Method and system for simulating correlation of signals between sonar array elements changing along with space

Abstract

The invention discloses a method and a system for simulating correlation of signals between sonar array elements changing along with space. The method comprises the following steps: (1) generating uncorrelated Gaussian white noise; (2) converting uncorrelated Gaussian white noise into Gaussian white noise with spatiality through a spatial correlation generation algorithm; and (3) converting the Gaussian white noise with the spatiality into sonar array element signals with the spatiality through AR (Augmented Reality) filtering. Aiming at certain spatial correlation between marine environment noise caused by limited spacing between array elements of a sonar array, dynamic decomposition is carried out on frequency bands in an effective bandwidth, and then Gaussian white noise with spatial correlation characteristics is synthesized; and the related Gaussian white noise excites the marine environment noise AR model to obtain a signal time sequence between sonar array elements with spatial correlation. According to the method, the sparse characteristic of correlation is fully utilized, the number of filters is reduced, the sparse matrix is adopted to accelerate the calculation process, and the calculation efficiency of the sonar simulation system is effectively improved.

Description

Technical Field

[0001] This invention relates to the field of simulation technology for signals between sonar array elements, and in particular to a method and system for simulating the correlation of signals between sonar array elements as they vary with space. Background Technology

[0002] Marine environmental noise, as a significant component of the background noise of underwater acoustic arrays, is a major focus of sonar element signal simulation. Current simulations of sonar element signals mostly concentrate on the spectral characteristics of the marine environment for individual elements, with little research on simulations involving spatial correlation. Given the limited spacing between sonar array elements and the spatial correlation between marine environmental noise levels, simulations that ignore this spatial correlation will not reflect reality. This will lead to performance differences in array signal processing algorithms between simulation debugging and actual use, and may even cause system failure during real-world operation. Summary of the Invention

[0003] Objective: To address the problems and shortcomings of existing technologies, this invention studies the spatial correlation characteristics of signals between sonar array elements in signal simulation and establishes a method for generating sonar array element time series that ensures consistent spectral characteristics for each element and meets set requirements for spatial correlation between pairs of elements. This is significant for improving the realism of sonar array element signal simulation and accurately evaluating array signal processing algorithms. This invention provides a method and system for simulating the spatial correlation of signals between sonar array elements as they vary spatially, addressing the problem of spatial correlation between marine environmental noise caused by limited spacing between sonar array elements. Based on the spatial coherence function of marine environmental noise, and according to a set simulation accuracy for the spatial correlation coefficient of marine environmental noise, this method dynamically decomposes the frequency band within the effective bandwidth, synthesizes Gaussian white noise with spatial correlation characteristics, and excites the marine environmental noise AR model with the relevant Gaussian white noise to obtain the spatially correlated time series of sonar array element signals. This invention fully utilizes the sparsity characteristics of spatial correlation, reduces the number of filters, and uses sparse matrices to accelerate the calculation process, effectively improving the computational efficiency of the sonar simulation system.

[0004] Technical solution: A method for simulating the correlation of signals between sonar array elements as a function of space, comprising the following steps: (1) Set the number of array elements of the sonar and use the normal distribution random number function to generate uncorrelated Gaussian white noise; (2) Set the simulation accuracy of the spatial correlation coefficient of marine environmental noise, and dynamically decompose the frequency band within the effective bandwidth of the signal between sonar array elements based on the spatial coherence function of marine environmental noise. Then, through the sparse characteristic generation algorithm of spatial correlation, the uncorrelated Gaussian white noise is transformed into Gaussian white noise with spatiality. (3) The AR model with marine environmental noise characteristics is solved according to the Yule-Walker equation, and the spatial Gaussian white noise is converted into spatial sonar array element signals through the AR model.

[0005] Furthermore, step (1) specifically includes: (1-1) Set the number of array elements of the sonar to be M The array elements are numbered 1, 2, ... M ; (1-2) Generation M A Gaussian white noise sequence , , ..., ,in , N is the length of the Gaussian white noise sequence.

