A method for positioning moving targets in deep-sea active detection

Abstract

The present disclosure relates to the field of deep-sea exploration, and proposes a method for positioning moving targets in deep-sea active exploration, including: a sonar tracks moving targets with constant depth to obtain a set of incident angles and echo time delays of the moving target echoes; based on the incident angles and echo time delay data of the target echoes, the least squares method is used to estimate the polynomial coefficient a without relying on the sound speed profile; the arrival time delay of the sea surface reverberation is obtained through the rising edge of the arrival time of the sea surface reverberation, and the estimated target depth is obtained based on the difference between the arrival time delay of the sea surface reverberation and the echo time delay of the moving target echo; in combination with the eikonal equation and ray trajectory equation of ray acoustics, based on the incident angle, echo time delay and sonar depth, an estimated value of the target horizontal distance is obtained. The present invention extracts the parameters related to the sound speed profile as polynomial coefficients, and uses multiple echo parameters during the target movement process to estimate the polynomial coefficients, realizing weak dependence on different sound speed profile data in different waters.

Description

Technical Field

[0001] The present invention belongs to the field of deep - sea exploration, and provides a method for positioning moving targets in active deep - sea exploration. Background Art

[0002] With the increasing expansion of China's maritime rights and interests, the demand for long - distance detection in deep - sea areas is growing. To achieve long - distance detection of targets, specific waveguides are generally required. Traditional waveguides for medium - and long - distance target detection include surface waveguides, deep - sea sound channels, and reliable sound paths.

[0003] Among them, for a surface waveguide, the sound - speed gradient near the sea surface needs to be a positive gradient. According to the characteristic that sound waves always bend towards the region with lower sound speed, the energy of sound waves will be confined near the sea surface and propagate over a long distance through multiple reflections with the sea surface. Since the sound speed near the sea surface is greatly affected by the sea - surface environment, the sound speed may not satisfy the positive - gradient distribution. Therefore, the surface waveguide may not exist. In addition, when sound waves propagate over a long distance, they will have multiple reflections with the sea surface, resulting in a large amount of energy loss during the propagation of sound waves.

[0004] Affected by temperature, salinity, and pressure, the sound speed in the deep sea first decreases and then increases with depth. Then, there will be a minimum value of sound speed at a certain depth, which is called the deep - sea sound - channel axis. According to the characteristic that sound rays always bend towards the region with lower sound speed, the energy of sound waves will be confined near the deep - sea sound - channel axis and propagate far away. Although the deep - sea sound channel can achieve low - attenuation long - distance propagation, due to its energy being confined near the deep - sea sound - channel axis, there is a detection blind area for detecting targets near the sea surface, which is not conducive to the detection of near - sea - surface targets.

[0005] When the sea depth is relatively large, the sound speed of seawater near the seabed is generally higher than that near the sea surface. The sound speed at a certain depth in the deep ocean is equal to the sound speed near the sea surface. This depth is the lower boundary of the SOFAR channel and is called the "critical depth". On the premise of not interacting with the sea - surface and seabed interfaces, a receiver located below the critical depth can receive sound waves emitted by small - depth sound sources within a medium - distance range. Small - depth and large - depth points can be connected by direct sound rays without being affected by interfaces and hydrological parameters. Since this sound channel has robustness to the randomness of the sea - surface sound - speed profile and is not affected by the sea - surface and seabed interface effects, the reliable sound path has the advantages of being unaffected by the sea surface and seabed, having small propagation loss, having no sound - shadow area for near - sea - surface targets at medium horizontal distances, and having a lower noise level in the ocean below the critical depth, providing superior physical conditions for underwater target detection.

[0006] The most significant difficulty in achieving relatively accurate positioning of underwater targets near the sea surface by selecting reliable sound paths is that due to the variation of the sound speed in the deep sea with temperature, salinity, and depth, the sound speeds at different depths are different, resulting in the bending of sound rays. Traditional target positioning methods that assume sound rays are straight will introduce significant deviations in the estimation of target depth and horizontal distance, which is not conducive to target positioning. Therefore, to achieve accurate estimation of target depth and horizontal distance, it is necessary to take into account the factor of sound ray bending to correct target positioning.

[0007] To achieve the correction of sound rays, generally, accurate environmental information of the surrounding environment is required, especially the sound speed profile information.

[0008] For passive detection, the method of matched-field localization is used to achieve accurate target positioning in the deep sea. The matched-field localization method constructs a matched field by measuring ocean environmental parameters and combining an acoustic propagation model, and then correlates the matched field with the measured ocean environmental parameters to find the most matching point as the sound source position. To achieve precise underwater target positioning using the matched field, it is necessary to construct a copy field of all possible target positions in combination with the sound speed profile and the underwater acoustic propagation model, and perform a correlation operation between these copy fields and the target echo, which requires a large amount of computation. In addition, the matched-field localization method is relatively sensitive to ocean environmental information and is prone to mismatching.

