An underwater DOA estimation method in autocorrelation domain based on sparse nested linear arrays

Abstract

The present application proposes an underwater DOA estimation method based on the autocorrelation domain of a sparse nested linear array, which specifically includes the following steps: obtaining source signals of multiple different angles received by a sparse nested linear array transducer; performing denoising on the received source signals using a DWT denoising module; further optimizing the parameters to obtain a spatial spectrum based on the autocorrelation domain; obtaining the predicted angle of the signal source by searching for the peak of the spatial spectrum in the autocorrelation domain; and evaluating the performance of the DOA estimation method by the root mean square error. The underwater acoustic signal model constructed based on the sparse nested linear array SNLA is denoised by the DWT denoising module to improve the signal-to-noise ratio, thereby improving the DOA estimation performance in a marine environment with severe multipath effects; the predicted angle of the signal source is obtained by this method, and the analysis of the mean square error of these predicted angles can ensure accurate positioning of the signal source.

Description

Technical Field

[0001] The present application belongs to the technical field of target positioning, and specifically relates to an underwater DOA estimation method based on the autocorrelation domain of a sparse nested linear array. Background Art

[0002] In recent years, Direction of Arrival (DOA) estimation has been one of the research hotspots in the field of array signal processing. It has received extensive attention and applications in civil and military fields, such as marine information acquisition, modern underwater defense, underwater environment monitoring, wireless communications, navigation, and radar. However, in the marine environment with severe multipath effects, the complex ocean channel poses a great challenge to the estimation of underwater signals. Therefore, it is necessary to study an effective algorithm to improve the accuracy of DOA estimation of signals in complex underwater environments.

[0003] In most practical applications, achieving high-precision estimation, acceptable performance and low cost is the most urgent problem to be solved. Therefore, the current research hotspot is to use fewer physical sensors to detect more sources, and many research results have been achieved. The mainstream idea to solve this problem is to change the structure of the physical array to generate a virtual linear array with greater freedom, rather than directly increasing the number of physical arrays. Recently, based on this idea, a sparse array configuration with a non-uniform linear array structure has been proposed, and the most typical of these sparse array configurations are minimum redundant arrays, minimum hole arrays, nested arrays and coprime arrays.

[0004] However, when the number of physical sensors is uncertain, MRA and MHA have the disadvantage that the physical position of the sensors cannot obtain achievable degrees of freedom in a closed form, which hinders the in-depth study of MRA and MHA in DOA estimation. In traditional nested arrays, due to the small distance between sensor elements, mutual coupling effects are generated, which in turn affects the DOA estimation performance. While coprime arrays obtain many more degrees of freedom than the total number of sensors, there is no mutual coupling problem. In order to reduce the influence of mutual coupling effects, Li et al. proposed a sparse nested linear array. On the basis of the traditional nested array, the distance between sensor elements is increased by the sparse coefficient, which reduces the mutual coupling effect and increases the array aperture.

[0005] In most studies on DOA estimation, high-resolution subspace-based algorithms such as MUSIC, ESPRIT, and the partial spectrum search MUSIC method (PSS-MUSIC) are used for DOA estimation. However, these methods may produce some pseudo DOAs when there are many signal sources. Zhang et al. applied the ESPRIT method to the obtained covariance matrix to obtain the closed-form DOA and reduce the computational complexity. Yin et al. introduced LASSO to perform DOA estimation using all virtual sensors of the coprime array, which is based on sparse representation. However, this method will cause DOA performance degradation due to the grid mismatch effect. Li et al. proposed the SULA-DFT algorithm to solve the DOA estimation problem of sparse ULA.

[0006] The present invention proposes an underwater DOA estimation method based on the autocorrelation domain of a sparse nested linear array. First, an underwater acoustic signal model is constructed based on the sparse nested linear array, and the original signal received by the array is denoised using a DWT denoising module. Then, the autocorrelation domain is constructed based on the covariance matrix of the sparse nested linear array, and the generalized eigenvalue problem is solved based on the autocorrelation domain. Finally, based on the idea of ​​alternating optimization, the parameters are optimized to obtain a spatial spectrum based on the autocorrelation domain, and DOA estimation is performed by searching for the peak of the spatial spectrum. This method is a more accurate DOA estimation method, which can accurately locate different signal sources in a complex marine environment.

