Deep sea reliable sound path long baseline robust positioning method based on iteration equivalent sound velocity correction

Abstract

The invention particularly relates to a deep sea reliable sound path long baseline robust positioning method based on iterative equivalent sound velocity correction, which comprises the following steps: firstly, selecting a coordinate origin, and delimiting a positioning area by taking the coordinate origin as a center; a sonar receiving array is distributed to a proper position, a hydroacoustics numerical calculation ray model is utilized to establish a sound field model according to data such as a sound velocity profile, a target sound source depth and a horizontal distance range, and an equivalent sound velocity table is obtained. Then, inputting an initial equivalent sound velocity vector and an initial relative propagation time vector, and obtaining initial target position estimation by using a hyperbolic intersection method; next, the equivalent sound velocity and the target position are updated through iteration, and an adaptive adjustment item is introduced, so that the convergence and robustness of the algorithm are improved; and finally, judging whether iteration is terminated or not by utilizing a maximum likelihood error function. The method combines the hyperbolic intersection method to efficiently solve and adaptively adjust items, is high in positioning precision, is high in calculation efficiency, and is suitable for underwater real-time high-precision positioning tasks.

Description

Technical Field

[0001] This invention relates to the field of underwater positioning technology, specifically to a robust long-baseline positioning method for deep-sea reliable acoustic paths based on iterative equivalent sound velocity correction, applicable to various marine environments. Background Art

[0002] With the increasing demand for deep-sea development, higher precision measurement is required for the real-time position of marine operating platforms, especially underwater operating platforms such as underwater vehicles, in order to complete highly complex deep-sea operations. Long baseline positioning systems based on time delay of arrival (TDOA) are one of the commonly used positioning systems in the deep sea. These systems require the deployment of three or more sonar receiving arrays in a specific geometric pattern on the seabed or surface, precise measurement of the relative coordinates of each array, and the determination of the target's position using the signal transmission delay information from the target to each array.

[0003] Traditional long-baseline pulse signal localization methods based on arrival delay difference, such as the hyperbolic intersection method (see "Long-Baseline Landing Point Underwater Acoustic Localization Method and Application in Lake Environments," published in the Proceedings of the 2020 Academic Annual Meeting of the Science and Technology Committee of the China Academy of Aerospace Electronics Technology), rely on the equivalent sound velocity as a key parameter. This equivalent sound velocity is defined as the horizontal distance between the receiver and the sound source divided by the propagation time. In shallow sea environments, the sound velocity gradient is small, and the curvature of sound ray propagation is low, resulting in a relatively constant equivalent sound velocity value. Therefore, traditional localization methods still maintain high accuracy. However, in deep sea environments, the sound velocity gradient is large, and the curvature of sound ray propagation is high. The equivalent sound velocity value for different target points varies with the horizontal distance, leading to significant errors in the calculation results of traditional localization methods. Therefore, traditional long-baseline pulse signal localization methods based on arrival delay difference no longer meet the requirements of high adaptability and high accuracy.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] To address the shortcomings of traditional long baseline positioning methods based on arrival delay difference, such as poor adaptability and large errors in the deep-sea environment, this invention provides a robust long baseline positioning method for reliable acoustic paths in the deep sea based on iterative equivalent sound velocity correction, which can improve the adaptability and accuracy of deep-sea surface or underwater target position measurement.

[0006] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0007] According to a first aspect of the present invention, a robust long-baseline localization method for reliable acoustic paths in the deep sea based on iterative equivalent sound velocity correction is provided, the method comprising: Input the initial equivalent sound velocity vector and the initial relative propagation time vector, calculate the measured arrival time delay difference vector based on the initial equivalent sound velocity vector and the initial relative propagation time vector; set the iteration parameters and start the iteration; During the iteration number k-1, where k≥1; based on the equivalent sound speed vector and the relative propagation time vector, the current estimated target position is obtained using the hyperbola intersection method, the horizontal distance to the receiving array is calculated based on the estimated target position, the horizontal distance to the receiving array and the equivalent sound speed table are calculated based on the estimated target position, and the corrected equivalent sound speed vector is calculated using the interpolation method; The estimated propagation time vector is calculated based on the corrected equivalent sound velocity vector and horizontal distance; The estimated arrival delay difference vector is calculated based on the estimated propagation time vector, and the arrival delay difference residual vector is calculated based on the estimated arrival delay difference vector and the measured arrival delay difference vector. The adjustment term is calculated based on the arrival delay difference residual vector. The adjustment term is used to correct the current estimated target position to obtain the corrected target position, which is the estimated target position at iteration number k. The horizontal distance between the corrected target position and the receiving array is calculated based on the corrected target position, the horizontal distance between the corrected target position and the receiving array and the equivalent sound velocity table are used to calculate the corrected equivalent sound velocity vector at iteration number k using the interpolation method. The estimated propagation time vector at iteration number k is calculated based on the corrected equivalent sound velocity vector and the horizontal distance at iteration number k. Update the relative propagation time vector at iteration number k based on the estimated propagation time vector at iteration number k. The estimated arrival delay difference vector at iteration number k is calculated based on the estimated propagation time vector at iteration number k, and the maximum likelihood error function is calculated based on the estimated arrival delay difference vector at iteration number k. The iteration termination is determined based on the maximum likelihood error function or the number of iterations until the iteration terminates. The target position at the current iteration number at the time of iteration termination is output as the final target position.

