Any array MIMO radar angle estimation method and system based on phase compensation

Abstract

The invention provides an arbitrary array MIMO radar angle estimation method and system based on phase compensation, and relates to the technical field of radar positioning. Comprising the following steps: calculating a covariance matrix of a signal from a signal model after array matching filtering of a receiving end, blocking the obtained covariance matrix, obtaining a permutation matrix, constructing a matrix by using the permutation matrix and a unit matrix, carrying out blocking operation on the matrix, obtaining an initial phase difference matrix of array elements, and obtaining an initial phase difference matrix of the array elements; the method comprises the following steps: roughly estimating a non-fuzzy low-precision phase difference matrix by using a phase difference matrix in which the distance between adjacent sensor array elements is smaller than half wavelength, solving ambiguity, and compensating the ambiguity to an initial ambiguous phase difference matrix to obtain a non-fuzzy high-precision phase difference matrix; and finally, accurately estimating azimuth angles and pitch angles of the two-dimensional wave departure angle 2D-DOD and the two-dimensional direction of arrival 2D-DOA. The phase ambiguity is avoided, the estimation accuracy is improved, and the calculation complexity is reduced.

Description

Technical Field

[0001] The present invention relates to the field of radar positioning technology, and in particular to an arbitrary array MIMO radar angle estimation method and system based on phase compensation. Background Art

[0002] MIMO (Multiple Input Multiple Output) radar is a radar system with multiple transmitting antennas and receiving antennas. The introduction of the MIMO radar concept marks a major development in radar technology and has aroused great interest from many scholars and research institutions at home and abroad. MIMO radar technology draws on the MIMO principle in the field of wireless communications. Unlike traditional phased array radars, MIMO radars transmit mutually orthogonal waveforms through multiple active antennas, giving the radar system both spatial and temporal diversity, while creating a virtual aperture, improving angular resolution, and enabling the radar system to more accurately determine the location of the target. Due to the use of multiple independent signal paths, the anti-interference ability of MIMO radars is also greatly increased. With the rapid development of MIMO radars, they have shown unique advantages in the fields of air surveillance, ground surveillance, maritime surveillance, and missile guidance.

[0003] At present, the estimation of departure direction DOD and arrival direction DOA in MIMO radar is the key issue to accurately determine the target position and movement. Many excellent angle estimation methods have emerged, such as: maximum likelihood method, multiple signal classification method, signal parameter estimation method using rotation invariance technology and propagation operator method. Among them, the multiple signal classification algorithm needs to search for spectrum peaks during the estimation process, which has high computational cost but high estimation accuracy; while the signal parameter estimation algorithm using rotation invariance technology utilizes the invariance of MIMO radar angle estimation and does not require spectrum peak search, but needs to construct the covariance matrix of the received signal and its eigendecomposition; while the propagation operator algorithm does not require eigendecomposition of the covariance matrix of the received signal. Therefore, the propagation operator algorithm has lower computational complexity than the signal parameter estimation algorithm using rotation invariance technology. However, the propagation operator algorithm has poor estimation accuracy under low signal-to-noise ratio conditions and may even fail; especially in the traditional scalar array signal model, when the array element spacing is greater than half a wavelength, there will be fuzzy values ​​in the angle estimation.

[0004] Most of the existing technical research is applicable to the transmitting and receiving arrays that are uniform linear arrays (ULA). However, the layout of uniform linear arrays is often fixed. In some specific application scenarios, it is difficult to achieve such a fixed uniform linear layout. Therefore, the research on arbitrary arrays is also crucial. At present, the research on angle estimation of arbitrary arrays includes: Capon (minimum variance distortion-free response MVDR algorithm), multiple signal classification algorithm and interpolation method. Although Capon and multiple signal classification algorithms can estimate the angle of arbitrary arrays, they both require four-dimensional spectral peak search, and the calculation complexity is very high. Although the interpolation method does not require spectral peak search, it requires prior knowledge of the spatial sector of the event target, which is usually unavailable to radar systems. Although the recently popular polarization array can also perform two-dimensional angle estimation, the vector components may suffer from severe mutual coupling, resulting in inaccurate predicted estimation results. Summary of the invention

