MIMO millimeter wave radar two-dimensional super-resolution angle measurement method using space-time virtual transformation

Abstract

The application relates to a kind of MIMO millimeter wave radar two-dimensional super-resolution angle measurement methods using space-time virtual conversion, comprising: using the orthogonality of transmitting signal, MIMO sparse array is carried out MIMO virtual array transformation, obtain space domain virtual array, obtain the received signal data of space domain virtual array, using the independence of received time domain multiple fast shot data, then carry out time domain virtual transformation, obtain space-time virtual array;Under the antenna layout of space domain virtual array, if the received signal data is single fast shot data, then two-dimensional super-resolution angle measurement is realized using orthogonal matching pursuit (OMP) sparse reconstruction method, if the received signal data is a small amount of fast shot data, then two-dimensional super-resolution angle measurement is realized using sparse bayesian learning (SBL) sparse reconstruction method;If the received signal data is multiple fast shot data, under the antenna layout of space-time virtual array, super-resolution angle measurement is realized using OMP method.The method of the application can increase the effective aperture of array, and significantly improve the angle measurement accuracy of pitch and azimuth dimension.

Description

Technical Field

[0001] This invention belongs to the technical field of radar signal processing methods, specifically relating to a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation. Background Technology

[0002] Currently, 4D millimeter-wave radar methods have become a research hotspot in the field of autonomous driving. Compared to 3D millimeter-wave radar, it can simultaneously provide information on four dimensions of a target: distance, velocity, azimuth, and elevation, offering advantages such as high recognition accuracy, high dynamic range, and longer detection distance. However, it also faces the challenge that existing methods cannot meet the requirements for high-precision, high-resolution measurements. Currently, especially in terms of angular resolution, high-resolution / super-resolution angle measurement methods have become one of the core competitive advantages of 4D millimeter-wave radar imaging.

[0003] Addressing the issues of low angular resolution and lack of elevation-dimensional angle measurement capabilities in traditional automotive millimeter-wave radars, enabling them to achieve two-dimensional high-resolution or super-resolution angle measurement has become a research hotspot in the field of autonomous driving. According to array signal processing theory, angular resolution depends on the physical aperture of the array (Rayleigh limit). The most effective way to improve angular resolution is to increase the number of antennas, thereby increasing the physical aperture. However, considering constraints such as radar size, chip computing power, and hardware cost in practical automotive radar applications, the number of antennas that can be added is limited. Furthermore, the radar itself moves with the vehicle, resulting in a high data update rate, making conventional multi-shot super-resolution angle measurement methods insufficient for real-world scenarios. An even more challenging problem is that coherent source signals are more common in dynamic and complex vehicle traffic environments. Achieving two-dimensional super-resolution angle measurement in coherent source signal scenarios is also a crucial issue that urgently needs to be addressed. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, this invention provides a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation. The technical problem to be solved by this invention is achieved through the following technical solution:

[0005] This invention provides a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation, comprising:

[0006] Step 1: Perform MIMO virtual array transformation on the MIMO sparse array to obtain a spatial virtual array, acquire the received signal data of the spatial virtual array, and obtain a spatiotemporal virtual array based on the spatial virtual array;

[0007] Step 2: If the received signal data is a single snapshot, then super-resolution angle measurement is achieved using the OMP sparse reconstruction method; if the received signal data is a small number of snapshots, then super-resolution angle measurement is achieved using the SBL small number of snapshots super-resolution angle measurement method; if the received signal data is multiple snapshots, then super-resolution angle measurement is achieved using the OMP sparse reconstruction method based on the received signal data of the spatiotemporal virtual array.

[0008] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0009] 1. The present invention utilizes a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar using spatiotemporal virtual transformation. By using spatiotemporal virtual transformation of sparse MIMO array, the array sparsity can be significantly reduced and the array aperture can be effectively increased. Based on the independent conditions of different snapshot signal sample data, the covariance matrix of the received signal is vectorized. By exchanging time accumulation information gain for spatial degrees of freedom, the spatial degrees of freedom of the virtual array can be improved.

[0010] 2. The present invention utilizes a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar based on spatiotemporal virtual transformation. It leverages the decoherence characteristic of compressed sensing to solve the problem that traditional spatial smoothing methods are difficult to apply to sparse and non-uniform array scenarios.

[0011] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar using spatiotemporal virtual transformation provided by an embodiment of the present invention;

[0013] Figure 2 This is a flowchart of a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar using spatiotemporal virtual transformation, provided by an embodiment of the present invention.