[0007] Application Contents

[0008] The technical problem solved by the present invention is to provide an underwater DOA estimation method based on the autocorrelation domain of a sparse nested linear array to solve the shortcomings of the above-mentioned background technology.

[0009] This application proposes an underwater DOA estimation method based on the autocorrelation domain of a sparse nested linear array, which specifically includes the following steps:

[0010] Step 1: obtaining signal sources at multiple different angles received by the sparse nested linear array transducer;

[0011] Step 2: Use the DWT denoising module to perform denoising on the received signal source;

[0012] Step 3: construct an autocorrelation sequence based on the covariance matrix, and use the autocorrelation sequence to solve the generalized eigenvalue;

[0013] Step 4: Further optimize the parameters to obtain the spatial spectrum based on the autocorrelation domain;

[0014] Step 5: obtaining the predicted angle of the signal source by searching for the peak of the spatial spectrum in the autocorrelation domain; and

[0015] Step 6: Evaluate the performance of the DOA estimation method by the root mean square error.

[0016] The underwater acoustic signal model constructed based on the sparse nested linear array SNLA is denoised by the DWT denoising module to improve the signal-to-noise ratio of the signal, thereby improving the DOA estimation performance in the marine environment with severe multipath effects; the spatial spectrum obtained based on the autocorrelation domain of the sparse nested linear array SNLA has the characteristics of no false peaks and small sidelobe width, which can improve the directivity and anti-interference ability of underwater DOA estimation; by controlling the signal-to-noise ratio and the number of snapshots of the signal at the transmitting end, the signals transmitted by the signal source in a complex marine environment can be received, and the accuracy of this method is better than that of discrete Fourier transform and smoothed MUSIC; the predicted angle of the signal source is obtained by this method, and the mean square error of these predicted angles can be analyzed to ensure the accurate positioning of the signal source.

[0017] Preferably, in the first step, it includes defining an underwater acoustic signal array model:

[0018] In the sparse nested linear array SNLA, the location of the physical sensor of the sparse nested linear array SNLA is represented as Sαd, where α is the sparsity coefficient, d=λ / 2, and S is represented as:

[0019]

[0020] Further definition

[0021] Then a1(θ q ) and a2(θ q ) are respectively expressed as:

[0022]

[0023] Where a1(θ q ) is the direction subvector of the qth source corresponding to the first uniform linear array ULA, a2(θ q ) is the direction subvector of the qth source corresponding to the second uniform linear array ULA; therefore, the direction matrix of the sparse nested linear array SNLA is expressed as:

[0024]

[0025] Further preferably, it is further assumed that there are Q uncorrelated narrowband underwater acoustic signal sources from {θ1, θ2, ..., θ q ,…,θ Q} direction hits the sparse nested linear array SNLA, and the target transmits a signal with a carrier frequency of f0Hz and an amplitude of a q(t), since w0=2πf0, the signal is expressed as:

[0026]

[0027] And the signal received by the sparse nested linear array at time t can be expressed as:

[0028]

[0029] where s(t) is the signal vector and n(t) is a vector with zero mean and variance σ. 2 The additive white Gaussian noise vector of . The sparse nested linear array SNLA has the characteristics of being less affected by the mutual coupling effect and having a large array aperture to receive signals from multiple sources at different angles, and can receive more signal sources.

[0030] Preferably, in the second step, a DWT denoising module is defined:

[0031] The DWT denoising module for the time domain signal x(t) is defined as:

[0032]

[0033] where j = 0, 1, 2, ..., log2(T), k = 1, 2, ..., T2 -j , T represents the number of snapshots of the signal.

[0034] The DWT denoising module can improve the signal-to-noise ratio of the signal and reduce the impact of the complex ocean environment on the DOA estimation performance.

