CN115980721A - Array self-correcting method for error-free covariance matrix separation - Google Patents
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Abstract
An array self-correcting method for error-free covariance matrix separation specifically relates to a method for separating an error-free covariance matrix and an amplitude phase error matrix from an uncorrected covariance matrix of an array with errors, and aims to solve the problem that when an underwater sound target direction is estimated, a feature structure configuration method is not suitable for correcting a small-aperture array, so that the accuracy of the estimated underwater sound target direction result is low when the small-aperture array is estimated. Solving a covariance matrix of uncorrected array output signals in a small-aperture uniform linear array consisting of underwater acoustic signal receiving transducers according to signals of an underwater ship; constructing a covariance matrix of the noiseless error-free array output signal by using the matrix, and acquiring a signal component of the matrix; estimating the underwater sound target azimuth by using a signal component and MUSIC method; and solving the array amplitude phase error by using a characteristic structure configuration method and the target azimuth. Belonging to the field of underwater sound target direction estimation.
Description
Technical Field
The invention relates to an array self-correcting method, in particular to a method for separating an error-free array covariance matrix and an amplitude phase error matrix from an error-free uncorrected array covariance matrix, and belongs to the field of underwater sound target direction estimation.
Background
Direction of arrival (DOA) estimation is a prerequisite and a basis for research such as identification, positioning and tracking of underwater acoustic targets, and is one of important research contents of array signal processing. It obtains the orientation information of the object of interest from the noise and interference background. Today, there are many methods for estimating the direction of arrival, most typically the Conventional Beamforming (CBF) method, which has the advantages of high algorithm robustness and small influence of array errors. However, in practical applications, the size of a ship carrying the array is limited, and the ship cannot carry an array with a long aperture, but when the aperture of the array is small, the angular resolution of the CBF method is low, and two target orientations with a small spatial angular interval cannot be resolved, in this case, a high-resolution orientation estimation method is generally used to improve the resolution, such as a high-resolution beamforming Capon method and a multiple signal classification Method (MUSIC), which have better resolution than the CBF method. However, the Capon method is an adaptive algorithm, the MUSIC method is a subspace algorithm based on feature decomposition, the two methods are seriously affected by errors, and the estimation performance of the two methods can be sharply reduced due to small array element deviation. Not only in these two methods, the actual array bias will deteriorate the performance of most high-resolution algorithms, but in actual array manufacturing and installation processes, various array errors cannot be avoided, wherein the array element amplitude phase error is the most common array error, and in order to improve the performance of the azimuth estimation algorithm, the array error needs to be corrected first, so that researchers have proposed many array error correction methods.
When the underwater sound target azimuth is estimated, the self-correcting algorithm regards the corrected source azimuth as unknown parameters, and jointly solves the array error and the source azimuth. This approach is more widely used and accepted due to its good performance and greater containment with respect to the calibration environment. While Friedlander and Weiss propose that the feature-based configuration method is a classical self-correction method, which estimates array errors using orthogonality between noise subspaces and array manifold vectors, unfortunately the method is limited to small array perturbations and cannot effectively correct arrays in low signal-to-noise environments, and in addition, the method requires a large number of array elements, and thus the method is not suitable for correcting small aperture arrays. In order to more effectively correct the small-aperture array, the invention designs an array correction method which can more accurately correct array errors under the conditions of low signal-to-noise ratio and less array element number.
Disclosure of Invention
The invention aims to solve the problem that when the underwater sound target orientation is estimated, the method based on the characteristic structure configuration is not suitable for correcting a small-aperture array, so that the accuracy of the estimated underwater sound target orientation result is low when the small-aperture array is used, and further provides an array self-correcting method of error-free covariance matrix separation.
It comprises the following steps:
s1, acquiring signals of an underwater ship, and solving a covariance matrix of uncorrected array output signals formed by underwater sound signal receiving transducers according to the signals;
s2, acquiring a signal component of a covariance matrix of the error-free array output signal by using the covariance matrix of the uncorrected array output signal;
s3, estimating the underwater sound target azimuth by using the signal component obtained in the S2 and an MUSIC method;
s4, solving an array amplitude phase error by using a characteristic structure configuration method and the estimated underwater sound target direction;
s5, iterating S1-S4, setting a minimum threshold epsilon, and when | t [iter] -t [iter-1] If | > ε, update
And returning to S1 for next iteration, wherein iter represents the number of iterations; when | t [iter] -t [iter-1] And if the | < epsilon, stopping iteration and outputting the current array amplitude phase error and the estimated underwater sound target azimuth.
