A centralized array partial amplitude and phase error self-correction angle estimation method

Abstract

This invention discloses a centralized array partial amplitude and phase error self-correction angle estimation method, comprising: constructing a received signal model for a bistatic MIMO radar array where some array elements of the transmitting and receiving arrays have amplitude and phase errors; performing identity transformations on the steering vector matrices of the receiving and transmitting arrays respectively to obtain the rank-loss intermediate matrices of the receiving and transmitting arrays; obtaining the estimated value matrices of the steering vector matrices of the receiving and transmitting arrays by performing PARAFAC decomposition on the radar received signal model; performing eigenvalue decomposition on the covariance matrix of the estimated value matrices to obtain the noise subspace corresponding to the received signals of the receiving and transmitting arrays; obtaining the estimated values ​​of the amplitude and phase error vectors of the receiving and transmitting arrays using the relationship between eigenvectors and eigenvalues; constructing a spectral peak function using the estimated values ​​of the amplitude and phase error vectors of the receiving and transmitting arrays, obtaining the 2D-DOD estimate and the 2D-DOA estimate through two-dimensional space search, and performing target pairing based on the maximum likelihood function.

Description

Technical Field

[0001] This invention relates to the field of radio signal direction finding, and more specifically to a method for estimating the angle of partial amplitude and phase error self-correction of a centralized array. Background Technology

[0002] Most existing methods for jointly estimating the Direction-of-Departure (DOD) and Direction-of-Arrival (DOA) angles typically rely on error-free array steering matrix processing of radar signal echo data. However, in practice, array elements are often affected by factors such as device aging and ambient temperature and humidity, leading to different gain and phase responses across multiple element channels—that is, amplitude and phase errors. These errors affect the accuracy of the array steering vector matrix, making subspace algorithms and sparse algorithms relying on comprehensive dictionaries unable to accurately estimate angles.

[0003] Current methods for addressing amplitude and phase errors in bistatic MIMO radar array elements can avoid the impact of these errors and obtain accurate target angle estimates. However, these methods are only applicable to array types such as uniform linear arrays and cannot be applied to uniform planar array bistatic MIMO radars. Summary of the Invention

[0004] The purpose of this invention is to provide a centralized array partial amplitude and phase error self-correction angle estimation method to solve the problem of low target angle estimation accuracy of existing methods under unknown amplitude and phase errors.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A centralized array partial amplitude and phase error self-correction angle estimation method includes:

[0007] For bistatic MIMO radar arrays, a received signal model is constructed where some elements of the transmitting and receiving arrays have amplitude and phase errors.

[0008] By performing identity transformations on the steering vector matrices of the receiving array and the transmitting array respectively, the rank-loss intermediate matrices of the receiving array and the transmitting array are obtained.

[0009] By performing PARAFAC decomposition on the received signal model, the estimated values ​​of the steering vector matrices of the receiving array and the transmitting array are obtained; by performing eigenvalue decomposition on the covariance matrix of the estimated values, the noise subspace corresponding to the received signals of the receiving array and the transmitting array is obtained.

[0010] Based on the rank loss intermediate matrix of the receiving array and the transmitting array, and combined with the noise subspace corresponding to the received signals of the receiving array and the transmitting array, the estimated values ​​of the amplitude and phase error vectors of the receiving array and the transmitting array are obtained by using the relationship between the eigenvector and the eigenvalue.

[0011] The spectral peak function is constructed using the estimated amplitude and phase error vectors of the receiving array and the transmitting array, and the 2D-DOD estimate and 2D-DOA estimate are obtained through two-dimensional spatial search.

[0012] Construct the maximum likelihood function of the received signal, and use the maximum likelihood function to perform target pairing between the 2D-DOD estimate and the 2D-DOA estimate.