[0014] Figure 3 This is a schematic diagram of the positions of the MIMO spatial virtual array and spatiotemporal virtual array elements provided by the present invention;

[0015] Figure 4a This is a diagram showing the physical location of the 12 transmit and 16 receive antennas provided in this invention example;

[0016] Figure 4b This is a diagram showing the actual antenna layout of the 12 transmit and 16 receive antennas provided in this invention example;

[0017] Figure 5 This is a diagram showing the positional arrangement of the 12-transmit 16-receive MIMO virtual (MIMO-VA) array elements provided in this invention example.

[0018] Figure 6 The results of a single snapshot OMP recovery of the directions of arrival of three targets (two coherent sources) under different signal-to-noise ratio scenarios provided by the present invention are shown in the example.

[0019] Figure 7 This is an example of the RMSE plot of 100 MC experiments in a single snapshot of OMP (SMV-OMP) provided by the present invention.

[0020] Figure 8 This invention provides the reconstruction power of 100 MC experiments in a single snapshot of OMP (SMV-OMP) provided in this example.

[0021] Figure 9 This is the average time spent on 100 MC experiments in a single snapshot of OMP (SMV-OMP) provided in the example of this invention;

[0022] Figure 10 This is a diagram showing the positional arrangement of the 12-transmit 16-receive MIMO spatiotemporal virtual (MIMO-II-VA) array elements provided in this invention example;

[0023] Figure 11 This is a sparse recovery result image of multiple snapshots of MUSIC (MMV-MUSIC) provided in this invention example;

[0024] Figure 12 This is an example of the sparse recovery results of multiple snapshot OMP (MMV-OMP) in MIMO-II-VA provided by the present invention.

[0025] Figure 13 This is an example of the sparse recovery result of multiple snapshot SBL (MMV-SBL) under a MIMO virtual array provided by the present invention.

[0026] Figure 14 This is an example of the average OSPA error of three super-resolution angle measurement methods under different number of snapshots provided by the present invention.

[0027] Figure 15 This is a graph showing the success rate of angle estimation for three super-resolution angle measurement methods under different numbers of snapshots, as provided in this invention example.

[0028] Figure 16 This is a graph showing the average time spent by three super-resolution angle measurement methods under different number of snapshots provided in this invention. Detailed Implementation

[0029] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following describes in detail, with reference to the accompanying drawings and specific embodiments, a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar using spatiotemporal virtual transformation proposed according to the present invention.

[0030] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0031] Please see Figure 1 and Figure 2 , Figure 1 This is a schematic diagram of a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar using spatiotemporal virtual transformation provided by an embodiment of the present invention; Figure 2 This is a flowchart of a two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar that utilizes spatiotemporal virtual transformation, provided by an embodiment of the present invention.

[0032] This embodiment of the MIMO millimeter-wave radar two-dimensional super-resolution angle measurement method utilizing spatiotemporal virtual transformation includes:

[0033] Step 1: Perform MIMO virtual array transformation on the MIMO sparse array to obtain a spatial virtual array, acquire the received signal data of the spatial virtual array, and obtain the spatiotemporal virtual array based on the spatial virtual array;

[0034] In an optional embodiment, step 1 includes:

[0035] Based on the actual positions of the transmitting and receiving elements of the MIMO sparse array, the spatial virtual array virtual element positions are obtained by performing MIMO virtual array transformation.

[0036] The received signal vector data is divided using a two-dimensional spatial angular grid to generate a spatial virtual array manifold matrix, thereby obtaining the received signal data of the spatial virtual array.

[0037] A time-domain virtual transformation is performed on the spatial virtual array to obtain a spatiotemporal virtual array.

[0038] Furthermore, the process of transforming a MIMO virtual array into a spatial virtual array is explained in detail.

[0039] Assume that K far-field narrowband signals are incident on a co-located MIMO non-uniform sparse array with M transmitters and N receivers, where K ≤ M * N, and the coordinates of each array element are as follows: Figure 3As shown, (a) is the spherical coordinate system, (b) is the actual element position of the MIMO sparse array, (c) is the virtual element position of the MIMO sparse array, and (d) is the element position of the MIMO spatiotemporal virtual array. For vehicle-mounted millimeter-wave radar, without loss of generality, the azimuth is assumed to be... The range of pitch angle θ is set to ,

[0040]

[0041] The number of transmitting array elements is set to M, and the number of receiving array elements is set to N. The position coordinates of the transmitting array elements are defined as follows:

[0042] P ey =(y e1 ,…y eM ),P ez =(z e1 ,…z eM (2);

[0043] The corresponding coordinates of the receiving array element positions are,

[0044] P ry =(y r1 ,…y rM ),P rz =(z r1 ,…z rM (3);

[0045] For MIMO millimeter-wave radar, each transmitting element emits orthogonal waveforms. After matched filtering at the receiver, an equivalent virtual array with M×N elements can be obtained, i.e., a spatial virtual array. For ease of description, this spatial virtual array is denoted as MIMO-VA. For the transmitting array, the corresponding transmit steering vector is...

