A joint estimation method of underwater sound source depth and distance using a single geophone across ice

Abstract

A single-detector method for jointly estimating the depth and distance of underwater sound sources across ice, belonging to the field of underwater acoustic signal processing technology, involves establishing a sound propagation model for underwater sound sources across ice, classifying the cross-ice detection acoustic signals, obtaining the time difference between characteristic sound lines along different propagation paths, establishing a target cost function, and applying a combined Bayesian estimation of depth and distance to achieve joint estimation of the depth and distance of underwater sound sources. This method addresses the challenges of difficult hydrophone array deployment and high underwater interference under sea ice conditions. Only a single three-dimensional geophone is required, eliminating the need to dig through the ice, making it simple and easy to implement with fast response. Using an on-ice geophone eliminates the need for considerations such as current mitigation and noise reduction. The selected detection acoustic signal type offers a high signal-to-noise ratio, resulting in improved interference resistance and stability. The high sampling frequency of the geophones results in high temporal accuracy of the detection acoustic signals, resulting in higher accuracy in locating the distance and depth of the sound source.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic signal processing, and in particular relates to a single-detector cross-ice layer underwater sound source depth-distance joint estimation method using a single three-dimensional geophone to cross the ice layer to perform depth-distance estimation on the sound source of an underwater target. Background Art

[0002] Over the past two decades, with the advancement of ocean observation technology, the United States, Russia, and Europe have begun to continuously explore new research hotspots, methods, and technologies in their Arctic research, shifting towards comprehensive three-dimensional observations and establishing and planning submarine observation networks. Using ice detectors deployed on the ice surface to observe various underwater acoustic signals is also an important part of this. In the high latitudes of the Arctic, there are many large marine mammals, such as blue whales and baleen whales. When they move in the water, they often emit various low-frequency sounds with large sound source levels. Even submarine earthquakes and distant storms can generate low-frequency sound waves in the ice. Therefore, by deploying ice detectors, marine mammals, submarine earthquake sources, etc. can be monitored and located across the ice layer (I. Arvelo. Arctic marine mammal passive monitoring and tracking with a single acoustic sensor. J. Acoust. Soc. Am. 2012, 132(3):1949).

[0003] For estimating the depth or distance of underwater sound sources, conventional passive measurement methods use hydrophones or hydrophone arrays placed in the water and various methods are used. For example, Gao Tianfu et al. (Gao Tianfu, Chen Yaoming, Yang Yiqing. Sound source localization using simple normal wave matching of short vertical arrays [J] Acta Acoustica Sinica, 1996, 21(4):493-505) used hydrophones to receive acoustic signals and then localized the sound source using a fast iterative algorithm of simple normal wave decomposition. Chen Yaoming et al. (Chen Yaoming, Yang Yiqing, Huang Qing. Sound source localization using multi-line spectrum weighted matching simple normal wave processing [J] Acta Acoustica Sinica, 1999(2):167-173) proposed a method of multi-line spectrum weighted matching simple normal wave processing to localize the sound source using the radiated noise of a small speedboat received by hydrophones. Shi Guoquan (Shi Guoquan. Passive positioning and parameter estimation of moving targets under low signal-to-noise ratio [J]. Acoustics and Electronic Engineering, 2000(02):5-9) used a two-stage space-time integration positioning algorithm to implement passive positioning of maneuvering targets. Zhao Weiwei et al. (Zhao Weiwei. Research on passive ranging technology of underwater acoustic targets using three-element array [D]. Shanghai: Shanghai Jiaotong University, 2009) used a three-element hydrophone array for passive ranging. Sheng Yuanping et al. (Sheng Yuanping, Chen Tao, Li Ying, et al. Research on methods to improve the ranging accuracy of three-element arrays [J]. Journal of Naval Aeronautical Engineering Academy, 2007, 22(4):454-456) used an improved three-element array method for passive ranging. However, if there is ice covering the sea, such as in the ice-covered waters of the Arctic Ocean, it will bring inconvenience to the deployment and recovery of the hydrophone array. In addition, the under-ice currents and other factors will have a great impact on the hydrophone. Therefore, it is possible to consider deploying a simple single-detector array element directly above the ice layer that can measure three-dimensional (3D) particle motion, and combine the multipath sound propagation in the ice layer and water to estimate the depth and distance of the target sound source in the water under the ice surface.

