A rapid calculation method and system for the incident angle and propagation time of a sound ray directly between two points.

Abstract

This invention relates to the field of underwater acoustic positioning and topographic detection in marine environments, providing a rapid calculation method and system for the incident angle and propagation time of a direct sound ray between two points. The method includes: dividing seawater into layers based on a sound velocity profile; adaptively dividing the incident angle interval according to a preset comprehensive error threshold; calculating the horizontal displacement and propagation time of the sound ray corresponding to different incident angles; and constructing an interpolation coefficient table through third-order polynomial fitting; combining the piecewise displacement of the water depth intervals where the sound ray originates and terminates, obtaining the third-order polynomial fitting coefficients of the horizontal displacement with respect to the incident angle from the polynomial interpolation coefficient table, constructing a cubic equation with respect to the incident angle, solving it using the Cardano method, and iteratively obtaining the incident angle correction value according to a preset angle error threshold; calculating the propagation time; and finally outputting the incident angle and propagation time of the sound ray. This method replaces layer-by-layer calculation with interpolation modeling, achieving high accuracy, rapid convergence, and coefficient table reuse.

Description

Technical Field

[0001] This invention relates to the field of marine acoustic seabed topography detection and underwater positioning technology, and in particular to a method and system for rapidly calculating the incident angle and propagation time of a direct sound ray between two points. Background Technology

[0002] Sound ray calculation is a crucial component of underwater positioning, topographic exploration, and acoustic simulation in marine science. The speed of sound in seawater varies with temperature, salinity, and hydrostatic pressure, exhibiting horizontal stratification and depth-dependent characteristics. Sound wave propagation in the marine medium produces phenomena similar to light refraction, and sound ray propagation in inhomogeneous media follows Snell's law. Therefore, sound rays in seawater are curved, requiring calculation of their trajectories and propagation times based on corresponding sound speed profiles. Sound speed profiles contain sound speed information at different depths in seawater, vertically stratifying the seawater. By calculating the horizontal propagation distance and time of sound rays in different layers, the overall horizontal propagation distance and time of the sound ray can be obtained; this process is called sound ray tracking. The assumption of constant gradient sound speed variation provides theoretical support for precise sound ray calculation in each layer. To obtain accurate sound ray propagation paths, sound rays need to be calculated layer by layer, with the computational workload increasing with water depth. In underwater positioning and acoustic simulation systems, it is typically necessary to calculate the incident angle and propagation time of the direct sound ray between two points.

[0003] Existing methods for calculating direct sound ray distances between two points often employ a bisection method to iteratively calculate the ray's incident angle and propagation time, or, while performing constant gradient sound ray tracking, calculate the first-order derivatives of the horizontal displacement and propagation time with respect to the incident angle, and then iteratively approximate the true values. However, these two methods still involve a significant computational burden during large-scale sound ray calculations. There is an urgent need to research new methods to reduce the computational burden of calculating direct sound ray distances between two points, and to achieve high-precision and rapid calculation of the sound ray's incident angle and propagation time. Summary of the Invention

[0004] The purpose of this invention is to propose a high-precision and rapid calculation method and system for the incident angle and propagation time of a direct sound ray between two points, based on constant gradient sound ray calculation, third-order polynomial interpolation, and the Cardano method, thereby improving the efficiency of underwater acoustic simulation and underwater positioning.

