A Low Elevation Angle Estimation Method for MIMO Radar Based on Spatial Smooth Sparse Reconstruction

Abstract

This invention discloses a low elevation angle estimation method for MIMO radar based on spatially smooth sparse reconstruction, comprising the following steps: Step 1, establishing a MIMO radar multipath effect signal reception model X(t); Step 2, performing generalized matched filtering on the received signal to obtain a virtual matrix Y(t), and calculating the average covariance matrix R of each column of the virtual matrix. f (t), then calculate R f R(t) is the inverse covariance matrix. b (t); Step 3, according to R f (t) and R b (t), to achieve forward and backward spatial smoothing of the virtual matrix Y(t), and obtain the average covariance matrix R after bidirectional spatial smoothing. fb Step 4: For R fb Vectorize y to obtain y, construct a redundant dictionary and a sparse matrix, and use convex optimization to sparsely reconstruct y. Then calculate R. fb The variance η of all element errors 2 The error threshold η is obtained. Based on the error threshold η, step five is to draw a spatial spectrum from the sparse matrix obtained by the solution. The angle corresponding to the peak value on the spatial spectrum is the estimated value of the elevation angle of the low-altitude target.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, specifically relating to a method for estimating the low elevation angle of MIMO radar based on spatial smooth sparse reconstruction. Background Technology

[0002] In modern warfare, low-altitude penetration has become a crucial means of gaining air superiority. Research on low-altitude penetration target direction finding has broad military application prospects for winning future informationized local wars. However, in low-altitude environments, multipath effects cause strong fluctuations and even cancellation of echo signals, significantly impacting target detection and direction finding. Multiple-input multiple-output (MIMO) radar's excellent spatial, frequency, and waveform diversity characteristics can overcome signal fading caused by multipath effects, and are of great significance for optimizing detection and tracking performance and improving direction finding resolution and accuracy.

[0003] Currently, some research results have been achieved in MIMO radar direction of arrival (DOA) estimation. Hou Yunshan proposed an M-SSMUSIC method, which reduces the variance of the noise subspace while achieving decoherence by spatially smoothing the sample covariance matrix, thereby improving the angle estimation performance of coherent signals under low signal-to-noise ratio conditions. Chen Genhua proposed a high-precision estimation method for low elevation angles of meter-wave interferometric array radar. By extending the conventional spatial smoothing algorithm to the interferometric array, decoherence of low-elevation multipath signals is achieved. Finally, the elevation angle of low-altitude targets is solved using the dual-scale unitary algorithm (Estimating Signal Parameters via Rotational Invariance Techniques, ESPRIT). Zhang Qin proposed a DOA estimation method based on spatial difference reconstruction. Utilizing the spatial diversity characteristics of MIMO radar, after optimizing the echo signal of multipath echo energy, spatial difference iterative calculation reduces the impact of noise on estimation accuracy, improving the DOA estimation performance of low-altitude targets. However, the aforementioned decoherence algorithms require prior information about the number of information sources and will lose the effective aperture of the array.

[0004] In recent years, the enormous application potential of compressed sensing (CS) theory has further promoted the development of array signal processing technology. Scholars have begun to study the sparsity characteristics of targets in the direction-finding field to resolve the contradiction between computational accuracy and computational complexity. D. Malioutov proposed the l1-SVD algorithm, constructing an overcomplete basis matrix based on array propagation. He used l1-norm convex optimization to complete DOA estimation under single-shot conditions and extended it to multi-shot cases. Combining singular value decomposition to reduce matrix dimensionality and computational complexity, he successfully solved the multi-measurement vector problem in arrays. However, because this method relies on the SVD step required by subspace-based methods, inaccurate estimation of the number of signal sources leads to a decrease or failure in estimation performance. Furthermore, neglecting some noise components under low signal-to-noise ratio conditions also results in performance degradation. J. Yin proposed the l1-SRACV algorithm, which uses the asymptotically normal distribution of the error in the covariance matrix of array output data to perform DOA estimation of coherent signals without knowing the number of signal sources. However, its computational complexity is relatively high. WKMa introduced the Khatri-Rao product transform into the l1-SRACV algorithm for DOA estimation, reducing the computational load, but it could not estimate the DOA of coherent signals. Cai Jingjing, based on spatial smoothing theory, combined the Khatri-Rao product transform with the l1-SRACV algorithm, proposing the SS-CMSR algorithm, which significantly reduced the computational load compared to the l1-SRACV algorithm, but its DOA estimation capability for multipath signals was poor. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for estimating the low elevation angle of MIMO radar based on spatial smooth sparse reconstruction.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for estimating low elevation angles of MIMO radar based on spatially smooth sparse reconstruction includes the following steps:

