FDA-MIMO Radar Super-Resolution Target Localization Method Based on Multidimensional Parameter Spectrum Reconstruction

Abstract

The present invention belongs to the technical field of radar target positioning. Specifically, it is a new method for super-resolution parameter estimation of the angle-distance two-dimensional spectrum reconstruction technology of an FDA-MIMO radar. It is characterized in that, first, the MIMO radar transceiver array is used to receive the signals of far-field space targets, and then the received signals are processed to obtain the signal and noise subspaces. The angle-distance two-dimensional spectrum reconstruction processing is carried out on the transceiver signals, and the noise projection is divided into sub-arrays. After constructing the root-finding polynomial of the angle spectrum by using the matrix subspace root-finding technology, the root-finding operation is directly carried out on the angle spectrum polynomial to obtain the angle estimation value of the target signal. The angle estimation value is substituted into the reconstruction cost function, and according to the root-finding super-resolution algorithm, the distance estimation value of the target signal is obtained. Through the automatic pairing of the angle and the distance, the accurate positioning of the target is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar target positioning. Specifically, it is a new method for super-resolution parameter estimation of two-dimensional spectrum reconstruction of angle-distance of FDA-MIMO radar. Background Art

[0002] One of the main functions of modern radar systems is to accurately locate spatial targets, that is, to extract the angle and distance information of targets from radar echoes using advanced signal processing methods. Traditional phased array radars have been widely used in target positioning work. However, phased arrays only provide angle-dependent waveforms, and each angle of its beam steering vector corresponds to all distances; in other words, for all distances, it is determined in one angle direction. In the process of target positioning research, MIMO (Multiple-Input Multiple-Output, MIMO) radar has become a typical representative of new-generation radars in recent years due to its high degree of freedom. However, MIMO radar is a special phased array radar, so the distance information of the target cannot be directly obtained from the peak response of the waveform output.

[0003] FDA (Frequency Diverse Array, FDA) radar has been proposed as a new type of flexible array radar in the past decade. The frequency diverse array is fundamentally still an equally spaced linear array, but the difference from the traditional array is that a frequency increment much smaller than the transmit carrier frequency is introduced between the transmit antenna elements, and the frequency increment increases with the element index, thus generating a distance-angle-dependent waveform, increasing the new degree of freedom in the distance dimension, and laying a theoretical foundation for the joint estimation and positioning application of target angle-distance parameters.

[0004] Unfortunately, due to the existence of range and azimuth coupling problems, the range and angle of a target cannot be directly estimated in an FDA radar. The proposed dual-pulse FDA radar scheme can effectively solve this problem. However, the dual-pulse method faces the problems of multiple pulse transmissions and relatively low estimation accuracy. As a classic parameter estimation scheme in the field of array signal processing, the super-resolution estimation technology can resolve different signals in space with high precision and improve the ability to resolve signals from different directions in space within a half-power beamwidth. To achieve super-resolution target localization for an FDA radar, the subarray segmentation method divides the transmitting array of the FDA radar into several subarrays, and each subarray transmits different signals. Then, the subspace-based MUSIC method is applied to jointly estimate the range and azimuth of the target. Similarly, the subarray method can also divide the transmitting array into two stacked subarrays with different frequency offsets, obtaining a transmit-receive direction pattern that decouples range-angle coupling and realizing the radar's target localization function. However, in the case of multiple targets, the subarray division method will produce false targets, which will pose great difficulties for target recognition and localization. In the super-resolution target localization method, although the two-dimensional MUSIC algorithm in the traditional array signal processing field can be used to accurately estimate the angle and range of an FDA-MIMO radar, it still cannot get rid of the huge computational complexity of two-dimensional search.

