A fast ray tracing algorithm based on polynomial fitting

Abstract

The present invention relates to the field of marine surveying and mapping technology, and in particular, to a fast sound ray tracking algorithm based on polynomial fitting. The method includes using the empirical value of the influence of depth on sound velocity, simulating sound rays by using a sound ray tracking algorithm based on a constant sound velocity within a layer, fitting and obtaining a time delay-horizontal distance polynomial by using a least squares algorithm, dividing the initial beam angle and the initial sound velocity and tabulating the polynomial parameters corresponding to the two, approximating the obtained initial beam angle and initial sound velocity, and calculating the coordinates of the beam footprint in the base array coordinate system. The design of the present invention can be applied to fast sound ray tracking during post-processing homing of near-bottom deep-sea multi-beam detection. By using the objective advantages of the near-bottom deep sea and the powerful computing power advantages of computers, polynomial fitting is performed on the sound rays, making the sound rays more realistic, and the data processing method is more efficient, thereby improving the speed and accuracy of sound velocity tracking, and realizing accurate and fast near-bottom deep-sea multi-beam sound ray tracking.

Description

Technical Field

[0001] The invention relates to the technical field of ocean surveying and mapping, and in particular to a fast sound ray tracking algorithm based on polynomial fitting. Background Art

[0002] As a very important measurement method in seabed topography measurement, near-bottom multi-beam measurement has the advantages of high resolution and high efficiency. Due to the characteristics of deep-sea near-bottom multi-beam, its detection carrier is usually below the main jump layer of seawater, and the sound speed at this depth is minimally affected by salinity and temperature. Current multi-beam homing calculations usually assume that the sound line is a straight line or use the sound velocity gradient for sound line tracking. The former has a large calculation error when measuring over long distances, and the latter requires the sound velocity profile as a parameter for calculation, which cannot meet the requirements of high-precision fast calculations. However, there is no fast sound line tracking method in the prior art that is advantageous for deep-sea near-bottom ocean conditions. Summary of the invention

[0003] The object of the present invention is to provide a fast sound ray tracking algorithm based on polynomial fitting to solve the problems raised in the above background technology.

[0004] In order to solve the above technical problems, one of the objectives of the present invention is to provide a fast sound ray tracking algorithm based on polynomial fitting, comprising the following steps:

[0005] S1. Using the empirical value of the effect of depth on sound velocity, the sound line is simulated by using the sound line tracking algorithm based on the constant sound velocity in the layer under different initial sound velocities and initial beam angles, and the relationship between the horizontal component of the path and the time delay is calculated;

[0006] S2. Use the least squares algorithm to fit the delay-depth and delay-horizontal distance polynomials that are closest to the sound line and save the fitting parameters. Use the relationship between the horizontal component of the path and the delay to obtain the delay-horizontal distance polynomial;

[0007] S3, evenly divide the initial beam angle and the initial sound speed within a commonly used range, and make a table of polynomial parameters corresponding to each initial beam angle and initial sound speed for easy calling;

[0008] S4. Approximate the obtained initial beam angle and initial sound velocity to make them correspond to the initial beam angle and initial sound velocity in the table, retrieve the required polynomial parameters and use the obtained time delay to calculate the coordinates of the beam footprint in the base array coordinate system.

[0009] As a further improvement of the present technical solution, in S1, a sound ray tracking algorithm based on a constant sound speed within the layer is adopted, which involves three parameters, namely, the initial beam angle, the initial sound speed and the layer thickness; because the sound speed is only affected by the pressure under the conditions of deep sea near the bottom, the empirical data of the change of sound speed with pressure is used, that is, the sound speed increases by about 1.75m / s for every increase of 100m in depth.

