A radar forward-looking super-resolution imaging method based on echo energy correction

Abstract

The application discloses a radar forward-looking super-resolution imaging method based on echo energy correction, belongs to the technical field of radar imaging, and aims to solve the imaging error problem of a traditional imaging method on a high-speed motion platform caused by speed error. The motion platform speed is accurately estimated based on an echo energy correction criterion, the influence of platform motion error on super-resolution imaging performance is effectively reduced, and the dependence of the traditional method on a high-precision external speed measuring device is overcome. Firstly, a complex convolution model containing Doppler phase information is constructed. Secondly, the platform speed is estimated based on the echo energy correction criterion, so that accurate speed information is obtained. Subsequently, the Doppler phase matrix is updated by using the corrected speed, and the complex convolution echo model is corrected. Finally, a sparse super-resolution algorithm based on power weighting is proposed, the target power and noise power are optimized through alternating iteration, and robust super-resolution imaging under the motion platform is realized, so that the target recognition and situation awareness capability of the motion platform is significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to a radar forward-looking super-resolution imaging method based on echo energy correction. Background Technology

[0002] In real-world scenarios such as aircraft landing in adverse weather conditions, ground mapping, and target reconnaissance, forward-looking super-resolution imaging technology is crucial for target identification of moving platforms. However, due to the limitation of the radar's true aperture size, the angular resolution of traditional real-beam radars is insufficient to meet the requirements. The deconvolution method improves the angular resolution of the forward-looking region by modeling the echo as the convolution of antenna pattern amplitude information and target scattering coefficients, thus transforming the imaging problem into an inversion problem.

[0003] Given the known amplitude information of the antenna and the echo, researchers have proposed various deconvolution methods based on different criteria. Zhang Q et al. proposed a sparse-based fast maximization-minimization super-resolution algorithm, which, compared with the standard sparse maximization-minimization method, improves the forward-looking imaging angular resolution of the radar while accelerating the convergence speed.

[0004] Traditional convolutional models reconstruct targets based on antenna pattern amplitude information. However, in high-speed platforms, the Doppler phase caused by platform motion alters the convolution process, affecting the convolution matrix and leading to image distortion or even false targets. Zhang HH et al. proposed a Bayesian forward-looking super-resolution imaging algorithm based on extended beamspace Doppler deconvolution. This method integrates the Doppler phase information of the high-speed moving platform with antenna pattern characteristics, achieving efficient Doppler deconvolution. In high-speed platform scenarios, this method significantly improves angular resolution and effectively suppresses noise. Y. Wu et al. proposed a complex deconvolution method that simultaneously utilizes amplitude and Doppler phase information. This method constructs a complex convolution matrix using the correspondence between amplitude and Doppler phase and employs truncated singular value decomposition to suppress noise amplification, achieving forward-looking super-resolution imaging of moving platforms.

[0005] These methods achieve superior imaging results under ideal platform motion conditions. However, in practical applications, platform speed is often affected by factors such as weather changes and the platform's own acceleration, leading to measurement errors. Currently, most forward-looking radar platforms rely on inertial navigation systems to measure flight speed to meet imaging requirements, but high-precision measurements often require high equipment costs. Therefore, determining platform speed through estimation methods is particularly necessary. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a radar forward-looking super-resolution imaging method based on echo energy correction. This method utilizes an echo energy correction criterion to accurately estimate the velocity of the moving platform, thereby effectively reducing the impact of platform motion errors on super-resolution imaging performance. Furthermore, it employs a power-weighted sparse super-resolution algorithm to iteratively optimize target power and noise power, thereby improving imaging resolution and noise resistance.

[0007] The specific technical solution of the present invention is as follows:

[0008] 1. A radar forward-looking super-resolution imaging method based on echo energy correction, characterized by comprising the following steps:

[0009] Step 1: The radar transmits a linear frequency modulated signal toward the target area and performs pulse compression and range migration correction on the received echo signal to obtain the echo signal model;

[0010] Step 2: Based on the echo energy correction-based velocity estimation method, set the velocity search interval, calculate the one-dimensional waveform entropy of the velocity search interval based on the obtained echo signal model, and iteratively converge the velocity search interval based on the one-dimensional waveform entropy until the convergence criterion is met to obtain the final estimated velocity.