Further, the specific process of S1 is:
defining M underwater acoustic signal receiving transducers in water as array elements to form a uniform linear array, acquiring signals of an underwater ship, and making signals far away from the uniform linear array be plane waves, wherein if K narrow-band plane waves are all incident to the uniform linear array, the covariance matrix of the signals output by the error-free array is as follows:
wherein,
is an error-free array manifold vector of signals, is->
Is to diagonalize the signal power and->
Is paired with>
Is transposed and is present>
Is diagonalized for the noise power, R s Is the signal component of the covariance matrix, R n Is the noise component of the covariance matrix;
suppose that the amplitude error of the m-th array element is a m The phase error is
The array amplitude phase error matrix is then expressed as:
wherein,
represents a pair->
Diagonalization, M =1,2, …, M;
the covariance matrix of the uncorrected array output signal:
wherein,
represents T e The conjugate transpose of (c).
Further, the specific process of S2 is:
assuming covariance matrix of reconstructed error-free array output signals
Consisting of signal and noise, i.e. the signal component and the noise component of the covariance matrix of the error-free array output signal are ≥ respectively>
And &>
The array amplitude phase error matrix is denoted as T e Then, obtaining a covariance matrix of the reconstructed error-free array output signal by using a covariance fitting criterion according to the covariance matrix of the uncorrected array output signal:
wherein,
is a Toeplitz matrix, determined by the first row element r, then ^ er>
And->
If the matrix is a semi-positive definite matrix, toeplitz (r) is more than or equal to 0, toeplitz (r) represents that r Toeplitz is converted; assuming that the noise power is σ and the elements therein are all real numbers greater than 0, then ≧>
Solving r in the formula (4) by using an optimization algorithm formula based on a covariance fitting criterion to obtain a signal component of a covariance matrix of the noiseless error-free array output signal:
further, the covariance fitting criterion in S2:
wherein X and
respectively a known matrix and a matrix to be fitted.
Further, the specific process of S3 is:
wherein,
represents->
Is in the noise subspace, < >>
Represents->
A (theta) represents an error-free array manifold vector of the signal, a H And (theta) represents the conjugate transpose of a (theta).
Further, the specific process of S4 is:
covariance matrix of uncorrected array output signals
Performing a feature value decomposition in that->
Of the noise subspace
And/or>
And (3) performing stretched space orthogonality, and constructing a cost function of a characteristic structure configuration method by using orthogonal characteristics:
wherein T represents T e Column vector of diagonal elements, K' representing estimated orientation
Estimated number of targets, D k Denotes a (θ) k ) A diagonalized M × M dimensional matrix;
solving T by using a Lagrange multiplier method to obtain an array amplitude phase error T e ＝diag(t)。
Has the advantages that:
the method solves the covariance matrix of output signals of an uncorrected array (array with errors) in a small-aperture uniform linear array consisting of underwater acoustic signal receiving transducers according to signals of an underwater ship; the covariance matrix of the uncorrected array output signals is utilized to construct a covariance matrix of the noiseless error-free array output signals, and the signal components of the covariance matrix of the noiseless error-free array output signals are obtained by utilizing an optimization algorithm based on a covariance fitting criterion; estimating the underwater sound target azimuth by utilizing the signal components and the MUSIC method; solving the array amplitude phase error by using a characteristic structure configuration method and the estimated target azimuth; and improving the estimation precision of the underwater sound target direction and the array amplitude phase error by using an iteration mode, and finally obtaining the array amplitude phase error and the underwater sound target direction. The invention provides a novel array self-correction method for amplitude phase errors of a uniform linear array with a small aperture, which is combined with a covariance matrix reconstruction method (formula 11), a characteristic structure configuration method (formula 13) and an iteration method to realize the separation of a covariance matrix and an amplitude phase error matrix of an error-free array output signal from a covariance matrix of an uncorrected array output signal. The invention obtains an accurate array error matrix and a covariance matrix of a reconstructed error-free array output signal which is approximate to error-free and noise-free, and utilizes the signal component of the covariance matrix of the reconstructed error-free array output signal to estimate the underwater sound target direction, thereby being capable of accurately estimating the underwater sound target direction.
