Method and device for multi-target super-resolution positioning by frequency-modulated continuous wave radar

Abstract

A method and apparatus for super-resolution localization of multiple targets using frequency-modulated continuous wave radar includes: determining the number K of targets based on the number of eigenvalues ​​satisfying a condition in the covariance matrix of the acquired radar array signal; finding the frequency values ​​corresponding to the K largest spectral peaks based on the acquired number of targets K, using these frequency values ​​as coarsely estimated intermediate frequency (IF) values, and determining the final IF value using the coarsely estimated IF values; calculating the distance of the corresponding target relative to the center O of the antenna array based on the final IF value; obtaining the noise subspace of the array signal and the steering vector related to the target distance and angle based on the eigenvalues ​​of the covariance matrix of the array signal, constructing a MUSIC spectral function, and determining the estimated value of the target echo signal direction; and then determining the position of the corresponding target. This invention has higher range and angle resolution and lower algorithm complexity, enabling super-resolution localization of multiple targets.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and in particular to a method and apparatus for super-resolution localization of multiple targets using frequency-modulated continuous wave radar. Background Technology

[0002] Frequency-modulated continuous-wave (FMCW) radar offers advantages in target localization, including high range resolution, no blind spots, simple structure, and low transmission power, attracting widespread attention in academia and frequently used as a component of mobile scene localization products. Localization systems based on FMCW signal reflection differ from traditional systems based on direct measurement of signal arrival time (TOA). It indirectly obtains the signal propagation time between the target and the transmitter through frequency mixing, converting the measurement time into a measurement frequency, significantly reducing the system's time accuracy requirements. However, traditional baseline algorithms achieve low resolution, failing to meet the growing demands for super-resolution localization; multiple signal classification (MUSIC) algorithms also suffer from low resolution and susceptibility to noise interference; while existing compressed sensing algorithms effectively improve resolution, their high complexity and challenging nature present significant challenges.

[0003] Therefore, designing robust, low-complexity algorithms to achieve super-resolution positioning of objects, thereby improving the resolution and product competitiveness of FMCW signal reflection positioning systems, has become an urgent problem to be solved.

[0004] There is a method for achieving radar range super-resolution, referencing Figure 1 The method includes: 1) performing frequency domain de-chirping and sparse representation processing on the linear frequency modulated echo signal (LFM) of the radar target to obtain a processed frequency domain de-chirped signal; 2) performing low-dimensional linear observation on the processed frequency domain de-chirped signal; 3) calculating the maximum a posteriori probability estimate of the unknown sparse amplitude vector in the processed frequency domain de-chirped signal to obtain the amplitude of the target echo signal, thereby obtaining the target range and achieving radar range super-resolution. Existing positioning algorithms have low resolution and poor robustness, while traditional compressed sensing algorithms have high computational complexity and are difficult to implement, failing to simultaneously meet the goals of low complexity and super-resolution positioning. Summary of the Invention

[0005] This invention proposes a method and apparatus for super-resolution localization of multiple targets using frequency-modulated continuous wave radar, aiming to improve resolution, reduce complexity, and enhance robustness.

[0006] This invention proposes a method for super-resolution localization of multiple targets using frequency-modulated continuous wave radar, comprising:

[0007] The number of targets K is determined by the number of eigenvalues ​​in the covariance matrix of the radar array signal.

[0008] Based on the frequency domain transformation of the radar array signal to obtain the corresponding spectrum, the frequency values ​​corresponding to the K largest spectral peaks are found according to the number of targets K, and these frequency values ​​are used as the rough estimated intermediate frequency values.

[0009] Multiple frequency points are selected at equal intervals in the neighborhood of the intermediate frequency signal corresponding to the roughly estimated intermediate frequency value. The original signal is reconstructed by linear combination of the multiple frequency points. The weight of each frequency point is calculated. The frequency points with a weight greater than a threshold are taken as the final intermediate frequency value.

[0010] The distance of the target relative to the center O of the antenna array is calculated based on the final intermediate frequency.