[0005] To solve the above-mentioned technical problems, the present invention provides a method for rapidly calculating the incident angle and propagation time of a direct sound ray between two points, comprising: Based on the sound speed profile, seawater is vertically divided into... Layer, to obtain Each water depth value and its corresponding sound velocity value; The preset incident angle interval is divided, and the horizontal displacement and propagation time of the sound ray corresponding to different initial incident angles are calculated. The function of the sound ray with respect to the initial incident angle is obtained by fitting a third-order polynomial function. The horizontal displacement and propagation time of the sound ray corresponding to the incident angle are calculated with the midpoint of the divided angle interval as the midpoint, and the comprehensive error is calculated. The incident angle interval is adaptively divided according to the relationship between the comprehensive error and the preset comprehensive error threshold, and a polynomial interpolation coefficient table is generated. Based on the water depths at the starting and ending points of the sound ray and the horizontal displacement between the two points, the initial value of the incident angle of the sound ray at the starting water depth is calculated, and the water depth intervals at the starting and ending points of the sound ray are determined according to the sound velocity profile. The horizontal displacement of the sound ray within the water depth interval at the starting point and the horizontal displacement within the water depth interval at the ending point are calculated. The angle sequence number is found according to the polynomial interpolation coefficient table. According to the angle sequence, the third-order polynomial fitting coefficients of the horizontal displacement with respect to the incident angle are obtained from the polynomial interpolation coefficient table, and a cubic equation with respect to the incident angle is constructed. The cubic equation is solved using a preset method to correct the initial value of the incident angle, and the corrected value of the incident angle is obtained. Determine whether the deviation between the incident angle correction value and the initial incident angle is less than a preset angle error threshold. If it is less than the preset angle error threshold, then the incident angle correction value is used as the incident angle of the sound ray. Otherwise, the incident angle correction value is used as the new initial incident angle value to continue the correction until the preset angle error threshold is met. Based on the polynomial interpolation coefficient table and the incident angle, the propagation time of the sound ray in each water depth interval is calculated, and the propagation time of each water depth interval is accumulated to obtain the propagation time of the sound ray. The incident angle and propagation time of the sound ray are then output.

[0006] According to the fast calculation method proposed in this invention, the steps for calculating the horizontal displacement and propagation time of the sound ray corresponding to different initial incident angles are as follows: Divide the incident angle interval into one-third equal intervals to obtain an angle sequence. ; Calculate separately Four sound rays at the initial incident angle at water depth horizontal displacement and transmission time , set the first Layer is , The voice in the first The formulas for calculating the horizontal displacement of the layer and the propagation time are as follows: ; ; ; ; in, The initial angle of incidence of the sound ray. For the sound of the water depth angle of incidence, For the sound of the water depth The sound speed gradient, For the sound of the water depth Horizontal displacement, For the sound of the water depth The spread time.

[0007] According to the fast calculation method proposed in this invention, the function of the sound ray with respect to the initial incident angle includes: The horizontal displacement of the sound ray with respect to the initial angle of incidence function The propagation time of the chords with respect to the initial angle of incidence function Its expression is: ; ; ; ; in, , are the interpolation coefficients for fitting a third-order polynomial function.

[0008] According to the rapid calculation method proposed in this invention, the calculation uses the midpoint of the divided angular interval as the horizontal displacement and propagation time of the sound ray corresponding to the incident angle, specifically including: With the angle sequence The midpoint of the three angular intervals Given the initial angle of incidence, calculate its value at the water depth. Corresponding horizontal displacement and transmission time and the horizontal displacement function with respect to the initial incident angle. and propagation time function , in, , , .

[0009] According to the fast calculation method proposed in this invention, the comprehensive error The calculation formula is: ; ; ; in, This represents the horizontal displacement fitting error. For the propagation time fitting error, water depth The speed of sound.

[0010] According to the fast calculation method proposed in this invention, the adaptive division of the incident angle interval based on the relationship between the comprehensive error and a preset comprehensive error threshold includes: When the overall error exceeds a preset overall error threshold, the divided angle intervals are further divided into equal-interval segments, and the overall error of each sub-interval is calculated. This process continues until the overall error of all sub-intervals does not exceed the preset overall error threshold, resulting in the divided angle sequence. ; in, The number of angles in the angle sequence.

[0011] According to the fast calculation method proposed in this invention, the generation of the polynomial interpolation coefficient table includes: Based on the divided angle sequence, Calculate the corresponding sound ray at the water depth for the initial incident angle. horizontal displacement and transmission time , obtain the horizontal displacement table and transmission time table , , ; The horizontal displacement and transmission time The calculation formula is: ; ; For each angle range By calculating the corresponding sound ray at water depth Horizontal displacement and propagation time with respect to the initial incident angle function , , Record the coefficients of the polynomial function fit to obtain a coefficient table. , , , , .

