A centralized array amplitude and phase error angle estimation method

Abstract

This invention discloses a centralized array amplitude and phase error angle estimation method, comprising: for a bistatic MIMO radar array, modeling the received signals with amplitude and phase errors for all elements of the transmitting and receiving arrays; moving the receiving and transmitting arrays to obtain the steering vector matrices of the transmitting and receiving arrays before and after the movement; obtaining the estimated values ​​of the steering vector matrices of the transmitting and receiving arrays before and after the movement by performing PARAFAC decomposition on the received signals before and after the movement; constructing the synthetic steering vector matrix of the transmitting and receiving arrays; performing row transformations on the rows with equal amplitude and phase error coefficients in the synthetic steering vector matrix of the transmitting and receiving arrays to construct the transformed synthetic steering vector matrix; then performing matrix identity transformations on the column vectors corresponding to each target to obtain the rank-loss intermediate matrix of the transmitting and receiving arrays and the amplitude and phase error coefficient vector; constructing a spectral peak function, obtaining the 2D-DOD estimate and the 2D-DOA estimate through two-dimensional space search, and performing target pairing.

Description

Technical Field

[0001] This invention relates to the field of radio signal direction finding, and more specifically to a centralized array amplitude and phase error angle estimation method. 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] Currently, most methods for suppressing amplitude and phase errors in array elements employ active correction algorithms. Active correction algorithms typically require an error-free auxiliary source to compensate for and correct array elements with perturbation errors. However, in practical applications, the difficulty in obtaining and utilizing accurate error-free correction sources hinders the effective implementation of such algorithms. Furthermore, in the field of bistatic MIMO radar, most array configurations studied for amplitude and phase errors are uniform linear arrays, which can only provide one-dimensional angle estimates of the target for both the transmitting and receiving arrays. This fails to provide effective angle estimates for targets existing in three-dimensional space, significantly limiting the widespread adoption and application of bistatic MIMO radar. Summary of the Invention

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

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

[0006] A centralized array amplitude and phase error angle estimation method includes:

[0007] For bistatic MIMO radar arrays, a model is constructed for the received signal with amplitude and phase errors in all elements of the transmitting and receiving arrays.

[0008] The receiving and transmitting arrays are moved to obtain the steering vector matrices of the receiving and transmitting arrays before and after the movement; by performing PARAFAC decomposition on the received signals before and after the movement, the estimated values ​​of the steering vector matrices of the receiving and transmitting arrays before and after the movement are obtained.

[0009] The estimated values ​​of the steering vector matrices of the receiving array and the transmitting array before and after the movement are synthesized to construct the synthesized steering vector matrices of the receiving array and the transmitting array; the covariance matrix of the synthesized steering vector matrix is ​​decomposed by eigenvalue to obtain the noise subspace corresponding to the received signals of the receiving array and the transmitting array.

[0010] Row transformations are performed on the rows with equal amplitude and phase error coefficients in the composite steering vector matrices of the receiving array and the transmitting array, respectively, to construct the transformed composite steering vector matrices; then matrix identity transformations are performed on the column vectors corresponding to each target to obtain the rank loss intermediate matrices of the receiving array and the amplitude and phase error coefficient vectors of the transmitting array.

[0011] The spectral peak function is constructed using the amplitude and phase error coefficient vectors of the receiving array and the transmitting array, and the rank loss intermediate matrix. The 2D-DOD estimate and the 2D-DOA estimate are obtained by searching in two-dimensional space.

[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, the received signal with amplitude and phase errors in all elements of the transmitting and receiving arrays is modeled, specifically 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, the receiving array and the transmitting array are set as movable arrays; within Δt, the receiving array and the transmitting array are translated by a distance of λ / 2 along the x-axis and y-axis, respectively; the target echo signals are all far-field narrowband signals, and the received signals and Gaussian white noise are considered to be the same before and after the movement, and the amplitude and phase error coefficients are also unchanged; thus, the steering vector matrices of the translated receiving array and transmitting array are obtained;

[0019] The received signals before and after the translation satisfy a trilinear model. By decomposing the received signals before and after the translation using PARAFAC and normalizing them column-wise, the estimated values ​​of the steering vector matrices of the receiving array and transmitting array before and after the translation are obtained.

