Amplitude-phase error self-correction method based on uniform linear array signal covariance matrix

Abstract

The invention discloses an amplitude-phase error self-correction method based on a uniform linear array signal covariance matrix, and relates to the technical field of array signal processing, and the method comprises the steps: obtaining a linear equation set related to an amplitude-phase error according to a received signal of a sensor array, the received signal being a signal considering the internal noise of a receiver; calculating according to the estimated covariance matrix of the received signal to obtain statistical characteristics of noise errors; constructing boundary conditions according to the phase prior information; according to the system of linear equations and the statistical characteristics and boundary conditions of noise errors, constructing a weighted least square estimation problem which contains equality constraints and is related to amplitude-phase errors; and solving a weighted least square estimation problem to obtain an estimated value of the amplitude-phase error, and correcting the received signal by using the estimated value of the amplitude-phase error. According to the method, a more generalized signal model containing internal noise is considered, a high-precision amplitude-phase error correction algorithm with lower calculation cost is constructed, and compared with an existing algorithm, the method is more in line with the actual situation.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and particularly relates to a method for self-correcting amplitude-phase errors based on the covariance matrix of signals of a uniform linear array. Background Art

[0002] The direction-of-arrival (DOA) estimation algorithm can accurately determine the direction of arrival of target signals reaching a sensor array. This technology has important application value in the field of array signal processing and is one of the main tasks in many fields such as radar, communication, and sonar. Existing high-precision estimation algorithms can already achieve very high estimation accuracy and can be applied to harsh conditions with low snapshot numbers and low signal-to-noise ratios.

[0003] However, these high-resolution estimation algorithms need to assume that the array steering vector is accurate and error-free. In reality, due to the existence of various factors, the mathematical model does not match the actual situation, resulting in a significant decline in the performance of traditional high-resolution estimation algorithms. Array errors have become a non-negligible factor restricting the performance of various high-precision algorithms.

[0004] Self-correcting amplitude-phase errors based on the covariance matrix of received signals of a uniform linear array is an effective method to reduce the computational complexity. Existing methods, based on the Toeplitz property of the covariance matrix of an error-free uniform linear array, construct a linear equation system related to the amplitude-phase error parameters, and consider the measurement deviation between the covariance matrix calculated due to finite samples and the actual signal covariance matrix, thereby improving the estimation accuracy. Finally, the original problem is transformed into a weighted least squares estimation problem, and its closed-form solution can be obtained. However, in previous methods, in order to simply linearly represent the amplitude-phase error parameters, the models of these methods usually only consider the influence of external noise of the receiver, making the noise signal also affected by the amplitude-phase error, and simply assuming that the external noise follows a complex Gaussian distribution. In fact, the external noise often has certain spectral characteristics and is not complex Gaussian white noise. And in high-frequency radar systems, the influence of internal noise of the receiver is crucial. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method for self-correcting amplitude-phase errors based on the covariance matrix of signals of a uniform linear array. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] The present invention provides a method for self-correcting amplitude-phase errors based on the covariance matrix of signals of a uniform linear array, including:

[0007] Obtaining a linear equation system about the amplitude-phase error according to the received signals of the sensor array, wherein the received signals are signals considering the internal noise of the receiver;

[0008] Calculate the statistical characteristics of the noise error based on the estimated covariance matrix of the received signal;

[0009] Construct boundary conditions according to the phase prior information;

[0010] Construct a weighted least - squares estimation problem with equality constraints for the amplitude - phase error based on the linear equations, the statistical characteristics of the noise error, and the boundary conditions;

[0011] Solve the weighted least - squares estimation problem to obtain the estimated value of the amplitude - phase error, and use the estimated value of the amplitude - phase error to correct the received signal.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0013] The amplitude - phase error self - calibration method based on the covariance matrix of the uniform linear array signal of the present invention, in the framework of amplitude - phase error calibration based on the covariance matrix of the received signal of the linear array, considers a more generalized signal model with internal noise. By introducing additional parameters, the covariance matrix of the received data is linearly represented by the amplitude error and the phase error, constructs a set of equations with noise error, and in view of the defect of amplitude - phase error calibration for the linear array, introduces the prior information of the phase as the boundary condition, and constructs a high - precision amplitude - phase error calibration algorithm with lower computational cost through a weighted least - squares algorithm with constraints. Compared with the existing algorithms, it is more in line with the actual situation.

