Angle estimation method and system for arbitrary array MIMO radar based on phase compensation

Abstract

The present invention provides a phase-compensated arbitrary array MIMO radar angle estimation method and system, relating to the field of radar positioning technology. The method includes calculating the signal covariance matrix based on a signal model after array matched filtering at a receiving end, dividing the obtained covariance matrix into blocks, obtaining a permutation matrix, constructing a matrix using the permutation matrix and the identity matrix, performing block operations on the matrix, obtaining an initial phase difference matrix of the array elements, using a phase difference matrix with a spacing of less than half a wavelength between adjacent sensor elements, roughly estimating an unambiguous, low-precision phase difference matrix, resolving ambiguity, compensating the matrix with ambiguity into the initial phase difference matrix, obtaining an unambiguous, high-precision phase difference matrix, and ultimately accurately estimating the azimuth and elevation angles of the two-dimensional wave departure angle (2D-DOD) and the two-dimensional wave arrival angle (2D-DOA). Phase ambiguity is avoided, the estimation accuracy is improved, and the computational complexity is reduced.

Description

Technical Field

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

[0002] MIMO (Multiple Input Multiple Output) radar, or MIMO, radar systems with multiple transmit and receive antennas, represents a significant advancement in radar technology and has garnered significant interest from numerous scholars and research institutions both domestically and internationally. MIMO radar technology draws on the MIMO principles of wireless communications. Unlike traditional phased array radar, MIMO radar uses multiple active antennas to transmit mutually orthogonal waveforms, enabling the radar system to achieve both spatial and temporal diversity. This creates a virtual aperture, improving angular resolution and enabling the radar system to more accurately determine the target's location. By utilizing multiple independent signal paths, MIMO radar also significantly enhances its anti-interference capabilities. With its rapid development, MIMO radar has demonstrated unique advantages in areas such as air surveillance, ground surveillance, maritime surveillance, and missile guidance.

[0003] Estimating the direction of departure (DOD) and direction of arrival (DOA) in MIMO radars is a key issue for accurately determining target position and motion. Numerous excellent angle estimation methods have emerged, including maximum likelihood methods, multiple signal classification (MSC), methods using rotational invariance to estimate signal parameters, and propagation operator methods. The MSC algorithm requires a spectral peak search during the estimation process, which is computationally expensive but offers high estimation accuracy. The rotational invariance-based signal parameter estimation algorithm exploits the invariance of MIMO radar angle estimation and does not require a spectral peak search, but requires constructing the covariance matrix of the received signal and performing its eigendecomposition. The propagation operator algorithm, on the other hand, does not require eigendecomposition of the covariance matrix of the received signal. Therefore, the propagation operator algorithm has lower computational complexity than the rotational invariance-based signal parameter estimation algorithm. However, the propagation operator algorithm suffers from poor estimation accuracy and may even fail under low signal-to-noise ratio conditions. In particular, in traditional scalar array signal models, when the array element spacing is greater than half a wavelength, the angle estimation may be ambiguous.

[0004] Existing research primarily applies to transmitting and receiving arrays that are uniform linear arrays (ULAs). However, the layout of ULAs is often fixed, making it difficult to achieve such a fixed layout in certain application scenarios. Therefore, research on arbitrary arrays is crucial. Currently, research on angle estimation for arbitrary arrays includes methods such as Capon (minimum variance distortionless response (MVDR) algorithm), multiple signal classification (MSC) algorithms, and interpolation methods. While Capon and MSC algorithms can estimate the angle of arbitrary arrays, they both require a four-dimensional spectral peak search, resulting in high computational complexity. While interpolation methods do not require a spectral peak search, they require prior knowledge of the spatial sector of the event target, which is typically unavailable to radar systems. While the recently popular polarization array can also perform two-dimensional angle estimation, the vector components can suffer from severe mutual coupling, resulting in inaccurate predicted estimates. 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] 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:

[0007] S1: Obtain the covariance matrix based on the signal model after array matching filtering at the receiving end;

[0008] S2: Divide the covariance matrix into blocks to obtain a block matrix, and obtain a permutation matrix based on the block matrix. Use the permutation matrix and an identity matrix to construct the initial matrix.