[0035] Further preferably, the DWT denoising module includes signal decomposition, threshold processing and signal reconstruction.

[0036] Further preferably, in the signal decomposition, the original signal x(t) is first passed through a half-band high-pass filter and a low-pass filter to eliminate half of the samples, and then the signal is down-sampled for further decomposition.

[0037] Further preferably, in the threshold processing, a soft method or a hard method is used to perform threshold processing on the signal to obtain an optimal component for reconstructing the denoised signal;

[0038] The calculation formula for threshold processing of the signal by the hard method is as follows:

[0039]

[0040] The calculation formula for the soft method to process the signal threshold is as follows:

[0041] Soft threshold y=sign(x)(|x|-ξ).

[0042] Further preferably, in the signal reconstruction, the signal of each level is downsampled, and then passed through a half-band high-pass filter and a low-pass filter respectively, and finally the outputs of the half-band high-pass filter and the low-pass filter are added to obtain a signal

[0043] Further preferably, in the third step, after denoising by the DWT denoising module, The covariance matrix of is:

[0044]

[0045] Further preferably, in the third step, it includes defining the spatial autocorrelation sequence of the sparse nested linear array SNLA:

[0046]

[0047] Where L = M2(M1+1)-1,

[0048] Further is defined as the generalized eigenvalue, where B, C, and γ are set to:

[0049]

[0050]

[0051] γ=σ 2

[0052] The specific steps for solving the generalized eigenvalue are as follows:

[0053] S31. Define the matrix necessary to solve the generalized eigenvalue

[0054] A2=B H B

[0055] S32, Reconstruction Matrix

[0056]

[0057] S33, obtaining eigenvalues ​​and eigenvectors by solving Px=γJx;

[0058] S34, taking the smallest eigenvalue among the obtained eigenvalues ​​as γ, and taking its corresponding eigenvector as x;

[0059] S35. Dividing vector x by its first element can obtain vector C.

[0060] The spatial spectrum generated by the autocorrelation domain of the sparse nested linear array SNLA has no false peaks, which realizes the accurate estimation of the angle and achieves the purpose of accurate positioning; from the given mean square error, it can be seen that when the signal-to-noise ratio and the number of snapshots increase, the performance of this method is better than the DFT method and the SSMUSIC method, ensuring the estimation accuracy of different angle signal sources in complex ocean environments.

[0061] Compared with the prior art, the beneficial results of this application are:

[0062] (1) The underwater acoustic signal model based on the sparse nested linear array (SNLA) is denoised by the DWT denoising module to improve the signal-to-noise ratio, thereby improving the DOA estimation performance in the marine environment with severe multipath effects.

[0063] (2) Based on the characteristics of no false peaks and small sidelobe width of the spatial spectrum obtained in the autocorrelation domain based on the sparse nested linear array SNLA, the directivity and anti-interference ability of underwater DOA estimation can be improved;

[0064] (3) By controlling the signal-to-noise ratio and the number of snapshots at the transmitting end, the signals transmitted by the signal source in complex ocean environments can be received, and the accuracy of this method is better than that of discrete Fourier transform and smoothed MUSIC;

[0065] (4) The predicted angles of the signal source are obtained by this method, and the mean square error of these predicted angles can be analyzed to ensure accurate positioning of the signal source. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and are used together with the description to explain the principles of the present application. It will be easy to recognize other embodiments and many expected advantages of the embodiments because they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. The same reference numerals refer to corresponding similar parts.