[0012] ; ; in, , are the interpolation coefficients for fitting a third-order polynomial function.

[0013] According to the fast calculation method proposed in this invention, the construction of a cubic equation with respect to the incident angle is as follows: ; in, Let be the angle of incidence to be determined. , The coefficients for the third-order polynomial fitting of the corresponding horizontal displacement with respect to the incident angle are: This refers to the horizontal displacement of the vocal tract. and These refer to the horizontal displacement of the sound ray within the water depth range of the starting point and the horizontal displacement within the water depth range of the ending point, respectively.

[0014] According to the fast calculation method proposed in this invention, the preset method is the Cardano method.

[0015] This invention also proposes a rapid calculation system for the incident angle and propagation time of a direct sound ray between two points, used to implement any of the above methods, comprising: Layering module: used to vertically layer seawater according to the sound velocity profile, and obtain the water depth value and the corresponding sound velocity value; The polynomial interpolation coefficient table generation module is used to divide the incident angle interval, calculate the horizontal displacement and propagation time of the sound ray corresponding to different incident angles, construct a functional relationship about the incident angle through polynomial fitting, adaptively divide the incident angle interval based on the fitting error, and generate a polynomial interpolation coefficient table. Incident Angle Correction Module: Based on the water depths at the starting and ending points of the sound ray and the horizontal displacement between the two points, the module calculates the initial incident angle of the sound ray at the starting water depth, and determines the water depth intervals at the starting and ending points of the sound ray based on the sound velocity profile; it calculates the horizontal displacement of the sound ray within the water depth interval at the starting point and the horizontal displacement within the water depth interval at the ending point; based on the horizontal displacement relationship, it determines the corresponding angle sequence number from the polynomial interpolation coefficient table; based on the angle sequence, it obtains the third-order polynomial fitting coefficients of the horizontal displacement with respect to the incident angle from the polynomial interpolation coefficient table, and constructs a cubic equation with respect to the incident angle; it solves the cubic equation using the Cardano method to correct the initial incident angle value, obtaining the incident angle correction value; Angle error judgment module: Determines whether the deviation between the incident angle correction value and the incident angle initial value is less than a preset angle error threshold. If it is less than the preset angle error threshold, the incident angle correction value is used as the incident angle of the sound ray. Otherwise, the incident angle correction value is used as the new incident angle initial value to continue the correction until the preset angle error threshold is met. Data calculation module: Based on the polynomial interpolation coefficient table and the incident angle, calculate the propagation time of the sound ray in each water depth interval, accumulate the propagation time of each water depth interval to obtain the propagation time of the sound ray, and output the incident angle and propagation time of the sound ray.

[0016] The advantages of this invention are: 1. By adaptively generating a table of third-order polynomial interpolation coefficients, the process of vocal ray calculation is simplified, and high-precision vocal ray interpolation calculation is achieved; 2. By combining the Cardano method with a third-order polynomial interpolation coefficient table, efficient iterative calculation of the incident angle and propagation time of a direct sound ray between two points was achieved; 3. For the same sound velocity profile, only one calculation of the coefficient table is needed to achieve high-precision and rapid calculation of the incident angle and propagation time of the direct sound ray between any two points in space.

[0017] In summary, this invention combines constant gradient ray calculation, third-order polynomial interpolation, and the Cardano method to achieve rapid correction and updating of the incident angle of a direct ray between two points. It can quickly converge to the true value, ensuring the accuracy of ray calculation while improving computational efficiency, thus enhancing the efficiency of underwater acoustic simulation and underwater positioning. Attached Figure Description

[0018] Figure 1 This is a flowchart of the fast calculation method proposed in this invention. Detailed Implementation

[0019] The technical solutions provided by the present invention will be further illustrated below with reference to the embodiments.

