Radar robust compressed sensing imaging method under grid mismatch

Abstract

The invention relates to the technical field of radar signals, in particular to a radar robust compressed sensing imaging method under grid mismatch, which comprises the following steps: acquiring MIMO radar time domain signals, constructing a radar imaging model, and setting initial parameters of the radar imaging model and initial parameters of a target; searching a column with the maximum correlation with the residual vector in the observation matrix through a plurality of iterations; storing the selected support set; estimating a complex scattering coefficient and horizontal and vertical coordinate values at the same time by using nonlinear least squares; performing residual error updating by using the estimated complex scattering coefficient and the horizontal and vertical coordinate values; when the residual value is smaller than the threshold value, iteration is stopped; and outputting the complex scattering coefficient and the coordinate of the target. According to the method, under the condition that prior distribution is not assumed, target complex scattering coefficient reconstruction and position coordinate estimation under MIMO radar grid mismatch are achieved at the same time.

Description

Technical Field

[0001] The present invention relates to the field of radar signal technology, and in particular to a radar robust compressed sensing imaging method under grid mismatch. Background Art

[0002] In recent years, sparse imaging based on compressed sensing (CS) has developed rapidly. Constructing the observation matrix in the imaging process is a necessary step for sparse imaging. It samples according to the preset discrete grid points and realizes the inversion of the imaging area based on the one-to-one correspondence between each grid point and the grid point. However, in actual situations, it is difficult for the real position of the target to fall on the grid points, that is, the grid mismatch problem, which causes the sparse imaging results to be defocused. The grid mismatch problem is common in CS imaging. The simplest solution is to refine the grid so that the grid points are close to the real position coordinates of the target. However, reducing the grid spacing will cause the isometric constraint characteristics of the observation matrix to fail and the solution efficiency to decrease.

[0003] Compressive Sensing-based Robust Off-the-grid StretchProcessing by Ilhan I et al., in which the mismatched grid error is a real number and the target scattering coefficient. The contradiction between the complex numbers leads to the fact that only the real part is taken during the solution process, which results in errors in the final solution result.

[0004] Parameter-refined OMP for Compressive Radar Imaging of Rotating Targets by Nguyen NH et al. The OMP method is used to solve the grid mismatch problem in compressive radar imaging of rotating targets, but this method only focuses on robust CS imaging of single-frequency radar.

[0005] The patent with publication number CN 118707518A obtains the array receiving element position error based on the array transmitting element position error estimation result and the scattering coefficient; when the target scattering coefficient change is less than a threshold, the iteration is stopped, thereby suppressing the imaging defocus problem; however, this method solves the element position mismatch problem and only focuses on the MIMO array element error, ignoring the influence of grid mismatch in CS imaging, that is, it cannot solve the grid error problem. Summary of the invention

[0006] In view of the shortcomings of the existing methods, the present invention solves the grid mismatch problem, that is, the problem of grid error when the target point is not on the preset grid point.

[0007] The technical solution adopted by the present invention is: a radar robust compressed sensing imaging method under grid mismatch comprises the following steps:

[0008] Step 1: Obtain the MIMO radar time domain signal, build a radar imaging model, and set the initial parameters of the radar imaging model and the initial parameters of the target;

[0009] As a preferred implementation manner of the present invention, the radar imaging model parameters include: residual, support set, and complex scattering coefficient.

[0010] As a preferred implementation of the present invention, the target initial parameters are the horizontal and vertical coordinates of the target.

[0011] Step 2: Search the column with the largest correlation with the residual vector in the observation matrix through several iterations;

[0012] As a preferred embodiment of the present invention, the formula for the column with the greatest correlation is:

[0013]

[0014] Among them, Λ [i-1] is the support set of the i-1th iteration, A is the observation matrix, and r is the residual vector.

[0015] Step 3: Save the selected support set;

[0016] As a preferred embodiment of the present invention, the formula of the selected support set is:

[0017] Λ [i] =Λ [i-1] ∪j [i] (2)

[0018] Among them, Λ [i-1] is the support set of the i-1th iteration, j [i] is the column with the highest correlation.

[0019] Step 4: Use nonlinear least squares to simultaneously estimate the complex scattering coefficient and the horizontal and vertical coordinate values;

[0020] As a preferred embodiment of the present invention, the formula for estimating the complex scattering coefficient and the horizontal and vertical coordinate values ​​is:

[0021]

[0022] in, and They are the current support set Λ [i] The corresponding complex scattering coefficient and position coordinates, f l is the center frequency of the lth pulse,

[0023] R tr(m,n,k) is the two-way distance from the mth transmitting element to the kth target and from the nth receiving element to the kth grid point.

[0024] Step 5: Update the residual using the estimated complex scattering coefficient and the horizontal and vertical coordinate values;

[0025] As a preferred implementation of the present invention, the formula for updating the residual is:

[0026]

[0027] where d(k) is the complex scattering coefficient at the kth grid point.