[0046]

[0047] in, Let θ be the azimuth angle, θ be the elevation angle, and λ be the carrier wavelength. The receiving steering vector can be expressed as:

[0048]

[0049] The steering vector of MIMO-VA can be expressed as,

[0050]

[0051] in, This represents the Kronecker product.

[0052] More specifically, the virtual array steering vector can be further represented as,

[0053]

[0054] After MIMO virtualization, the positions of each array element can be represented as follows:

[0055]

[0056] The array apertures of the spatial virtual array along the y-axis and z-axis are respectively,

[0057]

[0058] According to the Rayleigh criterion, the azimuth and elevation angle resolution of a MIMO radar is:

[0059] The MIMO transmit waveform is implemented using the DDMA scheme, employing Quasi-Continuous Frequency Modulation Continuous Wave (FMCW). The L consecutive chirp periods of the transmitted signal from the m-th element are:

[0060]

[0061] Among them, the l-th DDMA transmit waveform generated by the m-th array element is,

[0062]

[0063] Where Q represents the number of chirp cycles in a frame of data, and T chirp Let f0 represent the duration of one chirp cycle, f0 represent the constant carrier frequency, and α represent the chirp cycle duration. m qT chirp U represents the initial phase of the m-th transmitting element in the l-th chirp cycle. p If (t) is the envelope of a single chirp, then the transmit signal matrix of the M transmit array elements is S = [s1s2…s...]. m ] T .

[0064] Assume there are K far-field moving targets located in the same range cell, and the direction of arrival of each signal is... Within one chirp cycle, the echo signal received by the MIMO radar is,

[0065]

[0066] Where N = [n1n2,…,n L [ ] is a noise matrix, with each element having a mean of zero and a variance of σ. 2 Complex Gaussian white noise, i.e.

[0067] For each receiving array element, the echo signal is matched and filtered with the M transmitted signals to obtain the received signal vector data.

[0068]

[0069] Where vec represents the vectorization operation, and H is the conjugate transpose. Since the MIMO transmit signals are orthogonal and the noise of each array element is independent, the above equation can be further simplified to:

[0070]

[0071] Where d=[ζ1,…,ζ K ] T It is a vector composed of the amplitudes of each signal.

[0072] Assuming that all targets are independent, the reflection coefficient of each target is denoted as γ. k If k = 1, 2, ..., K, then the received signal matrix can be written as follows:

[0073] Z = VBΛ + W (15);

[0074] Where γ = [γ(1)γ(2)…γ(L)] is the K×L dimension target reflection coefficient matrix, and γ(l) = [γ1γ2…γ... K ] T Λ=diag(d(1),d(2),…,d(L)), W=[w(1),w(2),…,w(L)] is an MN×L dimensional noise matrix.

[0075] Step 2: If the received signal data is a single snapshot, use the OMP (Orthogonal Matching Pursuit Compressed Sensing) sparse reconstruction method to achieve super-resolution angle measurement. If the received signal data is a small number of snapshots (less than 16), use the SBL (Sparse Bayesian Learning) sparse reconstruction method to achieve super-resolution angle measurement. If the received signal data is multiple snapshots, use the OMP sparse reconstruction method to achieve super-resolution angle measurement based on the received signal data from the spatiotemporal virtual array.

[0076] Optionally, if the received signal is single-shot data, super-resolution angle measurement is achieved using the OMP sparse reconstruction method (SMV-OMP), including:

[0077] Step i: Divide the space into G×P continuous grids in the azimuth and elevation dimensions, and transform the problem of estimating the direction of the signal arrival angle into the problem of recovering sparse signals;

[0078] In this embodiment, the space is divided into G×P continuous grids in the azimuth and pitch dimensions, and the gridded angle can be expressed as... like Figure 4bAs shown, observation reveals that the incoming signal exhibits spatial sparsity. Therefore, compressed sensing can be used to transform the estimation problem of the signal's angle of arrival into a sparse recovery problem. A set of atom sequences, also known as the spatial steering matrix, is constructed using the meshed potential signal direction vectors as atoms. By ensuring that the spatial steering matrix satisfies the Restricted Isometry Property (RIP), a unique sparse solution can be obtained, which recovers the support set as the signal's direction of arrival.