[0005] The main purpose of the present invention is to provide a method and system for angle estimation of arbitrary array MIMO radar based on phase compensation, so as to solve at least one of the above technical problems.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: an arbitrary array MIMO radar angle estimation method based on phase compensation, comprising the following steps: S1: Obtain the covariance matrix according to the signal model after the receiving end array matching filtering; S2: Divide the covariance matrix into blocks to obtain a block matrix, and obtain a permutation matrix based on the block matrix, and construct an initial matrix using the permutation matrix and a unit matrix; S3: Divide the initial matrix into blocks, and perform eigendecomposition on the results of the first two block matrices to obtain the first eigenvalue matrix and reference eigenvectors, use the remaining adjacent block matrices and reference eigenvectors to calculate the remaining eigenvalue matrix, convert all eigenvalue matrices into row vectors and place them in the initial phase matrix, and then take the phase to obtain the blurred initial phase difference matrix; S4: using the phase difference when the array element spacing is less than half a wavelength, an unambiguous low-precision Poynting vector matrix is ​​estimated, and then an unambiguous low-precision phase difference matrix is ​​obtained, and the unambiguous low-precision phase difference matrix and the initial phase difference matrix are solved to obtain ambiguity, and then the ambiguity is used to perform phase compensation to obtain an unambiguous high-precision phase difference matrix; S5: The unambiguous and high-precision phase difference matrix is ​​solved by the least square method to estimate the unambiguous and high-precision Poynting vector matrix to obtain the azimuth and elevation angles of 2D-DOD, and then S3 and S4 are simulated to obtain the azimuth and elevation angles of 2D-DOA; Among them, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

[0007] In the preferred embodiment, the specific steps of step S1 are as follows: S101: Based on the fact that the array element positions of the transmitting end and the receiving end are arbitrary, and the array element spacings of the transmitting array element and the receiving array element are D in number and greater than half a wavelength, the coordinates of the first row of the transmitting array and the receiving array are used as reference array elements, and the arrival time differences relative to the mth transmitting sensor and the nth receiving sensor are respectively: (1); (2); In the formula, For the m The location of the transmitting antenna, For the n The location of the receiving antenna, Respectively k The azimuth and elevation of the 2D-DOD of a target, Respectively k The azimuth and elevation of the 2D-DOA of a target; S102: Under the narrowband assumption, the spatial response vector of the transmitting sensor array and the receiving sensor array spatial response vector They are: (3); (4); in, For the m The arrival time difference of the transmitting sensor relative to the reference sensor array element, For the n The arrival time difference of the receiving sensor relative to the reference array element, The wavelength of the transmitted signal.

[0008] S103: The output formula of the receiving end matched filter is: (5); or: (6); In the formula, is the transmit array response matrix, is the receiving array response matrix, , is the Doppler shift, is the amplitude, is the Gaussian white noise matrix; represents the Khatri-Rao product, represents the Kroc inner product, L is the number of snapshots; S104: Define the matrix according to step S103 : (7); In the formula, Represented by the transmit array response matrix No. m Construct a diagonal matrix with rows, and obtain the signal model as follows: (8); Then the covariance matrix of the received signal is for: (9); In the formula, the superscript H is the conjugate transpose, L The number of snapshots.

[0009] In the preferred embodiment, the specific steps of step S2 are as follows: S201: The matrix Divide into blocks and take the front K Row Construction Matrix , take the remaining MN-K Row Construction Matrix ,Right now: (10); Similarly, the covariance matrix Divide into blocks and take the front K Column Construction Matrix , take the remaining MN - K Column Construction Matrix ,Right now: (11); Moreover, the matrix The matrix Right multiply by a permutation matrix It is concluded that: (12); Similarly, the matrix The matrix Left multiply the permutation matrix It is concluded that: (13); S202: Using an identity matrix And the permutation matrix above Construct an initial matrix ,Right now: (14); use Right multiply the initial matrix : (15); Right now: (16); Then the matrix in formula (7) Substituting in, we get: (17).

[0010] In the preferred embodiment, the specific steps of step S3 are as follows: S301: Matrix Divided into M Blocks, namely: (18); Right now: , ,in For the matrix Before N OK, For the matrix No. N+ Line 1 to Line 2 N OK, and ,but: (19); in, , , , diag means converting the row matrix into a diagonal matrix; make , , ,but: (20); S302: From formula (19), we can get ,in represents the generalized inverse of a matrix, Indicates the inverse of the matrix. Perform eigendecomposition to obtain the first eigenvalue matrix and the reference eigenvector : (twenty one); (twenty two); From formula (18), we can see that , ,and Similarly: (twenty three); at this time , , , , replace the formula (22) Substituting into formula (23) we get: (twenty four); (25); Similarly, Simulate equations (23), (24), (25) to obtain; S303: Take The diagonal elements of , , put M-1 row vectors into the initial phase matrix In the result: (26); The initial phase matrix Take the phase and get the initial phase difference matrix with ambiguity :

[0011] Right now: (27); Where: ; .

[0012] In the preferred solution, a phase compensation process is performed in step S4, and the specific steps are as follows: S401: After use ( M -1- D ) The phase difference between the array elements is less than half a wavelength, and a rough estimate is made to obtain the unambiguous low-precision Poynting vector matrix , and according to Find the unambiguous low-precision phase difference matrix Then, solve the ambiguity , the formula is: (28); S402: Initial phase difference matrix to compensate for periodic ambiguity The unambiguous and high-precision phase difference matrix is ​​obtained , the formula is: (29).

[0013] In the preferred solution, the azimuth and elevation angles of the 2D-DOD are obtained in step S5, specifically: Will The least squares method is used to solve and estimate the unambiguous and high-precision Poynting vector matrix , the formula is: (30); Then, the azimuth and elevation angle estimation of 2D-DOD can be expressed as: (31); (32).

