WO2020252945A1 - 基于泰勒展开的初始掠射角求解方法、声线弯曲修正方法和设备 - Google Patents

基于泰勒展开的初始掠射角求解方法、声线弯曲修正方法和设备 Download PDF

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WO2020252945A1
WO2020252945A1 PCT/CN2019/105178 CN2019105178W WO2020252945A1 WO 2020252945 A1 WO2020252945 A1 WO 2020252945A1 CN 2019105178 W CN2019105178 W CN 2019105178W WO 2020252945 A1 WO2020252945 A1 WO 2020252945A1
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initial
angle
glancing angle
sound
sound ray
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PCT/CN2019/105178
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English (en)
French (fr)
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徐晓苏
金博楠
张涛
李瑶
姚逸卿
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东南大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/66—Sonar tracking systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/74—Systems using reradiation of acoustic waves, e.g. IFF, i.e. identification of friend or foe
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00

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  • the invention belongs to the technical field of underwater acoustic detection and positioning, and specifically relates to an initial glancing angle solution method, a sound ray bending correction method and equipment for sound ray tracking.
  • the acoustic signal propagates underwater it is subject to different salinity, temperature, depth and pressure, and its propagation speed is also different. Different sound speeds cause sound waves to no longer propagate in a straight line in the water. From the cross-sectional view, the sound ray between the emitter and the hydrophone is a curve instead of a straight line. Not only does the length of the sound ray become longer, the time it takes is also longer. .
  • the commonly used method of ranging is the sound ray tracking algorithm, which simulates the sound ray path hierarchically according to the sound velocity profile to estimate the horizontal distance.
  • Acoustic ray tracking requires an initial glancing angle. Use this angle as the starting direction to track the acoustic ray path. The precise initial glancing angle can also correct the direction finding error in the ultra-short baseline. Such scenarios often occur in practical applications.
  • the measuring ship detects the underwater fixed transponder and obtains the signal round-trip delay of 2t. In the process of delay conversion position slant distance, accurate sound ray glancing angle is required.
  • Voice tracking except for a small number of underwater acoustic sensors that can detect the direction of emission or incidence of the signal, most devices cannot accurately know the initial glancing angle of the sound ray. For this, the existing method uses a step search method in the range of 0-90° Find the most approximate initial glancing angle. This method requires sound ray tracking over the entire range, which is very cumbersome. If the step length is too large, the actual glancing angle may be skipped. If the step length is too small, the efficiency will be low and the calculation burden will increase. .
  • the present invention proposes a method for solving the initial glancing angle based on Taylor expansion, a method for correcting sound ray bending, and computer equipment, which can quickly and accurately obtain the initial glancing angle and effectively solve the problem Under the influence of line bending, when the sound ray tracking method is used to correct the ranging error, the problem of the increase of the slope distance measurement error due to the inaccurate initial glancing angle.
  • a method for solving the initial glancing angle based on Taylor expansion includes the following steps:
  • the initial glancing angle ⁇ 0 is estimated by the triangulation principle , and the sine of the refraction angle ⁇ 0 complementary to the initial glancing angle ⁇ 0 Is the initial value of the iteration;
  • a method for correcting sound ray bending obtains an initial glancing angle according to the initial glancing angle solution method described in the first aspect, and based on the initial glancing angle, the isocratic sound ray is tracked. The method obtains the horizontal distance, and then obtains the slope distance according to the Pythagorean theorem.
  • a computer device comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory , And configured to be executed by the one or more processors, and when the program is executed by the processor, the method according to the first aspect of the present invention is implemented.
  • the present invention solves the practical problem that the initial glancing angle cannot be accurately determined according to the measurement time delay due to the bending of the sound ray in underwater acoustic detection and positioning, thereby correcting the slant distance.
  • the present invention reverses the initial glancing angle according to the sound ray tracking correction model developed by Taylor, and finally accurately corrects the sound ray error.
  • the present invention does not need to search, the amount of calculation is small, and the estimated initial glancing angle has extremely high accuracy in most ranges, thereby correcting the sound ray bending and improving the measurement accuracy of the slant distance.