[0067] Figure 1 A flowchart of the underwater DOA estimation method based on the autocorrelation domain of sparse nested linear arrays of the present application;

[0068] Figure 2 A schematic diagram of an array model of SNLA in the underwater DOA estimation method based on the autocorrelation domain of sparse nested linear arrays of the present application;

[0069] Figure 3 A schematic diagram of a DWT denoising module in the underwater DOA estimation method based on the autocorrelation domain of a sparse nested linear array of the present application;

[0070] Figure 4 It is the spatial spectrum of the SSMUSIC method in the embodiment of the present application;

[0071] Figure 5 It is the spatial spectrum of the DFT method in the embodiment of this application;

[0072] Figure 6 Spatial spectrum of the SNLA-AD-DWT method in the underwater DOA estimation method based on the autocorrelation domain of the sparse nested linear array of the present application;

[0073] Figure 7 Schematic diagram of the root mean square error of the SSMUSIC, DFT, and SNLA-AD-DWT methods under different signal-to-noise ratios in the embodiments of the present application;

[0074] Figure 8 The root mean square error of SSMUSIC, DFT, and SNLA-AD-DWT methods under different snapshot numbers in the embodiments of the present application. DETAILED DESCRIPTION

[0075] In the following detailed description, reference is made to the accompanying drawings, which form a part of the detailed description and are shown by illustrative specific embodiments in which the present application can be practiced. To this end, directional terms, such as "top", "bottom", "left", "right", "up", "down", etc., are used with reference to the orientation of the figures described. Because the components of the embodiments can be positioned in several different orientations, directional terms are used for the purpose of illustration and are by no means limiting. It should be understood that other embodiments may be utilized or logical changes may be made without departing from the scope of the present application. Therefore, the following detailed description should not be adopted in a limiting sense, and the scope of the present application is defined by the appended claims.

[0076] Figure 1 FIG. 1 is a flow chart of an underwater DOA estimation method based on the autocorrelation domain of a sparse nested linear array (SNLA). Figure 1 As shown, the present application proposes an underwater DOA estimation method based on the autocorrelation domain of a sparse nested linear array, and the method specifically includes the following steps:

[0077] Step 1: obtaining signal sources at multiple different angles received by the sparse nested linear array transducer;

[0078] Specifically, define the underwater acoustic signal array model:

[0079] In the sparse nested linear array SNLA, the location of the physical sensor of the sparse nested linear array SNLA is represented as Sαd, where α is the sparsity coefficient, d=λ / 2, and S is represented as:

[0080]

[0081] Further definition

[0082] Then a1(θ q ) and a2(θ q ) are respectively expressed as:

[0083]

[0084] Where a1(θ q ) is the direction subvector of the qth source corresponding to the first uniform linear array ULA, a2(θ q ) is the direction subvector of the qth source corresponding to the second uniform linear array ULA; therefore, the direction matrix of the sparse nested linear array SNLA is expressed as Figure 2 As shown:

[0085]

[0086] Further assume that there are Q uncorrelated narrowband underwater acoustic signal sources from {θ1, θ2, …, θ q ,…,θ Q} direction hits the sparse nested linear array SNLA, and the target transmits a signal with a carrier frequency of f0Hz and an amplitude of a q (t), since w0=2πf0, the signal is expressed as:

[0087]

[0088] And the signal received by the sparse nested linear array at time t can be expressed as:

[0089]

[0090] where s(t) is the signal vector and n(t) is a vector with zero mean and variance σ. 2 The additive white Gaussian noise vector of . The sparse nested linear array SNLA has the characteristics of being less affected by the mutual coupling effect and having a large array aperture to receive signals from multiple sources at different angles, and can receive more signal sources.

[0091] Step 2: Use the DWT denoising module to denoise the received signal source;

[0092] like Figure 3 As shown, the DWT denoising module is further defined:

[0093] The DWT denoising module of the time domain signal x(t) is defined as:

[0094]

[0095] where j = 0, 1, 2, ..., log2(T), k = 1, 2, ..., T2 -j , T represents the number of snapshots of the signal.

[0096] The DWT denoising module can improve the signal-to-noise ratio of the signal and reduce the impact of the complex ocean environment on the DOA estimation performance.

