Method for estimating sound source radiation signal power by using robust normal wave

Abstract

The invention relates to the technical field of sound source radiation signal power estimation, and discloses a method for estimating sound source radiation signal power by using robust normal waves, which comprises the following steps of: S1, calculating a modal coefficient vector and a modal domain receiving signal by using a sound field model; s2, selecting a robust normal wave reconstruction modal coefficient vector and a modal domain receiving signal vector; and S3, estimating the power of the sound source radiation signal. According to the method, the environment mismatch robustness of the sound source radiation signal power estimation result can be improved only by using the robust normal wave, and the environment mismatch robustness of the sound source radiation signal power estimation result obtained by the RM-SRPE method is higher than that of the C-SRPE method due to the fact that the robust normal wave is less affected by the environment mismatch. As the robust normal wave is selected in the hypothetical marine environment, the environmental mismatch robustness improvement effect of the RM-SRPE method is related to the mismatch degree of the hypothetical marine environment.

Description

Technical Field

[0001] The present invention relates to the technical field of sound source radiation signal power estimation, and in particular to a method for estimating the sound source radiation signal power by using a robust normal wave. Background Art

[0002] The power measurement of the sound source radiation signal is the basis of the research related to vibration reduction and noise reduction. Accurately estimating the power characteristics of the sound source radiation signal is an important part of the sound source radiation signal power measurement. Power spectral density is an important physical quantity that describes the power characteristics of the sound source radiation signal. When estimating the power spectral density, it can be obtained by estimating the power of the sound source radiation signal at each frequency point in the frequency domain. Therefore, the core problem of power spectral density estimation is the problem of estimating the power of the sound source radiation signal at a single determined frequency point. The power estimation of the sound source radiation signal is generally carried out in shallow sea environments, and vertical arrays are often used to receive signals. The schematic diagram is shown in Figure 1 The basic idea of estimating the power of the sound source radiation signal is to calculate the received signal power from the received data, and then compensate for the propagation loss to obtain the power of the sound source radiation signal.

[0003] Traditional methods for estimating the power of sound source radiation signals usually use the direct wave signal received by the receiving unit to calculate the received signal power. By designing a suitable beamformer, the main lobe is aligned with the direct wave direction, and the seabed and sea surface reflection waves are suppressed. The schematic diagram is shown in Figure 2 Given. Ideally, the received signal only contains direct waves. Then, the power of the signal radiated by the sound source can be obtained by compensating the propagation loss of the received signal power according to the spherical wave or cylindrical wave expansion. The traditional method for estimating the power of the signal radiated by the sound source faces three problems. First, it uses a simplified sound propagation model, which is very different from the actual sound field environment. Second, it is difficult to completely remove the reflected waves from the seabed and the sea surface, and the received signal contains not only the direct wave. Third, the error of using geometric expansion to compensate for the propagation loss is large. Although the propagation loss compensation method was subsequently refined according to the distance from the sound source to the receiving unit, there is always a large error with the actual sound propagation loss. Therefore, the error of the traditional method for estimating the power of the signal radiated by the sound source is always large.

[0004] The conventional matched-field source radiated power estimation method (C-SRPE) uses the sound field model to calculate the actual sound field environment characteristics. Figure 3Given that the sound field model used by the C-SRPE method is very similar to the actual sound field environment, and the received signal power can be directly calculated without removing the reflected waves from the seabed and the sea surface, and the propagation loss can be accurately calculated according to the sound field model. It can be seen that the C-SRPE method has better solved the three problems faced by the traditional method for estimating the power of the source radiated signal. The factors affecting the performance of the C-SRPE method are only the environmental parameters and the accuracy of the prior information such as the source position parameters. When the prior information is accurately known, the sound field propagation loss can be accurately obtained, and the C-SRPE method has much better performance than the traditional method for estimating the power of the source radiated signal. However, since both the ocean environment and the source position are time-varying, it is very difficult to accurately obtain the prior information, resulting in poor performance of the C-SRPE method in actual use and unable to achieve the theoretical optimal performance. Aiming at the problem of uncertain prior information, a method for estimating the power of the source radiated signal by extending the search domain dimension of the robust matched field and a method for estimating the power of the source radiated signal by fitting the covariance matrix of the matched field are proposed. These two methods have good robustness under the condition of uncertain prior information, but they respectively require prior information such as the uncertainty range of the channel transfer function and the search domain of the channel transfer function. Moreover, the method for estimating the power of the source radiated signal by extending the search domain dimension of the robust matched field needs to search for the channel transfer function, with a large amount of calculation and not suitable for real-time data processing. The setting of the search domain of the channel transfer function has a great influence on the performance of the method for estimating the power of the source radiated signal by fitting the covariance matrix of the matched field, and setting the search domain of the channel transfer function requires a relatively comprehensive understanding of the ocean environment; in the face of an unfamiliar sea area, the performance of the method for estimating the power of the source radiated signal by fitting the covariance matrix of the matched field will decline. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the performance of the method for estimating the power of the source radiated signal based on the sound field model is poor when the prior information is uncertain, and the existing robust matched field method for estimating the power of the source radiated signal is not suitable for real-time estimating the power of the source radiated signal in an unfamiliar sea area.