[0028] Step 6: Repeat steps 2 to 5. When the residual value is less than the threshold, stop the iteration; output the complex scattering coefficient and coordinates of the target;

[0029] As a preferred embodiment of the present invention, a radar robust compressed sensing imaging system under grid mismatch includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement a radar robust compressed sensing imaging method under grid mismatch.

[0030] As a preferred embodiment of the present invention, a computer readable medium stores a computer program code, and when the computer program code is executed by a processor, a radar robust compressed sensing imaging method under grid mismatch is implemented.

[0031] Beneficial effects of the present invention:

[0032] 1. Simultaneously realize the reconstruction of target complex scattering coefficients and position coordinate estimation under MIMO radar grid mismatch without assuming prior distribution;

[0033] 2. Aiming at the grid mismatch problem in the compressed sensing imaging process, the target complex scattering coefficient and two-dimensional position coordinate information are firstly modeled as a joint optimization problem and solved using the nonlinear least squares method. This can effectively suppress the target energy dispersion caused by grid mismatch and provide the target's complex scattering coefficient and two-dimensional coordinate information.

[0034] 3. Compared with the parameter perturbation orthogonal matching pursuit method proposed by Ilhan I et al. to solve the grid mismatch problem, the method of the present invention models the target complex scattering coefficient and two-dimensional position coordinate information as a joint optimization problem. Simulation data verifies that this method can suppress the target energy dispersion caused by grid mismatch, thereby significantly improving the quality of compressed sensing imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the radar robust compressed sensing imaging method under grid mismatch of the present invention;

[0036] Figure 2 It is the result diagram of the two-dimensional imaging of OMP of the present invention;

[0037] Figure 3 This is the NLS-OMP two-dimensional imaging result diagram of the present invention. DETAILED DESCRIPTION

[0038] The present invention is further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, and therefore it only shows the components related to the present invention.

[0039] like Figure 1 As shown, a radar robust compressed sensing imaging method under grid mismatch includes the following steps:

[0040] Step 1: Obtain MIMO radar time domain signals, build a radar imaging model, and set initial values ​​of radar imaging model parameters and initial values ​​of target positions;

[0041] The radar imaging model parameters include: residual, support set, complex scattering coefficient; initial values ​​of the target's horizontal and vertical coordinates;

[0042] The horizontal and vertical coordinates are the horizontal and vertical coordinate position information of the target position in the radar image coordinate system.

[0043] The initial value of the residual is r [0] =y tr The initial value of the support set is The initial value of the complex scattering coefficient is d [0] =[], the initial value of the horizontal axis is x [0] =[], the initial value of the ordinate is the initial value y [0] = [], the initial value of the number of iterations i = 1.

[0044] Step 2: Under the condition of setting the initial parameters of the radar imaging model, in the i-th iteration, search for the column with the largest correlation with the residual vector r in the observation matrix A;

[0045] In the i-th iteration, the formula for searching the column in the observation matrix A that has the greatest correlation with the residual vector r is:

[0046]

[0047] Among them, Λ [i-1] is the support set of the i-1th iteration.

[0048] Step 3: In the i-th iteration, save the selected support set as:

[0049] Λ [i] =Λ [i-1] ∪j [i](2)

[0050] Step 4: In the i-th iteration, the complex scattering coefficient, the abscissa and the ordinate are estimated simultaneously using nonlinear least squares. The current support set Λ [i] The complex scattering coefficient, abscissa and ordinate formulas are:

[0051]

[0052] in, and are the current support set Λ [i] The corresponding complex scattering coefficient and position coordinates.

[0053] Complex scattering coefficient d k is a complex number, and the target position coordinate (x k ,y k ) are obviously real numbers and cannot be estimated simultaneously using the gradient method. The NLS minimization problem in equation (3) is solved by jointly estimating the complex scattering coefficient and position information of the target. This NLS problem is divided into real and imaginary parts. For simplicity, the superscript [i] And rewrite the NLS problem as follows:

[0054]

[0055] The optimization problem is thus transformed into an NLS problem related only to real numbers, which can be solved by various optimization methods.

[0056] Step 5: In the i-th iteration, use d in step 4 [i] ,x [i] ,y [i] The estimated result updates the residual, the formula is:

[0057]

[0058] Among them, R tr (m,n,k) is the two-way distance from the mth transmitting element to the kth target and from the nth receiving element to the kth grid point, f l is the center frequency of the lth pulse, and d(k) is the complex scattering coefficient of the kth grid point.

[0059] Step 6: Set the number of iterations i=i+1 and return to step 2; when the residual is less than the threshold, terminate the loop; and give the complex scattering coefficient, abscissa and ordinate of the target.

[0060] Simulation conditions

[0061] The center frequency of the MIMO radar transmit signal is set to 3 GHz, the bandwidth is 1 GHz, the transmit signal adopts a stepped frequency signal system, the total number of system frequency points is 256, the number of transmitting array elements is 2, the number of receiving array elements is 9, the number of randomly selected frequency points is 32, the number of scene azimuth points is 41, and the number of scene distance points is 41.