[0020] The following describes in detail, with reference to the accompanying drawings and specific examples, a method for rapidly calculating the incident angle and propagation time of a direct sound ray between two points, provided by the present invention.

[0021] Example 1 like Figure 1 As shown, a rapid method for calculating the incident angle and propagation time of a sound ray between two points includes the following steps: 1. Adaptive generation of polynomial interpolation coefficient table a. Input sound velocity profile and comprehensive error threshold The maximum angle of incidence in the coefficient table The sound speed profile contains water depth value and the corresponding speed of sound Given an initial incident angle interval .

[0022] b. Calculate the polynomial interpolation coefficients and overall error for this interval. Divide the interval into thirds equal intervals to obtain the angle sequence. Calculate using formulas (1)-(4) respectively. Four sound rays at the initial incident angle at water depth horizontal displacement and transmission time .

[0023] (1) (2) (3) (4) in, The initial angle of incidence of the sound ray. For the sound of the water depth angle of incidence, For the sound of the water depth The sound speed gradient, For the sound of the water depth Horizontal displacement, For the sound of the water depth The spread time.

[0024] By fitting a third-order polynomial function, the horizontal displacement and propagation time of the sound ray with respect to the initial incident angle were obtained. function , .

[0025] (5) (6) (7) (8) in, , are the interpolation coefficients for fitting a third-order polynomial function.

[0026] Selecting angle sequences Midpoint of the three angular intervals ,in, , , Calculate using formulas (1)-(4) respectively. The three sound rays at the initial incident angle at the water depth horizontal displacement and transmission time A polynomial fitting function is used. , Interpolation calculations are performed using formulas (5)-(6) to calculate... The three sound rays at the initial incident angle at the water depth horizontal displacement and transmission time The overall error is calculated using the following formula. .

[0027] (9) (10) (11) in, This represents the horizontal displacement fitting error. For the propagation time fitting error, water depth The speed of sound.

[0028] c. If the comprehensive error of this interval Greater than Divide the interval into two equal sub-intervals, and calculate the combined error of the two sub-intervals respectively using step 1.b. Continue dividing the interval until the combined error of all sub-intervals does not exceed [the specified value]. .

[0029] d. Obtain the divided angle sequence ,in The number of angles in the angle sequence.

[0030] e. Based on the angle sequence Calculate using formulas (12) and (13) The sound ray at the initial incident angle at water depth horizontal displacement and transmission time , obtain the horizontal displacement table and transmission time table , , .

[0031] (12) (13) For each angle range Step 1.b calculates the sound ray at water depth. Horizontal displacement and propagation time with respect to the initial incident angle function , , Record the coefficients of the polynomial function fit to obtain a coefficient table. , , , , .

[0032] (14) (15) in, , are the interpolation coefficients for fitting a third-order polynomial function.

[0033] 2. Iteratively calculate the angle of incidence and propagation time of the direct sound ray between the two points. a. Input parameters. Sound ray starting point depth. Speed ​​of sound The final water depth Horizontal displacement of the vocal tract sound speed profile , Angular error threshold .

[0034] b. Calculate the initial values. Calculate the sound ray at water depth using formula (16). initial value of the angle of incidence Based on the sound speed profile, the depth of the water layer where the sound ray originates and terminates can be determined. , ,satisfy , .

[0035] (16) c. Calculate the correction value. The angle of incidence is calculated using the following formula: The voice in the water depth horizontal displacement In the water depth horizontal displacement .

[0036] (17) (18) (19) (20) (twenty one) in, water depth The sound speed gradient, , , The sound timbre at different water depths , , The angle of incidence.

[0037] In the horizontal displacement table Find the angle sequence number This makes the sound waves resonate at different depths of water. The horizontal displacement satisfies Find the third-order polynomial fitting coefficients of the horizontal displacement with respect to the incident angle based on the coefficient table. , The angle of incidence to be determined It satisfies equation (22).

[0038] (twenty two) The system of equations (22) can be simplified to the system of equations (23) by substitution and completing the square.