[0004] The technical difficulties often encountered when using a single detector to estimate the depth and distance of underwater sound sources are as follows: First, due to the complex and changeable structure of the sea ice layer, its acoustic characteristics, physical parameters and interface conditions are closely related to the local environment, climate and formation time (Yang TC, Giellis GR. Experimental characterization of elastic waves in a floating ice sheet J. Acoust. Soc. Am., 1994, 96 (5): 2993-3009). The sound waves emitted by the underwater sound source need to cross the ice layer to reach the detector on the ice surface. When the underwater acoustic signal acts on the complex sea ice layer, it will produce different reflections, scattering, propagation attenuation, etc., which makes the sound propagation path greatly disturbed and the characteristic path unclear, affecting the depth and distance estimation of the underwater sound source. Secondly, the Arctic sea ice is an elastic solid that can transmit various types of ground sound waves, including longitudinal plate waves L P waves and horizontal shear waves S Hwave, transverse wave S perpendicular to the propagation direction V Miller BE, Schmidt H. Observation and inversion of seismo-acoustic waves in a complex arctic ice environment. J. Acoust. Soc. Am., 1991, 89(4): 1668-1685. Complex ice layers have different effects on the type of acoustic waves, and the choice of acoustic wave type also has a significant impact on the depth and distance estimation of underwater sound sources. Currently, there is a lack of methods for estimating the distance and depth of underwater sound sources using ice detectors. Summary of the Invention

[0005] The purpose of the present invention is to provide a single-detector method for jointly estimating the depth and distance of underwater sound sources across ice layers, addressing the difficulties of deploying traditional hydrophone arrays in ice-covered seas and the large amount of underwater interference. This method is characterized by simple deployment, fast response, and high positioning accuracy. It only requires a single three-dimensional detector and integrates acoustic modeling, signal processing, and Bayesian estimation techniques to achieve relatively accurate and reliable estimation results.

[0006] To enable a single three-dimensional geophone to estimate the depth and distance of underwater sound sources under ice, the present invention provides the following technical solutions: establishing a sound propagation model for underwater sound sources across ice layers, classifying cross-ice detection sound signals, obtaining the propagation time difference of various sound signals, establishing a target cost function, and applying a joint Bayesian estimation of depth and distance.

[0007] The present invention specifically comprises the following steps:

[0008] 1) Establishing a sound propagation model for underwater sound sources across ice: Based on the characteristics of sound propagation across ice from underwater sound sources, we established sound propagation models for four typical sound propagation paths. These four typical sound propagation paths include propagation in water and in ice, two of which are parallel to the ice layer, and the other two include a direct path from the water to the sea surface, a seabed reflection path, and a perpendicular propagation path through the ice layer.

[0009] 2) Classification of cross-ice detection acoustic signals: Classification is performed based on the propagation speed, propagation channel, amplitude, and underwater propagation characteristics of various types of cross-ice detection acoustic signals;

[0010] 3) Obtaining the time difference of characteristic sound lines along a typical sound propagation path: Based on the actual measurement results of a single detector, select signals with a high signal-to-noise ratio to determine the typical sound propagation path and obtain the time difference of different characteristic sound lines;

[0011] 4) Establishing the target cost function: By observing and setting the arrival time difference of sound rays of different characteristic paths, the target cost function is established. Through statistical analysis and setting uncertainty, the problem of finding the minimum value is established.