[0011] Step 3: Correct the Doppler phase matrix of the echo signal based on the echo energy correction speed, and update the echo signal model;

[0012] Step 4: Based on the power-weighted sparse super-resolution algorithm, construct a power-weighted sparse constraint optimization problem according to the updated echo signal model and target power matrix, and solve iteratively to obtain the super-resolution imaging results.

[0013] The echo signal, within the same distance cell r, can be formally represented by the following formula:

[0014] ;

[0015] in

[0016] ,

[0017] ;

[0018] In the formula, For noise vectors, The echo signal is represented as a fixed distance unit. The echo signal acquired at a time t. Indicates a fixed distance unit as Time A slow time The acquired echo signal, of which The distance between the radar and the target is At that time, the round-trip time of the corresponding radar electromagnetic wave signal, This indicates the position of the imaging point in the corresponding imaging scene in the ground coordinate system, and the superscript T indicates transpose; This indicates the distance between the radar and the target is... At different slow-time imaging points, the scattering coefficients Represents the distance along the axis. Location of each scattering point Represents angular dimension; Indicates the first The complex convolution matrix corresponding to each distance unit is constructed as follows:

[0019]

[0020] in, This is a conventional convolution matrix constructed based on the antenna pattern. This represents the dot product operation. The Doppler phase matrix is ​​constructed from the Doppler phases of the discretized echo signal.

[0021] Step 2 is described in detail below:

[0022] Step 2.1: Acquire echo data , its origin The samples obtained from each directional dimension Composed of column vectors, with a dimension of ,in Represents a distance dimension sampling unit. Indicates the azimuth dimension sampling unit;

[0023] Step 2.2: Set the speed search range. ,in As the lower limit of speed, Set the speed limit to [value]. , and iteration termination threshold ,in It is the speed measured by the inertial navigation system;

[0024] Step 2.3: Calculate the velocities respectively. and One-dimensional waveform entropy of the distance migration correction result:

[0025] ;

[0026] ;

[0027] in, , For speed and The corrected one-dimensional waveform entropy, Represents the one-dimensional waveform entropy function. This represents the inverse fast Fourier transform. This represents the Fast Fourier Transform, where j represents the imaginary unit. Indicates the frequency of the radar's transmitted signal. This indicates the angle of view of the radar beam center line of sight relative to the frontal side view direction. The speed of light;

[0028] Step 2.4: If Then shrink the search interval, and then:

[0029] like The contraction interval is as follows:

[0030] ;

[0031] And update the calculation ;in Indicates the shrinkage ratio;

[0032] like The contraction interval is as follows:

[0033] ;

[0034] And update the calculation Iteration continues until the convergence criterion is met. If so, the speed search will terminate;

[0035] Step 2.5: Output the estimated speed :

[0036] If the iteration terminates, ,but Conversely, .

[0037] The one-dimensional waveform entropy function is as follows:

[0038]

[0039]

[0040] in, This represents the normalized probability density of the signal. express Norm, G is a discrete signal, and , The length of the signal. The first vector of the discrete signal G represents the first vector. One signal.

[0041] The Doppler phase matrix is ​​used to estimate velocity correction, as expressed by the following formula:

[0042]

[0043] in The corrected Doppler phase matrix; The wavelength of the electromagnetic waves emitted by radar. The pitch angle, It is the initial slant range of the target. For the 1st, ..., A slow-time sampling moment, for The oblique angle of view corresponding to the moment; let The echo signal model is updated as follows:

[0044]

[0045] Where y represents the echo signal and s represents the scattering coefficient.

