Deep sea sound source localization method based on eikonal equation

Abstract

The embodiment of the invention provides a deep sea sound source localization method based on an eikonal equation, and the method comprises the steps: S1, carrying out the data collection and preprocessing, deploying an underwater sensor array, collecting sound wave signals and environment parameters in a target region, carrying out the filtering and noise reduction of the collected sound wave signals, and extracting the arrival time stamp of each sensor; s2, constructing a model, and calculating a sound velocity profile according to the collected environmental parameters; s3, discretizing and initializing a computational domain; s4, performing numerical solution on the eikonal equation, and performing numerical solution by adopting a fast propulsion method; s5, calculating theoretical propagation time, and extracting the theoretical propagation time from the propagation time field for each sensor position; and S6, solving the position of the sound source. According to the embodiment of the invention, the propagation path and the arrival time of the sound wave in the deep sea can be accurately described, so that the sound source can be accurately positioned, and the method can be suitable for application scenes such as underwater unmanned underwater vehicles, sonar systems, ocean monitoring and seabed detection.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic signal processing technology, and in particular to a method for locating deep-sea acoustic sources based on a procedural function equation. Background Technology

[0002] Sound source localization in deep-sea environments has always been a key issue in underwater acoustics. Traditional sonar localization methods are affected by the complex characteristics of the water environment, such as variations in temperature, salinity, and depth, leading to complex sound wave propagation paths and posing a significant challenge to localization accuracy. Furthermore, the multipath propagation and non-uniform underwater sound velocity profiles in the deep-sea environment further increase the difficulty of localization. Existing technologies mostly employ geometric localization and time-of-flight localization methods, which often require complex multi-point deployment and calculations, and their accuracy is greatly affected by the underwater propagation path. Summary of the Invention

[0003] In view of the above-mentioned problems in the prior art, the present invention provides a deep-sea sound source localization method based on the process function equation to solve the technical problems in the prior art that require complex multi-point layout and calculation, and whose accuracy is greatly affected by the underwater propagation path.

[0004] This invention provides a method for locating deep-sea sound sources based on a procedural functional equation, comprising the following steps:

[0005] Step S1, data acquisition and preprocessing: deploy an underwater sensor array, acquire acoustic signals and environmental parameters in the target area, filter and denoise the acquired acoustic signals, and extract the arrival timestamps of each sensor.

[0006] Step S2, Model building: Calculate the sound velocity profile based on the collected environmental parameters;

[0007] Step S3: Discretize and initialize the computational domain;

[0008] Step S4: Numerical solution of the functional equation using the fast-progression method;

[0009] Step S5: Calculate the theoretical propagation time. For each sensor location, extract the theoretical propagation time from the propagation time field.

[0010] Step S6: Solve for the location of the sound source.

[0011] In one embodiment, it also includes,

[0012] Step S7: Dynamic correction and optimization. Construct a sound velocity profile error model using historical positioning data. Repeat steps S2 to S6. Recalculate the propagation time field and sound source location using the corrected sound velocity profile.

[0013] In one embodiment, it also includes,

[0014] Step S8, Results Output and Visualization: Output the final coordinates of the sound source and the estimated positioning error, visualize the propagation time field, draw contour lines and sensor positions, and assist in the analysis of the sound wave propagation path.

[0015] In one embodiment, the underwater sensor array is a hydrophone array, and the environmental parameters include water temperature, salinity, and depth, which are measured by a CTD profiler.

[0016] In one embodiment, in step S2, the change of sound speed with depth is calculated using an empirical formula, and the discrete sound speed data is used to construct a continuous sound speed profile model using an interpolation algorithm as input to the equation.

[0017] In one embodiment, step S3 specifically includes,

[0018] Step S31, Set the computational domain: Define the three-dimensional computational domain according to the target area range;

[0019] Step S32, mesh generation: Discretize the computational domain into a uniform mesh, with the mesh size set according to the accuracy requirements;

[0020] Step S33: Initialize the propagation time field. Set the initial value of the propagation time field τ. For candidate sound source locations, τ is initialized to 0. For other grid points, τ is initialized to a large value.

[0021] In one embodiment, step S4 specifically includes,

[0022] Step S41: Derive the equation describing the time field of sound source propagation in water;

[0023] Step S42: Perform finite difference discretization on the functional equation;

[0024] Step S43: Solve iteratively using the fast-progression method.