[0013] Furthermore, a received signal model is constructed for which some elements of the transmitting and receiving arrays have amplitude and phase errors, specifically expressed as follows:

[0014] X = [B r ⊙B t ]S T +N

[0015] Where N is a Gaussian white noise matrix with zero mean, and the superscript T denotes transpose; the steering vector matrix of the receiving array. The steering vector matrix of the transmitting array S is the echo signal matrix; A r With A t These are the receiver array stream and the transmitter array stream, respectively. Indicates the receiving array steering vector. The 2D-DOD of the k-th target relative to the origin element of the Cartesian coordinate system of the launch array is represented as: θ tk Indicates azimuth. The pitch angle is represented by the 2D-DOA of the k-th target relative to the origin of the receiver array. Where θ rk Expressed as azimuth, Let K represent the elevation angle and K represent the number of targets; the amplitude and phase errors of the receiving array and the transmitting array can be expressed as follows:

[0016]

[0017] Where ρ rp and φ rp ρ represents the unknown gain error vector and phase error vector of the p-th element of the receiving array. tp and φ tp Let e ​​represent the unknown gain error vector and phase error vector of the p-th element of the transmitting array, where e is the natural constant and j is the imaginary unit.

[0018] Furthermore, identity transformations are performed on the steering vector matrices of the receiving array and the transmitting array respectively to obtain the rank-loss intermediate matrices of the receiving array and the transmitting array. The processing procedure for the receiving array is as follows:

[0019]

[0020] in,

[0021] Where a ki (i = 1, 2, ..., N) x N y ) is the receiving array steering vector corresponding to the k-th target. The i-th element; the receiving array has N elements along the x-axis. x There are N array elements, with N along the y-axis. y Each array element; Let ξ be the rank-loss intermediate matrix of the receiving array. r This is the amplitude and phase error vector of the receiving array.

[0022] Furthermore, by performing PARAFAC decomposition on the received signal model and normalizing it column-wise, the steering vector matrix B of the receiving array is obtained. r With the guiding vector matrix B of the transmitting array t The estimated value matrix and The covariance matrices of the receiving array and the transmitting array are calculated as follows:

[0023]

[0024] In the formula, E{·} represents the expectation, and the superscript H represents the conjugate transpose;

[0025] By performing eigenvalue decomposition on the covariance matrix, the noise subspace E corresponding to the received signals of the receiving array and the transmitting array is obtained. rn and E tn .

[0026] Furthermore, the relationship between eigenvectors and eigenvalues ​​is used to obtain estimates of the amplitude and phase error vectors of the receiving array and transmitting array, including:

[0027] Based on the noise subspace E corresponding to the received signals of the receiving array and the transmitting array rn and E tn Rank-loss intermediate matrices for receiver and transmitter arrays and definition:

[0028]

[0029] Then there is

[0030] make Then the amplitude and phase error vectors ξ of the receiving array and the transmitting array r With ξ t H respectively r With H t The eigenvector corresponding to the eigenvalue of 0 in H; r With H t After performing eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors, the amplitude and phase error vectors ξ of the receiving array and transmitting array can be obtained by sorting the eigenvectors corresponding to the smallest eigenvalues. r With ξ t The estimated value and

[0031] Furthermore, spectral peak functions are constructed using the estimated amplitude and phase error vectors of the receiving and transmitting arrays. 2D-DOD and 2D-DOA estimates are obtained through a two-dimensional spatial search, including:

[0032] Construct the following equation:

[0033]

[0034] make:

[0035]

[0036] And the estimated value of the amplitude and phase error vector and Substituting, we get:

[0037]

[0038] Construct the following spectral function to search for and obtain the 2D-DOA estimate:

[0039]

[0040] Where det[·] denotes the determinant of a matrix; These represent the azimuth and elevation angles, respectively.

[0041] Similarly, constructing similar spectral peak functions yields 2D-DOD estimates:

[0042]

[0043] Based on the above peak functions, the 2D-DOA estimates for all K targets are obtained respectively. and 2D-DOD estimates in Indicates to The estimated value, Indicates to The estimated value.