[0005] FDA radars and MIMO radars have become the focus of research for scholars at home and abroad. However, in terms of target localization, existing methods such as the dual-pulse method, the transmitting subarray method, and the frequency offset change method still have problems of multi-target matching and artifacts. In addition, after the combination of FDA radars and super-resolution theory, the huge computational complexity still becomes an obstacle to the engineering promotion of radar target localization. Therefore, considering the particularity of the FDA structure and the superiority of the large degrees of freedom of MIMO, it is particularly important to explore a range-angle joint super-resolution estimation technology with high precision, high velocity measurement, and ultra-real-time measurement requirements. Summary of the Invention

[0006] Aiming at the serious coupling problem of target angle and range information in an FDA-MIMO radar, the present invention proposes a new super-resolution target localization method for an FDA-MIMO radar based on multi-dimensional parameter spectrum reconstruction.

[0007] The present invention is achieved through the following measures:

[0008] A super-resolution target localization method for FDA-MIMO radar based on multi-dimensional parameter spectrum reconstruction, characterized in that first, the MIMO radar transceiver array is used to receive the far-field space target signal, then the received signal is processed to obtain the signal and noise subspaces, two-dimensional spectrum reconstruction processing of the transceiver signal in terms of angle and distance is performed, and subarray division of the noise projection is carried out; by using the matrix subspace root-finding technique, after constructing the root-finding polynomial of the angle spectrum, direct root-finding operation is performed on the angle spectrum polynomial to obtain the angle estimation value of the target signal, substituting the angle estimation value into the reconstruction cost function, according to the root-finding super-resolution algorithm, the distance estimation value of the target signal is obtained, and through automatic pairing of the angle and distance, accurate target localization is achieved.

[0009] In the present invention, when using the MIMO radar transceiver array to receive the far-field space target signal, assume a MIMO radar with M transmitting antenna elements and N receiving antenna elements, and both the transmitting and receiving arrays are half-wavelength equally spaced linear arrays. Considering that there are P far-field target signals in space, assuming P is known a priori, the maximum unambiguous detection distance r of the radar max = c / 2Δf, where c is the electromagnetic wave propagation speed and Δf is the frequency offset, then the target echo signal under the l-th pulse after matched filtering is expressed as:

[0010] x(l) = A(θ,r)s(l) + n(l),

[0011] where, A(θ,r) = [a(θ 1 ,r 1 ), …, a(θ P ,r P )] is an MN×P-dimensional transceiver array manifold matrix, and the p-th element in the transceiver array manifold matrix is s(l) is a P×1-dimensional signal vector after matched filtering, n(l) is an MN×1-dimensional additive Gaussian white noise vector, and the transmitting array manifold vector a p ,r p ) and the receiving array manifold vector a tp (θ p ,r p ) and a rp (θ p ) are respectively

[0012]

[0013]

[0014] After L transmitting pulses are accumulated, the echo signal is

[0015] X = A(θ,R)S + N.

[0016] Among them, S = [s(1), …, s(L)] is an MN×L-dimensional signal accumulation matrix, N = [n(1), …, n(L)] is an MN×L-dimensional noise accumulation matrix, and X = [x(1), …, x(L)] is an MN×L-dimensional echo signal accumulation matrix.

[0017] In the present invention, according to the subspace estimation theory, the noise subspace is obtained specifically as follows:

[0018] The MN×MN-dimensional array covariance matrix is:

[0019]

[0020] The complex eigenvalue decomposition of R is expressed as:

[0021]

[0022] Among them, Λ s and Λ n are diagonal matrices composed of P large eigenvalues and MN - P small eigenvalues respectively, and U s is the signal subspace span(U s ) spanned by the eigenvectors corresponding to the P large eigenvalues, and U n is the noise subspace span(U n ) spanned by the eigenvectors corresponding to the MN - P small eigenvalues.

[0023] The spatial spectrum of the two-dimensional MUSIC algorithm is:

[0024]

[0025] Among them, a(θ, r) is the steering vector of the FDA - MIMO radar transceiver array.