[0079] Step ii: Construct the mathematical model of the sparse signal to be recovered as y = A(Φ,Θ)x + n, where y is the observation data, A is the two-dimensional spatial steering matrix, (Φ,Θ) represents the angle after gridding, n is the observation noise, and x is the sparse signal to be recovered containing the signal wave direction information;

[0080] In this embodiment, a mathematical model for two-dimensional direction-of-arrival estimation is constructed using compressed sensing technology in a single snapshot. Here, y represents M×1 dimensional observation data, A is an M×GP dimensional two-dimensional spatial steering matrix, n is M×1 dimensional observation noise, and x is a GP×1 dimensional sparse signal to be recovered, containing information about the direction of arrival of the signal wave.

[0081] Step iii: Based on the OMP sparse reconstruction method, orthogonally project the observed data onto the array manifold matrix atoms corresponding to the current support set. For the currently selected coefficients, minimize the following formula to obtain the sparse solution.

[0082]

[0083] Among them, T [i] Let V be the support set for recovering the sparse solution in the i-th iteration, V be the spatial virtual array manifold matrix, and ||||2 denote the norm operation. The support set is T [i] The sparse solution vector.

[0084] Step iv: Obtain the azimuth and elevation angles of the incoming wave signal based on the location of the support set of the recovered sparse signal.

[0085] For example, the pseudocode for SMV-OMP implementing super-resolution angle measurement under MIMO-VA is as follows:

[0086] Input: array manifold matrix V(Φ,Θ), maximum number of iterations k max

[0087] Output: r [i] ,

[0088]

[0089] Optionally, if the received signal data consists of a small number of snapshots, super-resolution angle measurement can be achieved using the Sparse Reconstruction Method (MMV-SBL), including:

[0090] Step I: Set random initial covariance Build

[0091] Step II: Calculate the statistical covariance Σ y =σ 2 I+V(Φ,Θ)ΓV(Φ,Θ) T Where GP is the number of grid points in the two-dimensional angular domain space, and σ 2 Let V be the noise variance, I be the identity matrix, V be the spatial virtual array manifold matrix, and (Φ,Θ) represent the meshed angles.

[0092] Step 3: Calculate the posterior mean y represents the observed data, and the covariance is updated iteratively based on MacKay.

[0093] Step IV: Return to Step II and iterate until the preset stopping condition is met, and calculate the covariance matrix Σ. x =Γ-ΓV(Φ,Θ) T (Σ y ) -1 ΓV(Φ,Θ);

[0094] Step V: Based on the covariance, posterior mean, and covariance matrix obtained after iteration, the recovered sparse signal is obtained. Based on the support set position of the recovered sparse signal, the azimuth and elevation angles of the incoming wave signal are obtained.

[0095] Furthermore, the process of super-resolution angle measurement using the sparse reconstruction method based on SBL (MMV-SBL) under a small number of snapshots in 2D MIMO-VA is described in detail.

[0096] Based on the Bayesian statistical learning framework, it is assumed that the noise follows a mean of zero and a variance of σ. 2 Given Gaussian white noise, the prior knowledge of the sparse signal x to be recovered follows a Gaussian distribution with zero mean and unknown variance.

[0097]

[0098] Where T is the number of snapshots.

[0099] In the type-II maximum likelihood maximization method, the maximum likelihood is obtained... The estimated value,

[0100]

[0101] in, Let X = [x1(t)x2(t)…x] be the row sparse signal corresponding to T snapshots. T (t)] with Let be the hierarchical prior probability distribution function of the hyperparameters. To measure the distribution of the likelihood function.

[0102] If we assume that the likelihood function of the observed data y also follows a Gaussian distribution, then the posterior distribution of the sparse signal to be recovered also has a Gaussian form and can be expressed as follows:

[0103]

[0104] Estimate the mean of the posterior parameters Covariance Σ x Then, by minimizing the marginal likelihood The negative logarithm is used to update the variance in turn.

[0105]

[0106] Based on the Legendre-Fenchel duality principle, the above equation can be equivalently expressed as the joint minimization of X and

[0107]

[0108] in, x is a model-dependent regularization factor. n Let n be the nth atom activated in the t-th snapshot. Utilizing a hierarchical prior probability model allows for more flexible acquisition of the true direction information of the incoming wave signal.

[0109] Considering that the logarithmic determinant of the above expression is concave, based on The conjugate of is defined as ω * (η),

[0110]

[0111] in,

[0112] Again, regarding the concave function log|σ 2 I+A(Φ,Θ)ΓA(Φ,Θ) T Applying the Legendre-Fenchel duality principle to the conjugate of |, we have:

[0113]

[0114] Furthermore, substituting this into the regularization formula, we get:

[0115]

[0116] Define a new auxiliary variable according to MacKay update rules. It can be written as,

[0117]

[0118] Introducing another cost function, the above equation can be further rewritten as follows:

[0119]

[0120] Among them, h * (η) is the conjugate of the convex function h(η). Substituting the above equation into... The min-max optimization problem under the MacKay rule can be solved by alternately minimizing γ and maximizing the bound of the upper expression, i.e.,

[0121]

[0122] definition for In the k-th iteration, Substituting into the above equation, by letting about The partial derivative of is zero, so its minimum value can be obtained, that is,

[0123]

[0124] After that, regarding To maximize this, we can derive its MacKay update formula.