[0009] Due to the large scale of the deep sea, the multi-path of deep-sea sound rays can be separated. By using the time-delay difference, angle difference, and coherence fringe differences of multi-paths such as the direct wave and the sea surface reflection wave of near-sea surface targets, combined with the sound speed profile, precise target positioning can be achieved. Using the time-delay of multi-path arrival, arrival angle of multi-path, and multi-path interference fringes of the direct wave and the sea surface reflection wave to achieve the positioning of the target echo requires the existence of the sea surface reflection wave in the target echo. The sea surface reflection wave is greatly affected by sea conditions. In high-sea conditions, the sea surface is not stable, and the sea surface reflection wave may not exist, losing the advantage of the stable reliable sound path channel, which is not conducive to underwater target positioning.

[0010] In the field of active detection, a monostatic sonar can obtain information such as the arrival angle and arrival time delay of the target echo. By combining the echo parameters with the sound ray tracking method, the positioning error caused by sound ray bending can be solved, and precise underwater target positioning can be achieved. An active sonar uses the target echo parameters, combines the sound speed profile with the ocean environmental propagation model, and adopts the sound ray tracking method to achieve underwater target positioning. Its positioning accuracy is related to the accuracy of the collected sound speed profile, and the more complete the collected sound speed profile is, the higher the accuracy, and the greater the computational amount of the sound ray tracking method.

[0011] Moreover, the biggest drawback of the above methods is that they all inevitably require an accurate sound speed profile, have a strong dependence on the ocean environment, and do not have the universality for the deep-sea environment. Summary of the Invention

[0012] To solve the above-mentioned drawbacks, the present application discloses an active detection moving target localization method with weak dependence on the sound speed profile. The method includes:

[0013] The sonar tracks a near-sea surface moving target with a constant depth and a changing horizontal distance, and obtains a set of incident angles and echo time delays of the moving target echoes. Among them, the sonar is placed below the critical depth and adopts an upward detection mode for target detection. For targets with the same depth and different horizontal positions, the coordinates composed of the secant value of the incident angle and the echo time delay of the target echoes are on the same polynomial function. Among them, a is the polynomial coefficient in the polynomial function that is only related to the sound speed profile;

[0014] Based on the set of incident angles and echo time delay data of the moving target echoes, the least squares method is used to estimate the polynomial coefficient a without depending on the sound speed profile;

[0015] The arrival time delay of the sea surface reverberation is obtained through the rising edge of the arrival time of the sea surface reverberation, and the estimated target depth is obtained based on the difference between the arrival time delay of the sea surface reverberation and the echo time delay when the moving target reaches directly above the sonar;

[0016] Combined with the ray acoustic eikonal equation and ray trajectory equation, based on the incident angle, echo time delay, sonar depth and polynomial coefficient a, the estimated value of the target horizontal distance is obtained;

[0017] According to the estimated target depth and the estimated value of the target horizontal distance, the coordinates of the moving target are output.

[0018] The coordinates composed of the secant value of the incident angle and the echo time delay of the target echoes with the same depth and different horizontal positions are on the same polynomial function, which specifically includes:

[0019] For the coordinates composed of the secant value of the incident angle and the echo time delay of the target echoes with the same depth and different horizontal positions, τ = Aa + ΔE is satisfied;

[0020] Among them, τ is the echo time delay of the moving target echo, A is the power of the secant value of the incident angle of the moving target echo, ΔE is the error, and a is the polynomial coefficient that is only related to the sound speed profile. Specifically:

[0021]

[0022] The Z T is the target depth, the c N is the sound speed of the layer where the sonar depth is located, the c(z) is the sound speed profile, and the x(z) is specifically x(z) = [c N / c(z)] 2 -1.

[0023] The step of estimating the target depth based on the difference between the arrival time delay of the sea surface reverberation and the echo time delay when the moving target reaches directly above the sonar specifically includes:

[0024] Calculate the echo time delay when the moving target reaches directly above the sonar, which satisfies:

[0025]

[0026] Calculate that the arrival time delay of the sea surface reverberation directly above the sonar is τ rec ;

[0027] Estimate the approximate value Z of the target depth T as:

[0028]

[0029] The eikonal equation of ray acoustics is:

[0030]

[0031] According to the eikonal equation of ray acoustics, the first estimated value of the horizontal distance of the moving target can be obtained as:

[0032]

[0033] The ray trajectory equation is:

[0034]

[0035] According to the eikonal equation of ray acoustics, the second estimated value of the horizontal distance of the moving target can be obtained as:

[0036]

[0037] The step of obtaining the estimated value of the target horizontal distance based on the incident angle, echo time delay and sonar depth specifically includes:

[0038] Based on the incident angle, echo time delay, sonar depth and polynomial coefficient a, calculate the estimated value of the target horizontal distance, and the estimated value of the target horizontal distance satisfies the following formula:

[0039]

[0040] The present invention has the following advantages:

