CN116338574B - Sparse Bayesian learning underwater sound source positioning method based on matched beam - Google Patents
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Abstract
The invention discloses a sparse Bayesian learning underwater sound source positioning method based on a matched beam, which aims at the environmental mismatch problem existing in the existing sparse Bayesian learning matching field positioning algorithm, utilizes a beam forming technology to convert sound pressure data received by an array into a beam domain space, limits or tracks sound signals in a specific direction in the beam domain, converts the positioning problem in the beam domain into a problem of solving a underdetermined equation with sparse constraint, and finally carries out iterative solution through a sparse Bayesian learning updating formula. Compared with the prior method, the invention has the advantages that: (1) The method has stronger tolerance to environment mismatch while ensuring the positioning result of high resolution and low sidelobe, and effectively improves the positioning robustness; (2) faster running speeds.
Description
Technical Field
The invention relates to an underwater sonar array signal processing algorithm, in particular to a sparse Bayesian learning underwater sound source positioning method based on matched beams, belonging to the underwater acoustic array signal processing neighborhood.
Background
The matching field localization method has been widely studied in the last 50 years, and its development is not separated from the close intersection of signal processing technology and underwater sound physics. The matching field positioning is essentially a generalized beam forming method, which makes full use of the space complexity of a sound field in a marine waveguide, calculates copy field vectors by adopting an acoustic propagation model based on the multipath propagation characteristics of acoustic signals through known or inversion acquired underwater acoustic environment parameter information, and realizes passive positioning of an underwater sound source by matching with measurement data. However, since the calculation of the copy field depends on the modeling of the sound field environment, it is often difficult to accurately know the environmental parameter information in practice, so that the matching field positioning faces the problem of environmental mismatch from the beginning of development.
The compressed sensing algorithm which is rising in recent years is greatly focused in the underwater passive sound source positioning, the compressed sensing processing is to convert a positioning problem into an underdetermined equation set solving problem with sparse constraint, and then various sparse iterative algorithms are utilized to solve the problem, and the sparsity of a sound field is utilized to obtain better processing performance. Among various sparse iterative algorithms, the sparse Bayesian learning algorithm has the advantages of good robustness, high resolution and no need of sparsity selection, and has been widely applied to underwater sound source localization. Although the classical sparse Bayesian learning matching field positioning algorithm has better sparse recovery performance, the situation when the environment is mismatched is not considered. When the degree of mismatch of the marine environment is high, the positioning performance of the algorithm is greatly reduced, and even the algorithm cannot be positioned.
Disclosure of Invention
The invention aims to provide a sparse Bayesian learning underwater sound source positioning method based on matched beams, which can ensure the positioning result of high resolution and low sidelobe, has stronger tolerance to environment mismatch and effectively improves the positioning robustness.
In order to solve the technical problems, the invention comprises the following steps:
step 1: and selecting a proper sound propagation model according to priori knowledge, and determining good grid division and a sound source searching range. And meanwhile, preprocessing array received data, and obtaining frequency information of a sound source signal through technologies such as time-frequency analysis and the like.
Step 2: the data received by the array and the copy field data calculated from the acoustic propagation model are converted into beam domain space by a beam forming technique.
Step 3: and (3) carrying out wave beam filtering in a wave beam domain, limiting or tracking acoustic signals in a specific direction, and reasonably selecting the wave beam integration width.
Step 4: and (3) performing sparse iteration in a beam domain, converting a positioning problem in the beam domain into a problem of solving a less-defined equation with sparse constraint, and performing iterative solution by adopting a sparse Bayesian learning updating formula.
Step 5: and outputting the sound source estimation position according to the iteration result.
Further:
the beamforming technique described in step 2 can be described as:
in the method, in the process of the invention,for measuring beam domain data of the field, +.>In order to copy the beam domain data of the field,for noise field data on the beam domain, the superscript B indicates the beam domain, and M is the number of selected beam domain angles. k is wave number, z n And the depth of the nth array element is theta, namely the beam pointing angle, and if the beam angle is not limited, the value range of theta is-90 degrees to 90 degrees. P is p data (z n ) Receiving data for measuring the sound pressure of the nth array element of the field,>is sound source located +.>Where the sound pressure of the nth array element of the copy field receives data,/for the copy field>The complex amplitude of the sound source is taken for the first snapshot.
