Multi-channel radar foresight imaging method based on sparse and weighted low rank

Abstract

The invention discloses a multi-channel radar foresight imaging method based on sparse and weighted low rank, and solves the problem that the foresight super-resolution imaging effect is limited in a complex imaging scene in the prior art. The method comprises the following steps: establishing an echo signal model in a multi-channel radar single-transmitting single-receiving mode, and obtaining an echo signal corresponding to each target; carrying out pulse compression and correction processing, representing a two-dimensional echo matrix, and carrying out weighting processing on a target signal matrix in the two-dimensional echo matrix to obtain a weighted target signal matrix with a low-rank characteristic; obtaining a foresight imaging model according to the sparsity of the target in the echo signal model and the low-rank characteristic of the weighted target signal matrix; solving the foresight imaging model based on ALM under an ADMM framework to obtain a reconstructed foresight high-resolution image; according to the method, the high-quality and high-resolution reconstructed foresight high-resolution image is obtained through sparse and weighted low-rank dual constraints.

Description

Technical Field

[0001] The present invention relates to the technical field of radar imaging, and in particular to a multi-channel radar forward-looking imaging method based on sparse and weighted low rank. Background Art

[0002] Radar forward-looking imaging can provide the refined electromagnetic scattering characteristics of the targets directly in front of a moving platform, and has various applications in military and civilian fields, including terrain mapping, autonomous driving, precision guidance, etc., and has become a hot and difficult point in the current research on radar imaging technology. In recent years, small moving platforms such as unmanned aerial vehicles and missiles carrying multi-channel radar high-resolution imaging systems have become an important direction in the development of modern radar imaging modes. Compared with traditional single-channel radars, multi-channel radars have a higher spatial degree of freedom, and because they can independently emit electromagnetic waves, they show stronger initiative and autonomy in information acquisition. By adjusting parameters such as the carrier frequency and waveform of the signal, multi-channel radars can significantly improve the imaging performance of the system. In addition, considering that the targets of interest usually only occupy a small area in the entire imaging scene, this sparsity characteristic enables Compressed Sensing (CS) technology to be effectively applied to the reconstruction of high-resolution forward-looking images. Therefore, it becomes possible to use multi-channel radars combined with sparse reconstruction technology to provide forward-looking high-resolution images for small moving platforms.

[0003] However, in multi-channel radar forward-looking sparse imaging, data extrapolation is involved, so there are also many new problems and challenges in the design of super-resolution imaging methods. As the signal-to-noise ratio is a key factor affecting the performance of multi-channel radar forward-looking super-resolution imaging, it is crucial to explore methods for suppressing strong noise. The insufficient sparsity of the noise distribution will have a significant impact on the reconstruction of target information, which poses a challenge to the technology of using sparse reconstruction to achieve forward-looking super-resolution imaging. Currently, the research methods for strong noise in radar imaging in the literature are divided into two categories. The first category of methods preprocess the echo by denoising. This category of methods extracts the signal in the radar echo using the characteristics of the radar signal to separate the target signal from the noise, but the suppression ability of this category of methods is very limited. The second category of methods is to add additional constraints in addition to sparsity, and among them, low-rank constraint is the most widely used method. However, in complex imaging scenarios, the low-rank characteristics of the data matrix are often not obvious, which limits the super-resolution imaging effect of directly applying low-rank constraints. Therefore, how to enhance the low-rank characteristics of the constraint matrix is crucial for improving the imaging quality. Summary of the Invention

[0004] The present invention provides a multi-channel radar forward-looking imaging method based on sparsity and weighted low rank, which solves the problem in the prior art that the super-resolution imaging effect is limited in complex imaging scenarios, and realizes the suppression of noise through dual constraints of sparsity and weighted low rank, so as to obtain a high-quality and high-resolution reconstructed forward-looking high-resolution image.