[0012] 5) Joint Bayesian estimation of depth and distance: When solving the minimum problem, positioning is restricted to a limited search space (the sound source depth typically ends at the seabed, and the distance ends at the maximum detectable distance). Based on Bayes' theorem, known observation sample information is used to estimate the unknown depth and distance, achieving joint depth-distance estimation of underwater sound sources across ice layers using a single geophone.

[0013] In step 2), the cross-ice detection acoustic signal classification mainly includes four categories, which can be specifically:

[0014] (1) The longitudinal plate wave L generated after reaching the ice layer P Wave;

[0015] (2) S excited after reaching the ice layer H Wave;

[0016] (3) Water waves W waves that propagate from the water directly to the bottom of the detector and then couple with the ice layer;

[0017] (4) The water wave W2 propagates from the water, is reflected by the seabed, reaches the bottom of the detector, and then couples with the ice layer.

[0018] In step 3), at least three signal types with a high signal-to-noise ratio are screened out; the single geophone is used to receive and detect underwater acoustic signals, and the basic performance requirements of the single geophone are as follows: detection dimension, frequency response range, and acceleration measurement range; detection dimension: 3 channels / unit, of which 2 horizontal channels are at a 90° angle and 1 vertical channel; vibration acceleration signals in three directions of sound wave propagation in the ice layer can be tested simultaneously; frequency response range is 1Hz to 1kHz, capable of receiving general underwater broadband sound source signals or low-frequency sound signals; sampling rate is ≥4kHz; acceleration measurement range: 0.003g to 40g.

[0019] In step 4), the target cost function is set as the observed characteristic sound line time difference and the prior characteristic sound line time difference, as follows:

[0020]

[0021] Where i represents the ordinal number; t i o represents the i-th observation time difference data set; m represents the estimated parameter set, m = [rz] T , r represents horizontal distance estimation, z represents depth estimation, T represents matrix transpose; t i is the i-th prior time difference data set; σ i is the standard deviation of the observed data of the i-th estimated parameter in the Gaussian distribution; Represents σ i The square of .

[0022] The standard deviation σ is obtained through observation and statistical analysis i ; Express distance and depth as standard deviation σ i If is an independent Gaussian distribution random variable, the discretized posterior probability density distribution PPD of the sound source distance and depth within the search range is:

[0023]

[0024] Where X represents the observed sample; X() is the prior sample.

[0025] Select the appropriate uncertainty, find the minimum value of the time difference, and obtain the required distance and depth joint PPD. On this basis, using Bayesian estimation, the marginal probability density distribution of distance and depth can be obtained respectively as:

[0026] P(rX)=∫ Mz ψ(m / X)dz

[0027] P(zX)=∫ Mr ψ(m / X)dr

[0028] Where, represents the distance probability density distribution, Mz is the depth search space, Mr is the distance search space, dz represents the depth epsilon, dr represents the distance epsilon; P(z / X) represents the depth probability density distribution;

[0029] After obtaining the marginal probability density distribution of distance and depth, the distance and depth estimation can be obtained.

[0030] Compared with the existing technologies (hydrophone array, vector hydrophone), the present invention has the following advantages:

[0031] 1. The present invention only requires one three-dimensional geophone and does not require digging up the ice layer, so it is simple and easy to operate with fast response.

[0032] 2. When using ice detectors, there is no need to consider anti-current noise reduction, etc. The selected detection acoustic signal type has a high signal-to-noise ratio, so it is more resistant to interference and has strong stability.

[0033] 3. The sampling frequency of the detector is high, so the time accuracy of the detected sound signal is high, and the sound source distance and depth positioning accuracy are higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of four sound propagation paths.

[0035] Figure 2 It is the vertical z-direction ice detection signal (direct echo from the sea surface and reflected echo from the seabed).

[0036] Figure 3 It is the detection signal across the ice layer in three directions.

[0037] Figure 4 is the S in the detection signal H Wave and W wave diagram.