  • the simulation experiment shows , In the 3000m depth, the ranging error does not exceed 10m.
  • Fig. 1 is a flowchart of a sound ray correction method according to an embodiment of the present invention
  • Fig. 2 is a schematic diagram of sound ray geometry according to an embodiment of the present invention.
  • Figure 3 is a sound velocity profile according to an embodiment of the present invention.
  • Fig. 4 shows sound ray traces at different angles according to an embodiment of the present invention
  • Figure 5 is a comparison of initial glancing angle errors according to an embodiment of the present invention.
  • Figure 6 is a comparison of horizontal distance errors according to an embodiment of the present invention.
  • Fig. 7 is a comparison of slant distance errors according to an embodiment of the present invention.
  • Fig. 8 is a schematic diagram of search and tracking when the glancing angle is 3.624° according to an embodiment of the present invention.
  • Figure 1 is a flow chart of a sound ray correction method proposed by the present invention. Aiming at the problem of underwater acoustic ranging in a constant depth environment, the present invention proposes a method for solving the initial glancing angle based on Taylor expansion, using sound velocity profile and measurement The obtained depth and time delay information reversely deduces the initial glancing angle of the sound ray.
  • the basic variables are shown in Figure 2:
  • Output the initial glancing angle ⁇ 0 of the sound ray, the horizontal distance R and the slope distance r.
  • Step 1 Select the initial iterative value of the initial glancing angle ⁇ 0 ;
  • the initial grazing angle is calculated based on the slope distance estimated by the weighted average sound velocity as the initial value of the iteration.
  • the weighted average sound velocity is obtained as follows:
  • g i is the sound velocity gradient of each layer
  • g i (c i+1 -c i )/(z i+1 -z i )
  • the refraction angle is the angle between the sound ray and the vertical. Because the glancing angle and the refraction angle are complementary, the sine of the refraction angle follows snell's law, and p is a constant:
  • ⁇ is used to represent the sine of the refraction angle
  • the initial glancing angle ⁇ 0 arccos ⁇ 0
  • ⁇ 0 is used as the initial value
  • Step 2 Estimate the time delay with the isocratic sound ray tracking method
  • the horizontal distance and time delay can be estimated from the initial glancing angle:
  • ⁇ i c i /c 0 .
  • Step 3 Calculate the initial value increment and correct it
  • the initial value is updated based on the increment, and the initial value is corrected to:
  • ⁇ 0 ⁇ 0 +d ⁇ 0
  • Step 4 Complete the iterative process and solve
  • Steps 2 and 3 are repeated continuously to iterate until ⁇ t ⁇ ( ⁇ is the threshold) or the number of iterations n exceeds the upper limit N to end the iteration.
  • ⁇ 0 arccos ⁇ 0 is the final initial glancing angle, and the corresponding is obtained according to the isogradient tracking method
  • the slope distance can be obtained according to the Pythagorean theorem.
  • FIG. 3 A simulation test is carried out on a deep sea environment with a water depth of 3000m.
  • the sound velocity profile is shown in Figure 3.
  • Ten glancing angles ⁇ 0 at different angles are selected from 0 to 90° as the test.
  • the corresponding horizontal distance R and time delay t are shown in Table 1. Shown.
  • Figure 4 is a schematic diagram of sound ray trajectories at different angles.
  • the present invention is combined with the empirical sound velocity method and the traditional search and tracking method. Compare. In addition to the time delay t, individual points are selected for the sound velocity in Figure 3 and white noise is added as the actual measured sound velocity profile. The average value of the white noise is zero and the standard deviation is 0.1m/s.
  • the empirical sound velocity method uses the empirical sound velocity to convert the time delay into the slant distance.
  • the weighted average sound velocity is used as the empirical sound velocity.
  • the empirical sound velocity method does not consider the bending of sound rays, and the horizontal distance and glancing angle can be calculated from the triangle relationship.
  • Both the search and tracking method and the present invention take into account the influence of sound ray curvature. It is necessary to calculate the initial glancing angle and then use the isogradient sound ray tracking method to track the sound ray to obtain the corresponding horizontal distance and slant distance. Therefore, the accuracy of the initial glancing angle and the calculation speed determine the accuracy and ease of use of the slope distance.