[0014] The above description is only an overview of the technical solution of the present invention. In order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the specification. And in order to make the above and other purposes, features, and advantages of the present invention more obvious and understandable, the following specific preferred embodiments are given and described in detail in conjunction with the drawings as follows. Brief Description of the Drawings

[0015] Figure 1 is a flowchart of an amplitude - phase error self - calibration method based on the covariance matrix of the uniform linear array signal provided by an embodiment of the present invention;

[0016] Figure 2 is a graph of amplitude estimation performance provided by an embodiment of the present invention;

[0017] Figure 3 is a graph of phase estimation performance provided by an embodiment of the present invention;

[0018] Figure 4 is a graph of DOA estimation results using the MUSIC algorithm before and after amplitude - phase error calibration provided by an embodiment of the present invention. Detailed Embodiment

[0019] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, the following provides a detailed description of a method for self-calibrating amplitude-phase errors based on the signal covariance matrix of a uniform linear array in combination with the accompanying drawings and specific embodiments.

[0020] The foregoing and other technical contents, features, and effects of the present invention can be clearly presented in the following detailed description in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and specific understanding of the technical means and effects adopted by the present invention to achieve the intended purpose can be obtained. However, the accompanying drawings are only for reference and illustration, and are not used to limit the technical solution of the present invention.

[0021] An embodiment of the present invention provides a method for self-calibrating amplitude-phase errors based on the signal covariance matrix of a uniform linear array. Please refer to Figure 1 , Figure 1 which is a flowchart of a method for self-calibrating amplitude-phase errors based on the signal covariance matrix of a uniform linear array provided by an embodiment of the present invention. As shown in Figure 1 , the method for self-calibrating amplitude-phase errors based on the signal covariance matrix of a uniform linear array in this embodiment may include the following steps:

[0022] Step 1: Obtain a linear equation set regarding amplitude-phase errors based on the received signals of the sensor array, where the received signals are signals considering the internal noise of the receiver.

[0023] Consider a uniform linear array containing M omnidirectional sensors with different amplitude-phase errors, the element spacing is d, and there are K far-field signal sources in space respectively emitting narrowband signals with wavelength λ to the array at angles θ = [θ1, θ2,..., θ K . The k-th signal source signal is denoted as s k (t), k = 1, 2,..., K. Then, the received signal of the array at time t, that is, the array observation signal, can be expressed as:

[0024] x(t) = ΓA(θ)s(t) + n(t) = ΨΦA(θ)s(t) + n(t)

[0025] where 1 ≤ t ≤ T, T is the number of snapshots, s(t) represents the signal sources in space, s(t) = [s1(t), s2(t),..., s K (t)] T , K represents the number of signal sources in space, s(t) follows a circularly symmetric complex Gaussian distribution with zero mean and covariance matrix , represents the variance of the k-th signal, n(t) is the internal noise of the receiver, and n(t) ~ CN(0, Q n ) follows a zero-mean and covariance matrix of Qn circularly symmetric complex Gaussian white noise, is the noise variance, and the noise is independent of the signal. It should be noted that the internal noise of the receiver is not affected by the amplitude-phase error. I is the identity matrix, Γ is the diagonal matrix of the array amplitude-phase error, Γ = ΨΦ, Ψ represents the diagonal matrix of the amplitude error, Φ represents the diagonal matrix of the phase error, and A(θ) is the array manifold matrix.