[0009] 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 eigenvector. 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 into the initial phase matrix. Then, perform phase extraction to obtain the initial phase difference matrix with ambiguity.

[0010] 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. This unambiguous, low-precision phase difference matrix and the initial phase difference matrix are solved to obtain ambiguity, and this ambiguity is then used to perform phase compensation to obtain an unambiguous, high-precision phase difference matrix.

[0011] S5: The unambiguous and high-precision phase difference matrix is ​​solved using the least squares method to estimate the unambiguous and high-precision Poynting vector matrix to obtain the azimuth and elevation angles of the 2D-DOD. S3 and S4 are then simulated to obtain the azimuth and elevation angles of the 2D-DOA.

[0012] Wherein, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

[0013] In the preferred embodiment, the specific steps of step S1 are as follows:

[0014] S101: Assuming that the array element positions at the transmitting end and the receiving end are arbitrary, and that both the transmitting array elements and the receiving array elements have D array element spacings greater than half a wavelength, and the coordinates of the first row of the transmitting array and the receiving array are used as reference array elements, the arrival time differences relative to the mth transmitting sensor and the nth receiving sensor are:

[0015] (1);

[0016] (2);

[0017] Where, 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 the target, Respectively k The azimuth and elevation of the 2D-DOA of a target;

[0018] S102: Under the narrowband assumption, the spatial response vector of the transmitting sensor array and the receiving sensor array spatial response vector They are:

[0019] (3);

[0020] (4);

[0021] 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 each receiving sensor relative to the reference array element, The wavelength of the transmitted signal.

[0022] S103: The output formula of the matched filter at the receiving end is:

[0023] (5);

[0024] Or:

[0025] (6);

[0026] Where, 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 Crocker inner product, L is the number of snapshots;

[0027] S104: Define the matrix according to step S103 :

[0028] (7);

[0029] Where, Represented by the transmit array response matrix No. m Construct a diagonal matrix with the rows, and obtain the signal model as follows:

[0030] (8);

[0031] Then the covariance matrix of the received signal is for:

[0032] (9);

[0033] In the formula, the superscript H is the conjugate transpose, L Snap count.

[0034] In the preferred embodiment, the specific steps of step S2 are as follows:

[0035] S201: The matrix Divide into blocks and take the front K Row construction matrix , take the remaining MN-K Row construction matrix ,Right now:

[0036] (10);

[0037] 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:

[0038] (11);

[0039] Moreover, the matrix Can be represented by the matrix Right multiply by a permutation matrix It is concluded that:

[0040] (12);

[0041] Similarly, the matrix The matrix can also be Left multiply the permutation matrix It is concluded that:

[0042] (13);

[0043] S202: Using an identity matrix And the permutation matrix above Construct an initial matrix ,Right now:

[0044] (14);

[0045] use Right multiply the initial matrix :

[0046] (15);

[0047] Right now:

[0048] (16);

[0049] Then the matrix in formula (7) Substituting in:

[0050] (17).

[0051] In the preferred embodiment, the specific steps of step S3 are as follows:

[0052] S301: The matrix Divided into M Block, that is:

[0053] (18);

[0054] Right now: , ,in is a matrix Before N OK, is a matrix No. N+ Row 1 to row 2 N OK, and ,but:

[0055] (19);

[0056] in, , , , diag means converting the row matrix into a diagonal matrix;

[0057] make , , ,but:

[0058] (20);

[0059] S302: From formula (19), we can get ,in It means to find the generalized inverse of the matrix, Indicates the inverse of the matrix. Perform eigendecomposition to obtain the first eigenvalue matrix and the reference eigenvector :

[0060] (twenty one);

[0061] (twenty two);

[0062] From formula (18), we can see that , ,and Similarly:

[0063] (twenty three);

[0064] at this time , , , , replace the formula (22) Substituting into formula (23) we get:

[0065] (twenty four);

[0066] (25);

[0067] Similarly, The simulation formula (23) (24) (25) is obtained;

[0068] S303: Take The diagonal elements of the row vector are constructed , , put M-1 row vectors into the initial phase matrix We get:

[0069] (26);

[0070] The initial phase matrix Take the phase and get the initial phase difference matrix with ambiguity :

[0071]

[0072] Right now: (27);

[0073] Where:

[0074] ;

[0075] .