[0025] In one embodiment, step S6 specifically includes,

[0026] Step S61: Define the objective function. Based on the residual between the measured arrival time difference and the theoretical propagation time difference, define the least squares objective function.

[0027] Step S62: Minimize the objective function using either gradient descent or Newton's iteration method;

[0028] Step S63: Output the localization result. The final iteration result is the precise location of the sound source.

[0029] Compared with existing technologies, the beneficial effects of the deep-sea sound source localization method based on the process function equation provided by the embodiments of the present invention are as follows: The embodiments of the present invention achieve an accurate description of the propagation characteristics of sound waves in the deep-sea environment through the process function equation, and further utilize the second-order finite difference method to numerically solve the process function equation, accurately characterizing the propagation path and arrival time of sound waves in the deep sea, obtaining the propagation time field, and using the arrival time difference to iteratively solve for the accurate location of the underwater sound source based on the sound wave propagation time received by different sensors, thereby achieving accurate sound source localization, which can be applied to application scenarios such as underwater unmanned submersibles, sonar systems, marine monitoring and seabed exploration. Attached Figure Description

[0030] Figure 1 A schematic diagram of the Munk sound velocity profile involved in a deep-sea sound source localization method based on the process function equation provided in an embodiment of the present invention;

[0031] Figure 2 This is a schematic diagram of the sound propagation time field involved in a deep-sea sound source localization method based on the process function equation provided in an embodiment of the present invention. Detailed Implementation

[0032] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] Various embodiments and features of this application are described herein with reference to the accompanying drawings.

[0034] These and other features of this application will become apparent from the following description of preferred forms of embodiments given as non-limiting examples, with reference to the accompanying drawings.

[0035] It should also be understood that although this application has been described with reference to some specific examples, those skilled in the art can certainly implement many other equivalent forms of this application, which have the features described in the claims and are therefore all within the scope of protection defined herein.

[0036] The above and other aspects, features and advantages of this application will become more apparent when taken in conjunction with the accompanying drawings and in view of the following detailed description.

[0037] Specific embodiments of this application are described below with reference to the accompanying drawings; however, it should be understood that the claimed embodiments are merely examples of this application, which can be implemented in various ways. Well-known and / or repeated functions and structures are not described in detail to ascertain the true intent based on the user's historical operations, and to avoid unnecessary or redundant details that would obscure this application. Therefore, the specific structural and functional details claimed herein are not intended to be limiting, but merely serve as the basis and representative basis for the claims to teach those skilled in the art to use this application in various ways with substantially any suitable detailed structure.

[0038] This specification may use the phrases “in one embodiment,” “in another embodiment,” “in yet another embodiment,” or “in other embodiments,” all of which may refer to one or more of the same or different embodiments according to this application.

[0039] The principles and features of the present invention are described below with reference to the accompanying drawings. The embodiments described are for illustrative purposes only and are not intended to limit the scope of the invention. The following description, in conjunction with... Figure 1-2 The preferred embodiments of the present invention will be described in further detail below:

[0040] like Figure 1-2 As shown, this embodiment of the invention provides a deep-sea sound source localization method based on a procedural functional equation, comprising the following steps:

[0041] [Step S1] Data Acquisition and Preprocessing: Deploy an underwater sensor array (such as a hydrophone array) to collect data.

[0042] The data includes acoustic signals and environmental parameters within the target area. Environmental parameters include water temperature, salinity, and depth, measured using a CTD (Celestial-Salinity-Depth) profiler. Acoustic signal records include the arrival times of the acoustic signals received by each sensor. Data preprocessing includes filtering and denoising the acoustic signals and extracting the arrival timestamps from each sensor.

[0043] [Step S2] Model Construction: Calculate the sound velocity profile based on the collected environmental parameters. The sound velocity c varies with depth z.

[0044] The changes are calculated using empirical formulas (such as the Mackenzie formula):

[0045] c(z)=1448.96+4.591T-0.05304T 2 +0.0002374T 3 +1.340(S-35)+0.0163z

[0046] Where T is water temperature (°C), S is salinity (‰), and z is depth (meters). Discrete sound velocity data are used to construct a continuous sound velocity profile model using interpolation algorithms (such as linear interpolation or spline interpolation), which serves as the input to the equation.

[0047] [Step S3] Discretize and initialize the computational domain.

[0048] (1) Set up the computational domain: Define the three-dimensional computational domain according to the target area range (e.g., horizontal range X×Y, depth range Z).