[0005] The present invention provides a multi-channel radar forward-looking imaging method based on sparsity and weighted low rank, and the method includes:

[0006] Establish an echo signal model in the single-transmission and single-reception mode of the multi-channel radar, and simultaneously obtain the echo signals corresponding to each target by using this model;

[0007] Perform signal compression and correction processing on the echo signals to obtain corrected echo signals;

[0008] Represent the corrected echo signals as a two-dimensional echo matrix, and perform weighting processing on the target signal matrix in the two-dimensional echo matrix to obtain a weighted target signal matrix with low-rank characteristics; wherein, the two-dimensional echo matrix includes: a target signal matrix and a noise matrix;

[0009] According to the sparsity of the targets in the echo signal model and the low-rank characteristics of the weighted target signal matrix, obtain a forward-looking imaging model;

[0010] Solve the forward-looking imaging model based on ALM in the ADMM framework to obtain a reconstructed forward-looking high-resolution image.

[0011] In a possible implementation manner, the obtaining of the echo signals corresponding to each target by using this model includes:

[0012] Determine the distance between target p and the nth antenna element according to the echo signal model at slow time t;

[0013] Perform coherent demodulation on the target by using the transmitted signal and the distance to obtain the echo signals corresponding to each target.

[0014] In a possible implementation manner, the echo signals are expressed as:

[0015]

[0016] wherein, C represents the complex scattering coefficient of the target; w r represents the range window function; τ represents the fast time; R(t) represents the distance from target P to the nth array antenna element at slow time t; c represents the speed of light; γ represents the frequency modulation slope; s(τ, t) represents the echo signal at fast time τ and slow time t.

[0017] In a possible implementation, the signal compression and correction processing of the echo signal to obtain the corrected echo signal includes:

[0018] Performing range-direction pulse compression processing on the echo signal to obtain a pulse-compressed echo signal;

[0019] Constructing a range migration correction factor corresponding to the pulse-compressed echo signal in the frequency domain, and performing motion compensation and correction on the pulse-compressed echo signal to obtain the corrected echo signal.

[0020] In a possible implementation, the weighted processing of the target signal matrix in the two-dimensional echo matrix to obtain a weighted target signal matrix with low-rank characteristics includes:

[0021] Using an adaptive algorithm based on the linearly constrained minimum variance criterion under the ADMM framework to solve the covariance matrix of the pulse-compressed echo signals corresponding to each array element in the echo signal model, and obtaining the weighted weights;

[0022] Using the weighted weights to weight the elements in the target signal matrix to obtain a weighted target signal matrix with low-rank characteristics.

[0023] In a possible implementation, the weighted weights are expressed as:

[0024] W = μ(S rc S rc H ) -1 ;

[0025] where μ represents a constant factor; S rc represents the two-dimensional echo matrix; (·) H represents the conjugate transpose rank of the matrix.

[0026] In a possible implementation, the corrected echo signal is expressed as:

[0027]

[0028] where B represents the bandwidth; R(t) represents the distance from the target P to the nth array antenna element at the slow time t; c represents the speed of light; C represents the complex scattering coefficient of the target; represents the Doppler frequency caused by the equivalent motion of the array antenna; t represents the slow time; exp(·) represents the exponential function; represents the Doppler frequency caused by the platform motion; τ represents the fast time; S rc (τ, t) represents the corrected echo signal at the fast time τ and the slow time t.

[0029] In a possible implementation, the two-dimensional echo matrix is expressed as:

[0030] S rc = Y + E = FX + E;

[0031] where Y represents the target signal matrix; E represents the noise matrix; F represents the dictionary matrix; and X represents the reconstructed forward-looking high-resolution image.

[0032] In a possible implementation, the forward-looking imaging model is expressed as:

[0033]

[0034] where W represents the weighting weight; F represents the dictionary matrix; X represents the reconstructed forward-looking high-resolution image; ||·|| * represents the nuclear norm; λ 1 is the first regularization parameter; ||·|| 1 represents the l 1 norm; λ 2 is the second regularization parameter; S rc represents the two-dimensional echo matrix; ||·|| F represents the F norm; ||WFX|| * represents the nuclear norm of the weighted matrix WFX.

