A sparse bayesian learning shallow target depth and horizontal distance passive estimation method

Abstract

This invention discloses a sparse Bayesian learning-based passive estimation method for the depth and horizontal distance of shallow-sea targets. Based on a priori sound velocity profiles and a hypothetical range of horizontal wavenumbers, the method calculates the hypothesis space of the mode depth function using the finite difference method. Vertical array data is preprocessed to the frequency domain, and a system of linear underdetermined equations relating the frequency domain vertical array data and the hypothesis space under sparse constraints is constructed. These equations are then solved using a sparse Bayesian learning algorithm to obtain an estimate of the horizontal wavenumber spectrum. Peak searching is performed on the horizontal wavenumber spectrum to estimate the order of the actual excitation mode and the horizontal wavenumber. The finite difference method is then used to estimate the mode depth function for each mode. The vertical array copy sound field at different depths and horizontal distances is calculated using the normal mode sound field formula. The vertical array copy sound field is multiplied by the conjugate transpose of the actual data to obtain a depth-horizontal distance ambiguity surface. The location of the surface maximum value is then used as an estimate of the source's depth and horizontal distance.

Description

Technical Field

[0001] This invention belongs to the field of target detection technology, specifically relating to a passive estimation method for the depth and horizontal distance of shallow sea targets using sparse Bayesian learning. Background Technology

[0002] The passive estimation of depth and horizontal distance of shallow-sea targets has always been a challenge in underwater acoustic signal processing. This is because the depth and horizontal distance information of shallow-sea targets is primarily contained in the vertical normal mode acoustic field. Model-driven methods, such as matched-field processing, require precise marine environmental parameters (mainly including sound velocity profiles, sea depth, and seabed characteristic parameters) to simulate the normal mode acoustic field as a copy. Then, the vertical receiver array data and the copy are correlated to estimate the target depth and horizontal distance. However, in reality, measuring seabed parameters is very costly and often difficult to obtain. Furthermore, the sea depth obtained from nautical charts is not accurate enough. The inaccuracies of these two types of parameters lead to a mismatch between the modeled acoustic field and the actual data, further resulting in serious position estimation errors or even complete estimation failure. Against this backdrop, research on passive positioning methods for shallow-sea targets under conditions of unknown seabed characteristics and precise sea depth has emerged in large numbers.

[0003] To address the issue of mismatch between the modeled sound field and actual data in traditional passive localization methods, existing and widely studied approaches include machine learning / deep learning, employing models such as support vector machines and deep neural networks. These methods directly learn the mapping relationship between data and target location, requiring no prior marine environmental parameters. However, they necessitate a large amount of reliable labeled data as a training set, which is relatively difficult to obtain in the underwater acoustics field. Furthermore, the trained models exhibit weak generalization ability and lack interpretability, limiting their application in marine environments with significant spatial and temporal variations. Summary of the Invention

[0004] The purpose of this invention is to provide a sparse Bayesian learning passive estimation method for the depth and horizontal distance of shallow sea targets under unknown seabed characteristics and precise sea depth conditions. This addresses the problem that traditional passive estimation methods for the depth and horizontal distance of shallow sea targets (matching field processing) proposed in the background art require precise marine environmental parameter modeling to copy the sound field, while in practice, the difficulty in obtaining seabed characteristic parameters and precise sea depth often leads to mismatch in matching field processing.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A passive estimation method for the depth and horizontal distance of shallow sea targets using sparse Bayesian learning includes the following steps:

[0007] Step 1: Based on the prior sound velocity profile and the horizontal wave number assumption interval, calculate the mode depth function assumption space using the finite difference method based on wave equation solving.

[0008] Step 2: Preprocess the vertical array data to the frequency domain, construct a linear underdetermined system of equations for the modulus depth function of the frequency domain vertical array data and hypothesis space under sparse constraints, and solve it using a sparse Bayesian learning algorithm to obtain an estimate of the horizontal wavenumber spectrum.

[0009] Step 3: Perform peak search on the estimated horizontal wavenumber spectrum to estimate the order and horizontal wavenumber of the actual excitation mode, and use the finite difference method to estimate the mode depth function of each mode.

[0010] Step 4: Calculate the vertical array copy sound field at different depths and horizontal distances according to the normal mode sound field formula;

[0011] Step 5: Multiply the vertical array copy sound field without depth and horizontal distance by the actual data using the conjugate transpose to obtain the depth-horizontal distance ambiguity surface. Find the location of the maximum value on the surface as the estimate of the source's depth and horizontal distance.