[0076] In the preferred solution, a phase compensation process is performed in step S4, and the specific steps are as follows:

[0077] 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:

[0078] (28);

[0079] S402: Initial phase difference matrix to compensate for periodic ambiguity In the above example, we obtain the unambiguous and high-precision phase difference matrix , the formula is:

[0080] (29).

[0081] In the preferred solution, the azimuth and elevation angles of the 2D-DOD are obtained in step S5, specifically:

[0082] Will The least squares method is used to solve and estimate the unambiguous and high-precision Poynting vector matrix , the formula is:

[0083] (30);

[0084] Then, the azimuth and elevation angle estimation of 2D-DOD can be expressed as:

[0085] (31);

[0086] (32).

[0087] In the preferred solution, step S5 simulates S3 and S4 to obtain the azimuth and elevation angles of the 2D-DOA, specifically:

[0088] Using transformation matrix C , for the matrix Perform a finite number of column operations such that:

[0089] (33);

[0090] Right now:

[0091] (34);

[0092] Multiply both sides of Equation (16) by the matrix C ,Right now:

[0093] (35);

[0094] Will Divide N piece:

[0095] (36);

[0096] Similarly, using formula (22) , and solve the equations (24)-(30) in turn to obtain the azimuth and elevation angles of 2D-DOA, which are:

[0097] (37); (38).

[0098] In a preferred embodiment, an arbitrary array MIMO radar angle estimation system based on phase compensation includes:

[0099] A covariance matrix acquisition module is used to obtain the covariance matrix according to the signal model after the receiving end array matching filter;

[0100] The matrix construction module is used to divide the covariance matrix into blocks to obtain the block matrix, and obtain the permutation matrix based on the block matrix, and construct the initial matrix using the permutation matrix and an identity matrix;

[0101] Obtaining the 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 to obtain the first eigenvalue matrix and reference eigenvectors. The remaining adjacent block matrices and reference eigenvectors are used to calculate the remaining eigenvalue matrix, convert all eigenvalue matrices into row vectors and place them into the initial phase matrix, and then perform phase extraction to obtain the blurred initial phase difference matrix.

[0102] A phase compensation module is used to estimate an unambiguous and low-precision Poynting vector matrix using a phase difference when the array element spacing is less than half a wavelength, and then calculate an unambiguous and low-precision phase difference matrix. The unambiguous and low-precision phase difference matrix is ​​solved with the initial phase difference matrix to obtain ambiguity, and the ambiguity is then used to perform phase compensation to obtain an unambiguous and high-precision phase difference matrix.

[0103] The azimuth prediction module is used to use the unambiguous and high-precision phase difference matrix and then use the least squares method to solve it to estimate the unambiguous and high-precision Poynting vector matrix to obtain the azimuth and elevation angles of the 2D-DOD. It then simulates the operation of the fuzzy initial phase difference matrix module and the phase compensation module to obtain the azimuth and elevation angles of the 2D-DOA.

[0104] Wherein, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

[0105] 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 using the permutation matrix and the unit matrix, dividing the matrix into blocks, and 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 elements less than half a wavelength, roughly estimating an unambiguous, low-precision phase difference matrix; then solving the ambiguity and compensating it into the ambiguous initial phase difference matrix to obtain an unambiguous, high-precision phase difference matrix, and finally accurately estimating a two-dimensional wave departure angle (2D-DOD) azimuth and elevation angle.

[0106] The solution of the present invention has the following beneficial effects:

[0107] 1. Phase compensation technology avoids phase ambiguity caused by array element spacing greater than half a wavelength. Accurate predictions can be made even when some array element spacing is greater than half a wavelength, improving estimation accuracy. This eliminates the need for peak search and eigenvalue decomposition of the received signal's covariance matrix, reducing computational complexity.