[0014] In the preferred solution, step S5 simulates S3 and S4 to obtain the azimuth and elevation angles of 2D-DOA, specifically: Using transformation matrix C , for the matrix Perform a finite number of column operations such that: (33); Right now: (34); Multiply both sides of equation (16) by the matrix C ,Right now: (35); Will Divide N piece: (36); Similarly, using formula (22) , and then solve the equations (24)-(30) in turn to obtain the azimuth and elevation angles of 2D-DOA. The equations are: (37); (38).

[0015] In a preferred embodiment, an arbitrary array MIMO radar angle estimation system based on phase compensation includes: A covariance matrix acquisition module is used to acquire a covariance matrix according to a signal model after array matching filtering at the receiving end; A matrix construction module is used to divide the covariance matrix into blocks to obtain a block matrix, obtain a permutation matrix based on the block matrix, and construct an initial matrix using the permutation matrix and a unit matrix; Obtaining a blurred initial phase difference matrix module, which is used to divide the initial matrix into blocks, and perform eigendecomposition on the results of the first two block matrices, obtain the first eigenvalue matrix and the reference eigenvector, use the remaining adjacent block matrices and the reference eigenvector to calculate the remaining eigenvalue matrix, convert all eigenvalue matrices into row vectors and place them in the initial phase matrix, and then take the phase to obtain the blurred initial phase difference matrix; A phase compensation module is used to estimate an unambiguous and low-precision Poynting vector matrix by using a phase difference when the array element spacing is less than half a wavelength, and then obtain an unambiguous and low-precision phase difference matrix, and solve the unambiguous and low-precision phase difference matrix and the initial phase difference matrix to obtain ambiguity, and then use the ambiguity to perform phase compensation to obtain an unambiguous and high-precision phase difference matrix; Azimuth prediction module, used to use the unambiguous high-precision phase difference matrix, and then use the least square method to solve, estimate the unambiguous high-precision Poynting vector matrix, obtain the azimuth and elevation angles of 2D-DOD, and then simulate the operation of the fuzzy initial phase difference matrix module and the phase compensation module to obtain the azimuth and elevation angles of 2D-DOA; Among them, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

[0016] The present invention provides an arbitrary array MIMO radar angle estimation method and system based on phase compensation, comprising starting from a signal model after array matched filtering at a receiving end, calculating a signal covariance matrix, dividing the obtained covariance matrix into blocks, obtaining a permutation matrix, constructing a matrix by using the permutation matrix and a unit matrix, dividing the matrix into blocks, using these block matrices to obtain an initial phase difference matrix (with ambiguity) of an array element, using a phase difference matrix with a spacing of adjacent sensor array elements less than half a wavelength, roughly estimating an unambiguous and low-precision phase difference matrix, then solving the ambiguity, compensating it to the ambiguous initial phase difference matrix, obtaining an unambiguous and high-precision phase difference matrix, and finally accurately estimating a two-dimensional wave departure angle 2D-DOD azimuth and pitch angle.

[0017] The solution of the present invention has the following beneficial effects: 1. Phase compensation technology is used to avoid phase ambiguity caused by the spacing of array elements being greater than half a wavelength. Accurate prediction can still be performed when the spacing of some array elements is greater than half a wavelength, which improves the accuracy of estimation and does not require spectral peak search and eigenvalue decomposition of the covariance matrix of the received signal, reducing the computational complexity.

[0018] 2. Compared with some more traditional angle estimation algorithms, accurate angle estimation can still be performed when the spacing between some array elements is greater than half a wavelength, providing a new idea for angle estimation in sparse sensor arrays.

[0019] 3. Compared with uniform arrays, the antennas of the transmitting array elements and the receiving array elements of this algorithm can be placed on irregular surfaces, such as the fuselage or hull of an aircraft, and can be widely used in radar detection, wireless communication, target tracking and other fields. It is suitable for MIMO radar systems with arbitrary array configurations and can be adjusted according to specific needs, allowing for improved coverage and reduced radar cross-sections, thereby enhancing the stealth and efficiency of the radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will be further described below in conjunction with the accompanying drawings and embodiments: Figure 1 is a flow chart of the MIMO radar angle estimation method of the present invention; Figure 2 It is a schematic diagram of a bistatic MIMO radar system applicable to the present invention; Figure 3 This is a 2D-DOD scatter plot result diagram of the Monte Carlo test simulation used in the present invention; Figure 4 This is a 2D-DOA scatter plot result diagram of the Monte Carlo test simulation used in the present invention; Figure 5 The number of array element spacings greater than half a wavelength in the present invention D =4Compare different signal-to-noise ratios picture; Figure 6 The number of array element spacings greater than half a wavelength in the present invention D =4Comparison of different sample numbers picture; Figure 7 The present invention is a method for obtaining a plurality of array elements with a spacing greater than half a wavelength. picture. DETAILED DESCRIPTION

[0021] Example 1 like Figure 1-7 As shown, a method for angle estimation of an arbitrary array MIMO radar based on phase compensation comprises the following steps: S1: Obtain the covariance matrix based on the signal model after matching filtering at the receiving end array .