[0020] Furthermore, the composite steering vector matrix of the receiving array and the transmitting array It is expressed as follows:

[0021]

[0022] in, and B is the steering vector matrix of the receiving array and the transmitting array before movement. r With B t The estimated value, and B′ is the steering vector matrix of the receiving array and the transmitting array after the movement. r and B′ t The estimated value; and For the receiver array stream type A before and after the move r With A' r The estimated value, and Transmit array manifold A before and after the transmit array is moved t With A' t The estimated value;

[0023] Find the composite guiding vector matrix Covariance matrix:

[0024]

[0025] In the formula, E{·} represents the expectation, and the superscript H represents the conjugate transpose;

[0026] 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 .

[0027] Furthermore, in step 4, the synthesized steering vector matrix of the receiving array... The processing steps include:

[0028] The synthesized steering vector matrix of the receiving array Represented as:

[0029]

[0030] in, and They are respectively and The i-th (i = 1, 2, ..., N) x N y ) elements; and These are the estimated values ​​of the receiving array steering vector before and after the receiving array is moved;

[0031] Synthesize the guide vector matrix Medium amplitude phase error coefficient Rows of equal elements are transformed to obtain the transformed composite guiding vector matrix; the column vector corresponding to the k-th target can then be subjected to matrix identity transformation:

[0032]

[0033] Thus, the rank-loss intermediate matrix of the receiving array is obtained. and the amplitude and phase error coefficient vector ξ t .

[0034] Furthermore, using the amplitude and phase error coefficient vectors of the receiving array and the transmitting array, and the rank loss intermediate matrix, a spectral peak function is constructed. 2D-DOD estimates and 2D-DOA estimates are obtained through a two-dimensional spatial search, including:

[0035] Construct the following equation:

[0036]

[0037] Based on matrix identity transformation, the amplitude and phase error coefficient vectors ξ of the receiving array and transmitting array are obtained. r and ξ t Substituting, the above expression can be equivalently expressed as:

[0038]

[0039] Then, a spectral function can be constructed to perform a two-dimensional search to obtain the 2D-DOA angle estimate:

[0040]

[0041] Where det[·] denotes the determinant of a matrix; These represent the azimuth and elevation angles, respectively.

[0042] Similarly, constructing similar spectral peak functions yields 2D-DOD estimates:

[0043]

[0044] Based on the above spectral peak functions, the 2D-DOA estimates of all targets are obtained respectively. and 2D-DOD estimates in Indicates to The estimated value, Indicates to The estimated value.

[0045] 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:

[0046] 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:

[0047]

[0048] 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;

[0049] 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 rAmong the values ​​of ), the minimum 2D-DOD estimate is taken, which is the pairing result of the 2D-DOA estimate.

[0050] 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 amplitude and phase error angle estimation method.

[0051] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the centralized array amplitude and phase error angle estimation method.

[0052] Compared with the prior art, the present invention has the following technical features:

[0053] Existing bistatic MIMO radar angle estimation algorithms are mostly only applicable to uniform linear arrays, and their performance degrades or even fails when unknown amplitude and phase errors exist in the array elements. This invention estimates the target angle by synthesizing a steering vector matrix through array movement and utilizing the rank-deficient property of the intermediate matrix after matrix identity transformation. 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

[0054] Figure 1 A schematic diagram of the amplitude and phase error received signal model for a bistatic MIMO array;

[0055] 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;

[0056] Figure 3 This is a graph showing the relationship between target angle estimation accuracy and signal-to-noise ratio when all array elements have unknown amplitude and phase errors in an embodiment of the present invention.

[0057] Figure 4 This is a graph showing the relationship between target angle estimation accuracy and the number of snapshots when there is an unknown amplitude and phase error in an embodiment of the present invention.

[0058] Figure 5 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0059] 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, based on the idea of ​​synthesizing steering vectors using a moving array and the principle of Rank Reduced (RARE), provides an angle estimation method for all array elements with amplitude and phase errors. This method synthesizes the steering vector matrices before and after movement, assuming that the amplitude and phase errors of the array elements do not change with array movement. Row and matrix transformations are then performed on the synthesized steering vector matrix to obtain a rank-deficient intermediate matrix. A spectral function is constructed from this intermediate matrix, and peak search is performed to obtain the angle estimate. This invention solves the problem of low target angle estimation accuracy under all unknown amplitude and phase errors without requiring auxiliary array elements.

[0060] Step 1: For a bistatic MIMO radar array, model the received signal with amplitude and phase errors for all elements of the transmitting and receiving arrays.

[0061] 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.

[0062] 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 θ rk Expressed as azimuth, It is expressed as pitch angle.