[0041] 1. The present invention proposes to extract the parameters related to the sound speed profile as polynomial coefficients, and use multiple echo parameters during the target movement process to estimate the polynomial coefficients, realizing weak dependence on different sound speed profile data in different waters;

[0042] 2. The present invention proposes a method for estimating the horizontal distance of a target using polynomial coefficients and target echo parameters. This method does not require the sound speed profile information of the sea area where it is located and is not affected by the target depth estimation error. When the target incident angle is too small or too large, the horizontal distance estimation deviation of the present invention converges and does not diverge. Description of the Drawings

[0043] Figure 1 is the sound speed profile, propagation sound ray and sound attenuation curve corresponding to the surface waveguide;

[0044] Figure 2 is the sound speed profile, propagation sound ray and sound attenuation curve corresponding to the deep sea channel;

[0045] Figure 3 is the sound speed profile, propagation sound ray and sound attenuation curve corresponding to the reliable sound path;

[0046] Figure 4 is the detection mode diagram of near-surface targets at medium and long distances using the reliable sound path in an embodiment of the present invention;

[0047] Figure 5 is the sound speed stratification principle of the target echo detection model based on the reliable sound path in an embodiment of the present invention;

[0048] Figure 6 is the deep sea backscattering reverberation intensity diagram measured in an embodiment of the present invention;

[0049] Figure 7 is the cylindrical coordinate system model for target positioning in an embodiment of the present invention;

[0050] Figure 8 is the flow chart of the moving target positioning method for detecting near-surface targets at medium and long distances using the reliable sound path in an embodiment of the present invention;

[0051] Figure 9 is the MUNK standard sound speed profile and detection mode of the simulated ocean environment in an embodiment of the present invention;

[0052] Figure 10 is the comparison diagram of the target depth estimated value and the true value and the target depth estimation deviation of the moving target positioning method in an embodiment of the present invention;

[0053] Figure 11 is the comparison diagram of the target horizontal distance estimated value and the true value and the target horizontal distance estimation deviation of the moving target positioning method in an embodiment of the present invention. Detailed Embodiment

[0054] The following describes the best implementation mode of the present invention through embodiments. It should be understood that the specific implementation mode here is used to explain the present invention in detail and should not be construed as a limitation on the present invention. It should be noted that various changes and modifications can be made on the premise of following the principles and core scope of the present invention, and these changes should be regarded as falling within the protection scope of the present invention. The specific implementation steps of the present invention will be described in detail in conjunction with the accompanying drawings.

[0055] With the increasing expansion of China's maritime rights and interests, the demand for long-distance detection in deep sea areas is growing. To achieve long-distance detection of targets, specific waveguides are generally required. Traditional waveguides for medium- and long-range detection of targets include surface waveguides, deep sea sound channels, and reliable acoustic paths.

[0056] Among them, for a surface waveguide, the sound speed gradient near the sea surface needs to be a positive gradient (in many cases, the underwater sound speed gradually changes with depth. A positive gradient distribution means that the sound speed gradually increases with depth (that is, in the depth direction from the sea surface to the seabed, the sound speed gradually increases)). According to the characteristic that sound waves always bend towards the area with a lower sound speed, the energy of sound waves will be confined near the sea surface and propagate over a long distance through multiple reflections with the sea surface. The sound speed profile, propagation sound ray, and sound attenuation curve corresponding to the surface waveguide are respectively as Figure 1 shown in (a), (b), and (c) of the figure. Among them, (a) is the sound speed profile corresponding to the surface waveguide, with the sound speed on the horizontal axis and the depth on the vertical axis; (b) is the propagation sound ray diagram corresponding to the surface waveguide, with the horizontal distance on the horizontal axis and the depth on the vertical axis; (c) is the sound attenuation curve corresponding to the surface waveguide, with the horizontal distance on the horizontal axis and the depth on the vertical axis.

[0057] Since the sound speed near the sea surface is greatly affected by the sea surface environment, the sound speed may not satisfy the positive gradient distribution. Therefore, the surface waveguide may not exist. In addition, when sound waves propagate over a long distance, they will have multiple reflections with the sea surface, resulting in a large amount of energy loss during the propagation of sound waves.

[0058] Affected by temperature, salinity, and pressure, the sound speed in the deep sea first decreases and then increases with depth. Then, there will be a minimum value of sound speed at a certain depth, which is called the deep sea sound channel axis. According to the characteristic that sound rays always bend towards the area with a lower sound speed, the energy of sound waves will be confined near the deep sea sound channel axis and propagate far away. The sound speed profile, propagation sound ray, and sound attenuation curve corresponding to the deep sea sound channel are as Figure 2 shown in (a), (b), and (c) of the figure. Among them, (a) is the sound speed profile corresponding to the deep sea sound channel, with the sound speed on the horizontal axis and the depth on the vertical axis; (b) is the propagation sound ray diagram corresponding to the deep sea sound channel, with the horizontal distance on the horizontal axis and the depth on the vertical axis; (c) is the sound attenuation curve corresponding to the deep sea sound channel, with the horizontal distance on the horizontal axis and the depth on the vertical axis.

