A method for fast joint estimation of array shape and orientation of a linear array

Abstract

The application discloses a method for quickly estimating the array shape and direction of a towed line array, and aims at solving the problem of the decline of direction finding performance caused by the maneuvering of the towed line array and reducing the calculation amount of sparse Bayesian learning. The method comprises the following steps: dividing the spatial angle into N grid points averagely, and constructing a sparse signal model in space; modeling the towed line array to obtain an array manifold matrix containing an arch height variable; using the Gaussian generalized approximation message passing and the sparse Bayesian learning algorithm to reconstruct the sparse signal in space and estimate the arch height; and outputting a spatial spectrum diagram to estimate the direction of arrival. The method can estimate the direction of arrival while estimating the arch height under the distortion condition of the maneuvering towed line array, adjust the array manifold matrix, and solve the problems of the decline of direction finding precision caused by the array shape distortion and the loss of weak targets caused by the sidelobe lifting.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of towed line array direction of arrival estimation and array shape estimation, and particularly relates to a method for fast joint estimation of towed line array shape and direction. BACKGROUND

[0002] Direction of arrival estimation is a key research content of array signal processing, and is widely used in military fields such as radar and sonar and civilian communication fields. The estimation and correction of the towed line array shape can provide a more accurate array flow matrix for the DOA estimation related algorithm. Although the hydrophones of the towed line array are installed in the oil-filled flexible cable, the overall deployment flexibility and anti-torsion of the array are improved, but at the same time, the problem of array shape distortion is also brought, and the array shape distortion will lead to a serious mismatch between the array flow matrix and the actual array shape, and finally lead to a serious decline in the performance of DOA estimation, and even the loss of weak targets. With the proposal of the Adaptive Bow Sparse Bayesian Learning (ABSBL) algorithm DOA estimation, the bow height and DOA of the towed line array shape are jointly estimated, which to some extent solves the problem of performance decline caused by array shape distortion, but the calculation amount is too large, and the real-time performance of the algorithm is poor. Therefore, it is necessary to optimize the time complexity of the algorithm and reduce the running time of the algorithm on this basis. SUMMARY

[0003] In view of the problems existing in the prior art, the present application solves the problem of providing a method for fast joint estimation of towed line array shape and direction, which realizes joint estimation of towed line array shape and direction based on Gaussian generalized approximation message passing and sparse Bayesian learning.

[0004] The technical scheme adopted by the present application is: a method for fast joint estimation of towed line array shape and direction, which comprises the following steps:

[0005] Step 1: modeling the received signal: dividing the spatial angle into N grid points on average, and constructing a sparse signal model in space;

[0006] Step 2: approximating the parabolic modeling of the towed line array, and constructing an array flow matrix containing the bow height variable;

[0007] Step 3: restoring the sparse signal based on the received signal of the towed line array and the array flow matrix containing the bow height variable, specifically: using the Gaussian generalized approximation message passing and sparse Bayesian learning algorithm to iteratively solve the posterior mean, posterior covariance, signal power distribution, noise variance and bow height of the signal;

[0008] Step 4: outputting the normalized spatial spectrum as the result of the direction of arrival estimation.

[0009] Further, the step 1 models the received signal, and the specific steps are as follows:

[0010] For a towed line array with M hydrophones, the array receives K far-field narrow-band signals, where K << M, and the received signal equation is expressed as:

[0011]

[0012] where represents the received wave signal of the mth hydrophone in the array, the received wave signal of the mth hydrophone in the array, the Gaussian white noise, the manifold matrix of the towed line array, which is composed of N steering vectors of M dimensions, N is the number of angle division, and each steering vector is defined as:

[0013]

[0014] where is the position coordinate of the mth array element, is the angular frequency of the signal, is the sound speed, is the nth angle of the spatial division.