[0063] The amplitude and phase errors of the receiving array and the transmitting array can be expressed as follows:

[0064]

[0065] 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 and j is the imaginary unit.

[0066] Therefore, considering the amplitude and phase errors between the elements of the receiving and transmitting arrays, the receiver, after matching filtering the received signal after L snapshots, can be represented by the following received signal model:

[0067] X=[Γ r A r ⊙Γ t A t ]S T +N

[0068] 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:

[0069]

[0070] 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... A ry The array manifold representing the y-axis sub-linear array of the receiving array, whose steering vector for the k-th target is: A tx The array manifold representing the x-axis sub-linear array of the launch array, with the steering vector of the k-th target being: 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;

[0071] This represents the receiving 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 sub-array and the y-axis sub-array. 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.

[0072] Let the steering vector matrix B of the receiving array r =Γ r A r The guiding vector matrix B of the transmitting array t =Γ t A t The model of the received signal can then be further expressed as:

[0073] X = [B r ⊙B t ]S T +N.

[0074] Step 2: Move the receiving array and the transmitting array to obtain the steering vector matrices of the receiving array and the transmitting array before and after the movement; obtain the estimated values ​​of the steering vector matrices of the receiving array and the transmitting array before and after the movement by performing PARAFAC decomposition on the received signals before and after the movement.

[0075] To obtain the unknown amplitude and phase error coefficients and target angle without correction elements, the receiving and transmitting arrays can be configured as movable arrays. To ensure that the synthesized array still satisfies the condition that the element spacing is half a wavelength, the receiving signal model in this section requires setting the initial element spacing of the receiving and transmitting arrays to d = λ. Since the received signal after reflection from the far-field target is a slow-fluctuating far-field narrowband signal, after each snapshot of the received signal, the receiving and transmitting arrays are translated by a distance of λ / 2 along the x-axis and y-axis respectively within a very short time delay. The received signal can then be considered the same as the received signal before the translation. Thus, the steering vector matrices before and after the translation are merged, and an intermediate matrix with rank loss is constructed through matrix identity transformation. Finally, a two-dimensional spectral peak search can be performed to obtain the target angle estimate; λ is the signal wavelength.

[0076] Based on the received signal model, the received signal before the receiving array and transmitting array are translated is as follows:

[0077] X(t)=[B r ⊙B t S(t) + N(t) = [Γ r A r ⊙Γ t A t S(t)+N(t)

[0078] Where X(t), N(t), and S(t) represent the received signal, Gaussian white noise, and echo signal at time t, respectively;

[0079] If the translation of the receiving array and the transmitting array is completed after a very small time delay Δt, the received signal after translation can be obtained as follows:

[0080] X(t+Δt)=[B′ r ⊙B′ t S(t+Δt)+N(t+Δt)

[0081] Since the target's echo signals are all far-field narrowband signals, the received signal S(t+Δt) after Δt can be considered the same as the received signal S(t) before. The noise is Gaussian white noise, meaning it is a random stationary signal unaffected by time. Therefore, N(t+Δt) = N(t) can also be obtained. Furthermore, since each array element only undergoes translation without changing the array element channel, the amplitude and phase error coefficients corresponding to each array element remain unchanged. Also, the far-field target angle can be considered the same for the array before and after translation. Therefore, the above equation can be rewritten as:

[0082] X(t+Δt)≈[B′ r ⊙B′ t S(t) + N(t) = [Γ r A′ r ⊙Γ t A′ t S(t)+N(t)

[0083] Among them, B′ r and B′ t Let the steering vector matrices of the moved receiver and transmitter arrays be given. Then the manifolds of the translated receiver and transmitter arrays are: and in The included vectors are as follows:

[0084]

[0085] According to tensor decomposition theory, the received signal X(t) before and after the translation is equal to [B]. r ⊙B t S(t)+N(t) and X(t+Δt)=[B′ r ⊙B′ t S(t+Δt)+N(t+Δt) satisfies a trilinear model; by decomposing the received signals X(t) and X(t+Δt) using PARAFAC and normalizing them column-wise, B can be obtained from the noisy received signal. r With B t The estimated value and and B′ r and B′ t The estimated value and

[0086] Step 3: Synthesize the estimated values ​​of the steering vector matrices of the receiving array and the transmitting array before and after the movement to construct the synthesized steering vector matrices of the receiving array and the transmitting array; perform eigenvalue decomposition on the covariance matrix of the synthesized steering vector matrix to obtain the noise subspace corresponding to the received signals of the receiving array and the transmitting array.