[0026] In the present invention, reconstructing the two-dimensional angle - distance spectrum and performing sub - array partitioning on the noise projection specifically includes the following steps:

[0027] Step 3 - 1: The coupled transmit array steering vector a t (θ, r) is rewritten as

[0028] a t (θ, r) = a tr (r) ⊙ a tθ (θ) = diag{a tθ (θ)}a tr (r),

[0029] Among them

[0030] a tθ (θ) = [1, …, e -j(M-1)πsinθ T ,​

[0031]

[0032] Then the transceiver array manifold vector a(θ,r) is further expressed as

[0033]

[0034] where

[0035] Step 3-2: Considering that The decoupled two-dimensional spatial spectrum is reconstructed as:

[0036]

[0037] Step 3-3: Let the noise projection Perform subarray partitioning on it:

[0038]

[0039] where G ij is an M×M dimensional submatrix;

[0040] In the present invention, the matrix subspace root-finding technique is used to construct the root-finding polynomial of the angle spectrum, specifically as:

[0041] Step 4-1: Observe the reconstructed two-dimensional spectrum J(θ,r), select the angle spectrum therein, and let At the same time, define

[0042] a r (z)=[1,z,…,z N-1 T ,

[0043] a tθ (z)=[1,z,…,z M-1 T ,

[0044] where z = e -jπsinθ , therefore, is equivalent to:

[0045]

[0046] where is an MN×M dimensional matrix containing the unknown angle information variable z, and the reconstructed angle spectrum J 1 (θ) can be rewritten as:

[0047]

[0048] Different from the traditional root-finding super-resolution algorithm, since ​​is a matrix, thus, it is impossible to directly perform a root-finding operation on J 1 (z) to obtain the angle information;

[0049] Step 4-2: Perform subarray partitioning on to construct the matrixized unknown variable

[0050] Therefore, can be rewritten as:

[0051]

[0052] Substitute into J 1 (z), then we can get:

[0053]

[0054] Step 4-3: Since the angle information z is included in the cost function and is an N×N matrix, thus, the root-finding polynomial f 2D-root,θ (z) for the angle dimension is the determinant of:

[0055]

[0056] At this time, the order of f 2D-root,θ (z) is 2M(N - 1);

[0057] In the present invention, a root-finding operation is directly performed on the angle spectrum polynomial to obtain the angle estimation value of the target signal. Specifically: Considering the existence of errors, after directly performing a root-finding operation on f 2D-root,θ (z) and selecting P pairs of roots z i close to the unit circle, the angle information of the target signal is solved according to the following formula:

[0058]

[0059] In the present invention, the angle estimation value is substituted into the reconstruction cost function, and according to the root-finding super-resolution algorithm, the distance estimation value of the target signal is obtained, including the following steps:

[0060] Step (1) After obtaining , substitute their corresponding into J(θ, r) respectively. Thus, the distance spectrum with angle prior information can be obtained, that is:

[0061]

[0062] In order to effectively estimate the target distance information using the root - finding super - resolution algorithm, the reconstruction cost function is defined as:

[0063]

[0064] where f 2D-root,r (u) is of order 2(M - 1);

[0065] In step (2), directly perform root - finding operations on f 2D-root,r (u), and select the root u closest to the unit circle of distance. According to the following formula, the distance information of the target can be obtained: i

[0066]

[0067] The automatic pairing of angles and distances in the present invention realizes accurate target positioning, specifically:

[0068] Since That is, the distance and angle information have been decoupled. Therefore, after obtaining the estimated values of all angles of the target, substitute them all into J(θ, r). Through parallel operations and the root - finding super - resolution algorithm, all the estimated values of the target distance can be obtained, and the angles and distances are automatically paired.

[0069] The comparison results of the computational complexity between the present invention and the two - dimensional MUSCI algorithm and the double - pulse method are shown in Table 1, where represents the computational complexity of complex - valued calculations. Assume that the total number of search points in the two - dimensional spatial spectrum of the classical 2D - MUSIC algorithm is J 1 , the number of search points in the angle spatial spectrum and the distance spatial spectrum in the double - pulse method are Q 1 and Q 2 respectively. At the same search interval, J 1 ≈Q 1 ×Q 2 ; The calculated amounts counted mainly include: covariance matrix acquisition calculation unit, eigenvalue decomposition calculation unit, spectral peak search calculation unit (2D - MUSIC algorithm and double - pulse method), and polynomial root - finding calculation unit (2D - root algorithm proposed in the present invention). It can be seen from Table 1 that the computational amount of the polynomial root - finding calculation unit is proportional to the cube of the polynomial order. On the other hand, usually, J 1 >>Q 1 ,Q 2 >>M, N>>P; It can be seen from Table 1 that compared with the 2D - MUSIC algorithm and the double - pulse method, the 2D - root method proposed in the present invention significantly reduces the computational complexity of angle - distance super - resolution.