  • Figure 5 is a comparison of the error of the initial glancing angle calculated by the present invention, the empirical speed of sound method and the search and tracking method. It can be seen that the error of the empirical speed of sound method is relatively large, and the present invention is at a large glancing angle (the transponder is near directly below) Compared with the search and tracking method, the present invention has a certain error. This is due to the fact that ⁇ 0 is near 0, which makes it necessary to face the problem of zero denominator or negative square root in the calculation process. A series of approximate processing increases the error, especially When the delay error is large, the situation becomes more serious. However, when the grazing angle is approximately less than 80°, the advantages of the present invention are highlighted.
  • the calculation accuracy of the initial grazing angle is always higher than that of the search and tracking method, especially when the grazing angle is small, the error of the search and tracking method becomes larger. This is mainly because when the angle is small, the time delay is very sensitive to the small change of the glancing angle, and the relatively large search step size causes a large error.
  • the size of the initial glancing angle error is reflected in the sound velocity tracking method to calculate the horizontal distance, and the slant distance error changes accordingly with the horizontal distance error, as shown in Figure 6 and Figure 7.
  • the slant distance error of the present invention is relatively large in the opening angle of about 10° directly below the sound source, and has the smallest error in most other ranges.
  • the horizontal distance error and the slant distance error increase with the increase of the initial grazing angle of the search under the small glancing angle, and it is even lower than the empirical sound velocity method.
  • Table 2 The numerical results of this experiment are shown in Table 2.
  • the search and tracking method requires a lot of attempts to search with a certain step length, and the accuracy is also affected by the compensation resolution.
  • the glancing angle provided by the empirical sound velocity method can narrow the search range. When the initial glancing angle is large, the range is small, but when the initial glancing angle is large, the glancing angle and the actual glancing angle obtained by the empirical sound velocity method The gap is large, and the search workload is still huge, as shown in Figure 8.
  • the present invention solves the practical problem of sound ray bending in underwater acoustic detection and positioning, and the initial glancing angle cannot be accurately determined according to the measurement time delay, thereby correcting the slant distance.
  • the present invention reverses the initial glancing angle according to the sound ray tracking correction model developed by Taylor, and finally accurately corrects the sound ray error.
  • the present invention does not need to search, the calculation amount is small, and the estimated initial glancing angle has extremely high accuracy in most ranges, thereby correcting the sound ray bending and improving the measurement accuracy of the slope distance.
  • a computer device includes: one or more processors; a memory; and one or more programs, wherein the one One or more programs are stored in the memory and configured to be executed by the one or more processors, and when the programs are executed by the processor, each step in the method embodiment is implemented.
  • the embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.
  • a computer-usable storage media including but not limited to disk storage, CD-ROM, optical storage, etc.
  • These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing equipment to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including the instruction device.
  • the device implements the functions specified in one process or multiple processes in the flowchart and/or one block or multiple blocks in the block diagram.
  • These computer program instructions can also be loaded on a computer or other programmable data processing equipment, so that a series of operation steps are executed on the computer or other programmable equipment to produce computer-implemented processing, so as to execute on the computer or other programmable equipment.
  • the instructions provide steps for implementing functions specified in a flow or multiple flows in the flowchart and/or a block or multiple blocks in the block diagram.