[0097] Specifically, the DWT denoising module includes signal decomposition, threshold processing and signal reconstruction. In signal decomposition, the original signal x(t) is first passed through a half-band high-pass filter and a low-pass filter to eliminate half of the samples, and then the signal is downsampled for further decomposition; in threshold processing, the signal is threshold processed using a soft method or a hard method to obtain the optimal component of the reconstructed denoised signal;

[0098] Among them, the calculation formula for threshold processing of the signal by the hard method is as follows:

[0099]

[0100] The calculation formula for the soft method to process the signal threshold is as follows:

[0101] Soft threshold y=sign(x)(|x|-ξ);

[0102] In signal reconstruction, the signal of each level is downsampled, and then passed through a half-band high-pass filter and a low-pass filter respectively, and finally the outputs of the half-band high-pass filter and the low-pass filter are added to obtain the signal

[0103] Step 3: construct an autocorrelation sequence based on the covariance matrix, and use the autocorrelation sequence to solve the generalized eigenvalue;

[0104] After denoising by the DWT denoising module, we get The covariance matrix of is:

[0105]

[0106] Furthermore, it also includes defining the spatial autocorrelation sequence of the sparse nested linear array SNLA:

[0107]

[0108] Where L = M2(M1+1)-1,

[0109] Further is defined as the generalized eigenvalue, where B, C, and γ are set to:

[0110]

[0111] γ=σ 2

[0112] The specific steps for further solving the generalized eigenvalues ​​are as follows:

[0113] S31. Define the matrix necessary to solve the generalized eigenvalue

[0114] A2=B H B

[0115] S32, Reconstruction Matrix

[0116]

[0117] S33, obtaining eigenvalues ​​and eigenvectors by solving Px=γJx;

[0118] S34, taking the smallest eigenvalue among the obtained eigenvalues ​​as γ, and taking its corresponding eigenvector as x;

[0119] S35. Dividing vector x by its first element can obtain vector C.

[0120] Step 4: Further optimize the parameters to obtain the spatial spectrum based on the autocorrelation domain;

[0121] In a specific embodiment, the obtained eigenvalue γ and the vector C are optimized to further obtain a spatial spectrum based on the autocorrelation domain.

[0122] Step 5: obtaining the predicted angle of the signal source by searching for the peak of the spatial spectrum in the autocorrelation domain; and

[0123] Step 6: Evaluate the performance of the DOA estimation method by the root mean square error.

[0124] Figure 4-Figure 6 The spatial spectra of the SSMUSIC method, DFT method and SNLA-AD-DWT method are shown as follows: Figure 4-Figure 6 As shown in Figure 3, the DOA estimation performance of the three methods is evaluated by the presence or absence of false peaks in the spatial spectrum and the sidelobe width.

[0125] Figure 7-Figure 8 The following table shows the root mean square error of SSMUSIC, DFT, and SNLA-AD-DWT methods under different signal-to-noise ratios and snapshot numbers. Figure 7 , 8 As shown in Figure 3, the DOA estimation performance of the three methods is evaluated by calculating the root mean square error between the predicted angle and the actual angle.

[0126] The purpose of the present invention is to use the DWT denoising module to perform denoising on the original signal received by SNLA to improve the signal-to-noise ratio of the signal; the spatial spectrum obtained by the autocorrelation domain of SNLA has the characteristics of no false peaks and small sidelobe width, which can improve the directionality and anti-interference ability of underwater DOA estimation; by controlling the signal-to-noise ratio and the number of snapshots of the signal at the transmitting end, the signal transmitted by the signal source in a complex marine environment can be received, and the accuracy of the method is better than that of discrete Fourier transform and smoothed MUSIC.

[0127] The predicted angles of the signal source are obtained by the above method, and the mean square errors of these predicted angles can be analyzed to ensure accurate positioning of the signal source.

[0128] The above description is only a preferred embodiment of the present application and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the present application is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above invention concept. For example, the above features are replaced with the technical features with similar functions disclosed in this application (but not limited to) by each other to form a technical solution.