[0008] Step 1: Establish the MIMO radar multipath effect signal reception model X(t);

[0009] Step 2: Perform generalized matched filtering on the received signal to obtain the virtual matrix Y(t), and calculate the average covariance matrix R of each column of the virtual matrix. f (t), then calculate R f R(t) is the inverse covariance matrix. b (t);

[0010] Step 3: According to R f (t) and R b(t), yielding the average covariance matrix R after bidirectional spatial smoothing. fb To achieve decoherence of direct and reflected signals to the same target;

[0011] Step 4: Vectorize R fb Obtain y, and construct a redundant dictionary based on the principle of compressed sensing. sparse matrix By using convex optimization to sparsely reconstruct y, we obtain Then calculate the average covariance matrix R after bidirectional spatial smoothing. fb The variance η of all element errors 2 The error threshold η is obtained, and combined with the error threshold η, the following is applied: Perform the conversion to obtain

[0012] Step 5, according to The sparse matrix obtained by solving The image is plotted as a spatial spectrum, and the angle corresponding to the peak value on the spatial spectrum is the estimated value of the elevation angle of the low-altitude target.

[0013] Preferably, the specific steps for establishing the MIMO radar multipath effect signal receiving model X(t) in step one are as follows:

[0014] Suppose a MIMO radar is a uniform linear array composed of M isotropic elements, with an element spacing of d = λ / 2, where λ is the signal wavelength. There are K targets in the air. Then the transmission matrix of the M elements is:

[0015] S L (t)=[s L1 (t) s L2 (t) ··· s LM (t)] T

[0016] Among them, s Lm (t) represents the transmitted signal of the m-th array element, and the signals transmitted by the M array elements are mutually orthogonal;

[0017] The received K target signals are:

[0018]

[0019] Where A(θ) is the direction matrix, A(θ) = [a(θ)] d1 ),a(θ r1 ),…,a(θ dK ),a(θ rK )],a(θ dk () represents the steering vector of the direct wave from the k-th target. β dk=2πdsinθ dk / λ,a(θ rk () represents the steering vector of the reflected wave from the k-th target. β rk =2πdsinθ rk / λ, ω=blkdiag([1 ε1] T ,…,[1 ε K ] T ), ε k Let be the total ground reflectance of the k-th target. ρ k For a complex number, 2πΔR k / λ represents the phase difference caused by the path difference between the direct wave and the reflected wave, (·) T Indicates transpose, (·) H Indicates conjugate transpose;

[0020] The MIMO radar multipath effect signal reception model X(t) is:

[0021] X(t)=A(θ)ωαS R (t)+n(t)

[0022] =A(θ)ωαω T A(θ) H S L (t)+n(t)

[0023] Where α represents the target scattering coefficient, α=diag(α1,α2,…,α) K ), ω=blkdiag([1 ε1] T ,…,[1ε K ] T ), (·) T Let n(t) represent the transpose, where n(t) is the mean of the M array elements and the variance is 0. The noise is additive white Gaussian noise, and the noise received by each array element is uncorrelated.