The method for reasonably selecting the beam integration width in the step 3 is as follows: when the sound pressure field data is converted into the beam domain space through the beam forming technology, a beam pointing diagram can be obtained, the beam pointing diagram reflects the intensity of the energy of the signals received by the array in different directions, and at the moment, a proper beam can be selected for processing by controlling the range of the beam pointing angle theta. If the beam pointing angle can be made smaller than a certain value in order to limit the reflected beam from the seafloor; while to limit the beam from the direct propagation of seawater, the beam pointing angle may be made larger than a certain value. The user can reasonably select the beam integration width according to the mismatching type of the beam pointing diagram and the actual environment.
The sparse iterative update formula described in step 4 can be described as:
in the method, in the process of the invention,the superscript + represents the mole-penrose generalized inverse of the matrix for a matrix of K non-zero value-corresponding copy field dictionary vectors in γ. Although K sound sources are needed to be assumed in the sparse Bayesian framework, the actual number of sound sources is not limited by the K sound sources, the performance of the sparse Bayesian framework is insensitive to K, and sparsity selection is not needed. />Is a sampling covariance matrix of the beam domain, wherein +.>In practical processing, the iteration is terminated when the noise variance is less than a certain threshold or the iteration reaches a maximum number of iterations, typically a noise threshold of 0.001, a maximum number of iterations of 100 is desirable.
Compared with the prior art, the invention has the beneficial effects that:
the beams in different angle ranges are affected by environment mismatch, and the beams are filtered and sparse iterated on the beam domain, so that the high-resolution low-sidelobe positioning result is ensured, the environment mismatch is more tolerant, and the positioning robustness is effectively improved.
In addition, compared with the classical sparse Bayesian learning matching field method, the algorithm provided by the invention has a faster running speed, and the extra time is obtained by the fact that the number of signal beams is generally smaller than that of hydrophones, so that the correlation calculation is reduced by several times. The invention can be applied to the problem of passive positioning of the underwater sound source in the scene when the environment mismatch degree is high.
Drawings
FIG. 1 is a flow chart of a sparse Bayesian learning underwater sound source localization method based on matched beams;
FIG. 2 is an environmental schematic of an example demonstration experiment;
FIG. 3 is a time-frequency analysis diagram of an embodiment array received signal;
FIG. 4 is an embodiment beam pattern;
FIG. 5 (a) is a conventional Bartlett match field algorithm localization result;
FIG. 5 (b) is a graph of the localization results of a classical sparse Bayesian learning matching field algorithm;
fig. 5 (c) is a diagram of the positioning result of the proposed algorithm of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
The invention provides an environment tolerant high-resolution matching field positioning algorithm, which aims at the situation that the existing sparse Bayesian learning matching field positioning algorithm performs sparse iteration on sound pressure space and does not consider the situation that the environment is mismatched. As shown in fig. 1, a flowchart of a sparse bayesian underwater sound source localization method based on matched beams is shown. According to the method, sound pressure data received by an array is converted into a beam domain space by utilizing a beam forming technology, sound signals in specific directions are limited or tracked in the beam domain, a positioning problem in the beam domain is converted into a problem of solving a underdetermined equation with sparse constraint, and finally iterative solution is carried out through a sparse Bayesian learning updating formula. The specific implementation method comprises the following steps:
and step 1, inputting related parameters and preprocessing.
According to priori knowledge, a proper acoustic propagation model is selected, grid division and a sound source searching range are determined, array parameters are input, array receiving data and environment parameter information (sea depth, sound velocity profile, substrate parameters and the like) are input. And meanwhile, preprocessing array received data, and obtaining frequency information of a sound source signal through technologies such as time-frequency analysis and the like.
And 2, converting the data received by the array and the copy field data calculated by the acoustic propagation model into a beam domain space through a beam forming technology.
For an N-ary vertical receiving array, when the frequency is f, the single snapshot data can be expressed as:
in the method, in the process of the invention,sound pressure data received for the first snapshot of the vertical array, is->Is sound source located +.>Copy field sound pressure data generated at +.>Representing sound source position information, & lt + & gt>For the first snapshot the complex amplitude of the sound source,/->Is the noise data of the first snapshot.
The beam domain data of the measurement field and the copy field can be obtained from the corresponding sound pressure field by a beam forming technique:
in the method, in the process of the invention,for measuring beam domain data of the field, +.>For copying beam domain data of a field, the superscript B indicates a beam domain, and M is the number of selected beam domain angles. k is wave number, z n And the depth of the nth array element is theta, namely the beam pointing angle, and if the beam angle is not limited, the value range of theta is-90 degrees to 90 degrees. P is p data (z n ) Receiving data for measuring the sound pressure of the nth array element of the field,>is sound source located +.>The nth array element of the copy field receives data at sound pressure. When converting from sound pressure space to beam domain space, equation (1) can be rewritten as:
in the method, in the process of the invention,is noise field data on the beam domain, where the sound pressure field data has been translated into beam domain space.