[0008] In some exemplary embodiments, the method further includes: a method for obtaining the equivalent speed of sound table, specifically: Establish a coordinate system, divide the positioning area with the origin as the center, deploy a sonar receiving array within the positioning area, establish a sound field model using the underwater acoustic numerical calculation ray model, and obtain an equivalent sound velocity table.

[0009] In some exemplary embodiments, the calculation of the horizontal distance to the receiving array based on the estimated target location uses the following formula:

[0010] in, To estimate the target position at iteration number k-1, It is a sonar receiver array.

[0011] In some exemplary embodiments, the calculation of the arrival delay difference residual vector based on the estimated arrival delay difference vector and the measured arrival delay difference vector uses the following formula: in, Let be the measured arrival delay difference vector. This is the estimated arrival delay difference vector at iteration number k-1.

[0012] In some exemplary embodiments, the adjustment term is calculated based on the arrival delay difference residual vector using the following formula:

[0013] in, This is the adjustment term at iteration number k-1. The estimated arrival delay difference at iteration number k-1. The coefficient is determined based on the target location, whether it is inside or outside the baseline. This is the corrected equivalent sound velocity vector at iteration number k-1. For the first n The location of the sonar array This represents the current estimated position at iteration number k-1.

[0014] In some exemplary embodiments, the revised target position is obtained by correcting the current estimated target position using an adjustment term, using the following formula:

[0015] in, To correct the target position, This represents the current estimated target position at iteration number k-1.

[0016] In some exemplary embodiments, the maximum likelihood error function is calculated based on the estimated arrival delay difference vector at iteration number k, using the following formula:

[0017] in, Let be the maximum likelihood error function. Let k be the estimated propagation time vector at iteration number k. Let be the measured arrival delay difference vector. This represents the number of sonar receiver arrays.

[0018] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the deep-sea reliable acoustic path long baseline robust positioning method based on iterative equivalent sound velocity correction as described in the first aspect.

[0019] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, it implements the deep-sea reliable acoustic path long baseline robust positioning method based on iterative equivalent sound velocity correction as described in the first aspect above.

[0020] According to a fourth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the deep-sea reliable acoustic path long baseline robust localization method based on iterative equivalent sound velocity correction as described in the first aspect when executing the executable instructions.

[0021] The deep-sea reliable acoustic path long-baseline robust positioning method based on iterative equivalent sound velocity correction provided by the embodiments of the present invention predefines the positioning area and deploys a sonar receiving array, establishes a ray model by combining sound velocity profile and seabed topography data, and generates an equivalent sound velocity table; calculates the target position based on the initial equivalent sound velocity vector and relative propagation time, dynamically updates the equivalent sound velocity value and position estimate through an iterative mechanism, and introduces an adaptive adjustment term to correct the positioning position; and uses the maximum likelihood error function to determine convergence.

[0022] Compared with existing technologies, it has the following beneficial effects: 1. By pre-building an equivalent sound velocity table and using a dynamic correction mechanism, the positioning failure problem caused by changes in the deep-sea sound velocity gradient is overcome. Robust positioning is achieved across the entire domain (inside and outside the baseline) in long baseline scenarios, which is significantly better than traditional algorithms such as the hyperbola intersection method based on the constant sound velocity assumption.

[0023] 2. This method combines the hyperbola intersection method with an adaptive adjustment term for efficient solution, resulting in high positioning accuracy and fast computation, making it suitable for real-time high-precision underwater positioning tasks.

[0024] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0025] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0026] Figure 1 A schematic diagram of the sound velocity profile used in a computer simulation example.

[0027] Figure 2 This is a flowchart of a long-baseline robust localization method for reliable acoustic paths in the deep sea based on iterative equivalent sound velocity correction, according to an embodiment of the present invention.

[0028] Figure 3 This is a schematic diagram showing the deployment location of the sonar receiving array.