[0026] where Ψ = diag([ψ1,…,ψ M ), where ψ m ,m = 1,2,…,M represents the amplitude error of the m-th array element; Φ = diag([φ1,…,φ M ), where φ m ,m = 1,2,…,M represents the phase error of the m-th array element. Without loss of generality, let the first array element be the reference array element, i.e., ψ1 = 1, φ1 = 0. A(θ) = [a(θ1),a(θ2),…,a(θ K )] is the array manifold matrix, and a(θ k ) is the array steering vector, which is expressed as:

[0027]

[0028] In this embodiment, a linear equation set about the amplitude-phase error is obtained according to the received signal of the sensor array, including:

[0029] Step i: Calculate the estimated covariance matrix of the received signal according to the received signal of the sensor array; the estimated covariance matrix of the received signal is calculated according to the following formula:

[0030]

[0031] In the formula, represents the estimated covariance matrix of the received signal, T is the number of snapshots, t represents the time, x(t) represents the received signal of the sensor array at time t, and H represents the matrix conjugate.

[0032] Step ii: Take the logarithm of the estimated covariance matrix, define the unknown parameter vector, and obtain a linear equation set according to the unknown parameter vector and the real and imaginary parts of the logarithm of the estimated covariance matrix.

[0033] First, the process of obtaining a linear equation set without "measurement error" for the true covariance matrix of the received signal based on a linear array is described.

[0034] Assume that the signal s follows a complex Gaussian distribution with zero mean and covariance matrix R s , that is:

[0035] s(t) ~ CN(0,R s);

[0036] Therefore, the received signals of the array also follow a complex Gaussian distribution with a mean of 0 and a covariance matrix of R, i.e.:

[0037] x(t) ~ CN(0, R);

[0038] wherein,

[0039] Then, the element in the i-th row and j-th column of the covariance matrix is:[[]]

[0040]

[0041] Taking the logarithm of it, a linear equation about the amplitude error and phase error can be obtained:[[]]

[0042]

[0043] wherein, K represents the number of signal sources in space, is the noise variance, represents the variance of the k-th signal. And since C is a Toeplitz matrix in the uniform linear array, define c i , i = 1, 2,..., M are the M constituent elements of the matrix C. Taking the real part and imaginary part of it, a linear equation set about the logarithm of the amplitude and the phase can be obtained respectively:[[]]

[0044] Taking the real part:[[]]

[0045]

[0046] Taking the imaginary part:[[]]

[0047]

[0048] Define the unknown parameter vector:[[]]

[0049]

[0050] wherein:[[]]

[0051] φ = [φ1,..., φ M T ;

[0052]

[0053] Δ = [Δ1,..., Δ M T ;

[0054] wherein, is the logarithm of the amplitude error parameter, ψ​​m , where \(m = 1, 2, \ldots, M\), represents the amplitude error of the \(m\)-th array element, \(\varphi\) is the phase error parameter, \(\varphi\) m , where \(m = 1, 2, \ldots, M\), represents the phase error of the \(m\)-th array element, \(M\) represents the number of array elements, and \(\rho\), \(l\), \(\Delta\) are all redundant parameters. denotes taking the real part. denotes taking the imaginary part, \(c\) i , where \(i = 1, 2, \ldots, M\) are the \(M\) constituent elements of matrix \(C\), and \(C\) is a Toeplitz matrix.

[0055] Among them, and \(\varphi\), that is, the first \(2M\) parameters are amplitude-phase error parameters, which are the target parameters, and \(\rho\), \(\iota\), \(\Delta\), that is, the last \(3M\) parameters are redundant parameters.

[0056] In specific implementation, considering the solvability of the equation, since the redundant parameters \(\Delta\) and \(\rho_1\) only appear in the main diagonal elements of the covariance matrix, let \(\Delta'=\Delta + \rho_1\). At the same time, because \(C\) is a Hermitian matrix, so \(\iota_1 = 0\), thus reducing the number of redundant parameters. Therefore, the number of parameters to be finally solved is \(5M - 2\).

[0057] Based on this, a linear equation system without measurement error can be obtained:

[0058]

[0059] In the formula, is the coefficient matrix, represents all redundant parameter vectors.

[0060] Since the true covariance matrix is often difficult to obtain directly, the estimated covariance matrix can be obtained by estimating it through the received data to replace the true covariance matrix.