The method does not need a specific correction source, is not influenced by interference signals, and can correct the array in a real marine environment to realize array self-correction; the array can still be accurately corrected when the number of the array elements is small without needing more array elements; the reconstructed covariance matrix obtained by the method has no array error and no noise component, so the method still has good performance when the environmental signal-to-noise ratio is low, and the covariance matrix without error and noise has no error
Ratio->
The underwater sound target position can be estimated more accurately, and the accurate underwater sound target position estimation guarantees the accurate estimation result of the array error. In the iterative process, the underwater sound target estimation direction and the estimation array amplitude phase error are gradually accurate, and the effect of positive feedback is realized.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic view of a uniform linear array;
FIG. 3 is a schematic diagram of MUSIC azimuth spectra before and after array calibration in simulation analysis;
FIG. 4 is a schematic representation of the estimated variance of Array Error (AED) as a function of iteration number in a simulation analysis;
FIG. 5 is a schematic diagram of variation of AED with array element number in simulation analysis;
FIG. 6 (a) is a schematic diagram of the variation of the estimated orientation MSE with the number of array elements in simulation analysis;
FIG. 6 (b) is a schematic diagram of the variation of the resolution probability with the number of array elements in simulation analysis;
FIG. 7 is a schematic diagram of the variation of the AED with signal-to-noise ratio in a simulation analysis;
FIG. 8 (a) is a schematic diagram of the variation of the estimated azimuth MSE with the signal-to-noise ratio in simulation analysis;
FIG. 8 (b) is a diagram illustrating the variation of the resolution probability with the signal-to-noise ratio in the simulation analysis;
Detailed Description
The first specific implementation way is as follows: the embodiment is described with reference to fig. 1-2, and the method for array self-calibration without error covariance matrix separation according to the embodiment includes the following steps:
s1, obtaining signals of an underwater ship, and solving a covariance matrix of uncorrected array output signals formed by underwater acoustic signal receiving transducers according to the signals.
In actual environments such as oceans and lakes, a large number of targets such as ships exist, most mechanical devices including power systems transmit signals with different frequency bands, usually, signals transmitted by sound sources far away from the array can be assumed to be plane waves, that is, signals received by all array elements come from the same direction and are incident in parallel. The method comprises the steps of obtaining signals of an underwater ship, and assuming that K narrow-band plane waves are incident to an M-element uniform linear array with a small aperture, wherein a uniform linear array model is shown in figure 2, the array consists of M array elements, and the array elements are underwater acoustic signal receiving transducers. Orientation theta k Is the angle between the incident direction of the kth signal and the normal direction of the uniform linear array. The kth signal has time t denoted as s k (t), then the output signal of the uniform linear array error-free array is represented as:
wherein,
a(θ k ) Is an error-free array manifold vector for the kth signal, specifically expressed as:
wherein,
j is an imaginary part, d is the distance between the array elements, lambda is the signal wavelength, M is the serial number of the array elements, and M =1,2, …, M. S (t) = [ S ] 1 (t),…,s K (t)] T Is a set of K uncorrelated narrowband signals, N (t) = [ N = 1 (t),…,n M (t)] T Is zero-mean white Gaussian noise, n, of temporal and spatial irrelevancy m (t) is the noise received by the mth array element, (. Cndot.) T And (·) H Representing the transpose and conjugate transpose of a vector or matrix, respectively, an error-free array is a uniform linear array that contains no errors. Then the covariance matrix R of the error-free array x (t) output signal x ＝E[x(t)x H (t)]Comprises the following steps:
wherein,
is the signal component of the covariance matrix, is->
Indicates whether or not a combination>
Diagonalization of (A), R n Is the noise component of the covariance matrix, is->
Represents the power of the signal +>
Representing the noise power.