[0044] Furthermore, a maximum likelihood function for the received signal is constructed, and the maximum likelihood function is used to perform target pairing between the 2D-DOD estimate and the 2D-DOA estimate, including:

[0045] By straightening the received signal model X, we construct the maximum likelihood function of the received signal; by simplifying the maximum likelihood function and taking its logarithm, we obtain:

[0046]

[0047] Where Y D F(ζ) represents the result after straightening the received signal model X. t ,ζ r () is the simplified and logarithmic expression of the maximum likelihood function. To find the pseudo-inverse of a matrix, It is B k and Generate projection matrices that are orthogonal to the subspace. I mn It is an MN×MN dimensional identity matrix;

[0048] For each target's 2D-DOA estimate, this 2D-DOA estimate, along with each 2D-DOD estimate from all targets, forms a set of estimation parameters. These parameters are then substituted into the calculation of F(ζ). t ,ζ r The value of ) is obtained by obtaining all F(ζ) t ,ζ r Among the values ​​of ), the minimum 2D-DOD estimate is taken, which is the pairing result of the 2D-DOA estimate.

[0049] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the centralized array partial amplitude and phase error self-correction angle estimation method.

[0050] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the centralized array partial amplitude and phase error self-correction angle estimation method.

[0051] Compared with the prior art, the present invention has the following technical features:

[0052] Existing bistatic MIMO radar angle estimation algorithms are mostly only applicable to uniform linear arrays, and their performance degrades or even fails when some array elements have unknown amplitude and phase errors. This invention estimates the target angle based on the identity transformation of the amplitude and phase error matrix and the RARE (Radar Recognition and Arithmetic) principle. It can also estimate the unknown amplitude and phase error coefficients of the transmitting and receiving arrays, and further substitute these coefficients into the original data model to improve angle estimation accuracy. Compared to the RARE angle estimation method without amplitude and phase error matrix transformation, this invention achieves better angle estimation accuracy, and the corrected angle estimation performance approaches that of the RARE algorithm with known amplitude and phase error coefficients. Attached Figure Description

[0053] Figure 1 A schematic diagram of a uniform planar array bistatic MIMO radar signal receiving model;

[0054] Figure 2 The following is a spatial spectrum diagram for angle estimation in an embodiment of the present invention, wherein (a) is a spatial spectrum diagram for DOD, (b) is a DOD result diagram, (c) is a spatial spectrum diagram for DOA, and (d) is a DOA result diagram;

[0055] Figure 3 The diagram shows the amplitude and phase error coefficient estimation results in an embodiment of the present invention, where (a) is the constellation diagram for DOD angle estimation and (b) is the constellation diagram for DOA angle estimation.

[0056] Figure 4 The above are the corrected angle estimation spatial spectra in this embodiment of the invention, where (a) is the DOD spatial spectra, (b) is the DOD result diagram, (c) is the DOA spatial spectra, and (d) is the DOA result diagram.

[0057] Figure 5 This is a graph showing the relationship between target angle estimation accuracy and signal-to-noise ratio when some array elements have unknown amplitude and phase errors in an embodiment of the present invention.

[0058] Figure 6 This is a graph showing the relationship between target angle estimation accuracy and the number of snapshots when some array elements have unknown amplitude and phase errors in an embodiment of the present invention.

[0059] Figure 7 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0060] Since bistatic MIMO radar angle estimation requires an accurate steering vector matrix, and the presence of amplitude and phase errors in array elements affects the accuracy of steering vector structure information, traditional methods struggle to obtain correct target angle estimates. Furthermore, existing uniform linear arrays can only provide one-dimensional target angle estimates, failing to capture three-dimensional spatial angle information. To address these issues, this invention provides a self-correcting target angle estimation algorithm based on the Rank Reduced (RARE) principle and matrix transformation. This method obtains the transmit / receive steering vector matrix containing noise and amplitude / phase errors through tensor decomposition. Then, it performs matrix transformations on the obtained transmit / receive steering vector matrices to separate the vectors containing only amplitude / phase error coefficients. A spatial spectral peak search is performed on the intermediate matrix containing angle information to obtain the target angle estimate. The amplitude / phase error coefficients are then obtained based on the properties of eigenvectors and eigenvalues. Finally, the estimated amplitude / phase error coefficients are substituted into the original data signal model to further improve the accuracy of angle estimation. This invention solves the problem of low target angle estimation accuracy in existing methods under unknown amplitude / phase errors.

