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

Abstract

The present invention discloses a method for estimating target velocity and inverting sound velocity profiles based on modal decomposition. The method comprises the following steps: Step 1: Acquire a two-dimensional frequency domain sound field, obtain the normal wave vertical modal function through singular value decomposition, and obtain the normal wave horizontal wave number through Fourier transform; Step 2: Substitute the normal wave vertical modal function and the normal wave horizontal wave number into a modal difference equation to obtain the estimated sound velocity profile of each normal wave mode; Step 3: Set a loss function that measures the similarity between the sound velocity profiles corresponding to each normal wave mode, set a target velocity search interval, scan the target velocity search interval, and use the velocity value corresponding to the minimum loss function as the target velocity estimate. The present invention utilizes the narrowband signal radiated by the moving target to achieve target velocity estimation and sound velocity profile inversion in an unknown ocean environment.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater target detection and sound velocity profile inversion, and in particular to a target motion velocity estimation method and a sound velocity profile inversion method based on modal decomposition. Background Art

[0002] Underwater carriers such as buoys and submersibles can be used for underwater target detection and marine environmental monitoring. Target velocity is a key parameter in underwater target motion, and its estimation can be applied in underwater target positioning and navigation. Sound speed is closely related to oceanographic physical factors such as temperature and salinity. Therefore, research on sound velocity profile inversion can provide theoretical and technical support for marine environmental monitoring. Furthermore, acoustic inversion of sound velocity profiles can yield acoustically time-averaged and spatially integrated sound velocity profiles, which are of great significance for underwater target positioning, sound field prediction, and underwater acoustic communications.

[0003] Currently, research on underwater target velocity estimation primarily relies on the Doppler shift of the target's line spectrum. This approach uses time-frequency analysis to extract the instantaneous frequency of the received Doppler signal. The instantaneous frequency and the Doppler shift model are then fitted using the least squares method to estimate the target's velocity. However, this method requires prior information about the ocean environment, such as the sound velocity profile, which limits its application. Furthermore, underwater target radiation signals are primarily concentrated in the low-frequency band, where the Doppler effect is weak, making it difficult to estimate target velocity.

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

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

[0006] The purpose of the present invention is to address the shortcomings of the existing technology and propose a target motion velocity estimation method based on modal decomposition and a sound velocity profile inversion method based on modal decomposition. The narrowband signal radiated by the moving target is used to realize the target motion velocity estimation in an unknown ocean environment, and the passive sound velocity profile inversion is realized in the case of non-cooperative sound sources.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for estimating target motion speed based on modal decomposition comprises the following steps:

[0009] Step 1: Obtain the two-dimensional frequency domain sound field, obtain the vertical mode function of the simple normal wave through singular value decomposition, and obtain the horizontal wave number of the simple normal wave through Fourier transform;

[0010] Step 2: Substitute the normal wave vertical mode function and the normal wave horizontal wave number into the modal difference equation to obtain the estimated sound velocity profile of each normal wave mode;

[0011] Step 3: Set a loss function to measure the similarity between the sound velocity profiles corresponding to each simple normal wave mode, set the target motion speed search interval, scan the target motion speed search interval, and the speed value corresponding to the minimum loss function is the target motion speed estimation value.

[0012] Furthermore, the step 1 includes the following steps:

[0013] Step 1.1: Obtain the target narrowband radiation signal received by the vertical array sensor array ;

[0014] Step 1.2: Radiate narrowband signal to target Perform short-time Fourier transform to construct a two-dimensional frequency domain sound field P, which is in the following form:

[0015] ;

[0016] in, The vertical array sensor array The depth of the sensor, is the number of sensors in the vertical array sensor, The first distance between the target and the vertical array sensor array The sampling points correspond to the horizontal distance, is the number of horizontal distance sampling points;

[0017] The matrix product of the two-dimensional frequency domain sound field P is in the following form:

[0018] ;

[0019] 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 vector of the matrix U is the simple normal wave vertical mode function ;

[0020] Step 1.4: Assume that the target moving speed is , perform Fourier transform on the matrix V to obtain the horizontal wave number of the simple normal wave .