[0046] Step 4 is described in detail below:

[0047] Based on the updated echo signal model, let

[0048] ;

[0049] In the formula, Indicates echo signal The autocorrelation matrix, It is an echo signal The conjugate transpose of . It is a matrix The conjugate transpose of . It is a matrix No. column vectors, This means diagonalizing a vector into a diagonal matrix. Represents the target power matrix. The diagonal vector representing the target power matrix The There are 1 element; then the following sparse constraint criterion is constructed:

[0050] ;

[0051] in Indicates the weighting factor. The first one represents the target The power is then minimized iteratively to achieve monotonically decreasing and globally convergent results, yielding the final super-resolution imaging solution.

[0052] ;

[0053] in This indicates that the target is being updated. One power, Indicates the first During the iteration, for the ... An estimated value for the power. express The conjugate transpose of . Indicates the first The estimated echo covariance matrix is ​​obtained in the next iteration.

[0054] The beneficial effects of this invention are as follows:

[0055] By using an echo energy correction criterion to accurately estimate the velocity of the moving platform, the impact of platform motion error on super-resolution imaging performance is effectively reduced, overcoming the dependence of traditional methods on high-precision external velocity measurement equipment. At the same time, by combining a power-weighted sparse super-resolution algorithm to iteratively optimize target power and noise power, the imaging resolution and noise resistance are significantly improved. This enables the method to obtain more stable, clearer, and more accurate radar forward-looking super-resolution images in complex real-world application scenarios, thereby significantly enhancing the target recognition and situational awareness capabilities of the moving platform. Attached Figure Description

[0056] Figure 1 This is a flowchart of the present invention.

[0057] Figure 2 This is an analysis diagram of the echo generation process described in this invention.

[0058] Figure 3 This is the waveform entropy curve described in this invention.

[0059] Figure 4 This is a graph showing the velocity estimation error under different signal-to-noise ratios as described in this invention.

[0060] Figure 5 This is a comparison chart of the super-resolution results of different methods described in this invention. Detailed Implementation

[0061] This invention employs simulation experiments to demonstrate the effectiveness of the proposed method. All steps and conclusions of this invention have been verified on the Matlab 2022b simulation platform. To enable those skilled in the art to understand the invention, it is further described below with reference to the accompanying drawings.

[0062] A radar forward-looking super-resolution imaging method based on echo energy correction, such as... Figure 1 As shown, it includes the following steps:

[0063] Step 1: Method for characterizing model errors caused by platform speed;

[0064] The radar transmits a linear frequency modulated (LFM) signal towards the target area and performs pulse compression and range migration correction on the received echo signal. After discretization, the azimuth echo signal can be expressed as:

[0065]

[0066] in, As a dual summation operator, the imaging scene is discretized into multiple scattering points on a two-dimensional grid, and this operator accumulates the echo signals from these scattered points. Indicates a two-dimensional scene located at The scattering coefficient of the target, for The position coordinates of the scattering point on the ground corresponding to the radar illumination at any given time in a two-dimensional coordinate system. That is, the line of sight of the radar antenna beam center is exactly aligned with the ground coordinates. The precise point in time. Indicates a fast time. Indicates slow time. Function Indicates antenna mode modulation. Indicates the carrier frequency. represent function( ), This refers to the bandwidth of the transmitted signal. It is the initial slant range of the target. It is the speed of light. In slow time Real-time radar antenna and scattering point The instantaneous slant distance between them. This represents the baseband signal obtained by the radar receiver.

[0067] Traditional deconvolution methods typically ignore the Doppler phase. The echo signal is constructed as a convolution of the antenna pattern amplitude information and the target scattering coefficient. However, on high-speed platforms, the Doppler phase affects the antenna modulation function, transforming the convolution operation into a vector operation, leading to false targets and reduced angular resolution. To overcome this problem, this invention constructs a complex convolution matrix that incorporates the Doppler phase.

