Target motion velocity estimation method based on modal decomposition and sound velocity profile inversion method

Abstract

The invention discloses a modal decomposition-based target motion velocity estimation method and a sound velocity profile inversion method, and the method comprises the following steps: 1, obtaining a two-dimensional frequency domain sound field, obtaining a normal wave vertical mode function through singular value decomposition, and obtaining a normal wave horizontal wave number through Fourier transform; 2, substituting the normal wave vertical mode function and the normal wave horizontal wave number into a mode difference equation to obtain a sound velocity profile estimated by each normal wave mode; and step 3, setting a loss function for measuring similarity between sound velocity profiles corresponding to each normal wave mode, setting a target motion velocity search interval, scanning the target motion velocity search interval, and taking a velocity value corresponding to the minimum loss function as a target motion velocity estimation value. According to the invention, target motion velocity estimation and sound velocity profile inversion in an unknown marine environment are realized by using a narrow-band signal radiated by a moving target.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater target detection and sound speed profile inversion, and particularly relates to a method for estimating the moving speed of a target based on modal decomposition and a method for inverting the sound speed profile. Background Art

[0002] Underwater vehicles such as buoys and submersibles can be used to achieve underwater target detection, ocean environment monitoring, etc. The moving speed of a target is one of the important parameters of underwater target movement. The estimation of the moving speed of a target can be applied in fields such as underwater target positioning and underwater navigation. The sound speed is closely related to ocean physical factors such as temperature and salinity. Therefore, studying the inversion of the sound speed profile can provide theoretical and technical support for ocean environment monitoring. In addition, using acoustic means to invert the sound speed profile can obtain the time-averaged and space-integrated sound speed profile results in terms of acoustics, which is of great significance for fields such as underwater target positioning, sound field prediction, and underwater acoustic communication.

[0003] Currently, the research on the estimation of the moving speed of an underwater target mainly uses the Doppler frequency shift of the target line spectrum to estimate the moving speed of the target. This method uses time-frequency analysis to extract the instantaneous frequency of the received Doppler signal, and then fits the instantaneous frequency and the Doppler frequency shift model by the least squares method to estimate the moving speed of the target. This method requires prior information on ocean environments such as the sound speed profile, which limits its application to a certain extent. In addition, the radiation signal of an underwater target is mainly concentrated in the low-frequency band, and the Doppler effect is weak, which is not conducive to the estimation of the moving speed of the target.

[0004] Currently, the methods for inverting the sound speed profile using acoustic data mostly use shape functions such as empirical orthogonal functions to characterize the sound speed profile to reduce the parameter dimension in the inversion of the sound speed profile. The currently commonly used methods for inverting the sound speed profile mainly include matched field processing and compressive sensing. The inversion of the sound speed profile based on matched field processing means that by establishing a suitable underwater acoustic propagation model to calculate the replica sound field, selecting a suitable cost function to perform correlation processing on the measured sound field and the replica sound field, and using an optimization algorithm to search for the coefficients of shape functions such as empirical orthogonal functions when the cost function is optimal, so as to obtain the sound speed profile information. The inversion of the sound speed profile based on compressive sensing means that on the premise that the sound speed profile can be sparsely represented by a shape function, the acoustic propagation characteristics are linearized into a function of the shape function coefficients through Taylor expansion, and compressive sensing technology is used to estimate the coefficients of the shape function from limited observation data to achieve the inversion of the sound speed profile. The inversion method of the sound speed profile based on matched field processing and the inversion method of the sound speed profile based on compressive sensing have obvious limitations. Both require sufficient historical sound speed profile data in the target sea area, and often require the seabed sediment parameters to be known, but the unknown sea areas do not meet these conditions.

[0005] In view of this, this invention is specifically proposed. Summary of the Invention

[0006] The object of the present invention is to solve the drawbacks existing in the prior art, and a method for estimating the moving speed of a target based on modal decomposition and a method for inversely retrieving the sound speed profile based on modal decomposition are proposed. The moving speed of the target is estimated in an unknown ocean environment by using the narrowband signal radiated by the moving target, and the passive sound speed profile inversion is realized under the condition of a non-cooperative sound source.