[0011] Based on the eigenvalues ​​of the covariance matrix of the radar array signal, the noise subspace of the radar array signal and the steering vector related to the target distance and angle are determined. A MUSIC spectrum function is constructed. The value of the MUSIC spectrum function is calculated along the circumference with a specified step size, starting from the y-axis of the rectangular coordinate system established with the antenna array center O as the origin. If the MUSIC spectrum function has a spectral peak, the angle of the echo signal direction corresponding to the spectral peak relative to the positive y-axis is used as the estimated value of the target echo signal direction.

[0012] S7 determines the position of each target based on the distance of each target relative to the center O of the antenna array and the estimated direction of the corresponding target echo signal.

[0013] Furthermore, the radar array signal is acquired by: determining the direction matrix V(θ) corresponding to time t within the linear frequency modulation period of the radar array signal, and the vector v in the direction matrix V(θ). k (θ) is θ k A guide vector in the direction, where θ k For the goal o k The angle between the line connecting to the center O of the antenna array and the y-axis of the Cartesian coordinate system established with O as the origin, and then based on the target O. k The distance r to the center O of the antenna array k θ k Given the antenna aperture L and the number of antenna elements Na in the antenna array, establish a received signal model, and then establish the received radar array signal based on the received signal model.

[0014] Furthermore, the number of targets K is determined based on the number of eigenvalues ​​in the covariance matrix of the radar array signal, specifically including:

[0015] Arrange all eigenvalues ​​of the covariance matrix of the radar array signal in descending order. When there is no noise in the radar array signal, take the number of non-zero eigenvalues ​​as the target number K. When there is noise in the radar array signal, take a specified number of non-zero eigenvalues ​​from front to back in the descending order of all eigenvalues, and take the number of these non-zero eigenvalues ​​as the target number K.

[0016] Furthermore, the step of selecting multiple frequency points at equal intervals of a specified size in the neighborhood of the intermediate frequency signal corresponding to the roughly estimated intermediate frequency value, and reconstructing the original signal using a linear combination of the multiple frequency points, specifically includes:

[0017] Based on the multiple frequency points, an F matrix and an S matrix are constructed. Each row vector of the F matrix represents the signal vector established at each frequency point, and each column vector represents all sampling points within one period. The S matrix represents the signal received by an element in the antenna array within one period.

[0018] A sparse basis matrix for receiving radar array signals is established using each frequency point. An unconstrained convex optimization problem equation is established based on the F matrix and S matrix to solve for and reconstruct the original received signal.

[0019] This invention also proposes a device for super-resolution localization of multiple targets using frequency-modulated continuous wave radar, comprising:

[0020] The target quantity determination module determines the number of targets K based on the number of eigenvalues ​​in the covariance matrix of the radar array signal.

[0021] The intermediate frequency rough estimation module obtains the corresponding spectrum by performing frequency domain transformation on the radar array signal, finds the frequency values ​​corresponding to the K largest spectral peaks based on the number of targets K, and uses these frequency values ​​as the rough estimated intermediate frequency values.

[0022] The intermediate frequency (IF) precise estimation module selects multiple frequency points at equal intervals of a specified size in the neighborhood of the IF signal corresponding to the roughly estimated IF frequency value, reconstructs the original signal using a linear combination of the multiple frequency points, calculates the weight of each frequency point, and uses the frequency points with a weight greater than a threshold as the final IF frequency value.

[0023] The target range estimation module calculates the precise distance of the target relative to the center O of the antenna array based on the final intermediate frequency.

[0024] The target direction estimation module determines the noise subspace of the radar array signal and the steering vector related to the target distance and angle based on the eigenvalues ​​of the covariance matrix of the radar array signal. It constructs a MUSIC spectrum function and calculates the value of the MUSIC spectrum function along the circumference with a specified step size, starting from the y-axis of a rectangular coordinate system established with the antenna array center O as the origin. If the MUSIC spectrum function has a spectral peak, the angle of the echo signal direction corresponding to the spectral peak relative to the positive y-axis is used as the estimated value of the target echo signal direction.

[0025] The target position indication module determines and indicates the position of each target based on the estimated distance of each target relative to the center O of the antenna array and the direction of the corresponding target echo signal.