[0022] S2: The covariance matrix Divide into blocks and obtain two construction matrices and , and according to the block matrix and Find the permutation matrix ,use and an identity matrix Construct the initial matrix .

[0023] S3: The initial matrix Divided into ,Will Perform eigendecomposition and obtain the first eigenvalue matrix (including the phase information of the first two adjacent sensor elements) and the reference eigenvector ,use , find the remaining eigenvalue matrix (including the phase information of the remaining adjacent sensor array elements), the diagonal matrix Convert to a row vector and place it into the initial phase matrix Then, the phase is taken to obtain the initial phase difference matrix with ambiguity ;in It means to find the generalized inverse of a matrix.

[0024] S4: Using the phase difference of array element spacing less than half a wavelength, estimate the unambiguous low-precision Poynting vector matrix ,according to Find the unambiguous low-precision phase difference matrix ,according to and Solve the ambiguity ,use Perform phase compensation to obtain an unambiguous and high-precision phase difference matrix .

[0025] S5: Unambiguous and high-precision phase difference matrix , using the least squares method to solve and estimate the unambiguous and high-precision Poynting vector matrix , obtain the azimuth and elevation angles of 2D-DOD, and then simulate S3 and S4 to obtain the azimuth and elevation angles of 2D-DOA.

[0026] Among them, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

[0027] like Figure 1As shown, this embodiment includes starting from the signal model after the array matched filtering at the receiving end, calculating the covariance matrix of the signal, dividing the obtained covariance matrix into blocks, obtaining the permutation matrix, constructing a matrix with the permutation matrix and the unit matrix, dividing the matrix into blocks, using these block matrices, obtaining the initial phase difference matrix with ambiguity of the array element, using the phase difference matrix with the spacing between adjacent sensor array elements less than half a wavelength, roughly estimating the unambiguous low-precision phase difference matrix, and then solving the ambiguity, compensating it to the initial phase difference matrix with ambiguity, obtaining the unambiguous high-precision phase difference matrix, and finally accurately estimating the azimuth and pitch angle of the two-dimensional wave departure angle 2D-DOD. This embodiment avoids phase ambiguity through phase compensation technology, and can still make accurate predictions when the spacing between some array elements is greater than half a wavelength, thereby improving the accuracy of the estimation, and does not need to perform spectrum peak search and eigenvalue decomposition on the covariance matrix of the received signal, thereby reducing the computational complexity, and is suitable for MIMO radar systems with any array configuration, and can be adjusted according to specific needs, and can be widely used in radar detection, wireless communication, target tracking and other fields.

[0028] In this embodiment, a bistatic MIMO radar system is involved, in which the array elements at the transmitting end and the receiving end are in arbitrary positions. D The number of array element spacings is greater than half a wavelength, and the transmitting array elements have M antennas, the receiving array elements are N Antennas, transmitting elements m The location of the transmitting antenna is ( ), receiving element n The location of the receiving antenna is ( ).

[0029] like Figure 2 As shown, assuming that the MIMO radar far field has K Target, k The two-dimensional departure direction angle 2D-DOD of a target relative to the transmitting array is ( ), the two-dimensional receiving direction angle 2D-DOA relative to the receiving array is ( ). The orthogonal waveforms emitted by the transmitting antenna have the same bandwidth and center frequency, and the wavelength is .

[0030] In the preferred embodiment, the specific steps of step S1 are as follows: S101: Taking the coordinates of the first row of the transmitting array and the receiving array as reference array elements, the arrival time differences relative to the mth transmitting sensor and the nth receiving sensor are respectively: (1); (2); In the formula, For the m The location of the transmitting antenna, For the n The location of the receiving antenna, Respectively k The azimuth and elevation of the 2D-DOD of a target, Respectively k The azimuth and elevation of the 2D-DOA of a target.

[0031] S102: Under the narrowband assumption, the spatial response vector of the transmitting sensor array and the receiving sensor array spatial response vector They are: (3); (4); in, For the m The arrival time difference of the transmitting sensor relative to the reference sensor array element, For the n The arrival time difference of the receiving sensor relative to the reference array element, The wavelength of the transmitted signal.

[0032] S103: The output formula of the receiving end matched filter is: (5); or: (6); In the formula, is the transmit array response matrix, is the receiving array response matrix, , is the Doppler shift, is the amplitude, is the Gaussian white noise matrix; represents the Khatri-Rao product, represents the Kroc inner product, L is the number of snapshots; S104: Define the matrix according to step S103 : (7); In the formula, Represented by the transmit array response matrix No. m Construct a diagonal matrix with rows.