[0035] In a possible implementation, solving the forward-looking imaging model based on ALM in the ADMM framework to obtain the reconstructed forward-looking high-resolution image includes:

[0036] Converting the forward-looking imaging model into the representation form of the Lagrangian function to obtain the first conversion result;

[0037] Alternately updating multiple variables in the first conversion result according to the ADMM method until the termination condition is satisfied;

[0038] Modifying the first conversion result according to the values of multiple variables under the termination condition to obtain the second modification result;

[0039] Solving the unknowns in the second modification result to obtain the reconstructed forward-looking high-resolution image.

[0040] One or more technical solutions provided in the present invention have at least the following technical effects or advantages:

[0041] In the present invention, by performing a weighting process on the target signal matrix in the two-dimensional echo matrix, a weighted target signal matrix with low-rank characteristics is obtained. By weighting the target signal matrix, its low-rank characteristics are effectively enhanced; through the dual constraints of the sparsity of the target and the low-rank characteristics of the weighted target signal matrix, noise suppression is achieved, and a high-quality and high-resolution reconstructed forward-looking high-resolution image is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flowchart of the steps of the multi-channel radar forward-looking imaging method based on sparsity and weighted low-rank provided by an embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of the forward-looking imaging observation geometry in the "single transmit and single receive" mode of a small moving platform-mounted multi-channel radar provided by an embodiment of the present invention;

[0044] Figure 3a and Figure 3b It is a curve of the contribution ratio of the maximum pixel to the total imaging energy provided by an embodiment of the present invention;

[0045] Figure 4 It is a schematic diagram of the eigenvalue change before and after weighting of the target signal matrix provided by an embodiment of the present invention;

[0046] Figure 5 It is a schematic diagram of the scattering point distribution of the simulation experiment provided by an embodiment of the present invention;

[0047] Figure 6 It is a schematic diagram of the radar platform parameters of the simulation experiment provided by an embodiment of the present invention;

[0048] Figure 7a It is an imaging diagram of the scattering points in the same range cell obtained by using the real beam method provided by an embodiment of the present invention;

[0049] Figure 7b It is an imaging diagram of the scattering points in the same range cell obtained by using the traditional CS imaging method provided by an embodiment of the present invention;

[0050] Figure 7c It is an imaging diagram of the scattering points in the same range cell obtained by using the sparse and low-rank imaging method provided by an embodiment of the present invention;

[0051] Figure 7d It is an imaging diagram of the scattering points in the same range cell obtained by using the method of the present invention provided by an embodiment of the present invention;

[0052] Figure 8 It is a schematic diagram of the measured experimental scene provided by an embodiment of the present invention;

[0053] Figure 9 It is a schematic diagram of the radar platform parameters of the measured experiment provided by an embodiment of the present invention;

[0054] Figure 10a This is the imaging result diagram of the real beam method provided by the embodiment of the present invention;

[0055] Figure 10b This is the imaging result diagram of the traditional CS method under low SNR provided by the embodiment of the present invention;

[0056] Figure 10c This is the imaging result diagram of the sparse and low-rank method under low SNR provided by the embodiment of the present invention;

[0057] Figure 10d This is the imaging result diagram of the present invention provided by the embodiment of the present invention. Detailed implementation manners

[0058] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0059] The present invention provides a multi-channel radar forward-looking imaging method based on sparsity and weighted low rank. Refer to Figure 1 , and this method includes the following steps S101 to S105.

[0060] S101. Establish an echo signal model in the single-transmission and single-reception mode of a multi-channel radar, and at the same time use this model to obtain the echo signal s(τ, t) corresponding to each target;

[0061] Specifically, in step S101, using this model to obtain the echo signal corresponding to each target includes the following steps S1011 to S1012.

[0062] S1011. Determine the distance R(t) between the target p and the nth antenna element in the echo signal model at the slow time t;

[0063] S1012. Coherently demodulate the target using the transmitted signal s(τ) and the distance R(t) to obtain the echo signal s(τ, t) corresponding to each target.