[0059] Although the deep - sea sound channel can achieve low - attenuation long - distance propagation, since its energy is confined near the deep - sea sound channel axis, there are detection blind spots for near - surface targets, which is not conducive to the detection of near - surface targets.

[0060] When the sea depth is relatively large, the sound speed of seawater near the seabed is generally higher than that of the sea surface. The sound speed at a certain depth in the deep ocean is equal to the sound speed of the sea surface. This depth is the lower boundary of the SOFAR channel and is called the "critical depth". On the premise of not interacting with the sea - surface and seabed interfaces, a receiver located below the critical depth can receive sound waves emitted by small - depth sound sources within a medium - distance range. The points between small depth and large depth can be connected by direct sound rays without being affected by the interface and hydrological parameters. Since this sound channel has robustness to the randomness of the sea - surface sound - speed profile and is not affected by the sea - surface and seabed interface effects. The direct - wave sound ray between the receiving hydrophone and the near - surface target is called the reliable sound path. The sound - speed profile, propagation sound ray, and sound - attenuation curve corresponding to the reliable sound path are as Figure 3 (a), (b), and (c). In figure (a), it is the sound - speed profile corresponding to the reliable sound path, where the abscissa is the sound speed and the ordinate is the depth. In figure (b), it is the propagation sound - ray diagram corresponding to the reliable sound path, where the abscissa is the horizontal distance and the ordinate is the depth. In figure (c), it is the sound - attenuation curve corresponding to the reliable sound path, where the abscissa is the horizontal distance and the ordinate is the depth.

[0061] The reliable sound path has the advantages of being unaffected by the sea - surface and seabed, having small propagation loss, having no sound - shadow area for near - surface targets at medium horizontal distances, and having a lower noise level in the ocean below the critical depth, etc., providing superior physical conditions for underwater target detection. Therefore, it is chosen to place the monostatic sonar below the critical depth and adopt an upward detection mode to achieve the detection of medium - and long - distance targets using the reliable sound path. The detection mode is as Figure 4 shown.

[0062] The main difficulty in using the reliable sound path to achieve relatively accurate positioning of near - surface underwater targets is that due to the variation of deep - sea sound speed with temperature, salinity, and depth, the sound speeds at different depths are different, resulting in the bending of sound - ray propagation. The traditional target - positioning method assuming a straight sound ray will bring huge deviations to the estimation of target depth and horizontal distance, which is not conducive to target positioning. Therefore, to achieve accurate estimation of target depth and horizontal distance, it is necessary to consider the factor of sound - ray bending to correct target positioning.

[0063] To achieve the correction of the sound ray, accurate environmental information of the surrounding environment is generally required, especially the sound speed profile information. For passive detection, in the deep sea, the accurate target positioning is achieved by the matched field positioning method. The matched field positioning method constructs a matched field by measuring the ocean environmental parameters and combining with the acoustic propagation model, and then correlates the matched field with the measured ocean environmental parameters to find the most matching point as the sound source position.

[0064] Due to the large scale of the deep sea, the multi-path of the deep sea sound ray can be separated. By using the time delay difference, angle difference and coherent fringe differences of the direct wave and the sea surface reflection wave of the near-sea surface target and other multi-paths, combined with the sound speed profile, the accurate positioning of the target can be achieved.

[0065] In the field of active detection, a monostatic sonar can obtain information such as the arrival angle and arrival time delay of the target echo. By using the echo parameters and combining with the sound ray tracking method, the positioning error caused by the sound ray bending can be solved, and the accurate positioning of the underwater target can be achieved.

[0066] Using the matched field to achieve the accurate positioning of the underwater target requires combining the sound speed profile and the underwater acoustic propagation model to construct a copy field of all possible target positions, and correlating these copy fields with the target echo, which requires a large amount of calculation. In addition, the matched field positioning method is sensitive to the ocean environmental information and is prone to mismatch.

[0067] Using the multi-path arrival time delay of the direct wave and the sea surface reflection wave, the arrival angle of the multi-path and the multi-path interference fringe to achieve the positioning of the target echo requires the existence of the sea surface reflection wave in the target echo. The sea surface reflection wave is greatly affected by the sea state. In the case of high sea state, the sea surface is not stable, and the sea surface reflection wave may not exist, losing the advantages of a reliable sound path channel stability, which is not conducive to underwater target positioning.

[0068] The active sonar uses the target echo parameters, combines with the sound speed profile and the ocean environmental propagation model, and adopts the sound ray tracking method to achieve the positioning of the underwater target. Its positioning accuracy is related to the accuracy of the collected sound speed profile, and the more complete the collected sound speed profile is, the higher the accuracy is, and the greater the calculation amount of the sound ray tracking method is.