[0061] See Figure 1 The present invention provides a centralized array partial amplitude and phase error self-correction angle estimation method, comprising the following steps:

[0062] Step 1: For a bistatic MIMO radar array, construct a received signal model with amplitude and phase errors in some elements of the transmitting and receiving arrays.

[0063] The transmitting and receiving arrays of a bistatic MIMO radar array are deployed separately in different locations. Both the transmitting and receiving arrays are rectangular planar arrays with uniformly distributed element spacing. The total number of elements in the transmitting array is M. A Cartesian coordinate system is established with the plane containing the rectangular planar array as the origin, and a vertex element of the rectangular planar array is used as the origin of the coordinate system. The x-axis is established on one side of the element and the y-axis is established on the other side, so that the elements of the transmitting array are distributed in the first quadrant, with M elements along the x-axis. x There are M array elements along the y-axis. y The receiving array has N elements; a Cartesian coordinate system is established for the receiving array using the same method, with N elements along the x-axis. x There are N array elements, with N along the y-axis. y Each array element.

[0064] Suppose there are K independent targets in the far field, where the 2D-DOD of the k-th target relative to the original lattice element of the Cartesian coordinate system of the emission array is represented as follows: Where θ tk Indicates azimuth. This represents the pitch angle; similarly, the 2D-DOA of the k-th target relative to the origin of the receiving array is represented as... Where θrk Expressed as azimuth, It is expressed as pitch angle.

[0065] If the amplitude and phase error coefficients of the correction elements in the receiving and transmitting arrays have an amplitude of 1 and a phase of 0, then the amplitude and phase errors of the receiving and transmitting arrays can be expressed as follows:

[0066]

[0067] Where ρ rp and φ rp Let ρ represent the unknown gain error vector and phase error vector of the p-th (p>1) element of the receiving array. tp and φ tp Let e ​​represent the unknown gain error vector and phase error vector of the p-th (p>1) element of the transmitting array, where e is the natural constant, j is the imaginary unit, and p = 1, 2, ..., P; P represents the number of elements with unknown gain error vectors and phase error vectors.

[0068] Therefore, when there is amplitude and phase error between the elements of the receiving array and the transmitting array, the received signal after matched filtering can be represented as the following received signal model:

[0069] X=[Γ r A r ⊙Γ t A t ]S T +N

[0070] In the formula, N is a Gaussian white noise matrix with zero mean, and the superscript T indicates transpose, the same below; in Let K×L be the complex space, and L be the number of received snapshots. β represents the echo signal of K targets captured in the t-th snapshot, where t = 1, 2, ..., L; k and f k A represents the amplitude of the k-th target and the Doppler shift caused by the k-th target's own motion, which is much smaller than the carrier frequency of the transmitted signal. r With A t These are the receiver array manifold and the transmitter array manifold, respectively, which can be specifically represented as follows:

[0071]

[0072] In the formula, ⊙ represents the Khatri-Rao product. Let A represent the Kronecker product. rx This represents the array manifold of the x-axis sub-linear array of the receiving array, where the steering vector of the k-th target is...

[0073] k = 1, ..., K; A ry Indicates receiving

[0074] The array manifold of the y-axis sub-linear array, whose guiding vector for the k-th target is: A tx The array manifold representing the x-axis sub-linear array of the launch array, where the steering vector of the k-th target is... A ty The array manifold representing the y-axis sub-linear array of the launch array, whose steering vector for the k-th target is: The element spacing d is λ / 2;

[0075] The receiving array steering vector is represented by the Kronecker product between the steering vectors of the k-th target in the array manifolds of the x-axis and y-axis sub-arrays. This represents the launch array steering vector, which is the Kronecker product between the steering vectors of the k-th target in the array manifolds of the x-axis and y-axis sub-linear arrays.