[0033] The signal model is obtained as: (8); Then the covariance matrix of the received signal is for: (9); In the formula, the superscript H is the conjugate transpose, L The number of snapshots.

[0034] In the above steps, by selecting the first row of the transmitting array and the receiving array as the reference, the arrival time difference relative to the reference array element is calculated for the mth transmitting sensor and the nth receiving sensor, and then the spatial response vectors of the transmitting and receiving sensors are derived to obtain the output of the receiving end matched filter, thereby constructing and solving the covariance matrix. The matrix contains key information about the target position, sensor array structure, and signal characteristics, providing important data support for subsequent angle estimation and other processing.

[0035] In the preferred embodiment, the specific steps of step S2 are as follows: S201: The matrix Divide into blocks and take the front K Row Construction Matrix , take the remaining MN-K Row Construction Matrix ,Right now: (10).

[0036] Similarly, the covariance matrix Divide into blocks and take the front K Column Construction Matrix , take the remaining MN - K Column Construction Matrix ,Right now: (11).

[0037] Moreover, the matrix The matrix Right multiply by a permutation matrix It is concluded that: (12).

[0038] Similarly, the matrix The matrix Left multiply the permutation matrix It is concluded that: (13).

[0039] S202: Using an identity matrix And the permutation matrix above Construct an initial matrix ,Right now: (14).

[0040] use Right multiply the initial matrix have to: (15); Right now: (16).

[0041] Then the matrix in formula (7) Substituting in, we get: (17).

[0042] In the above steps, through matrix partitioning, permutation, and the construction and operation of special matrices, complex data sets or signal models can be effectively processed and analyzed to ensure the accuracy and reliability of subsequent results.

[0043] In the preferred embodiment, the specific steps of step S3 are as follows: S301: Initial matrix Divided into M blocks, namely: (18); Right now: , ,in is the initial matrix Before N OK, is the initial matrix No. N+ Line 1 to Line 2 N OK, and ,but: (19); in, , , , diag means converting the row matrix into a diagonal matrix, It can be represented as the Poynting vector of the emission array.

[0044] make , , ,but: (20).

[0045] S302: From formula (19), we can get ,in represents the generalized inverse of a matrix, Indicates the inverse of the matrix. Perform eigendecomposition to obtain the first eigenvalue matrix and the reference eigenvector : (twenty one); (twenty two).

[0046] From formula (18), we can see that , ,and Similarly: (twenty three).

[0047] at this time , , , , replace the formula (22) Substituting into formula (23) we get: (twenty four); (25).

[0048] Similarly, Use simulation formulas (23), (24), and (25) to obtain the result.

[0049] S303: Take The diagonal elements of , , put M-1 row vectors into the initial phase matrix In the result: (26).

[0050] Will Take the phase and get the initial phase difference matrix with ambiguity :

[0051] Right now: (27); Where: ; .

[0052] Step S3 is mathematically rigorous and logical through matrix block processing, feature decomposition, matrix operation and phase difference matrix construction, and can provide accurate and reliable operation results to ensure the accuracy of data in the process.

[0053] At this time, due to the previous DThe distance between array elements is greater than half a wavelength, so the phase difference matrix of adjacent sensors is There will be phase ambiguity, which will cause errors in the estimation results. Therefore, the following phase compensation process is required to obtain accurate estimation results.

[0054] In the preferred solution, a phase compensation process is performed in step S4, and the specific steps are as follows: S401: After use ( M -1- D ) The phase difference between the array elements is less than half a wavelength, and a rough estimate is made to obtain the unambiguous low-precision Poynting vector matrix , and according to Find the unambiguous low-precision phase difference matrix Then, solve the ambiguity , the formula is: (28); S402: Initial phase difference matrix to compensate for periodic ambiguity The unambiguous and high-precision phase difference matrix is ​​obtained , the formula is: (29).

[0055] In the above steps, the unambiguous and low-precision Poynting vector matrix is ​​obtained from the phase difference matrix of some array elements with a spacing less than half a wavelength (some array elements with a spacing less than half a wavelength). , from the unambiguous low-precision Poynting vector matrix , find out the unambiguous and low-precision phase difference matrix (of the entire array element), and then use the unambiguous and low-precision phase difference matrix to find out the ambiguity and compensate it to the initial periodically ambiguous phase difference matrix.

[0056] After obtaining the initial phase difference matrix, an ambiguity problem needs to be solved. Due to the periodicity of the phase difference (that is, the phase difference is periodic in the range of [0, 2π]), there may be multiple possible phase difference values ​​corresponding to the same observation result. This problem is usually called the phase ambiguity problem.

[0057] The ambiguity is used to compensate the initial phase difference matrix to eliminate the influence of phase ambiguity, thereby obtaining a more accurate phase difference matrix and extracting the most accurate and reliable information.

[0058] In the preferred solution, the azimuth and elevation angles of the 2D-DOD are obtained in step S5, specifically: Will The least squares method is used to solve and estimate the unambiguous and high-precision Poynting vector matrix , the formula is: (30); Then, the azimuth and elevation angle estimation of 2D-DOD can be expressed as: (31); (32).