[0070] ​The present invention realizes the precise positioning of far-field space targets by an FDA-MIMO radar, and the estimated angles and distances can be automatically paired. At the same time, compared with traditional target positioning schemes, it has the computational advantage of low complexity, avoiding the huge computational redundancy in large transceiver antenna arrays, and providing support for the promotion of the engineering, marketization, and industrialization of radar target positioning. Description of the Drawings:

[0071] Attached Figure 1 is the flowchart of the present invention.

[0072] Attached Figure 2 is the schematic diagram of target positioning in Embodiment 1 of the present invention, where M = 6, N = 8, SNR = 10 dB, L = 100, P = 3, and the positions are (10°, 25 Km), (45°, 15 Km), and (30°, 40 Km) respectively.

[0073] Attached Figure 3 is the variation of the angle estimation RMSE with the input signal-to-noise ratio for different algorithms in Embodiment 1 of the present invention, where M = 3, N = 4, L = 100, P = 2, and the positions are (10°, 30 Km) and (45°, 15 Km) respectively.

[0074] Attached Figure 4 is the variation of the distance estimation RMSE with the input signal-to-noise ratio for different algorithms in Embodiment 1 of the present invention, where M = 3, N = 4, L = 100, P = 2, and the positions are (10°, 30 Km) and (45°, 15 Km) respectively.

[0075] Attached Figure 5 is the variation of the angle RMSE with the number of snapshots for different algorithms in Embodiment 1 of the present invention, where M = 3, N = 4, SNR = 10 dB, P = 2, and the positions are (10°, 30 Km) and (45°, 15 Km) respectively.

[0076] Attached Figure 6 is the variation of the angle RMSE with the number of snapshots for different algorithms in Embodiment 1 of the present invention, where M = 3, N = 4, SNR = 10 dB, P = 2, and the positions are (10°, 30 Km) and (45°, 15 Km) respectively.

[0077] Attached Figure 7 is the comparison of the theoretical computational amount with the number of transceiver antenna elements for different algorithms in Embodiment 1 of the present invention, where SNR = 10 dB, L = 100, P = 2, and the positions are (15°, 30 Km) and (30°, 20 Km) respectively.

[0078] Attached Figure 8 Table 1 in it is the theoretical computational amount of different algorithms in Embodiment 1.

[0079] Appendix Figure 9 Table 2 in the following shows the comparison of the CPU running time of the present invention and different algorithms with the number of transceiver antenna units in Embodiment 1. Specific Embodiments

[0080] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0081] Embodiment 1:

[0082] This example proposes a new method for super-resolution target localization of FDA-MIMO radar based on multi-dimensional parameter spectrum reconstruction. The specific steps are as Figure 1 shown. In the first step, the MIMO radar transceiver antenna array is used to receive far-field target signals:

[0083] Assume a MIMO radar with M transmitting antenna units and N receiving antenna units, and both the transmitting and receiving arrays are half-wavelength equally spaced linear arrays. Considering that there are P far-field target signals in space, assuming P is known a priori, the maximum unambiguous detection range r max = c / 2Δf, where c is the electromagnetic wave propagation speed and Δf is the frequency offset. Then the target echo signal under the l-th pulse after matched filtering is expressed as:

[0084] x(l) = A(θ, r)s(l) + n(l),

[0085] where A(θ, r) = [a(θ 1 , r 1 ), …, a(θ P , r P )] is an MN×P-dimensional transceiver array manifold matrix, and the p-th element in the transceiver array manifold matrix is is a P×1-dimensional signal vector after matched filtering, n(l) is an MN×1-dimensional additive Gaussian white noise vector, and the transmitting array manifold vector a p , r p ) and the receiving array manifold vector a tp (θ p , r p ) and a rp (θ p ) are respectively

[0086]

[0087]

[0088] After L transmitted pulses are accumulated, the echo signal is

[0089] X = A(θ, R)S + N.