[0068] Within the same distance cell, the echo can be represented as:

[0069]

[0070] in

[0071]

[0072]

[0073] in Indicates a fixed distance unit as Time A slow time The acquired echo signal, of which The distance between the radar and the target is At that time, the round-trip time of the corresponding radar electromagnetic wave signal, This indicates the position of the imaging point in the corresponding imaging scene within the ground coordinate system. This indicates the distance between the radar and the target is... At different slow-time imaging points, the scattering coefficients This represents the position of the M'-th scattering point on the distance-direction axis. M' represents the angular dimension. Indicates the first The complex convolution matrix corresponding to each distance unit is constructed as follows:

[0074]

[0075] in, The Doppler phase matrix is ​​constructed from the Doppler phases in equation (1). (Symbols) This represents the dot product operation. This is a conventional convolution matrix constructed based on the antenna pattern. The Doppler phase matrix is ​​shown below. The format is as follows:

[0076]

[0077] in, The imaginary unit, The wavelength of the electromagnetic waves emitted by radar. The pitch angle, For the speed of the radar platform, For the 1st, ..., A slow-time sampling moment, for The azimuth angle corresponding to the moment.

[0078] Finally, the echo signal can be represented as:

[0079]

[0080] in, This is the noise vector.

[0081] Step 2: A velocity estimation method based on echo energy correction is used to achieve accurate velocity estimation by minimizing the echo waveform entropy. In super-resolution imaging, velocity errors significantly affect the reconstruction performance of the target scene. Complex convolution models rely on the phase and amplitude information of the echo signal, but velocity errors introduce phase distortion, compromising the model's accuracy, leading to image blurring and reduced image quality. Therefore, to ensure the accuracy of super-resolution imaging, accurate estimation and compensation of the platform velocity are essential.

[0082] First, define waveform entropy for discrete signals. Waveform entropy Defined as:

[0083]

[0084] in, The first vector of the discrete signal G represents the first vector. One signal, ,in This represents the normalized probability density of the signal. express Norm, where G is the time series of the echo signal. The length of the signal.

[0085] Waveform entropy can effectively assess the impact of motion parameters on the target distance direction. Waveform entropy increases when the platform's motion causes the peak value in the one-dimensional distance image to diverge; conversely, it reaches its minimum when the velocity compensation error is zero. Therefore, by searching for the global minimum of waveform entropy on the velocity axis, the platform's motion parameters can be determined.

[0086] In practice, due to noise, the entropy curve may exhibit spurious peaks, affecting the performance of the interval search method. To address this issue, the definition of waveform entropy is optimized as follows:

[0087]

[0088] in This represents the optimized waveform entropy definition, which is different from equation (6).

[0089] The specific steps of the velocity estimation method based on echo energy correction are as follows:

[0090] Step 2.1. Acquire the pulse-compressed echo data That is, by The samples obtained from each directional dimension Composed of column vectors, its dimension is ,in Represents a distance dimension sampling unit. This indicates the azimuth dimension sampling unit.

[0091] Step 2.2. Set the speed search range ,in As the lower limit of speed, Set the speed limit to [value]. , and iteration termination threshold ,in The speed is measured by an inertial navigation system, which has limited accuracy and is subject to certain measurement errors.

[0092] Step 2.3. Calculate the velocity respectively. With speed One-dimensional waveform entropy of the distance travel compensation result:

[0093]

[0094]

[0095] in, , For speed and The corrected one-dimensional waveform entropy, The entropy function of a one-dimensional waveform is defined by equation (7), i.e. , This represents the inverse fast Fourier transform. Represents the Fast Fourier Transform. Indicates the frequency of the radar's transmitted signal. This indicates the angle of view of the radar beam center line of sight relative to the frontal side view direction.

[0096] Step 2.4. If If so, then the search interval will shrink;

[0097] like The contraction interval is as follows:

[0098]

[0099]

[0100] like The contraction interval is as follows:

[0101]

[0102]

[0103] in This represents the shrinkage ratio; after several iterations, it continues until the convergence criterion is met. If the speed search is terminated, then the search will end.

[0104] Step 2.5. Output the estimated velocity If the iteration terminates, ,but Conversely, .

[0105] Step 3: Correction and processing of the complex convolution echo model;

[0106] Based on the echo energy correction velocity, this invention can obtain a more accurate platform motion velocity compared to inertial navigation measurement. Therefore, a more accurate phase measurement matrix can be constructed. Furthermore, the Doppler phase matrix D can be modified as follows:

[0107]

[0108] in This is the corrected Doppler phase matrix.