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Acoustics & Sound (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

一种基于泰勒展开的初始掠射角求解方法、声线弯曲修正方法和设备。方法包括：（1）根据声速剖面c（z）、测量时延t、应答器深度H，由三角原理预估初始掠射角θ0，取与初始掠射角θ0互余的折射角的正弦Θ0为迭代初值；（2）根据迭代初值利用等梯度声线跟踪法求取水平距离和估计时延 d 将等梯度声线跟踪公式在初值处泰勒展开，根据时延偏差计算正弦增量并更新初值；（4）重复步骤2-3，直到满足迭代结束条件时结束迭代，根据此时的正弦值Θ0得到最终的初始掠射角θ0＝arccosΘ0。由此缩小了搜索范围，提高了搜索分辨率，显著地改善了搜索时间和精度，简单高效，适用于水下探测和定位。

Description

基于泰勒展开的初始掠射角求解方法、声线弯曲修正方法和设备 技术领域
本发明属于水声探测和定位技术领域，具体涉及一种用于声线跟踪的初始掠射角求解方法、声线弯曲修正方法和设备。
背景技术
水下探测和定位都用到测距，通过斜距确定几何位置。声信号在水下传播时，受到不同的盐度、温度、深度和压力，其传播速度也各不相同。不同的声速导致声波在水中不再按照直线传播，从剖面看，发射源到水听器之间的声线是一条曲线，而非直线，不仅声线长度变大，所经历的时间也变长。测距常用的方法是声线跟踪算法，根据声速剖面分层模拟声线路径，估计水平距离。
声线跟踪需要初始掠射角，以该角度为起始方向追踪声线路径，精确的初始掠射角还能够校正超短基线中的测向误差。在实际应用中常常出现这样的场景，测量船对水下固定的应答器进行探测，获得了信号往返的时延2t，在时延转换位斜距的过程中需要准确的声线掠射角进行声线跟踪。然而除了少部分水声传感器能够检测信号的出射或入射方向，大部分设备无法准确获知声线的初始掠射角，对于此，现有的方法采用在0～90°范围内步进搜索的方式找到最近似的初始掠射角，这种方法要求对全范围进行声线跟踪，十分繁琐，而且步长过大可能会跳过实际掠射角，步长过小又导致效率低下，计算负担增加。
因此，如何快速精确地锁定初始掠射角成为当前亟待解决的问题。
发明内容
发明目的：针对现有技术的不足，本发明提出了一种基于泰勒展开的初始掠射角求解方法、声线弯曲修正方法以及计算机设备，能够快速精确地获得初始掠射角，有效解决在声线弯曲影响下，采用声线跟踪法校正测距误差时由于初始掠射角不准而导致的斜距测量误差增大的问题。
技术方案：根据本发明的第一方面，提供一种基于泰勒展开的初始掠射角求解方法，所述方法包括以下步骤：
(1)根据声速剖面c(z)、测量时延t、应答器深度H，由三角原理预估初始掠射角θ 0，取与初始掠射角θ 0互余的折射角的正弦Θ 0为迭代初值；
(2)根据迭代初值利用等梯度声线跟踪法求取水平距离和估计时延
Figure PCTCN2019105178-appb-000001
(3)计算时延偏差
Figure PCTCN2019105178-appb-000002
将等梯度声线跟踪公式在初值处泰勒展开，根据时延偏差计算正弦增量并更新初值；
(4)重复步骤2-3，直到满足迭代结束条件时结束迭代，根据此时的正弦值Θ 0得到最终的初始掠射角θ 0＝arccosΘ 0。
根据本发明的第二方面，提供一种声线弯曲修正方法，所述方法根据第一方面所述的初始掠射角求解方法得到初始掠射角，基于初始掠射角根据等梯度声线跟踪方法求得水平距离，再根据勾股定理得到斜距。
根据本发明的第三方面，提供一种计算机设备，所述设备包括：一个或多个处理器；存储器；以及一个或多个程序，其中所述一个或多个程序被存储在所述存储器中，并且被配置为由所述一个或多个处理器执行，所述程序被处理器执行时实现如本发明第一方面所述的方法。
有益效果：本发明很好地解决了水声探测和定位中由于声线弯曲而无法根据测量时延准确确定初始掠射角，进而修正斜距的现实问题。本发明在已知深度和声速剖面情况下，根据泰勒展开的声线跟踪校正模型反推初始掠射角，最终精确修正声线误差。相比于传统方法，本发明无需搜索，计算量小，估算出的初始掠射角在大部分范围内具有极高的精度，进而修正了声线弯曲，提高了斜距测量精度，仿真实验表明，在3000m深度内，测距误差不超过10m。