[0038] Figure 5 The preliminary results of horizontal distance and depth estimation are shown in Figure 2. (a) is not magnified, and (b) is magnified.

[0039] Figure 6 is the distance probability density distribution P(r / X) and the depth probability density distribution P(z / X). DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will be further described in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0041] The embodiment of the present invention uses ice detection experiments conducted during Arctic expeditions to obtain three-directional detection data on the ice layer excited by underwater sound sources. This data is used as known observation sample information. A single detector is deployed above the ice layer. Combined with multipath sound propagation through the ice layer and water, the depth and distance of the target sound source in the water under the ice surface are estimated through acoustic modeling, signal processing, Bayesian estimation and other technologies.

[0042] The basic performance requirements of the single detector are:

[0043] Detection dimension: 3 channels / station;

[0044] The detector should have three channels, which can simultaneously test the vibration acceleration signals in three directions of the sound wave propagation process in the ice layer; the two horizontal channels are perpendicular to each other, forming a 90° angle to cover the two orthogonal components in the horizontal direction; one vertical channel is used to detect vibrations in the vertical direction and to analyze the movement of the ice layer in the up and down directions; the detector can comprehensively capture the vibration of the ice layer in three-dimensional space.

[0045] Frequency response range: 1Hz~1kHz; under this condition, general broadband sound source signals or low-frequency sound signals can be obtained underwater.

[0046] Acceleration measurement range: 0.003g ~ 40g.

[0047] Sampling rate: Sampling rate ≥ 4kHz.

[0048] The frequency response range, acceleration range and sampling rate of the detector have an impact on the cross-ice detection of underwater sound source signals, which in turn affects the classification of various types of waves detected across the ice.

[0049] The sound propagation across the ice layer includes four characteristic sound propagation paths. The first is the longitudinal plate wave L excited after reaching the ice layer. P The second wave is the S wave generated after reaching the ice layer. H The third is the water wave that propagates from the water to the bottom of the detector and then couples with the ice layer. Since the path of this wave in the water is relatively long, the propagation time in the water is also long, which is the W wave; the fourth is the propagation path of propagation in the water through the seabed reflection. Since the seabed reflection wave of this path is mainly propagated in the water, it is the W2 wave.

[0050] According to the first sound line propagation path, the propagation is the longitudinal plate wave L P Wave. If the thickness of the ice layer is known to be h, L P The wave propagation speed is c L , L P The speed of the wave in water is c W , L P The incident wave has a grazing angle of θ L , the horizontal estimated distance is r, the depth estimated distance is z, t0 is the propagation instantaneous delay of the sound source, then L P The propagation time t of the wave to the detector L for:

[0051]

[0052] The second term on the right side of equation B1 represents the propagation time in water, and the third term represents the L in ice. P Wave propagation time.

[0053] According to the second sound line propagation path, the propagation is horizontal polarization shear wave S H Wave. If S is known H The wave propagation speed is c s , S H The incident wave has a grazing angle of θ S , other parameters are the same as above, then S H The propagation time t of the wave to the detector S for:

[0054]

[0055] The second term on the right side of equation B2 represents the propagation time in water, and the third term represents the S in ice. H Wave propagation time.

[0056] According to the third sound line propagation path, the water wave W wave is propagated, and the propagation time of the W wave to the detector is t W for:

[0057]

[0058] Where T represents the period of the W wave, and its value is determined by the frequency of the incident wave. The second term on the right side of equation B3 represents the propagation time in water. The third term represents the vertical upward propagation time after reaching the ice layer to the detector. The fourth term represents the maximum time interval for coherent interference.

[0059] According to the fourth sound line propagation path, the seabed reflected wave W2 is propagated, and the propagation time of this wave to the detector is t W2 for:

[0060]

[0061] Similar to the third ray, T represents the period of the W2 wave, and its value is determined by the frequency of the incident wave. The second term on the right side of equation B4 represents the propagation time in water. The third term represents the vertical upward propagation time after reaching the ice layer to the detector. The fourth term represents the maximum time interval for coherent interference.

