An array self-calibration method without error covariance matrix separation

Abstract

An array self-calibration method for separating the error covariance matrix, specifically related to a method for separating the covariance matrix of an error-free array and the amplitude-phase error matrix from the covariance matrix of an uncalibrated array with errors, to solve the problem that when estimating the azimuth of an underwater acoustic target, the eigenstructure configuration method is not applicable to calibrating small-aperture arrays, resulting in a low accuracy rate of the estimated azimuth result of the underwater acoustic target for small-aperture arrays. Solve the covariance matrix of the output signal of the uncalibrated array in a uniform linear array with a small aperture composed of underwater acoustic signal receiving transducers according to the signals of ships in water; construct the covariance matrix of the output signal of the error-free array without noise using the above matrix, and obtain the signal components of this matrix; estimate the azimuth of the underwater acoustic target using the signal components and the MUSIC method; use the eigenstructure configuration method and the target azimuth to solve the array amplitude-phase error. It belongs to the field of underwater acoustic target azimuth estimation.

Description

Technical Field

[0001] The present invention relates to an array self-calibration method, specifically to a method for separating the covariance matrix of an error-free array and the amplitude-phase error matrix from the covariance matrix of an uncalibrated array with errors, belonging to the field of underwater acoustic target azimuth estimation. Background Art

[0002] Direction of Arrival (DOA) estimation is the premise and basis for research on underwater acoustic target recognition, positioning, tracking, etc., and is one of the important research contents of array signal processing. It obtains the azimuth information of the target of interest from the background of noise and interference. Nowadays, there are many methods for DOA estimation. The most representative one is the Conventional Beamforming (CBF) method, whose advantage lies in its high algorithm robustness and little influence by array errors. However, in practical applications, the size of the ship carrying the array is limited and an array with a very long aperture cannot be carried. But when the array aperture is small, the angular resolution of the CBF method is low and it cannot distinguish the azimuths of two targets with a small spatial angular interval. In this case, high-resolution azimuth estimation methods are usually used to improve the resolution, such as the high-resolution beamforming Capon method and the Multiple Signal Classification (MUSIC) method, etc. These methods have better resolution than the CBF method. However, the Capon method is an adaptive algorithm and the MUSIC method is a subspace algorithm based on eigenvalue decomposition. These two methods are severely affected by errors, and a very small element deviation may cause the estimation performance of these two types of methods to drop sharply. Not only these two types of methods, in fact, array deviation will deteriorate the performance of most high-resolution algorithms. However, various array errors are inevitable during the actual array manufacturing and installation process, and the element amplitude-phase error is the most common array error. In order to improve the performance of the azimuth estimation algorithm, it is necessary to first correct the array errors. Therefore, scholars have proposed many array error correction methods.

[0003] When estimating the azimuth of an underwater acoustic target, the self-calibration algorithm regards the calibration source azimuth as an unknown parameter and jointly solves the array error and the source azimuth. Due to its good performance and stronger inclusiveness for the calibration environment, this method has been more widely applied and recognized. The method proposed by Friedlander and Weiss based on the eigenstructure configuration method is a classical self-calibration method. This method estimates the array error by using the orthogonality between the noise subspace and the array manifold vector. Unfortunately, this method is limited to small array perturbations and cannot effectively calibrate the array in a low signal-to-noise ratio environment. In addition, this method requires a large number of array elements. Therefore, this method is not applicable to calibrating small-aperture arrays. In order to more effectively calibrate small-aperture arrays, the present invention designs an array calibration method, which can more accurately correct array errors in the case of low signal-to-noise ratio and fewer array elements. Summary of the Invention

[0004] To solve the problem that the feature structure configuration method is not applicable to calibrating small-aperture arrays when estimating the azimuth of underwater acoustic targets, resulting in a low accuracy of the estimated azimuth of underwater acoustic targets for small-aperture arrays, the present invention further proposes an array self-calibration method without error covariance matrix separation.