Suppose the amplitude error of the m-th array element is a m The phase error is
The array amplitude phase error matrix is then expressed as:
the uncorrected array signal consists of the error-free array signal and the array amplitude phase error matrix, so the error-free uniform linear array is called the "uncorrected array", the uncorrected array manifold vector being based on equations (2) and (4)
Expressed as:
for the K underwater acoustic target orientations,
the output signal of the uncorrected array is expressed according to equations (1) and (4):
the invention adopts a multiple signal classification Method (MUSIC) to carry out high-resolution azimuth estimation on the underwater sound target, and because the MUSIC high-resolution method is generally greatly influenced by array errors and noise, the method utilizes
The DOA estimation result is far more error-free than the error-free array R s The DOA estimation result of (1).
And S2, acquiring the signal component of the covariance matrix of the error-free array output signal by using the covariance matrix of the uncorrected array output signal.
Signal component R according to equation (3) s The (m, n) th element of (a) is
Obviously, R s Are identical and two elements symmetrical about the main diagonal are conjugate to each other, and therefore, R is s Is a Toeplitz matrix. Due to the fact that ^ in the formula (7)>
Has a signal component of->
Based on the formulae (4) and (5)>
The (m, n) th item of (a) is represented as:
according to the formula (8), although
Two elements of (4) that are symmetrical about a main diagonal are conjugate to each other, but the main diagonal elements are not the same, nor are the elements parallel to the main diagonal, and therefore->
No longer a Toeplitz matrix.
First, the signal component R of the covariance matrix of the error-free array output signal in equation (3) is solved using equation (11) s And constraining the covariance matrix of the reconstructed error-free array output signal to be a Toeplitz matrix. Consider the covariance fitting criterion:
covariance fitting criteria are detailed in Zhang G P, liu K X, fu J et al, covariance matrix reconstruction method on amplification and phase constraints with application to extended array adaptation.J.Acoust.Soc.Am., 2022;151 (5) < 3164 > -3176, | | α | | non-combustible cells F And delta does not count 2 The F-norm and 2-norm of the matrix alpha and vector delta, respectively. X in the formula (9) and
minimization of a known matrix and a matrix to be fitted, respectively>
Can realize that from X to->
Minimizing the fit of->
Can be converted into: />
Wherein Tr (alpha) represents the trace of the matrix alpha, and alpha is more than or equal to 0, which means that the matrix alpha is a semi-positive definite matrix.
The method of the invention utilizes
Covariance matrix fitted to the reconstructed error-free array output signal->
Like equation (7), assume->
Still consisting of both signal and noise, without errorsThe signal component and the noise component of the covariance matrix of the difference array output signal are ≥ respectively>
And &>
The array amplitude phase error matrix is denoted as T e Then, the covariance matrix of the reconstructed error-free array output signal is obtained according to the covariance matrix of the uncorrected array output signal by using the covariance fitting criterion
Based on the above introduction, theoretically->
Is a Toeplitz matrix that can be determined by its first row element, so assuming that its first row element is r, then ≦ H>
And->
Is a semi-positive definite matrix expressed by Toeplitz (r) ≧ 0, and Toeplitz (r) expresses that r is converted into Toeplitz. Assuming that the noise power vector is σ and all elements thereof are real numbers greater than 0, then ≧>
And σ > 0. Based on the above, the matrix to be fitted->
Is particularly shown as
Solving r using an optimization algorithm formula (11) based on a covariance fitting criterion:
due to the objective function in the optimization algorithm
Cannot be solved directly, requiring the introduction of an M × M-dimensional variable G matrix in place of->
And adds a restraint>
The invention is an iterative method, T in equation (11) e Is a known quantity, and in the first iteration, T is measured e Set as an M-dimensional identity matrix. Equation (11) is a semi-positive convex optimization problem that can be solved with a tool box, such as the SeDumi software or CVX convex optimization tool box. Finally, the signal component { [ MEANS ]) of the reconstructed noise-free covariance matrix is obtained using r solved by equation (11)>
And S3, estimating the underwater sound target azimuth by using the signal component obtained in the S2 and the MUSIC method.
Obtaining a noise-free signal component using r solved for by equation (11)
Performing the orientation estimation of the MUSIC method:
wherein,
indicating underwater sound target bearing, pair>
Performing a characteristic value decomposition and/or a value combination>
Is->
Is in the noise subspace, < >>
Means that a parameter a, which minimizes the function f (a) is found>
A ratio may be obtained>
And a more accurate orientation estimation result lays a foundation for estimating array errors more accurately in the follow-up process.