[0090] Among them, \(S = [s(1),\cdots,s(L)]\) is an \(MN\times L\) - dimensional signal accumulation matrix, \(N = [n(1),\cdots,n(L)]\) is an \(MN\times L\) - dimensional noise accumulation matrix, and \(X = [x(1),\cdots,x(L)]\) is an \(MN\times L\) - dimensional echo signal accumulation matrix.

[0091] Step 2: According to the subspace estimation theory, obtain the noise subspace. The second step includes the following steps:

[0092] The \(MN\times MN\) - dimensional array covariance matrix is:

[0093]

[0094] The complex - valued eigenvalue decomposition of \(R\) can be expressed as:

[0095]

[0096] Among them, \(\Lambda\) s and \(\Lambda\) n are diagonal matrices composed of \(P\) large eigenvalues and \(MN - P\) small eigenvalues respectively. \(U\) s is the signal subspace \(\text{span}(U\) s ) spanned by the eigenvectors corresponding to the \(P\) large eigenvalues, and \(U\) n is the noise subspace \(\text{span}(U\) n ) spanned by the eigenvectors corresponding to the \(MN - P\) small eigenvalues.

[0097] The two - dimensional MUSIC algorithm spatial spectrum is:

[0098]

[0099] Among them, \(a(\theta,r)\) is the array manifold vector of the FDA - MIMO radar transceiver array.

[0100] Step 3: Reconstruct the two - dimensional spectrum of angle - distance and perform sub - array partitioning on the noise projection. The third step includes the following steps:

[0101] (1) The coupled transmit - array manifold vector \(a\) t (\(\theta,r\)) is rewritten as

[0102] \(a\) t (\(\theta,r\)) = \(a\) tr (r)\(\odot a\) tθ (\(\theta\)) = \(\text{diag}\{a\) tθ (\(\theta\)}\(a\) tr (r),

[0103] Among them

[0104]

[0105]

[0106] Therefore, the transceiver array manifold vector a(θ, r) can be further expressed as

[0107]

[0108] where

[0109] (2) Considering The decoupled two-dimensional spatial spectrum is reconstructed as:

[0110]

[0111] (3) Let the noise projection Perform subarray partitioning on it:

[0112]

[0113] where G ij is an M×M dimensional submatrix.

[0114] Step 4: Use the novel matrix subspace root-finding technique to construct the root-finding polynomial of the angle spectrum. The fourth step includes the following steps:

[0115] (1) Observe the reconstructed two-dimensional spectrum J(θ, r), select the angle spectrum among them, and let Meanwhile, define

[0116] a r (z) = [1, z, …, z N-1 T ,

[0117] a tθ (z) = [1, z, …, z M-1 T ,

[0118] where z = e -jπsinθ . Therefore, can be equivalently expressed as:

[0119]

[0120] where is an MN×M dimensional matrix containing the unknown angle information variable z. The reconstructed angle spectrum J 1 (θ) can be rewritten as:

[0121]

[0122] Different from the traditional root-finding super-resolution algorithm, since is a matrix, therefore, J cannot be directly​​1 (z) performs a root-finding operation to obtain angle information.

[0123] (2) Perform subarray partitioning on to construct matrixized unknown variables

[0124] Therefore, can be rewritten as:

[0125]

[0126] Substitute into J 1 (z), and then we can get:

[0127]

[0128] (3) Since the angle information z is included in the cost function and is an N×N matrix, therefore, the root-finding polynomial f 2D-root,θ (z) for the angle dimension is the determinant of:

[0129]

[0130] At this time, the order of f 2D-root,θ (z) is 2M(N - 1).