[0006] To solve the above technical problems, the technical solution of the present invention is to provide a method for estimating the power of the source radiated signal using robust normal modes (Robust Modes based Source Radiated Power Estimation method, RM-SRPE), including the following steps:

[0007] S1. Calculate the mode coefficient vector and the received signal in the mode domain using the sound field model;

[0008] S2. Select the robust normal modes to reconstruct the mode coefficient vector and the received signal vector in the mode domain;

[0009] S3. Estimate the power of the source radiated signal.

[0010] Optionally, in S1, when using the acoustic field model, information such as signal frequency, environmental parameters, and sound source position parameters is required. Since the signal frequency is considered known when estimating the sound source radiation power at each frequency point one by one, the environmental parameters are obtained based on experience or measured on-site using instruments such as CTD (conductivity-temperature-depth profiler), and the sound source position can be calculated by underwater acoustic positioning methods.

[0011] Optionally, in S1, the modal coefficient vector a is obtained from the normal mode theory, specifically as follows:

[0012] S11. According to the normal mode theory, the channel transfer function from the sound source to the nth array element is:

[0013]

[0014] In the formula, is the imaginary unit, m represents the order of the normal mode, M is the total number of normal modes, z s is the sound source depth, r is the horizontal distance from the sound source to the N-element vertical line array, α m , Ψ m and k rm are respectively the absorption coefficient, modal function, and horizontal wavenumber of the mth order normal mode;

[0015] S12. According to formula (1), g can be expressed as:

[0016] g = ψ(z)a (2);

[0017] In the formula, ψ(z) is the sampling of the modal functions of M normal modes on the receiving array element at a depth of z n :

[0018] ψ(z n ) = [Ψ1(z n ) Ψ2(z n ) … Ψ M (z n )] (3);

[0019] S13. The modal coefficient vector a is an M×1-dimensional column vector:

[0020]

[0021] where γ represents a coefficient independent of the horizontal wavenumber k rm and the modal function Ψ m , and its expression is:

[0022]

[0023] Optionally, in S1, the deployment and retrieval of instruments such as CTD require a large amount of time, and there are still deviations between the environmental parameters obtained from on-site measurements and the environmental parameters corresponding to the received data. Therefore, the assumed environmental parameters are usually mismatched. Thus, the actually calculated modal coefficient vector a is the modal coefficient vector under mismatched ocean environmental conditions.

[0024]

[0025] wherein, and are the absorption coefficient, modal function, and horizontal wavenumber of the m-th normal mode respectively.

[0026] Optionally, in S1, the calculation method of the received signal in the modal domain is:

[0027] S14. Construct the -dimensional modal function matrix

[0028]

[0029] In the formula,

[0030] S15. Assume that within a short period, the characteristics of the shallow sea channel and the power characteristics of the sound source radiation signal remain unchanged. The received signal frequency-domain snapshot x can be modeled as:

[0031] x = Ha s + n (9);

[0032] In the formula, a s represents the spectrum amplitude of the sound source radiation signal, Ha s is the received signal, and n is the environmental noise;

[0033] S16. Use to construct the modal decomposition matrix as:

[0034]

[0035] In the formula, the subscript "D" represents modal decomposition, and the dimension of Ψ D is

[0036] S17. Adopt the modal decomposition method to transform the frequency-domain received signal model given by formula (9) into a modal-domain received signal model. Multiply the left side of formula (9) by Ψ D to obtain the modal-domain received signal x m :

[0037] x m = Ψ D x (11);

[0038] wherein, x m is an m-dimensional vector, and the subscript "m" represents the modal domain.