Claims

1. An underwater DOA estimation method based on the autocorrelation domain of sparse nested linear arrays, characterized in that: The method specifically comprises the following steps: Step 1: Obtain signal sources at multiple different angles received by the sparse nested linear array transducer; including defining the underwater acoustic signal array model: In the sparse nested linear array SNLA, the location of the physical sensor of the sparse nested linear array SNLA is represented as Sαd, where α is the sparsity coefficient, d=λ / 2, and S is represented as: Further definition Step 2: Use the DWT denoising module to perform denoising on the received signal source; Including defining a DWT denoising module: defining the DWT denoising module of the time domain signal x(t) as: where j = 0, 1, 2, ..., log2(T), k = 1, 2, ..., T2 -j , T represents the number of snapshots of the signal; Step 3: construct an autocorrelation sequence based on the covariance matrix, and use the autocorrelation sequence to solve the generalized eigenvalue; After denoising by the DWT denoising module, we get The covariance matrix of is: Step 4: Further optimize the parameters to obtain the spatial spectrum based on the autocorrelation domain; Step 5: Obtain the predicted angle of the signal source by searching for the peak value of the spatial spectrum in the autocorrelation domain; as well as Step 6: Evaluate the performance of the DOA estimation method by the root mean square error.

2. The underwater DOA estimation method based on the autocorrelation domain of sparse nested linear array according to claim 1, characterized in that: In the first step, Then a1(θ q ) and a2(θ q ) are respectively expressed as: Where a1(θ q ) is the direction subvector of the qth source corresponding to the first uniform linear array ULA, a2(θ q ) is the direction subvector of the qth source corresponding to the second uniform linear array ULA; therefore, the direction matrix of the sparse nested linear array SNLA is expressed as:

3. The underwater DOA estimation method based on the autocorrelation domain of sparse nested linear array according to claim 2, characterized in that: Further assume that there are Q uncorrelated narrowband underwater acoustic signal sources from {θ1, θ2, …, θ q ,…,θ Q } direction hits the sparse nested linear array SNLA, and the target transmits a signal with a carrier frequency of f0Hz and an amplitude of a q (t), since w0=2πf0, the signal is expressed as: And the signal received by the sparse nested linear array at time t can be expressed as: where s(t) is the signal vector and n(t) is a vector with zero mean and variance σ. 2 Additive white Gaussian noise vector.

4. The underwater DOA estimation method based on the autocorrelation domain of sparse nested linear array according to claim 1, characterized in that: The DWT denoising module includes signal decomposition, threshold processing and signal reconstruction.

5. The underwater DOA estimation method based on the autocorrelation domain of sparse nested linear array according to claim 4, characterized in that: In the signal decomposition, the original signal x(t) is first passed through a half-band high-pass filter and a low-pass filter to eliminate half of the samples, and then the signal is downsampled for further decomposition.

6. The underwater DOA estimation method based on the autocorrelation domain of sparse nested linear array according to claim 5, characterized in that: In the threshold processing, a soft method or a hard method is used to perform threshold processing on the signal to obtain an optimal component for reconstructing the denoised signal; The calculation formula for threshold processing of the signal by the hard method is as follows: The calculation formula for the soft method to process the signal threshold is as follows: Soft threshold y=sign(x)(|x|-ξ).

7. The underwater DOA estimation method based on the autocorrelation domain of sparse nested linear array according to claim 6, characterized in that: In the signal reconstruction, the signal of each level is downsampled, and then passed through a half-band high-pass filter and a low-pass filter respectively, and finally the outputs of the half-band high-pass filter and the low-pass filter are added to obtain a signal 8. The underwater DOA estimation method based on the autocorrelation domain of sparse nested linear array according to claim 1, characterized in that: The third step consists in defining the spatial autocorrelation sequence of the sparse nested linear array SNLA: Where L = M2(M1+1)-1, Further is defined as the generalized eigenvalue, where B, C and γ are set to: The specific steps for solving the generalized eigenvalue are as follows: S31. Define the matrix necessary to solve the generalized eigenvalue S32, Reconstruction Matrix S33, obtaining eigenvalues ​​and eigenvectors by solving Px=γJx; S34, taking the smallest eigenvalue among the obtained eigenvalues ​​as γ, and taking its corresponding eigenvector as x; S35. Dividing vector x by its first element can obtain vector C.

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