[0039] (twenty three) (twenty four) in, , , , .

[0040] Solving the system of equations (23) using the Cardano method yields the following results regarding... Three solutions: (25) in, , , , .

[0041] In relation to Among the three solutions, find the one in the interval real solutions The correction value of the incident angle is calculated using formula (26). .

[0042] (26) d. If If not, proceed to step e; otherwise, update the parameters. Proceed to step b.

[0043] e. Calculate the propagation time of the sound ray. Let The angle of incidence is calculated using formulas (27) and (28). The voice in the water depth transmission time In the water depth transmission time Find the corresponding third-order polynomial fitting coefficients for the propagation time with respect to the incident angle based on the coefficient table. , The sound rays at water depth are calculated using formula (29). transmission time The sound ray at water depth is calculated according to formula (30). transmission time .

[0044] (27) (28) (29) (30) f. Angle of incidence of the output sound ray Dissemination time .

[0045] Example 2 A rapid method for calculating the angle of incidence and propagation time of a sound ray directly between two points, comprising: Based on the sound speed profile, seawater is vertically divided into... Layer, to obtain Each water depth value and its corresponding sound velocity value; The preset incident angle interval is divided, and the horizontal displacement and propagation time of the sound ray corresponding to different initial incident angles are calculated. The function of the sound ray with respect to the initial incident angle is obtained by fitting a third-order polynomial function. The horizontal displacement and propagation time of the sound ray corresponding to the incident angle are calculated with the midpoint of the divided angle interval as the midpoint, and the comprehensive error is calculated. The incident angle interval is adaptively divided according to the relationship between the comprehensive error and the preset comprehensive error threshold, and a polynomial interpolation coefficient table is generated. Based on the water depths at the starting and ending points of the sound ray and the horizontal displacement between the two points, the initial value of the incident angle of the sound ray at the starting water depth is calculated, and the water depth intervals at the starting and ending points of the sound ray are determined according to the sound velocity profile. The horizontal displacement of the sound ray within the water depth interval at the starting point and the horizontal displacement within the water depth interval at the ending point are calculated. The angle sequence number is found according to the polynomial interpolation coefficient table. According to the angle sequence, the third-order polynomial fitting coefficients of the horizontal displacement with respect to the incident angle are obtained from the polynomial interpolation coefficient table, and a cubic equation with respect to the incident angle is constructed. The cubic equation is solved using a preset method to correct the initial value of the incident angle, and the corrected value of the incident angle is obtained. Determine whether the deviation between the incident angle correction value and the initial incident angle is less than a preset angle error threshold. If it is less than the preset angle error threshold, then the incident angle correction value is used as the incident angle of the sound ray. Otherwise, the incident angle correction value is used as the new initial incident angle value to continue the correction until the preset angle error threshold is met. Based on the polynomial interpolation coefficient table and the incident angle, the propagation time of the sound ray in each water depth interval is calculated, and the propagation time of each water depth interval is accumulated to obtain the propagation time of the sound ray. The incident angle and propagation time of the sound ray are then output.

[0046] According to the fast calculation method proposed in this invention, the steps for calculating the horizontal displacement and propagation time of the sound ray corresponding to different initial incident angles are as follows: Divide the incident angle interval into one-third equal intervals to obtain an angle sequence. ; Calculate separately Four sound rays at the initial incident angle at water depth horizontal displacement and transmission time , set the first Layer is , The voice in the first The formulas for calculating the horizontal displacement of the layer and the propagation time are as follows: ; ; ; ; in, The initial angle of incidence of the sound ray. For the sound of the water depth angle of incidence, For the sound of the water depth The sound speed gradient, For the sound of the water depth Horizontal displacement, For the sound of the water depth The spread time.

[0047] According to the fast calculation method proposed in this invention, the function of the sound ray with respect to the initial incident angle includes: The horizontal displacement of the sound ray with respect to the initial angle of incidence function The propagation time of the chords with respect to the initial angle of incidence function Its expression is: ; ; ; ; in, , are the interpolation coefficients for fitting a third-order polynomial function.