[0006] Furthermore, step (2) specifically includes: (2-1) Define the spatial correlation function for marine environmental noise ,in Q Γ is the spatial correlation coefficient, and Γ is the spatial coherence function (obtained experimentally or theoretically). To extract the real part within the parentheses, d The element spacing (in meters) γ The elevation angle (in rad) of the line connecting the array elements. The azimuth angle (in rad) of the line connecting the array elements. f Frequency (unit: Hz) For the selected angular frequency point, For the integration interval, It is the integral variable.

[0007] (2-2) Setting the accuracy of the correlation coefficient ,according to ( The simulation frequency band is divided into (the minimum distance between array elements). K For each sub-band, the difference between the maximum and minimum values ​​of the correlation function corresponding to each frequency within the interval is not less than [amount missing]. , and before K The correlation function value within the -1 sub-band changes monotonically, and the th... k Each sub-band is represented as , No. K Each sub-band is represented as ( (sampling rate) .

[0008] (2-3) Before calculation K The correlation coefficient matrix of the -1 sub-bands, the thk The correlation coefficient matrix of each sub-band is , Each element is , For the first u Each array element and the first v The spacing between the array elements.

[0009] (2-4) For all If we set it to 0, then Since it is a sparse matrix, the sparse matrix algorithm can be used to accelerate the subsequent steps (2-5) and (2-8).

[0010] (2-5) Perform Cholesky decomposition, i.e. ,in It is an upper triangular matrix, since For the coefficient matrix, this step uses a sparse matrix algorithm to accelerate the process.

[0011] (2-6) Adopt K -1 bandpass filter pair M The Gaussian white noise is filtered, and the... k ( The passband range of each bandpass filter is determined by... Decision. (Number) m ( Gaussian white noise After the first k After passing through a bandpass filter, the filtered signal is obtained. Transpose it to form a column vector. And thus form a matrix .

[0012] (2-7) Use one high-pass filter to... M Filter the Gaussian white noise, with the cutoff frequency set to... Decision, number m ( Gaussian white noise The filtered signal is obtained after passing through a high-pass filter. Transpose it to form a column vector. And thus form a matrix .

[0013] (2-8) Calculation ,in ,make ,because For the coefficient matrix, this step uses a sparse matrix algorithm to accelerate the process.

[0014] (2-9) Calculation That is M The channel has spatial Gaussian white noise, in which The m Column corresponding to the first m Each array element.

[0015] Furthermore, step (3) specifically includes: (3-1) Based on the required power spectrum characteristics of the sonar array element signals, the Levinson-Durbin method is used to obtain the AR filter coefficients; (3-2) By using AR filtering, spatial Gaussian white noise is converted into spatial sonar array element signals.

[0016] A simulation system for the correlation of signals between sonar array elements as a function of space includes the following modules: The first module is used to set the number of array elements of the sonar and generate uncorrelated Gaussian white noise using a normal distribution random number function. The second module is used to set the simulation accuracy of the spatial correlation coefficient of marine environmental noise. Based on the spatial coherence function of marine environmental noise, the effective bandwidth of the signal between sonar array elements is dynamically decomposed. Then, through the sparse characteristic generation algorithm of spatial correlation, the uncorrelated Gaussian white noise is transformed into Gaussian white noise with spatiality. The third module solves the AR model with marine environmental noise characteristics based on the Yule-Walker equation, and transforms the spatial Gaussian white noise into spatial sonar array element signals through the AR model.

[0017] The implementation process and methods of the system are the same and will not be described again.

[0018] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the simulation method for the correlation of signals between sonar array elements with spatial variation as described above.

[0019] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the simulation method for the correlation of signals between sonar array elements as described above with spatial variation.