[0039] Optionally, different types of normal modes are affected by environmental mismatch to different degrees. The normal modes can be divided into partial-depth propagation modes, full-depth propagation modes, and evanescent modes according to the relationship between the phase velocity v m of the normal mode and the sound velocity at the interface. Among them, the phase velocity of the normal mode is:

[0040]

[0041] wherein, ω is the angular frequency. In step S2, the robust normal mode is the normal mode less affected by environmental mismatch, specifically, all the normal modes of the partial-depth propagation modes excited by the sound source plus one normal mode of the low-order full-depth propagation mode.

[0042] Optionally, the phase velocity of the normal mode of the partial-depth propagation mode satisfies c2 < v m ≤ c1. Based on this, the number of normal modes of the partial-depth propagation mode can be obtained, where c1 is the sound velocity at the upper surface of the seawater and c2 is the sound velocity at the lower surface of the seawater.

[0043] Optionally, since environmental parameter and sound source position parameter are required, only the normal mode numbers corresponding to various normal modes in the mismatched environment can be obtained during actual use.

[0044] Optionally, in S2, the reconstruction methods of the modal coefficient vector and the modal domain received signal vector are as follows:

[0045] Assume that there are M1 robust normal modes, and the normal mode number range is Select M1 elements within the range from the modal coefficient vector under the mismatched ocean environmental conditions and the modal domain received signal x m respectively to reconstruct the vectors and The subscript "P" indicates that only partial normal modes are used.

[0046] Optionally, in S3, the estimated result of the sound source radiation signal power is

[0047]

[0048] In summary, the present invention has at least one of the following beneficial effects:

[0049] ​1. The present invention can improve the environmental mismatch robustness of the sound source radiation signal power estimation result by only using the robust normal modes. Since the robust normal modes are less affected by environmental mismatch, the environmental mismatch robustness of the sound source radiation signal power estimation result obtained by the RM-SRPE method is higher than that of the C-SRPE method. Since the robust normal modes are selected under the assumed ocean environment, the improvement effect of the environmental mismatch robustness of the RM-SRPE method is related to the degree of mismatch of the assumed ocean environment.

[0050] 2. The present invention only using partial normal modes will not lead to inaccurate estimation of the sound source radiation signal power. The RM-SRPE method removes some normal modes. Although it may change the received signal power, the sound source radiation signal power can be obtained by making targeted compensation for the calculated received signal power. The method of the present invention uses to calculate the propagation loss compensation amount and only compensates for the selected robust normal modes to improve the robustness. Description of the Drawings

[0051] Figure 1 is a schematic diagram of the principle of sound source radiation signal power estimation;

[0052] Figure 2 is a schematic diagram of the traditional sound source radiation signal power estimation;

[0053] Figure 3 is a schematic diagram of the existing matched-field sound source radiation signal power estimation;

[0054] Figure 4 is a flowchart of the implementation of the method of the present invention;

[0055] Figure 5 is a schematic diagram of the shallow sea sound speed profile;

[0056] Figure 6 is a schematic diagram of the robust normal mode;

[0057] Figure 7 is a schematic diagram of vector reconstruction;

[0058] Figure 8 is a schematic diagram of the robust normal mode simulation;

[0059] Figure 9 is a schematic diagram of the change of the sound source radiation signal power estimation result with the signal-to-noise ratio and the signal frequency;

[0060] Figure 10 is a schematic diagram of the change of the sound source radiation signal power estimation result with the sound source position;

[0061] Figure 11 is a schematic diagram of the experimental data processing result. Detailed Embodiment

[0062] The following is combined withFigures 1 - 11 A further detailed description of the present invention will be given.