附图说明
图1为根据本发明实施例的声线修正方法流程图；
图2为根据本发明实施例的声线几何示意图；
图3为根据本发明实施例的声速剖面；
图4为根据本发明实施例的不同角度的声线轨迹；
图5为根据本发明实施例的初始掠射角误差对比；
图6为根据本发明实施例的水平距离误差对比；
图7为根据本发明实施例的斜距误差对比；
图8为根据本发明实施例的掠射角为3.624°时的搜索跟踪示意图。
具体实施方式
下面结合附图对本发明的技术方案作进一步说明。应当了解，以下提供的实施例仅是为了详尽地且完全地公开本发明，并且向所属技术领域的技术人员充分传达本发明的技术构思，本发明还可以用许多不同的形式来实施，并且不局限于此处描述的实施例。对于表示在附图中的示例性实施方式中的术语并不是对本发明的限定。
图1所示为本发明所提的一种声线修正方法流程图，本发明针对深度恒定环境下水声测距问题，提出一种基于泰勒展开的初始掠射角求解方法，利用声速剖面和测量获得的深度、时延信息反推声线的初始掠射角。基本变量如图2所示：
已知量：测量船收发声头测得的时延t；该水域的声速剖面c(z)；应答器的深度H；
输出量：声线的初始掠射角θ 0、水平距离R和斜距r。
步骤1：选取初始掠射角θ 0的迭代初值；
以加权平均声速估计出的斜距计算初始掠射角作为迭代初值。加权平均声速这样求得：
Figure PCTCN2019105178-appb-000003
其中c i＝c(z i)表示声速剖面各层的声速值，z m<H<z m+1，Δz i＝z i+1-z i是层高。考虑到声剖数据是离散的，和深度H间存在分辨率误差，定义z 0＝0，z m+1＝H，则有c 0＝c 1-g 1Δz 0为表层声速，c m+1＝c m+g mΔz m为底层声速，g i为各层的声速梯度，g i＝(c i+1-c i)/(z i+1-z i)，这样就有
Figure PCTCN2019105178-appb-000004
若测得的时延为t，根据三角原理算得折射角的正弦为：
Figure PCTCN2019105178-appb-000005
折射角为声线与垂线的夹角，因为掠射角和折射角互余，折射角的正弦遵循snell定律，p是常数：
Figure PCTCN2019105178-appb-000006
所以用Θ表示折射角的正弦，初始掠射角θ 0＝arccosΘ 0，用Θ 0作为初值；
步骤2：用等梯度声线跟踪法估算出时延
Figure PCTCN2019105178-appb-000007
根据等梯度声线跟踪法，可以由初始掠射角估计出水平距离和时延：
Figure PCTCN2019105178-appb-000008
式中μ i＝c i/c 0。
步骤3：计算初值增量并校正；
当Θ 0＞0时，将等梯度声线跟踪公式在初始值处泰勒展开：
Figure PCTCN2019105178-appb-000009
其中
Figure PCTCN2019105178-appb-000010
，
Figure PCTCN2019105178-appb-000011
是高阶无穷小，可以忽略。令时延偏差：
Figure PCTCN2019105178-appb-000012
可以得到Θ 0的增量：
Figure PCTCN2019105178-appb-000013
基于增量对初值进行更新，初值被校正为：
Θ 0＝Θ 0+dΘ 0
校正时应当注意不能超过一定区间，0＜Θ 0＜Θ max，其中：
Figure PCTCN2019105178-appb-000014
是声线发生全反射的临界值。
步骤4：完成迭代过程并求解；
不断重复步骤2和步骤3，进行迭代，直至Δt<τ(τ为阈值)或迭代次数n超过上限N结束迭代。此时的θ 0＝arccosΘ 0为最终的初始掠射角，根据等梯度跟踪方法求得对应的
Figure PCTCN2019105178-appb-000015
为最终水平距离，再根据勾股定理可得斜距。
下面通过一具体实例进一步描述本发明的效果。对水深3000m的深海环境进行仿真试验，其声速剖面如图3所示，从0～90°选取10个不同角度的掠射角θ 0作为测试，对应的水平距离R和时延t如表1所示。图4为不同角度的声线轨迹示意图。
表1不同掠射角对应的水平距离和时延
θ0 Θ 0 R(m) t(s)
87.13° 0.05 141.538 2.068144
80.21° 0.17 486.888 2.092947