And step 3, carrying out wave beam filtering in a wave beam domain, limiting or tracking acoustic signals in a specific direction, and reasonably selecting wave beam integration width.
The beam directivity pattern can be obtained by converting the sound pressure field data into the beam domain space through the beam forming technology, as shown in fig. 4, which reflects the intensity of the signal energy received by the array in different directions, and at this time, a proper beam can be selected for processing by controlling the range of the beam directivity angle θ. If the beam pointing angle is made smaller than a certain value in order to limit the reflected beam from the sea floor, and if the beam directly propagating from the sea is limited, the beam pointing angle is made larger than a certain value. The user can reasonably select the beam integration width according to the mismatching type of the beam pointing pattern and the actual environment, and for the following demonstration case, the reflected beam from the seabed is limited, and the beam pointing angle is selected to be in the range of 0-15 degrees.
Step 4, sparse iteration is carried out in a beam domain, a positioning problem in the beam domain is converted into a problem of solving a short equation with sparse constraint, and a sparse Bayesian learning update formula is adopted for carrying out iterative solution on super parameters gamma and sigma 2 。
When a sound field has a plurality of sound sources, and the number of sound sources is assumed to be K, when the number of snapshots is L, it is possible to obtain:
Y (B) ＝G (B) X+N (B) (5)
in the method, in the process of the invention,beam domain data of the measurement field is taken for L shots,copying a field dictionary for the beam domain, wherein the column vector +.>Indicating that the sound source is +.>And (3) calculating a normalized copy field vector, wherein D is grid points divided by the area to be searched.Wherein column vector->Representing the complex amplitude of the sound source at the different grid points under the first snapshot, the superscript T represents the vector transpose. />Is beam domain noise data.
In general, the number of underwater sound sources is limited, i.e., D > K, so equation (5) is a system of under-determined equations with sparse constraints. The underwater sound source localization problem can be converted into an underdetermined equation problem solving the following sparse constraint.
min||X|| 0 s.t.Y (B) ＝G (B) X+N (B) (6)
Solving the above 0 The norm is a classical NP-hard problem and is solved iteratively in the beam domain using a sparse bayesian learning algorithm. Assuming that the unknown sound source amplitude obeys complex gaussian distribution with zero mean value, and different snapshot data are mutually independent, the prior probability of X can be obtained by the following formula:
wherein Γ=diag (γ) 1 ,...,γ D ) =diag (γ) is a diagonal covariance matrix, where vector γ is the sound source power on all grid points in the area to be searched. Assuming that the noise in the beam domain meets zero mean, the variance is σ 2 Is based on Bayes theory to obtain Y (B) Probability density function of (c):
in the formula, covariance matrix sigma y ＝σ 2 I M +(G (B) )Γ(G (B) ) H ，I M The super parameter gamma can be obtained by maximizing the unit matrix of M order (8) d Sum sigma 2 Is a value of (2).
Thus deriving the sound source power gamma and the noise variance sigma 2 Is an iterator of:
in the method, in the process of the invention,the superscript + represents the mole-penrose generalized inverse of the matrix for a matrix of K non-zero value-corresponding copy field dictionary vectors in γ. Although K sound sources are needed to be assumed in the sparse Bayesian framework, the actual number of sound sources is not limited by the K sound sources, the performance of the sparse Bayesian framework is insensitive to K, and sparsity selection is not needed. />Is a sampling covariance matrix of the beam domain, wherein +.>
In practical processing, the iteration is terminated when the noise variance is less than a certain threshold or the iteration reaches a maximum number of iterations, typically a noise threshold of 0.001, a maximum number of iterations of 100 is desirable.
And step 5, outputting the estimated position of the sound source according to the iteration result.
And when the iteration is terminated, the first K maximum peaks in the sound source power gamma are taken to be the corresponding sound source positions.
The technical effects of the present invention will be described in detail with reference to experiments.
The experiment adopts SACLANT research center 10 months in 1993 to carry out an offshore experiment in the shallow sea area in the North of Italy, and only the sound velocity profile measurement is carried out in the experiment process, and the rest of the environment parameters are unknown and are shown in figure 2 according to the previous experiment record. The data from the trial on day 26 was selected for processing where the sound source emitted a continuous pseudo-random signal with a center frequency of 170Hz and a 3dB bandwidth of about 12Hz, and figure 3 is a time-frequency analysis plot of the array received signal. The sound source is anchored at a distance of 5600 + -200 m from the receiving array, at a depth of 80 + -2 m under water. The receiving array is a 48-element vertical linear array, the first element is positioned under water by 18.7m, the last element is positioned under water by 112.7m, and the interval between the elements is 2m.