[0010] As a further improvement of the technical solution, in S1, the approximate value of the sound velocity of each layer is calculated using the above-mentioned empirical value. The smaller the layer thickness is, the more accurate the sound velocity profile based on the constant sound velocity in the layer is, and then:

[0011] C i =C i-1 +i×0.0175 (1)

[0012] Formula (1) is the sound velocity C of layer i i Calculation formula;

[0013] And then:

[0014]

[0015] Formula (2) is the beam angle θ of layer i i The calculation formula is: In formula (2), C0 and θ0 are the initial sound velocity and the initial beam angle respectively;

[0016] The initial parameters of each layer are calculated according to equations (1) and (2), and the sound propagation time t in layer i is calculated using the initial parameters. i and the horizontal propagation component x i , as shown below:

[0017]

[0018] x i =h×tanθ i (4)

[0019] In equations (3) and (4), h is the layer thickness;

[0020] The sound propagation time and horizontal propagation component of each layer are calculated. The sound propagation time, horizontal propagation component and depth of each layer are accumulated to obtain the following formula:

[0021]

[0022]

[0023] H i =n×h (7) Wherein, formula (5) is the time T to reach layer i iThe calculation formula of the horizontal component X i The calculation formula of depth H is given by formula (7). i The calculation formula for .

[0024] As a further improvement of the technical solution, in S2, the least squares polynomial curve fitting is used, assuming X = f(T), and assuming that there is a curve g(T) that is closest to X, and the expression of this curve is g(T) = a0+a1T+a2T 2 +…+a n T n , and select the fitting curve based on the principle of minimum sum of squared deviations. The selection principle is as follows:

[0025]

[0026] In formula (8), is the sum of squared deviations, f(T) n To simulate the sound line, g(T) n To fit the sound line.

[0027] As a further improvement of the technical solution, in S2, the sound propagation time to each layer and the corresponding horizontal component of the sound propagation distance are used as data for fitting by utilizing the powerful computing power of the computer;

[0028] After research, it is found that fitting the sound line into an even-order polynomial fitting curve is more in line with the sound line tracking curve based on the constant sound velocity in the layer. Using a quadratic polynomial fitting can fit the curve when the sum of square deviations is small; then:

[0029] X'=a0+a1T+a2T 2 +…+a n T n (9)

[0030] Formula (9) is the sound line fitting curve obtained after fitting; where: a0, a1, a2…a n is the polynomial fitting coefficient, T is the independent variable sound propagation time, and X' is the horizontal component of the fitted sound propagation distance;

[0031] Among them, this fitting finally obtains the functional relationship between the sound propagation time and the corresponding horizontal component of the sound propagation distance when the initial sound speed and the initial beam angle are certain values, and fits the discrete data of each layer into a continuous function, so that the corresponding horizontal component of the sound propagation distance can be calculated under any sound propagation time;

[0032] In addition, the fitting parameters between the sound propagation time and its corresponding depth can be calculated using equations (8) and (9).

[0033] As a further improvement of the technical solution, in S3, the specific method of evenly dividing the initial beam angle and the initial sound speed and tabulating the polynomial parameters corresponding to the two comprises the following steps:

[0034] S3.1. Divide the initial beam angle and the initial sound velocity into several intervals according to a certain span, solve the sound line fitting curve parameters between the sound propagation time and the horizontal component of the sound propagation distance corresponding to different initial beam angles and initial sound velocities, and generate a two-dimensional matrix;

[0035] S3.2, and using the same method to generate a two-dimensional matrix storing the sound line fitting curve parameters between the sound propagation time and the depth;

[0036] S3.3. Using a smaller span to divide the initial beam angle and initial sound velocity will result in a higher accuracy of the final polynomial fitting to replace the sound line. At the same time, the amount of data stored in the memory increases, which increases the retrieval and processing time.