[0061] Considering the measurement noise \(\varepsilon\) generated when calculating the covariance matrix due to the finite sample size, then, the estimated covariance matrix can be expressed as:

[0062]

[0063] Similarly, take the logarithm of the estimated covariance matrix and take the real and imaginary parts:

[0064]

[0065] Take the real part:

[0066]

[0067] Take the imaginary part:

[0068]

[0069] In the formula, is the noise error of the equation. Taking its real and imaginary parts, we can get And let the noise error vector ξ = [ε T , ∈ T T , where ε = […, ε ij ,…] T , ∈ = […, ∈ ij ,…] T .

[0070] Then, the linear equation system to be solved with noise error can be expressed as: y = HΘ + ξ, where ξ is the noise error vector.

[0071] Step 2: Calculate the statistical characteristics of the noise error according to the estimated covariance matrix of the received signal.

[0072] In this embodiment, the statistical characteristics of the noise error include the mean and covariance matrix of the noise error vector. Among them, the mean of the noise error vector is calculated according to the following formula:

[0073]

[0074] The covariance matrix of the noise error vector is calculated according to the following formula:

[0075]

[0076] In the formula, represents the expectation, represents taking the real part, represents taking the imaginary part, ε ij represents taking the real part of the noise error after taking the logarithm of the element in the i-th row and j-th column of kl represents taking the real part of the noise error after taking the logarithm of the element in the k-th row and l-th column of ij represents taking the imaginary part of the noise error after taking the logarithm of the element in the i-th row and j-th column of kl represents taking the imaginary part of the noise error after taking the logarithm of the element in the k-th row and l-th column of represents the estimated covariance matrix, ε represents the vector composed of ε ij ∈ represents the vector composed of ∈ ij i, j, k, l respectively represent the row and column indices in * represents the conjugate, and T represents the transpose.

[0077] ​Step 3: Construct boundary conditions according to the phase prior information.

[0078] In an actual signal processing scenario, prior information about system errors can often be obtained. For phase errors, they generally fluctuate within a certain range. It can be assumed that the phase information follows a uniform distribution with zero mean, i.e., φ ∼ U[-φ e , φ e , where φ e is the maximum modulus of phase fluctuation, and its probability density function is:

[0079]

[0080] Since the linear equations to be solved are an underdetermined system of equations and there is no unique unbiased solution, therefore, considering the case where the phase error is small, in a statistical sense, the mean of all phase errors is approximately:

[0081]

[0082] Taking this as the boundary condition, solve the linear equations, and use the first array element as the reference array element, i.e.,

[0083] Step 4: According to the linear equations, the statistical characteristics of the noise error, and the boundary conditions, construct a weighted least squares estimation problem for the amplitude-phase error with equality constraints.

[0084] In this embodiment, the weighted least squares estimation problem for the amplitude-phase error with equality constraints can be expressed as:

[0085]

[0086]

[0087] In the formula, s.t. represents the constraint condition.

[0088] Convert the constraint into matrix form:

[0089]

[0090] In the formula,

[0091] Step 5: Solve the weighted least squares estimation problem to obtain the estimated value of the amplitude-phase error, and use the estimated value of the amplitude-phase error to correct the received signal.

[0092] In this embodiment, the Lagrange multiplier method is used to solve the weighted least squares estimation problem to obtain the weighted least squares solution with constraints. The first 2M values of the weighted least squares solution are used as the estimated value of the amplitude-phase error, and the received signal is corrected according to the estimated value of the amplitude-phase error.

[0093] Specifically, the Lagrangian function is as follows:

[0094]

[0095] Taking the derivatives of the parameters Θ and the Lagrange multipliers λ respectively and setting them to zero, the final system of linear equations is obtained:

[0096]

[0097] Solving this system of linear equations, the weighted least squares solution with constraints can be obtained:

[0098]

[0099] Finally, the weighted least squares estimates of the amplitude and phase errors can be obtained:

[0100]

[0101] Using the estimated amplitude and phase error results to correct the received data, the corrected received signal is expressed as: Based on the corrected received signal, the corrected data can be processed by other high-resolution direction-of-arrival estimation algorithms to obtain a higher-precision direction-of-arrival estimation result.