[0063] The present invention discloses a method for estimating the power of a sound source radiation signal using robust normal mode estimation, referring to Figure 4 , including the following steps:

[0064] S1. Use a sound field model to calculate the modal coefficient vector and the received signal in the modal domain;

[0065] When using the sound field model, information such as signal frequency, environmental parameters, and sound source position parameters is required. Since the sound source radiation power at each frequency point is estimated one by one, the signal frequency is considered known. The environmental parameters are obtained according to experience or measured on-site using instruments such as CTD. If the sound source to be measured is a non-cooperative target, the sound source position can be calculated by an underwater acoustic positioning method; if the sound source to be measured is a cooperative target, the sound source position can be obtained more accurately through satellite positioning. However, there are errors in both the underwater acoustic positioning method and the satellite positioning results. The elements of the modal coefficient vector a are the modal coefficients corresponding to each order of normal mode. The magnitude of the modal coefficient reflects the signal energy contained in the normal mode, which is specifically obtained from the normal mode theory. The sound field channel transfer function describes the sound field characteristics of the sound wave from the sound source to the receiving array element, including propagation loss and phase change. The sound field characteristics calculated using mismatched environmental parameters and sound source position parameters are also inaccurate. According to the normal mode model, the sound field channel transfer function is the result of the superposition of each order of normal mode excited by the sound source. Different normal modes are affected by uncertain parameters, and the degrees of influence are different. Specifically:

[0066] S11. Assume that the sound source depth is z s , the horizontal distance from the sound source to the N-element vertical line array is r, and the channel transfer function g(f, r, z n , φ) of the sound source to the nth array element is related to the signal frequency f, the position r = (r s , z s ) of the sound source to be measured, the depth z n of the receiving array element, and the environmental parameters φ. For the convenience of writing, the parameters in the brackets will be omitted later. According to the normal mode theory, the channel transfer function from the sound source to the nth array element is:

[0067]

[0068] In the formula, is the imaginary unit, m represents the order of the normal mode, M is the total number of normal modes, α m , Ψ m and k rm are respectively the absorption coefficient, modal function, and horizontal wavenumber of the mth order normal mode;

[0069] S12. According to formula (1), g can be expressed as:

[0070] g = ψ(z)a (2);

[0071] where ψ(z) is the sampling of the modal functions of M normal modes at the receiving array element at depth z n :

[0072] ψ(z n ) = [Ψ1(z n ) Ψ2(z n ) … Ψ M (z n )] (3);

[0073] S13. The modal coefficient vector a is an M×1 column vector:

[0074]

[0075] where γ represents a coefficient independent of the horizontal wave number k rm and the modal function Ψ m , and its expression is:

[0076]

[0077] However, the deployment and retrieval of instruments such as CTDs require a large amount of time, and there are still deviations between the environmental parameters obtained from on-site measurements and the environmental parameters corresponding to the received data. Therefore, the assumed environmental parameters are usually mismatched. Therefore, assume that the number of normal modes excited by the sound source is The actually calculated modal coefficient vector a is the modal coefficient vector under mismatched ocean environmental conditions

[0078]

[0079] where and are the absorption coefficient, modal function, and horizontal wave number of the m-th normal mode, respectively;

[0080] The calculation method of the received signal in the modal domain is:

[0081] S14. Construct the -dimensional modal function matrix under mismatched ocean environmental conditions

[0082]

[0083] where

[0084] S15. Assume that within a short period of time, the characteristics of the shallow water channel and the power characteristics of the sound source radiation signal remain unchanged. The received signal frequency-domain snapshot x can be modeled as:

[0085] x = Has +n(9);

[0086] Wherein, a s represents the spectral amplitude of the sound source radiation signal, Ha s is the received signal, and n is the ambient noise; is the power of the sound source radiation signal, which is the physical quantity to be estimated;

[0087] S16. Use to construct the modal decomposition matrix as:

[0088]

[0089] Wherein, the subscript "D" represents modal decomposition, and Ψ D has a dimension of

[0090] S17. Adopt the modal decomposition method to transform the frequency-domain received signal model given by equation (9) into a modal-domain received signal model. Multiply the left side of equation (9) by Ψ D to obtain the modal-domain received signal x m :

[0091] x m = Ψ D x(11);

[0092] Wherein, x m is dimensional vector, the subscript "m" represents the modal domain. Estimate the power of the sound source radiation signal by using and some elements in x m ;

[0093] S2. Select the robust normal mode reconstruction modal coefficient vector and the modal-domain received signal vector. The method of the present invention only uses the vector elements corresponding to the robust normal modes to estimate the power of the sound source radiation signal, improving robustness. Select the robust normal modes according to the type of normal modes. The robust normal modes are the normal modes less affected by environmental mismatch. Specifically,