[0037] As a further improvement of the technical solution, in S4, the specific method for calculating the coordinates of the beam footprint in the array coordinate system includes the following steps:

[0038] S4.1. After obtaining the initial beam angle and initial sound velocity of the deep-sea near-bottom multi-beam, approximate processing is performed to make them correspond to the initial beam angle and initial sound velocity in the table, and the corresponding sound line fitting curve parameters are retrieved;

[0039] S4.2. Using the retrieved sound line fitting parameters, it is easy to obtain the polynomial function relationship between the sound propagation time and the corresponding horizontal component of the sound propagation distance;

[0040] S4.3, and using the time delay of the sound propagation received by the sensor, calculate the horizontal component of the sound propagation distance after fitting;

[0041] S4.4. Use the same method to calculate the depth of sound propagation, and finally obtain the depth and horizontal distance coordinates after a certain propagation time under the conditions of the initial beam angle and initial sound speed.

[0042] The second object of the present invention is to provide a system and operating device for a fast sound ray tracing algorithm based on polynomial fitting, including a processor, a memory, and a computer program stored in the memory and running on the processor, and the processor is used to implement any of the above-mentioned steps of the fast sound ray tracing algorithm based on polynomial fitting when executing the computer program.

[0043] A third object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements any of the steps of the above-mentioned fast sound ray tracking algorithm based on polynomial fitting.

[0044] Compared with the prior art, the invention has the following beneficial effects: the fast sound ray tracking algorithm based on polynomial fitting can be applied to fast sound ray tracking during post-processing homing of near-bottom deep-sea multi-beam detection, and utilizes the objective advantages of the near-bottom deep sea and the powerful computing power of computers to perform polynomial fitting on the sound lines, thereby overcoming some shortcomings of the current algorithms and making the sound lines more realistic. In addition, the data processing method is more efficient, which improves the speed and accuracy of sound speed tracking and realizes accurate and fast near-bottom deep-sea multi-beam sound ray tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flowchart of the overall algorithm of the present invention;

[0046] Figure 2 It is one of the local algorithm flow charts of the present invention;

[0047] Figure 3 This is the second local algorithm flow chart of the present invention;

[0048] Figure 4 A schematic diagram of simulating sound rays based on a sound ray tracking algorithm at a constant sound velocity within a layer in the present invention;

[0049] Figure 5 is a schematic diagram of the sound line after polynomial fitting in the present invention;

[0050] Figure 6 is a schematic diagram of the relative error between the simulated sound line and the fitted sound line in the present invention;

[0051] Figure 7 It is a schematic diagram of the structure of an exemplary electronic computer device in the present invention. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] Example 1

[0054] like Figure 1-Figure 7 As shown, this embodiment provides a fast sound ray tracking algorithm based on polynomial fitting, comprising the following steps:

[0055] S1. Using the empirical value of the effect of depth on sound velocity, the sound line is simulated by using the sound line tracking algorithm based on the constant sound velocity in the layer under different initial sound velocities and initial beam angles, and the relationship between the horizontal component of the path and the time delay is calculated;

[0056] S2. Use the least squares algorithm to fit the delay-depth and delay-horizontal distance polynomials that are closest to the sound line and save the fitting parameters. Use the relationship between the horizontal component of the path and the delay to obtain the delay-horizontal distance polynomial;

[0057] S3, evenly divide the initial beam angle and the initial sound speed within a commonly used range, and make a table of polynomial parameters corresponding to each initial beam angle and initial sound speed for easy calling;

[0058] S4. Approximate the obtained initial beam angle and initial sound velocity to make them correspond to the initial beam angle and initial sound velocity in the table, retrieve the required polynomial parameters and use the obtained time delay to calculate the coordinates of the beam footprint in the base array coordinate system.

[0059] In this embodiment, in S1, a sound ray tracking algorithm based on a constant sound speed within the layer is used, which involves three parameters, namely, the initial beam angle, the initial sound speed and the layer thickness; because the sound speed is only affected by the pressure under deep sea near the bottom, the empirical data of the sound speed changing with pressure is used, that is, the sound speed increases by about 1.75m / s for every 100m increase in depth.