[0015] Further, the step 2 models the towed line array as an approximate parabola, and the specific steps are as follows:

[0016] The position coordinates of the M hydrophones are , the distance between the hydrophones is d, the arch height of the parabola is a, represents the arc length of the array; represents the chord length of the array; the position of the mth element in the parabola model is approximately

[0017] ;

[0018] Substitute the position of the mth element in the parabola model into the array manifold matrix of the towed line array to obtain the array manifold matrix containing the arch height variable.

[0019] Further, the step 3 specifically includes the following sub-steps, and the specific steps are as follows:

[0020] Step 31, initialize the posterior mean x, variance , intermediate variable , arch height a, signal power and noise variance , intermediate variable ; is the manifold matrix of the towed line array; ​​

[0021] Step 32, according to the Gaussian generalized approximation message passing algorithm, iteratively calculate the approximate posterior mean and variance, the kth iteration step as follows:

[0022]

[0023] Wherein is the estimated posterior mean, is the estimated posterior variance; is the posterior variance of and is the damping factor, the upper index k and k-1 means the result of the kth iteration and the k-1th iteration, and is the input-output function in the case of Gaussian channel, as follows:

[0024] ,

[0025] ,

[0026] Wherein is the derivative of , is the derivative of , is , is ; is , is ;

[0027] Step 33, if the maximum number of iterations is reached or the convergence condition is met, stop the iteration of the posterior mean and variance, otherwise repeat step 32, the convergence condition is as follows:

[0028]

[0029] Wherein is the convergence threshold of , the upper index k+1 means the k+1th iteration;

[0030] Step 34, based on the estimated and after the iteration of step 33, update the estimated super parameter signal power and noise variance , as follows:

[0031]

[0032] wherein is the nth term of the series, new is the current iteration estimate, old is the last iteration estimate, is the nth term of the series;

[0033] Step 35, according to step 32, step 33 and step 34, the gradient descent method is used to update the arch height a every j times of repeated iterations, and the array manifold matrix is updated, the nth term of the array manifold matrix is specifically represented as follows:

[0034]

[0035] Step 36, if the maximum number of iterations is reached or the final convergence condition is met, the iteration is stopped, otherwise, steps 32, 33, 34 and 35 are repeated, and the final convergence condition is specifically as follows:

[0036]

[0037] wherein is the convergence threshold.

[0038] Further, the step 4 outputs the normalized spatial spectrum, which is specifically as follows:

[0039] The posterior mean x estimated by the last iteration is used as the DOA estimation result.

[0040] The beneficial effects of the present application are: the present application realizes the estimation of the towed line array array shape by modeling the towed line array as an approximate parabola, introducing the hyperparameter estimation of the arch height in the sparse Bayesian learning algorithm, and introducing the Gaussian generalized approximate message passing algorithm to approximately solve the posterior mean and variance in the sparse Bayesian learning algorithm, thereby reducing the running time of the algorithm. Compared with the traditional DOA estimation algorithm, it has higher resolution and less running time than the adaptive arch height sparse Bayesian learning algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is the flow chart of the fast joint estimation method of the towed line array array shape and direction in the specific embodiment of the present application;

[0042] Figure 2 is the direction of arrival estimation result graph of the ABSBL algorithm test data in the specific embodiment of the present application;

[0043] Figure 3 is the direction of arrival estimation result graph of the GGAMP-ABSBL algorithm test data in the specific embodiment of the present application. DETAILED DESCRIPTION ​

[0044] A method for fast joint estimation of array shape and orientation is described in detail below in combination with embodiments and drawings.

[0045] Figure 1 A general flowchart of the present application is given. First, array received signal modeling is performed, the spatial angle is divided into N grids, then the array is modeled as an approximate parabola, the array manifold matrix containing the arch height variable is constructed, the Gaussian generalized approximate message passing and sparse Bayesian learning (GGAMP-ABSBL) algorithm is used to solve the posterior mean, posterior covariance, signal power distribution, noise variance and array arch height, and finally the GGAMP-ABSBL output is used as the spatial spectrum diagram for DOA estimation.