[0024] Preferably, the specific steps of step two are as follows:

[0025] 2.1. Based on the MIMO radar multipath effect signal receiving model X(t) obtained in step one, perform generalized matched filtering on the received signal to obtain the virtual matrix Y(t). The expression for Y(t) is:

[0026] Y(t)=E[X(t)S L (t) H ]

[0027] =Aθωω T A(θ H +V t

[0028] Where V(t) represents an M×M dimensional noise matrix, and each element of V(t) follows a noise law with a mean of 0 and a variance of 0. They are Gaussian distributed and uncorrelated;

[0029] 2.2 For the i-th column of the virtual matrix Y(t) obtained in step 2.1, i.e., the output of the i-th transmitted signal after generalized matched filtering, it is:

[0030] Y(t) ci =A(θ)C i ′+V(t) ci

[0031] Where, Y(t) ci Let A(θ) be an M×1 dimensional matrix, A(θ) be an M×2K dimensional direction matrix, and C′ be a 2K×1 dimensional matrix. (·) H V(t) represents the conjugate transpose. ci Let V(t) be the i-th column;

[0032] 2.3. Utilizing the translation invariance of the steering vectors corresponding to each column of the virtual matrix Y(t), the direct and reflected signals of different targets are decohered, and the average covariance matrix of each column of the virtual matrix Y(t) is calculated as R. f (t), the expression is:

[0033]

[0034] in, Ps represents the direct signal power reflected from each target to the radar, since rank(R c =K, which achieves the decoherence of the synthesized signal from direct and reflected signals from different targets, I M Let J be an M×M dimensional identity matrix, and define matrix J as an M×M transformation matrix.

[0035] Calculate R f The reverse covariance matrix of (t) is R b (t), the expression is:

[0036]

[0037] in, (·) * This indicates taking the conjugate.

[0038] Preferably, in step three, the average covariance matrix R fb The expression is:

[0039]

[0040] in, L represents the number of snapshots.

[0041] Preferably, in step four, the expression for y is:

[0042]

[0043] Where vec(·) denotes matrix vectorization, and B(θ) = A(θ) * ⊙A(θ) is M 2 A ×2K dimensional matrix, where ⊙ denotes the Khatri-Rao product operation. It is a 2K×1 dimensional power vector.

[0044] Preferably, in step four, the expression for the error threshold η is:

[0045]

[0046] in, The variance is calculated for elements other than the diagonal elements, where var(·) represents the variance calculation, and M is the number of array elements. The error of the diagonal elements of the covariance matrix is... Variance over time.

[0047] Compared with the prior art, the advantages of this invention are as follows:

[0048] (1) The method provided by the present invention utilizes the translation invariance between subarrays of the MIMO radar virtual matrix and the spatial smoothing decoherence of the subarrays in the forward and backward directions to overcome the disadvantage of array aperture loss. Compared with the spatial smoothing algorithm of conventional array radar that relies on reducing aperture decoherence, it has higher angle resolution.

[0049] (2) This invention utilizes the Khatri-Rao product transformation to vectorize the covariance matrix after bidirectional spatial smoothing. Therefore, the complexity of the method provided by this invention is O(N). 3 The complexity is on the order of magnitude of 0, the same as the SS-CMSR algorithm, and O(M) of the l1-SRACV algorithm. 3 N 3 Compared to the complexity of the l1-SVD algorithm with K targets, the computational complexity is significantly reduced and the real-time performance is better.

[0050] (3) Simulation experiments show that the method provided by this invention has good low-altitude target direction finding performance, especially under low signal-to-noise ratio and low snapshot conditions, it is superior to the classic DOA estimation algorithm based on compressed sensing. Attached Figure Description

[0051] Figure 1A flowchart of the estimation method provided in the embodiments of the present invention;

[0052] Figure 2 Spatial spectrum of the method and other algorithms provided in the embodiments of the present invention;

[0053] in, Figure 2 (a) shows the spatial spectrum of the l1-SVD algorithm. Figure 2 (b) shows the spatial spectrum of the l1-SRACV algorithm. Figure 2 (c) is the spatial spectrum of the SS-CMSR algorithm. Figure 2 (d) is the spatial spectrum of the method provided in the embodiments of the present invention;

[0054] Figure 3 The relationship curves between the mean square error of the method provided in this embodiment of the invention and other algorithms as a function of signal-to-noise ratio and number of snapshots are shown.