[0012] Preferably, in step 1, the method for obtaining the horizontal wavenumber hypothesis interval includes the following steps:

[0013] Determine the horizontal wavenumber k corresponding to the depth function of each mode excited by the ocean waveguide at that frequency based on the frequency value and sound velocity. r The interval 2πf / c b ≤k r ≤2πf / c w , where c w It is the lowest sound speed in the water layer, c b The speed of sound on the seabed is measured by sampling the interval at equal intervals, resulting in the hypothetical horizontal wavenumber interval [2πf / c]. b ]≤[k r1 k r2 , ..., k rm , ..., k rM ]≤[2πf / c w M represents the total number of horizontal wavenumber sampling points within the assumed interval.

[0014] Preferably, in step 1, the calculation process of the modulus depth function hypothesis space is as follows:

[0015] Linear interpolation of the sound velocity profile yields c(z) i ), i=1, 2,...,I, where z i =ih, where h is the depth interval between two difference points, and I is the total number of sampling points after interpolation;

[0016] Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, the modal depth function corresponding to each sampling point within the horizontal wave number assumption interval is solved. Then, all modal depth functions are sampled according to the depth of each element of the vertical array to obtain the modal depth function assumption space.

[0017] Preferably, step 2 includes the following steps:

[0018] Step 2.1: Read the vertical array data, divide each array element into time frames, and after performing windowed discrete Fourier transform, extract the frequency points of interest on the spectrum to obtain the frequency domain vertical array data y(f) of multiple snapshots.

[0019] Step 2.2, construct a system of linear underdetermined equations Where y(f) represents the preprocessed vertical matrix data in the frequency domain, with a dimension of J×1, where J is the number of elements in the vertical matrix; w = [w1, w2, ..., w m , ..., w M ] represents the horizontal wavenumber spectrum to be estimated; Φ m (z j k rm ) represents the horizontal wavenumber k rm The corresponding modulus depth function at the depth z of the j-th element j The sampled value at point n; n is the noise term;

[0020] Step 2.3: Solve using the sparse Bayesian learning algorithm to obtain an estimate of the horizontal wavenumber spectrum.

[0021] Preferably, step 3 includes the following steps:

[0022] Search horizontal wavenumber spectrum Each spectral peak in the spectrum is considered to have a peak position [k]. r1 , ...k rp , ..., k rP ] is an estimate of the horizontal wavenumber corresponding to each actual excitation mode, where P is the number of spectral peaks, i.e. the number of actual excitation modes;

[0023] Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, the horizontal wave number estimate [k] is obtained. r1 , ...k rp , ..., k rP The modulus depth function corresponding to each sampling point within the matrix is ​​obtained, and all modulus depth functions are sampled according to the depth of each element of the vertical matrix to obtain the estimated modulus depth function [Φ1, ... Φ]. p , …, Φ P ].

[0024] Preferably, step 4 includes the following steps:

[0025] Input depth z s Horizontal distance r s Vertical array element depth vector z, horizontal wavenumber estimation [k] r1 , ...k rp , ..., k rP] and modulus depth function estimation [Φ1,…Φ p , …, Φ P The copy sound field at different depths and horizontal distances is calculated based on the normal mode sound field formula: Then normalize p: p = p / ||p||2.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] The finite difference method is used to calculate the modulus-depth function corresponding to different horizontal wavenumbers. Based on this, a sparsity constraint is introduced, and a horizontal wavenumber spectrum estimation method based on sparse Bayesian learning is proposed. The normal mode acoustic field structure at different depths and horizontal distances is reconstructed from the horizontal wavenumber spectrum and modulus-depth function estimation, and further used for passive estimation of target depth and horizontal distance. This invention does not rely on seabed parameters and precise sea depth, requires less data, and does not require depth and horizontal distance labels. Attached Figure Description

[0028] Figure 1 This is a flowchart of the present invention.

[0029] Figure 2 This is a schematic diagram of the data preprocessing principle.

[0030] Figure 3 This is a schematic diagram of the sparse Bayesian learning algorithm.

[0031] Figure 4 This is a schematic diagram of a data processing program interface based on MATLAB.

[0032] Figure 5 These are schematic diagrams showing the estimation results of the horizontal wavenumber spectrum and the excitation mode depth function, respectively.

[0033] Figure 6 This is a schematic diagram of the target depth and horizontal distance ambiguity surface. Detailed Implementation

[0034] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0035] Reference Figure 1 As shown, this invention provides a sparse Bayesian learning passive estimation method for shallow sea target depth and horizontal distance under unknown seabed characteristics and precise sea depth conditions. The method mainly includes two parts: a horizontal wavenumber spectrum estimator and source depth and horizontal distance estimators based on the horizontal wavenumber spectrum estimator.