[0125]

[0126] in, Through iterative calculations, it was found that most of them The value is zero, therefore the corresponding recovery signal x n (t) is sparse.

[0127] For example, applying the SBL sparse recovery method to MIMO-VA, the pseudocode for implementing super-resolution angle measurement using MMV-SBL is as follows:

[0128] Input: array manifold matrix V(Φ,Θ), noise variance σ 2 T-times snapshot received signal measurement matrix, maximum number of iterations k max , After the second virtualization, it is equivalent to a single snapshot y

[0129] Output: Estimated prior source signal covariance Posterior mean of source signal With covariance matrix Σ x

[0130] 1. Initialization

[0131] Set random initial variables Build

[0132] Calculate the statistical covariance Σ y =σ 2 I+V(Φ,Θ)ΓV(Φ,Θ) T

[0133] 2. Iterative loop:

[0134]

[0135] 2.1 Calculate the posterior mean

[0136] 2.2 Iterative updates based on MacKay

[0137] 2.3 By selection Recalculate the selected set of atoms.

[0138] 2.4k←k+1

[0139] End

[0140] 3. Calculate the posterior covariance matrix Σ x =Γ-ΓV(Φ,Θ) T (Σ y ) -1 ΓV(Φ,Θ)

[0141] Furthermore, the method for obtaining the spatiotemporal virtual array is explained in detail. In this embodiment, performing a temporal virtual transformation on the spatial virtual array to obtain the spatiotemporal virtual array includes: vectorizing the covariance matrix of the echo signal to obtain the spatiotemporal virtual array manifold matrix; and vectorizing the covariance matrix of the echo signal, represented as:

[0142]

[0143] Among them, R ZZ Let be the covariance matrix of the echo signal, vec be the vectorization operation, and K be the number of echo signals. For transmitting and receiving guide vectors, Let I be the noise power, and I be the identity matrix. The power of the kth echo signal is δi (i = 1, 2, ..., N) indicates that the i-th element is 1 and the rest are 0. The symbol ⊙ represents the Kr product, * represents the conjugate operation, and H = V. * ⊙V is the spatiotemporal virtual array manifold matrix, and V is the spatial virtual array manifold matrix.

[0144] Based on the spatial virtual array, a spatiotemporal virtual array is obtained by performing temporal virtualization according to the nested array virtual transformation rule. For ease of description, the spatiotemporal virtual array is denoted as MIMO-II-VA. The aperture of the virtual array is doubled, and the spatial degrees of freedom can be increased to MN×MN, significantly improving the element density and reducing the energy loss of the main lobe caused by the side lobes. The detailed implementation process is described below.

[0145] When the number of chirp cycles of the transmitted signal (similar to the number of snapshots in direction-of-arrival estimation) is large, the covariance matrix of the echo signal is:

[0146]

[0147] in, The power of the kth echo signal is This represents the total noise power.

[0148] Next, the covariance matrix is ​​vectorized, as shown in equation (30), where H = V * ⊙V is the MN×K dimensional spatiotemporal virtual array manifold matrix. The vectorized signal vector is equivalent to the single-shot received signal vector of the MIMO virtual array manifold H.

[0149] The element positions of MIMO-II-VA, such as Figure 3 As shown in Figure d, the virtual array elements after the KR product operation are equivalent to the difference between the array elements of the MIMO array. The coordinates of the MIMO-II-VA array elements in the YZ vertical plane are...

[0150] {((y e,i +y r,j )-(y e,l +y r,k ),(z e,i +z r,j )-(z e,l +z r,k ))|1≤i,l≤MN,1≤j,k≤MN}(32);

[0151] The physical interpretation of MIMO-II-VA is that it trades the temporal gain of multi-frame data sampling for spatial degrees of freedom, achieving twice the spatial degrees of freedom compared to a MIMO virtual array. The spatial degrees of freedom after spatiotemporal virtualization are MN×MN, and the aperture expansion is doubled, i.e., 2Lx×2Ly. It is worth noting that the prerequisite for trading temporal gain for spatial gain is that the data samples must satisfy independence; otherwise, the spatial gain will be less than MN.