[0055] in, Figure 3 (a) is the curve showing the relationship between mean square error and signal-to-noise ratio. Figure 3 (b) shows the relationship between the mean square error and the number of snapshots;

[0056] Figure 4 The relationship curves between the discovery probability of the method provided in this embodiment of the invention and other algorithms as a function of signal-to-noise ratio and number of snapshots;

[0057] In the picture, Figure 4 (a) is the curve showing the relationship between the probability of discovery and the signal-to-noise ratio. Figure 4 (b) is the curve showing the relationship between the probability of discovery and the number of snapshots. Detailed Implementation

[0058] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0059] like Figure 1 As shown, this embodiment of the invention provides a method for estimating the low elevation angle of MIMO radar based on spatially smooth sparse reconstruction, specifically including the following steps:

[0060] Step 1: Establish the MIMO radar multipath effect signal reception model X(t). The specific steps for establishing the MIMO radar multipath effect signal reception model X(t) are as follows:

[0061] Suppose a MIMO radar is a uniform linear array composed of M isotropic elements, with an element spacing of d = λ / 2, where λ is the signal wavelength. There are K targets in the air. Then the transmission matrix of the M elements is:

[0062] S L (t)=[s L1 (t) s L2 (t) ··· s LM (t)] T

[0063] Among them, s Lm (t) represents the transmitted signal of the m-th array element, and the signals transmitted by the M array elements are mutually orthogonal;

[0064] The received K target signals are:

[0065]

[0066] Where A(θ) is the direction matrix, A(θ) = [a(θ)] d1 ),a(θ r1 ),…,a(θ dK ),a(θ rK )],a(θ dk () represents the steering vector of the direct wave from the k-th target. β dk =2πd sinθ dk / λ,a(θ rk () represents the steering vector of the reflected wave from the k-th target. β rk =2πd sinθ rk / λ, ω=blkdiag([1ε1) T ,…,[1 ε K ] T ), ε k Let be the total ground reflectance of the k-th target. ρ k For a complex number, 2πΔR k / λ represents the phase difference caused by the path difference between the direct wave and the reflected wave, (·) T Indicates transpose, (·) H Indicates conjugate transpose;

[0067] The MIMO radar multipath effect signal reception model X(t) is:

[0068] X(t)=A(θ)ωαS R (t)+n(t)

[0069] =A(θ)ωαω T A(θ) H SL (t)+n(t)

[0070] Where α represents the target scattering coefficient, α=diag(α1,α2,…,α) K ), where n(t) is the mean of the M array elements received by the array, and the variance is 0. The additive white Gaussian noise is received by each array element and the noise received by each element is uncorrelated.

[0071] Step 2: Perform generalized matched filtering on the received signal to obtain the virtual matrix Y(t), and calculate the average covariance matrix R of each column of the virtual matrix. f (t), then calculate R f R(t) is the inverse covariance matrix. b (t), the specific steps are as follows:

[0072] 2.1. Based on the MIMO radar multipath effect signal receiving model X(t) obtained in step one, perform generalized matched filtering on the received signal to obtain the virtual matrix Y(t). The expression for Y(t) is:

[0073] Y(t)=E[X(t)S L (t) H ]

[0074] =Aθωω T A(θ H +V t

[0075] Where V(t) represents an M×M dimensional noise matrix, and each element of V(t) follows a noise law with a mean of 0 and a variance of 0. They are Gaussian distributed and uncorrelated;

[0076] 2.2 For the i-th column of the virtual matrix Y(t) obtained in step 2.1, i.e., the output of the i-th transmitted signal after generalized matched filtering, it is:

[0077] Y(t) ci =A(θ)C i ′+V(t) ci

[0078] Where, Y(t) ci Let A(θ) be an M×1 dimensional matrix, and C′ be an M×2K dimensional direction matrix. (·) H V(t) represents the conjugate transpose. ci Let V(t) be the i-th column;

[0079] 2.3. Utilizing the translation invariance of the steering vectors corresponding to each column of the virtual matrix Y(t), the direct and reflected signals of different targets are decohered, and the average covariance matrix of each column of the virtual matrix Y(t) is calculated as R. f (t), the expression is:

[0080]

[0081] in, Ps represents the direct signal power reflected from each target to the radar, since rank(R c =K, thus achieving the decoherence of the synthesized signal from direct and reflected signals from different targets, I M Let J be an M×M dimensional identity matrix, and define matrix J as an M×M transformation matrix.