[0087] Composite steering vector matrix of receiver array and transmitter array It is expressed as follows:

[0088]

[0089] in, and For the receiver array manifold A before and after the receiver array is moved r With A' r The estimated value, and Transmit array manifold A before and after the transmit array is moved t With A' t The estimated value.

[0090] Find the composite guiding vector matrix Covariance matrix:

[0091]

[0092] In the formula, E{·} represents the expectation, and the superscript H represents the conjugate transpose;

[0093] The covariance matrix is ​​obtained by eigenvalue decomposition:

[0094]

[0095] Where the superscript H indicates taking the conjugate transpose of the matrix, and 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 Etn The corresponding eigenvalue matrix.

[0096] Step 4: Perform row transformations on the rows with equal amplitude and phase error coefficients in the synthetic steering vector matrices of the receiving array and the transmitting array respectively to construct the transformed synthetic steering vector matrices; then perform matrix identity transformations on the column vectors corresponding to each target to obtain the rank loss intermediate matrix of the receiving array and the amplitude and phase error coefficient vector of the transmitting array.

[0097] Synthetic steering vector matrix of the receiving array For example, we can Further expressed as:

[0098]

[0099] in, and They are respectively and The i-th (i = 1, 2, ..., N) x N y ) elements; and These are the estimated values ​​of the receiving array steering vector before and after the receiving array is moved.

[0100] Observing the above formula, in order to make the intermediate matrix after matrix transformation satisfy the missing rank characteristic, it is necessary to synthesize the guiding vector matrix. Medium amplitude phase error coefficient Rows of equal length are transformed to obtain the following composite guiding vector matrix:

[0101]

[0102] We can perform matrix identity transformations on the column vector corresponding to the k-th target:

[0103]

[0104] in For 2N x N y ×N x N y The rank-loss intermediate matrix of the dimensional receiver array, ξ r For N x N y A 1×1 dimension vector of amplitude and phase error coefficients for the receiving array.

[0105] The amplitude and phase error coefficients can be extracted into a column vector ξ using the above method. r This results in the rank-loss intermediate matrix after the identity transformation. The matrix contains only angle information; similarly, the intermediate matrix of the rank loss of the transmission array can be obtained. and amplitude and phase error coefficient vector ξ t .

[0106] Step 5: Construct the spectral peak function using the amplitude and phase error coefficient vectors of the receiving array and the transmitting array, and the rank loss intermediate matrix. Obtain the 2D-DOD estimate and the 2D-DOA estimate through two-dimensional spatial search.

[0107] Due to the orthogonality between the receiving array steering vector, the transmitting array steering vector, and the corresponding noise subspace, the following equation holds:

[0108]

[0109] Based on the matrix identity transformation in step 4, the obtained amplitude and phase error coefficient vectors ξ of the receiving array and transmitting array are... r and ξ t Substituting, the above expression can be equivalently expressed as:

[0110]

[0111] Then, a spectral function can be constructed to perform a two-dimensional search to obtain the 2D-DOA angle estimate:

[0112]

[0113] Where det[·] denotes the determinant of a matrix; These represent the azimuth and elevation angles, respectively.

[0114] Similarly, similar spectral peak functions can be constructed to obtain 2D-DOD estimates:

[0115]

[0116] Based on the above spectral peak functions, the 2D-DOA estimates of all targets are obtained respectively. and 2D-DOD estimates in Indicates to The estimated value, Indicates to The estimated value.

[0117] 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.

[0118] By straightening the received signal model X, we can obtain:

[0119] Y D =Dη+N D

[0120] In the formula YD 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.

[0121] Then the maximum likelihood function of the received signal can be obtained as:

[0122]

[0123] 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:

[0124]

[0125] 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.

[0126] 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 Construct 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 under the amplitude and phase error of the centralized array.

[0127] Simulation experiment:

[0128] The basic experimental setup is as follows: the receiver and transmitter 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 targets 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 amplitude and phase error coefficients were generated using the rand function in Matlab, and the same amplitude and phase error coefficients were set at both the transmitting and receiving ends. The experimental comparison methods were the RARE method without matrix transformation and the RARE method with known amplitude and phase error coefficients.

[0129] 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.

[0130] 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 3 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.

[0131] The formula for calculating RMSE is:

[0132]

[0133] 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.

[0134] 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 4 The 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 3 and Figure 4 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.