[0152] Optionally, if the received signal data consists of multiple snapshots, super-resolution angle measurement is achieved using the OMP sparse reconstruction method (MMV-OMP) based on the received signal data from the spatiotemporal virtual array, including:

[0153] Step 1: Transform the problem of estimating the direction of the signal's angle of arrival into the problem of recovering the sparse signal, and construct a mathematical model of the sparse signal to be recovered;

[0154] Step 2: Based on the OMP sparse reconstruction method, orthogonally project the observed data onto the array manifold matrix atoms corresponding to the current support set. For the currently selected coefficients, minimize the following formula to obtain the sparse solution.

[0155]

[0156] Among them, T [i] Let H be the support set for recovering the sparse solution in the i-th iteration, H be the spatiotemporal virtual array manifold matrix, and ||||2 denote the norm operation. The support set is T [i] The sparse solution vector, (Φ,Θ) represents the angle after meshing;

[0157] Step 3: Obtain the azimuth and elevation angles of the signal based on the location of the support set of the recovered sparse signal.

[0158] It should be noted that when applying the OMP sparse recovery method to the spatiotemporal virtual array MIMO-II-VA, the key processing step is the spatiotemporal virtual array manifold matrix H(Φ,Θ). Similar to the super-resolution angle measurement achieved by SMV-OMP under MIMO-VA, the spatiotemporal virtual array manifold matrix H(Φ,Θ) is substituted into the OMP sparse reconstruction method to obtain the sparse solution.

[0159] For example, the pseudocode for MMV-OMP to implement super-resolution angle measurement under MIMO-II-VA is as follows:

[0160] Input: T snapshot observation vectors (equivalent to a single snapshot after spatiotemporal virtualization), array manifold matrix H(Φ,Θ), maximum number of iterations k max

[0161] Output: r [i] ,

[0162]

[0163]

[0164] It is worth noting that the subspace-based multiple signal classification (MUSIC) algorithm, as a commonly used sparse reconstruction method, exhibits good performance under scenarios with sufficient snapshot count and signal-to-noise ratio. The calculation formulas for two-dimensional MUSIC spectrum estimation in MIMO-VA and MIMO-II-VA scenarios are as follows:

[0165]

[0166]

[0167] Among them, E N For an MN×(1-K) dimensional noise subspace, Let be a noise subspace of (MN*MN)×(1-K) dimensions.

[0168] However, spatial smoothing MUSIC algorithms will be difficult to implement in scenarios with non-uniform arrays, coherent sources, and limited snapshot numbers.

[0169] The two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation in this invention significantly reduces array sparsity and effectively increases array aperture through sparse MIMO nested quadratic virtual transformation. Based on the independence of different snapshot signal sample data, the received signal covariance matrix is ​​vectorized, using time-accumulated information gain to exchange for spatial degrees of freedom, thereby increasing the spatial degrees of freedom of the virtual array. Furthermore, leveraging the decoherence properties of compressed sensing, it addresses the problem that traditional spatial smoothing methods are difficult to apply to sparse and non-uniform array scenarios.

[0170] Furthermore, the performance of the method of the present invention in achieving super-resolution angle measurement is evaluated through simulation experiments, including two evaluation indicators: root mean square error (RMSE) and optimal submode allocation (OSPA).

[0171] (1) Root Mean Square Error (RMSE)

[0172] To evaluate the super-resolution angle measurement accuracy and robustness of the proposed method, angle measurement accuracy is defined as the root mean square error (RMSE) of the angle estimation, and robustness is measured by the signal sparse recovery success rate ρ, calculated as follows.

[0173]

[0174] Among them, TMC Let K be the number of Monte Carlo iterations and K be the number of information sources. These represent the actual incoming signal direction and the corresponding estimated incoming signal direction for the k-th cycle, respectively.

[0175]

[0176] Here, sum(·) is the summation operation for the elements in the vector.

[0177] (2) Optimal Submode Allocation OSPA

[0178] It is particularly noteworthy that when there are missed detections and false alarms, the RMSE estimation accuracy metric suffers from a mismatch between the dimension of the actual target information and the dimension of the estimated information. Therefore, Optimal Sub-pattern Assignment (OSPA) is introduced to provide a metric for angle estimation accuracy under conditions of missed detections and false alarms. The mathematical description of the OSPA metric is as follows:

[0179] Let the estimated angle set be J = {ξ1,…,ξ} n}, n is the estimated number of targets, and the true target angle set Λ={γ1,…,γ m}, m is the number of real targets.

[0180] ① Find the n-element subset Λ that is closest to J J

[0181]

[0182] in, for The optimal allocation (note that n ≤ m) is obtained by minimizing the operation by traversing all permutations π of 1, ..., n. It is a Euclidean distance.

[0183]

[0184] ②For each γ∈Λ, let

[0185]

[0186] Where, β γ Let γ be the association cutoff distance between γ and its best associated object in X.