[0064] Exemplarily, refer to Figure 2 , Figure 2 This is the schematic diagram of the forward-looking imaging observation geometry in the "single-transmission and single-reception" mode of a multi-channel radar carried by a small moving platform provided by the implementation of the present invention.

[0065] On a radar platform with a height of H, N transmit-receive integrated antenna elements are uniformly arranged at equal intervals of d, and the length of the array antenna is L. Among them, the radar platform moves at a speed of v, and the N antenna elements are switched at intervals of Pulse Repetition Interval (PRI), and sequentially transmit signals and receive echoes, that is, the "single transmit and single receive" operating mode.

[0066] Assume that there is a target P(x 0 ,y 0 ,0) directly in front of the radar platform. Then, the distance R(t) from the target P to the nth array antenna element at slow time t can be approximately expressed as:

[0067]

[0068] Among them, t represents the slow time; x 0 , y 0 respectively represent the abscissa and ordinate of the target P; v a = d / PRI is the equivalent azimuth motion speed; is the slant range from the target P to the center of the radar antenna.

[0069] Assume that the radar emits a Linear Frequency Modulation (LFM) signal s(τ), which is specifically expressed as:

[0070]

[0071] Among them, τ represents the fast time, w r represents the range window function, f c represents the carrier frequency, and γ represents the frequency modulation slope.

[0072] S102. Perform signal compression and correction processing on the echo signal s(τ,t) to obtain the corrected echo signal S rc (τ,t);

[0073] Specifically, in step S102, performing signal compression and correction processing on the echo signal s(τ,t) to obtain the corrected echo signal S rc (τ,t) includes the following steps S1021 to S1022.

[0074] S1021. Perform range-direction pulse compression processing on the echo signal s(τ,t) to obtain the pulse-compressed echo signal S rc1 (τ,t);

[0075] S1022. Construct a range migration correction factor corresponding to the pulse-compressed echo signal S rc (τ,t) in the frequency domain, and for the pulse-compressed echo signal Src1 Perform motion compensation and correction on (τ, t) to obtain the corrected echo signal S rc (τ, t).

[0076] Here, the echo signal s(τ, t) is expressed as:

[0077]

[0078] where C represents the complex scattering coefficient of the target; w r represents the range window function; τ represents the fast time; R(t) represents the distance from the target P to the nth array antenna element at the slow time t; c represents the speed of light; γ represents the frequency modulation slope.

[0079] Here, the corrected echo signal S rc (τ, t) is expressed as:

[0080]

[0081] where B represents the bandwidth; R(t) represents the distance from the target P to the nth array antenna element at the slow time t; c represents the speed of light; C represents the complex scattering coefficient of the target; represents the Doppler frequency caused by the equivalent motion of the array antenna; t represents the slow time; exp(·) represents the exponential function; represents the Doppler frequency caused by the platform motion; τ represents the fast time.

[0082] Exemplarily, perform pulse compression processing on the echo signal s(τ, t), and the echo S rc1 (τ, t) after range pulse compression can be expressed as:

[0083]

[0084] where B is the bandwidth and c is the speed of light.

[0085] Construct a range migration correction factor for the echo signal after pulse compression in the frequency domain to obtain the corrected echo signal S rc (τ, t) to eliminate the influence of platform motion on the echo.

[0086] S103. Represent the corrected echo signal S rc (τ, t) as a two-dimensional echo matrix S rc , and perform weighting processing on the target signal matrix in the two-dimensional echo matrix S rc to obtain a weighted target signal matrix with low-rank characteristics; where the two-dimensional echo matrix S rc includes: a target signal matrix and a noise matrix;

[0087] Here, the two-dimensional echo matrix S rcExpressed as:

[0088] S rc = Y + E = FX + E (6)

[0089] Wherein, Y represents the target signal matrix; E represents the noise matrix; F represents the dictionary matrix; X represents the reconstructed forward-looking high-resolution image.

[0090] Specifically, in step S103, the target signal matrix in the two-dimensional echo matrix S rc is weighted to obtain a weighted target signal matrix with low-rank characteristics, including the following steps S1031 to S1032.