[0069] And the biggest drawback of the above methods is that they all inevitably require an accurate sound speed profile, have a strong dependence on the ocean environment, and do not have the universality of the deep sea environment. Based on the above drawbacks, this patent proposes an active detection moving target positioning method with weak dependence on the sound speed profile.

[0070] Step 1: The sonar tracks the near-sea surface moving target with a constant depth and a changing horizontal distance, and obtains a set of incident angles and echo time delays of the moving target echo;

[0071] It should be noted that considering that underwater targets generally do not easily change their depth during movement, it is assumed that the detected target is a moving target with a constant depth.

[0072] In a specific embodiment, a typical deep - sea sound - speed profile and an upward detection mode based on a reliable sound path are respectively as Figure 3 and Figure 4 shown. Given that the underwater sound speed in the deep sea is generally only a function of depth, the theoretical basis of the underwater sound - ray drawing principle is generally the sound - speed gradient stratification hypothesis. The sound - speed profile is equally spaced into multiple sound - speed layers along the depth direction. Assume that the depth width of each divided sound - speed layer is Δz. If the divided Δz is very small, it can be considered that the sound speed within the layer remains unchanged, and the sound ray propagates in a straight line within the layer. The sound speed changes between layers, and the sound ray refracts when propagating between layers, and the refraction satisfies Snell's law (the law of refraction). The sound - speed stratification principle is as Figure 5 shown.

[0073] According to Figure 5 , the water column through which the sound ray passes is divided into N layers, and the sound speed of the i - th layer is c i . Define the incident angle as the angle between the sound - ray propagation direction and the vertical direction, and the sound - ray propagation direction of the i - th layer is θ i .

[0074] Let the target depth be Z T , in the n - th sound - speed layer; the depth of the monostatic sonar is Z N , in the N - th sound - speed layer, the incident angle of the target echo received by the monostatic sonar is θ r , then θ r = θ n .

[0075] The two - way propagation time delay τ r between the monostatic sonar and the target satisfies the following equation:

[0076]

[0077] where c i is the sound speed along the sound - ray direction, and c i cos(θ i ) is the sound speed obtained by decomposing the original sound speed along the depth - axis direction. The distance in the depth - axis direction divided by this depth gives the time.

[0078] According to the law of refraction, we have:

[0079]

[0080] Substitute the law of refraction into Equation (1), and Equation 1 can be written as:

[0081]

[0082] When Δz approaches 0, the above equation can be written as:

[0083]

[0084] where c(z) is the sound speed profile.

[0085] Equation (4) is only applicable to the case where the sound ray refracts between layers and is not applicable to the case where the sound ray undergoes total reflection within a layer. Therefore, this application adds a restriction to the reliable sound path, that is, during the propagation of the sound ray of the reliable sound path, the propagation direction (upward or downward) of the one-way sound ray does not reverse.

[0086] Given the incident angle θ of the target echo r and the echo time delay τ r The relationship is as shown in Equation (4). Since the equation contains the sound speed profile to be measured, assume:

[0087]

[0088] Then Equation (4) can be expressed as:

[0089]

[0090] Taking the Maclaurin expansion of τ r with respect to the result obtained is:

[0091]

[0092] where

[0093]

[0094] To ensure the convergence of Equation (7), the sound speed profile c(z) and the incident angle θ of the target echo r need to satisfy the following equation:

[0095]

[0096] Considering that in most ocean environments, the sound speed in seawater generally varies within the range of 1450 m / s to 1540 m / s, then |x(z)| = |[c N / c(z)] 2 - 1| << 1, and x(z) is close to 0. According to Equation (7), the larger n is, the value of |a n | decreases exponentially, indicating that the polynomial can be described by a finite number of polynomial coefficients a n . Additionally, it can be known that the smaller max(|x(z)|) is, the incident angle θ of the target echo that satisfies Equation (8) rThe larger the upper bound is, the larger the horizontal distance r of the corresponding target is. Therefore, the smaller x(z) is, the larger the range of the target horizontal distance that satisfies the incident angle requirement is.

[0097] As can be seen from Equation (7), when the target echo θ r satisfies Equation (8), for targets with the same depth but different horizontal positions, the secant values of the incident angles of the target echoes cos(θ r ) and the echo time delays τ r corresponding coordinates are all on the same polynomial function, and the polynomial coefficients a n only depend on the target depth Z T , the monostatic sonar depth Z N and the sound speed profile c(z), and are independent of the incident angle of the target echo.

[0098] Assume that the target depth remains unchanged during the target movement. Suppose that during the target movement, the active sonar conducts Q + 1 detections on the target, and the incident angles θ of the Q + 1 detection echoes r all satisfy Equation (8). According to Equation (7), it can be known that the first M polynomial coefficients a n can be used to represent this polynomial more accurately.

[0099] Then the target echo parameters obtained from multiple detections

[0100] satisfy the following equation:

[0101] where:

[0102] τ = Aa + ΔE (9) ro τ = [τ r1 τ rQ ... τ T

[0103]

[0104] a = [a0 a n ... a M-1 T

[0105] ΔE = [Δe0 Δe1... Δe Q T

[0106] [x] T represents the transpose of the vector or matrix x.