70.12° 0.34 1014.897 2.181152
60° 0.5 1603.690 2.343158
50.21° 0.64 2271.849 2.592557
39.65° 0.77 3175.169 3.009818
29.54° 0.87 4333.020 3.631203
19.95° 0.94 5855.171 4.531528
11.48° 0.98 7650.351 5.655900
3.624° 0.998 9674.782 6.961336
根据实际使用需求，在时延t上加入标准差为1ms的零均值白噪声，由t反推初始掠射角θ 0和水平距离R时，将本发明与经验声速法、传统搜索跟踪法进行比较。除了时延t，对图3中的声速选取个别点并加入白噪声作为实际测量的声速剖面，白噪声均值为零，标准差为0.1m/s。
经验声速法采用经验声速将时延转化为斜距，这里用加权平均声速作为经验声速，
Figure PCTCN2019105178-appb-000016
经验声速法不考虑声线弯曲，水平距离和掠射角可以由三角关系求出。
搜索跟踪法和本发明都了考虑声线弯曲的影响，需要先计算出初始掠射角后再利用等梯度声线跟踪法进行声线跟踪，求出相应的水平距离及斜距。因此初始掠射角的精度和计算速度决定斜距的精度和使用便捷性。
图5是本发明与经验声速法、搜索跟踪法计算出的初始掠射角的误差对比，可以看 出经验声速法误差较大，本发明在大掠射角(应答器在正下方附近)时，本发明和搜索跟踪法相比有一定的误差，这是由于Θ 0在0附近使得运算过程中需要面对分母为零或者负数开方的问题，一系列的近似处理增大了误差，尤其是时延误差较大时，情况更加严重。不过在掠射角大约小于80°后，本发明的优势凸显，初始掠射角的计算精度始终高于搜索跟踪法，尤其是在小角度掠射角时，搜索跟踪法误差变大。这主要是由于小角度时，时延对掠射角的微小变化非常敏感，搜索步长相对较大导致了较大的误差。
初始掠射角误差的大小反映在声速跟踪法计算水平距离则更为明显，斜距误差则随着水平距离误差相应变化，如图6和图7所示。本发明斜距误差在声源正下方约10°的开角内较大，在此外大部分范围内均具有最小的误差。搜索跟踪法在小掠射角下水平距离误差、斜距误差随着搜索的初始掠射角的误差变大不断增大，甚至不及经验声速法。本实验数值结果如表2所示。
表2初始掠射角误差、水平距离误差以及斜距误差对比
Figure PCTCN2019105178-appb-000017
搜索跟踪法以一定步长搜索需要进行大量的尝试，精度还会受到补偿分辨率的影响。 以经验声速法提供的掠射角可以缩小搜索范围，在大初始掠射角时，该范围很小，但当初始掠射角较大时，经验声速法得到的掠射角和实际掠射角差距较大，搜索的工作量依旧十分庞大，如图8所示。
综上所述，本发明很好地解决了水声探测和定位中声线弯曲而无法根据测量时延准确确定初始掠射角，进而修正斜距的现实问题。本发明在已知深度和声速剖面情况下，根据泰勒展开的声线跟踪校正模型反推初始掠射角，最终精确修正声线误差。相比于传统方法，本发明无需搜索，计算量小，估算出的初始掠射角在大部分范围内具有极高的精度，进而修正了声线弯曲，提高的斜距测量精度。
基于与方法实施例相同的技术构思，根据本发明的另一实施例，提供一种计算机设备，所述设备包括：一个或多个处理器；存储器；以及一个或多个程序，其中所述一个或多个程序被存储在所述存储器中，并且被配置为由所述一个或多个处理器执行，所述程序被处理器执行时实现方法实施例中的各步骤。
本领域内的技术人员应明白，本发明的实施例可提供为方法、系统、或计算机程序产品。因此，本发明可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本发明可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。
本发明是参照根据本发明实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算 机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。
最后应当说明的是：以上实施例仅用以说明本发明的技术方案而非对其限制，尽管参照上述实施例对本发明进行了详细的说明，所属领域的普通技术人员应当理解：依然可以对本发明的具体实施方式进行修改或者等同替换，而未脱离本发明精神和范围的任何修改或者等同替换，其均应涵盖在本发明的权利要求保护范围之内。