[0036] Specifically, the sparse Bayesian learning method for passively estimating the depth and horizontal distance of shallow sea targets includes six steps.

[0037] Step 1: Based on the prior sound velocity profile and the horizontal wavenumber assumption interval, calculate the hypothesis space of the mode depth function using the finite difference method.

[0038] The specific process for this step is as follows:

[0039] Step 1.1: Determine the horizontal wavenumber k corresponding to the depth function of each mode excited by the ocean waveguide at that frequency point based on the frequency value and the sound velocity. r The interval 2πf / c b ≤k r ≤2πf / c w , where c w It is the lowest sound speed in the water layer, c b The speed of sound on the seabed is measured by sampling the interval at equal intervals, resulting in the hypothetical horizontal wavenumber interval [2πf / c]. b ]≤[k r1 k r2 , ..., k rm , ..., k rM ]≤[2πf / c w M represents the total number of horizontal wavenumber sampling points within the assumed interval, and m is the index of one of the sampling points.

[0040] Step 1.2: Perform linear interpolation on the sound velocity profile (SSP) data to obtain c(z). i ), i=1, 2,...,I, where z i =ih, where h is the depth difference between the two interpolation points, and I is the total number of sampling points after interpolation;

[0041] Step 1.3: Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, solve for the horizontal wave number assumption interval [2πf / c]. b ]≤[k r1 k r2 , ..., k rm , ..., k rM ]≤[2πf / c w [Sampling points (horizontal wave values) k] rm The modulus depth function corresponding to m = 1, 2, ..., M is shown below:

[0042] Φ m (0, k) rm ) = 0,

[0043] Φ m (z1, k) rm ) = h,

[0044]

[0045] Φ m (z i k rm ) represents the horizontal wavenumber k rm The corresponding modulus depth function at depth z i The sampled value at point; c(z) i () is the sound velocity profile interpolated at depth z i The sampled value at the location, where I is the total number of sampled points after interpolation; h is the interval between two depth interpolation points;

[0046] Step 1.4: Sample all modulus depth functions based on the depth of each element of the vertical array to obtain the modulus depth function hypothesis space.

[0047] Step 2: Preprocess the vertical array data to the frequency domain, and construct the modulus depth function [Φ1, Φ2, ..., Φ] of the frequency domain vertical array data y(f) and the hypothesis space. m , ..., Φ M The linear underdetermined equations under sparse constraints are solved using a sparse Bayesian learning algorithm, yielding an estimate of the horizontal wavenumber spectrum. Figure 5 As shown in (a).

[0048] Reference Figure 2 As shown, the preprocessing of the vertical array data includes the following steps:

[0049] In this embodiment, MATLAB is used to read the vertical array data, and the N array data elements are divided into frames with a frame length of 1 second and an inter-frame overlap rate of 50%, resulting in a total of L frames of data. Windowed FFT is performed on each frame of data for each array element to obtain the spectrum. The Kasier window is selected as the window function with a parameter of 4.7. The complex sound pressure value of the frequency of interest is extracted from it to obtain the frequency domain vertical array data of L snapshots. Each snapshot contains N array elements and is an N×1 vector.

[0050] In step 2 of this invention, the frequency domain vertical matrix data can be viewed as a weighted sum of the depth functions of each mode in the hypothetical space, denoted as:

[0051]

[0052] Where y(f) is the preprocessed vertical array data to the frequency domain, with a dimension of J×1, where J is the number of vertical array elements;

[0053] w = [w1, w2, ..., w m , ..., w M ] represents the horizontal wavenumber spectrum to be estimated; Φ m (z j k rm ) represents the horizontal wavenumber krm The corresponding modulus depth function at the depth z of the j-th element j The sampled value at point n; n is the noise term.

[0054] Since the number of mode depth functions in the hypothesis space is often much larger than the number of array elements, the system of equations is underdetermined. Furthermore, since the number of modes actually excited is very limited and much smaller than the number of mode depth functions in the hypothesis space, the solution w of this linear underdetermined system of equations is sparse. At this point, the problem of estimating the horizontal wavenumber and mode depth function can be transformed into a linear underdetermined inverse problem under sparse constraints.

[0055] Reference Figure 3 As shown, the implementation of this sparse Bayesian learning algorithm consists of the following parts:

[0056] ① Parameter prior distribution modeling, which involves modeling each element w in the parameter vector w to be determined. m The model is based on a mean of 0 and a variance of γ. m The elements are distributed by a complex Gaussian distribution, and are independent of each other, with a variance of γ. m The unknown variable is vector w, which follows a multivariate complex Gaussian distribution.