[0005] It includes the following steps:

[0006] S1. Obtain the signals of ships in water, and solve the covariance matrix of the output signals of the uncalibrated array composed of underwater acoustic signal receiving transducers according to the signals;

[0007] S2. Use the covariance matrix of the output signals of the uncalibrated array to obtain the signal components of the covariance matrix of the output signals of the error-free array;

[0008] S3. Use the signal components obtained in S2 and the MUSIC method to estimate the azimuth of underwater acoustic targets;

[0009] S4. Use the feature structure configuration method and the estimated azimuth of underwater acoustic targets to solve the array amplitude and phase errors;

[0010] S5. Iterate S1 - S4, set a minimum threshold ε, when |t [iter] -t [iter-1] | > ε, update and return to S1 for the next iteration, where iter represents the number of iterations; when |t [iter] -t [iter-1] | < ε, stop the iteration, and output the current array amplitude and phase errors and the estimated azimuth of underwater acoustic targets.

[0011] Furthermore, the specific process of S1 is as follows:

[0012] Define M underwater acoustic signal receiving transducers in water as array elements to form a uniform linear array, obtain the signals of ships in water, let the signals far from the uniform linear array be plane waves, assume that K narrowband plane waves are incident on the uniform linear array, then the covariance matrix of the output signals of the error-free array:

[0013]

[0014] Wherein, is the error-free array manifold vector of the signal, is the diagonalization of the signal power, is the conjugate transpose of ; is the diagonalization of the noise power, R s is the signal component of the covariance matrix, R n is the noise component of the covariance matrix;

[0015] Assume that the amplitude error of the m-th array element is a m , and the phase error is Then the array amplitude-phase error matrix is expressed as:

[0016]

[0017] where, denotes the diagonalization of , m = 1, 2,..., M;

[0018] Then the covariance matrix of the uncorrected array output signal:

[0019]

[0020] where, denotes the conjugate transpose of T e .

[0021] Furthermore, the specific process of S2 is as follows:

[0022] Assume that the covariance matrix of the reconstructed error-free array output signal consists of a signal and noise, that is, 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 expressed as T e , then according to the covariance matrix of the uncorrected array output signal, the covariance matrix of the reconstructed error-free array output signal is obtained using the covariance fitting criterion:

[0023]

[0024] where, is a Toeplitz matrix, determined by the first row element r, then and is a positive semi-definite matrix, then Toeplitz(r) ≥ 0, Toeplitz(r) means to Toeplitzize r; assume that the noise power is σ, and all elements in it are real numbers greater than 0, then

[0025] Use the optimization algorithm formula based on the covariance fitting criterion to solve r in Equation (4) to obtain the signal component of the covariance matrix of the noise-free error-free array output signal:

[0026]

[0027] Furthermore, the covariance fitting criterion in S2:

[0028]

[0029] where, X and They are the known matrix and the matrix to be fitted respectively.

[0030] Furthermore, the specific process of S3 is as follows:

[0031]

[0032] Among them, represents the noise subspace of represents the conjugate transpose of H a(θ) represents the error-free array manifold vector of the signal, and a

[0033] Furthermore, the specific process of S4 is as follows:

[0034] Perform eigenvalue decomposition on the covariance matrix of the uncalibrated array output signal. Since the noise subspace of is orthogonal to the space spanned by , use the orthogonality property to construct the cost function of the eigenstructure configuration method:

[0035]

[0036] Among them, t represents T e the column vector composed of the diagonal elements, K′ represents the estimated azimuth the number of estimated targets, D k represents the M×M-dimensional matrix obtained by diagonalizing a(θ k );

[0037] Use the Lagrange multiplier method to solve for t, that is, obtain the array amplitude and phase error T e = diag(t).