[0026] Furthermore, the radar array signal is acquired by: determining the direction matrix V(θ) corresponding to the time within the linear frequency modulation period, and the vector v in the direction matrix V(θ). k (θ) is θ k A guide vector in the direction, where θ k For the goal o k The angle between the line connecting to the center O of the antenna array and the y-axis of the Cartesian coordinate system established with O as the origin, and then based on the target O. k The distance r to the center O of the antenna array k θ k Given the antenna aperture L and the number of antenna elements Na in the antenna array, establish a received signal model, and then establish the received radar array signal based on the received signal model.

[0027] Furthermore, the target quantity determination module specifically performs the following steps:

[0028] Arrange all eigenvalues ​​of the covariance matrix of the radar array signal in descending order. When there is no noise in the radar array signal, take the number of non-zero eigenvalues ​​as the target number K. When there is noise in the radar array signal, take a specified number of non-zero eigenvalues ​​from front to back in the descending order of all eigenvalues, and take the number of these non-zero eigenvalues ​​as the target number K.

[0029] Furthermore, the intermediate frequency (IF) precise estimation module selects multiple frequency points at equal intervals of a specified size in the neighborhood of the IF signal corresponding to the roughly estimated IF frequency value, and reconstructs the original signal using a linear combination of the multiple frequency points, specifically including:

[0030] Based on the multiple frequency points, an F matrix and an S matrix are constructed. Each row vector of the F matrix represents the signal vector established at each frequency point, and each column vector represents all sampling points within one period. The S matrix represents the signal received by an element in the antenna array within one period.

[0031] A sparse basis matrix for receiving radar array signals is established using each frequency point. An unconstrained convex optimization problem equation is established based on the F matrix and S matrix to solve for and reconstruct the original received signal.

[0032] Compared to traditional technologies, this invention offers higher distance and angular resolution and lower algorithmic complexity, enabling super-resolution localization of multiple targets. This invention simplifies the parameters in the guide vector using the first-order Taylor approximation, reducing mathematical computational complexity by utilizing the simplified guide vector for azimuth estimation. In target distance estimation, this invention employs sparse reconstruction, establishing a sparse matrix based on coarse frequency measurements, improving the accuracy of mid-frequency measurements and achieving super-resolution localization in range measurement. In target angle estimation, this invention establishes a direction matrix closely related to practical applications and applicable to both far-field and near-field conditions, and utilizes the spectral peak search concept from the MUSIC algorithm for accurate target angle estimation. Attached Figure Description

[0033] Figure 1 This is a flowchart of a method for achieving radar range super-resolution in the prior art;

[0034] Figure 2 This is a flowchart of a method for super-resolution localization of multiple targets using frequency-modulated continuous wave radar according to the present invention;

[0035] Figure 3 This is a schematic diagram of the antenna array positioning of the present invention;

[0036] Figure 4 This is a graph showing the descending sorting of the eigenvalues ​​of the array signal covariance matrix;

[0037] Figure 5 This is the solution graph of the sparse matrix obtained from the first array element;

[0038] Figure 6 This is a diagram showing the peak point locations of the sparse matrix solutions corresponding to the antenna array elements;

[0039] Figure 7 This is a diagram showing the second-highest point location of the sparse matrix solution corresponding to the antenna array element;

[0040] Figure 8 This is a graph showing the variation of the error magnitude with respect to the antenna array elements;

[0041] Figure 9 It is a spatial spectral image generated at the r1 distance;

[0042] Figure 10 It is a spatial spectral image generated at the r2 distance;

[0043] Figure 11 It is a polar coordinate graph of the detected target object's position. Detailed Implementation

[0044] This invention proposes a method and apparatus for super-resolution localization of multiple targets using frequency-modulated continuous wave radar. The specific implementation of this invention is described in detail below.

[0045] The overall scheme of this invention includes the following steps: establishing a received signal model and deriving the steering vector; estimating the number of targets based on eigenvalue decomposition; roughly estimating the intermediate frequency (IF) based on FFT; constructing a small-scale Fourier dictionary locally at the roughly estimated IF based on the sparsity assumption, and achieving high-precision estimation of the target IF by establishing a regularized optimization model; estimating the target distance by combining the relationship between the IF and the target distance; and estimating the target angle based on a multi-signal classification algorithm.