[0007] To achieve the above object, the present invention adopts the following technical solutions: A method for estimating the moving speed of a target based on modal decomposition includes the following steps: Step 1: Obtain the two-dimensional frequency-domain sound field, obtain the vertical modal function of the normal mode through singular value decomposition, and obtain the horizontal wavenumber of the normal mode through Fourier transform; Step 2: Substitute the vertical modal function of the normal mode and the horizontal wavenumber of the normal mode into the modal difference equation to obtain the sound speed profile estimated by each normal mode; Step 3: Set a loss function for measuring the similarity between the sound speed profiles corresponding to each normal mode, set the search interval for the moving speed of the target, scan the search interval for the moving speed of the target, and the speed value corresponding to the minimum of the loss function is the estimated value of the moving speed of the target.

[0008] Furthermore, the Step 1 includes the following steps: Step 1.1: Obtain the narrowband radiation signal of the target received by the vertical array sensor array ; Step 1.2: Perform short-time Fourier transform on the narrowband radiation signal of the target to construct a two-dimensional frequency-domain sound field P, and the form of P is as follows: ; wherein, is the depth of the th sensor in the vertical array sensor array, is the number of sensors in the vertical array sensor array, is the horizontal distance corresponding to the th sampling point between the target and the vertical array sensor array, is the number of horizontal distance sampling points; The matrix product form of the two-dimensional frequency-domain sound field P is as follows: ; Step 1.3: Perform singular value decomposition on the two-dimensional frequency-domain sound field P to obtain the matrix U = Φ and the matrix V = R. The column vectors of the matrix U are the vertical modal functions of the normal mode ; Step 1.4: Assume that the moving speed of the target is , the Fourier transform of matrix V is performed to obtain the normal wave horizontal wave number .

[0009] Furthermore, step 1.4 includes the following steps: Step 1.4.1: Perform the Fourier transform on matrix V to obtain , The form of is as follows: ; Among them, is the wave number sampling point, , is the number of the normal wave propagation mode; is the horizontal distance between the target and the vertical array sensor array when the target motion speed is , is the initial horizontal distance, is the time resolution of the short-time Fourier transform of the target narrowband radiation signal . Step 1.4.2: The corresponding to the peak position is the normal wave horizontal wave number .

[0010] Furthermore, in step 2, the normal wave mode parameters and the normal wave horizontal wave number are substituted into the mode difference equation. The mode difference equation is as follows: ; Among them, is the vertical difference step size, , is the angular frequency, , is the frequency of the target radiation signal, is the sound speed.

[0011] Furthermore, step 2 includes the following steps: Step 2.1: Substitute the normal wave mode parameters and the normal wave horizontal wave number into the mode difference equation to obtain the first sound speed profile estimated by each normal wave mode, and the form is as follows: ; Step 2.2: Eliminate the invalid points from the first sound speed profile estimated by each normal wave mode: ; Among them, is the node of the th normal wave vertical mode function, that is, the zero crossing point; Step 2.3: Smooth the first sound speed profile estimated for each normal mode after removing invalid points to obtain the second sound speed profile estimated for each normal mode, in the following form: .

[0012] Furthermore, in the said Step 3, the loss function is in the following form: .

[0013] To achieve the above object, the present invention also adopts the following technical solution: A sound speed profile inversion method based on modal decomposition, including the sound speed profile inversion method provided by any one of the present invention, further includes the following steps: Step 4: Calculate the estimated result of the sound speed profile through the sound speed profiles estimated for each normal mode corresponding to the estimated value of the target motion speed, and the calculation formula is as follows: ; Furthermore, it further includes the following steps: Step 5: Perform maximum-minimum normalization processing on the estimated result of the sound speed profile to obtain , and input into the denoising autoencoder neural network to obtain the output result of the network, and perform an anti-normalization operation on to obtain the optimized result of the sound speed profile, where the denoising autoencoder neural network is trained through simulated generated data.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Based on the physical facts that the target motion speed and the normal mode parameters are not independent, and the sound speed profile is correlated with the normal mode parameters, in Step 2, the sound speed profile is estimated using the modal difference equation, and in Steps 3 and 4, the similarity between the sound speed profiles estimated for each normal mode is used to estimate the target motion speed, realizing the joint estimation of the target motion speed and the sound speed profile; 2. The narrowband signal radiated by the moving target is used to realize the estimation of the target motion speed in an unknown ocean environment, and to realize the passive sound speed profile inversion in the case of a non-cooperative sound source; effectively solving the limitation that the sound speed profile needs to be known in traditional target speed estimation, and at the same time avoiding the dependence on prior information such as the historical sound speed profile and the seabed sediment in traditional sound speed profile inversion, and can be used for underwater target positioning, underwater navigation and communication, etc., and is applicable to carrier platforms such as moored buoys and floating buoys. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Flow chart of the target motion speed estimation method based on modal decomposition; Figure 2 Schematic diagram of a specific embodiment of a submersible buoy; Figure 3 Schematic diagram of a simulation environment; Figure 4 Graph of the target motion speed estimation result; Figure 5 Graph of the sound speed profile inversion result. Specific implementation manners