[0029] Figure 4 This is a schematic diagram of the positioning iteration process.

[0030] Figure 5 This is a schematic diagram of the positioning results. Detailed Implementation

[0031] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0032] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0033] To address the shortcomings and deficiencies of existing technologies, this example embodiment provides a robust long-baseline localization method for reliable acoustic paths in the deep sea based on iterative equivalent sound velocity correction, referencing... Figure 2 As shown, the specific steps may include: Step 1: Establish a two-dimensional coordinate system by selecting the origin O. Using point O as the center, define a coordinate system of length... L km, width is DGiven a rectangular positioning area of ​​km (where L≤25, D≤25), the longest distance between any two points within the rectangular positioning area is: km. Will M ( M ≥2) sonar receiver arrays are evenly distributed within the positioning area, with a deployment depth of [missing information]. r 1m ( r 1≥5). Denote the sonar receiving array. m The coordinates are Assume the depth of the target's sound source is... r 2m. The reference time is defined as yyyy year mm month dd day hh hour mm minute ss second.

[0034] Step 2: with step m(0.1≤ step ≤1) is the step size, from 0 km to R The horizontal range of km is divided into ( R ×10 3 / step +1) nodes, with node numbers defined as... i Data such as sound velocity profile, horizontal range, receiving depth, and source depth are input into an underwater acoustic numerical calculation ray model (which can be implemented using general-purpose software like Bellhop) to establish a sound field model and predict the propagation time at each node. Thus, the equivalent speed of sound is obtained. The table containing the equivalent sound velocity for each node is as follows: .

[0035] The equivalent speed of sound is defined as the ratio of the horizontal distance between the target and the sonar receiving array to the propagation time.

[0036] The initial relative propagation time refers to the time difference (in seconds) between the arrival time of the target sound source signal detected by the sonar receiving array and the reference time.

[0037] Step 3: Set the initial number of iterations The maximum number of iterations is The error function threshold is Input the initial equivalent sound speed vector. and the initial relative propagation time vector Calculate the measured arrival time delay difference. :

[0038] Then the measured arrival delay difference vector for: .

[0039] Step 4: The localization iteration process is as follows: 1) and Input the hyperbola intersection method, output the current estimated position. Computation and receiving array m horizontal distance : .

[0040] Based on equivalent speed of sound tables The corresponding value is calculated using the cubic spline interpolation method. Corrected equivalent sound velocity Then the corrected equivalent sound speed vector for: .

[0041] 2) According to and Calculate the estimated propagation time : .

[0042] Then the estimated propagation time vector for: .

[0043] 3) Calculate the estimated arrival time delay difference : .

[0044] Then the estimated arrival delay difference vector for: .

[0045] Then the arrival delay difference residual vector for:

[0046] remember The element with the largest absolute value is Its corresponding sonar array number is n .

[0047] 4) Calculate the adjustment items : .

[0048] in Based on the baseline, take 0.5 (inside and outside). Located within the baseline) or 2 ( (Located outside the baseline). The baseline is defined as the largest convex polygon formed by and surrounding all sonar receiver arrays.

[0049] Correction position for: .

[0050] 5) According to Computing and receiving array m horizontal distance : .

[0051] Based on equivalent speed of sound tables The corresponding value is calculated using the cubic spline interpolation method. Corrected equivalent sound velocity Then the corrected equivalent sound speed vector for: .

[0052] according to and Calculate the estimated propagation time : .

[0053] Then the estimated propagation time vector for: .

[0054] Update the relative propagation time vector : .

[0055] 6) Calculate the estimated arrival time delay difference. : .

[0056] Then the estimated arrival delay difference vector for: .

[0057] Calculate the maximum likelihood error function : .

[0058] like (Error function threshold) or (Maximum number of iterations), stop iteration, let ;otherwise , Continue iterating.

[0059] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and embodiments.

[0060] Example 1 To verify the effectiveness of the method of this invention, a computer simulation experiment was conducted. This embodiment selected a marine environment at latitude and longitude coordinates (14.641°N, 115.998°E), a sea depth of 4090m, a seawater density of 1g / cm³, and the sound velocity profile was generated from the SODA ocean dataset, as shown in the attached figure. Figure 1 As shown, the speed of sound in the half-space beneath the sea is 1555.3 m / s, and the density is 1.6 g / cm³.