[0038] Beneficial effects:

[0039] The present invention solves the covariance matrix of the output signal of an uncorrected array (array with errors) of a small-aperture uniform linear array composed of underwater acoustic signal receiving transducers according to the signals of ships in water; constructs the covariance matrix of the output signal of an error-free and noise-free array by using the covariance matrix of the output signal of the uncorrected array, and obtains the signal components of the covariance matrix of the output signal of the error-free and noise-free array by using an optimization algorithm based on a covariance fitting criterion; estimates the underwater acoustic target azimuth by using the signal components and the MUSIC method; solves the array amplitude and phase errors by using the eigenstructure configuration method and the estimated target azimuth; and improves the estimation accuracy of the underwater acoustic target azimuth and the array amplitude and phase errors in an iterative manner, and finally obtains the array amplitude and phase errors and the underwater acoustic target azimuth. The present invention proposes a new method for array self-calibration of amplitude and phase errors applicable to a small-aperture uniform linear array, which combines a covariance matrix reconstruction method (Formula 11), an eigenstructure configuration method (Formula 13) and an iterative method to separate the covariance matrix of the output signal of the error-free array and the amplitude and phase error matrix from the covariance matrix of the output signal of the uncorrected array. The present invention obtains an accurate array error matrix and a reconstructed covariance matrix of the output signal of the error-free array that is approximately error-free and noise-free, and uses the signal components of the reconstructed covariance matrix of the output signal of the error-free array to estimate the underwater acoustic target azimuth, and can accurately estimate the underwater acoustic target azimuth.

[0040] The present invention does not require a specific calibration source, is not affected by interference signals, can calibrate the array in a real ocean environment, and realizes array self-calibration; does not require a large number of array elements, and can still accurately calibrate the array when the number of array elements is small; the reconstructed covariance matrix obtained by this method not only has no array errors, but also has no noise components, so the present invention still has good performance when the environmental signal-to-noise ratio is low, and the covariance matrix without errors and noise than can more accurately estimate the underwater acoustic target azimuth, and the accurate estimated azimuth of the underwater acoustic target ensures the accurate estimation result of the array error. During the iterative process, the estimated azimuth of the underwater acoustic target and the estimated array amplitude and phase errors become more and more accurate, realizing the "positive feedback" effect. Brief Description of the Drawings

[0041] Figure 1 is the flowchart of the present invention;

[0042] Figure 2 is a schematic diagram of a uniform linear array;

[0043] Figure 3 is a schematic diagram of the MUSIC azimuth spectrum before and after array calibration in simulation analysis;

[0044] Figure 4 is a schematic diagram of the change of the estimated deviation (AED) of the array error with the number of iterations in simulation analysis;

[0045] Figure 5 It is a schematic diagram showing the variation of AED with the number of array elements in simulation analysis;

[0046] Figure 6(a) is a schematic diagram showing the variation of the estimated azimuth MSE with the number of array elements in simulation analysis;

[0047] Figure 6(b) is a schematic diagram showing the variation of the resolution probability with the number of array elements in simulation analysis;

[0048] Figure 7 It is a schematic diagram showing the variation of AED with the signal-to-noise ratio in simulation analysis;

[0049] Figure 8(a) is a schematic diagram showing the variation of the estimated azimuth MSE with the signal-to-noise ratio in simulation analysis;

[0050] Figure 8(b) is a schematic diagram showing the variation of the resolution probability with the signal-to-noise ratio in simulation analysis; Detailed implementation manners

[0051] Detailed implementation manner 1: In combination with Figure 1 - Figure 2 This detailed implementation manner will be described. The array self-calibration method without error covariance matrix separation described in this detailed implementation manner includes the following steps:

[0052] S1. Obtain the signals of ships in water, and solve the covariance matrix of the output signals of the uncalibrated array composed of underwater acoustic signal receiving transducers according to the signals.