[0048] According to the rapid calculation method proposed in this invention, the calculation uses the midpoint of the divided angular interval as the horizontal displacement and propagation time of the sound ray corresponding to the incident angle, specifically including: With the angle sequence The midpoint of the three angular intervals Given the initial angle of incidence, calculate its value at the water depth. Corresponding horizontal displacement and transmission time and the horizontal displacement function with respect to the initial incident angle. and propagation time function , in, , , .

[0049] According to the fast calculation method proposed in this invention, the comprehensive error The calculation formula is: ; ; ; in, This represents the horizontal displacement fitting error. For the propagation time fitting error, water depth The speed of sound.

[0050] According to the fast calculation method proposed in this invention, the adaptive division of the incident angle interval based on the relationship between the comprehensive error and a preset comprehensive error threshold includes: When the overall error exceeds a preset overall error threshold, the divided angle intervals are further divided into equal-interval segments, and the overall error of each sub-interval is calculated. This process continues until the overall error of all sub-intervals does not exceed the preset overall error threshold, resulting in the divided angle sequence. ; in, The number of angles in the angle sequence.

[0051] According to the fast calculation method proposed in this invention, the generation of the polynomial interpolation coefficient table includes: Based on the divided angle sequence, Calculate the corresponding sound ray at the water depth for the initial incident angle. horizontal displacement and transmission time , obtain the horizontal displacement table and transmission time table , , ; The horizontal displacement and transmission time The calculation formula is: ; ; For each angle range By calculating the corresponding sound ray at water depth Horizontal displacement and propagation time with respect to the initial incident angle function , , Record the coefficients of the polynomial function fit to obtain a coefficient table. , , , , .

[0052] ; ; in, , are the interpolation coefficients for fitting a third-order polynomial function.

[0053] According to the fast calculation method proposed in this invention, the construction of a cubic equation with respect to the incident angle is as follows: ; in, Let be the angle of incidence to be determined. , The coefficients for the third-order polynomial fitting of the corresponding horizontal displacement with respect to the incident angle are: This refers to the horizontal displacement of the vocal tract. and These refer to the horizontal displacement of the sound ray within the water depth range of the starting point and the horizontal displacement within the water depth range of the ending point, respectively.

[0054] According to the fast calculation method proposed in this invention, the preset method is the Cardano method.