[0107] Step 2: Based on the data of the incident angles and echo time delays of the set of moving target echoes, use the least squares method to estimate the polynomial coefficients a without relying on the sound speed profile;

[0108] Calculate the weighted coefficient a according to the least squares method, that is, estimate the value of a without relying on the sound speed profile data. Specifically:

[0109] a = (A T A) -1 A T τ. (10)

[0110] Step 3: Obtain the arrival time delay of the sea surface reverberation through the rising edge of the arrival time of the sea surface reverberation, and obtain the estimated target depth based on the difference between the arrival time delay of the sea surface reverberation and the echo time delay when the moving target reaches directly above the sonar.

[0111] It is known that the reverberation received in the large-depth bottom-up detection mode is mainly the sea surface backscattering reverberation, that is, the reverberation phenomenon where sound waves are reflected back underwater when encountering the sea surface. According to Chapman and its modified model, the backscattering intensity S of the sea surface reverberation b(面) decreases with the decrease of the grazing angle (the angle between the sound wave shooting towards the sea surface and the sea surface). Since the grazing angle of the reverberation echo scattered by the sea surface directly above the sonar is the largest and its backscattering intensity is the largest, and according to the geometric relationship, when the sound wave shoots out from directly above, its sound path to the receiving hydrophone is the shortest and the propagation loss TL is the smallest. Therefore, the sea surface reverberation from directly above the sonar will reach the receiving hydrophone first and the reverberation level reaching the hydrophone is relatively large. According to Figure 6 it can be seen that the reverberation attenuation trend in the actual measurement data conforms to the theoretical analysis.

[0112] From Figure 6 it can be seen that since the intensity of the sea surface reverberation reaching the receiving hydrophone first is relatively large, the arrival time delay of the sea surface reverberation can be measured more accurately through the rising edge of the echo. According to the geometric relationship, the arrival time delay of this reverberation is the same as the arrival time delay of the sea surface target echo directly above the sonar.

[0113] It is known that the echo of the target at any horizontal position at the same depth is on the same polynomial function. And according to the geometric relationship, the incident angle θ of the target echo directly above the sonar r = 0°, and according to the refraction theorem, when the target is directly above the sonar, the propagation sound ray is a straight line. By extrapolation, if the target moves to directly above the sonar, the echo time delay is:

[0114]

[0115] It is known that the arrival time delay of the sea surface reverberation directly above the sonar is τ rec , which is the same as the arrival time delay of the sea surface target directly above the sonar. Therefore, the approximate value Z of the estimated target depth T is:

[0116]

[0117] Step 4: Combining the ray acoustic eikonal equation and the ray trajectory equation, obtain the estimated value of the target horizontal distance based on the incident angle, echo time delay, sonar depth, and polynomial coefficient a;

[0118] In a specific embodiment, based on the ray acoustic eikonal equation and the ray trajectory equation, two methods for estimating the target horizontal distance can be obtained, which are described below.

[0119] Method 1: According to the ray acoustic model, assume that a sound wave with a sound pressure of A(0, 0, 0)exp[jωt] is emitted at the reference point [0, 0, 0]. The formal solution of the sound pressure at the coordinate [x, y, z] under ray acoustics is

[0120] p(x, y, z, t) = A(x, y, z)exp[jωt - k0φ(x, y, z)] (13)

[0121] where k0 = ω / c0 is the wave number and c0 is the sound speed at the reference point. is the eikonal. When the sound speed of the medium is only a function of depth, the eikonal represents the equivalent sound ray trajectory length at the reference sound speed, indicating the relationship between the wave number of the sound wave propagation path (ray direction) and the refractive index in the medium.

[0122] The eikonal equation in ray acoustics is expressed as:

[0123]

[0124] where c0 is the sound speed at the reference point and n(x, y, z) is the refractive index.

[0125] Generally, the sound speed profile in the deep sea is only a function of depth. In the case of a sound speed profile where the sound speed is only a function of depth, the eikonal equation is transformed to make it explicit, and the following equation holds, where r is the projection of the sound ray trajectory on the x - y plane, that is, the target horizontal distance value:

[0126]

[0127] where θ r is the sound ray exit angle emitted from the reference point, and c(z) is the sound speed profile.

[0128] Assume that the monostatic sonar is arranged as Figure 4 shown. Assume the coordinate is [0, Z N , and assume the target coordinate is [r0, Z N . In acoustics, the propagation of sound waves in a medium is reversible, that is, the positions of the sound source and the receiver can be interchanged, and the propagation result will not change, that is, the reciprocity of sound propagation. According to this property, the two - way echo τ r time delay of active detection satisfies the following equation:

[0129]

[0130] where θ r is the incident angle of the target echo, τ r is the two-way echo time delay, and c N is the sound speed at the monostatic sonar.