[0076] The received signal model can then be further expressed as:

[0077] X = [B r ⊙B t ]S T +N

[0078] The steering vector matrix of the receiving array The steering vector matrix of the transmitting array

[0079] Step 2: Perform identity transformations on the guide vector matrices of the receiving array and the transmitting array respectively to obtain the rank-loss intermediate matrices of the receiving array and the transmitting array.

[0080] Receiver array steering vector matrix B r The k-th term can be written as:

[0081]

[0082] Where a ki (i = 1, 2, ..., N) x N y ) is the receiving array steering vector corresponding to the k-th target. The i-th element.

[0083] Then, a matrix identity transformation can be performed to convert it into a column vector, which can then be extracted:

[0084]

[0085] in,

[0086] Obtain the rank-loss intermediate matrix of the receiving array It is by It is reconstructed from each element; among which ξ r ∈(N x N y -P+1)×1 is the unknown amplitude and phase error vector of the receiving array; the rank loss intermediate matrix of the transmitting array can be obtained using the same method. and the unknown amplitude and phase error vector ξ t .

[0087] Step 3: By performing PARAFAC decomposition on the received signal model, the estimated values ​​of the steering vector matrices of the receiving array and the transmitting array are obtained; the covariance matrix of the estimated values ​​is decomposed into eigenvalues ​​to obtain the noise subspace corresponding to the received signals of the receiving array and the transmitting array.

[0088] According to tensor decomposition theory, the expression for the received signal model is X = [B r ⊙B t ]S T +N satisfies the trilinear model; by performing PARAFAC decomposition and column normalization, the steering vector matrix B of the receiving array can be obtained in the noisy receiving signal model. r With the guiding vector matrix B of the transmitting array t The estimated value matrix and The covariance matrices of the receiving array and the transmitting array are calculated as follows:

[0089]

[0090] In the formula, E{·} represents the expectation, and the superscript H represents the conjugate transpose.

[0091] Eigenvalue decomposition of the covariance matrix yields:

[0092]

[0093] Among them, E rs and E rn D represents the signal subspace and noise subspace corresponding to the received signal of the receiving array. rs and D rn For E rs and E rn The corresponding eigenvalue matrix; E ts and E tn D represents the signal subspace and noise subspace corresponding to the received signal of the transmitting array. ts and D tn For E ts and E tnThe corresponding eigenvalue matrix.

[0094] Step 4: Based on the rank loss intermediate matrix of the receiving array and the transmitting array, and combined with the noise subspace corresponding to the received signals of the receiving array and the transmitting array, the estimated values ​​of the amplitude and phase error vectors of the receiving array and the transmitting array are obtained by using the relationship between the eigenvector and the eigenvalue.

[0095] Based on the noise subspace E corresponding to the received signals of the receiving array and the transmitting array rn and E tn Rank-loss intermediate matrices for receiver and transmitter arrays and definition:

[0096]

[0097] Then there is

[0098] Then let Theoretically, the amplitude and phase error vectors ξ of the receiving array and the transmitting array are... r With ξ t H respectively r With H t The eigenvector corresponding to the eigenvalue of 0; therefore, for H r With H t After performing eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors, the amplitude and phase error vectors ξ of the receiving array and transmitting array can be obtained by sorting the eigenvectors corresponding to the smallest eigenvalues. r With ξ t The estimated value and

[0099] Step 5: Construct spectral peak functions using the estimated amplitude and phase error vectors of the receiving array and transmitting array, and obtain 2D-DOD and 2D-DOA estimates through two-dimensional spatial search.

[0100] Due to the orthogonality between the receiving array steering vector, the transmitting array steering vector, and the corresponding noise subspace, the following equation is satisfied:

[0101]

[0102] Based on the matrix identity transformation in step 2 and The above formula can be equivalently expressed as:

[0103]

[0104] make:

[0105]

[0106] And the estimated value of the amplitude and phase error vector and Substituting, we get:

[0107]

[0108] The following spectral function can then be constructed to search for and obtain the 2D-DOA estimate:

[0109]

[0110] Where det[·] denotes the determinant of a matrix; These represent the azimuth and elevation angles, respectively.