[0053] In actual marine, lake and other real environments, there are a large number of targets such as ships. Most mechanical devices, including power systems, will emit signals with different frequency bands. Generally speaking, the signals emitted by sound sources far from the array can be assumed to be plane waves, that is, the signals received by all array elements come from the same direction and are parallel incident. Obtain the signals of ships in water. Assume that K narrowband plane waves are incident on a uniform linear array with M elements and a small aperture. The uniform linear array model is as Figure 2 shown. This array is composed of M array elements, and the array elements are underwater acoustic signal receiving transducers. Azimuth θ k is the angle between the incident direction of the k-th signal and the normal direction of the uniform linear array. The k-th signal at time t is expressed as s k (t). Then the output signal of the error-free array of the uniform linear array is expressed as:

[0054]

[0055] Among them, a(θ k ) is the error-free array manifold vector of the k-th signal, and is specifically expressed as:

[0056]

[0057] Among them, j is the imaginary part, d is the element spacing, λ is the signal wavelength, m is the serial number of the element, and m = 1, 2, …, M. S(t) = [s1(t), …, s K (t)] T is a set of K mutually uncorrelated narrowband signals, and N(t) = [n1(t), …, n M (t)] T is a zero-mean Gaussian white noise with spatio-temporal uncorrelation, and n m (t) is the noise received by the m-th element, and (·) T and (·) H respectively represent the transpose and conjugate transpose of a vector or matrix. The error-free array is a uniform linear array without errors. Then, the covariance matrix R x = E[x(t)x H (t)] is as follows:

[0058]

[0059] Among them, is the signal component of the covariance matrix, represents the diagonalization of , and R n is the noise component of the covariance matrix, represents the signal power, represents the noise power.

[0060] Assume that the amplitude error of the m-th element is a m , and the phase error is Then, the array amplitude-phase error matrix is expressed as:

[0061]

[0062] The signal of the uncalibrated array is composed of the signal of the error-free array and the array amplitude-phase error matrix. Therefore, the uniform linear array with errors is called the "uncalibrated array". According to equations (2) and (4), the manifold vector of the uncalibrated array is expressed as:

[0063]

[0064] For the azimuths of K underwater acoustic targets, According to equations (1) and (4), the output signal of the uncalibrated array is expressed as:

[0065]

[0066] The covariance matrix of

[0067]

[0068] The present invention adopts the multiple signal classification method (MUSIC) to perform high-resolution azimuth estimation of underwater acoustic targets. Since high-resolution methods such as MUSIC are usually greatly affected by array errors and noise, The DOA estimation result of the error-free array R is much worse than that of the error-free array R s The DOA estimation results are shown in Figure 2.

[0069] S2. Obtain a signal component of the covariance matrix of the error-free array output signal using the covariance matrix of the uncorrected array output signal.

[0070] According to formula (3), the signal component R s The (m,n)th element of Obviously, R s The elements parallel to the main diagonal are the same, and the two elements symmetric about the main diagonal are conjugate to each other, so R s is a Toeplitz matrix. Since in formula (7) The signal component is According to formulas (4) and (5), The (m,n)th term of is expressed as:

[0071]

[0072] According to formula (8), although The two elements symmetric about the main diagonal are conjugate to each other, but the main diagonal elements are different, and the elements parallel to the main diagonal are also different, so It is no longer a Toeplitz matrix.

[0073] First, use formula (11) to solve the signal component R of the covariance matrix of the error-free array output signal in formula (3): s , and the covariance matrix of the constrained reconstructed error-free array output signal is a Toeplitz matrix. Consider the covariance fitting criterion:

[0074]

[0075] The covariance fitting criterion can be found in Zhang G P, Liu K X, Fu J et al. Covariance matrix reconstruction method based on amplitude and phase constraints with application to extend array aperture. J. Acoust. Soc. Am., 2022; 151(5): 3164–3176, ||α|| F and ||δ||2 are the Frobenius norm and the 2-norm of matrix α and vector δ respectively. In formula (9), X and are the known matrix and the matrix to be fitted respectively. Minimizing can achieve the fitting from X to Minimizing can be transformed into:

[0076]

[0077] where Tr(α) represents the trace of matrix α, and α ≥ 0 means that matrix α is a positive semi-definite matrix.