[0108] 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.

[0109] 3. Compared to uniform arrays, the algorithm's transmitting and receiving antennas can be placed on irregular surfaces, such as aircraft fuselages or ship hulls. This makes it widely applicable to radar detection, wireless communications, and target tracking. It is suitable for MIMO radar systems with arbitrary array configurations and can be adjusted to specific needs, improving coverage and reducing radar cross-sections, thereby enhancing the stealth and efficiency of radar systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] The present invention will be further described below with reference to the accompanying drawings and examples:

[0111] Figure 1 This is a flow chart of the MIMO radar angle estimation method of the present invention;

[0112] Figure 2 Schematic diagram of a bistatic MIMO radar system applicable to the present invention;

[0113] Figure 3 This is a 2D-DOD scatter plot result diagram using Monte Carlo test simulation in the present invention;

[0114] Figure 4 This is a 2D-DOA scatter plot result diagram using Monte Carlo test simulation in the present invention;

[0115] Figure 5 The number of array element spacings greater than half a wavelength in the present invention D =4Comparison of different signal-to-noise ratios picture;

[0116] Figure 6 The number of array element spacings greater than half a wavelength in the present invention D =4Comparison of different sample numbers picture;

[0117] Figure 7 The present invention is the number of different array element spacing greater than half the wavelength picture. DETAILED DESCRIPTION

[0118] Example 1

[0119] like Figure 1-7 As shown, a method for angle estimation of an arbitrary array MIMO radar based on phase compensation includes the following steps:

[0120] S1: Obtain the covariance matrix based on the signal model after matching filtering at the receiving end array .

[0121] S2: Covariance matrix Divide the blocks and obtain two construction matrices and , and according to the block matrix and Obtain the permutation matrix ,use and an identity matrix Construct the initial matrix .

[0122] S3: The initial matrix Divided into ,Will Perform eigendecomposition to 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.

[0123] S4: Using the phase difference of the array element spacing less than half a wavelength, estimate the unambiguous low-precision Poynting vector matrix ,according to Obtain 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 .

[0124] S5: Unambiguous and high-precision phase difference matrix , using the least squares method to solve, 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.

[0125] Wherein, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

[0126] like Figure 1 As shown, this embodiment includes starting from the signal model after array matched filtering at the receiving end, calculating the signal covariance matrix, dividing the obtained covariance matrix into blocks, obtaining a permutation matrix, constructing a matrix using the permutation matrix and the identity matrix, dividing the matrix into blocks, and using these block matrices to obtain the initial ambiguous phase difference matrix of the array element. Using the phase difference matrix when the spacing between adjacent sensor array elements is less than half a wavelength, a rough estimate of the unambiguous low-precision phase difference matrix is ​​obtained. The ambiguity is then resolved and compensated to the ambiguous initial phase difference matrix to obtain an unambiguous high-precision phase difference matrix, and finally accurately estimates the 2D-DOD azimuth and pitch angle. This embodiment avoids phase ambiguity through phase compensation technology, and can still perform accurate prediction when the spacing between some array elements is greater than half a wavelength, thereby improving the accuracy of the estimation. It does not require spectral peak search and eigenvalue decomposition of the covariance matrix of the received signal, reducing the computational complexity. It is applicable to MIMO radar systems with any array configuration and can be adjusted according to specific needs. It can be widely used in radar detection, wireless communication, target tracking and other fields.

[0127] In this embodiment, a bistatic MIMO radar system is involved, in which the array elements at both the transmitting and receiving ends are positioned arbitrarily. D The number of array element spacing is greater than half a wavelength, and the transmitting array element has M antennas, the receiving array elements are N Antenna, transmitting element m The location of the transmitting antenna is ( ), receiving element n The location of the receiving antenna is ( ).

[0128] 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 .