[0057]

[0058]

[0059] Γ=E[ww H ]=diag(γ)

[0060] ② Data likelihood distribution modeling: The pseudo-frequency domain vertical matrix data y and the noise term n are independent of each other, and each element in n is independent and follows a mean of 0 and a variance of σ. 2 Gaussian white noise with variance σ 2 The unknown is the likelihood distribution of the data, which can be written as a multivariate complex Gaussian distribution: p(y|w)=CN(y;Ψw,σ 2 I); Expanded to a multi-shot format

[0061]

[0062] ③ Stochastic maximum likelihood parameter estimation: Multiply the prior distribution of the parameter and the likelihood distribution of the data, and integrate to find the marginal distribution of the parameter w. This is called the second similarity distribution; the unknown parameters are obtained by maximizing the second similarity distribution. Here, a fixed-point update algorithm with low computational complexity is used for parameter estimation, as shown in the code below. Figure 5 As shown.

[0063] ④ Calculate the posterior probability distribution of parameter w, which follows a Gaussian distribution:

[0064] The estimate of parameter w is equal to the posterior mean μ. w .

[0065] In this invention, the method of using sparse Bayesian learning algorithm to solve linear underdetermined inverse problems is a conventional technique in the field, and those skilled in the art will not elaborate further.

[0066] Step 3: Perform peak search on the estimated horizontal wavenumber spectrum to estimate the order and horizontal wavenumber of the actual excitation mode, and use the finite difference method to estimate the mode depth function of each mode.

[0067] In step 3 of this invention, the horizontal wavenumber spectrum is obtained by solving the linear underdetermined inverse problem based on the sparse Bayesian learning algorithm in step 2. Then, search the horizontal wavenumber spectrum. The peak positions [k] of each spectral peak in the spectrum are obtained. r1 , ...k rp , ..., k rP ], that is, the estimation results of the horizontal wavenumbers corresponding to each actual excitation mode, where P is the number of spectral peaks and p represents the index, i.e., the number of actual excitation modes, based on the horizontal wavenumber estimation results [k r1 , ...k rp , ..., k rP The modulus depth function [Φ1, ... Φ1] is calculated using the finite difference method. p , …, Φ P The specific process is as follows:

[0068] Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, the horizontal wave number estimate [k] is obtained. r1 , ...k rp , ..., k rP Sampling points k within ] rp The corresponding modulus depth function is obtained, and all modulus depth functions are sampled according to the depth of each element of the vertical array to obtain the estimated modulus depth function [Φ1, ... Φ]. p , …, Φ P ]like Figure 5 As shown in (b).

[0069] Step 4: Calculate the vertical array copy sound field at different depths and horizontal distances according to the normal mode sound field formula.

[0070] In step 4 of this invention, the depth z is input. s Horizontal distance r s Vertical array element depth vector z, horizontal wavenumber [k] r1 , ...k rp , ..., k rP ] and modulus depth function [Φ1, ... Φ p , …, Φ PThe copy sound field at different depths and horizontal distances is calculated based on the normal mode sound field formula: The attenuation effect of each mode is ignored, and P is normalized to P = P / ||P||2.

[0071] Step 5: Perform correlation processing (conjugate transpose multiplication) on the vertical array copy sound field with different depth and horizontal distances respectively with the actual data to obtain the depth-horizontal distance ambiguity surface. The calculation process is as follows:

[0072]

[0073] Among them, B(z) s r s f) is the ambiguity surface at frequency f, p(z) s r s () represents the depth z after normalization. s Horizontal distance r s The corresponding copy sound field, y(f), is the frequency domain vertical array data; the location of the maximum value of the ambiguity surface is found as the estimate of the depth and horizontal distance of the source.

[0074] Reference Figure 6 As shown, the location of the maximum value on the surface (that is, the reddest part in the figure) is the estimate of the depth and horizontal distance of the source.

[0075] This invention combines data-driven and model-driven approaches. It constructs a hypothesis space for the modulus-depth function using the finite difference method and sound velocity profiles. Based on this, it transforms the estimation of the horizontal wavenumber spectrum into a sparsely constrained linear underdetermined inverse problem using the formula for the normal modulus solution of the wave equation. Then, it estimates the horizontal wavenumber spectrum using a sparse Bayesian learning algorithm. Furthermore, it constructs a copy sound field and estimates the target's depth and horizontal distance using a correlator. Compared to traditional model-driven matching field processing methods, it is more tolerant as it does not rely on seabed parameters and precise sea depth. Compared to data-driven machine learning / deep learning methods, it requires less data and does not need depth and horizontal distance labels. In summary, the method proposed in this invention overcomes the problem of the difficulty in effectively utilizing marine environmental knowledge in passive target localization.