[0060] Furthermore, in S1, the approximate value of the sound velocity of each layer is calculated using the above empirical value. The smaller the layer thickness, the more accurate the sound velocity profile based on the constant sound velocity in the layer, and then:

[0061] C i =C i-1 +i×0.0175 (1)

[0062] Formula (1) is the sound velocity C of layer i i Calculation formula;

[0063] And then:

[0064]

[0065] Formula (2) is the beam angle θ of layer i i The calculation formula is: In formula (2), C0 and θ0 are the initial sound velocity and the initial beam angle respectively;

[0066] The initial parameters of each layer are calculated according to equations (1) and (2), and the sound propagation time t in layer i is calculated using the initial parameters. i and the horizontal propagation component x i , as shown below:

[0067]

[0068] x i =h×tanθ i (4)

[0069] In equations (3) and (4), h is the layer thickness;

[0070] The sound propagation time and horizontal propagation component of each layer are calculated. The sound propagation time, horizontal propagation component and depth of each layer are accumulated to obtain the following formula:

[0071]

[0072]

[0073] H i =n×h (7)

[0074] Wherein, formula (5) is the time T to reach layer i i The calculation formula of the horizontal component X i The calculation formula of depth H is given by formula (7). i The calculation formula for .

[0075] In this embodiment, in S2, the least squares polynomial curve fitting is used, and X=f(T) is assumed, and it is assumed that there is a curve g(T) that is closest to X. The expression of this curve is g(T)=a0+a1T+a2T 2 +…+a n T n , and select the fitting curve based on the principle of minimum sum of squared deviations. The selection principle is as follows:

[0076]

[0077] In formula (8), is the sum of squared deviations, f(T) n To simulate the sound line, g(T) n To fit the sound line.

[0078] Furthermore, in S2, the sound propagation time to each layer and the corresponding horizontal component of the sound propagation distance are used as data for fitting by utilizing the powerful computing power of computers;

[0079] After research, it is found that fitting the sound line into an even-order polynomial fitting curve is more in line with the sound line tracking curve based on the constant sound velocity in the layer. Using a quadratic polynomial fitting can fit the curve when the sum of square deviations is small; then:

[0080] X'=a0+a1T+a2T 2+…+a n T n (9)

[0081] Formula (9) is the sound line fitting curve obtained after fitting; where: a0, a1, a2…a n is the polynomial fitting coefficient, T is the independent variable sound propagation time, and X' is the horizontal component of the fitted sound propagation distance;

[0082] Among them, this fitting finally obtains the functional relationship between the sound propagation time and the corresponding horizontal component of the sound propagation distance when the initial sound speed and the initial beam angle are certain values, and fits the discrete data of each layer into a continuous function, so that the corresponding horizontal component of the sound propagation distance can be calculated under any sound propagation time;

[0083] In addition, the fitting parameters between the sound propagation time and its corresponding depth can be calculated using equations (8) and (9).

[0084] In this embodiment, in S3, the specific method of evenly dividing the initial beam angle and the initial sound speed and tabulating the polynomial parameters corresponding to the two comprises the following steps:

[0085] S3.1. Divide the initial beam angle and the initial sound velocity into several intervals according to a certain span, solve the sound line fitting curve parameters between the sound propagation time and the horizontal component of the sound propagation distance corresponding to different initial beam angles and initial sound velocities, and generate a two-dimensional matrix;

[0086] S3.2, and using the same method to generate a two-dimensional matrix storing the sound line fitting curve parameters between the sound propagation time and the depth;

[0087] S3.3. Using a smaller span to divide the initial beam angle and initial sound velocity will result in a higher accuracy of the final polynomial fitting to replace the sound line. At the same time, the amount of data stored in the memory increases, which increases the retrieval and processing time.