[0020] Compared with existing technologies, the significant advantages of this invention are as follows: This invention considers the spatial correlation between marine environmental noise caused by the limited spacing between sonar array elements. Based on the spatial correlation function of marine environmental noise and according to the set simulation accuracy of the spatial correlation coefficient, the effective bandwidth frequency band is dynamically decomposed to synthesize Gaussian white noise with spatial correlation characteristics. The Gaussian white noise is then used to excite the marine environmental noise AR model to obtain the time series of signals between sonar array elements with spatial correlation. This invention has the advantage of controllable simulation accuracy of the marine environmental noise spatial correlation coefficient and fully utilizes the sparsity characteristics of spatial correlation, reducing the number of filters and using sparse matrices to accelerate the calculation process, effectively improving the computational efficiency of the sonar simulation system and possessing good engineering practical value. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating an embodiment of the present invention; Figure 2 This is a schematic diagram of the spatial correlation generation process; Figure 3 It is the spatial correlation coefficient between array elements; Figure 4 This is a comparison between the simulated values ​​of the spatial coherence function between array elements with a spacing of 0.5m and the values ​​of the reference model. Figure 5 This is a comparison between the simulated values ​​of the spatial coherence function between array elements with an element spacing of 1.0m and the values ​​of the reference model. Figure 6 This is a comparison between the simulated values ​​of the spatial coherence function between array elements with a spacing of 1.5m and the values ​​of the reference model. Figure 7 This is a comparison between the simulated values ​​of the spatial coherence function between array elements with a spacing of 2.0m and the values ​​of the reference model. Figure 8 It is the marine environmental noise spectrum level; Figure 9 These are the ocean environmental noise spectrum levels for each array element. Detailed Implementation

[0022] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0023] A method for simulating the correlation of signals between sonar array elements as a function of space, such as... Figure 1 As shown, it includes: (1) Generate uncorrelated Gaussian white noise. Specifically, this includes: (1-1) Set the number of array elements of the sonar to 5, and the serial numbers of each array element to 1, 2, ..., 5. Set the coordinate matrix as follows: , Each column corresponds to one array element.

[0024] (1-2) Five Gaussian white noise sequences were generated using the Box-Muller algorithm. , , ..., The number of points is 15000, that is The expected values ​​are all 0, and the variances are all 1.

[0025] (2) Using a spatial correlation generation algorithm, uncorrelated Gaussian white noise is transformed into spatially relevant Gaussian white noise, such as... Figure 2 As shown. Specifically includes: (2-1) Define the probability density function in, θ The vertical pitch angle is the angle of the storm noise. The horizontal azimuth angle of the storm noise. ω Angular velocity, α 1 represents the ratio of the height of the von Mises peak to the azimuth level generated by wave breaking. u 1 represents the intensity at the storm's center. θ 1 and 1. Indicates the location of the storm center. a 0 and A As an intermediate variable, the specific expression is as follows: in, I 0(·) is the zeroth-order Bessel function of the first kind, and its parameters take the following values: , , ; Calculate the coherence function in , , , c The speed of sound (1500 m / s).

[0026] Calculate the correlation function , Where the frequency resolution Δ f =0.1Hz, , .

[0027] (2-2) Setting the accuracy of the correlation coefficient ,according to ( The simulation frequency band is divided into sections based on the minimum distance between array elements (i.e., 0.5m). The correlation function values ​​in the first 14 sub-bands change monotonically, and the... k Each sub-band is represented as The 15th sub-band is represented as ( (For the sampling rate, set to 15kHz), then we can obtain... They are 0 Hz, 194.3 Hz, 388.5 Hz, 582.7 Hz, 776.9 Hz, 971.1 Hz, 1165.3 Hz, 1359.5 Hz, 1553.7 Hz, 1747.9 Hz, 1942.1 Hz, 2136.3 Hz, 2330.5 Hz, 3013.5Hz, 3696.5Hz.

[0028] (2-3) Calculate the correlation coefficient matrix for the first 14 sub-bands, with each element being... , For the first u Each array element and the first v The spacing between the array elements, due to the symmetry of the array, means that each matrix actually has only four independent parameters, namely... .

[0029] The specific value is

[0030] (2-4) For all Set it to 0, and accelerate the subsequent algorithm using a sparse matrix algorithm, that is...

[0031] (2-5) Perform Cholesky decomposition, i.e. ,in It is an upper triangular matrix.