Since the substrate parameters are not measured during the test, but only empirical reference values are used, a serious environmental mismatch occurs in the matching field localization. Fig. 4 is a beam pattern reflecting the intensity of the signal energy received by the array in different directions, with the beam integration angle set between 0 deg. and 15 deg. to limit the reflected beam from the seafloor in order to reduce the effect of the mismatch of the geophones parameters.
Fig. 5 (a) to 5 (c) show the positioning result diagrams of different algorithms, respectively, in which the circle symbols represent the algorithm estimation results. Fig. 5 (a) and fig. 5 (b) are positioning results of a conventional Bartlett matching field algorithm and a sparse bayesian learning algorithm, respectively, which have larger positioning deviation, and fig. 5 (c) is a positioning result diagram of the method provided by the invention, wherein the depth positioning result is 80m, the distance positioning result is 5800m, and the target is accurately positioned within the allowable deviation. It can be seen that in the severe mismatch scene of the geosonic parameters, the conventional Bartlett matching field algorithm and the classical sparse bayesian learning algorithm cannot be accurately positioned, but the method provided by the invention has stronger tolerance to environment mismatch by performing beam filtering and sparse iteration in a beam domain, and effectively improves the positioning robustness.
Meanwhile, compared with the prior method, the algorithm provided by the invention has higher running speed, and the extra time is obtained by the fact that the number of signal beams is generally smaller than that of hydrophones, so that the correlation calculation is reduced by several times. The invention can be applied to the problem of passive positioning of the underwater sound source in the scene when the environment mismatch degree is high.
Claims (3)
1. A sparse Bayesian learning underwater sound source positioning method based on matched beams is characterized by comprising the following steps:
step 1: selecting an acoustic propagation model according to priori knowledge, and determining good grid division and an acoustic source searching range; preprocessing array received data to obtain frequency information of a sound source signal;
step 2: converting data received by the array and copy field data calculated by the acoustic propagation model into a beam domain space by a beam forming technology;
the beamforming technique described in step 2 is described as:
in the method, in the process of the invention,for measuring beam domain data of the field, +.>In order to copy the beam domain data of the field,the superscript B represents the beam domain, and M is the number of the selected beam domain angles; k is wave number, z n For the depth of the nth array element, theta is the beam pointing angle, and if the beam angle is not limited, the value range of theta is-90 degrees to 90 degrees; p is p data (z n ) Receiving data for measuring the sound pressure of the nth array element of the field,>is sound source located +.>Where the sound pressure of the nth array element of the copy field receives data,/for the copy field>Complex amplitude of sound source is taken for the first snapshot;
step 3: performing wave beam filtering in a wave beam domain, limiting or tracking acoustic signals, and selecting wave beam integration width;
step 4: performing sparse iteration in a beam domain, converting a positioning problem in the beam domain into a problem of solving a less-defined equation with sparse constraint, and performing iterative solution by adopting a sparse Bayesian learning updating formula;
step 5: and outputting the estimated position of the sound source according to the iteration result.
2. The method for sparse Bayesian learning underwater sound source localization based on matched beams according to claim 1, wherein the method comprises the following steps: and 3, reasonably selecting the beam integration width, wherein the method comprises the following steps of:
when the sound pressure field data are converted into a beam domain space through a beam forming technology, a beam pointing diagram is obtained, the beam pointing diagram reflects the intensity of signal energy received by the array in different directions, and at the moment, a beam is selected for processing by controlling the range of the beam pointing angle;
if the beam pointing angle is made smaller than a certain value in order to limit the reflected beam from the seafloor; and to limit the beam from the direct propagation of seawater, the beam pointing angle is made larger than a certain value;
the user reasonably selects the beam integration width according to the mismatching type of the beam pointing diagram and the actual environment.
3. The method for sparse Bayesian learning underwater sound source localization based on matched beams according to claim 1, wherein the method comprises the following steps: the sparse iterative update formula described in step 4 is described as:
in the method, in the process of the invention,the matrix formed by the copy field dictionary vectors corresponding to K non-zero values in gamma is marked with the superscript +to represent the mole-Penrose generalized inverse of the matrix; />Is a sampling covariance matrix of the beam domain, wherein +.>When the noise variance is less than the threshold or the maximum number of iterations is reachedAnd stopping iteration.
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