[0061] The deep-sea reliable acoustic path long-baseline robust localization method based on iterative equivalent sound velocity correction provided in this embodiment includes the following specific steps: Step 1: Establish a two-dimensional coordinate system with (14.641°N, 115.998°E) as the origin O. With point O as the center, delineate a rectangular positioning area with a length of 12km and a width of 12km. The longest distance between any two points within this area is... km. Four sonar receiver arrays were evenly distributed throughout the positioning area, at a depth of 4000m. The deployment locations of the four sonar receiver arrays are shown in the attached figure. Figure 3 As shown, the coordinates of sonar receiving arrays 1, 2, 3, and 4 are respectively , , , .

[0062] Assume the target sound source depth is 50 m. Define the reference time as 00:00:00 on June 17, 2025.

[0063] Step 2: Divide the horizontal range from 0 km to 17 km into 34001 nodes with a step size of 0.5 m, and define the node number as i. Input the sound velocity profile, horizontal range, receiving depth, and sound source depth data into the underwater acoustic numerical calculation ray model (the general software Bellhop can be used) to establish the sound field model and predict the propagation time of each node. Thus, the equivalent speed of sound is obtained. The table containing the equivalent sound velocity for each node is as follows: Taking the 20001st node as an example, its horizontal distance is 10 km, and the propagation time is... The equivalent speed of sound is 7.1685 s. It is 1394.9831 m / s.

[0064] Step 3: Set the initial number of iterations Maximum number of iterations The threshold value is 50, representing the error function threshold. The value is 10⁻¹⁰. In the computer simulation, the target location is assumed to be (2km, 3km), and the sound source emitted at 00:00:10 on June 17, 2024. Input the initial equivalent sound velocity vector. and the initial relative propagation time vector Taking sonar receiver array 2 as an example, the measured arrival delay difference is calculated. :

[0065] Then the measured arrival delay difference vector for: .

[0066] Step 4: The localization iteration process is as follows (taking the first iteration as an example, and the calculation process using sonar receiver array 1 as an example): 1) and Input the hyperbola intersection method, output the current estimated position. Calculate the horizontal distance to receiver array 1. : .

[0067] Based on equivalent speed of sound tables The corresponding value is calculated using the cubic spline interpolation method. Corrected equivalent sound velocity Then the corrected equivalent sound speed vector for: .

[0068] 2) According to and Calculate the estimated propagation time : .

[0069] Then the estimated propagation time vector for: .

[0070] 3) Calculate the estimated arrival time delay difference : .

[0071] Then the estimated arrival delay difference vector for: .

[0072] Then the arrival delay difference residual vector for: .

[0073] but The element with the largest absolute value is Its corresponding sonar array is numbered 3.

[0074] 4) Due to Located within the baseline, therefore Take 0.5. Calculate the adjustment item. : .

[0075] Correction position for: .

[0076] 5) According to Calculate the horizontal distance to receiver array 1 : .

[0077] Based on equivalent speed of sound tables The corresponding value is calculated using the cubic spline interpolation method. Corrected equivalent sound velocity Then the corrected equivalent sound speed vector for: .

[0078] according to and Calculate the estimated propagation time : .

[0079] Then the estimated propagation time vector for: .

[0080] Update the relative propagation time vector : .

[0081] 6) Calculate the estimated arrival time delay difference. : .

[0082] Then the estimated arrival delay difference vector for: .

[0083] Calculate the maximum likelihood error function : .

[0084] because and ,but Continue iterating.

[0085] After completing the above steps, the target iteration path is as follows: Figure 4 As shown in the attached figure, the final positioning result is as follows. Figure 5 As shown, the coordinates are (2km, 3km), which is consistent with the assumed target location. This embodiment demonstrates that the method proposed in this invention can achieve a robust positioning method for long-baseline deep-sea environments based on iterative equivalent sound velocity correction.

[0086] This invention relates to a robust long-baseline localization method for reliable acoustic paths in deep sea based on iterative equivalent sound velocity correction, belonging to the fields of sonar technology, underwater acoustic engineering, array signal processing, and long-baseline localization. A coordinate origin is selected, and the localization area is delineated centered on the origin. A sonar receiving array is deployed to a suitable position. Based on data such as the sound velocity profile, target sound source depth, and horizontal distance range, a sound field model is established using a ray model for underwater acoustic numerical calculation (using general-purpose software Bellhop), obtaining an equivalent sound velocity table. Then, an initial equivalent sound velocity vector and an initial relative propagation time vector are input, and the initial target position estimate is obtained using the hyperbolic intersection method. Next, the equivalent sound velocity and target position are iteratively updated, and an adaptive adjustment term is introduced to improve the algorithm's convergence and robustness. Finally, the maximum likelihood error function is used to determine whether the iteration terminates. This invention is applicable to various marine environments, exhibits high adaptability, and significantly improves accuracy.