[0016] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0017] Embodiment 1: A target motion speed estimation method based on modal decomposition, as Figures 1 - 2 shown, includes the following steps: Step 1: Obtain a two-dimensional frequency-domain sound field, obtain the normal mode vertical modal function through singular value decomposition, and obtain the normal mode horizontal wave number through Fourier transform; Step 2: Substitute the normal mode vertical modal function and the normal mode horizontal wave number into the modal difference equation to obtain the sound speed profile estimated by each normal mode; Step 3: Set a loss function for measuring the similarity between the sound speed profiles corresponding to each normal mode, set a search interval for the target motion speed, scan the search interval for the target motion speed, and the speed value corresponding to the minimum of the loss function is the target motion speed estimation value.

[0018] In an optional embodiment, the step 1 includes the following steps: Step 1.1: Obtain the target narrowband radiation signal received by the vertical array sensor array ; Step 1.2: Perform short-time Fourier transform on the target narrowband radiation signal to construct a two-dimensional frequency-domain sound field P, and the form of P is as follows: ; wherein, is the depth of the th sensor in the vertical array sensor array, is the number of sensors in the vertical array sensor array, is the horizontal distance corresponding to the th sampling point between the target and the vertical array sensor array, is the number of horizontal distance sampling points; In addition, the following formula can be used for calculation : ; ; wherein, is the horizontal distance between the target and the vertical sensor at the initial time, , is the target motion speed search range, is the time resolution for performing short-time Fourier transform on the sensor received signal; The matrix product form of the two-dimensional frequency domain sound field P is as follows: ; wherein, ; wherein, is the water density, is the normal mode vertical mode function, is the depth of the target in water, is the normal mode horizontal wave number, is the Kronecker delta function, , is the number of the normal mode propagation mode; Step 1.3: Perform singular value decomposition on the two-dimensional frequency domain sound field P to obtain matrix U = Φ and matrix V = R. The column vectors of matrix U are the normal mode vertical mode functions ; Step 1.4: Assume that the target motion speed is , and perform Fourier transform on matrix V to obtain the normal mode horizontal wave number .

[0019] In an alternative embodiment, said Step 1.4 includes the following steps: Step 1.4.1: Perform Fourier transform on matrix V to obtain , The form of is as follows: ; wherein, is the wave number sampling point, , is the number of the normal mode propagation mode; is the horizontal distance between the target and the vertical array sensor array when the target motion speed is , is the initial horizontal distance, is for the target narrowband radiation signal The time resolution for performing short-time Fourier transform; Step 1.4.2: The one corresponding to the peak position is the normal mode horizontal wave number .

[0020] In this optional embodiment, perform a Fourier transform on the matrix V to obtain , and plot the curve. The one corresponding to the peak on the curve is the normal mode horizontal wave number .

[0021] In an optional embodiment, in the said step 2, substitute the normal mode parameters and the normal mode horizontal wave number into the modal difference equation. The modal difference equation is as follows: ; where is the vertical difference step size, , is the angular frequency, , is the frequency of the target radiation signal, is the sound speed.

[0022] In an optional embodiment, the said step 2 includes the following steps: Step 2.1: Substitute the normal mode parameters and the normal mode horizontal wave number into the modal difference equation to obtain the first sound speed profile estimated for each normal mode, in the following form: ; Step 2.2: Eliminate the invalid points from the first sound speed profiles estimated for each normal mode: ; where is the node of the th normal mode vertical mode function, i.e., the zero crossing point; Step 2.3: Smooth the first sound speed profiles estimated for each normal mode after eliminating the invalid points to obtain the second sound speed profiles estimated for each normal mode, in the following form: .

[0023] In this optional embodiment, when the loss function is minimized, that is, the similarity between the sound speed profiles estimated for each normal mode is the greatest; specifically, set the target motion speed , and the search interval , scan the search range of the target motion speed, and take the speed value corresponding to the minimum loss function as the estimated value of the target motion speed , at this time, the similarity between the estimated sound speed profiles of each normal mode is the largest.

[0024] In addition, in this optional embodiment, the loss function can be calculated using the second sound speed profiles of each normal mode after the smoothing process in step 2.3.