[0131] Step 5: Directly perform a root-finding operation on the angle spectrum polynomial to obtain the angle estimate of the target signal. The fifth step includes the following steps:

[0132] In practical applications, considering the existence of errors, after directly performing a root-finding operation on f 2D-root,θ (z) and selecting P pairs of roots z i close to the unit circle, the angle information of the target signal can be solved according to the following formula:

[0133]

[0134] Step 6: Substitute the angle estimate into the reconstruction cost function, and according to the root-finding super-resolution algorithm, obtain the distance estimate of the target signal. The sixth step includes the following steps:

[0135] (1) After obtaining , substitute their corresponding into J(θ,r) respectively. Therefore, the distance spectrum with angle prior information can be obtained, that is:

[0136]

[0137] In order to effectively estimate the target distance information using the root super-resolution algorithm, the reconstruction cost function is defined as:

[0138]

[0139] where f 2D-root,r (u) is of order 2(M - 1).

[0140] (2) Perform a direct root operation on f 2D-root,r (u), and select the root u closest to the unit circle of distance. According to the following formula, the distance information of the target can be obtained: i That is,

[0141]

[0142] Step 7: Automatically pair the angle and distance to achieve accurate target positioning. The seventh step includes the following steps:

[0143] Since That is, the distance and angle information have been decoupled. Therefore, after obtaining the estimated values of all angles of the target, substitute them all into J(θ, r). Through parallel operation and the root super-resolution algorithm, all the target distance estimated values can be obtained, and the angle and distance are automatically paired.

[0144] The performance of this example can be illustrated by the following simulation:

[0145] 1. Simulation conditions

[0146] To illustrate the effectiveness and feasibility of the algorithm proposed in the present invention, computer simulation is used to verify the function and performance of the proposed 2D-root algorithm and make a comparative analysis with the 2D-MUSIC algorithm and the classical "double-pulse" method. The FDA-MIMO radar parameter configuration is as follows: carrier frequency f 0 = 3 GHz, frequency offset Δf = 1 KHz, and the spacing between the transmitting and receiving antenna elements is 0.05 m.

[0147] 2. Simulation content and results

[0148] Simulation 1, assuming that there are P = 3 far-field targets in space, the number of transmitting antenna elements is M = 6, the number of receiving antenna elements is N = 8, the signal-to-noise ratio is 10 dB, and the number of snapshots is 100. To effectively analyze the target positioning situation of the 2D-root algorithm, the target positions are preset as (10°, 25 Km), (45°, 15 Km), and (30°, 40 Km); the target positioning situation is as Figure 2 shown.

[0149] From Figure 2It can be seen that the 2D-root algorithm proposed in the present invention can effectively estimate the angles and positions of multiple targets, thereby achieving the purpose of precise positioning; at the same time, the true positions of the targets coincide highly with the estimated positions.

[0150] Simulation 2. To compare and analyze the performance of the algorithm proposed in the present invention, the root mean square error (RMSE) is used as the evaluation index, and the results of each performance test are the statistical averages of 500 Monte Carlo runs. For the estimated value of the target signal angle and the estimated value of the distance , the RMSEs are respectively defined as

[0151]

[0152]

[0153] Investigate the influence of the signal-to-noise ratio on the performance of the present invention and two classical algorithms. Among them, the number of transmitting antenna elements is M = 3, the number of receiving antenna elements is N = 4, the signal-to-noise ratio varies from -10 dB to 20 dB, the number of snapshots is 100, the position information of P = 2 target signals is (10°, 30 Km) and (45°, 15 Km) respectively, the search interval of the angle spectrum is 0.017°, and the search interval of the distance spectrum is 0.057 Km. The results are as Figure 3 and Figure 4 shown.

[0154] From Figure 3 it can be seen that when the signal-to-noise ratio is less than 2 dB, the 2D-root algorithm proposed in the present invention and the classical 2D-MUSIC algorithm and the double-pulse method have similar angle estimation accuracies. When the signal-to-noise ratio is greater than 2 dB, the performance of the two proposed algorithms is completely superior to that of the classical algorithms. From Figure 4 it can be seen that when the signal-to-noise ratio is greater than 8 dB, the algorithm proposed in the present invention has the optimal distance estimation performance.

[0155] Simulation 3. Further discuss the influence of the number of snapshots on the performance of the algorithm proposed in the present invention. To ensure the consistency of the experiment, the simulation parameters are the same as those in Simulation 2. The results are as Figure 5 and Figure 6 shown.