[0046] refer to Figure 2 The method for multi-target super-resolution localization using frequency-modulated continuous wave radar of the present invention includes the following steps:

[0047] (1) Establish the received signal model and derive the steering vector. When deriving the steering vector, the algorithm complexity was reduced by simplifying the steering vector and reducing the data dimension. The parameters in the steering vector were simplified using the idea of ​​first-order Taylor approximation. The simplified steering vector was used for azimuth estimation, which can reduce the complexity of mathematical calculation.

[0048] (2) The number of targets is estimated based on eigenvalue decomposition. The number of targets is determined by obtaining the number of relatively large eigenvalues ​​of the covariance matrix of the radar echo signal data.

[0049] (3) Based on FFT, the intermediate frequency is roughly estimated. The signal spectrum is obtained by performing Discrete Fourier Transform on the fast time dimension data. The intermediate frequency value is obtained by the peak search method. In the form of a spectrum diagram, according to the number of targets K, the frequency values ​​corresponding to the K largest spectral peaks are found. These frequency values ​​are the required intermediate frequency values.

[0050] (4) Based on the sparsity assumption, a small-scale Fourier dictionary is constructed locally at the roughly estimated intermediate frequency (IF). A regularized optimization model is then established to further achieve high-precision estimation of the target IF. According to the sparse reconstruction theory in compressed sensing, a super-resolution distance estimation model based on sparse reconstruction is established using the sparsity constraint of the signal in the frequency domain. After solving the optimization equation, the frequency point with the greatest influence on the signal is selected. The distance calculated from this frequency is the target distance, thus completing super-resolution localization in the distance dimension. The specific steps are as follows:

[0051] ① Use the sparse reconstruction-based super-resolution distance estimation model to sparse the frequency points and construct the corresponding F and S matrices.

[0052]

[0053] In the formula, each row vector of the F matrix represents the signal vector established by 16 frequency points, and each column vector represents 256 sampling points in one period.

[0054]

[0055] In the formula, S represents the signal received by an array element within one period.

[0056] ② Based on the relevant theories of convex optimization, the following optimization problem is listed as an unconstrained convex optimization problem, which can be solved using the cvx toolbox in MATLAB.

[0057] min||Fx-S||2+λ||x||1,λ=1

[0058]

[0059] In the formula, x represents the sparse basis matrix of the radar received signal.

[0060] ③ Observe the solution results and find the frequency components that have a greater impact on the signal, so as to calculate the distance corresponding to that frequency.

[0061] (5) Estimate the target distance by combining the relationship between the intermediate frequency and the target distance.

[0062] (6) The target angle is estimated based on the multiple signal classification algorithm. The angle value of the target is estimated by using the idea of ​​establishing a spectral function and searching for spectral peaks in the MUSIC algorithm. Within the angle space, such as θ∈[-50°, 50°], the value of the spectral function is calculated. If the target angle is found, the spectral function will show a clear spectral peak. By finding the θ value corresponding to the very obvious spectral peak, the estimated value of the incoming wave direction can be obtained.

[0063] (7) Determine the target location and number of targets by combining the estimated values.

[0064] Example

[0065] To verify the superiority of the established algorithm in low-complexity, high-resolution multi-target localization using frequency-modulated continuous wave radar, this invention uses sampling data in a single slow time dimension. The main simulation technical parameters of the frequency-modulated continuous wave are shown in the table below: Table 1 shows the main technical parameters of the frequency-modulated continuous wave radar used.

[0066] Table 1 shows the main technical parameters used.

[0067] parameter <![CDATA[T s (s)]]> T(s) <![CDATA[N f ]]> L(m) γ (Hz / s) <![CDATA[N a ]]> <![CDATA[f0(Hz)]]> N size <![CDATA[1.25×10 -7 ]]> <![CDATA[3.2×10 5 s]]> 32 0.0815 <![CDATA[78.986×10 12 ]]> 86 <![CDATA[78.8×10 9 ]]> 256

[0068] The main technical parameters of frequency modulated continuous wave radar include: T s N represents the sampling interval, T represents the linear frequency modulation period, and N represents the sampling interval. f To obtain the number of linear frequency modulation cycles, L represents the aperture size, γ is the modulation slope of the frequency modulation signal, and N... a This represents the number of array elements, N represents the number of sampling points, and f0 is the carrier frequency. The specific steps include:

[0069] 1. Establish the received signal model and derive the steering vector. Figure 3 The diagram shown is a schematic of the antenna array positioning. Figure 3 The origin point is the center of the antenna array; the radar antenna is an equivalent virtual antenna array with Na uniformly arranged antennas of aperture L on a horizontal plane. A coordinate system is established with the center of the antenna array as the origin, the antenna array as the horizontal axis, and the direction perpendicular to the antenna array as the vertical axis; Na is the number of antenna elements, and Na can also be used as the antenna element number; L is the antenna aperture. For time t within a linear frequency modulation period, the intermediate frequency signals with noise received by the nth antenna from K target objects are mixed as follows:

[0070] In the formula,

[0071]

[0072]

[0073] X k =r k sinθ k , k = 1, 2, ..., K (4)

[0074] Y k =r k cosθ k , k = 1, 2, ..., K (5)

[0075]

[0076] Where Sn,k(t) represents the intermediate frequency signal received by the nth antenna from the kth target object at time t of the FMCW radar; wn(t) is the noise signal at time t; T is the linear frequency modulation period of the frequency-modulated continuous wave radar; Ts is the sampling interval; t is the current time; τ is the reception delay; a k R represents the reflectivity of an object. n，k Let x be the two-way echo distance of the nth antenna. n y n Let be the coordinates of the nth antenna, and let o be the target.k The distance to the center is r k The angle between the y-axis and the y-axis is θ. k , (X k Y k That is, the target. k The coordinates in this plane coordinate system.

[0077] Array signals are always transformed to baseband before processing. Therefore, under normal circumstances, the array signal model can be conveniently described using a matrix as follows:

[0078] Z(t)=V(Θ)S(t)+N(t) (7)

[0079] Here, matrix Z(t) represents the received target signal matrix, and matrix V(Θ), which is related to the shape of the array and the source of the signal, is called the direction matrix. Any column vector v(θ) k ) is a spatial source of the array signal with direction θ k The response vector. S(t) represents the target signal received at the reference point at time t. N(t) represents the noise signal received at time t. In this invention, Z(t) is the response vector of N. a A ×1 matrix, V(Θ) is an N-order matrix. a The direction matrix is ​​a K×K matrix, S(t) is a K×1 column vector, and assuming there is no noise signal, let N(t) be a zero matrix.

[0080] This invention represents the signal received per unit time as a matrix form according to formula (7). From (2), it can be seen that the direction of the spatial source signal can be determined through... The performance of the term, then for discrete time The total incoming signal vector can be expressed as:

[0081]

[0082] make

[0083]

[0084]

[0085] Combining formulas (3), (4), (5), and (6), we can obtain:

[0086]

[0087] but V(θ) is the direction matrix corresponding to time t, v k (θ) corresponds to θ k A guiding vector in the direction, a = [a1 a2…a] K ] T, which represents the reflectivity of an object, and ak represents the reflectivity of the k-th object.

[0088] The steering vector in this signal model differs from the response vector in the traditional model. In the traditional model, the response vector is established based solely on the reference position of the first array element and is closely related to the direction of a spatial source signal. However, the orientation matrix constructed in this model has been adjusted to be a universal expression applicable to both the far and near fields. As shown in equation (10), the steering vector in this model contains R... n，k It contains both distance and angle information. Therefore, the direction matrix V(θ), the angle and distance information obtained from the origin, and the direction matrix V(θ) are all connected through the variable R. n，k They got in touch.

[0089] To reduce computational complexity, based on formulas (3) and (6), R is modified. n，k Perform the following processing:

[0090]

[0091] Furthermore, the antenna radius is much smaller than the distance to the object, i.e. but The term can be eliminated as a small quantity in this expression. Also... have:

[0092]

[0093] The term relative to r k This is also a relatively small term. According to the Taylor expansion formula... have:

[0094]

[0095] but

[0096]

[0097] Clearly, after approximation, the model will be equivalent to a far-field model of a traditional antenna array.

[0098] Here, the parameters in the steering vector are simplified using the idea of ​​first-order Taylor approximation. Using the simplified steering vector for orientation estimation can reduce the complexity of mathematical calculations.