[0187] ③ Calculate the cutoff distance β γ p-th order mean

[0188]

[0189] Among them, the angle positioning error Error in estimating the number of targets They are as follows:

[0190]

[0191] The physical interpretation of each parameter in the OPSA criterion is as follows: c is a positive real number with the same dimensions as ξ (associated cutoff radius), and its value determines the importance of target number estimation accuracy relative to angle estimation accuracy. If the value of c is small, positioning accuracy is emphasized more than target number estimation accuracy. The value of p determines the sensitivity of this metric to statistical "outliers". The larger the value of p, the greater the "penalty" of the angle estimation algorithm for poor angle estimation.

[0192] Simulation Experiment 1. Simulation Experiment of Two-Dimensional Super-Resolution Angle Measurement in a Single Quick Shot under a Coherent Source Scene

[0193] like Figure 4a , Figure 4b and Figure 5 As shown, based on the physical positions of four cascaded 12-transmitter, 16-receiver antennas (3 transmit, 4 receive), a virtual MIMO array is obtained using MIMO virtual rules. A two-dimensional super-resolution angle measurement simulation experiment is then conducted based on this array. To verify the super-resolution angle measurement and decoherence capabilities of the OMP algorithm, three targets are set in the scenario, and the true direction of the incoming signal is: azimuth. Pitch θ0 = [0 1 2]°, where two are coherent sources, intermediate frequency FI = [15 15 20]MHz, six different signal-to-noise ratios are set, and the directions of the three incoming signals are obtained based on the single-shot OMP reconstruction algorithm (SMV-OMP). The angle estimation results under different SNRs are as follows: Figure 6 As shown. Observation Figure 6 It can be seen that when the signal-to-noise ratio is greater than 3.6 dB, the directions of the three incoming signals can be accurately reconstructed. Furthermore, the robustness of the two-dimensional angle estimation of SMV-OMP is verified through 200 Monte Carlo experiments, such as... Figures 7-9 Simulation results show that as the signal-to-noise ratio increases, the reconstruction RMSE gradually converges to 0, and when the signal-to-noise ratio is greater than 4.8dB, the reconstruction success rate of the three signals is 100%. At the same time, the average time consumption is statistically analyzed, and it is observed that the average calculation time of SMV-OMP is less than 56.75ms, which shows relatively high real-time performance.

[0194] Simulation Experiment 2. Simulation Experiment of Multi-Shot Multi-Target 2D Super-Resolution Angle Measurement in Coherent Source Scene

[0195] In fact, simulation experiments revealed that SMV-OMP suffers from inaccurate angle estimation and significant missed detections when dealing with more than three nearby targets. Therefore, the multiple snapshot reconstruction method described above was used to conduct a two-dimensional angle estimation experiment on five nearby targets in space. The simulation parameters were set as follows: SNR = [15 15 18 18 20], azimuth... Pitch θ0 = [0 1 2 3 4]°, intermediate frequency FI = [15 15 20 25 30]MHz, by comparing the MUSIC (MMV-MUSIC) and Sparse Bayesian (MMV-SBL) methods under MIMO virtual arrays, and the methods under MIMO quadratic virtual nested arrays ( Figure 10 The OMP method comprises three approaches. Simulation results are as follows: Figures 11-13 As shown, it can be observed that both the MMV-SBL and MMV-OMP methods can accurately estimate the arrival directions of the five signals in 36 snapshots. However, the MUSIC method misses two coherent source targets, thus verifying that in scenarios with multiple nearby coherent source targets, the multi-snapshot method based on sparse recovery has high angle estimation accuracy and is insensitive to coherent source signals. Furthermore, to verify robustness, 200 Monte Carlo experiments were conducted under different snapshot scenarios. The experimental results are shown below. Figures 14-16 As shown in the figure, the experimental results show that for both sparse recovery algorithms, the OSPA estimation error of the angle gradually converges to 0 as the number of snapshots increases. However, the MUSIC method underestimates the two coherent sources, resulting in a persistent angle estimation error. It is worth noting that the sparse recovery method with multiple snapshots exhibits poor real-time performance, taking an order of magnitude longer than the MUSIC method. Therefore, in practical applications, a trade-off must be made between recovery accuracy and real-time performance.

[0196] It should be noted that, in this document, some relational terms are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element.