[0111] Similarly, similar spectral peak functions can be constructed to obtain 2D-DOD estimates:

[0112]

[0113] Based on the above peak functions, the 2D-DOA estimates for all K targets are obtained respectively. and 2D-DOD estimates in Indicates to The estimated value, Indicates to The estimated value.

[0114] Step 6: Construct the maximum likelihood function of the received signal, and use the maximum likelihood function to perform target pairing between the 2D-DOD estimate and the 2D-DOA estimate.

[0115] By straightening the received signal model X, we can obtain:

[0116] Y D =Dη+N D

[0117] In the formula Y D This represents the result after the received signal model X is straightened. D = B r ⊙B t It includes the angle information of all targets, N D It is a Gaussian noise vector of MN×1.

[0118] Then the maximum likelihood function of the received signal can be obtained as:

[0119]

[0120] In the formula, the 2D-DOA estimation parameters 2D-DOD Estimation Parameters Let V be the variance of Gaussian white noise. Simplifying the above equation and taking its logarithm, we get:

[0121]

[0122] Where F(ζ) t ,ζ r () is the simplified and logarithmic expression of the maximum likelihood function. To find the pseudo-inverse of a matrix, It is B k and Generate projection matrices that are orthogonal to the subspace. I mn It is an MN×MN dimensional identity matrix.

[0123] Therefore, for each target, the 2D-DOA estimate is obtained. Compare this 2D-DOA estimate with the 2D-DOD estimates of all targets. In the middle, each 2D-DOD estimate Constitute a set of estimated parameters and Substitute and calculate F(ζ) respectively t ,ζ r The value of ) is obtained by obtaining all F(ζ) t ,ζ r From the values ​​of ), take the 2D-DOD estimate corresponding to the minimum value. This is the 2D-DOA estimate. The pairing results are obtained; this step is repeated to obtain the 2D-DOA estimate for each target. Pairing the values ​​with the 2D-DOD estimate yields the angle estimate for partial amplitude and phase error self-correction.

[0124] Simulation experiment:

[0125] See Figures 2 to 5 The basic experimental setup is as follows: the receiving and transmitting antennas of the uniform planar bistatic MIMO radar array each have 5 elements along the x-axis and y-axis, i.e., M... x =M y =N x =N y =5, the element spacing is set to d = λ, and there are K = 2 uncorrelated far-field narrowband targets. The target angles to be estimated are respectively set to and The Doppler frequencies of the target were set to f1 = 100 Hz and f2 = 300 Hz, respectively, with a mean RCS of 1. The noise signal received by the array elements was set to zero-mean Gaussian white noise. The first nine array elements in the transceiver array were set as correction elements with an amplitude and phase error coefficient of 1. The real and imaginary parts of the amplitude and phase error coefficients of the remaining array elements were randomly generated by the rand function in Matlab, and the amplitude and phase errors of the transceiver arrays were set to be the same. The comparison method in the experiment was the RARE method without matrix transformation and the RARE method with known amplitude and phase error coefficients.

[0126] Experiment 1: Assume the number of signal snapshots is fixed at 200 and the signal-to-noise ratio is fixed at 5dB. Figure 2 This is a spatial spectrum of the target angle estimation method of the present invention. As can be seen from the figure, the method of the present invention exhibits a sharp and distinct spectral peak in the direction of the target's arrival, indicating that the present invention can obtain a relatively accurate target angle estimate. Figure 3 The scatter plot shows the amplitude and phase error coefficients of the transceiver array estimated by the method of the present invention. It can be seen that the estimated values ​​are very close to the true values. Therefore, the accuracy of the target angle estimation can be further improved by self-correction using the estimated amplitude and phase error coefficients. Figure 4 The spatial spectrum obtained by the method of this invention after estimating the amplitude and phase error coefficients and substituting them into the signal model for spectral peak search is a self-corrected spectrum. It can be seen that self-correction using the estimated amplitude and phase error coefficients can yield sharper spectral peaks and improve the accuracy of angle estimation.