[0099] 2. Calculate the covariance matrix of the array signals: When each signal source is independent, the eigenvectors corresponding to the largest eigenvalues ​​of the covariance matrix span the same space as the steering vectors of the incident signals. Arrange the eigenvalues ​​of the resulting mixed data covariance matrix from largest to smallest as follows: λ1 ≥ λ2 ≥ … ≥ λ Na≥0, when there is no noise in the sample, the number of non-zero feature values ​​is taken as the target number; when there is noise in the sample, let γ be... k =λ k / λ k+1 (k = 1, 2, ..., N) a -2) is used as the principal eigenvalue of the sample matrix. Then the number of sources K should take the value such that... That is, the number of larger feature values ​​is selected as the target number. For example, Figure 4 The eigenvalues ​​of the array signal covariance matrix are sorted in descending order, with the first two eigenvalues ​​being non-zero and the subsequent eigenvalues ​​being zero. Therefore, it can be estimated that there are multiple targets at two different distances in this scenario.

[0100] 3. Perform frequency domain analysis on the array signal Z(t), i.e., use Discrete Fourier Transform, and find the frequency values ​​f1, ..., f2 corresponding to the K largest spectral peaks in the form of a spectrum graph, based on the number of targets K. k These frequency values ​​are rough estimates of the intermediate frequency (IF) values.

[0101] 4. Select 16 frequency points at equal intervals of Δf2 = Δf / 16 near the intermediate frequency signal obtained by the FFT-based target position estimation method. Use the linear combination of these 16 frequency points to reconstruct the original signal and observe the weight of different frequency points. The frequency points with larger weights will be determined as the final intermediate frequency values.

[0102] Construct a signal vector matrix F of size 256×16:

[0103]

[0104] Each row vector of the matrix represents a signal vector established by 16 frequency points, and each column vector represents 256 sampling points within one period.

[0105] Since 16 frequency points are used to reconstruct the original signal, the sparse basis matrix of the radar received signal can be expressed as:

[0106]

[0107] To solve for the sparse basis matrix, we construct the following unconstrained optimization problem:

[0108] min||Fx-S||2+λ||x||1, λ=1 (14)

[0109] In the formula, S is a 256-dimensional column vector, representing the signal received by an array element within one period:

[0110]

[0111] Specifically, there are three steps:

[0112] A. Use the sparse reconstruction-based super-resolution distance estimation model to sparse the frequency points and construct the corresponding F and S matrices;

[0113] B. According to the relevant theories of convex optimization, the optimization problem is an unconstrained convex optimization problem, which can be solved using the cvx toolbox in MATLAB.

[0114] C. Observe the solution results and find the frequency components that have a greater impact on the signal.

[0115] Figure 5 This is the solution to the sparse matrix obtained from the first array element. It can be seen that points 12 and 13 contribute the most to the corresponding frequencies, with corresponding weights of 3.7745 and 1.63011, respectively. Calculations were performed on data obtained from different antenna elements to obtain solutions to the sparse matrix, and it was found that most solutions have… Figure 5 The properties of. Figure 6 and Figure 7 These represent the peak and second-highest points of the solution for the sparse matrix corresponding to the 86 antennas. It can be seen that most peak points are located at point 12, and most second-highest points are located at point 13. Therefore, this invention selects the frequency points corresponding to points 12 and 13 to reconstruct the original signal, with corresponding frequency values ​​of 4.3203MHz and 4.3223MHz, respectively. The target distances obtained at these two points are r1 = 8.20457897602106m and r2 = 8.208288098523790m, respectively. The radar resolution at this point is less than 0.0037 meters, enabling precise positioning in the range dimension.

[0116] When reconstructing the data using the frequencies of the 12th and 13th points, the resulting error e is expressed as follows:

[0117] e = ||Fx-S||2-||Fm-S||2 (16)

[0118] Where x is a solution to the sparse matrix, and m takes the values ​​of the sparse matrix at points 12 and 13, with all other values ​​being zero. That is, m = [0…0 x 12 x 13 0…0] T F is the matrix corresponding to equation (12), and S is the observation data of the antenna in one period. The magnitude of e varies with the antenna elements as follows: Figure 8As shown in the figure, most of the error values ​​are near 0, with only a small number of points having larger error values. Therefore, it can be considered that frequency points 12 and 13 can reconstruct the information well, indicating that two distance values ​​for the target can be obtained at these two frequency points. When estimating the target distance, the idea of ​​sparse reconstruction was adopted. A sparse matrix was established based on the coarse frequency measurement, improving the accuracy of the mid-frequency measurement and achieving super-resolution positioning in ranging.