[0032] (2-6) Adopt K -1 bandpass filter pair Perform filtering, the first k ( The passband range of each bandpass filter is determined by... Decision made. An FIR bandpass filter will be designed using the functional method, with a Hamming window as the window function, and each filter will be of order 512. The filtered result... Arranged as column vectors and form a matrix .

[0033] (2-7) Use a high-pass filter for Filtering is performed, and the cutoff frequency is determined by... Decision made. A functional approach is adopted to design an FIR bandpass filter, using a Hamming window as the window function, and the filter is of order 512. The filtered result is... Arranged as column vectors and form a matrix ; (2-8) Calculation ,in ,make ; (2-9) Calculation That is M The channel has spatial Gaussian white noise, in which The m Column corresponding to the first m Each array element.

[0034] (3) By using AR filtering, spatial Gaussian white noise is converted into spatial sonar array element signals.

[0035] (3-1) The required power spectrum characteristics of the sonar array elements are set using the three-parameter method. in, For power, f m =200Hz, f 0 = 500Hz λ =0, σ =0.01.

[0036] The AR filter coefficients were obtained using the Levinson-Durbin method, and the results are as follows:

[0037] (3-2) By using AR filtering, spatial Gaussian white noise is converted into spatial sonar array element signals.

[0038] The following will verify this example.

[0039] First, verify the calculation of the relevant functions. Because in this example... There are only four possible values, thus generating four curves, such as... Figure 3As shown. The sonar array element signals are generated according to the steps described in this example. The spatial coherence function is solved pairwise for each generated sonar array element signal, and compared with the set spatial coherence function model. The above simulation is repeated 10 times, and the results of the 10 simulations are averaged, as shown. Figures 4 to 7 As shown in the figure, the overall simulation results of the spatial coherence function of marine environmental noise between the array elements are consistent with the model in terms of frequency variation, and show good fit in each frequency band.

[0040] Then, the power spectrum of each sonar element signal is verified. The set power spectrum is as follows: Figure 8 As shown, the power spectrum of the generated sonar element signal is as follows: Figure 9 As shown, the spectral level characteristics of the generated sonar array element time output sequence are consistent in each element and are consistent with the set spectral level.

[0041] Finally, the analysis results are as follows: The results of the verification data processing show that the method can effectively realize the time series simulation generation of broadband noise signals with spatial correlation of sonar array elements. The spectral characteristics of each array element in the generated signal are consistent, and the spatial correlation characteristics between array elements are consistent with the set model.

[0042] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

[0043] Obviously, those skilled in the art should understand that the steps of the simulation method for simulating the spatial correlation of sonar array elements' signals in the above-described embodiments of the present invention, or the modules of the simulation system for simulating the spatial correlation of sonar array elements' signals, can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those presented here, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the embodiments of the present invention are not limited to any particular hardware and software combination.

Claims

1. A method for simulating the correlation of signals between sonar array elements as a function of space, characterized in that: Based on the spatial coherence function of marine environmental noise, and according to the simulation accuracy of the set spatial correlation coefficient of marine environmental noise, the effective bandwidth frequency band is dynamically decomposed, and Gaussian white noise with spatial correlation characteristics is synthesized. Then, the marine environmental noise AR model is excited by the relevant Gaussian white noise to obtain the time series of sonar array elements with spatial correlation. The specific steps include the following: (1) Set the number of array elements of the sonar and use the normal distribution random number function to generate uncorrelated Gaussian white noise; (2) Set the simulation accuracy of the spatial correlation coefficient of marine environmental noise, and dynamically decompose the frequency band within the effective bandwidth of the signal between sonar array elements based on the spatial coherence function of marine environmental noise. Then, through the sparse characteristic generation algorithm of spatial correlation, the uncorrelated Gaussian white noise is transformed into Gaussian white noise with spatiality. (3) The AR model with marine environmental noise characteristics is solved according to the Yule-Walker equation, and the spatial Gaussian white noise is converted into spatial sonar array element signals through the AR model.