And S4, solving the array amplitude phase error by using a characteristic structure configuration method and the estimated underwater sound target direction.
Using feature configuration methods and underwater acoustic target orientations
And solving the array amplitude phase error. Covariance matrix based on uncorrected array output signal>
Performing a characteristic value decomposition, theoretically->
Signal subspace->
And &>
Open spaces are identical and a signal subspace +>
And the noise subspace->
Is orthogonal, and therefore pick>
And &>
Are stretched in a spatial orthogonal manner, i.e.
span (A) represents the space spanned by the column vectors in matrix A. Constructing a cost function of a feature structure configuration method by using the orthogonal characteristic:
t in pair (13) e a(θ k ) Is transformed by e a(θ k )＝diag(a(θ k ) T, wherein diag (a (θ) k ) Is a (theta) k ) Diagonalized M × M dimensional matrix, which is simply denoted as D k . T is T e Column vectors formed by diagonal elements, i.e.
Then formula (13) can be converted again to:
estimated azimuth obtained by equation (12)
Estimating the target number K' to obtain D k In, to>
The characteristic value is resolved into->
The result in parentheses in equation (14) can therefore be solved and expressed as U:
cost function conversion to J = t H Ut. With the first array element as a standard, assuming that the first array element has no error, i.e.
Then t H w =1, where w = [1,0, …,0]Is an M-dimensional column vector with a first value of 1 and the remaining values of 0. Solving t using a constrained quadratic minimization problem as follows:
the solution of equation (16) is quite classical and can be obtained using the Lagrangian multiplier method
Wherein T is T e So that the array amplitude phase error is T e ＝diag(t)。
And S5, improving the estimation precision of the underwater sound target direction and the array amplitude phase error in the S3 and the S4 by utilizing a mode of iteration S1-S4. Using iterative means to make T e Is more accurate and makes
Approaches to R s . The iterative process is as follows, wherein A [iter] Represents the result of the iter iteration of a:
initialization: t is e [1] Is an M-dimensional identity matrix
In the iterative process, T e And
the method and the device are more accurate, and finally the covariance matrix and the amplitude phase error matrix of the error-free array output signals are separated from the covariance matrix of the uncorrected array. If ITER iterations are performed in total, then finally->
For estimating array error and using->
And carrying out orientation estimation.
The invention has the following advantages: firstly, the method can realize array self-correction without a specific correction source; secondly, the method obtains the signal components of the covariance matrix of the approximate noiseless error-free array output signal by using the covariance matrix reconstruction method (formula 11)
A ratio may be obtained>
The orientation is estimated more accurately, and the accurate estimation of the orientation ensures an accurate estimation result of the array error. In the iterative process, the estimation of the azimuth and the estimation of the array errors are gradually accurate, and the effect of positive feedback is realized.
Simulation analysis
The array error correction capability and the azimuth estimation performance after array correction of the invention are examined by using a MUSIC method. In addition, as a comparison, the results of the uncorrected array and the theoretical error-free array are also given in the simulation. In the simulation, the receiving signals (plane waves) of the underwater acoustic signal receiving transducer are all narrow-band signals with the frequency of 3kHz, and have random phases, the fast beat number of the receiving signals is 500, and the spacing between array elements (underwater acoustic signal receiving transducers) is half wavelength of 3kHz, namely 0.25m.
A. Position spectrogram
Two underwater ships are used as targets in the space, the directions of the two underwater ships are respectively 10 degrees and 17 degrees, the signal-to-noise ratio is 0dB, and the number of array elements is 10. Assuming no error in the first array element, the array amplitude error a of the uncorrected uniform linear array 1 To a 10 Is [1,0.7,0.4,3,1.8,0.9,1.2,1.5,2,1.6]Error in phase
Eta in m Is [0 °,30 °, -10 °,10 °, -20 °,16 °, -10 °,20 °,10 °,15 ° ]]X pi/180. Fig. 3 shows MUSIC azimuth spectrograms before and after the uniform linear array correction, and black circles in the spectrograms represent the actual azimuth of a ship target. The minimum amplitude of the recess at the uncorrected array peak in the figure is about-0.9 dB, two ship targets can hardly be distinguished, but the invention has very deep recess and can clearly distinguish two ship targets.