[0094] S21. Refer to Figure 5 , the environmental parameters marked in the figure are respectively the seawater depth d1, the sound speed c1 on the upper surface of the seawater and the sound speed c2 on the lower surface, the sound speed c3 on the upper surface of the sediment layer and the sound speed c4 on the lower surface, the sediment layer density ρ and the sediment layer absorption coefficient α. The seawater sound speed gradient is a negative gradient, denoted as G1; the sediment layer gradient is a positive gradient, denoted as G2; the magnitude relationship of the seawater sound speed and the sediment layer sound speed is c2 < c1 < c3 < c4. The sound speed of the basement half-space is consistent with the sound speed on the lower surface of the sediment layer. Different types of normal modes are affected by environmental mismatch to different degrees. The robust normal modes can be determined according to the phase velocity v mThe relationship between the magnitude of the interface sound speed divides the normal modes into partial-depth propagating modes (PPM), full-depth propagating modes (FPM), and evanescent modes (EM). The phase velocity of the normal mode is:

[0095]

[0096] where ω is the angular frequency;

[0097] As Figure 6 shown, specifically, the selected robust normal modes are the normal modes of all partial-depth propagating modes excited by the sound source plus one low-order full-depth propagating mode normal mode. Among them, the phase velocity of the normal mode of the partial-depth propagating mode satisfies c2 < v m ≤ c1. Based on this, the number of normal modes of the partial-depth propagating mode can be obtained. Since environmental parameters and sound source position parameters are required, only the normal mode numbers corresponding to various normal modes in the mismatched environment can be obtained during actual use;

[0098] The reconstruction methods for S22, the modal coefficient vector, and the modal domain received signal vector are as follows:

[0099] As Figure 7 shown, assuming there are M1 robust normal modes in total, and the normal mode numbers range from Select M1 elements within the range from the modal coefficient vector in the mismatched ocean environmental conditions and the modal domain received signal x m respectively to reconstruct the vectors and and The subscript "P" indicates that only partial normal modes are used;

[0100] S3. Estimation of the sound source radiation signal power.

[0101] The estimation result of the sound source radiation signal power is

[0102]

[0103] I. After obtaining the estimation result of the sound source radiation signal power, first conduct a simulation analysis:

[0104] The simulation analysis uses the Benchmark standard shallow sea sound speed profile and parameter uncertainty range provided by NRL Workshop'93. As Figure 8As shown in the figure, the black solid line represents the nominal sound speed profile. In seawater, it is a linear negative gradient sound speed profile, and in the sediment layer, it is a linear positive gradient sound speed profile. The sound speed in the basement half-space does not change with depth. The variation ranges of the various parameters of the ocean environment are given in Figure 10 and the environmental parameters all follow a uniform distribution within the variation range. The KrakenC sound field software based on the normal mode method is used for sound field calculation. A 100-element uniform vertical line array with an element spacing of 1 m is used to receive data. The depth of the element closest to the sea surface is 1 m. The source radiation signal is mostly a broadband signal. It is assumed that the signal frequency varies in the range of 100 Hz to 1000 Hz, and the number of Monte Carlo simulations used for simulation analysis is 1000 times.

[0105] Figure 9 In (a) of , the variation of the source radiation signal power estimation results of the RM-SRPE method and the traditional C-SRPE method with the signal-to-noise ratio SNR is given. When the SNR is low, the source radiation signal power estimation errors of both the RM-SRPE method and the C-SRPE method are very large. When the SNR is high, the source radiation signal power estimation error of the RM-SRPE method is about 1.1 dB, and that of the C-SRPE method is about 4.7 dB. The source radiation signal power estimation performance of the RM-SRPE method is better.

[0106] Assume that the nominal value of the source radiation signal power is 120 dB, and the horizontal distance from the source to the vertical array is 500 m. At this time, the influence of environmental noise on the RM-SRPE method and the C-SRPE method is very small, and the source radiation signal power estimation error mainly comes from environmental mismatch. Figure 9 In (b) of , the variation of the source radiation signal power estimation results of the RM-SRPE method and the C-SRPE method with the signal frequency is given. The number of robust normal modes used by the RM-SRPE method is different when estimating the source radiation signal power at different frequency points. The growth rate of the source radiation signal power estimation error of the RM-SRPE method with the signal frequency is much smaller than that of the C-SRPE method. Within the analysis frequency band in this paper, the source radiation signal power estimation error of the RM-SRPE method is always less than 3 dB. It can be seen that compared with the C-SRPE method, the RM-SRPE method has better source radiation signal power estimation performance for signals with different frequencies, higher environmental mismatch robustness, and more obvious performance improvement in the higher frequency band.

