are spaced 1 m apart. Figure 2 A schematic diagram of the geometric positions of the sound source and array in the simulation is provided. Figure 3 The deep-sea sound velocity profile used in the simulation is presented. Figure 4 The distance to the sound source is given. When the signal is located in the direction of the array's end-fire, spatial spectrum analysis is performed on the received signal of the array to obtain the spatial spectrum at different frequencies and the broadband spatial spectrum. Figure 5 The estimation results of the sound source distance using the method of the present invention under different sound source azimuth angles are shown in the figure.

[0074] Step 1: Using the array with an aperture of 256 m and an array spacing of 1 m in this example, and selecting the array element closest to the sound source as the reference array element, perform a time-domain Fourier transform on the sound signal recorded by the array, and use formula (1) to transform the signal to the frequency domain, extracting the signal in the mid-frequency band of 400-450 Hz, to obtain... .

[0075] Step 2: According to formula (2), convert the frequency domain signal... Transforming to the angular domain yields the spatial spectrum. In this example, the search angle range is from arrive Angular interval is Among them, at a receiving depth of The distance is The azimuth angle of the sound source is One of the results was displayed in Figure 4According to Figure 4 Analysis using marine acoustic theory shows that the spectral peak representing the leakage signal from the surface waveguide has a minimum angular value. The spectral peak representing a single seabed reflection signal has the second smallest angular value. .

[0076] Step 3: Using formula (3), analyze the obtained spatial spectrum. Incoherent accumulation is performed on the frequency axis to obtain the broadband spatial spectrum. From the obtained broadband spatial spectrum Extract the angle corresponding to the peak value and select the smallest angle as the minimum value. ,like Figure 4 The location is indicated by the red dashed line in the lower half of the image.

[0077] Step 4: Correct it using formula (4), where the sound velocity at the array is... surface waveguide boundary sound velocity The estimated azimuth angle is obtained. .

[0078] Step 5: Extract the spectral peak angle corresponding to the primary seabed reflection signal from the broadband spatial spectrum. Substituting this into formula (5) and correcting it, we can obtain an estimate of the angle of arrival of the seabed reflection signal. .

[0079] Step 6: Calculate the angle of arrival of the first seabed reflection signal estimated in Step 5. Substituting into formula (6), we can obtain an estimate of the sound source distance. .

[0080] Finally, the distance estimation results under different sound source azimuth angles and sound source distances are recorded to be displayed. Figure 5 In the simulation conditions of this example, the relative position of the distance estimation result of the method of the present invention stabilizes at... The results provide a relatively accurate estimate.

[0081] Example 2

[0082] This application also provides a horizontal linear array passive ranging system based on the surface waveguide leakage effect, implemented using the above method, the system comprising:

[0083] The detection and conversion module is used to obtain the time-domain sound pressure signal of the target sound source using a horizontal linear array, and to perform a Fourier transform on the time-domain sound pressure signal to obtain a frequency-domain signal.

[0084] A spatial spectrum acquisition module is used to perform beamforming on the frequency domain signal to obtain the spatial spectrum of the target sound source.

[0085] The minimum angle acquisition module is used to incoherently accumulate the obtained spatial spectrum on the frequency axis to obtain a broadband spatial spectrum; extract the angle value corresponding to the peak value from the amplitude of the broadband spatial spectrum, and take the minimum angle among them;

[0086] An azimuth estimation module is used to correct the minimum angle using diffraction theory to obtain an estimated value of the azimuth angle of the target sound source.

[0087] The angle of arrival estimation module is used to obtain the estimated angle of arrival of the first seabed reflection signal by using the spectral peak position of the corresponding first seabed reflection signal extracted from the spatial spectrum and the relationship between the angle of arrival and the azimuth.

[0088] The sound source distance estimation module is used to obtain the distance estimate of the target sound source by using the estimated angle of arrival of the seabed reflection signal and the ray geometry.

[0089] This application may also provide a computer device, including: at least one processor, memory, at least one network interface, and a user interface. The various components in this device are coupled together via a bus system. It is understood that the bus system is used to implement communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0090] The user interface can include a display, keyboard, or clicking device. Examples include a mouse, trackball, touchpad, or touchscreen.

[0091] It is understood that the memory in the embodiments disclosed in this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0092] In some implementations, the memory stores elements such as executable modules or data structures, or subsets thereof, or extended sets thereof: operating systems and applications.

[0093] The operating system includes various system programs, such as the framework layer, core library layer, and driver layer, used to implement various basic business functions and handle hardware-based tasks. The application programs include various applications, such as media players and browsers, used to implement various application functions. Programs implementing the methods of the embodiments of this disclosure can be included in the application programs.

[0094] In the above embodiments, the processor can also invoke programs or instructions stored in memory, specifically programs or instructions stored in an application program, for the following purposes:

[0095] Follow the steps described above.

[0096] The above methods can be applied to or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above methods can be completed by integrated logic circuits in the processor's hardware or by software instructions. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic diagrams disclosed above. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the disclosed methods can be directly implemented by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0097] It is understood that the embodiments described in this application can be implemented using hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0098] For software implementation, the technology of this application can be implemented by executing the functional modules (e.g., procedures, functions, etc.) of this application. The software code can be stored in memory and executed by a processor. The memory can be implemented in the processor or outside the processor.