[0091] S1031, using the Alternating Direction Method of Multipliers (ADMM) to frame an adaptive algorithm based on the linearly constrained minimum variance criterion, and solving the covariance matrix of the pulse compression echo signal S rc1 (τ, t) corresponding to each array element in the echo signal model to obtain the weighted weights;

[0092] Here, the weighted weights are expressed as:

[0093] W = μ(S rc S rc H ) -1 (7)

[0094] Wherein, μ represents a constant factor; S rc represents the two-dimensional echo matrix; (·) H represents the conjugate transpose rank of the matrix.

[0095] S1032, using the weighted weights to weight the elements in the target signal matrix to obtain a weighted target signal matrix.

[0096] Exemplarily, after motion compensation, the two-dimensional echo matrix S rc after pulse compression is obtained, wherein, Y ∈ C N×M and E ∈ C N ×M are the signal matrix and the noise matrix respectively, is the dictionary matrix, is the reconstructed forward-looking high-resolution image.

[0097] Adaptive Digital Beamforming (ADBF) is a technique where, when an adaptive antenna array is in a complex interference environment, according to different optimization criteria and using corresponding adaptive algorithms, the outputs of each array element are weighted and summed. This makes the array pattern achieve maximum gain in the desired direction and generate nulls in the interference directions, thereby enhancing the useful signal and suppressing interference.

[0098] Among them, the weighted weights are solved based on the Linearly Constrained Minimum Variance (LCMV) criterion as follows:

[0099]

[0100] Among them, R X is the covariance matrix of the two-dimensional echo matrix S rc after pulse compression, a represents the steering vector of the desired signal, and w represents the adaptive weight to be solved.

[0101] In the multi-channel radar forward-looking imaging of the present invention, the radar beam always points to the target, so the desired steering vector is the identity matrix, and the weighted weight in the present invention is formula (7).

[0102] S104. According to the sparsity of the target in the echo signal model and the low-rank property of the weighted target signal matrix, a forward-looking imaging model is obtained;

[0103] Here, the forward-looking imaging model is expressed as:

[0104]

[0105] Among them, W represents the weighted weight; F represents the dictionary matrix; X represents the reconstructed forward-looking high-resolution image; ||·|| * represents the nuclear norm; λ 1 is the first regularization parameter; ||·|| 1 represents the l 1 norm; λ 2 is the second regularization parameter; S rc represents the two-dimensional echo matrix; ||·|| F represents the F norm; ||WFX|| * represents the nuclear norm of the weighted matrix WFX, ||WFX|| * :=Σ i σ i σ i represents the i-th singular value of the weighted matrix WFX.

[0106] Exemplarily, in forward-looking image reconstruction, the low-rank property of the weighted target signal matrix Y and the sparse property of the target are utilized to improve the performance of forward-looking imaging. When applying the sparse and weighted low-rank property constraints, the forward-looking imaging model is as follows:

[0107]

[0108] where rank(·) represents the rank function, ||·|| 0 denotes the l 0 norm; λ 1 is the first regularization parameter; λ 2 is the second regularization parameter. λ 1 is used to balance the l 0 norm and the rank function of the weighted matrix WY, and λ 2 is a constant related to the noise.

[0109] Considering that the l 0 norm and the rank(·) function are usually NP-hard problems, the l 0 norm is convexly relaxed to the l 1 norm, and the rank(·) function is convexly relaxed to the nuclear norm. Then, the forward-looking imaging problem with joint constraints can be represented by the forward-looking imaging model, expressed as Equation (9).

[0110] S105. Solve the forward-looking imaging model based on the Augmented Lagrangian Method (ALM) in the ADMM framework to obtain the reconstructed forward-looking high-resolution image.

[0111] Specifically, in step S105, solving the forward-looking imaging model based on ALM in the ADMM framework to obtain the reconstructed forward-looking high-resolution image includes the following steps S1051 to S1054.