[0088] In this embodiment, in S4, the specific method for calculating the coordinates of the beam footprint in the array coordinate system includes the following steps:

[0089] S4.1. After obtaining the initial beam angle and initial sound velocity of the deep-sea near-bottom multi-beam, approximate processing is performed to make them correspond to the initial beam angle and initial sound velocity in the table, and the corresponding sound line fitting curve parameters are retrieved;

[0090] S4.2. Using the retrieved sound line fitting parameters, it is easy to obtain the polynomial function relationship between the sound propagation time and the corresponding horizontal component of the sound propagation distance;

[0091] S4.3, and using the time delay of the sound propagation received by the sensor, calculate the horizontal component of the sound propagation distance after fitting;

[0092] S4.4. Use the same method to calculate the depth of sound propagation, and finally obtain the depth and horizontal distance coordinates after a certain propagation time under the conditions of the initial beam angle and initial sound speed.

[0093] In addition, it is worth pointing out that the accuracy of the above algorithm has a large error when it is very close to the transmitter, that is, this algorithm cannot be used when it is close to the depth where the sound line is reversed.

[0094] like Figure 7 As shown, this embodiment also provides a system and an operating device for a fast sound ray tracking algorithm based on polynomial fitting, and the device includes a processor, a memory, and a computer program stored in the memory and running on the processor.

[0095] The processor includes one or more processing cores. The processor is connected to the memory through a bus. The memory is used to store program instructions. When the processor executes the program instructions in the memory, the above-mentioned fast sound ray tracking algorithm based on polynomial fitting is implemented.

[0096] Optionally, the memory can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk or optical disk.

[0097] In addition, the present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the above-mentioned fast sound ray tracking algorithm based on polynomial fitting are implemented.

[0098] Optionally, the present invention further provides a computer program product comprising instructions, which, when executed on a computer, enables the computer to execute the steps of the fast sound ray tracing algorithm based on polynomial fitting in the above aspects.

[0099] A person skilled in the art will appreciate that all or part of the steps to implement the above embodiments may be accomplished by hardware or by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a disk, or an optical disk, etc.

[0100] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A fast sound ray tracking algorithm based on polynomial fitting, characterized by: The steps include: S1. Using the empirical value of the effect of depth on sound velocity, the sound line is simulated by using the sound line tracking algorithm based on the constant sound velocity in the layer under different initial sound velocities and initial beam angles, and the relationship between the horizontal component of the path and the time delay is calculated; S2. Use the least squares algorithm to fit the delay-depth and delay-horizontal distance polynomials that are closest to the sound line and save the fitting parameters. Use the relationship between the horizontal component of the path and the delay to obtain the delay-horizontal distance polynomial; S3, evenly divide the initial beam angle and the initial sound speed within a commonly used range, and make a table of polynomial parameters corresponding to each initial beam angle and initial sound speed for easy calling; S4. Approximate the obtained initial beam angle and initial sound velocity to make them correspond to the initial beam angle and initial sound velocity in the table, retrieve the required polynomial parameters and use the obtained time delay to calculate the coordinates of the beam footprint in the base array coordinate system.

2. The fast sound ray tracing algorithm based on polynomial fitting according to claim 1, characterized in that: In S1, the sound ray tracking algorithm based on the constant sound speed in the layer involves three parameters, namely the initial beam angle, the initial sound speed and the layer thickness; because the sound speed is only affected by the pressure under the condition of deep sea near the bottom, the empirical data of the change of sound speed with pressure is used, that is, the sound speed increases by about 1.75m / s for every increase of 100m in depth.

3. The fast sound ray tracing algorithm based on polynomial fitting according to claim 2, characterized in that: In S1, the approximate value of the sound velocity of each layer is calculated using the above empirical value. The smaller the layer thickness, the more accurate the sound velocity profile based on the constant sound velocity in the layer, and then: C i =C i-1 +i×0.0175 (1) Formula (1) is the sound velocity C of layer i i Calculation formula; And then: Formula (2) is the beam angle θ of layer i i The calculation formula is: In formula (2), C0 and θ0 are the initial sound velocity and the initial beam angle respectively; The initial parameters of each layer are calculated according to equations (1) and (2), and the sound propagation time t in layer i is calculated using the initial parameters. i and the horizontal propagation component x i , as shown below: x i =h×tanθ i (4) In equations (3) and (4), h is the layer thickness; The sound propagation time and horizontal propagation component of each layer are calculated. The sound propagation time, horizontal propagation component and depth of each layer are accumulated to obtain the following formula: H i =n×h (7) Wherein, formula (5) is the time T to reach layer i i The calculation formula of the horizontal component X i The calculation formula of depth H is given by formula (7). i The calculation formula for .