Claims (8)

  1. 一种基于泰勒展开的初始掠射角求解方法，其特征在于，所述方法包括以下步骤：
    (1)根据声速剖面c(z)、测量时延t、应答器深度H，由三角原理预估初始掠射角θ 0，取与初始掠射角θ 0互余的折射角的正弦Θ 0为迭代初值；
    (2)根据迭代初值利用等梯度声线跟踪法求取水平距离和估计时延
    Figure PCTCN2019105178-appb-100001
    (3)计算时延偏差
    Figure PCTCN2019105178-appb-100002
    将等梯度声线跟踪公式在初值处泰勒展开，根据时延偏差计算正弦增量并更新初值；
    (4)重复步骤2-3，直到满足迭代结束条件时结束迭代，根据此时的正弦值Θ 0得到最终的初始掠射角θ 0＝arccosΘ 0。
  2. 根据权利要求1所述的基于泰勒展开的初始掠射角求解方法，其特征在于，所述步骤1包括：
    (11)根据声速剖面数据和应答器深度计算加权平均声速：
    Figure PCTCN2019105178-appb-100003
    其中c i＝c(z i)表示声速剖面各层的声速值，z m<H<z m+1，Δz i＝z i+1-z i是层高，且有
    Figure PCTCN2019105178-appb-100004
    (12)测得时延为t，根据三角原理算得折射角的正弦为：
    Figure PCTCN2019105178-appb-100005
    (13)因为掠射角和折射角互余，折射角的正弦遵循snell定律，p是常数：
    Figure PCTCN2019105178-appb-100006
    所以用Θ表示折射角的正弦，初始掠射角θ 0＝arccosΘ 0，用Θ 0作为初值。
  3. 根据权利要求2所述的基于泰勒展开的初始掠射角求解方法，其特征在于，所述步骤2中由初始掠射角估计出水平距离和时延的计算公式如下：
    Figure PCTCN2019105178-appb-100007
    式中μ i＝c i/c 0，c 0＝c 1-g 1Δz 0为表层声速，c m+1＝c m+g mΔz m为底层声速，g i为各层的声速梯度，g i＝(c i+1-c i)/(z i+1-z i)。
  4. 根据权利要求3所述的基于泰勒展开的初始掠射角求解方法，其特征在于，所述步骤3包括：
    (31)当Θ 0＞0时，将等梯度声线跟踪公式在初始值处泰勒展开：
    Figure PCTCN2019105178-appb-100008
    其中
    Figure PCTCN2019105178-appb-100009
    Figure PCTCN2019105178-appb-100010
    是高阶无穷小，将其忽略；
    (32)得到Θ 0的增量：
    Figure PCTCN2019105178-appb-100011
    (33)更新初值：Θ 0＝Θ 0+dΘ 0，且满足0＜Θ 0＜Θ max，其中
    Figure PCTCN2019105178-appb-100012
    是声线发生全反射的临界值。
  5. 根据权利要求1所述的基于泰勒展开的初始掠射角求解方法，其特征在于，所述迭代结束条件为时延偏差低于指定阈值或迭代次数达到指定次数。
  6. 一种声线弯曲修正方法，其特征在于，所述方法根据权利要求1-5中的任一项所述的初始掠射角求解方法得到初始掠射角，基于初始掠射角根据等梯度声线跟踪方法求得水平距离，再根据勾股定理得到斜距。
  7. 一种计算机设备，其特征在于，所述设备包括：
    一个或多个处理器；
    存储器；以及
    一个或多个程序，其中所述一个或多个程序被存储在所述存储器中，并且被配置为由所述一个或多个处理器执行，所述程序被处理器执行时实现如权利要求1-5中的任一项所述的方法。
  8. 一种计算机可读存储介质，用于存储计算机程序，所述计算机程序在被处理器执行时实现如权利要求1-5中的任一项所述的方法。
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