[0135] 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 centralized array amplitude and phase error angle estimation method, characterized in that, include: For bistatic MIMO radar arrays, a model is constructed for the received signal with amplitude and phase errors in all elements of the transmitting and receiving arrays. Move the receiving and transmitting arrays to obtain the steering vector matrices of the receiving and transmitting arrays before and after the movement; By performing PARAFAC decomposition on the received signals before and after the movement, the estimated values ​​of the steering vector matrices of the receiving array and the transmitting array before and after the movement are obtained. The estimated values ​​of the steering vector matrices of the receiving array and the transmitting array before and after the movement are synthesized to construct the synthesized steering vector matrices of the receiving array and the transmitting array; the covariance matrix of the synthesized steering vector matrix is ​​decomposed by eigenvalue to obtain the noise subspace corresponding to the received signals of the receiving array and the transmitting array. Row transformations are performed on the rows with equal amplitude and phase error coefficients in the composite steering vector matrices of the receiving array and the transmitting array, respectively, to construct the transformed composite steering vector matrices; then matrix identity transformations are performed on the column vectors corresponding to each target to obtain the rank loss intermediate matrices of the receiving array and the amplitude and phase error coefficient vectors of the transmitting array. The spectral peak function is constructed using the amplitude and phase error coefficient vectors of the receiving array and the transmitting array, and the rank loss intermediate matrix. The 2D-DOD estimate and the 2D-DOA estimate are obtained by searching in two-dimensional space. 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 amplitude and phase error angle estimation method according to claim 1, characterized in that, The received signal, which has amplitude and phase errors across all elements of the transmitting and receiving arrays, is modeled 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 transmission array along There is on the shaft Each array element, along There is on the shaft Each array element; receiving array edge 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 amplitude and phase error angle estimation method according to claim 1, characterized in that, The receiving array and transmitting array are configured as movable arrays; in The receiving array and transmitting array are respectively along shaft and Axis translation The distance; The target echo signals are all far-field narrowband signals. The received signals and Gaussian white noise are considered to be the same before and after the movement, and the amplitude and phase error coefficients are also unchanged. This yields the steering vector matrices of the translated receiving and transmitting arrays; Indicates time delay; The wavelength of the signal; The received signals before and after the translation satisfy a trilinear model. By decomposing the received signals before and after the translation using PARAFAC and normalizing them column-wise, the estimated values ​​of the steering vector matrices of the receiving array and transmitting array before and after the translation are obtained.

4. The centralized array amplitude and phase error angle estimation method according to claim 2, characterized in that, Composite steering vector matrix of receiver array and transmitter array , It is expressed as follows: in, and The steering vector matrix for the receiving array and transmitting array before movement. and The estimated value, and The steering vector matrix for the receiving array and transmitting array after movement. and The estimated value; and Receiver array stream before and after the move and The estimated value, and Transmission array manifold before and after transmission array movement and The estimated value; Find the composite guiding vector matrix , Covariance matrix: 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 amplitude and phase error angle estimation method according to claim 4, characterized in that, Synthetic steering vector matrix of the receiving array The processing steps include: The synthesized steering vector matrix of the receiving array Represented as: in, and They are respectively and The first in One element, ; and These are the estimated values ​​of the receiving array steering vector before and after the receiving array is moved; Synthesize the guide vector matrix Medium amplitude phase error coefficient Perform row operations on equal rows to obtain the transformed composite guiding vector matrix; take the first row from the transformed row... The column vectors corresponding to each target can be transformed using matrix identity: Thus, the rank-loss intermediate matrix of the receiving array is obtained. and amplitude and phase error coefficient vector .

6. The centralized array amplitude and phase error angle estimation method according to claim 5, characterized in that, A spectral peak function is constructed using the amplitude and phase error coefficient vectors of the receiving and transmitting arrays and the rank loss intermediate matrix. 2D-DOD and 2D-DOA estimates are obtained through a two-dimensional spatial search, including: Construct the following equation: Based on matrix identity transformation, the amplitude and phase error coefficient vectors of the receiving array and transmitting array are obtained. and Substituting, the above expression can be equivalently expressed as: Then, a spectral function can be constructed to perform a two-dimensional search to obtain the 2D-DOA angle 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 spectral peak functions, the 2D-DOA estimates of all targets are obtained respectively. and 2D-DOD estimates ;in Indicates to The estimated value, Indicates to The estimated value.

7. The centralized array amplitude and phase error angle estimation method 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 projection matrices that are 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 is all 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 amplitude and phase error 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 amplitude and phase error angle estimation method according to any one of claims 1-7.

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