B. Array error estimation bias and azimuth estimation performance
The invention estimates the amplitude phase error of the array as T e In order to distinguish the Array Error from the estimated Error, the estimated Error is referred to as "estimated Error development of Array Error" (AED), and is calculated as shown in equation (1):
in addition, the section will examine the orientation estimation accuracy and resolution probability before and after array correction when two ship targets exist in the space. The method utilizes Mean Square Error (MSE) to judge the ship target azimuth estimation precision, and if the azimuth estimation result satisfies the formula (2), the ship target azimuth is judged to be successfully distinguished.
Wherein, theta 1 And theta 2 Representing the true orientation of the two ship targets,
and &>
The estimated orientations of the two ship targets for the tth monte carlo experiment are shown separately. If a total of F trials were performed, with the estimated results of the F trials satisfying equation (2), the resolution probability was F/F, and each result in the graph was performed 200 independent Meng Teke experiments.
C. Number of iterations
Assuming that the first array element has no error, other array elements all have random amplitude and phase errors, and the amplitude error a of the m-th array element m Is a random number between 0 and 5, the phase error is measured in degrees,
eta in m Is a random number between-30 x pi/180 and 30 x pi/180. Assuming that the number of array elements is 10, the orientations of two ship targets are 10 degrees and 17 degrees respectively, and the signal-to-noise ratio is 10dB, fig. 4 examines the change condition of the AED of the invention along with the iteration times, and the iteration times are increased from 1 to 50. In fig. 4, the AED is gradually reduced along with the increase of the iteration times, the array error estimation is accurate, and the invention can satisfy | t by only 9 iterations [iter] -t [iter-1] |＜10 -4 。
D. Number of array elements
Assuming that two ship targets are in space, the directions of the two ship targets are 10 degrees and 17 degrees respectively, the signal-to-noise ratio is 10dB, and the number of array elements is increased from 5 to 20. Figures 5 and 6 examine the performance of the AED and DOA estimates of the present invention as a function of the number of elements. In fig. 5, the AED is progressively reduced and less than 0.3 as the number of array elements increases. The uncorrected array in FIG. 6 (b) has a resolution probability greater than 0.9 when the number of array elements is greater than 11. The resolution probability of the invention is close to 1 and the estimation accuracy is much higher than that of the uncorrected array.
E. Signal to noise ratio
The array error is still random amplitude phase error, the number of array elements is assumed to be 10, the directions of two ship targets are 10 degrees and 17 degrees respectively, and the signal-to-noise ratio is increased from-10 dB to 20dB. Fig. 7 and 8 examine the performance of the AED and DOA estimates of the present invention as the signal-to-noise ratio changes, with the AED of fig. 7 decreasing with increasing signal-to-noise ratio, and with the signal-to-noise ratio greater than 2db, the AED is less than 0.2. The present invention in fig. 8 effectively improves the estimation accuracy and resolution probability, which is much higher than the uncorrected array.
In practical engineering, when the aperture of the array is limited, a high-resolution azimuth estimation method is usually applied to improve resolution, but the performance of most high-resolution methods is seriously degraded due to array errors, so that the invention provides an array self-correction method for error-free covariance matrix separation aiming at amplitude phase errors.
The covariance matrix of the actual uncorrected array output signal is composed of a covariance matrix of the uncorrected array output signal and an amplitude phase error matrix, and for a uniform linear array, the covariance matrix of the uncorrected array output signal theoretically has a Toeplitz structure, but when the array has errors, the covariance matrix does not have the Toeplitz structure any more, so that the covariance matrix of the uncorrected array output signal is reconstructed by using the covariance matrix of the uncorrected array output signal, the reconstructed covariance matrix is constrained to be the Toeplitz matrix, and the covariance matrix and the amplitude phase error matrix of the uncorrected array output signal are separated from the covariance matrix of the uncorrected array output signal by combining a characteristic structure configuration method and an iteration method. Simulation results show that the invention can accurately estimate the amplitude and phase errors of the array, and obtain the covariance matrix of the reconstructed error-free array output signals which are approximately free of noise, and the covariance matrix can obviously improve the resolution and the estimation precision when being used in the MUSIC method. The method does not need a specific correction source, is not influenced by interference signals, and can correct the array in a real marine environment.