[0062] From the propagation time equations of the four paths, since the propagation instantaneous delay t0 of the sound source is unknown but the same, the time difference equation of the characteristic sound line of each propagation path is obtained by subtracting them respectively:

[0063] Δt1=t L (r,z)-t W (r,z)

[0064] Δt2=t S (r,z)-t W (r,z)

[0065] Δt3=t W2 (r,z)-t W (r,z)(B5)

[0066] Where Δt1 is the difference between the first and second acoustic propagation paths; Δt2 is the difference between the third and second acoustic propagation paths; and Δt3 is the difference between the fourth and second acoustic propagation paths. For the joint distance and depth estimation, select the two with the highest signal-to-noise ratio.

[0067] The target cost function is set as the time difference between the characteristic sound line of the observed propagation path and the time difference between the characteristic sound line of the prior propagation path:

[0068]

[0069] Where i represents the ordinal number; t i o represents the i-th observation time difference data set; m represents the estimated parameter set, m = [rz] T r represents horizontal distance estimation, z represents depth estimation, T represents matrix transpose; t i is the i-th prior time difference data set; σi is the standard deviation of the time difference data of the i-th observation in the Gaussian distribution; Represents σ i The square of σ is obtained through observation and statistical analysis. i The observed values ​​of distance and depth are expressed as standard deviation σ i If is an independent Gaussian distributed random variable, the posterior probability density distribution (PPD) of the discretized sound source distance and depth within the search range is:

[0070]

[0071] Where X represents the observed sample; X() is the prior sample.

[0072] Select an appropriate confidence interval, find the minimum value of the time difference, and obtain the required distance and depth joint PPD. Based on the obtained PPD, the marginal probability density distribution of distance and depth is obtained as follows:

[0073]

[0074] Where P(r|X) represents the distance probability density distribution, Mz is the depth search space, Mr is the distance search space, dz represents the depth minima, and dr represents the distance minima. Once the marginal probability density distributions of distance and depth are obtained, the distance and depth estimates can be obtained.

[0075] Therefore, based on Bayes' theorem, the horizontal distance and depth of the sound source can be obtained by measuring the time difference parameters of different paths and the residual of the Gaussian distribution. However, there are two possible outcomes for determining the sound source location. These outcomes require: first, elimination based on the relationship between distance and depth, as different types of waves in the ice layer are related to the incident distance and depth; second, elimination based on the actual sea depth and ice cover size.

[0076] This invention can support the design and development of new passive detection equipment on Arctic ice and has certain innovative significance.

[0077] Figures 1 to 6 An example of jointly estimating the underwater sound source distance and depth using the method of the present invention is given. In one example of the present invention, the actual underwater sound source distance is 185m and the depth is 60m.

[0078] like Figure 1 , cross-ice sound propagation includes four sound propagation paths. They are: longitudinal plate wave (L P Wave) path: The sound wave first propagates from the emission point through the water to the ice layer, and then excites the longitudinal plate wave (L P wave), θ in the figure L Indicates LP The incident wave grazing angle. L P The waves propagate along the ice layer and are received by the detectors on the ice layer. H Wave) path: with L P Similar to waves, sound waves propagate to the ice layer first, but what is excited on the ice surface is the horizontally polarized shear wave (S H Since the vibration direction of SH wave is horizontal, this path will cause horizontal vibration of ice layer. S Indicates S H The incident wave's grazing angle. Direct water wave (W-wave) path: Sound waves propagate directly from the launch point through the water to the detector below without passing through the ice. Seabed reflected water wave (W2-wave) path: Sound waves propagate through the water, reflect off the seabed, and form bottom waves (i.e., seabed reflected W2-waves). Waves along this path primarily propagate through the water before being received by the detector.