[0046] The technical method of the present application is specifically implemented as follows:

[0047] Step 1, model the received signal. For an array with M array elements, assume that the array receives K far-field narrowband signals, where K << M, then the received signal equation can be expressed as:

[0048]

[0049] where represents the received wave signal of the M th hydrophone in K fast shots, assume that it is Gaussian white noise, is the manifold matrix of the array, which is composed of N dimensional steering vectors, N is the number of angles divided in space, and each steering vector is defined as:

[0050]

[0051] where is the position coordinate of the m th array element, is the angular frequency of the signal, is the sound speed, is the n th angle divided in space.

[0052] Step 2, approximate parabolic modeling of the towed line array. Assume that the towed line array has M hydrophones, the position coordinates of the M hydrophones are , the distance between the hydrophones is d, the arch height of the parabola is a, represents the array arc length, i.e. the length of the original uniform straight line array, The chord length is represented as an array. The position of the mth element in the parabolic model can be approximately represented as

[0053]

[0054] The position of the mth element in the parabolic model is substituted into the array manifold matrix of the array stream, to obtain the array manifold matrix containing the arch height variable.

[0055] Step 3 specifically includes the following sub-steps, as follows:

[0056] Step 31, initialize the posterior mean x, variance , intermediate variable , arch height a, signal power and noise variance , intermediate variable .

[0057] Step 32, according to the Gaussian generalized approximation message passing algorithm, iteratively calculate the approximate posterior mean and variance, the kth iteration step is as follows:

[0058]

[0059] wherein is the estimated posterior mean, is the estimated posterior variance; is the posterior variance of , and are damping factors, and the upper indexes k and k-1 mean the results of the kth iteration and the k-1th iteration, and are input-output functions in the case of Gaussian channel, specifically as follows:

[0060] ,

[0061] ,

[0062] wherein is the derivative of , is the derivative of . is , is ; is , is ;

[0063] ​Step 33: If the maximum number of iterations is reached or the convergence condition is met, stop the iteration; otherwise, repeat step 32. The specific convergence criteria are as follows:

[0064]

[0065] in for The convergence threshold; the superscript k+1 means the (k+1)th iteration.

[0066] Step 34, based on the estimate after the iteration in step 33. and Update the estimated hyperparameter signal power and noise variance The details are as follows:

[0067]

[0068] in for The nth term, for The nth term; new is the current iteration estimate, old is the previous iteration estimate, for The nth term.

[0069] Step 35: Based on steps 32, 33, and 34, after each j-fold iteration, update the bow height 'a' using gradient descent and update the array manifold matrix. The 'j'th iteration of the array manifold matrix... The specific items are represented as follows:

[0070]

[0071] Step 36: If the maximum number of iterations is reached or the convergence condition is met, stop the iteration; otherwise, repeat steps 32, 33, 34, and 35. The specific convergence criteria are as follows:

[0072]

[0073] in for The convergence threshold.

[0074] Step 4 outputs a normalized spatial spectrum, using the posterior mean x or signal power distribution γ estimated in the last iteration as the DOA estimation result.

[0075] Example

[0076] This example applies the above-mentioned array shape and DOA joint estimation to a 16-element line array, the element spacing of the line array is 1m, and the true arch height of the line array is 1m. Two sound source targets are set to be from 77° and 82° respectively, the signal-to-noise ratio is 0dB, and the signal frequency is 750Hz. The conventional beamforming (CBF) and multiple signal classification (MUSIC) algorithms use the true array shape to estimate the DOA, and the initial arch height of the ABSBL and GGAMP-ABSBL algorithms is set to 0.3m.

[0077] The DOA estimation results of each algorithm are shown in Figure 2 and Figure 3 , wherein the estimated arch height of the ABSBL algorithm is 1.0009m, and the estimated arch height of the GGAMP-ABSBL algorithm is 1.0002m, which is basically the same as the true value 1m. CBF cannot distinguish between the two similar targets, while the ABSBL algorithm and the GGAMP-ABSBL algorithm have the characteristics of high resolution as the MUSIC algorithm, and can accurately estimate the directions of the two targets. The running time of the ABSBL algorithm is 1.7456s, and the running time of the GGAMP-ABSBL algorithm is 0.7556s, which effectively reduces the running time.