[0119] 5. Estimating the target distance by combining the relationship between intermediate frequency and target distance, the formula for frequency-modulated continuous wave ranging is as follows:

[0120]

[0121] Where R0 is the measured one-way distance value, f IF This represents the intermediate frequency (IF) after mixing the transmitted and received signals. In cases of undersampling, the sampling frequency should be added to the negative frequency to eliminate the range ambiguity caused by undersampling. The previous step yielded two frequency points corresponding to the reconstructed signal, corresponding to 4.3203MHz and 4.3223MHz. The calculated target distances at these two points are r1 = 8.20457897602106m and r2 = 8.208288098523790m, respectively. At this point, the radar resolution is less than 0.0037 meters, enabling precise positioning in the range dimension.

[0122] 6. When estimating the number of targets, the covariance matrix of the received array signal has been obtained and its eigenvalues ​​have been decomposed. Based on the eigenvalue decomposition results, the noise subspace of the array signal and the steering vector related to the target distance and angle are obtained. The target distance is known through the FFT algorithm. Since the steering vector is orthogonal to the noise subspace, the spectral function is constructed as follows:

[0123]

[0124] Within the angle space θ∈[-50°, 50°], calculate the value of the spectral function. If the target angle is found, the spectral function will show a clear spectral peak. By finding the θ value corresponding to the very clear spectral peak, the estimated value of the incoming wave direction can be obtained.

[0125] Figure 9 and Figure 10 To generate spatial spectral images at estimated distances r1 and r2, two targets exist on circles at distances r1 and r2 from the origin, respectively. When estimating the target angles, a direction matrix closely related to practical applications and applicable to both far-field and near-field conditions is established. The peak search concept from the MUSIC algorithm is employed to accurately estimate the target angles.

[0126] 7. Determine the target location and number of targets by combining all estimated values. Figure 11 This is a polar coordinate diagram of the detected target object position provided in an embodiment of the present invention, with a total of 4 targets.

[0127] This invention employs a low-complexity algorithm to achieve super-resolution positioning of objects, thereby improving the resolution of the FMCW signal reflection positioning system and demonstrating good practical results.

Claims

1. A method for multi-target super-resolution positioning of a frequency-modulated continuous wave radar, characterized in that, include: The number of targets K is determined by the number of eigenvalues ​​in the covariance matrix of the radar array signal. Based on the frequency domain transformation of the radar array signal to obtain the corresponding spectrum, the frequency values ​​corresponding to the K largest spectral peaks are found according to the number of targets K, and these frequency values ​​are used as the rough estimated intermediate frequency values. In the neighborhood of the intermediate frequency signal corresponding to the roughly estimated intermediate frequency value, multiple frequency points are selected at equal intervals of a specified size. The original signal is reconstructed using a linear combination of the multiple frequency points, specifically including: Based on the multiple frequency points, an F matrix and an S matrix are constructed. Each row vector of the F matrix represents the signal vector established at each frequency point, and each column vector represents all sampling points within one period. The S matrix represents the signal received by an element in the antenna array within one period. A sparse basis matrix for receiving radar array signals is established using each frequency point. An unconstrained convex optimization problem equation is established based on the F matrix and S matrix to solve the sparse basis matrix and reconstruct the original received signal. Calculate the weight of each frequency point, and take the frequency points with a weight greater than the threshold as the final intermediate frequency value; The distance of the target relative to the center O of the antenna array is calculated based on the final intermediate frequency. Based on the eigenvalues ​​of the covariance matrix of the radar array signal, the noise subspace of the radar array signal and the steering vector related to the target distance and angle are determined. A MUSIC spectrum function is constructed. The value of the MUSIC spectrum function is calculated along the circumference with a specified step size, starting from the y-axis of the rectangular coordinate system established with the antenna array center O as the origin. If the MUSIC spectrum function has a spectral peak, the angle of the echo signal direction corresponding to the spectral peak relative to the positive y-axis is used as the estimated value of the target echo signal direction. The position of each target is determined based on the distance of each target relative to the center O of the antenna array and the estimated direction of the corresponding target echo signal.