[0055] Example 3 A rapid calculation system for the incident angle and propagation time of a sound ray directly between two points, used to implement any of the above methods, comprising: Layering module: used to vertically layer seawater according to the sound velocity profile, and obtain the water depth value and the corresponding sound velocity value; The polynomial interpolation coefficient table generation module is used to divide the incident angle interval, calculate the horizontal displacement and propagation time of the sound ray corresponding to different incident angles, construct a functional relationship about the incident angle through polynomial fitting, adaptively divide the incident angle interval based on the fitting error, and generate a polynomial interpolation coefficient table. Incident Angle Correction Module: Based on the water depths at the starting and ending points of the sound ray and the horizontal displacement between the two points, the module calculates the initial incident angle of the sound ray at the starting water depth, and determines the water depth intervals at the starting and ending points of the sound ray based on the sound velocity profile; it calculates the horizontal displacement of the sound ray within the water depth interval at the starting point and the horizontal displacement within the water depth interval at the ending point; based on the horizontal displacement relationship, it determines the corresponding angle sequence number from the polynomial interpolation coefficient table; based on the angle sequence, it obtains the third-order polynomial fitting coefficients of the horizontal displacement with respect to the incident angle from the polynomial interpolation coefficient table, and constructs a cubic equation with respect to the incident angle; it solves the cubic equation using the Cardano method to correct the initial incident angle value, obtaining the incident angle correction value; Angle error judgment module: Determines whether the deviation between the incident angle correction value and the incident angle initial value is less than a preset angle error threshold. If it is less than the preset angle error threshold, the incident angle correction value is used as the incident angle of the sound ray. Otherwise, the incident angle correction value is used as the new incident angle initial value to continue the correction until the preset angle error threshold is met. Data calculation module: Based on the polynomial interpolation coefficient table and the incident angle, calculate the propagation time of the sound ray in each water depth interval, accumulate the propagation time of each water depth interval to obtain the propagation time of the sound ray, and output the incident angle and propagation time of the sound ray.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention 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 the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A rapid method for calculating the incident angle and propagation time of a sound ray directly between two points, comprising: Based on the sound speed profile, seawater is vertically divided into... Layer, to obtain Each water depth value and its corresponding sound velocity value; The preset incident angle interval is divided, and the horizontal displacement and propagation time of the sound ray corresponding to different initial incident angles are calculated. The function of the sound ray with respect to the initial incident angle is obtained by fitting a third-order polynomial function. The horizontal displacement and propagation time of the sound ray corresponding to the incident angle are calculated with the midpoint of the divided angle interval as the midpoint, and the comprehensive error is calculated. The incident angle interval is adaptively divided according to the relationship between the comprehensive error and the preset comprehensive error threshold, and a polynomial interpolation coefficient table is generated. Based on the water depths at the starting and ending points of the sound ray and the horizontal displacement between the two points, the initial value of the incident angle of the sound ray at the starting water depth is calculated, and the water depth intervals at the starting and ending points of the sound ray are determined according to the sound velocity profile. The horizontal displacement of the sound ray within the water depth interval at the starting point and the horizontal displacement within the water depth interval at the ending point are calculated. According to the polynomial interpolation coefficient table, the angle sequence number is found. According to the angle sequence number, the corresponding third-order polynomial fitting coefficients of the horizontal displacement with respect to the incident angle are found from the polynomial interpolation coefficient table, and a cubic equation with respect to the incident angle is constructed. The cubic equation is solved using a preset method to correct the initial value of the incident angle, and the corrected value of the incident angle is obtained. Determine whether the deviation between the incident angle correction value and the initial incident angle is less than a preset angle error threshold. If it is less than the preset angle error threshold, then the incident angle correction value is used as the incident angle of the sound ray. Otherwise, the incident angle correction value is used as the new initial incident angle value to continue the correction until the preset angle error threshold is met. Based on the polynomial interpolation coefficient table and the incident angle, the propagation time of the sound ray in each water depth interval is calculated, and the propagation time in each water depth interval is accumulated to obtain the propagation time of the sound ray. The incident angle and propagation time of the sound ray are then output.

2. The fast calculation method according to claim 1, characterized in that, The steps for calculating the horizontal displacement and propagation time of the sound ray corresponding to different initial incident angles are as follows: Divide the incident angle interval into one-third equal intervals to obtain an angle sequence. ; Calculate separately Four sound rays at the initial incident angle at water depth horizontal displacement and transmission time , set the first Layer is , The voice in the first The formulas for calculating the horizontal displacement of the layer and the propagation time are as follows: ； ； ； ； in, The initial angle of incidence of the sound ray. For the sound of the water depth angle of incidence, For the sound of the water depth The sound speed gradient, For the sound of the water depth Horizontal displacement, For the sound of the water depth The spread time.

3. The rapid calculation method according to claim 2, characterized in that, The function of the sound ray with respect to the initial incident angle includes: The horizontal displacement of the sound ray with respect to the initial angle of incidence function The propagation time of the chords with respect to the initial angle of incidence function Its expression is: ； ； ； ； in, , are the interpolation coefficients for fitting a third-order polynomial function.

4. The rapid calculation method according to claim 3, characterized in that, The calculation, which uses the midpoint of the divided angular interval as the incident angle and the corresponding horizontal displacement and propagation time of the sound ray, specifically includes: With the angle sequence The midpoint of the three angular intervals Given the initial angle of incidence, calculate its value at the water depth. Corresponding horizontal displacement and transmission time and the horizontal displacement function with respect to the initial incident angle. and propagation time function , in, , , .