[0102] The amplitude and phase error self-correction method based on the covariance matrix of uniform linear array signals in the embodiments of the present invention considers a more general signal model with internal noise in the framework of amplitude and phase error correction based on the covariance matrix of received signals of linear arrays. By introducing additional parameters, the covariance matrix of received data is linearly represented by amplitude error and phase error, a set of equations with noise errors is constructed, and aiming at the defect of amplitude and phase error correction for linear arrays, the prior information of phase is introduced as a boundary condition. Through the weighted least squares algorithm with constraints, a high-precision amplitude and phase error correction algorithm with lower computational cost is constructed, which is more in line with the actual situation compared with the existing algorithms.

[0103] Furthermore, the amplitude and phase error self-correction method based on the covariance matrix of uniform linear array signals provided in the embodiments of the present invention is further described through simulation experiments.

[0104] Specifically, a uniform linear array with 8 array elements is adopted, and the element spacing is half a wavelength, that is, d = λ / 2. There are signal sources with a carrier frequency of f = 3×10 8 Hz and a carrier wavelength of λ = c / f = 1m distributed in space.

[0105] Please refer to Figure 2 and Figure 3 , Figure 2It is the amplitude estimation performance graph provided by the embodiments of the present invention; Figure 3 It is the phase estimation performance graph provided by the embodiments of the present invention.

[0106] In this example, three signal sources with incident angles of [25°, 30°, 70°] respectively are placed in space. The amplitude errors of the array are [1, 1.15, 1.3, 1.2, 1.25, 0.8, 0.8, 1.3], and the phase errors are [0, 15°, 9°, -13°, 20°, -5°, -15°, -11°]. The performance index is measured by the estimated root mean square error (RMSE), and the index is defined as follows:

[0107] Amplitude parameter:

[0108]

[0109] Phase parameter:

[0110]

[0111] In the formula, L represents the number of Monte Carlo experiments, and CCRLB (Constraints Cramer-Rao Lower Bound) represents the Cramer-Rao lower bound with equality constraints, which is used as a reference standard for the estimation performance. As Figure 2 and 3 shown, it can be seen that the method of the present invention does not require iterative calculations, and its estimation performance for amplitude and phase can be close to CCRLB.

[0112] Please refer to Figure 4 , Figure 4 It is the DOA estimation result graph using the MUSIC algorithm before and after amplitude-phase error correction provided by the embodiments of the present invention. In this example, two signal sources with DOAs of [30°, 70°] respectively are placed in space, and the signal-to-noise ratio is 10 dB. From Figure 4 it can be seen that before the array is corrected, the estimation result error of the MUSIC algorithm is relatively large, and the spectral peaks are relatively not obvious. After being corrected by the method of the present invention and then performing DOA estimation, the spectral peaks are more obvious, and the estimation performance is improved.

[0113] It should be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant are intended to cover non-exclusive inclusion, so that an article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the article or device comprising said element. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The orientation or positional relationship indicated by "upper", "lower", "left", "right", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0114] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0115] The above content is a further detailed description of the present invention in connection with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for self-correcting amplitude and phase errors based on the covariance matrix of uniform linear array signals, characterized in that: include: A linear equation group about amplitude and phase errors is obtained according to a received signal of the sensor array, wherein the received signal is a signal taking into account internal noise of the receiver; Calculating the statistical characteristics of the noise error according to the estimated covariance matrix of the received signal; Construct boundary conditions based on phase prior information; According to the linear equations, the statistical characteristics of the noise error and the boundary conditions, construct a weighted least squares estimation problem on amplitude and phase errors with equality constraints; The weighted least squares estimation problem is solved to obtain an estimated value of the amplitude and phase error, and the received signal is corrected using the estimated value of the amplitude and phase error.

2. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 1 is characterized in that: The received signal of the sensor array at time t is expressed as: x(t)=ΓA(θ)s(t)+n(t)=ΨΦA(θ)s(t)+n(t); Where 1≤t≤T, T is the number of snapshots, s(t) represents the signal source in space, s(t)=[s1(t),s2(t),…,s K (t)] T , K represents the number of signal sources in space, s(t) obeys zero mean, and the covariance matrix is The circularly symmetric complex Gaussian distribution of k=1,…,K represents the variance of the kth signal, n(t) is the internal noise of the receiver, n(t)~CN(0,Q n ) is subject to zero mean, and the covariance matrix is ​​Q n Circularly symmetric complex Gaussian white noise, is the noise variance, I is the unit matrix, Γ is the diagonal matrix of array amplitude and phase errors, Γ=ΨΦ, Ψ represents the diagonal matrix of amplitude error, Φ represents the diagonal matrix of phase error, and A(θ) is the array flow matrix.

3. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 1 is characterized in that: According to the received signals of the sensor array, a linear equation group about the amplitude and phase errors is obtained, including: Calculating an estimated covariance matrix of the received signal according to the received signal of the sensor array; The estimated covariance matrix is ​​logarithmized, an unknown parameter vector is defined, and the linear equation system is obtained according to the unknown parameter vector and the real part and the imaginary part of the estimated covariance matrix after taking the logarithm.

4. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 3 is characterized in that: The estimated covariance matrix of the received signal is calculated according to the following formula: In the formula, represents the estimated covariance matrix of the received signal, T is the number of snapshots, t represents the time, x(t) represents the received signal of the sensor array at time t, and H represents the matrix conjugate.

5. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 3 is characterized in that: The unknown parameter vector is expressed as: in: φ=[φ1,…,φ M ] T ; Δ=[Δ1,…,Δ M ] T ; In the formula, is the logarithm of the amplitude error parameter, ψ m , m=1,2,…,M, represents the amplitude error of the mth array element, φ is the phase error parameter, φ m , m=1,2,…,M, represents the phase error of the mth array element, M represents the number of array elements, ρ, ι, Δ are all redundant parameters, represents the real part, represents the imaginary part, c i , i = 1, 2, ..., M is the M component elements of the matrix C, C is the Toeplitz matrix, definition i=1,2,…,M, K represents the number of signal sources in the space, is the noise variance, represents the variance of the kth signal.

6. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 5 is characterized in that: The linear equation system is expressed as: y=HΘ+ξ; In the formula, is the coefficient matrix, Ξ represents all redundant parameter vectors, ξ is the noise error vector.

7. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 6 is characterized in that: The statistical characteristics of the noise error include the mean and covariance matrix of the noise error vector, wherein the mean of the noise error vector is calculated according to the following formula: The covariance matrix of the noise error vector is calculated according to the following formula: In the formula, Express expectations, represents the real part, represents the imaginary part, ε ij Express After taking the logarithm of the element in the i-th row and j-th column, the real part of the noise error, ε kl Express After taking the logarithm of the elements in the kth row and lth column, the real part of the noise error, ε ij Express After taking the logarithm of the element in the i-th row and j-th column, the imaginary part of the noise error, ∈ kl Express After taking the logarithm of the elements in the kth row and lth column, the imaginary part of the noise error is represents the estimated covariance matrix, ε represents the ij A vector composed of ∈ ij The vectors composed of i, j, k, and l represent The row and column indices in , * stands for conjugate and T stands for transpose.

8. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 7 is characterized in that: The boundary condition is expressed as: In the formula, M represents the number of array elements, φ m represents the phase error of the mth array element, It represents the logarithm of the amplitude error of the first array element, φ1 represents the phase error of the first array element, and the first array element is the reference array element.

9. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 8, characterized in that: The weighted least squares estimation problem of amplitude and phase errors with equality constraints is expressed as: In the formula, st represents the constraint condition.

10. The amplitude and phase error self-correction method based on the uniform linear array signal covariance matrix according to claim 9, characterized in that: Solving the weighted least squares estimation problem to obtain an estimated value of the amplitude and phase error, and correcting the received signal using the estimated value of the amplitude and phase error, comprising: The weighted least squares estimation problem is solved using the Lagrange multiplier method to obtain a constrained weighted least squares solution. 2M The received signal is corrected according to the estimated value of the amplitude-phase error.

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