[0127] Experiment 2: Assuming the number of signal snapshots is fixed at 200 and the signal-to-noise ratio varies between -10dB and 20dB, each point in the simulation is obtained through 500 independent Monte Carlo experiments. Figure 5 The graph shows the change in target angle estimation accuracy with signal-to-noise ratio (SNR), with the horizontal axis representing SNR and the vertical axis representing the root mean square error (RMSE). It can be seen that as the SNR increases, the RMSE of the proposed method gradually decreases and approaches that of the RARE method with known amplitude and phase error coefficients.

[0128] The formula for calculating RMSE is:

[0129]

[0130] in and Let be the estimated values ​​of the angle of the k-th target in the q-th Monte Carlo test, corresponding to the transmitting and receiving arrays, respectively, where Q is the number of Monte Carlo tests.

[0131] Experiment 3: Assuming the signal-to-noise ratio is fixed at 5dB, the number of signal snapshots varies between 50 and 600. Each point in the simulation is obtained through 500 independent Monte Carlo experiments. Figure 6The chart shows how the target angle estimation accuracy changes with the number of snapshots, with the horizontal axis representing the number of sampled snapshots and the vertical axis representing RMSE. From... Figure 5 and Figure 6 As can be seen, the present invention can solve the problem of target angle estimation under unknown amplitude and phase errors and achieve high estimation performance.

[0132] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for estimating the self-correcting angle of amplitude and phase error in a centralized array, characterized in that, include: For bistatic MIMO radar arrays, a received signal model is constructed where some elements of the transmitting and receiving arrays have amplitude and phase errors. By performing identity transformations on the steering vector matrices of the receiving array and the transmitting array respectively, the rank-loss intermediate matrices of the receiving array and the transmitting array are obtained. By performing PARAFAC decomposition on the received signal model, the estimated values ​​of the steering vector matrices of the receiving array and the transmitting array are obtained; by performing eigenvalue decomposition on the covariance matrix of the estimated values, the noise subspace corresponding to the received signals of the receiving array and the transmitting array is obtained. Based on the rank loss intermediate matrix of the receiving array and the transmitting array, and combined with the noise subspace corresponding to the received signals of the receiving array and the transmitting array, the estimated values ​​of the amplitude and phase error vectors of the receiving array and the transmitting array are obtained by using the relationship between the eigenvector and the eigenvalue. The spectral peak function is constructed using the estimated amplitude and phase error vectors of the receiving array and the transmitting array, and the 2D-DOD estimate and 2D-DOA estimate are obtained through two-dimensional spatial search. Construct the maximum likelihood function of the received signal, and use the maximum likelihood function to perform target pairing between the 2D-DOD estimate and the 2D-DOA estimate.

2. The centralized array partial amplitude and phase error self-correction angle estimation method according to claim 1, characterized in that, A received signal model is constructed where some elements of the transmitting and receiving arrays exhibit amplitude and phase errors, specifically represented as follows: in, The matrix is ​​a Gaussian white noise matrix with zero mean, and the superscript is... T Indicates transpose; steering vector matrix of the receiver array. The guiding vector matrix of the transmitting array ; The echo signal matrix; and These are the receiver array stream and the transmitter array stream, respectively. Indicates the receiving array steering vector. Represents the transmission array steering vector, the first The 2D-DOD representation of a target relative to the origin element of the Cartesian coordinate system of the launch array is as follows: , Indicates azimuth. Indicates the pitch angle; the first The 2D-DOA representation of the position of each target relative to the origin of the receiving array is as follows: ,in Expressed as azimuth, Expressed as pitch angle, This represents the number of targets; the amplitude and phase errors of the receiving array and the transmitting array can be expressed as follows: ， The receiving array along There is on the shaft Each array element, along There is on the shaft Each array element; the transmitting array along There is on the shaft Each array element, along There is on the shaft Each array element; and Indicates the receiving array number The unknown gain error vector and phase error vector of each array element. and Indicates the first transmission array The unknown gain error vector and phase error vector of each array element. It is a natural constant. It is the imaginary unit.