[0107] The above analysis assumes that the source depth is 50 m and the horizontal distance from the source to the vertical array is 500 m. In fact, the source may be at any position in the sea area. Assume that the maximum depth of the source to be measured is 100 m and the maximum distance from the source to the receiving array is 1000 m. The signal frequency is 500 Hz, and the nominal value of the source radiation signal power is 120 dB. Figure 10The variation of the estimated sound source radiation signal power of the C-SRPE method and the RM-SRPE method with the sound source position under environmental mismatch is given. The performance of the C-SRPE method varies significantly with the sound source position. When the horizontal distance from the sound source to the receiving array is greater than 250 m, the estimation error of the sound source radiation signal power is generally greater than 3 dB. In the sea area studied in this paper, the estimation error of the sound source radiation signal power of the RM-SRPE method is always less than 3 dB. It can be seen that when the sound source is at different positions, the performance of the RM-SRPE method in estimating the sound source radiation signal power is better than that of the C-SRPE method.

[0108] II. Experimental data analysis

[0109] The SWellEx-96 experimental data is used to verify the improvement of the environmental mismatch robustness of the RM-SRPE method. A set of single-frequency signals with a source level of about 158 dB is analyzed. The signal frequencies are 64 Hz, 79 Hz, 94 Hz, 112 Hz, 130 Hz, 148 Hz, 166 Hz, 201 Hz, 235 Hz, 283 Hz, 338 Hz, and 388 Hz respectively, and the sound source depth is 54 m.

[0110] When using the measured data, the performance of the sound source radiation signal power estimation is not only affected by the environmental mismatch. To more intuitively reflect the improvement of the environmental mismatch robustness of the RM-SRPE method, the absolute value of the estimation error E C of the sound source radiation signal power of the C-SRPE method and the absolute value of the estimation error E RM of the sound source radiation signal power of the RM-SRPE method are used, and the difference ΔE is used to describe the improvement effect of the environmental mismatch robustness of the RM-SRPE method:

[0111] ΔE = |E C | - |E RM | (14)

[0112] In the formula,

[0113]

[0114] is the estimated result of the sound source radiation signal power of the C-SRPE method. ΔE > 0 indicates that the environmental mismatch robustness of the RM-SRPE method is higher than that of the C-SRPE method. The magnitude of |ΔE| represents the degree of improvement in the environmental mismatch robustness of the RM-SRPE method compared with the C-SRPE method; ΔE < 0 indicates that the environmental mismatch robustness of the C-SRPE method is higher than that of the RM-SRPE method.

[0115] The signal is intercepted from 59 min 20 s, and the signal duration is 5 s. At this time, the sound source is about 900 m away from the receiving array. Figure 11 In (a), the ΔE of signals with different frequencies is given.Figure 11 In (b), the numbers of PPM and FPM excited by sound sources of different frequencies are given. The robust normal modes selected by the RM-SRPE method are all the PPMs excited by sound sources of different frequencies plus the first-order low-order FPM.

[0116] At each frequency point, ΔE > 0, indicating that the sound source radiation signal power estimation error of the RM-SRPE method is smaller and the environmental mismatch robustness is higher. At different frequency points, the magnitudes of |ΔE| are different; this shows that the environmental mismatch robustness of the RM-SRPE method has been improved to varying degrees compared with the C-SRPE method, which is related to the degree of mismatch between the assumed ocean environment and the actual ocean environment.

[0117] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for estimating the power of a sound source radiation signal using robust normal modes, characterized in that, It includes the following steps: S1. Calculate the modal coefficient vector and the modal-domain received signal using the acoustic field model; S2. Select the robust normal mode to reconstruct the modal coefficient vector and the modal-domain received signal vector; S3. Estimate the power of the sound source radiation signal.

2. The method for estimating the sound source radiation signal power using the robust normal mode as claimed in claim 1, wherein In S1, when using the acoustic field model, information such as the signal frequency, environmental parameters, and sound source position parameters is required. Since the sound source radiation power at each frequency point is estimated one by one, the signal frequency is considered known, the environmental parameters are obtained based on experience or measured on-site using instruments such as CTD, and the sound source position can be calculated by the underwater acoustic positioning method.