[0049] (2) Mesh Generation: The computational domain is discretized into a uniform grid. The grid size is set according to the accuracy requirements (e.g., Δx = Δy = Δz = 10 meters). The grid point coordinates are denoted as (i, j, k), corresponding to the spatial location (x, j, k). i ,y j ,z k ).

[0050] (3) Initialize the propagation time field: Set the initial value of the propagation time field τ. For candidate sound source locations, τ is initialized to 0; for other grid points, τ is initialized to a large value (e.g., 10). 6 Second)

[0051] [Step S4] Solve the equation numerically.

[0052] The equation describing the time field of sound propagation from a sound source in water is derived as follows:

[0053]

[0054] Assume the solution is in the form of:

[0055]

[0056] Where ψ is displacement, r is position vector, t is propagation time, c is velocity, A is amplitude, w is angular frequency, and τ is propagation time related to spatial position. Substituting equation (2) into equation (1) yields:

[0057]

[0058] If both the real part and the imaginary part are zero, then the real part can be expressed as:

[0059]

[0060] Divide both sides of equation (4) by ω 2 .

[0061] Since the wavelength of underwater acoustic propagation is usually much smaller than the propagation distance (including sea depth and horizontal range), a high-frequency approximation can be used: ω→∞, which yields the equation describing the propagation time field:

[0062]

[0063] That is, the equation is:

[0064]

[0065] Where τ is the propagation time and c is the speed of sound.

[0066] Sound source localization in water is a process of calculating the three-dimensional spatial location of the sound source. The location of the sound source can be determined by solving the least squares residual between the actual observed value and the theoretical simulation value of the sound propagation time. When the residual is minimized, the sound source location is determined. Methods for calculating sound field propagation time and ray paths can generally be classified into two categories: ray methods and mesh methods. (1) Ray methods solve the ray equations of kinematics. Ray methods calculate the propagation time along a single path of a ray, which is convenient for solving a small number of paths. However, in regions with strong changes in medium velocity, this method is unstable and the calculation results are inaccurate. Common methods include: target shooting method, bending method, pseudo-bending method, etc. (2) Mesh methods solve the kinematic equations using finite difference. Mesh methods calculate the entire propagation time field and then use the gradient of the time field to obtain a single ray path. Although the efficiency of obtaining a single ray path is low, the stability and accuracy are higher in regions with strong changes in medium velocity, and it is suitable for calculating a large number of propagation times. Common methods include: rapid advance method, rapid scan method, etc. This invention employs the fast-progression method to solve the propagation time field using the equation, and obtains the sound source location by fitting the minimum difference between the observed and theoretical travel times at the receiver. The numerical solution using the fast-progression method is as follows:

[0067] (1) Finite difference discretization: At grid point (i,j,k), the equation is discretized as

[0068]

[0069] Where D -x D +x These represent the backward and forward difference operators, respectively, for example:

[0070]

[0071] Similar to defining the difference in the y and z directions.

[0072] (2) Rapid iteration method:

[0073] 1) Add the candidate sound source points to the "accepted" set, and fix its τ value.

[0074] 2) Initialize the “narrowband” set, which contains the neighboring points of the “accepted” point, and calculate its τ value.

[0075] 3) Repeat the following steps until all points have been processed:

[0076] a. Select the point with the smallest τ value from the “narrow band” and move it into the “accepted” set.

[0077] b. Update the τ value of the neighboring points: For each neighboring point, solve the above discrete equation and take the smallest positive root as the new τ value.

[0078] c. If a neighboring point is not in the "narrow band", then add it to the "narrow band".

[0079] 4) Output the propagation time field τ of the entire computational domain.

[0080] [Step S5] Calculation of theoretical propagation time

[0081] For each sensor location, the theoretical propagation time τ is extracted from the propagation time field τ. calc For example, the sensor is located at grid point (i s ,j s ,k s ), then τ calc =i s ,j s ,k s .

[0082] [Step S6] Solve for the location of the sound source.

[0083] (1) Define the objective function: Based on the residual between the measured arrival time difference and the theoretical propagation time difference, define the least squares objective function:

[0084]

[0085] Where (x) s ,y s ,z s ) represents the candidate location of the sound source, M represents the number of sensors, and t represents the location of the sound source. m Let τ be the measured arrival time of sensor m. m Let m be the theoretical propagation time of sensor m.