[0079] Figure 2 The image shows the vertical z-axis ice detection signal, illustrating the propagation of sound waves in water. This includes signals that propagate directly to the sea surface and those reflected from the seabed. The circled portion represents the seabed reflection wave (W2 wave). Once the W2 wave is identified, its propagation time can be determined.

[0080] Figure 3 The geophone signals across the ice layer are given in the x, y, and z directions. In an ice-covered marine environment, sound wave propagation is significantly affected by the ice. As an inhomogeneous elastic medium, the ice layer affects the propagation speed, amplitude, and waveform of the sound waves. Therefore, these signals are detected using geophones positioned in different directions.

[0081] Figure 4 Given the S in the detection signal H Schematic diagram of S wave and W wave. As the sound wave propagates, it will cause the detector particle to vibrate and convert into acceleration signal. When the sound source is in the water under the ice, S H Due to its transverse vibration characteristics, the acceleration of the wave in the z direction is relatively small; while the W wave, as a longitudinal wave, has a relatively large acceleration in the z direction. By analyzing the characteristics of these two types of waves, including propagation speed, propagation channel, amplitude, and propagation characteristics in water, it can be determined that S H waves and W waves, thereby determining their propagation time.

[0082] Figure 5 The preliminary results of horizontal distance and depth estimation are shown in Figure (a) without magnification and Figure (b) with magnification. H wave and W wave, the observation time difference data and σ iThen, based on known environmental factors, including ice thickness, sound speed, and water layer sound speed, we can obtain the prior time difference data. Substituting these data into formula B(7) and setting the confidence level to 90%, we can obtain Figure 5 Distribution of horizontal range and depth estimates shown.

[0083] From the preliminary estimation results Figure 5 From the above, there are two possibilities for the distance and depth of underwater sound source. One is that the horizontal distance of the sound source is 187m and the depth is around 66m. The second is that the horizontal distance of the sound source is 123m and the depth is around 99m. H The refractive properties of the wave. In the second case, the incident distance and depth do not meet the total reflection conditions, and S H After excluding the second case, we get the estimated probability distribution of distance and depth: Figure 6 , where the upper figure is the distance probability density distribution P(r / X), and the lower figure is the depth probability density distribution P(z / X). Figure 6 It can be seen that the estimated horizontal distance of the sound source is 187m and the depth is 66m, which is close to the actual position.

[0084] This paper addresses the challenge of estimating the distance and depth of underwater sound sources under sea ice cover. By using a single geophone, this method, suitable for sea ice-covered environments, can estimate the distance and depth of underwater sound sources across the ice using a single geophone. By establishing a model for the propagation of underwater sound sources across the ice, classifying the cross-ice detection acoustic signals, obtaining the time difference between characteristic sound lines along different propagation paths, establishing a target cost function, and applying Bayesian estimation, experiments have shown that this method achieves a joint estimation of the depth and distance of underwater sound sources with minimal error.

[0085] The above embodiments are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent of the present invention.

Claims

1. A method for jointly estimating the depth and distance of underwater sound sources using a single geophone across ice layers, characterized in that The following steps are involved: 1) Establishing a sound propagation model for underwater sound sources across ice: Based on the characteristics of sound propagation across ice from underwater sound sources, we established sound propagation models for four typical sound propagation paths. These four typical sound propagation paths include propagation in water and in ice, two of which are parallel to the ice layer, and the other two include a direct path from the water to the sea surface, a seabed reflection path, and a perpendicular propagation path through the ice layer. 2) Classification of cross-ice detection acoustic signals: Classification is performed based on the propagation time, propagation channel, amplitude, and underwater propagation characteristics of various types of cross-ice detection acoustic signals; The cross-ice detection acoustic signal classification includes: The longitudinal plate wave L excited after reaching the ice layer P Wave; After reaching the ice layer, the S H Wave; Water waves W waves that propagate from the water directly to the bottom of the detector and then couple with the ice layer; The water wave W2 propagates from the water, is reflected by the seabed, reaches the bottom of the detector, and then couples with the ice layer; 3) Obtaining the time difference of characteristic sound lines along different sound propagation paths: Based on the actual measurement results of a single detector, select signals with a high signal-to-noise ratio to determine the typical sound propagation path and obtain the time difference of characteristic sound lines along different propagation paths; 4) Establishing the target cost function: By observing and setting the arrival time difference of the sound rays of different characteristic paths, the target cost function is established. Through statistical analysis and setting uncertainty, the problem of finding the minimum value is established. 5) Joint Bayesian estimation of depth and distance: Based on Bayes’ theorem, known observation sample information is used to estimate unknown depth and distance, enabling joint depth-distance estimation of underwater sound sources across ice layers using a single detector.