4. The fast sound ray tracing algorithm based on polynomial fitting according to claim 3, characterized in that: In S2, the least squares polynomial curve fitting is used, and X=f(T) is assumed, and it is assumed that there is a curve g(T) that is closest to X. The expression of this curve is g(T)=a0+a1T+a2T 2 +…+a n T n , and select the fitting curve based on the principle of minimum sum of squared deviations. The selection principle is as follows: In formula (8), is the sum of squared deviations, f(T) n To simulate the sound line, g(T) n To fit the sound line.

5. The fast sound ray tracing algorithm based on polynomial fitting according to claim 4, characterized in that: In S2, the powerful computing power of the computer is used to fit the sound propagation time to each layer and the corresponding horizontal component of the sound propagation distance as data; After research, it is found that fitting the sound line into an even-order polynomial fitting curve is more in line with the sound line tracking curve based on the constant sound velocity in the layer. Using a quadratic polynomial fitting can fit the curve when the sum of square deviations is small; then: X’=a0+a1T+a2T 2 +…+a n T n (9) Formula (9) is the sound line fitting curve obtained after fitting; where: a0, a1, a2…a n is the polynomial fitting coefficient, T is the independent variable sound propagation time, and X' is the horizontal component of the fitted sound propagation distance; Among them, this fitting finally obtains the functional relationship between the sound propagation time and the corresponding horizontal component of the sound propagation distance when the initial sound speed and the initial beam angle are certain values, and fits the discrete data of each layer into a continuous function, so that the corresponding horizontal component of the sound propagation distance can be calculated under any sound propagation time; In addition, the fitting parameters between the sound propagation time and its corresponding depth can be calculated using equations (8) and (9).

6. The fast sound ray tracing algorithm based on polynomial fitting according to claim 5, characterized in that: In S3, the specific method of evenly dividing the initial beam angle and the initial sound speed and tabulating the polynomial parameters corresponding to the two comprises the following steps: S3.

1. Divide the initial beam angle and the initial sound velocity into several intervals according to a certain span, solve the sound line fitting curve parameters between the sound propagation time and the horizontal component of the sound propagation distance corresponding to different initial beam angles and initial sound velocities, and generate a two-dimensional matrix; S3.2, and using the same method to generate a two-dimensional matrix storing the sound line fitting curve parameters between the sound propagation time and the depth; S3.

3. Using a smaller span to divide the initial beam angle and initial sound velocity will result in a higher accuracy of the final polynomial fitting to replace the sound line. At the same time, the amount of data stored in the memory increases, which increases the retrieval and processing time.

7. The fast sound ray tracing algorithm based on polynomial fitting according to claim 6, characterized in that: In S4, the specific method for calculating the coordinates of the beam footprint in the array coordinate system includes the following steps: S4.

1. After obtaining the initial beam angle and initial sound velocity of the deep-sea near-bottom multi-beam, approximate processing is performed to make them correspond to the initial beam angle and initial sound velocity in the table, and the corresponding sound line fitting curve parameters are retrieved; S4.

2. Using the retrieved sound line fitting parameters, it is easy to obtain the polynomial function relationship between the sound propagation time and the corresponding horizontal component of the sound propagation distance; S4.3, and using the time delay of the sound propagation received by the sensor, calculate the horizontal component of the sound propagation distance after fitting; S4.

4. Use the same method to calculate the depth of sound propagation, and finally obtain the depth and horizontal distance coordinates after a certain propagation time under the conditions of the initial beam angle and initial sound speed.

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