[0112] S1051. Convert the forward-looking imaging model into the representation form of the Lagrangian function to obtain the first conversion result;

[0113] S1052. Alternately update multiple variables in the first conversion result according to the ADMM method until the termination condition is satisfied;

[0114] S1053. Modify the first conversion result according to the values of multiple variables under the termination condition to obtain the second modified result;

[0115] S1054. Solve the unknowns in the second modified result to obtain the reconstructed forward-looking high-resolution image.

[0116] Exemplarily, for the convenience of calculation, first let G 1 -X = 0, G 2- If -X = 0, the ADMM form of the optimization problem is expressed as: s.t.

[0117]

[0118] Then, the above formula is expressed in the form of an augmented Lagrangian function:

[0119]

[0120] where Q 1 , Q 2 are Lagrange multiplier matrices, and u 1 , u 2 are penalty factors.

[0121] Use the ADMM method to alternately update the variables G 1 , G 2 , X, Q 1 and Q 2 , that is, while optimizing one variable, keep the other variables unchanged until a specific convergence condition is reached.

[0122] Update and iteratively solve the values of each variable. The (k + 1)-th iteration solution results of the variables G 1 , G 2 , and X are:

[0123]

[0124] where soft(·) represents the soft threshold function enhanced by the l 1 norm sparse regularization, and soft(Θ,α) = max(1 - α / |Θ(i,j)|, 0)·Θ(i,j), where Θ and α are a matrix and a constant respectively.

[0125] In addition, the Lagrange multiplier matrix and the penalty coefficient also need to be iteratively updated. The (k + 1)-th iteration result expressions of Q 1 k+1 , Q 2 k+1 , u 1 k +1 and u 2 k+1 are as follows:

[0126]

[0127] where ρ is the growth linear coefficient of u 1 and u 2 . The magnitude of ρ determines the speed of convergence, and ρ > 1.

[0128] By continuously iterating and solving until the termination condition is met, the image matrix X, that is, the reconstructed forward-looking high-resolution image, is finally obtained.

[0129] In the invention, the forward-looking image reflects the energy distribution of the target scattering field in the two-dimensional range-Doppler plane, and most of the energy is usually contributed by a few strong scattering centers. For example, in Figure 3a the automotive imaging case shown in, if all the pixels in the imaging plane are sorted and statistically analyzed according to the amplitude, it can be seen that the energy accounted for by the 1% largest pixels in the imaging plane exceeds 99% of the total energy, while the 10% largest pixels contribute almost all the energy (99.4%). Figure 3b Furthermore, the contribution ratio curve of the largest pixels to the total imaging energy is revealed, from which it can be clearly seen that the image usually has significant sparsity. This sparsity of the signal has great advantages for signal processing, which helps to improve the processing efficiency and imaging quality.

[0130] The low-rank property can be verified by the method of singular value decomposition, and the singular value distribution of the matrix can reflect whether it has the low-rank property. Therefore, the low-rank property can be verified by observing the decay of the singular values of the matrix before and after weighting. Figure 4 The scattering point models of one, two, and three ships are respectively given, as well as the corresponding singular value distribution results of the signal matrix. It can be observed from them that the singular value distribution of the original signal matrix shows a decaying trend, indicating that it has the low-rank property. However, it is worth noting that the descending curve of the singular values of the original signal matrix shows an upward-bending trend, which indicates that the decay rate of the singular values is relatively slow, especially when the number of targets in the scene increases. In contrast, after weighting the signal matrix by the proposed method, the decay rate of its singular values is significantly accelerated, and its descending curve becomes downward-bending, highlighting the low-rank property of the signal matrix. Therefore, the performance of forward-looking super-resolution imaging of the radar in a complex imaging field can be further improved by means of weighting the signal matrix.

[0131] Based on simulation and measured data experiments, the present invention is verified.

[0132] (1) Simulation conditions in the simulation experiment:

[0133] Please refer to Figure 5 , Figure 5 which is a schematic diagram of the distribution of ship targets in the simulation experiment provided by the implementation of the present invention. A forward-looking imaging geometric model of a multi-channel radar with "single transmit and single receive" is selected for the simulation experiment. There are 3 ship targets in the scene, and their scattering points are all distributed on the grid points. Each grid spacing in the range direction is 1 m, corresponding to the range resolution; each grid spacing in the azimuth direction is 4 m, corresponding to the azimuth resolution. Specific radar platform parameters are shown in Figure 6 .