[0082] Calculate R f The reverse covariance matrix of (t) is R b (t), the expression is:

[0083]

[0084] In its formula, A(θ) is an M×2K dimensional direction matrix, I M Let be an M×M dimensional identity matrix, (·) H This is the conjugate transpose. Let be the variance, (·) * To obtain conjugate.

[0085] Step 3: According to R f (t) and R b (t), yielding the average covariance matrix R after bidirectional spatial smoothing. fb To achieve decoherence of direct and reflected signals to the same target, the average covariance matrix R... fb The expression is:

[0086]

[0087] in, L represents the number of snapshots;

[0088] Step 4: Vectorize R fb Obtain y, and construct a redundant dictionary based on the principle of compressed sensing. sparse matrix By using convex optimization to sparsely reconstruct y, we obtain Then calculate the average covariance matrix R after bidirectional spatial smoothing. fb The variance η of all element errors 2The error threshold η is obtained, and combined with the error threshold η, the following is applied: Perform the conversion to obtain Specifically:

[0089] Based on the Khatri-Rao product transformation theory, R fb Vectorization yields y, whose expression is:

[0090]

[0091] Where vec(·) denotes matrix vectorization, and B(θ) = A(θ) * ⊙A(θ) is M 2 A ×2K dimensional matrix, where ⊙ denotes the Khatri-Rao product operation. It is a 2K×1 dimensional power vector;

[0092] Constructing a redundant dictionary sparse matrix Dividing the entire spatial domain into N (N >> K) directional spaces, according to the principle of compressed sensing, y can be sparsely represented as:

[0093]

[0094] in, For M 2 ×N-dimensional redundant dictionary It is an N×1 dimensional sparse vector;

[0095] By using convex optimization to sparsely reconstruct y, we obtain Represents the covariance matrix R fb The estimated value of β represents the error threshold.

[0096] Let the covariance matrix R(t) = R f (t), defined Let p1 represent the element at row p1 and column p2 of the covariance matrix R(t). When p1 = p2, the following relationship can be derived:

[0097]

[0098] Similarly, when p1≠p2:

[0099]

[0100] in,

[0101] From the above R f From the formula for calculating (t), we can see that the estimated value of the covariance matrix R(t) is... For the error covariance matrix The variance of the off-diagonal elements can be obtained as follows:

[0102]

[0103] in, var(·) represents calculating the variance. The estimated value is expressed as:

[0104]

[0105] For R fb The error covariance matrix ΔR fb The error for elements other than the diagonal elements is:

[0106]

[0107] right The variance is approximately calculated as follows:

[0108]

[0109] Assume the error covariance matrix ΔR fb The error of each element on the diagonal is... Then its variance is The error covariance matrix ΔR fb By summing the variances of all elements in the matrix, we can obtain the average covariance matrix R after two-way spatial smoothing. fb The variance of the errors of all elements is:

[0110]

[0111] in, This represents the error for elements other than the diagonal elements;

[0112] Based on the error threshold η, for Perform the conversion to obtain

[0113] Step 5, according to The sparse matrix obtained by solving The image is plotted as a spatial spectrum, and the angle corresponding to the peak value on the spatial spectrum is the estimated value of the elevation angle of the low-altitude target.

[0114] The following section presents simulation experiments and results analysis of the MIMO radar low elevation angle estimation method based on spatially smooth sparse reconstruction provided in this invention embodiment.

[0115] 1. Spatial spectrum

[0116] Suppose there are three targets in the low sky, and the angles of their direct and reflected waves are θ respectively.d1 =2°, θ r1 =-2°, θ d2 =6°, θ r2 =-6°, θ d3 =10°, θ r3 = -10°, the total reflection coefficient is ε1 = 0.5e j0 ε2=0.5e jπ2 and ε3=0.5e jπ . Figure 2 The spatial spectrum of different algorithms is shown when the number of array elements M=28, the number of snapshots L=500, and the signal-to-noise ratio is 10dB. The dotted lines in the figure represent the true angular directions.