[0025] In an optional embodiment, in the said step 3, the loss function has the following form: .

[0026] Embodiment 2: A sound speed profile inversion method based on modal decomposition includes the target motion speed estimation method provided in any one of the embodiments provided in this embodiment, and further includes the following steps: Step 4: Calculate the estimated result of the sound speed profile through the estimated sound speed profiles of each normal mode corresponding to the estimated value of the target motion speed , and the calculation formula is as follows: , the calculation formula is as follows: .

[0027] In this optional embodiment, the first sound speed profiles estimated by each normal mode after being processed in step 2.1 and step 2.2 can be used, or the second sound speed profiles estimated by each normal mode after the smoothing process in step 2.3 can be used to calculate the estimated result of the sound speed profile.

[0028] In an optional embodiment, it further includes the following steps: Step 5: Perform maximum-minimum normalization processing on the estimated result of the sound speed profile to obtain , and input into the denoising autoencoder neural network to obtain the output result of the network, and perform an inverse normalization operation on to obtain the optimized result of the sound speed profile, where the denoising autoencoder neural network is trained through the simulated generated data.

[0029] The denoising autoencoder network includes an encoder, a bottleneck layer, and a decoder. The input of the network is the estimated result of the sound speed profile containing noise, that is, the output of step 4, and the output of the network is the corresponding estimated result of the sound speed profile without noise.

[0030] Train the denoising autoencoder neural network with the data generated by simulation. Specifically, consider the sound speed profile as a simple and smooth curve on a two-dimensional plane, that is, use quadratic functions, linear functions, piecewise linear functions, etc. to generate the sound speed profile as the label. , and obtain the noisy sound speed profile as the input by adding random noise to the label. , then map the label and the input to the interval [0, 1] through min-max normalization to obtain the label and the input. and the input , and optimize the loss function with the Adaptive Moment Estimation Adam optimizer. The loss function is as follows: ; where is the output result of the denoising autoencoder neural network, are the network parameters of the autoencoder. The training method of the denoising autoencoder neural network can be completed by using the existing technology and will not be elaborated here.

[0031] After the denoising autoencoder neural network is trained, the estimated result of the sound speed profile is input into the trained denoising autoencoder neural network after min-max normalization to obtain the output result of the network. Perform an inverse normalization operation on to obtain the optimized result of the sound speed profile. Where is in the following form: ; where is the estimated result of the normalized sound speed profile.

[0032] For the method for estimating the target motion speed and inverting the sound speed profile based on modal decomposition in this embodiment, in step 2, the sound speed profile is estimated using the modal difference equation. In steps 3 and 4, starting from the physical fact that the target motion speed is not independent of the normal mode parameters and the sound speed profile is correlated with the normal mode parameters, the similarity between the sound speed profiles estimated by each normal mode is used to estimate the target motion speed.

[0033] The method for estimating the target motion speed and inverting the sound speed profile based on modal decomposition in this embodiment uses the narrowband signal radiated by the moving target to realize the estimation of the target motion speed in an unknown ocean environment and the passive inversion of the sound speed profile in the case of a non-cooperative sound source; effectively solves the limitation of the need for a known sound speed profile in traditional target speed estimation, and at the same time avoids the dependence on prior information such as historical sound speed profiles and seabed sediments in traditional sound speed profile inversion. It can be used for underwater target positioning, underwater navigation, and communication, etc., and is applicable to carrier platforms such as moored buoys and floating buoys.

[0034] Example 3: To verify the target motion speed estimation and sound speed profile inversion method based on modal decomposition in this example, the following simulation was carried out. The simulation parameters are as follows: The target moves away from the vertical array at a speed of 5 m / s, and its depth is 25 m; The interval between sensors in the vertical sensor array is 0.5 m, and the number of sensors is 80; The water depth is 40 m, the water density is 1 g / ml, the longitudinal wave sound speed of the seabed is 1688 m / s, and the seabed density is 1.81 g / ml, and the attenuation sparsity is 0.5 dB / λ, where λ is the wavelength.

[0035] Figure 4 This is the target motion speed estimation result graph. The blue line represents the loss function that measures the similarity between the sound speed profiles corresponding to each normal mode, the black asterisk represents the true target motion speed (5 m / s), and the red circle represents the estimated target motion speed (5 m / s). It can be seen that the method in this example can accurately estimate the target motion speed.