[0076] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A passive estimation method for the depth and horizontal distance of shallow sea targets using sparse Bayesian learning, characterized in that, Includes the following steps: Step 1: Based on the prior sound velocity profile and the horizontal wave number assumption interval, calculate the mode depth function assumption space using the finite difference method based on wave equation solving. Step 2: Preprocess the vertical array data to the frequency domain, construct a linear underdetermined system of equations for the modulus depth function of the frequency domain vertical array data and hypothesis space under sparse constraints, and solve it using a sparse Bayesian learning algorithm to obtain an estimate of the horizontal wavenumber spectrum. Step 3: Perform peak search on the estimated horizontal wavenumber spectrum to estimate the order and horizontal wavenumber of the actual excitation mode, and use the finite difference method to estimate the mode depth function of each mode. Step 4: Calculate the vertical array copy sound field at different depths and horizontal distances according to the normal mode sound field formula; Step 5: Multiply the vertical array copy sound field without depth and horizontal distance by the actual data with the conjugate transpose to obtain the depth-horizontal distance ambiguity surface, and find the location of the maximum value of the surface as the estimate of the depth and horizontal distance of the source. In step 1, the method for obtaining the horizontal wavenumber hypothesis interval includes the following steps: According to the frequency point value and the sound speed, a horizontal wave number k corresponding to a depth function of each order mode excited by the ocean waveguide at the frequency point is determined r of the interval 2πf / c b ≤k r ≤2πf / c w , wherein c w is the lowest sound speed of the water layer, c b is the sound speed of the seabed, the interval is sampled at equal intervals to obtain a horizontal wave number hypothesis interval [2πf / c b ]≤[k r1 , k r2 ,..., k rm ,..., k rM ]≤[2πf / c w ], and M is the total sampling point number of the horizontal wave number in the hypothesis interval; In step 1, the calculation process of the modulus depth function hypothesis space is as follows: Linear interpolation of the sound velocity profile yields c(z) i ), i=1, 2,...,I, where z i =ih, where h is the depth interval between two difference points, and I is the total number of sampling points after interpolation; Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, the modal depth function corresponding to each sampling point within the horizontal wave number assumption interval is solved, and all modal depth functions are sampled according to the depth of each element of the vertical array to obtain the modal depth function assumption space. Step 4 includes the following steps: Input depth z s Horizontal distance r s Vertical array element depth vector z, horizontal wavenumber estimation [k] r1 , ...k rp , ..., k rP ] and modulus depth function estimation [Φ1,…Φ p , …, Φ P The copy sound field at different depths and horizontal distances is calculated based on the normal mode sound field formula: And normalize p to p = p / ||p||2.

2. The passive estimation method for the depth and horizontal distance of a shallow sea target using sparse Bayesian learning as described in claim 1, characterized in that, Step 2 includes the following steps: Step 2.1: Read the vertical array data, divide each array element into time frames, and after performing windowed discrete Fourier transform, extract the frequency points of interest on the spectrum to obtain the frequency domain vertical array data y(f) of multiple snapshots. Step 2.2, construct a system of linear underdetermined equations Where y(f) represents the preprocessed vertical matrix data in the frequency domain, with a dimension of J×1, where J is the number of elements in the vertical matrix; w = [w1, w2, ..., w m , ..., w M ] represents the horizontal wavenumber spectrum to be estimated; Φ m (z j k rm ) represents the horizontal wavenumber k rm The corresponding modulus depth function at the depth z of the j-th element j The sampled value at point n; n is the noise term; Step 2.3: Solve using the sparse Bayesian learning algorithm to obtain an estimate of the horizontal wavenumber spectrum.

3. The passive estimation method for the depth and horizontal distance of shallow sea targets using sparse Bayesian learning as described in claim 1, characterized in that... Step 3 includes the following steps: Searching the horizontal wavenumber spectrum Each spectral peak is considered to have a peak position [k]. r1 , ...k rp , ..., k rP] It is an estimate of the horizontal wavenumber corresponding to each actual excitation mode, where P is the number of spectral peaks, i.e. the number of actual excitation modes; Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, the horizontal wave number estimate [k] is obtained. r1 , ...k rp , ..., k rp The modulus depth function corresponding to each sampling point within the matrix is ​​obtained, and all modulus depth functions are sampled according to the depth of each element of the vertical matrix to obtain the estimated modulus depth function [Φ1, ... Φ]. p , …, Φ P ].

Images