[0021] Furthermore, the step 1.4 includes the following steps:

[0022] Step 1.4.1: Perform Fourier transform on the matrix V to obtain , The form is as follows:

[0023] ;

[0024] in, is the wave number sampling point, , is the number of the simple normal wave propagation mode; The target movement speed is The horizontal distance between the target and the vertical array sensor array at time is the initial horizontal distance, To target narrowband radiation signal Time resolution of the short-time Fourier transform;

[0025] Step 1.4.2: The peak position corresponds to is the horizontal wave number of the simple normal wave .

[0026] Furthermore, in step 2, the normal wave modal parameters and the horizontal wave number of the simple normal wave Substituting into the modal difference equation, the modal difference equation is as follows:

[0027] ;

[0028] in, is the vertical difference step size, , is the angular frequency, , is the frequency of the target radiation signal, is the speed of sound.

[0029] Furthermore, step 2 includes the following steps:

[0030] Step 2.1: Set the normal wave modal parameters and the horizontal wave number of the simple normal wave Substituting into the modal difference equation, the first sound velocity profile of each simple normal wave mode estimate is obtained in the following form:

[0031] ;

[0032] Step 2.2: Eliminate invalid points from the first sound velocity profile estimated for each normal wave mode:

[0033] ;

[0034] in, For the The node of the vertical mode function of the simple normal wave, that is, the zero crossing point;

[0035] Step 2.3: Smooth the first sound velocity profile of each simple normal wave mode estimate after removing invalid points to obtain the second sound velocity profile of each simple normal wave mode estimate, which is in the following form:

[0036] .

[0037] Furthermore, in step 3, the loss function The form is as follows:

[0038] .

[0039] In order to achieve the above object, the present invention also adopts the following technical solutions:

[0040] A sound velocity profile inversion method based on modal decomposition, comprising any one of the sound velocity profile inversion methods provided by the present invention, further comprising the following steps:

[0041] Step 4: Estimated target speed The estimated sound velocity profiles of the corresponding simple normal wave modes are calculated. , the calculation formula is as follows:

[0042] ;

[0043] Furthermore, the method further comprises the following steps:

[0044] Step 5: Estimation of the sound velocity profile Perform maximum and minimum normalization to obtain , and Input into the denoising autoencoder neural network to get the output of the network ,right Perform the inverse normalization operation to obtain the optimized result of the sound velocity profile , where a denoising autoencoder neural network is trained using simulated generated data.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. Based on the physical facts that the target velocity and the simple normal wave modal parameters are not independent and the sound velocity profile is related to the simple normal wave modal parameters, the sound velocity profile is estimated using the modal difference equation in step 2, and the target velocity is estimated using the similarity between the sound velocity profiles estimated by each simple normal wave mode in steps 3 and 4, thus achieving the joint estimation of the target velocity and the sound velocity profile.

[0047] 2. The narrowband signal radiated by the moving target is used to estimate the target's motion speed in an unknown ocean environment, and to invert the passive sound velocity profile in the case of a non-cooperative sound source. This effectively solves the limitation of traditional target velocity estimation that requires a known sound velocity profile, while avoiding the dependence of traditional sound velocity profile inversion on prior information such as historical sound velocity profiles and seabed sediments. It can be used for underwater target positioning, underwater navigation and communication, and is suitable for carrier platforms such as buoys and buoys. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Flowchart of the target motion speed estimation method based on modal decomposition;

[0049] Figure 2 is a schematic diagram of a specific embodiment of a latent marker;

[0050] Figure 3 It is a schematic diagram of a simulation environment;

[0051] Figure 4 It is the target motion speed estimation result diagram;

[0052] Figure 5 This is the sound velocity profile inversion result diagram. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0054] Example 1:

[0055] A target motion velocity estimation method based on modal decomposition, such as Figures 1 and 2 As shown, the following steps are included:

[0056] Step 1: Obtain the two-dimensional frequency domain sound field, obtain the vertical mode function of the simple normal wave through singular value decomposition, and obtain the horizontal wave number of the simple normal wave through Fourier transform;

[0057] Step 2: Substitute the normal wave vertical mode function and the normal wave horizontal wave number into the modal difference equation to obtain the estimated sound velocity profile of each normal wave mode;

[0058] Step 3: Set a loss function to measure the similarity between the sound velocity profiles corresponding to each simple normal wave mode, set the target motion speed search interval, scan the target motion speed search interval, and the speed value corresponding to the minimum loss function is the target motion speed estimation value.