3. The method for estimating the sound source radiation signal power using the robust normal mode according to claim 2, characterized in that In S1, the modal coefficient vector a is obtained from the normal mode theory. Specifically: S11. According to the normal mode theory, the channel transfer function from the sound source to the nth array element is: In the formula, is the imaginary unit, m represents the order of the normal mode, M is the total number of normal modes, z s is the depth of the sound source, r is the horizontal distance from the sound source to the N - element vertical line array, α m , Ψ m and k rm are respectively the absorption coefficient, the mode function and the horizontal wave number of the m - th order normal mode; S12. According to Equation (1), g can be expressed as: g = ψ(z)a (2); where ψ(z) is the sampling of the modal functions of M normal modes on the receiving array element at depth z n : ψ(z n ) = [Ψ1(z n )Ψ2(z n )… Ψ M (z n )] (3); S13. The modal coefficient vector a is an M×1-dimensional column vector: where γ represents a coefficient independent of the horizontal wave number k rm and the mode function Ψ m and its expression is:

4. The method for estimating the sound source radiation signal power using the robust normal mode according to claim 3, characterized in that, In S1, it takes a lot of time to deploy and retrieve instruments such as CTD. There are still deviations between the environmental parameters obtained from on-site measurements and the environmental parameters corresponding to the received data. Therefore, the assumed environmental parameters are usually mismatched. As a result, the actually calculated modal coefficient vector a is the modal coefficient vector under mismatched ocean environmental conditions. wherein, and are respectively the absorption coefficient, modal function and horizontal wavenumber of the m-th order normal mode.

5. The method for estimating the sound source radiation signal power using the robust normal mode according to claim 4, characterized in that, In S1, the calculation method of the modal-domain received signal is: S14. Construct the dimensional modal function matrix under mismatched ocean environmental conditions In the formula, S15. Assume that within a short time, the characteristics of the shallow water channel and the power characteristics of the sound source radiation signal remain unchanged. The received signal frequency-domain snapshot x can be modeled as: x = Ha s + n (9); where a s represents the spectral amplitude of the sound source radiation signal, Ha s is the received signal, and n is the ambient noise; S16. Use Construct the modal decomposition matrix as follows: where the subscript "D" represents modal decomposition, and the dimension of Ψ D is S17. Use the modal decomposition method to transform the frequency-domain received signal model given by equation (9) into a modal-domain received signal model. Multiply the left side of equation (9) by Ψ D to obtain the modal-domain received signal x m : x m = Ψ D x (11); where x m is a vector of dimension, and the subscript "m" represents the modal domain.

6. The method for estimating the sound source radiation signal power using the robust normal mode according to claim 5, characterized in that, Different types of normal modes are affected by environmental mismatch to different degrees. The normal modes can be divided into partial-depth propagation modes, full-depth propagation modes, and evanescent modes according to the magnitude relationship between the normal mode phase velocity v m and the interface sound speed. Among them, the normal mode phase velocity is as follows: where ω is the angular frequency. In step S2, the robust normal mode is the normal mode less affected by environmental mismatch, specifically the normal mode of all partial-depth propagation modes excited by the sound source plus the normal mode of one low-order full-depth propagation mode.

7. The method for estimating the sound source radiation signal power using the robust normal mode according to claim 6, wherein The normal wave phase velocity of the partial depth propagation mode satisfies c2 < v m ≤ c1. Based on this, the number of normal waves of the partial depth propagation mode can be obtained, where c1 is the sound speed on the upper surface of the seawater and c2 is the sound speed on the lower surface of the seawater.

8. The method for estimating the sound source radiation signal power using the robust normal mode according to claim 7, characterized in that, Since environmental parameters and sound source position parameters are required, only the normal mode numbers corresponding to various normal modes in the mismatched environment can be obtained in actual use.

9. The method for estimating the sound source radiation signal power using the robust normal mode according to claim 8, characterized in that In S2, the reconstruction method of the modal coefficient vector and the modal-domain received signal vector is: Assume there are M1 robust normal modes, and the range of normal mode numbers is From the modal coefficient vector under the mismatched ocean environmental conditions m and the received signal x in the modal domain select M1 elements within the range to reconstruct the vectors respectively. The subscript "P" indicates that only partial normal modes are used.

10. The method for estimating the sound source radiation signal power using the robust normal mode according to claim 9, characterized in that, In S3, the estimated result of the sound source radiation signal power is

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