[0117] from Figure 2 It can be seen that the l1-SVD algorithm can estimate the incoming directions of direct and reflected waves from three low-altitude targets relatively well, but its accuracy is low; the l1-SRACV algorithm cannot effectively estimate the incoming directions of direct and reflected waves from multiple targets in multipath scenarios; the SS-CMSR method cannot estimate the total reflection coefficient as ε3 = 0.5e. jπ The target is a low-altitude target where the direct wave and the reflected wave weaken each other; the method provided in this embodiment of the invention can effectively estimate the direction of arrival of the direct wave and the reflected wave of three low-altitude targets without knowing the number of signal sources, and its performance is significantly better than other algorithms.

[0118] 2. Mean Square Error

[0119] Suppose there is a target in the low sky, and the directions of its direct and reflected waves are θ respectively. d1 =2°, θ r1 = -2°, the total reflection coefficient is ε1 = 0.5e j150° / 180°π , the number of array elements M = 12, Figure 3 (a) The mean square error of each algorithm when the number of snapshots L = 500 and the signal-to-noise ratio varies from -10 to 10 dB. Figure 3 (b) is the mean square error of each algorithm when the signal-to-noise ratio is 10dB and the number of snapshots varies from 30 to 300, with 200 Monte Carlo experiments in each algorithm.

[0120] pass Figure 3 It can be seen that the l1-SVD and l1-SRACV algorithms have poor performance. The SS-CMSR method has an estimation performance that is basically equivalent to the method provided in the embodiments of the present invention under high signal-to-noise ratio and high snapshot conditions. The method provided in the embodiments of the present invention has a significantly better performance than other algorithms under low signal-to-noise ratio and low snapshot conditions.

[0121] 3. Probability of discovery

[0122] The assumptions are the same as in Simulation 2. An angle estimation error within ±1.5° is defined as a successful estimation. The probability of a successful estimation is statistically analyzed. Figure 4 (a) is the detection probability of each algorithm when the number of snapshots L = 500 and the signal-to-noise ratio varies from -10 to 10dB. Figure 4 (b) is the discovery probability of each algorithm when the signal-to-noise ratio is 10dB and the number of snapshots varies from 30 to 300, with 200 Monte Carlo experiments in each case.

[0123] analyze Figure 4 It is evident that when processing multipath signals, the elevation angle estimation performance of each algorithm improves with increasing signal-to-noise ratio and number of snapshots. However, the method provided in this embodiment of the invention demonstrates significantly better elevation angle estimation performance for low-altitude targets under low signal-to-noise ratio and low snapshot conditions compared to other algorithms.

[0124] In summary, the low elevation angle estimation method for MIMO radar based on spatially smooth sparse reconstruction provided in this invention establishes a MIMO radar multipath effect model and combines it with compressed sensing theory to propose a spatially smooth sparse reconstruction-based method for low elevation angle estimation of MIMO radar. This method utilizes the translation invariance between virtual matrix subarrays and subarray smoothing techniques to overcome the shortcomings of array aperture loss, achieving effective elevation angle estimation for multiple low-altitude targets under conditions of unknown signal sources. Simulation experiments show that the method provided in this invention has good low-altitude target direction-finding performance, especially under low signal-to-noise ratio and low snapshot conditions, outperforming the classic compressed sensing-based DOA estimation algorithm.

[0125] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for estimating low elevation angle of MIMO radar based on spatially smooth sparse reconstruction, characterized in that, include: Step 1: Establish the MIMO radar multipath effect signal reception model X(t); Step 2: Perform generalized matched filtering on the received signal to obtain the virtual matrix Y(t), and calculate the average covariance matrix R of each column of the virtual matrix. f (t), calculate R f R(t) is the inverse covariance matrix. b (t), including: S2.