[0059] In an optional embodiment, step 1 includes the following steps:

[0060] Step 1.1: Obtain the target narrowband radiation signal received by the vertical array sensor array ;

[0061] Step 1.2: Radiate narrowband signal to target Perform short-time Fourier transform to construct a two-dimensional frequency domain sound field P, which is in the following form:

[0062] ;

[0063] in, The vertical array sensor array The depth of the sensor, is the number of sensors in the vertical array sensor, The first distance between the target and the vertical array sensor array The sampling points correspond to the horizontal distance, is the number of horizontal distance sampling points;

[0064] In addition, the following formula can be used to calculate :

[0065] ;

[0066] ;

[0067] in, is the horizontal distance between the target and the vertical sensor at the initial time, , is the target motion speed search interval, The time resolution of the short-time Fourier transform of the sensor received signal;

[0068] The matrix product of the two-dimensional frequency domain sound field P is in the following form:

[0069] ;

[0070] in,

[0071] ;

[0072] in, is the water density, is the simple normal wave vertical mode function, is the depth of the target in the water, is the horizontal wave number of the simple normal wave, is the Kronecker delta function, , is the number of the simple normal wave propagation mode;

[0073] 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 vector of the matrix U is the simple normal wave vertical mode function ;

[0074] Step 1.4: Assume that the target moving speed is , perform Fourier transform on the matrix V to obtain the horizontal wave number of the simple normal wave .

[0075] In an optional embodiment, step 1.4 includes the following steps:

[0076] Step 1.4.1: Perform Fourier transform on the matrix V to obtain , The form is as follows:

[0077] ;

[0078] in, is the wave number sampling point, , is the number of the simple normal wave propagation mode; The target movement speed is The horizontal distance between the target and the vertical array sensor array at time is the initial horizontal distance, To target narrowband radiation signal Time resolution of the short-time Fourier transform;

[0079] Step 1.4.2: The peak position corresponds to is the horizontal wave number of the simple normal wave .

[0080] In this optional embodiment, Fourier transform is performed on the matrix V to obtain , and draw The curve, The peak value on the curve corresponds to is the horizontal wave number of the simple normal wave .

[0081] In an optional embodiment, in step 2, the normal wave modal parameters and the horizontal wave number of the simple normal wave Substituting into the modal difference equation, the modal difference equation is as follows:

[0082] ;

[0083] in, is the vertical difference step size, , is the angular frequency, , is the frequency of the target radiation signal, is the speed of sound.

[0084] In an optional embodiment, step 2 includes the following steps:

[0085] Step 2.1: Set the normal wave modal parameters and the horizontal wave number of the simple normal wave Substituting into the modal difference equation, the first sound velocity profile of each simple normal wave mode estimate is obtained in the following form:

[0086] ;

[0087] Step 2.2: Eliminate invalid points from the first sound velocity profile estimated for each normal wave mode:

[0088] ;

[0089] in, For the The node of the vertical mode function of the simple normal wave, that is, the zero crossing point;

[0090] Step 2.3: Smooth the first sound velocity profile of each simple normal wave mode estimate after removing invalid points to obtain the second sound velocity profile of each simple normal wave mode estimate, which is in the following form:

[0091] .

[0092] In this optional embodiment, when the loss function is minimum, the similarity between the sound velocity profiles estimated by each simple normal wave mode is maximum; specifically, the target motion speed is set to , search interval , scan the target movement speed search interval, and take the speed value corresponding to the minimum loss function as the estimated value of the target movement speed , at this time, the similarity between the sound velocity profiles estimated by each simple normal wave mode is the largest.

[0093] In addition, in this optional embodiment, the loss function can be calculated using the second sound velocity profile of each normal wave mode after the smoothing process in step 2.3.

[0094] In an optional embodiment, in step 3, the loss function The form is as follows:

[0095] .

[0096] Example 2:

[0097] A sound velocity profile inversion method based on modal decomposition includes any one of the target motion velocity estimation methods provided in this embodiment, further comprising the following steps:

[0098] Step 4: Estimated target speed The estimated sound velocity profiles of the corresponding simple normal wave modes are calculated. , the calculation formula is as follows:

[0099] .