2. The method for simulating the correlation of signals between sonar array elements with spatial variation according to claim 1, characterized in that: Step (1) specifically includes: (1-1) Set the number of array elements of the sonar to be M The array elements are numbered 1, 2, ... M ; (1-2) Generation M A Gaussian white noise sequence , , ..., ,in , N is the length of the Gaussian white noise sequence.

3. The method for simulating the correlation of signals between sonar array elements with spatial variation according to claim 1, characterized in that: Step (2) specifically includes: (2-1) Define the spatial correlation function for marine environmental noise ,in: Q Let Γ be the spatial correlation coefficient, and Г be the spatial coherence function. To extract the real part within the parentheses, d For the spacing between array elements, γ The elevation angle of the line connecting the array elements. The azimuth angle of the line connecting the array elements. f For frequency, For the selected angular frequency point, The integral interval; (2-2) Setting the accuracy of the correlation coefficient ,according to The simulation frequency band is divided into K For each sub-band, the difference between the maximum and minimum values ​​of the correlation function corresponding to each frequency within the interval is not less than [amount missing]. , and before K The correlation function value within the -1 sub-band changes monotonically, and the th... k Each sub-band is represented as , No. K Each sub-band is represented as , Sampling rate, ; (2-3) Before calculation K The correlation coefficient matrix of the -1 sub-bands, the th k The correlation coefficient matrix of each sub-band is ， Each element is , For the first u Each array element and the first v The spacing between array elements; (2-4) For all If we set it to 0, then Since it is a sparse matrix, the subsequent steps (2-5) and (2-8) can be accelerated using a sparse matrix algorithm; (2-5) Perform Cholesky decomposition, i.e. ,in It is an upper triangular matrix, since For the coefficient matrix, this step uses a sparse matrix algorithm to accelerate the process; (2-6) Adopt K -1 bandpass filter pair M The Gaussian white noise is filtered, and the... k ( The passband range of each bandpass filter is determined by... Decision; m Gaussian white noise After the first k After passing through a bandpass filter, the filtered signal is obtained. Transpose it to form a column vector. And thus form a matrix ; ; (2-7) Use one high-pass filter to... M Filter the Gaussian white noise, with the cutoff frequency set to... Decision, number m Gaussian white noise The filtered signal is obtained after passing through a high-pass filter. Transpose it to form a column vector. And thus form a matrix ; (2-8) Calculation ,in ,make ,because For the coefficient matrix, this step uses a sparse matrix algorithm to accelerate the process; (2-9) Calculation That is M The channel has spatial Gaussian white noise, in which The m Column corresponding to the first m Each array element.

4. The method for simulating the correlation of signals between sonar array elements with spatial variation according to claim 1, characterized in that: Step (3) specifically includes: (3-1) Based on the required power spectrum characteristics of the sonar array element signals, the Levinson-Durbin method is used to obtain the AR filter coefficients; (3-2) By using AR filtering, spatial Gaussian white noise is converted into spatial sonar array element signals.

5. A simulation system for the correlation of signals between sonar array elements as a function of space, characterized in that: Includes the following modules: The first module is used to set the number of array elements of the sonar and generate uncorrelated Gaussian white noise using a normal distribution random number function. The second module is used to set the simulation accuracy of the spatial correlation coefficient of marine environmental noise. Based on the spatial coherence function of marine environmental noise, the effective bandwidth of the signal between sonar array elements is dynamically decomposed. Then, through the sparse characteristic generation algorithm of spatial correlation, the uncorrelated Gaussian white noise is transformed into Gaussian white noise with spatiality. The third module solves the AR model with marine environmental noise characteristics based on the Yule-Walker equation, and transforms the spatial Gaussian white noise into spatial sonar array element signals through the AR model.

6. A computer device, characterized in that: The computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method for simulating the correlation of signals between sonar array elements as described in any one of claims 1-4 with spatial variation.

7. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that: When the computer program / instruction is executed by the processor, it implements the steps of the simulation method for the correlation of signals between sonar array elements as described in any one of claims 1-4 as varying with space.

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