1. Perform generalized matched filtering on the received signal based on X(t) to obtain the virtual matrix Y(t); S2.

2. For the i-th column of the virtual matrix Y(t), i.e., the output of the i-th transmitted signal after generalized matched filtering, it is: Y(t) ci =A(θ)C i ′+V(t) ci ; where Y(t) ci Let A(θ) be an M×1 dimensional matrix, and A(θ) be an M×2K dimensional direction matrix. The superscript H denotes the conjugate transpose, and V(t) denotes the M×M dimensional noise matrix. ci Let V(t) be the i-th column; S2.

3. Using the translation invariance of the steering vectors corresponding to each column of the virtual matrix Y(t), the direct and reflected signals of different targets are decohered, and the average covariance matrix of each column of the virtual matrix Y(t) is calculated as R. f (t), the expression is: in, Let I be the variance. M It is an M×M dimensional identity matrix. Ps represents the direct signal power reflected from each target to the radar, with the superscript * indicating conjugate; R is calculated. f The reverse covariance matrix of (t) is R b (t), the expression is: Where J is the transformation matrix; Step 3: According to R f (t) and R b (t), to obtain the average covariance matrix R after bidirectional spatial smoothing. fb This enables the decoherence of direct and reflected signals to the same target. Step 4: Vectorize R fb Obtain y, and construct a redundant dictionary based on the principle of compressed sensing. sparse matrix By using convex optimization to sparsely reconstruct y, we obtain Calculate R fb The variance η of all element errors 2 We obtain the error threshold η, and then, combining the error threshold η, we transform to obtain... Step 5, according to The sparse matrix obtained by solving The image is plotted as a spatial spectrum, and the angle corresponding to the peak value on the spatial spectrum is the estimated value of the elevation angle of the low-altitude target.

2. The MIMO radar low elevation angle estimation method based on spatially smooth sparse reconstruction as described in claim 1, characterized in that, The specific steps for establishing the MIMO radar multipath effect signal reception model X(t) in step one are as follows: Suppose a MIMO radar is a uniform linear array composed of M isotropic elements, with an element spacing of d = λ / 2, where λ is the signal wavelength. There are K targets in the air. Then the transmission matrix of the M elements is: S L (t)=[s L1 (t) s L2 (t) ··· s LM (t)] T Among them, s Lm (t) represents the transmitted signal of the m-th array element, where m = 1, 2, ..., M; and the transmitted signals of the M array elements are mutually orthogonal. The received K target signals are: S R (t)=[s R1 (t) s R2 (t) … s RK (t)] T =ω T A(θ) H S L (t) Where A(θ) is the direction matrix, and the superscript T denotes transpose; The MIMO radar multipath effect signal reception model X(t) is: X(t)=A(θ)ωαS R (t)+n(t)=A(θ)ωαω T A(θ) H S L (t)+n(t) Where α represents the target scattering coefficient, α=diag(α1,α2,…,α) K ); ω=blkdiag([1 ε1] T ,…,[1 ε K ] T ), where n(t) is the mean of the M array elements and the variance is 0. The noise is additive white Gaussian noise, and the noise received by each array element is uncorrelated.

3. The MIMO radar low elevation angle estimation method based on spatially smooth sparse reconstruction as described in claim 1, characterized in that, In step two: J is an M×M dimensional transformation matrix.

4. The MIMO radar low elevation angle estimation method based on spatially smooth sparse reconstruction as described in claim 1, characterized in that, In step three, R fb The expression is: in, L represents the number of snapshots.

5. The MIMO radar low elevation angle estimation method based on spatially smooth sparse reconstruction as described in claim 1, characterized in that, In step four, the expression for y is: Where vec(·) denotes matrix vectorization, and B(θ) = A(θ) * ⊙A(θ) is M 2 A 2K-dimensional matrix, where ⊙ represents the Khatri-Rao product operation, and u is a 2K×1-dimensional power vector.

6. The MIMO radar low elevation angle estimation method based on spatially smooth sparse reconstruction as described in claim 1, characterized in that, In step four: in, The variance is calculated for elements other than the diagonal elements, where var(·) represents the variance calculation, and M is the number of array elements. The error of the diagonal elements of the covariance matrix is... Variance over time.

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