2. The method according to claim 1, characterized in that, The radar array signal is obtained by determining a time point in a linear frequency modulation period of the radar array signal A corresponding direction matrix The vector in the direction matrix is a steering vector in the direction, wherein is a steering vector in the direction, wherein is an angle between a line connecting the target to the center O of the antenna array and a y-axis of a rectangular coordinate system established with the center O as the origin, and then a receiving signal model is established based on the distance of the target to the center O of the antenna array, the angle , an antenna aperture L, and a number Na of antenna elements in the antenna array, and the received radar array signal is established based on the receiving signal model.​ 3. The method according to claim 2, characterized in that, The number of targets K is determined by the number of eigenvalues ​​in the covariance matrix of the radar array signal, specifically including: Arrange all eigenvalues ​​of the covariance matrix of the radar array signal in descending order. When there is no noise in the radar array signal, take the number of non-zero eigenvalues ​​as the target number K. When there is noise in the radar array signal, take a specified number of non-zero eigenvalues ​​from front to back in the descending order of all eigenvalues, and take the number of these non-zero eigenvalues ​​as the target number K.

4. A device for super-resolution localization of multiple targets using frequency-modulated continuous wave radar, characterized in that, include: The target quantity determination module determines the number of targets K based on the number of eigenvalues ​​in the covariance matrix of the radar array signal. The intermediate frequency rough estimation module obtains the corresponding spectrum by performing frequency domain transformation on the radar array signal, finds the frequency values ​​corresponding to the K largest spectral peaks based on the number of targets K, and uses these frequency values ​​as the rough estimated intermediate frequency values. The intermediate frequency (IF) precise estimation module selects multiple frequency points at equal intervals of a specified size in the neighborhood of the IF signal corresponding to the roughly estimated IF frequency value, and reconstructs the original signal using a linear combination of the multiple frequency points. Specifically, this includes: Based on the multiple frequency points, an F matrix and an S matrix are constructed. Each row vector of the F matrix represents the signal vector established at each frequency point, and each column vector represents all sampling points within one period. The S matrix represents the signal received by an element in the antenna array within one period. A sparse basis matrix for receiving radar array signals is established using each frequency point. An unconstrained convex optimization problem equation is established based on the F matrix and S matrix to solve the sparse basis matrix and reconstruct the original received signal. Calculate the weight of each frequency point, and take the frequency points with a weight greater than the threshold as the final intermediate frequency value; The target range estimation module calculates the precise distance of the target relative to the center O of the antenna array based on the final intermediate frequency. The target direction estimation module determines the noise subspace of the radar array signal and the steering vector related to the target distance and angle based on the eigenvalues ​​of the covariance matrix of the radar array signal. It constructs a MUSIC spectrum function and calculates the value of the MUSIC spectrum function along the circumference with a specified step size, starting from the y-axis of a rectangular coordinate system established with the antenna array center O as the origin. If the MUSIC spectrum function has a spectral peak, the angle of the echo signal direction corresponding to the spectral peak relative to the positive y-axis is used as the estimated value of the target echo signal direction. The target position indication module determines and indicates the position of each target based on the estimated distance of each target relative to the center O of the antenna array and the direction of the corresponding target echo signal.

5. The apparatus according to claim 4, characterized in that, The method for acquiring the radar array signal is as follows: determining the time within the linear frequency modulation period of the radar array signal. Corresponding direction matrix Direction matrix vectors in That is A guide vector in the direction, where, For the goal The angle between the line connecting to the center O of the antenna array and the y-axis of the Cartesian coordinate system established with O as the origin, and then based on the target... Distance to the center O of the antenna array Angle Given the antenna aperture L and the number of antenna elements Na in the antenna array, establish a received signal model, and then establish the received radar array signal based on the received signal model.

6. The apparatus according to claim 5, characterized in that, The target quantity determination module performs the following steps: Arrange all eigenvalues ​​of the covariance matrix of the radar array signal in descending order. When there is no noise in the radar array signal, take the number of non-zero eigenvalues ​​as the target number K. When there is noise in the radar array signal, take a specified number of non-zero eigenvalues ​​from front to back in the descending order of all eigenvalues, and take the number of these non-zero eigenvalues ​​as the target number K.

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