[0036] Figure 5 This is the sound speed profile inversion result graph. The black dashed line represents the true sound speed profile, the blue dotted line represents the estimated result of the sound speed profile, and the red solid line represents the optimized result of the sound speed profile estimated by the denoising autoencoder network output. The average relative error is 0.0004. It can be seen that the method in this example can accurately achieve the sound speed profile inversion.

[0037] As mentioned above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and all should be covered within the protection scope of the present invention.

Claims

1. A method for estimating the target motion speed based on modal decomposition, characterized in that It includes the following steps: Step 1: Obtain the two-dimensional frequency-domain sound field, obtain the vertical mode function of the normal mode through singular value decomposition, and obtain the horizontal wavenumber of the normal mode through Fourier transform; Step 2: Substitute the vertical mode function of the normal mode and the horizontal wavenumber of the normal mode into the modal difference equation to obtain the sound speed profile estimated for each normal mode; Step 3: Set a loss function for measuring the similarity between the sound speed profiles corresponding to each normal mode, set the search interval for the target motion speed, scan the search interval for the target motion speed, and the speed value corresponding to the minimum of the loss function is the estimated value of the target motion speed.

2. The method for estimating the target motion speed based on modal decomposition according to claim 1, wherein The said Step 1 includes the following steps: Step 1.1: Obtain the target narrowband radiation signal received by the vertical array sensor array ; Step 1.2: Perform short-time Fourier transform on the target narrowband radiation signal to construct a two-dimensional frequency-domain sound field P, and the form of P is as follows: ； Among them, is the depth of the -th sensor in the vertical array sensor array, is the number of sensors in the vertical array sensor array, is the horizontal distance corresponding to the -th sampling point between the target and the vertical array sensor array, is the number of horizontal distance sampling points; The matrix product form of the two-dimensional frequency-domain sound field P is as follows: ； Step 1.3: Perform singular value decomposition on the two-dimensional frequency-domain sound field P to obtain matrix U = Φ and matrix V = R. The column vectors of matrix U are the normal mode functions of the vertical ; Step 1.4: Assume that the target motion speed is , perform Fourier transform on matrix V to obtain the normal wave horizontal wave number .

3. The method for estimating the target motion speed based on modal decomposition according to claim 2, characterized in that, The said Step 1.4 includes the following steps: Step 1.4.1: Perform a Fourier transform on matrix V to obtain , in the following form: ； Among them, is the wavenumber sampling point, , is the number of the normal mode of wave propagation; is the horizontal distance between the target and the vertical array sensor array when the target motion speed is , is the initial horizontal distance, is the time resolution of the short-time Fourier transform for the narrowband radiation signal of the target; Step 1.4.2: corresponding to the peak position is the normal wave horizontal wave number .

4. A method for estimating the target motion speed based on modal decomposition according to claim 2, characterized in that, In step 2, the normal mode parameters and the normal mode horizontal wave number are substituted into the modal difference equation, and the modal difference equation is as follows: ； Among them, is the vertical differential step size, , is the angular frequency, , is the frequency of the target radiation signal, is the speed of sound.

5. The method for estimating the target motion speed based on modal decomposition according to claim 2, characterized in that The said Step 2 includes the following steps: Step 2.1: Substitute the normal mode parameters and the normal mode horizontal wavenumber into the modal difference equation to obtain the first sound speed profile estimated for each normal mode, in the following form: ； Step 2.2: Eliminate invalid points from the first sound speed profiles estimated for each normal mode; ； Among them, is the node of the vertical mode function of the th normal mode, that is, the zero crossing point; Step 2.3: Smooth the first sound speed profiles estimated for each normal mode after eliminating the invalid points to obtain the second sound speed profiles estimated for each normal mode, and the form is as follows: 。 6. The method for estimating the target motion speed based on modal decomposition according to claim 5, characterized in that In the said step 3, the loss function has the following form: 。 7. A method for inverting the sound speed profile based on modal decomposition, characterized in that, It includes the target motion speed estimation method according to any one of claims 5 or 6, and further includes the following steps: Step 4: Using the estimated value of the target motion speed calculate the estimated result of the sound speed profile from the sound speed profiles estimated for each corresponding normal wave mode , and the calculation formula is as follows: 。 8. A method for inverting sound speed profile based on modal decomposition according to claim 7, characterized in that, It further includes the following steps: Step 5: The estimation result of the sound speed profile is normalized by its maximum and minimum values to obtain , and is input into the denoising autoencoder neural network to obtain the output result of the network. An inverse normalization operation is performed on to obtain the optimized result of the sound speed profile , where the denoising autoencoder neural network is trained with the data generated by simulation.

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