[0099] This application may also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, it can implement the steps in the above method embodiments.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application, and should all be covered within the scope of the claims of this application.

Claims

1. A horizontal line array passive ranging method based on surface waveguide leakage effect, comprising: Step 1: obtaining a time-domain sound pressure signal of a target sound source by using a horizontal line array, and performing Fourier transform on the time-domain sound pressure signal to obtain a frequency-domain signal; Step 2: performing beamforming on the frequency-domain signal to obtain a spatial spectrum of the target sound source; Step 3: non-coherently accumulating the obtained spatial spectrum on a frequency axis to obtain a wideband spatial spectrum; extracting an angle value corresponding to a peak value from an amplitude of the wideband spatial spectrum, and taking a minimum angle among the angle values; Step 4: correcting the minimum angle by using a diffraction ray theory to obtain an estimated value of a bearing angle of the target sound source; Step 5: obtaining an estimated value of an angle of arrival of a first bottom-reflected signal according to a relationship between the angle of arrival and the bearing angle by using a spectral peak position corresponding to the first bottom-reflected signal extracted from the spatial spectrum; Step 6: obtaining an estimated value of a distance of the target sound source according to a ray geometric relationship by using the estimated value of the angle of arrival of the first bottom-reflected signal.

2. The surface waveguide leaky effect based horizontal line array passive ranging method according to claim 1, wherein, The Fourier transform on the time-domain sound pressure signal to obtain the frequency-domain signal is represented as: ; wherein, represents the frequency-domain signal on each array element; represents the time-domain sound pressure signal of the target sound source; represents the frequency; is the imaginary unit; is the number of array elements; represents the distance between the th array element and the sound source; represents time.

3. The surface waveguide leaky effect based horizontal line array passive ranging method according to claim 1, wherein, The beamforming on the frequency-domain signal to obtain the spatial spectrum of the target sound source is represented as: ; wherein, represents a spatial spectrum; represents a sound velocity at the array; represents a horizontal line array element spacing; represents a search angle; represents a frequency; is the imaginary unit; is the number of elements; represents a frequency domain signal on each element; represents a distance between the th element and the sound source.

4. The surface waveguide leaky effect based horizontal line array passive ranging method according to claim 1, wherein, The non-coherent accumulation of the obtained spatial spectrum on the frequency axis to obtain the wideband spatial spectrum is represented as: ; wherein, denotes a wideband spatial spectrum; denotes a spatial spectrum; denotes a search angle; denotes a frequency.

5. The surface waveguide leaky effect based horizontal line array passive ranging method according to claim 1, wherein, The correction of the minimum angle by using the diffraction ray theory to obtain the estimated value of the bearing angle of the target sound source is represented as: ; wherein, represents an estimate of the target sound source azimuth angle; represents the sound speed at which the surface waveguide meets the thermocline; represents the sound speed at the array; represents the minimum angle from which the peak value of the amplitude of the broadband spatial spectrum is extracted.

6. The surface waveguide leaky effect based horizontal line array passive ranging method according to claim 1, wherein, The obtaining of the estimated value of the angle of arrival of the first bottom-reflected signal according to the relationship between the angle of arrival and the bearing angle is represented as: ; wherein, denotes an estimate of the angle of arrival of the primary bottom bounce signal; denotes the position of the spectral peak corresponding to the primary bottom bounce signal extracted from the spatial spectrum; denotes an estimate of the azimuth of the target sound source.

7. The surface waveguide leaky effect based horizontal line array passive ranging method according to claim 1, wherein, The obtaining of the estimated value of the distance of the target sound source according to the ray geometric relationship by using the estimated value of the angle of arrival of the first bottom-reflected signal is represented as: ; wherein, represents a distance estimate of the target sound source; represents a depth of seawater; represents an angle of arrival estimate of the first bottom reflection signal.

8. A horizontal linear array passive ranging system based on surface waveguide leakage effect, implemented based on the method of any one of claims 1-7, characterized in that, The system comprises: a detection and conversion module for obtaining a time-domain sound pressure signal of a target sound source by using a horizontal line array, and performing Fourier transform on the time-domain sound pressure signal to obtain a frequency-domain signal; an acquisition spatial spectrum module for performing beamforming on the frequency-domain signal to obtain a spatial spectrum of the target sound source; an acquisition minimum angle module for non-coherently accumulating the obtained spatial spectrum on a frequency axis to obtain a wideband spatial spectrum; extracting an angle value corresponding to a peak value from an amplitude of the wideband spatial spectrum, and taking a minimum angle among the angle values; an estimated bearing angle module for correcting the minimum angle by using a diffraction ray theory to obtain an estimated value of a bearing angle of the target sound source; an estimated angle of arrival module for obtaining an estimated value of an angle of arrival of a first bottom-reflected signal according to a relationship between the angle of arrival and the bearing angle by using a spectral peak position corresponding to the first bottom-reflected signal extracted from the spatial spectrum; and an estimated sound source distance module for obtaining an estimated value of a distance of the target sound source according to a ray geometric relationship by using the estimated value of the angle of arrival of the first bottom-reflected signal.

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