[0131] θ r and τ r can be obtained through active detection for azimuth estimation and time-domain estimation. Therefore, the part related to the sound speed profile in Equation (16) can be extracted and adjusted to the following equation:

[0132]

[0133] where x(z) = [c N / c(z)] 2 -1. Expand Equation (17) with respect to to obtain the following equation

[0134]

[0135] where:

[0136]

[0137] It is known that the sound speed in most seawater generally varies within the range of 1450 m / s to 1540 m / s, that is, [c N / c(z)] 2 ≈ 1, and x(z) is close to 0. Comparing Equation (7) and Equation (18), the following equation holds:

[0138]

[0139] It is known that |b n (Z T )| < |a n (Z T )|. The larger n is, the exponentially decays |a n (Z T )|. Then |b n (Z T )| rapidly decays with the increase of n. Therefore, a finite number of coefficients can be used to describe Equation (18), and the estimated value of the target's horizontal distance is:

[0140]

[0141] Error estimation of Method 1:

[0142] Since Equation (20) uses a n (Z T ) to approximately replace bn (Z T ), so there is a deviation in the estimation of the horizontal distance of the target. Let the true value of the horizontal distance \(r_0\) be as shown in Equation (18), and the estimated value of the horizontal distance be as shown in Equation (20). Assume that the incident angle \(\theta\) of the target r and the echo time delay \(\tau\) r are accurately estimated, then the deviation \(|\Delta r\) b | of the estimated value of the horizontal distance can be expressed as

[0143]

[0144] According to Equations (7) and (19), it can be known that:

[0145]

[0146] Then \(\Delta r^2\) b satisfies the following equation:

[0147]

[0148] According to Taylor's expansion theorem of Lagrange remainder, \(\Delta r^3\) b satisfies the following equation:

[0149]

[0150] Where:

[0151]

[0152] Combining Equations (21), (23) and (24), the following equation holds:

[0153]

[0154] Since the monostatic sonar is generally placed below the deep - sea conjugate depth, then \(x(z)\geq0\), \(\Delta d_1\geq0\). Since the underwater sound speed varies roughly in the range of 1450 m / s to 1540 m / s, so \([c\) N / c(z)] 2 tends to 1 and \(x(z)\) tends to zero. According to Equation (23), the estimation deviation of Method 1 is related to the order \(M\), the incident angle \(\theta\) r , and the ocean environmental parameter \(x(z)\). The larger the order \(M\), the smaller the value of \(\Delta d_2(M)\), and the smaller the influence of \(|\Delta d_2(M)|\) on the deviation. When the incident angle \(\theta\) r tends to 0, \(\sin(\theta\) r ) tends to zero, resulting in an increase in the estimation deviation of the target horizontal distance, indicating that Method 1 is not applicable to the estimation of the horizontal distance of close - range targets.

[0155] Horizontal distance estimation method 2:

[0156] When the sound speed profile is only a function of depth, the horizontal distance r0 of the target and the incident angle θ of the target echo r satisfy the following equation (ray trajectory equation):

[0157]

[0158] where r0 is the horizontal distance of the target, Z T and Z N are the target depth and the monostatic sonar depth respectively, and θ r is the incident angle of the target echo. Equation (26) can be rearranged as follows

[0159]

[0160] Performing a Maclaurin expansion of r0 with respect to yields the following equation:

[0161]

[0162] where:

[0163]

[0164] Combining Equation (7) and Equation (28), the following equation holds:

[0165]

[0166] The estimated value of the horizontal distance of the target is:

[0167]

[0168] Error analysis of the second method for estimating the horizontal distance:

[0169] Since Equation (30) uses a n (Z T ) to approximately replace c n (Z T ), there is a deviation in the estimated horizontal distance of the target. Let the true value of the horizontal distance be r0 as shown in Equation (28), and the estimated value of the horizontal distance as shown in Equation (30). Assuming that the incident angle θ of the target r and the echo time delay τ r are accurately estimated, the deviation |Δr| of the estimated value of the horizontal distance can be expressed as

[0170]

[0171] According to Equation (7) and Equation (29), it can be seen that:

[0172]

[0173] Then Δr2 f satisfies the following equation

[0174]

[0175] According to Taylor's expansion theorem with Lagrange remainder, Δr3 f satisfies the following equation:

[0176]

[0177] where:

[0178]

[0179] Combining Equation (31), Equation (33) and Equation (34), the following equation holds:

[0180]

[0181] According to Equation (35), the estimation deviation of Method 2 is related to the order M, the incident angle θ r , and the ocean environmental parameter x(z). The larger the order M, the smaller the value of |Δd2(M)|, and the smaller the influence of |Δd2(M)| on the deviation. When the incident angle θ r is larger, cos(θ r ) approaches zero, resulting in an increase in the estimation deviation of the target horizontal distance, indicating that Method 2 is not applicable to the estimation of the horizontal distance of distant targets.