[0129] In the preferred embodiment, the specific steps of step S1 are as follows:

[0130] S101: Taking the coordinates of the first row of the transmitting array and the receiving array as reference elements, the arrival time differences relative to the mth transmitting sensor and the nth receiving sensor are:

[0131] (1);

[0132] (2);

[0133] Where, 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 the target, Respectively k The azimuth and elevation angles of the 2D-DOA of a target.

[0134] S102: Under the narrowband assumption, the spatial response vector of the transmitting sensor array and the receiving sensor array spatial response vector They are:

[0135] (3);

[0136] (4);

[0137] 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 each receiving sensor relative to the reference array element, The wavelength of the transmitted signal.

[0138] S103: The output formula of the matched filter at the receiving end is:

[0139] (5);

[0140] Or:

[0141] (6);

[0142] Where, 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 Crocker inner product, L is the number of snapshots;

[0143] S104: Define the matrix according to step S103 :

[0144] (7);

[0145] Where, Represented by the transmit array response matrix No. m Construct a diagonal matrix with rows.

[0146] The signal model is obtained as:

[0147] (8);

[0148] Then the covariance matrix of the received signal is for:

[0149] (9);

[0150] In the formula, the superscript H is the conjugate transpose, L Snap count.

[0151] 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, respectively. The spatial response vectors of the transmitting and receiving sensors are then derived, and the output of the receiving end matched filter is obtained, 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 processing such as angle estimation.

[0152] In the preferred embodiment, the specific steps of step S2 are as follows:

[0153] S201: The matrix Divide into blocks and take the front K Row construction matrix , take the remaining MN-K Row construction matrix ,Right now:

[0154] (10).

[0155] 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:

[0156] (11).

[0157] Moreover, the matrix Can be represented by the matrix Right multiply by a permutation matrix It is concluded that:

[0158] (12).

[0159] Similarly, the matrix The matrix can also be Left multiply the permutation matrix It is concluded that:

[0160] (13).

[0161] S202: Using an identity matrix And the permutation matrix above Construct an initial matrix ,Right now:

[0162] (14).

[0163] use Right multiply the initial matrix have to:

[0164] (15);

[0165] Right now:

[0166] (16).

[0167] Then the matrix in formula (7) Substituting in:

[0168] (17).

[0169] 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.

[0170] In the preferred embodiment, the specific steps of step S3 are as follows:

[0171] S301: Initial matrix Divided into M blocks, namely:

[0172] (18);

[0173] Right now: , ,in is the initial matrix Before N OK, is the initial matrix No. N+ Row 1 to row 2 N OK, and ,but:

[0174] (19);

[0175] in, , , , diag means converting the row matrix into a diagonal matrix, It can be represented as the Poynting vector of the emission array.

[0176] make , , ,but:

[0177] (20).

[0178] S302: From formula (19), we can get ,in It means to find the generalized inverse of the matrix, Indicates the inverse of the matrix. Perform eigendecomposition to obtain the first eigenvalue matrix and the reference eigenvector :

[0179] (twenty one);

[0180] (twenty two).

[0181] From formula (18), we can see that , ,and Similarly:

[0182] (twenty three).

[0183] at this time , , , , replace the formula (22) Substituting into formula (23) we get:

[0184] (twenty four);

[0185] (25).

[0186] Similarly, Use simulation formulas (23), (24), and (25) to calculate.

[0187] S303: Take The diagonal elements of the row vector are constructed , , put M-1 row vectors into the initial phase matrix We get:

[0188] (26).

[0189] Will Take the phase and get the initial phase difference matrix with ambiguity :

[0190]

[0191] Right now: (27);

[0192] Where:

[0193] ;

[0194] .

[0195] Step S3 is mathematically rigorous and logical through matrix block processing, eigendecomposition, matrix operations, and phase difference matrix construction, and can provide accurate and reliable calculation results to ensure the accuracy of data in the process.

[0196] At this time, due to the previous D The distance between the array elements is greater than half a wavelength, so the phase difference matrix of adjacent sensors is There will be phase ambiguity, which will lead to errors in the estimation results. Therefore, the following phase compensation process is required to obtain accurate estimation results.