[0086] (2) Minimize the objective function using gradient descent or Newton's iteration method. Taking gradient descent as an example: First, initialize the estimated sound source location (e.g., calculate the center of the domain). Iteratively update the sound source location:

[0087]

[0088] Where P = (x s ,y s ,z s ), where α is the step size. This is the gradient. The gradient is calculated approximated using numerical differencing, for example:

[0089]

[0090] Iteration termination condition: When the change in the objective function is less than a threshold (e.g., 10). -6 Stop when the maximum number of iterations is reached (e.g., 40 iterations).

[0091] (3) Output the positioning result: The final iteration result is the precise location of the sound source.

[0092] [Step S7] Dynamic correction and optimization.

[0093] To address the dynamic changes in the underwater environment, an adaptive correction method is employed: a sound velocity profile error model is constructed using historical positioning data. Steps 2 through 6 are repeated, and the propagation time field and sound source location are recalculated using the corrected sound velocity profile to further improve positioning accuracy.

[0094] [Step S8] Result Output and Visualization. Output the final coordinates of the sound source (x... s ,y s ,z s ) and positioning error estimation. Visualization of the propagation time field (e.g. Figure 2 As shown in the figure, the black pentagram represents the location of the sound source, the black triangle represents the location of the receiver, different colors represent the propagation time value, and the gray dashed line represents the time contour line. Plotting the contour lines and the sensor location helps to analyze the sound wave propagation path.

[0095] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. The scope of protection of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within its spirit and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of the present invention.

Claims

1. A method for locating deep-sea sound sources based on a functional equation, characterized in that, Includes the following steps: Step S1, data acquisition and preprocessing: deploy an underwater sensor array, acquire acoustic signals and environmental parameters in the target area, filter and denoise the acquired acoustic signals, and extract the arrival timestamps of each sensor. Step S2, Model building: Calculate the sound velocity profile based on the collected environmental parameters; Step S3: Discretize and initialize the computational domain; Step S4: Numerical solution of the functional equation using the fast-progression method; Step S5: Calculate the theoretical propagation time. For each sensor location, extract the theoretical propagation time from the propagation time field. Step S6: Solve for the location of the sound source.

2. The deep-sea sound source localization method based on the equation of process function as described in claim 1, characterized in that: It also includes, Step S7: Dynamic correction and optimization. Construct a sound velocity profile error model using historical positioning data. Repeat steps S2 to S6. Recalculate the propagation time field and sound source location using the corrected sound velocity profile.

3. The deep-sea sound source localization method based on the equation of process function according to claim 2, characterized in that: It also includes, Step S8, Results Output and Visualization: Output the final coordinates of the sound source and the estimated positioning error, visualize the propagation time field, draw contour lines and sensor positions, and assist in the analysis of the sound wave propagation path.

4. The deep-sea sound source localization method based on the equation of process function according to claim 1, characterized in that: The underwater sensor array is a hydrophone array, and the environmental parameters include water temperature, salinity, and depth, which are measured by a CTD profiler.

5. The deep-sea sound source localization method based on the equation of process function according to claim 1, characterized in that: In step S2, the change of sound speed with depth is calculated using an empirical formula, and the discrete sound speed data is used to construct a continuous sound speed profile model using an interpolation algorithm, which serves as the input to the equation.

6. The deep-sea sound source localization method based on the equation of process function according to claim 1, characterized in that: Step S3 specifically includes: Step S31, Set the computational domain: Define the three-dimensional computational domain according to the target area range; Step S32, mesh generation: Discretize the computational domain into a uniform mesh, with the mesh size set according to the accuracy requirements; Step S33: Initialize the propagation time field. Set the initial value of the propagation time field τ. For candidate sound source locations, τ is initialized to 0. For other grid points, τ is initialized to a large value.

7. The deep-sea sound source localization method based on the equation of process function according to claim 1, characterized in that: Step S4 specifically includes: Step S41: Derive the equation describing the time field of sound source propagation in water; Step S42: Perform finite difference discretization on the functional equation; Step S43: Solve iteratively using the fast-progression method.

8. The deep-sea sound source localization method based on the equation of process function according to claim 1, characterized in that: Step S6 specifically includes, Step S61: Define the objective function. Based on the residual between the measured arrival time difference and the theoretical propagation time difference, define the least squares objective function. Step S62: Minimize the objective function using either gradient descent or Newton's iteration method; Step S63: Output the localization result. The final iteration result is the precise location of the sound source.

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