Claims (6)
1. An array self-correction method for error-free covariance matrix separation, characterized in that: it comprises the following steps:
s1, acquiring signals of an underwater ship, and solving a covariance matrix of uncorrected array output signals formed by underwater sound signal receiving transducers according to the signals;
s2, acquiring a signal component of a covariance matrix of the error-free array output signal by using the covariance matrix of the uncorrected array output signal;
s3, based on the signal components obtained in the S2, estimating the underwater sound target azimuth by using an MUSIC method;
s4, solving an array amplitude phase error by using a characteristic structure configuration method and the estimated underwater sound target direction;
s5, iterating the S1-S4, setting a minimum threshold value epsilon, and when | t [iter] -t [iter-1] When | > epsilon, update T e [iter+1] ＝diag(t [iter] ) And returning to S1 for next iteration, iter representing the number of iterations, t [iter] Column vector, t, representing the current iteration [iter-1] A column vector representing a previous iteration; when | t [iter] -t [iter-1] And if the | < epsilon, stopping iteration and outputting the current array amplitude phase error and the estimated underwater sound target azimuth.
2. An error-free covariance matrix separation array self-correction method as claimed in claim 1, wherein: the specific process of S1 is as follows:
defining M underwater acoustic signal receiving transducers in water as array elements to form a uniform linear array, acquiring signals of an underwater ship, enabling the signals far away from the uniform linear array to be plane waves, and assuming that K narrow-band plane waves are incident to the uniform linear array, outputting a covariance matrix of signals by the error-free array:
wherein,
is an error-free array popularity vector of signals, is->
Is to diagonalize the signal power and->
Is to
In conjunction with the device, in conjunction with the device>
Is diagonalized for the noise power, R s Is the signal component of the covariance matrix, R n Is the noise component of the covariance matrix;
suppose the amplitude error of the m-th array element is a m The phase error is
The array amplitude phase error matrix is then expressed as:
wherein,
representing a pair>
Diagonalization, M =1,2, …, M;
the covariance matrix of the uncorrected array output signal:
wherein,
represents T e The conjugate transpose of (c).
3. An error-free covariance matrix separation array self-correction method as claimed in claim 2, wherein: the specific process of S2 is as follows:
assuming covariance matrix of reconstructed error-free array output signals
Consisting of signal and noise, i.e. the signal component and the noise component of the covariance matrix of the error-free array output signal are ≥ respectively>
And &>
The array amplitude phase error matrix is denoted as T e Then, obtaining a covariance matrix of the reconstructed error-free array output signal by using a covariance fitting criterion according to the covariance matrix of the uncorrected array output signal:
wherein,
is a Toeplitz matrix composed of a first row elementIs determined by the pixel r, then->
And->
If the matrix is a semi-positive definite matrix, toeplitz (r) is more than or equal to 0, toeplitz (r) represents that r Toeplitz is converted; assuming that the noise power is σ and the elements therein are all real numbers greater than 0, then ≧>
Solving r in the formula (4) by using an optimization algorithm formula based on a covariance fitting criterion to obtain a signal component of a covariance matrix of the noiseless error-free array output signal:
4. a method of array self-correction for error-free covariance matrix separation as claimed in claim 3, wherein: covariance fitting criterion in S2:
wherein X and
respectively a known matrix and a matrix to be fitted.
5. An array self-correction method without error covariance matrix separation as claimed in claim 4, wherein: the specific process of S3 is as follows:
the MUSIC method comprises the following steps:
wherein,
indicates the underwater sound target position>
Represents->
Is in the noise subspace, < >>
Represents->
A (theta) represents an error-free array prevailing vector of signals, a H And (theta) represents the conjugate transpose of a (theta).
6. An error-free covariance matrix separation array self-correction method as claimed in claim 5, wherein: the specific process of S4 is as follows:
covariance matrix of uncorrected array output signals
A characteristic value decomposition is carried out in that->
Is not in the noise subspace->
And with
The space formed by the stretching is orthogonal,constructing a cost function of a feature structure configuration method by using orthogonal characteristics:
wherein T represents T e Column vector of diagonal elements, K' representing estimated orientation
Estimated number of targets, D k Denotes a (theta) k ) A diagonalized M × M dimensional matrix;
solving T by using a Lagrange multiplier method to obtain the array amplitude phase error T e ＝diag(t)。
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