[0100] In this optional embodiment, the first sound speed profile estimated from each simple normal wave mode after processing in step 2.1 and step 2.2 can be used, or the second sound speed profile estimated from each simple normal wave mode after smoothing in step 2.3 can be used to calculate the estimated result of the sound speed profile.

[0101] In an optional embodiment, the method further includes the following steps:

[0102] Step 5: Estimation of the sound velocity profile Perform maximum and minimum normalization to obtain , and Input into the denoising autoencoder neural network to get the output of the network ,right Perform the inverse normalization operation to obtain the optimized result of the sound velocity profile , where a denoising autoencoder neural network is trained using simulated generated data.

[0103] 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 estimated result of the corresponding sound speed profile without noise.

[0104] The noise autoencoder neural network is trained by simulating the generated data. Specifically, the sound velocity profile is regarded as a simple smooth curve on a two-dimensional plane, that is, the sound velocity profile as a label is generated by using quadratic functions, linear functions, piecewise linear functions, etc. , by adding random noise to the label to obtain the sound velocity profile containing noise as input , and then map the label and input to the [0,1] interval through maximum-minimum normalization to obtain the label and input and input , and the adaptive moment estimation Adam optimizer optimizes the loss function, the loss function is as follows:

[0105] ;

[0106] in, is the output 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 using existing technology and will not be elaborated here.

[0107] After the denoising autoencoder neural network training is completed, the estimated results of the sound speed profile After the maximum-minimum normalization, the data is input into the trained denoising autoencoder neural network to obtain the output of the network. ,right Perform the inverse normalization operation to obtain the optimized result of the sound velocity profile .in, The form is as follows:

[0108] ;

[0109] in, is the estimated result of the normalized sound speed profile.

[0110] In the target motion velocity estimation and sound velocity profile inversion method based on modal decomposition of this embodiment, the sound velocity profile is estimated using the modal difference equation in step 2. In steps 3 and 4, based on the physical facts that the target motion velocity and the simple normal wave modal parameters are not independent and the sound velocity profile and the simple normal wave modal parameters are associated, the target motion velocity is estimated using the similarity between the sound velocity profiles estimated by each simple normal wave modal.

[0111] The modal decomposition-based target motion velocity estimation and sound velocity profile inversion method of this embodiment utilizes the narrowband signal radiated by the moving target to achieve target motion velocity estimation in an unknown ocean environment, and passive sound velocity profile inversion in the case of a non-cooperative sound source. This effectively solves the limitation of traditional target velocity estimation requiring a known sound velocity profile, while avoiding the dependence of traditional sound velocity profile inversion on prior information such as historical sound velocity profiles and seabed sediments. It can be used for underwater target positioning, underwater navigation, and communication, and is suitable for carrier platforms such as buoys and buoys.

[0112] Example 3:

[0113] In order to verify the target motion velocity estimation and sound velocity profile inversion method based on modal decomposition of this embodiment, a simulation was performed with the following parameters: 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, and the seabed longitudinal wave speed is 25 m. is 1688 m / s, and the seabed density 1.81 g / ml, sparse attenuation is 0.5dB / λ, where λ is the wavelength.

[0114] Figure 4 is a graph showing the target velocity estimation results, where the blue line represents the loss function that measures the similarity between the sound velocity profiles corresponding to each normal wave mode, the black asterisk represents the actual target velocity (5 m / s), and the red circle represents the estimated target velocity (5 m / s). It can be seen that the method of this embodiment can accurately estimate the target velocity.

[0115] Figure 5 : is the sound velocity profile inversion result diagram, where the black dashed line represents the true sound velocity profile, the blue dotted line represents the estimated result of the sound velocity profile, and the red solid line represents the optimized result of the sound velocity profile estimation output by the denoising self-editing network. The average relative error is 0.0004, which shows that the method of this embodiment can accurately realize the sound velocity profile inversion.