[0059] In the preferred solution, the azimuth and elevation angles of 2D-DOA are obtained in step S5, specifically: From formula (7), it can be seen that: , and there exists a transformation matrix C , corresponding to a finite number of column operations such that: (33); Right now: (34); Multiply both sides of equation (16) by the matrix C ,Right now: (35); Will Divide N piece: (36).

[0060] Similarly, using formula (22) , and then solve the equations (24)-(30) in turn to obtain the azimuth and elevation angles of 2D-DOA. The equations are: (37); (38).

[0061] So far, the joint estimation algorithm of 2D-DOD and 2D-DOA for arbitrary array MIMO radar based on phase compensation has been completed.

[0062] The practicality of the solution of the present invention is illustrated below with a specific example. In the dual-base MIMO radar system, the number of transmitting antennas is set to M =10, the number of receiving antennas N =10, the wavelength of the antenna =1, first control the array element spacing of the transmitting antenna and the receiving antenna to half a wavelength ( / 2) and then D = 4 antennas are pulled far apart, making the front D =4 The array element spacing is greater than half a wavelength. At this time, the array element spacing of the transmitting antenna and the receiving antenna are D = 4 array elements with spacing greater than half a wavelength and M -1-D =5 The spacing between array elements is less than half a wavelength. Assuming that K =3 targets appear within the range of the bistatic MIMO radar system, and the 2D-DOD and 2D-DOA of the three targets are , and , . In the sampling sample number L =300, signal-to-noise ratio SNR =10dB, the angle estimation is performed using the method proposed in the solution of the present invention. The scatter plot results of 100 Monte Carlo test simulations are as follows: Figure 3-4 As shown, it can be seen that the scheme of the present invention can effectively estimate the departure direction angle 2D-DOD of the target signal relative to the transmitting antenna array and the receiving direction angle 2D-DOA relative to the receiving antenna array. In order to evaluate the performance of the algorithm proposed in the scheme of the present invention, we use the root mean square error (RMSE), and the calculation formula is: (39); (40).

[0063] in express The estimate, , and Same reason.

[0064] like Figure 5 As shown, in this embodiment, the number of samples is L =300, number of transmitting antennas M =10, number of receiving antennas N =10, the number of array element spacing greater than half a wavelength D =4, comparing different signal-to-noise ratios SNR Next Figure. At this time, when the spacing between some array elements is greater than half a wavelength, the PM algorithm does not care about the signal-to-noise ratio. SNR No matter how to increase it, it is already ineffective. The algorithm proposed by the present invention increases as the signal-to-noise ratio SNR As increases, the accuracy of the estimation will become higher and higher.

[0065] like Figure 6 As shown, in this embodiment, the number of transmitting antennas M =10, number of receiving antennas N =10, the number of array element spacing greater than half a wavelength D =4, SNR=10dB, compare different sampling numbers L Next At this time, when the spacing between some array elements is greater than half a wavelength, the PM algorithm will L However, the algorithm proposed in this embodiment will fail as the number of samples increases. L As the value increases, the accuracy of the estimation will also increase.

[0066] like Figure 7 As shown, in this embodiment, the number of samples is L =300, number of transmitting antennas M =10, number of receiving antennas N =10, SNR=10dB, compare the number of different array element spacings greater than half a wavelength D Next Figure. It can be clearly seen that D <6 o'clock, with D As the number of increases, the angle estimation results are getting better and better. D= 7, 8, the algorithm of this embodiment fails. This is because the algorithm proposed in this embodiment needs to first use the phase difference when the array element spacing is less than half a wavelength to make a rough estimate, and then use the result of the rough estimate to resolve the ambiguity and perform phase compensation. D= 7 and 8, the number of array element spacings that can be used for rough estimation is too small, resulting in errors in the rough estimation result, which in turn leads to the failure of the application of this embodiment.

[0067] Combination Figure 5-Figure 7 It can be seen from the content that, compared with the more traditional angle estimation algorithm in the prior art, when the spacing between some array elements is greater than half a wavelength, this embodiment can still perform accurate angle estimation, providing a new idea for angle estimation of sparse sensor arrays.

[0068] In use, compared with uniform planar arrays, the antennas of the transmitting array elements and the receiving array elements of the algorithm of this embodiment can be placed on irregular surfaces, such as the fuselage or hull of an aircraft, with a wide range of applicability and high flexibility, allowing for improved coverage and reduced radar cross-section, thereby enhancing the stealth and efficiency of the radar system.

[0069] Example 2 In combination with Example 1, a phase compensation-based arbitrary array MIMO radar angle estimation system is provided, including: The module for obtaining the covariance matrix is ​​used to obtain the covariance matrix according to the signal model after the receiving array matching filter. .

[0070] Construct a matrix module to convert the covariance matrix Block, get two block matrices and , and according to and , find the permutation matrix ,use and an identity matrix Construct the initial matrix .