[0078] The method of the present invention utilizes the covariance matrix of the error-free array output signal fitted and reconstructed which is the same as formula (7). Assuming that still consists of two parts: signal and noise. At this time, 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 according to the covariance matrix of the uncalibrated array output signal, the covariance matrix of the reconstructed error-free array output signal is obtained by using the covariance fitting criterion According to the above introduction, theoretically is a Toeplitz matrix and can be determined by its first row elements. Therefore, assuming that its first row elements are r, then and is a positive semi-definite matrix, denoted as Toeplitz(r) ≥ 0, where Toeplitz(r) means to Toeplitzize r. Assuming that the noise power vector is σ, and all its elements are real numbers greater than 0, then and σ > 0. According to the above content, the matrix to be fitted is specifically expressed as Use the optimization algorithm formula (11) based on the covariance fitting criterion to solve for r:

[0079]

[0080] Since the objective function in the optimization algorithm cannot be solved directly, it is necessary to introduce an M×M-dimensional variable G matrix to replace and add constraints The present invention is an iterative method. T in formula (11) e is a known quantity. In the first iteration, T e is set as an M-dimensional identity matrix. Formula (11) is a semi-definite convex optimization problem, and this problem can be solved using a toolbox, such as the SeDumi software or the CVX convex optimization toolbox. Finally, the signal component of the reconstructed noise-free covariance matrix is obtained using r solved by formula (11)

[0081] S3. Estimate the underwater acoustic target azimuth using the signal component obtained in S2 and the MUSIC method.

[0082] The noise-free signal component is obtained using r solved by equation (11) Perform azimuth estimation using the MUSIC method:

[0083]

[0084] Among them, represents the underwater acoustic target azimuth. Perform eigenvalue decomposition on is the noise subspace of means finding the parameter a that minimizes the function f(a). A more accurate azimuth estimation result can be obtained than , which lays a foundation for more accurately estimating the array error subsequently.

[0085] S4. Solve the array amplitude and phase errors using the eigenstructure configuration method and the estimated underwater acoustic target azimuth.

[0086] Using the eigenstructure configuration method and the underwater acoustic target azimuth Solve the array amplitude and phase errors. Perform eigenvalue decomposition on the covariance matrix of the output signal of the uncalibrated array. Theoretically, the signal subspace of is the same as the space spanned by , and the signal subspace is orthogonal to the noise subspace . Therefore, is orthogonal to the space spanned by , that is, span(A) represents the space spanned by the column vectors in matrix A. Use this orthogonality property to construct the cost function of the eigenstructure configuration method: ​

[0087]

[0088] For \(T\) in (13) e \(a(\theta\) k ) is transformed, and \(T\) e \(a(\theta\) k ) = diag(\(a(\theta\) k ))·\(t\), where diag(\(a(\theta\) k )) is an \(M\times M\) - dimensional matrix that diagonalizes \(a(\theta\) k ), which is simply denoted as \(D\) k . \(t\) is the column vector composed of the diagonal elements of \(T\) e , that is Then equation (13) can be transformed into:

[0089]

[0090] Using the estimated azimuth obtained by equation (12) and the estimated number of targets \(K'\) to obtain \(D\) k , for eigenvalue decomposition gives Therefore, the result in the parentheses in equation (14) can be solved and denoted as \(U\):

[0091]

[0092] The cost function is transformed into \(J = t\) H \(U^t\). Taking the first array element as the standard, assuming there is no error in the first array element, that is Then \(t\) H \(w = 1\), where \(w=[1,0,\cdots,0]\) is an \(M\) - dimensional column vector with the first value being 1 and the remaining values being 0. Solve \(t\) using the following constrained quadratic - form minimization problem:

[0093]

[0094] The solution of equation (16) is very classical and can be obtained using the Lagrange multiplier method

[0095]

[0096] where \(t\) is the diagonal element of \(T\) e , so the array amplitude - phase error is \(T\) e = diag(\(t\)).