[0197] In the preferred solution, a phase compensation process is performed in step S4, and the specific steps are as follows:

[0198] 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:

[0199] (28);

[0200] S402: Initial phase difference matrix to compensate for periodic ambiguity In the above example, we obtain the unambiguous and high-precision phase difference matrix , the formula is:

[0201] (29).

[0202] In the above steps, the unambiguous 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). , by the unambiguous low-precision Poynting vector matrix , calculate the unambiguous low-precision phase difference matrix (of the entire array element), and then use the unambiguous low-precision phase difference matrix to calculate the ambiguity and compensate it to the initial periodically ambiguous phase difference matrix.

[0203] 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.

[0204] 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.

[0205] In the preferred solution, the azimuth and elevation angles of the 2D-DOD are obtained in step S5, specifically:

[0206] Will The least squares method is used to solve and estimate the unambiguous and high-precision Poynting vector matrix , the formula is:

[0207] (30);

[0208] Then, the azimuth and elevation angle estimation of 2D-DOD can be expressed as:

[0209] (31);

[0210] (32).

[0211] In the preferred solution, the azimuth and elevation angles of the 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:

[0212] (33);

[0213] Right now:

[0214] (34);

[0215] Multiply both sides of Equation (16) by the matrix C ,Right now:

[0216] (35);

[0217] Will Divide N piece:

[0218] (36).

[0219] Similarly, using formula (22) , and solve the equations (24)-(30) in turn to obtain the azimuth and elevation angles of 2D-DOA, which are:

[0220] (37);

[0221] (38).

[0222] At this point, the joint estimation algorithm of 2D-DOD and 2D-DOA for arbitrary array MIMO radar based on phase compensation has been completed.

[0223] The practicality of the solution of the present invention is illustrated below with a specific example. In the bistatic 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 element spacing between the transmitting antenna and the receiving antenna to half a wavelength ( / 2) near, then put the front D = 4 antennas are pulled further apart, making the front D =4 The spacing between array elements is greater than half a wavelength. At this time, the spacing between the transmitting antenna and the receiving antenna is 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 present invention. The scatter plot results of 100 Monte Carlo 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 reception direction angle 2D-DOA relative to the receiving antenna array. To evaluate the performance of the algorithm proposed in the scheme of the present invention, we use the root mean square error (RMSE), which is calculated as follows:

[0224] (39);

[0225] (40).

[0226] in express Estimates, 、 and Same thing.

[0227] like Figure 5 As shown, in this embodiment, the number of sampling samples 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 you increase it, it is already ineffective. However, the algorithm proposed by this invention increases with the signal-to-noise ratio. SNR As increases, the estimation accuracy will become higher and higher.

[0228] 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 not work regardless of the number of samples. L However, the algorithm proposed in this embodiment will fail as the number of samples increases. L As increases, the accuracy of the estimation will also increase.

[0229] like Figure 7 As shown, in this embodiment, the number of samples 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, and 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 of the array element spacing 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 failure of the application of this embodiment.

[0230] Combine Figure 5-Figure 7 As can be seen from the content, compared with the more traditional angle estimation algorithm in the prior art, this embodiment can still perform accurate angle estimation when the spacing between some array elements is greater than half a wavelength, providing a new idea for angle estimation in sparse sensor arrays.

[0231] In use, compared with a uniform array, 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 of an aircraft or the hull of a ship. It has a wide range of applications and high flexibility, allowing for improved coverage and reduced radar cross-section, thereby enhancing the stealth and efficiency of the radar system.

[0232] Example 2

[0233] In combination with Example 1, a phase-compensated arbitrary array MIMO radar angle estimation system is provided, comprising:

[0234] Get covariance matrix module, used to obtain the covariance matrix according to the signal model after receiving array matching filtering .

[0235] Construct a matrix module to convert the covariance matrix Block, get two block matrices and , and according to and , and obtain the permutation matrix ,use and an identity matrix Construct the initial matrix .

[0236] Obtain the fuzzy initial phase difference matrix module, which is used to convert the initial matrix Divided into ,Will Perform eigendecomposition to 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.

[0237] 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 Obtain 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 .