[0071] Obtain the blurred initial phase difference matrix module, which is used to convert the initial matrix Divided into ,Will Perform eigendecomposition and obtain the first eigenvalue matrix (including the phase information of the first two adjacent sensor elements) and the reference eigenvector ,use , find the remaining eigenvalue matrix (including the phase information of the remaining adjacent sensor array elements), the diagonal matrix Convert to a row vector and place it into the initial phase matrix Then, the phase is taken to obtain the initial phase difference matrix with ambiguity ;in It means to find the generalized inverse of a matrix.

[0072] The phase compensation module is used to estimate the unambiguous low-precision Poynting vector matrix using the phase difference when the array element spacing is less than half a wavelength. ,according to Find the unambiguous low-precision phase difference matrix ,according to and Solve the ambiguity ,use Perform phase compensation to obtain an unambiguous and high-precision phase difference matrix .

[0073] Azimuth prediction module, used to convert the unambiguous and high-precision phase difference matrix , using the least squares method to solve and estimate the unambiguous and high-precision Poynting vector matrix , obtain the azimuth and elevation angles of 2D-DOD, then simulate the operation of the blurred initial phase difference matrix module and the phase compensation module to obtain the azimuth and elevation angles of 2D-DOA.

[0074] Among them, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

[0075] The above embodiments are only preferred technical solutions of the present invention and should not be regarded as limiting the present invention. The protection scope of the present invention shall be the technical solutions recorded in the claims, including equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. An arbitrary array MIMO radar angle estimation method based on phase compensation, characterized in that: The following steps are involved: S1: Obtain the covariance matrix according to the signal model after the receiving end array matching filtering; S2: Divide the covariance matrix into blocks to obtain a block matrix, and obtain a permutation matrix based on the block matrix, and construct an initial matrix using the permutation matrix and a unit matrix; S3: Divide the initial matrix into blocks, and perform eigendecomposition on the results of the first two block matrices to obtain the first eigenvalue matrix and reference eigenvectors, use the remaining adjacent block matrices and reference eigenvectors to calculate the remaining eigenvalue matrix, convert all eigenvalue matrices into row vectors and place them in the initial phase matrix, and then take the phase to obtain the blurred initial phase difference matrix; S4: using the phase difference when the array element spacing is less than half a wavelength, an unambiguous low-precision Poynting vector matrix is ​​estimated, and then an unambiguous low-precision phase difference matrix is ​​obtained, and the unambiguous low-precision phase difference matrix and the initial phase difference matrix are solved to obtain ambiguity, and then the ambiguity is used to perform phase compensation to obtain an unambiguous high-precision phase difference matrix; S5: The unambiguous and high-precision phase difference matrix is ​​solved by the least square method to estimate the unambiguous and high-precision Poynting vector matrix to obtain the azimuth and elevation angles of 2D-DOD, and then S3 and S4 are simulated to obtain the azimuth and elevation angles of 2D-DOA; Among them, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

2. The method for angle estimation of arbitrary array MIMO radar based on phase compensation according to claim 1, characterized in that: The specific steps of step S1 are as follows: S101: Based on the fact that the array element positions of the transmitting end and the receiving end are arbitrary, and the array element spacings of the transmitting array element and the receiving array element are D in number and greater than half a wavelength, the coordinates of the first row of the transmitting array and the receiving array are used as reference array elements, and the arrival time differences relative to the mth transmitting sensor and the nth receiving sensor are respectively: （1）； （2）； In the formula, For the m The location of the transmitting antenna, For the n The location of the receiving antenna, Respectively k The azimuth and elevation of the 2D-DOD of a target, Respectively k The azimuth and elevation of the 2D-DOA of a target; S102: Under the narrowband assumption, the spatial response vector of the transmitting sensor array and the receiving sensor array spatial response vector They are: （3）； （4）； in, For the m The arrival time difference of the transmitting sensor relative to the reference sensor array element, For the n The arrival time difference of the receiving sensor relative to the reference array element, is the wavelength of the transmitted signal; S103: The output formula of the receiving end matched filter is: （5）； or: （6）； In the formula, is the transmit array response matrix, is the receiving array response matrix, , is the Doppler shift, is the amplitude, is the Gaussian white noise matrix; represents the Khatri-Rao product, represents the Kroc inner product, L is the number of snapshots; S104: Define the matrix according to step S103 : （7）； In the formula, Represented by the transmit array response matrix No. m Construct a diagonal matrix with rows, and obtain the signal model as follows: （8）； Then the covariance matrix of the received signal is for: （9）； In the formula, the superscript H is the conjugate transpose, L The number of snapshots.