[0116] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for estimating target motion speed based on modal decomposition, characterized in that: The steps include: Step 1: Obtain the two-dimensional frequency domain sound field, obtain the vertical mode function of the simple normal wave through singular value decomposition, and obtain the horizontal wave number of the simple normal wave through Fourier transform; Step 2: Substitute the normal wave vertical mode function and the normal wave horizontal wave number into the modal difference equation to obtain the estimated sound velocity profile of each normal wave mode; Step 3: Set a loss function to measure the similarity between the sound velocity profiles corresponding to each simple normal wave mode, set the target motion velocity search interval, scan the target motion velocity search interval, and the speed value corresponding to the minimum loss function is the target motion velocity estimation value; The step 1 comprises the following steps: Step 1.1: Obtain the target narrowband radiation signal s(t) received by the vertical array sensor array; Step 1.2: Perform short-time Fourier transform on the target narrowband radiation signal s(t) to construct a two-dimensional frequency domain sound field P. The form of P is as follows: [P] ij =p(z i ,r j ),i=1,2,...,N Z ,j=1,2,...,N R ; Among them, z i is the depth of the i-th sensor in the vertical array sensor array, N Z is the number of sensors in the vertical array sensor array, r j is the horizontal distance between the target and the vertical array sensor array corresponding to the jth sampling point, N R is the number of horizontal distance sampling points; The matrix product of the two-dimensional frequency domain sound field P is in the following form: P=e iπ / 4 ΦΛR; in, Where ρ is the water density, is the simple normal wave vertical mode function, z s is the depth of the target in the water, k m is the horizontal wave number of the simple normal wave, δ m′,m is the Kronecker delta function, m,m′=1,2,...,M, M is the number of the simple normal wave propagation mode; 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 vector of the matrix U is the simple normal wave vertical mode function Step 1.4: Assume the target speed is v k , perform Fourier transform on the matrix V to obtain the horizontal wave number k of the simple normal wave m (v k ); The step 2 comprises the following steps: Step 2.1: Set the normal wave modal parameters and the horizontal wave number k m (v k ) is substituted into the modal difference equation to obtain the first sound velocity profile of each simple normal wave mode estimate, which is in the following form: Step 2.2: Eliminate invalid points from the first sound velocity profile estimated for each normal wave mode: Where z(m) is the node of the mth normal wave vertical mode function, that is, the zero crossing point; Step 2.3: Smooth the first sound velocity profile of each simple normal wave mode estimate after removing invalid points to obtain the second sound velocity profile of each simple normal wave mode estimate, which is in the following form: In step 3, the loss function L(v k ) is of the following form:

2. The method for estimating target motion speed based on modal decomposition according to claim 1, characterized in that: The step 1.4 includes the following steps: Step 1.4.1: Perform Fourier transform on the matrix V to obtain g m (k′,v k ), g m (k′,v k ) is of the following form: Where k' is the wave number sampling point, m = 1, 2, ..., M, M is the number of the simple normal wave propagation mode; r j (v k )=r0+(j-1)v k Δt,j=1,2,...,N R The target movement speed is v k The horizontal distance between the target and the vertical array sensor array at time t, r0 is the initial horizontal distance, and Δt is the time resolution of the short-time Fourier transform of the target narrow-band radiation signal s(t); Step 1.4.2: g m (k′,v k ) The k' corresponding to the peak position is the horizontal wave number k of the simple normal wave m (v k ).

3. The method for estimating target motion speed based on modal decomposition according to claim 1, wherein: In step 2, the normal wave modal parameters and the horizontal wave number k m (v k ) is substituted into the modal difference equation, which is as follows: Where Δz is the vertical differential step size, Δz=z i+1 -z i , ω is the angular frequency, ω = 2πf, f is the frequency of the target radiation signal, and c is the speed of sound.

4. A sound velocity profile inversion method based on modal decomposition, characterized in that: The method for estimating target motion speed according to any one of claims 1 to 3 further comprises the following steps: Step 4: Estimated target speed The corresponding sound velocity profiles of each simple normal wave mode are calculated to estimate the sound velocity profile c est , the calculation formula is as follows:

5. The method for inverting a sound velocity profile based on modal decomposition according to claim 4, characterized in that: The following steps are also included: Step 5: Estimation of the sound velocity profile c est Perform maximum and minimum normalization to obtain c′ est , and c′ est Input into the denoising autoencoder neural network to obtain the network output c′ opt , for c′ opt Perform the inverse normalization operation to obtain the optimized result c of the sound velocity profile opt , where a denoising autoencoder neural network is trained using simulated generated data.

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