[0134] The simulation content in the simulation experiment: To verify the anti-noise ability of the proposed imaging method, the super-resolution multiple was set to 8 times (i.e., the antenna length was 0.2 m), and Gaussian white noise was added to the radar echo to form data with a signal-to-noise ratio of 5 dB. The imaging results of the method of the present invention were compared with those of the real beam imaging method, the traditional CS imaging method, and the sparse and low-rank imaging method under strong noise conditions, as shown in Fig. 7.

[0135] From Figure 7a it can be seen that the scatterers at the same range cell coincide and cannot be distinguished. Therefore, the real beam method does not have the super-resolution imaging ability; from Figure 7b it can be seen that although the traditional CS imaging method can distinguish some targets, it still cannot obtain a satisfactory high-resolution image under strong noise conditions. Similarly, from Figure 7c it can be seen that due to its limited noise suppression ability, the traditional sparse and low-rank imaging method can only reconstruct some targets and has a defocusing problem in a complex imaging environment. On the contrary, even at low SNR, the imaging results of the method proposed in the present invention show that the targets are clearly distinguishable, as Figure 7d shown, which demonstrates the superior performance of the proposed method.

[0136] (2) Field experiment, field conditions:

[0137] Please refer to Figure 8 , Figure 8 which is a schematic diagram of the field experiment scenario provided by the implementation of the present invention. The experimental equipment is an AWR2243 cascaded radar. The experimental site is located in a parking lot of Xidian University. The targets are two vehicles. The specific radar operating parameters are shown in Figure 9 .

[0138] Field experiment, simulation content:

[0139] The imaging results of the method of the present invention were compared with those of the real beam imaging method, the traditional CS imaging method, and the sparse and low-rank imaging method under strong noise conditions, as shown in Fig. 10.

[0140] From Figure 10a it can be seen that the two cars are fused together in the imaging result of the real beam method and cannot be distinguished at all. From Figure 10b and Figure 10c it can be seen that at low SNR, the images generated by the traditional CS method and the sparse and low-rank method are difficult to distinguish the two cars, and a large number of false targets appear. The imaging method proposed in the present invention can produce satisfactory imaging results, and the two cars are clearly distinguishable, as Figure 10dAs shown. The actual measurement experiments have proved that the proposed imaging method not only has super-resolution imaging ability, but also has strong anti-noise ability.

[0141] In summary, the feasibility of the present invention has been proved by experiments based on simulation and actual measurement data.

[0142] Aiming at the problem of low resolution of the existing forward-looking imaging method, the present invention proposes a multi-channel radar forward-looking imaging method based on sparse and weighted low rank, which improves the imaging resolution and has strong noise robustness. By analyzing the forward-looking imaging scene and the echo matrix respectively, the present invention obtains the characteristic that the targets in the imaging scene are sparsely distributed, and uses weighting to enhance the low-rank characteristic of the signal matrix in the echo matrix. Through the dual constraints of sparse and weighted low rank, a forward-looking super-resolution imaging model with noise robustness is obtained.

[0143] The various embodiments in this specification are described in a progressive manner. For the same or similar parts between the various embodiments, reference can be made to each other. The key point of each embodiment is to illustrate the differences from other embodiments. All or part of the present invention can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld devices or portable devices, tablet devices, mobile communication terminals, multi-processor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and so on.

[0144] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the present invention; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the present invention.

Claims

1. A multi-channel radar forward imaging method based on sparse and weighted low rank, characterized in that: include: Establish the echo signal model of multi-channel radar in single-transmit and single-receive mode, and use the model to obtain the echo signal corresponding to each target; Performing signal compression correction processing on the echo signal to obtain a corrected echo signal; The corrected echo signal is represented as a two-dimensional echo matrix, and a target signal matrix in the two-dimensional echo matrix is ​​weighted to obtain a weighted target signal matrix with a low-rank characteristic; wherein the two-dimensional echo matrix includes: a target signal matrix and a noise matrix; According to the sparsity of the target in the echo signal model and the low-rank characteristic of the weighted target signal matrix, a forward-looking imaging model is obtained; The forward-looking imaging model is solved based on ALM under the ADMM framework to obtain a reconstructed forward-looking high-resolution image.

2. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 1, characterized in that: The method of obtaining the echo signals corresponding to each target by using the model includes: Determine the distance between the target p and the nth antenna array element in the echo signal model at the slow time t; The target is coherently demodulated using the transmitted signal and the distance to obtain an echo signal corresponding to each target.

3. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 2, characterized in that: The echo signal is expressed as: Where C represents the complex scattering coefficient of the target; w r represents the range window function; τ represents the fast time; R(t) represents the distance from the target P to the nth array antenna element at the slow time t; c represents the speed of light; γ represents the frequency modulation slope; s(τ,t) represents the echo signal when the fast time is τ and the slow time is t.

4. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 1, characterized in that: The performing signal compression correction processing on the echo signal to obtain a corrected echo signal includes: Performing range-direction pulse compression processing on the echo signal to obtain a pulse compression echo signal; A range movement correction factor corresponding to the pulse compression echo signal is constructed in the frequency domain, and motion compensation correction is performed on the pulse compression echo signal to obtain a corrected echo signal.

5. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 4 is characterized in that: The step of performing weighted processing on the target signal matrix in the two-dimensional echo matrix to obtain a weighted target signal matrix with a low rank characteristic includes: Using an adaptive algorithm based on a linear constrained minimum variance criterion under an ADMM framework, the covariance matrix of the pulse compression echo signal corresponding to each array element in the echo signal model is solved to obtain a weighted weight value; The elements in the target signal matrix are weighted using the weighted values ​​to obtain a weighted target signal matrix with a low rank characteristic.

6. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 5, characterized in that: The weighted value is expressed as: Where μ represents a constant factor; S rc represents a two-dimensional echo matrix; (·) H Represents the conjugate transpose rank of a matrix.

7. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 4, characterized in that: The corrected echo signal is expressed as: Wherein, B represents bandwidth; R(t) represents the distance from target P to the nth array antenna element at slow time t; c represents the speed of light; C represents the complex scattering coefficient of the target; represents the Doppler frequency caused by the equivalent motion of the array antenna; t represents the slow time; exp(·) represents the exponential function; represents the Doppler frequency caused by platform motion; τ represents fast time; S rc (τ, t) represents the corrected echo signal when the fast time is τ and the slow time is t.

8. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 1, characterized in that: The two-dimensional echo matrix is ​​expressed as: S rc =Y+E=FX+E; Among them, Y represents the target signal matrix; E represents the noise matrix; F represents the dictionary matrix; and X represents the reconstructed forward-looking high-resolution image.

9. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 1, characterized in that: The forward-looking imaging model is expressed as: Where W represents the weighted value; F represents the dictionary matrix; X represents the reconstructed front-view high-resolution image; ||·|| * represents the nuclear norm; λ1 is the first regularization parameter; ||·||1 represents the l1 norm; λ2 is the second regularization parameter; S rc represents a two-dimensional echo matrix; ||·|| F represents the F-norm; ||WFX|| * Represents the nuclear norm of the weighting matrix WFX.

10. The multi-channel radar forward imaging method based on sparse and weighted low rank according to claim 1, characterized in that: The forward-looking imaging model is solved based on the ALM under the ADMM framework to obtain a reconstructed forward-looking high-resolution image, including: Converting the forward-looking imaging model into a representation of a Lagrangian function to obtain a first conversion result; Alternately updating a plurality of variables in the first conversion result according to the ADMM method until a termination condition is met; Modifying the first conversion result according to the values ​​of the plurality of variables under the termination condition to obtain a second modified result; The unknown quantity in the second modification result is solved to obtain a reconstructed forward-looking high-resolution image.

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