3. The method for angle estimation of arbitrary array MIMO radar based on phase compensation according to claim 2, characterized in that: The specific steps of step S2 are as follows: S201: The matrix Divide into blocks and take the front K Row construction matrix , take the remaining MN-K Row Construction Matrix ,Right now: （10）； Similarly, the covariance matrix Divide into blocks and take the front K Column Construction Matrix , take the remaining MN - K Column Construction Matrix ,Right now: （11）； Moreover, the matrix The matrix Right multiply by a permutation matrix It is concluded that: （12）； Similarly, the matrix The matrix Left multiply the permutation matrix It is concluded that: （13）； S202: Using an identity matrix And the permutation matrix above Construct an initial matrix ,Right now: （14）； use Right multiply the initial matrix : （15）； Right now: （16）； Then the matrix in formula (7) Substituting in, we get: （17）。 4. The method for angle estimation of arbitrary array MIMO radar based on phase compensation according to claim 3, characterized in that: The specific steps of step S3 are as follows: S301: Initial matrix Divided into M Blocks, namely: （18）； Right now: , ,in For the matrix Before N OK, For the matrix No. N+ Line 1 to 2 N OK, and ,but: （19）； in, , , , diag means converting the row matrix into a diagonal matrix; make , , ,but: （20）； S302: From formula (19), we can get ,in represents the generalized inverse of a matrix, Indicates the inverse of the matrix. Perform eigendecomposition to obtain the first eigenvalue matrix and the reference eigenvector : （21）； （22）； From formula (18), we can see that , ,and Similarly: （23）； at this time , , , , replace the formula (22) Substituting into formula (23) we get: （24）； （25）； Similarly, Simulate equations (23), (24), (25) to obtain; S303: Take The diagonal elements of are used to construct the row vector , , put M-1 row vectors into the initial phase matrix In the result: (26)； The initial phase matrix Take the phase and get the initial phase difference matrix with ambiguity : Right now: (27); Where: ； 。 5. The method for angle estimation of arbitrary array MIMO radar based on phase compensation according to claim 4, characterized in that: In step S4, a phase compensation process is performed, and the specific steps are as follows: S401: After use ( M -1- D ) The phase difference between the array elements is less than half a wavelength, and a rough estimate is made to obtain the unambiguous low-precision Poynting vector matrix , and according to Obtain unambiguous low-precision phase difference matrix Then, solve the ambiguity , the formula is: （28）； S402: Initial phase difference matrix to compensate for periodic ambiguity The unambiguous and high-precision phase difference matrix is ​​obtained , the formula is: （29）。 6. The method for angle estimation of arbitrary array MIMO radar based on phase compensation according to claim 5, characterized in that: In step S5, the azimuth and elevation angles of 2D-DOD are obtained, specifically: Will The least squares method is used to solve and estimate the unambiguous and high-precision Poynting vector matrix , the formula is: （30）； Then, the azimuth and elevation angle estimation of 2D-DOD can be expressed as: （31）； （32）。 7. The method for angle estimation of arbitrary array MIMO radar based on phase compensation according to claim 6, characterized in that: In step S5, S3 and S4 are simulated to obtain the azimuth and elevation angles of 2D-DOA, specifically: Using transformation matrix C , for the matrix Perform a finite number of column operations such that: （33）； Right now: （34）； Multiply both sides of equation (16) by the matrix C ,Right now: （35）； Will Divide N piece: （36）； Similarly, using formula (22) , and then solve the equations (24)-(30) in turn to obtain the azimuth and elevation angles of 2D-DOA. The equations are: （37）； （38）。 8. An arbitrary array MIMO radar angle estimation system based on phase compensation, characterized in that: include: A covariance matrix acquisition module is used to acquire a covariance matrix according to a signal model after array matching filtering at the receiving end; A matrix construction module is used to divide the covariance matrix into blocks to obtain a block matrix, obtain a permutation matrix based on the block matrix, and construct an initial matrix using the permutation matrix and a unit matrix; Obtaining a blurred initial phase difference matrix module, which is used to divide the initial matrix into blocks, and perform eigendecomposition on the results of the first two block matrices, obtain the first eigenvalue matrix and the reference eigenvector, use the remaining adjacent block matrices and the reference eigenvector to calculate the remaining eigenvalue matrix, convert all eigenvalue matrices into row vectors and place them in the initial phase matrix, and then take the phase to obtain the blurred initial phase difference matrix; A phase compensation module is used to estimate an unambiguous and low-precision Poynting vector matrix by using a phase difference when the array element spacing is less than half a wavelength, and then obtain an unambiguous and low-precision phase difference matrix, and solve the unambiguous and low-precision phase difference matrix and the initial phase difference matrix to obtain ambiguity, and then use the ambiguity to perform phase compensation to obtain an unambiguous and high-precision phase difference matrix; Azimuth prediction module, used to use the unambiguous high-precision phase difference matrix, and then use the least square method to solve, estimate the unambiguous high-precision Poynting vector matrix, obtain the azimuth and elevation angles of 2D-DOD, and then simulate the operation of the fuzzy initial phase difference matrix module and the phase compensation module to obtain the azimuth and elevation angles of 2D-DOA; Among them, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

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