[0182] In a specific embodiment, since the estimation deviation of Method 1 for short-range targets does not converge and the estimation deviation of Method 2 for long-range targets does not converge. And the estimation deviations of both are also strongly correlated with the estimation deviation of the target depth. Therefore, the present invention combines Method 1 and Method 2 to propose a new method for estimating the horizontal distance.

[0183] Combining Equation (18) and Equation (27), the following equation holds:

[0184]

[0185] According to Equation (18) and Equation (29), the estimated value of the target horizontal distance is as follows:

[0186]

[0187] Combining Equation (25) and Equation (35), the horizontal distance estimation deviation of Method 3 satisfies the following equation:

[0188]

[0189] By comparing Equation (25), Equation (35) and Equation (38), it can be seen that the horizontal distance estimation method of the present invention has two advantages over Method 1 and Method 2. First, the horizontal distance estimation method of the present invention does not require the depth value of the target to estimate the horizontal distance. Therefore, the depth estimation deviation does not affect the estimation of the target horizontal distance by the horizontal distance estimation method of the present invention. Second, when the incident angle of the target is too small or too large, the horizontal distance estimation deviation of the horizontal distance estimation method of the present invention converges and does not diverge.

[0190] Step Five: Obtain the position of the moving target according to the estimated target depth and the estimated value of the target horizontal distance.

[0191] In a specific embodiment, the position of a point in a three-dimensional space can be described by a rectangular coordinate system, a cylindrical coordinate system, and a spherical coordinate system. Among them, it is more reasonable to use the cylindrical coordinate system to describe the position of a target point in the deep sea relative to a monostatic sonar. The cylindrical coordinate system is as Figure 7 shown.

[0192] Define the reference point as the zero-depth position directly above the monostatic sonar. The three coordinate variables of the cylindrical coordinate system are r, φ, and z. Among them, r represents the horizontal distance from the target point to the reference point, φ represents the angle between the projection of the target on the x-o-y plane and the x-axis, and z represents the target depth. The coordinates of the monostatic sonar are (0, 0, Z N ). Since the sound speed profile only changes with depth, the position of the monostatic sonar, the target position, and the sound ray are all in the same vertical plane. Therefore, φ of the target in the cylindrical coordinate system can be obtained through the array horizontal azimuth estimation. The difficulty in realizing the positioning of the target is that due to the bending of the sound ray, it is impossible to directly obtain the target horizontal distance r and depth z by measuring the time delay and vertical incident angle of the target echo. When the detected target is a moving target with a constant depth, the depth and horizontal distance of the target can be obtained by the above method.

Claims

1. A method for positioning a moving target in deep-sea active detection, characterized in that: include: A sonar tracks a near-sea moving target at a constant depth and varying horizontal distance, obtaining a set of incident angles and echo delays of the moving target echoes; wherein the sonar is placed below a critical depth and adopts an upward detection mode for target detection; coordinates formed by the secant values of the incident angles and echo delays of target echoes at the same depth and different horizontal positions are on the same polynomial function; specifically, the coordinates formed by the secant values of the incident angles and echo delays of target echoes at the same depth and different horizontal positions satisfy τ=Aa+ΔE; Wherein τ is the echo delay of the moving target echo, A is the power of the secant value of the incident angle of the moving target echo, ΔE is the error, and a is the polynomial coefficient related only to the sound velocity profile, specifically: The Z T is the target depth, the c N is the sound velocity of the layer at the sonar depth, c(z) is the sound velocity profile, and x(z) is specifically x(z)=[c N / c(z)] 2 -1; estimating a polynomial coefficient a based on the incident angle and echo delay data of the set of moving target echoes using a least squares method without relying on a sound velocity profile; The method comprises the following steps: obtaining a sea surface reverberation arrival delay by a rising edge of the sea surface reverberation arrival moment, and obtaining an estimated target depth based on a difference between the sea surface reverberation arrival delay and the echo delay when the moving target arrives directly above the sonar; and specifically, calculating the echo delay when the moving target arrives directly above the sonar, which satisfies: The calculated arrival delay of the sea surface reverberation directly above the sonar is τ rec ; Estimate the approximate value of the target depth Z T for: Combining the Eikonal equation and the sound ray trajectory equation of ray acoustics, the target horizontal distance estimate is obtained based on the incident angle, echo delay, sonar depth and polynomial coefficient a. Specifically, it includes: Based on the incident angle, echo delay, sonar depth and polynomial coefficient a, the target horizontal distance estimate is calculated, and the target horizontal distance estimate satisfies the following formula: The position of the moving target is obtained according to the estimated target depth and the estimated target horizontal distance.

2. The method according to claim 1, characterized in that The eikonal equation for ray acoustics is: According to the Eikonal equation of ray acoustics, the estimated horizontal distance of the moving target can be obtained as:

3. The method according to claim 1, characterized in that The sound ray trajectory equation is: According to the Eikonal equation of ray acoustics, the second estimated value of the horizontal distance of the moving target can be obtained as:

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