3. The centralized array partial amplitude and phase error self-correction angle estimation method according to claim 2, characterized in that, Perform identity transformations on the steering vector matrices of the receiving and transmitting arrays respectively to obtain the rank-loss intermediate matrices of the receiving and transmitting arrays. The processing procedure for the receiving array is as follows: in, , in For the first The receiving array steering vector corresponding to each target The One element, ; For the rank-loss intermediate matrix of the receiving array, The amplitude and phase error vector of the receiving array. ; This represents the number of array elements with unknown gain error vectors and phase error vectors.

4. The centralized array partial amplitude and phase error self-correction angle estimation method according to claim 3, characterized in that, By performing PARAFAC decomposition on the received signal model and normalizing it column-wise, the steering vector matrix of the receiving array is obtained. With the guiding vector matrix of the transmitting array The estimated value matrix and The covariance matrices of the receiving array and the transmitting array are calculated as follows: In the formula Indicates the expectation, superscript H Indicates conjugate transpose; Eigenvalue decomposition of the covariance matrix yields the noise subspace corresponding to the received signals of the receiving and transmitting arrays. and .

5. The centralized array partial amplitude and phase error self-correction angle estimation method according to claim 4, characterized in that, The amplitude and phase error vectors of the receiving array and transmitting array are estimated using the relationship between eigenvectors and eigenvalues, including: Based on the noise subspace corresponding to the received signals of the receiving array and the transmitting array and Rank-loss intermediate matrices for receiving and transmitting arrays and ,definition: ， Then there is , ; make , Then the amplitude and phase error vectors of the receiving array and the transmitting array and They are respectively and The eigenvector corresponding to the eigenvalue of 0; for and After performing eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors, the amplitude and phase error vectors of the receiving array and transmitting array can be obtained by sorting the eigenvectors corresponding to the smallest eigenvalues. and The estimated value and .

6. The method for estimating the self-correcting angle of amplitude and phase error of a centralized array according to claim 5, characterized in that, A spectral peak function is constructed using the estimated amplitude and phase error vectors of the receiving and transmitting arrays. 2D-DOD and 2D-DOA estimates are obtained through a two-dimensional spatial search, including: Construct the following equation: make: And the estimated value of the amplitude and phase error vector and Substituting, we get: Construct the following spectral function to search for and obtain the 2D-DOA estimate: in This indicates finding the determinant of a matrix; These represent the azimuth and elevation angles, respectively. Similarly, constructing similar spectral peak functions yields 2D-DOD estimates: Based on the above peak functions, all of them are obtained respectively. 2D-DOA estimates of each target and 2D-DOD estimates ;in Indicates to The estimated value, Indicates to The estimated value.

7. The method for estimating the self-correcting angle of amplitude and phase error of a centralized array according to claim 6, characterized in that, Construct the maximum likelihood function of the received signal, and use the maximum likelihood function to perform target pairing between the 2D-DOD estimate and the 2D-DOA estimate, including: For the received signal model Perform a straightening operation to construct the maximum likelihood function of the received signal; simplify the maximum likelihood function and take its logarithm to obtain: in This represents the result after the received signal model X is straightened. To simplify and logarithmize the maximum likelihood function, To find the pseudo-inverse of a matrix, , yes and Generate a projection matrix that is orthogonal to the subspace. , yes A dimensional identity matrix; the total number of elements in the transmitting array is The total number of array elements in the receiving array is ; For each target's 2D-DOA estimate, this 2D-DOA estimate, along with each 2D-DOD estimate from all targets, forms a set of estimation parameters. These parameters are then substituted into the calculation... The value obtained Among the values, the 2D-DOD estimate corresponding to the minimum value is taken, which is the pairing result of the 2D-DOA estimate.

8. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the centralized array partial amplitude and phase error self-correction angle estimation method according to any one of claims 1-7.

9. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the centralized array partial amplitude and phase error self-correction angle estimation method according to any one of claims 1-7.

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