5. The fast calculation method according to claim 4, characterized in that, The aforementioned comprehensive error The calculation formula is: ； ； ； in, This represents the horizontal displacement fitting error. For the propagation time fitting error, water depth The speed of sound.

6. The rapid calculation method according to claim 5, characterized in that, The adaptive division of the incident angle interval based on the relationship between the comprehensive error and the preset comprehensive error threshold includes: When the overall error exceeds a preset overall error threshold, the divided angle intervals are further divided into equal-interval segments, and the overall error of each sub-interval is calculated. This process continues until the overall error of all sub-intervals does not exceed the preset overall error threshold, resulting in the divided angle sequence. ; in, The number of angles in the angle sequence.

7. The rapid calculation method according to claim 6, characterized in that, The generated polynomial interpolation coefficient table includes: Based on the divided angle sequence, Calculate the corresponding sound ray at the water depth for the initial incident angle. horizontal displacement and transmission time , obtain the horizontal displacement table and transmission time table , , ; The horizontal displacement and transmission time The calculation formula is: ； ； For each angle range By calculating the corresponding sound ray at water depth Horizontal displacement and propagation time with respect to the initial incident angle function , , Record the coefficients of the polynomial function fit to obtain a coefficient table. , , , , ; ； ； in, , are the interpolation coefficients for fitting a third-order polynomial function.

8. The rapid calculation method according to claim 7, characterized in that, The aforementioned construction of a cubic equation with respect to the angle of incidence is as follows: ； in, Let be the angle of incidence to be determined. , The coefficients for the third-order polynomial fitting of the corresponding horizontal displacement with respect to the incident angle are: This refers to the horizontal displacement of the vocal tract. and These refer to the horizontal displacement of the sound ray within the water depth range of the starting point and the horizontal displacement within the water depth range of the ending point, respectively.

9. The fast calculation method according to claim 1, characterized in that, The preset method is the Cardano method.

10. A system for rapidly calculating the incident angle and propagation time of a sound ray between two points, used to implement the method described in any one of claims 1-9, characterized in that, include: Layering module: used to vertically layer seawater according to the sound velocity profile, and obtain the water depth value and the corresponding sound velocity value; The polynomial interpolation coefficient table generation module is used to divide the incident angle interval, calculate the horizontal displacement and propagation time of the sound ray corresponding to different incident angles, construct a functional relationship about the incident angle through polynomial fitting, adaptively divide the incident angle interval based on the fitting error, and generate a polynomial interpolation coefficient table. Incident Angle Correction Module: Based on the water depths at the starting and ending points of the sound ray and the horizontal displacement between the two points, the module calculates the initial incident angle of the sound ray at the starting water depth, and determines the water depth intervals at the starting and ending points of the sound ray based on the sound velocity profile; it calculates the horizontal displacement of the sound ray within the water depth interval at the starting point and the horizontal displacement within the water depth interval at the ending point; based on the horizontal displacement relationship, it determines the corresponding angle sequence number from the polynomial interpolation coefficient table; based on the angle sequence, it obtains the third-order polynomial fitting coefficients of the horizontal displacement with respect to the incident angle from the polynomial interpolation coefficient table, and constructs a cubic equation with respect to the incident angle; it solves the cubic equation using the Cardano method to correct the initial incident angle value, obtaining the incident angle correction value; Angle error judgment module: Determines whether the deviation between the incident angle correction value and the incident angle initial value is less than a preset angle error threshold. If it is less than the preset angle error threshold, the incident angle correction value is used as the incident angle of the sound ray. Otherwise, the incident angle correction value is used as the new incident angle initial value to continue the correction until the preset angle error threshold is met. Data calculation module: Based on the polynomial interpolation coefficient table and the incident angle, calculate the propagation time of the sound ray in each water depth interval, accumulate the propagation time of each water depth interval to obtain the propagation time of the sound ray, and output the incident angle and propagation time of the sound ray.

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