[0156] From Figure 5 and Figure 6 it can be seen that Simulation 3 has the same conclusion as Simulation 2, that is, when the number of snapshots is greater than 2 3 = 8 (as Figure 5 ) and 2 4 = 16 (as Figure 6 ), the angle and distance estimation performances of the algorithm proposed in the present invention are superior to those of the classical 2D-MUSIC algorithm and the double-pulse method.

[0157] Simulation 4 is to investigate the computational efficiency of the proposed algorithm and classical algorithms in estimating the position information of target signals under different configurations of the number of transceiver antenna elements. Two far-field signals located at (15°, 30Km) and (30°, 20Km) are selected, the number of snapshots is 100, the search range of the angle spectrum is from 5° to 35° with a search interval of 0.033°, and the search range of the distance spectrum is from 15Km to 35Km with a search interval of 0.053Km. The MATLAB code is run in the same PC environment with an Intel(R) Core(TM) i5-9400 processor, 2.9GHz, and 16GB of memory. The computational efficiency is equivalently evaluated from the CPU running time (as shown in Table 2) and the theoretical computational amount (such as Figure 7 ).

[0158] As can be seen from Table 2, the computational efficiency of the 2D-root algorithm of the present invention is higher than that of the traditional 2D-MUSIC algorithm and the double-pulse method; at the same time, this is completely consistent with the Figure 7 conclusion of the theoretical computational amount in

[0159] The present invention first innovatively proposes the angle-distance two-dimensional spectrum reconstruction technology, which efficiently strips the two-dimensional parameter spectrum into one dimension. Different from the traditional vectorized subspace root-finding technology, the new method measures the target angle information with high precision through a novel matrixized root-finding technology. On the other hand, due to the multi-dimensional parameter decoupling advantage brought by the spectrum reconstruction technology, the new method then uses the vectorized root-finding technology to "parallelly" measure the target distance information and automatically pair it with the target angle. The new method meets the engineering requirements of high precision, high speed measurement, and ultra-real-time measurement, providing strong theoretical support for the engineering, marketization, and industrialization promotion of radar positioning.

Claims

1. An FDA-MIMO radar super-resolution target localization method based on multi-dimensional parameter spectrum reconstruction, characterized in that, it is realized through the following steps: In the first step, use the MIMO radar transceiver antenna array to receive the far-field space target signal; In the second step, obtain the noise subspace; In the third step, reconstruct the two-dimensional angle-distance spectrum and perform sub-array division on the noise projection; In the fourth step, use the matrix subspace root-finding technique to construct the root-finding polynomial of the angle spectrum; In the fifth step, perform root-finding operation to obtain the angle estimation value of the target signal; In the sixth step, substitute the angle estimation value into the reconstruction cost function, and according to the root-finding super-resolution algorithm, obtain the distance estimation value of the target signal; In the seventh step, automatically pair the angle and the distance to achieve accurate target positioning; The fourth step is realized through the following steps: (1) Observe the reconstructed two-dimensional spectrum J(θ,r), select the angular spectrum among them, and let Meanwhile, define a r (z) = [1, z, …, z N-1 T ,​ a tθ (z) = [1, z, …, z M-1 T ,​ where z = e -jπsinθ , so can be equivalently expressed as: Among them, is an \(M_N\times M\) dimensional matrix containing the unknown angle information variable \(z\), and the reconstructed angle spectrum \(J\) 1 (\(\theta\)) can be rewritten as: (2) For perform sub - array partitioning to construct matrix - formed unknown variables Therefore, It can be rewritten as: Substitute into J 1 (z), and we get: (3) Since the angle information z is included in the cost function and is an N×N matrix, therefore, the root polynomial f 2D-root,θ (z) of the angle dimension is the determinant of: At this time, f 2D-root,θ (z) has an order of 2M(N - 1).