[0097] S5. Use the iterative method of S1 - S4 to improve the estimation accuracy of the underwater acoustic target azimuth and the array amplitude - phase error in S3 and S4. Use the iterative method to make \(T\) e more accurate, and make Approaching R s The iterative process is as follows, where A [iter] represents the result of the iter-th iteration of A:

[0098] Initialization: T e [1] is an M-dimensional identity matrix

[0099] Step 1. Solve the covariance matrix of the actual uncorrected array output signal and substitute and T e [iter] into the optimization algorithm formula (11) to solve the signal component of the noise-free covariance matrix

[0100] Step 2. According to Equation (12), use to estimate the underwater acoustic target azimuth using the MUSIC method

[0101] Step 3. Perform eigenvalue decomposition on to obtain its noise subspace and use to solve D k , and substitute and D k into Equation (15) to solve the U [iter] matrix;

[0102] Step 4. Substitute U [iter] into Equation (17) to solve t [iter] ;

[0103] Step 5. Determine whether to perform the next iteration. Set a very small threshold ε. If |t [iter] - t [iter-1] | > ε, then update and return to S1 for the next iteration; if |t [iter] - t [iter-1] | < ε, then stop the iteration and output the current array amplitude and phase error and the estimated underwater acoustic target azimuth as the final result.

[0104] During the iteration process, T e and both become more accurate. Finally, the present invention realizes separating the covariance matrix of the error-free array output signal and the amplitude and phase error matrix from the covariance matrix of the uncorrected array. If a total of ITER iterations are performed, finally is the estimated array error, and use for azimuth estimation.

[0105] The present invention has the following advantages: First, this method does not require a specific calibration source and can achieve array self-calibration; Second, this method uses the covariance matrix reconstruction method (Equation 11) to obtain the signal component of the covariance matrix of the array output signal that is approximately noise-free and error-free. A more accurate estimated azimuth can be obtained, and the accurate estimated azimuth ensures the accurate estimation result of the array error. During the iteration process, both the estimated azimuth and the estimated array error become gradually accurate, achieving the effect of "positive feedback".

[0106] Simulation analysis

[0107] The MUSIC method is used to investigate the array error correction ability of the present invention and the azimuth estimation performance after array calibration. Additionally, for comparison, the results of the uncalibrated array and the theoretically error-free array are also given in the simulation. In the simulation, the received signals (plane waves) of the underwater acoustic signal receiving transducers are all narrowband signals with a frequency of 3 kHz and random phases. The number of snapshots of the received signals is 500, and the element (underwater acoustic signal receiving transducer) spacing is half the wavelength of 3 kHz, i.e., 0.25 m.

[0108] A. Azimuth spectrum

[0109] There are two underwater ships in space as targets, and their azimuths are 10° and 17° respectively, the signal-to-noise ratio is 0 dB, and the number of array elements is 10. Assuming that the first element has no error, the array amplitude errors a1 to a of the uncalibrated uniform linear array 10 are [1, 0.7, 0.4, 3, 1.8, 0.9, 1.2, 1.5, 2, 1.6], and the phase error η in m is [0°, 30°, -10°, 10°, -20°, 16°, -10°, 20°, 10°, 15°] × π / 180. Figure 3 The MUSIC azimuth spectra before and after the calibration of the uniform linear array are shown. The black circles in the figure represent the true azimuths of the ship targets. The minimum amplitude of the depression at the peak of the uncalibrated array in the figure is approximately -0.9 dB, and it is almost impossible to distinguish the two ship targets, while the present invention has a deep depression and can clearly distinguish the dual-ship targets.

[0110] B. Array error estimation deviation and azimuth estimation performance

[0111] The present invention estimates the array amplitude and phase error as T e . To distinguish the array error and the estimation error, this estimation error is called the "Array Error estimation Deviation" (AED), and its calculation method is shown in Equation (1):

[0112]

[0113] In addition, this section will examine the azimuth estimation accuracy and resolution probability before and after array calibration when there are two ship targets in space. The present invention uses the Mean Square Error (MSE) to judge the azimuth estimation accuracy of ship targets. If the azimuth estimation result satisfies Equation (2), it is determined that the azimuths of the two ship targets are successfully resolved.