2. A method for jointly estimating the depth and distance of underwater sound sources using a single geophone across ice layers as claimed in claim 1, characterized in that In step 3), at least three types of signals with high signal-to-noise ratio are screened out.

3. The method for jointly estimating the depth and distance of underwater sound sources by using a single geophone across ice layers as claimed in claim 1, characterized in that In step 3), the single geophone is used to receive and detect underwater acoustic signals. The performance requirements of the single geophone are as follows: detection dimension, frequency response range, and acceleration measurement range; detection dimension: 3 channels / unit, of which 2 horizontal channels are at a 90° angle and 1 vertical channel; vibration acceleration signals in three directions of the sound wave propagation process in the ice layer are tested simultaneously; sampling rate ≥ 4kHz; frequency response range: 1Hz to 1kHz; acceleration measurement range: 0.003g to 40g.

4. A method for jointly estimating the depth and distance of underwater sound sources using a single geophone across ice layers as claimed in claim 1, characterized in that In step 4), the target cost function is set as the time difference between the arrival of the observed characteristic path sound ray and the arrival of the prior characteristic path sound ray: Where i represents the ordinal number; t i o represents the i-th observation arrival time difference data set; m represents the estimated parameter set, m = [rz] T ; r represents horizontal distance estimation, z represents depth estimation, T represents matrix transpose; t i is the i-th prior arrival time difference data set; σ i is the standard deviation of the arrival time difference data of the i-th observation in the Gaussian distribution; Represents σ i The square of .

5. The method for jointly estimating the depth and distance of underwater sound sources using a single geophone across ice layers as claimed in claim 1, characterized in that In step 4), the problem of finding the minimum value is established by statistical analysis and setting uncertainty, specifically: Through observation and statistical analysis, we can get σ i ; Express the distance and depth as standard deviation σ i If is an independent Gaussian distribution random variable, the discretized posterior probability density distribution PPD of the sound source distance and depth within the search range is: Where X represents the observed sample; X() is the prior sample; m represents the estimated parameter set, m = [rz] T ; r represents horizontal distance estimation, z represents depth estimation, T represents matrix transpose; σ i is the standard deviation of the arrival time difference data of the i-th observation in the Gaussian distribution; Represents σ i the square of By statistical analysis and setting uncertainty, the minimum value is found and the optimized distance and depth PPD is obtained; On the basis of obtaining the optimized distance and depth PPD, the marginal probability density distribution of distance and depth is obtained by using Bayesian estimation: Among them, P(r|X) represents the distance probability density distribution, P(z / X) represents the depth probability density distribution; Mz is the depth search space, Mr is the distance search space; dz represents the depth minima, and dr represents the distance minima.

6. A method for jointly estimating the depth and distance of underwater sound sources using a single geophone across ice layers as claimed in claim 1, characterized in that In step 5), the depth and distance are jointly estimated by Bayesian estimation. Specifically, when solving the minimum problem, positioning is restricted to a limited search space, the sound source depth ends at the seabed, and the distance ends at the maximum detectable distance. According to Bayes' theorem, the known observation sample information is used to estimate the unknown depth and distance, realizing the joint estimation of the depth and distance of the underwater sound source by a single detector across the ice layer.

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