[0078] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for fast joint estimation of array shape and orientation of a linear array, characterized in that, The method comprises the following steps: Step 1: modeling the received signal: dividing the spatial angle into N grid points, constructing a sparse signal model in space; Step 2: approximating parabolic modeling of the towed line array, constructing an array manifold matrix containing the bow height variable; Step 3: recovering the sparse signal based on the received signal of the towed line array and the array manifold matrix containing the bow height variable, specifically: using the Gauss generalized approximation message passing and sparse Bayesian learning algorithm to iteratively solve the posterior mean, posterior covariance, signal power distribution, noise variance and bow height of the signal; The step 3 specifically comprises the following sub-steps, specifically as follows: Step 31, initialize posterior mean x, variance , intermediate variables , bow height a, signal power and noise variance , intermediate variables ; is the manifold matrix for the linear array; Step 32, according to the Gauss generalized approximation message passing algorithm, iteratively calculate the approximate posterior mean and variance, the kth iteration step is as follows: ； where is the estimated posterior mean, is the estimated posterior variance; is the posterior variance, and is a damping factor, the upper indices k and k-1 have the meaning of the result of the k-th iteration and the k-1-th iteration, and is the input-output function in the case of a Gaussian channel, in particular as follows: ， ； ， ； wherein is derivative of is derivative of is , is ; is , is ; Step 33, if the maximum iteration number is reached or the convergence condition is met, stop the iteration of the posterior mean and variance, otherwise repeat step 32, and the convergence judgment condition is specifically as follows: ； wherein is the convergence threshold, the upper index k+1 has the meaning of the k+1 iteration; Step 34, update the estimated and , based on the estimated and noise variance from the iteration completed in step 33, as follows: ； wherein is the nth term of the series; new is the current iteration estimate, old is the last iteration estimate, is the nth term of the series; M is the number of hydrophones. Step 35, according to step 32, step 33 and step 34, update the arch height a and update the array manifold matrix every j times of repeated iterations, the first column of the array manifold matrix is The item is specifically represented as follows: ； where d is the spacing of the hydrophones, denotes the array chord length; denotes the array chord length, is the angular frequency of the signal, is the speed of sound, is the nth angle of the spatial division; Step 36, if the maximum iteration number is reached or the final convergence condition is met, stop the iteration, otherwise repeat steps 32, 33, 34 and 35, and the final convergence condition is specifically as follows: ； wherein is a convergence threshold; Step 4: output the normalized spatial spectrum as the result of the DOA estimation.

2. The method of claim 1, wherein, The step 1 models the received signal, and the specific steps are as follows: For a towed line array with M hydrophones, the array receives K far-field narrowband signals, where K << M, and the received signal equation is represented as: ； wherein denotes hydrophones receive the incoming wave signals, is a Gaussian white noise, is a manifold matrix of the towed line array, composed of N steering vectors of dimensionality N is the number of angular divisions of the space, each steering vector being defined as: ； wherein is the mth element position coordinate, is the angular frequency of the signal, is the speed of sound, is the nth angle of the spatial division.

3. The method of claim 1, wherein, The step 2 approximates the parabolic modeling of the towed line array, and the specific steps are as follows: The position coordinates of M hydrophones are , the distance between hydrophones is d, the arch height of the parabola is a, represents the array arc length; represents the chord length of the array; the position of the th element in the parabolic model is approximated as ； Substitute the position of the mth element in the parabolic model into the array manifold matrix of the towed line array to obtain the array manifold matrix containing the bow height variable.

4. The method of claim 1, wherein, The step 4 outputs the normalized spatial spectrum, specifically as follows: The posterior mean x estimated in the last iteration is used as the DOA estimation result.

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