[0114]

[0115] Among them, θ1 and θ2 represent the true azimuths of the two ship targets. and respectively represent the estimated azimuths of the two ship targets in the t-th Monte Carlo experiment. If a total of F tests are carried out and the estimation results of f tests satisfy Equation (2), then the resolution probability is f / F. Each result in the figure is subjected to 200 independent Monte Carlo experiments.

[0116] C. Number of iterations

[0117] Assume that the first array element has no error, and other array elements have random amplitude-phase errors. The amplitude error a of the m-th array element m is a random number between 0 and 5, and the phase error is measured in degrees. η in m is a random number between -30°×π / 180 and 30°×π / 180. Assume that the number of array elements is 10, the azimuths of the two ship targets are 10° and 17° respectively, and the signal-to-noise ratio is 10 dB. Figure 4 Examine the variation of the AED of the present invention with the number of iterations. The number of iterations increases from 1 to 50. Figure 4 The AED in [iter] gradually decreases as the number of iterations increases, and the array error estimation is accurate. The present invention only requires 9 iterations to satisfy |t [iter-1] - t -4 .

[0118] D. Number of array elements

[0119] Assume that there are two ship targets in space, and their azimuths are 10° and 17° respectively, the signal-to-noise ratio is 10 dB, and the number of array elements increases from 5 to 20. Figure 5 And Figure 6 examines the variation of the AED and DOA estimation performance of the present invention with the number of array elements. Figure 5 In Figure 5 the AED gradually decreases as the number of array elements increases and is less than 0.3. In Figure 6(b), the uncalibrated array can have a resolution probability greater than 0.9 only when the number of array elements is greater than 11. The resolution probability of the present invention is close to 1, and the estimation accuracy is much higher than that of the uncalibrated array.

[0120] E, signal-to-noise ratio

[0121] The array error is still the random amplitude-phase error. Assume the number of array elements is 10, the bearings of two ship targets are 10° and 17° respectively, and the signal-to-noise ratio increases from -10 dB to 20 dB. Figure 7 And Figure 8 examines the variation of the AED and DOA estimation performance of the present invention with the signal-to-noise ratio. Figure 7 In the present invention, the AED gradually decreases as the signal-to-noise ratio increases. When the signal-to-noise ratio is greater than 2 dB, the AED is less than 0.2. In Figure 8, the present invention effectively improves the estimation accuracy and resolution probability, and its resolution probability is much higher than that of the uncalibrated array.

[0122] In practical engineering, when the array aperture is limited, high-resolution bearing estimation methods are usually applied to improve the resolution. However, the performance of most high-resolution methods will seriously degrade due to array errors. Therefore, for amplitude-phase errors, the present invention proposes an array self-calibration method without error covariance matrix separation, which can accurately solve the array error and the underwater acoustic target bearing simultaneously.

[0123] The covariance matrix of the output signal of the actual uncalibrated array is composed of two parts: the covariance matrix of the output signal of the error-free array and the amplitude-phase error matrix. For a uniform linear array, the covariance matrix of the output signal of the error-free array theoretically has a Toeplitz structure. However, when the array has errors, its covariance matrix no longer has a Toeplitz structure. Therefore, the present invention uses the covariance matrix of the output signal of the uncalibrated array to reconstruct the covariance matrix of the output signal of the error-free array, and constrains the reconstructed covariance matrix to be a Toeplitz matrix. And by combining the eigenstructure configuration method and the iterative method, the covariance matrix of the output signal of the error-free array and the amplitude-phase error matrix are separated from the covariance matrix of the output signal of the uncalibrated array. The simulation results show that the present invention can accurately estimate the array amplitude-phase error, and obtain a reconstructed covariance matrix of the output signal of the error-free array that is approximately noise-free, and using it in the MUSIC method can significantly improve the resolution and estimation accuracy. This method does not require a specific calibration source, is not affected by interference signals, and can calibrate the array in a real ocean environment.