[0062] Table 1 Target parameters and estimation results

[0063]

[0064] Seven targets are set in the imaging scene. The complex scattering coefficients of these seven targets are different. The amplitude of the complex scattering coefficient is randomly distributed between (0, 2), and the phase is randomly distributed between (-π, π). The specific information of the target complex scattering coefficient and position distribution is shown in Table 1. Target parameters. When using the OMP algorithm, the intervals of the horizontal and vertical coordinate grids used are 0.15m and 0.125m respectively. According to the grid interval, it can be seen that the horizontal coordinates of targets 1, 2, and 5 deviate from the grid; the vertical coordinates of targets 6 and 7 deviate from the grid; the horizontal and vertical coordinates of targets 3 and 4 deviate from the grid.

[0065] The present invention is used to perform two-dimensional imaging under grid mismatch; Figure 2 The OMP 2D imaging results are given. The obvious defocusing phenomenon in the figure is caused by the grid mismatch where the target is not distributed on the grid points. From the OMP estimation results in Table 1, it can be seen that target 2 is missing in the OMP 2D imaging results. Analysis of the scattering characteristics of target 2 shows that its complex scattering coefficient amplitude is significantly smaller than that of other targets. Therefore, it can be considered that OMP 2D imaging not only has the problem of inaccurate reconstruction of the target complex scattering coefficient and position, but also may lose targets with smaller complex scattering coefficient amplitudes among multiple targets. Figure 3 In the figure, the NLS-OMP imaging results of the present invention are given. It can be clearly seen from the figure that high-quality reconstruction of the target can be achieved at this time; from the NLS-OMP estimation results in Table 1, it can be seen that although the amplitude of the complex scattering coefficient of target 2 is smaller than that of other targets, it is still accurately reconstructed; so it can be considered that NLS-OMP two-dimensional imaging can not only accurately reconstruct the target complex scattering coefficient and two-dimensional coordinate information, but also has the ability to reconstruct targets with smaller complex scattering coefficient amplitudes.

[0066] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A radar robust compressed sensing imaging method under grid mismatch, characterized in that: The following steps are involved: Step 1: Obtain the MIMO radar time domain signal, build a radar imaging model, and set the initial parameters of the radar imaging model and the initial parameters of the target; Step 2: Search the column with the largest correlation with the residual vector in the observation matrix through several iterations; Step 3: Save the selected support set; Step 4: Use nonlinear least squares to simultaneously estimate the complex scattering coefficient and the horizontal and vertical coordinate values; Step 5: Update the residual using the estimated complex scattering coefficient and the horizontal and vertical coordinate values; Step 6: Repeat steps 2 to 5. When the residual value is less than the threshold, stop the iteration; output the complex scattering coefficient and coordinates of the target.

2. The radar robust compressed sensing imaging method under grid mismatch according to claim 1, characterized in that: The formula for the most relevant column is: When [i] ∈Λ [i-1] When to stop (1) where Λ [i-1] is the support set of the i-1th iteration, A is the observation matrix, and r is the residual vector.

3. The radar robust compressed sensing imaging method under grid mismatch according to claim 1, characterized in that: The formula for the selected support set is: L [i] =L [i-1] ∪j [i] (2) Among them, Λ [i-1] is the support set of the i-1th iteration, j [i] is the column with the highest correlation.

4. The radar robust compressed sensing imaging method under grid mismatch according to claim 1, characterized in that: The formula for estimating the complex scattering coefficient and the horizontal and vertical coordinate values ​​is: in, and are the current support set Λ [i] The corresponding complex scattering coefficient and position coordinates, f l is the center frequency of the lth pulse, R tr (m,n,k) is the two-way distance from the mth transmitting element to the kth target and from the nth receiving element to the kth grid point.

5. The radar robust compressed sensing imaging method under grid mismatch according to claim 1, characterized in that: The formula for residual update is: where d(k) is the complex scattering coefficient at the kth grid point.

6. The radar robust compressed sensing imaging method under grid mismatch according to claim 1, characterized in that: Radar imaging model parameters include: residual, support set, and complex scattering coefficient.

7. The radar robust compressed sensing imaging method under grid mismatch according to claim 1, characterized in that: The initial parameters of the target are the horizontal and vertical coordinates of the target.

8. A radar robust compressed sensing imaging system under grid mismatch, characterized in that: include: a memory for storing instructions executable by a processor; A processor, configured to execute instructions to implement the radar robust compressed sensing imaging method under grid mismatch as described in any one of claims 1 to 7.

9. A computer readable medium storing a computer program code, characterized in that: When the computer program code is executed by a processor, the radar robust compressed sensing imaging method under grid mismatch as claimed in any one of claims 1 to 7 is implemented.

Images