2. The FDA-MIMO radar super-resolution target localization method based on multi-dimensional parameter spectrum reconstruction according to claim 1, characterized in that, The first step is specifically: Assume an FDA-MIMO radar with M transmitting antenna elements and N receiving antenna elements, and both the transmitting and receiving arrays are half-wavelength equally spaced linear arrays. Considering that there are P far-field target signals in space, assuming P is known a priori, the maximum unambiguous detection range of the radar is r max = c / 2Δf, where c is the electromagnetic wave propagation speed and Δf is the frequency offset. Then, the target echo signal under the l-th pulse after matched filtering is expressed as: x(l) = A(θ,r)s(l) + n(l), A(θ,r) = [a(θ 1 ,r 1 ), …, a(θ P ,r P )] is an MN×P - dimensional transmit - receive array manifold matrix, and the p - th element in the transmit - receive array manifold matrix is s(l) is a P×1 - dimensional signal vector after matched filtering, n(l) is an MN×1 - dimensional additive white Gaussian noise vector, and in a(θ p ,r p ), the transmit array manifold vector a tp (θ p ,r p ) and the receive array manifold vector a rp (θ p ) are respectively After accumulating L transmitted pulses, the echo signal is X = A(θ,R)S + N, where S = [s(1),…,s(L)] is an MN×L dimensional signal accumulation matrix, N = [n(1),…,n(L)] is an MN×L dimensional noise accumulation matrix, and X = [x(1),…,x(L)] is an MN×L dimensional echo signal accumulation matrix.

3. The FDA-MIMO radar super-resolution target localization method based on multi-dimensional parameter spectrum reconstruction according to claim 2, characterized in that, The second step is specifically: The MN×MN dimensional array covariance matrix is: The complex eigenvalue decomposition of R can be expressed as: where Λ s and Λ n are diagonal matrices composed of P large eigenvalues and MN - P small eigenvalues respectively, and U s is the signal subspace spanned by the eigenvectors corresponding to the P large eigenvalues, span(U s ), and U n is the noise subspace spanned by the eigenvectors corresponding to the MN - P small eigenvalues, span(U n ); The two-dimensional MUSIC algorithm spatial spectrum is: where a(θ,r) is the FDA-MIMO radar transceiver array manifold vector.

4. The FDA-MIMO radar super-resolution target localization method based on multi-dimensional parameter spectrum reconstruction according to claim 3, characterized in that, The third step is specifically: (1) Coupled emission array manifold vector a t (θ, r) rewritten as a t (θ,r) = a tr (r) ⊙ a tθ (θ) = diag{a tθ (θ)}a tr (r), where a tθ (θ) = [1, …, e -j(M-1)πsinθ T ,​ The transceiver array manifold vector a(θ,r) is further expressed as Among them (2) Considering that The decoupled two-dimensional spatial spectrum is reconstructed as: (3) Let the noise projection Perform subarray partitioning on it: Among them, G ij is an M×M dimensional sub-matrix.

5. The FDA-MIMO radar super-resolution target localization method based on multi-dimensional parameter spectrum reconstruction according to claim 4, characterized in that: The sixth step is realized through the following steps: (1) After obtaining , substitute their corresponding into J(θ,r), so the distance spectrum with angle prior information can be obtained, that is: In order to effectively estimate the target distance information using the root-finding super-resolution algorithm, the reconstruction cost function is defined as: Among them f 2D-root,r (u) is of order 2(M - 1); (2) For f 2D-root,r (u), directly perform the root-finding operation and select the root u closest to the unit circle i . The distance information of the target can be obtained according to the following formula:

6. The FDA-MIMO radar super-resolution target localization method based on multi-dimensional parameter spectrum reconstruction according to claim 5, characterized in that, The fifth step is specifically: In practical applications, considering the existence of errors, for f 2D-root,θ (z), after directly performing a root-finding operation and selecting P roots z close to the unit circle i , the angle information of the target signal can be solved according to the following formula:

7. The FDA-MIMO radar super-resolution target localization method based on multi-dimensional parameter spectrum reconstruction according to claim 6, characterized in that, The seventh step is specifically: Since That is, the distance and angle information have been decoupled. Therefore, after obtaining the estimated values of all angles of the target, substituting all of them into J(θ,r), all the estimated target distance values can be obtained through parallel operations and the root-finding super-resolution algorithm, and the angles and distances are automatically paired.

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