[0087] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0088] It should be noted that, as another aspect, this application also provides a storage medium, which may be included in an electronic device or may exist independently without being assembled into the electronic device. The storage medium carries one or more programs, which, when executed by an electronic device, cause the electronic device to perform the methods described in the following embodiments.

[0089] In one embodiment, this application provides a computer program product including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0090] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0091] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0092] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A robust long-baseline localization method for reliable acoustic paths in deep sea based on iterative equivalent sound velocity correction, characterized in that, The method includes: Input the initial equivalent sound velocity vector and the initial relative propagation time vector, calculate the measured arrival time delay difference vector based on the initial equivalent sound velocity vector and the initial relative propagation time vector; set the iteration parameters and start the iteration; During the iteration number k-1, where k≥1; based on the equivalent sound speed vector and the relative propagation time vector, the current estimated target position is obtained using the hyperbola intersection method, the horizontal distance to the receiving array is calculated based on the estimated target position, the horizontal distance to the receiving array and the equivalent sound speed table are calculated based on the estimated target position, and the corrected equivalent sound speed vector is calculated using the interpolation method; The estimated propagation time vector is calculated based on the corrected equivalent sound velocity vector and horizontal distance; The estimated arrival delay difference vector is calculated based on the estimated propagation time vector, and the arrival delay difference residual vector is calculated based on the estimated arrival delay difference vector and the measured arrival delay difference vector. The adjustment term is calculated based on the arrival delay difference residual vector. The adjustment term is used to correct the current estimated target position to obtain the corrected target position, which is the estimated target position at iteration number k. The horizontal distance between the corrected target position and the receiving array is calculated based on the corrected target position, the horizontal distance between the corrected target position and the receiving array and the equivalent sound velocity table are used to calculate the corrected equivalent sound velocity vector at iteration number k using the interpolation method. The estimated propagation time vector at iteration number k is calculated based on the corrected equivalent sound velocity vector and the horizontal distance at iteration number k. Update the relative propagation time vector at iteration number k based on the estimated propagation time vector at iteration number k. The estimated arrival delay difference vector at iteration number k is calculated based on the estimated propagation time vector at iteration number k, and the maximum likelihood error function is calculated based on the estimated arrival delay difference vector at iteration number k. The iteration termination is determined based on the maximum likelihood error function or the number of iterations until the iteration terminates. The target position at the current iteration number at the time of iteration termination is output as the final target position.

2. The method according to claim 1, characterized in that, The method further includes: a method for obtaining the equivalent speed of sound table, specifically: Establish a coordinate system, divide the positioning area with the origin as the center, deploy a sonar receiving array within the positioning area, establish a sound field model using the underwater acoustic numerical calculation ray model, and obtain an equivalent sound velocity table.

3. The method according to claim 1, characterized in that, The horizontal distance to the receiving array is calculated based on the estimated target location using the following formula: in, To estimate the target position at iteration number k-1, It is a sonar receiver array.

4. The method according to claim 1, characterized in that, The arrival delay difference residual vector is calculated based on the estimated arrival delay difference vector and the measured arrival delay difference vector using the following formula: in, Let be the measured arrival delay difference vector. This is the estimated arrival delay difference vector at iteration number k-1.

5. The method according to claim 1, characterized in that, The adjustment term is calculated based on the arrival delay difference residual vector using the following formula: in, This is the adjustment term at iteration number k-1. The estimated arrival delay difference at iteration number k-1. The coefficient is determined based on the target location, whether it is inside or outside the baseline. This is the corrected equivalent sound velocity vector at iteration number k-1. For the first n The location of the sonar array This represents the current estimated position at iteration number k-1.

6. The method according to claim 5, characterized in that, The adjusted target position is obtained by correcting the current estimated target position using the adjustment term, and the formula is as follows: in, To correct the target position, This represents the current estimated target position at iteration number k-1.

7. The method according to claim 1, characterized in that, The maximum likelihood error function is calculated based on the estimated arrival delay difference vector at iteration number k, using the following formula: in, Let be the maximum likelihood error function. Let k be the estimated propagation time vector at iteration number k. Let be the measured arrival delay difference vector. This represents the number of sonar receiver arrays.

8. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the long baseline robust localization method for reliable acoustic paths in the deep sea based on iterative equivalent sound velocity correction as described in any one of claims 1 to 7.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the long baseline robust localization method for reliable acoustic paths in the deep sea based on iterative equivalent sound velocity correction as described in any one of claims 1 to 7.

10. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute, via executing the executable instructions, the long baseline robust localization method for deep-sea reliable acoustic paths based on iterative equivalent sound velocity correction as described in any one of claims 1 to 7.

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