Claims

1. An array self-calibration method without error covariance matrix separation, characterized in that: It includes the following steps: S1. Obtain the signals of ships in water, and solve the covariance matrix of the output signals of the uncalibrated array composed of underwater acoustic signal receiving transducers according to the signals; S2. Use the covariance matrix of the output signals of the uncalibrated array to obtain the signal components of the covariance matrix of the output signals of the error-free array; S3. Based on the signal components obtained in S2, use the MUSIC method to estimate the underwater acoustic target azimuth; S4. Use the eigenstructure configuration method and the estimated underwater acoustic target azimuth to solve the array amplitude and phase errors; S5. Iterate S1 - S4, set a very small threshold ε. When |t [iter] - t [iter-1] | > ε, update T e [iter+1] = diag(t [iter] ), and return to S1 for the next iteration. iter represents the number of iterations, t [iter] represents the column vector of the current iteration, and t [iter-1] represents the column vector of the previous iteration; when |t [iter] - t [iter-1] | < ε, stop the iteration and output the current array amplitude - phase error and the estimated underwater acoustic target azimuth.

2. The array self-calibration method for separating an error-free covariance matrix according to claim 1, wherein: The specific process of S1 is as follows: Define M underwater acoustic signal receiving transducers in water as array elements to form a uniform linear array, obtain the signals of ships in water, and let the signals far from the uniform linear array be plane waves. Assume that K narrowband plane waves are incident on the uniform linear array, then the covariance matrix of the output signals of the error-free array: Among them, is the error-free array manifold vector of the signal, diagonalizes the signal power, is for the conjugate transpose of, diagonalizes the noise power, R s is the signal component of the covariance matrix, R n is the noise component of the covariance matrix; Assume that the amplitude error of the m-th array element is a m , and the phase error is Then the array amplitude-phase error matrix is expressed as: Among them, represents the diagonalization, where m = 1, 2, …, M; Then the covariance matrix of the output signals of the uncalibrated array: Among them, represents the conjugate transpose of T e .

3. The array self-calibration method for separating error-free covariance matrix according to claim 2, characterized in that: The specific process of S2 is as follows: Suppose the covariance matrix of the reconstructed error-free array output signal is composed of signals and noise, that is, 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 according to the covariance matrix of the uncorrected array output signal, the covariance matrix of the reconstructed error-free array output signal is obtained by using the covariance fitting criterion: Among them, is a Toeplitz matrix, which is determined by the elements r in the first row. Then And is a positive semi-definite matrix. Then Toeplitz(r) ≥ 0, where Toeplitz(r) means to Toeplitz-ize r. Assuming that the noise power is σ and all the elements therein are real numbers greater than 0, then Use the optimization algorithm formula based on the covariance fitting criterion to solve r in formula (4) to obtain the signal components of the covariance matrix of the output signals of the noise-free error-free array:

4. An array self-calibration method for separating an error-free covariance matrix according to claim 3, characterized in that: The covariance fitting criterion in S2: Among them, X and are a known matrix and a matrix to be fitted, respectively.

5. An array self-calibration method for separating an error-free covariance matrix according to claim 4, characterized in that: The specific process of S3 is as follows: MUSIC method: Among them, represents the underwater acoustic target azimuth, represents the noise subspace of represents the conjugate transpose of, a(θ) represents the error-free array manifold vector of the signal, a H (θ) represents the conjugate transpose of a(θ).

6. The array self-calibration method for separating an error-free covariance matrix according to claim 5, characterized in that: The specific process of S4 is as follows: The covariance matrix of the uncorrected array output signal is subjected to eigenvalue decomposition. Since the noise subspace of is orthogonal to the space spanned by , the cost function of the eigenstructure configuration method is constructed using the orthogonality property: where t represents T e a column vector composed of diagonal elements, and K′ represents the estimated azimuth the estimated number of targets, D k represents a(θ k ) the diagonalized M×M-dimensional matrix; Solve for \(t\) using the Lagrange multiplier method, and the array amplitude and phase error \(T\) can be obtained. e = diag(\(t\)).

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