[0197] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation, characterized in that, include: Step 1: Perform MIMO virtual array transformation on the MIMO sparse array to obtain a spatial virtual array, acquire the received signal data of the spatial virtual array, and obtain a spatiotemporal virtual array based on the spatial virtual array; Step 2: If the received signal data is a single snapshot, super-resolution angle measurement is achieved using the OMP sparse reconstruction method; if the received signal data is a small number of snapshots, super-resolution angle measurement is achieved using the SBL sparse reconstruction method; if the received signal data is multiple snapshots, super-resolution angle measurement is achieved using the OMP sparse reconstruction method based on the received signal data of the spatiotemporal virtual array. Step 1 includes: Based on the actual positions of the transmitting and receiving elements of the MIMO sparse array, the spatial virtual array virtual element positions are obtained by performing MIMO virtual array transformation. The received signal vector data is divided using a two-dimensional spatial angular grid to generate a spatial virtual array manifold matrix, thereby obtaining the received signal data of the spatial virtual array. Perform a time-domain virtual transformation on the spatial virtual array to obtain a spatiotemporal virtual array; In step 2, if the received signal data consists of multiple snapshots, super-resolution angle measurement is achieved using the OMP sparse reconstruction method based on the received signal data from the spatiotemporal virtual array, including: Step 1: Transform the problem of estimating the direction of the signal's angle of arrival into the problem of recovering the sparse signal, and construct a mathematical model of the sparse signal to be recovered; Step 2: Based on the OMP sparse reconstruction method, orthogonally project the observed data onto the array manifold matrix atoms corresponding to the current support set. For the currently selected coefficients, minimize the following formula to obtain the sparse solution. , ； in, T [i] The support set for recovering the sparse solution in the i-th iteration. For a spatiotemporal virtual array manifold matrix, Represents norm operations, It is a support set T [i] sparse solution vectors, Indicates the angle after meshing; For observational data; Step 3: Obtain the azimuth and elevation angles of the incoming wave signal based on the location of the support set of the recovered sparse signal.

2. The two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation according to claim 1, characterized in that, The virtual element positions of the spatial virtual array are represented as follows: ； in, M The number of transmit elements in the MIMO sparse array. N For the number of receiver elements in a MIMO sparse array, The coordinates of the transmitting element's position are... These are the coordinates of the receiving array element's position.

3. The two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation according to claim 1, characterized in that, In step 2, if the received signal is single-shot data, super-resolution angle measurement is achieved using the OMP sparse reconstruction method, including: Step i: Divide the space into azimuth and elevation dimensions. G × P A continuous grid transforms the problem of estimating the direction of arrival of a signal into the problem of recovering a sparse signal; Step ii: Construct a mathematical model for the sparse signal to be recovered. ,in, It is a two-dimensional spatial guidance matrix. This represents the angle after meshing. To observe the noise, The sparse signal to be recovered contains information about the direction of signal arrival. Step iii: Based on the OMP sparse reconstruction method, orthogonally project the observed data onto the array manifold matrix atoms corresponding to the current support set. For the currently selected coefficients, minimize the following formula to obtain the sparse solution. , ； in, T [i] The support set for recovering the sparse solution in the i-th iteration. For spatial virtual array manifold matrix, Represents norm operations, It is a support set T [i] sparse solution vectors; Step iv: Obtain the azimuth and elevation angles of the incoming wave signal based on the location of the support set of the recovered sparse signal.

4. The two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation according to claim 1, characterized in that, In step 2, if the received signal data consists of a small number of snapshots, super-resolution angle measurement is achieved using the SBL sparse reconstruction method, including: Step I: Set random initial covariance , build , Step II: Calculate the statistical covariance ,in, The number of grid points in the two-dimensional angular domain. For noise variance, As a unit array, For spatial virtual array manifold matrix, Indicates the angle after meshing; Step 3: Calculate the posterior mean , For the observed data, the covariance is updated iteratively based on MacKay. ; Step IV: Return to Step II and iterate until the preset stopping condition is met, and calculate the covariance matrix. ; Step V: Based on the covariance, posterior mean, and covariance matrix obtained after iteration, the recovered sparse signal is obtained. Based on the support set position of the recovered sparse signal, the azimuth and elevation angles of the incoming wave signal are obtained.

5. The two-dimensional super-resolution angle measurement method for MIMO millimeter-wave radar utilizing spatiotemporal virtual transformation according to claim 1, characterized in that, Performing a time-domain virtual transformation on the spatial virtual array yields a spatiotemporal virtual array, comprising: Vectorizing the covariance matrix of the echo signal yields the spatiotemporal virtual array manifold matrix; the vectorization of the echo signal's covariance matrix can be mathematically described as follows: ； in, Let be the covariance matrix of the echo signal. For vectorization operations, The number of echo signals, For transmitting and receiving guide vectors, For noise power, As a unit array, , No. k The power of each echo signal is , , Indicates the first i One element is 1, and the rest are 0. (Symbol) For Kr product, * represents conjugate operation. For a spatiotemporal virtual array manifold matrix, It is a spatial virtual array manifold matrix.

Images