[0238] Azimuth prediction module, used to convert the unambiguous high-precision phase difference matrix , using the least squares method to solve, estimate the unambiguous and high-precision Poynting vector matrix , obtain the azimuth and elevation angles of 2D-DOD, 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.

[0239] Wherein, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

[0240] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection 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 based on the signal model after array matching filtering at the receiving end; S2: Divide the covariance matrix into blocks to obtain a block matrix, and obtain a permutation matrix based on the block matrix. Use the permutation matrix and an identity matrix to construct the initial 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 eigenvector. 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 into the initial phase matrix. Then, perform phase extraction to obtain the initial phase difference matrix with ambiguity. 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. This unambiguous, low-precision phase difference matrix and the initial phase difference matrix are solved to obtain ambiguity, and this ambiguity is then 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 using the least squares method to estimate the unambiguous and high-precision Poynting vector matrix to obtain the azimuth and elevation angles of the 2D-DOD. S3 and S4 are then simulated to obtain the azimuth and elevation angles of the 2D-DOA. Wherein, 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: Assuming that the array element positions at the transmitting end and the receiving end are arbitrary, and that both the transmitting array elements and the receiving array elements have D array element spacings greater than half a wavelength, and the coordinates of the first row of the transmitting array and the receiving array are used as reference array elements, the arrival time differences relative to the mth transmitting sensor and the nth receiving sensor are: （1）； （2）； Where, 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 the 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 each receiving sensor relative to the reference array element, is the wavelength of the transmitted signal; S103: The output formula of the matched filter at the receiving end is: （5）； Or: （6）； Where, 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 Crocker inner product, L is the number of snapshots; S104: Define the matrix according to step S103 : （7）； Where, Represented by the transmit array response matrix No. m Construct a diagonal matrix with the 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 Snap count.

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 Can be represented by the matrix Right multiply by a permutation matrix It is concluded that: （12）； Similarly, the matrix The matrix can also be Multiply the permutation matrix on the left 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: （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 Block, that is: （18）； Right now: , ,in is a matrix Before N OK, is a matrix No. N+ Row 1 to row 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 It means to find the generalized inverse of the 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, The simulation formula (23) (24) (25) is obtained; S303: Take The diagonal elements of the row vector are constructed , , put M-1 row vectors into the initial phase matrix We get: (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 In the above example, we obtain the unambiguous and high-precision phase difference matrix , 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 the 2D-DOD are obtained as follows: 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 the 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 solve the equations (24)-(30) in turn to obtain the azimuth and elevation angles of 2D-DOA, which 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 obtain the covariance matrix according to the signal model after the receiving end array matching filter; The matrix construction module is used to divide the covariance matrix into blocks to obtain the block matrix, and then obtain the permutation matrix based on the block matrix, and construct the initial matrix using the permutation matrix and an identity matrix; Obtaining the 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 to obtain the first eigenvalue matrix and reference eigenvectors. The remaining adjacent block matrices and reference eigenvectors are used to calculate the remaining eigenvalue matrix, convert all eigenvalue matrices into row vectors and place them into the initial phase matrix, and then perform phase extraction to obtain the blurred initial phase difference matrix. A phase compensation module is used to estimate an unambiguous and low-precision Poynting vector matrix using a phase difference when the array element spacing is less than half a wavelength, and then calculate an unambiguous and low-precision phase difference matrix. The unambiguous and low-precision phase difference matrix is ​​solved with the initial phase difference matrix to obtain ambiguity, and the ambiguity is then used to perform phase compensation to obtain an unambiguous and high-precision phase difference matrix. The azimuth prediction module is used to use the unambiguous and high-precision phase difference matrix and then use the least squares method to solve it to estimate the unambiguous and high-precision Poynting vector matrix to obtain the azimuth and elevation angles of the 2D-DOD. It then simulates the operation of the fuzzy initial phase difference matrix module and the phase compensation module to obtain the azimuth and elevation angles of the 2D-DOA. Wherein, 2D-DOD represents the two-dimensional departure angle, and 2D-DOA represents the two-dimensional arrival angle.

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