[0109] To further simplify the modified echo model formula, let Therefore, the echo signal can be updated as follows:

[0110]

[0111] Step 4: Power-weighted sparse super-resolution algorithm;

[0112] According to the signal echo model shown in equation (15), let

[0113]

[0114] In the formula, Indicates echo signal The autocorrelation matrix, yes The conjugate transpose of . yes The conjugate transpose of . It is a matrix No. column vectors, This means diagonalizing a vector into a diagonal matrix. Represents the target power matrix. The diagonal vector representing the target power matrix The There are 1 element. Then, the following sparse constraint criterion is constructed:

[0115]

[0116] in Indicates the weighting factor. The first one represents the target Power.

[0117] Equation (17) is a globally solvable convex optimization problem. Therefore, it can be minimized using an iterative loop, achieving monotonically decreasing and globally convergent results during the iteration.

[0118]

[0119] No. The target power for the next iteration can be expressed as:

[0120]

[0121] in This indicates that the target is being updated. One power, Indicates the first During the iteration, for the ... An estimated value for the power. express The conjugate transpose of . Indicates the first The estimated echo covariance matrix is ​​obtained in the next iteration.

[0122] Step 4: After iterative solution, the target super-resolution imaging result is obtained.

[0123] To verify the effectiveness of this invention, simulation verification was performed on the Matlab 2022b simulation platform. The simulation scenario of a two-dimensional multi-point target was as follows: Figure 2 As shown in (a) in the table, the relevant simulation parameters are detailed in Table 1, and the simulation environment and platform are consistent with those described in Table 2. Figure 2 (b) shows the original echo signal, which covers multiple range cells. For the echo profile of a specific range cell, the present invention integrates the data along the azimuth direction to observe and verify the waveform entropy characteristics of the range signal. Figure 2 (c) in the image is the echo image without distance migration correction; Figure 2(d) in the image is the echo image after range migration correction; Figure 2 (e) and Figure 2 In the figure, (f) represents the integral cross section after pulse compression without range migration correction and with range migration correction, respectively.

[0124] Table 1 Simulation Parameters

[0125] Simulation parameters numerical values carrier frequency 10.75 GHz bandwidth 80 MHz signal pulse width 2 μs Pulse repetition frequency 1000Hz Antenna scanning speed 60° / s° beamwidth 4° Scan range -15°~15° Measurement platform speed 200 m / s

[0126] Table 2 Simulation Environment

[0127] Hardware / Software Parameter value CPU Intel i7-9700K RAM 64 G Simulation software Matlab 2022a

[0128] Based on the above analysis, different distance waveform entropy curves are obtained by changing the speed compensation parameters, as shown below. Figure 3 As shown, when the waveform entropy reaches its minimum value, the estimated speed is very close to the actual speed of the platform. Figure 4 The results show that, under low signal-to-noise ratio conditions such as SNR=5 dB, the proposed method can control the velocity estimation error within approximately 0.18 m / s, thus fully verifying the effectiveness of the velocity estimation method based on echo energy correction.

[0129] This invention further employs a power-weighted sparse super-resolution algorithm to reconstruct the target scattering coefficients using super-resolution. A two-dimensional multi-point target simulation scenario is shown below. Figure 5 As shown in (a) of the table. The simulation parameters are detailed in Table 3, and the simulation environment is the same as that in Table 2.

[0130] Table 3 Simulation parameters for two-dimensional multi-point targets

[0131] Simulation parameters numerical values carrier frequency 10.75 GHz bandwidth 80 MHz signal pulse width 2 μs Pulse repetition frequency 1000Hz Antenna scanning speed 60° / s° beamwidth 4° Scan range -15°~15° Platform speed 200 m / s Measurement speed error 0.5 m / s

[0132] The targets are distributed in four distance cells as follows: one target is located at 0°, at a distance of 3.84 km; two targets are located at -0.5° and 0.5°, at a distance of 3.72 km; four targets are located at -1.5°, -0.5°, 0.5° and 1.5°, at a distance of 3.6 km; and six targets are located at -2.5°, -1.5°, -0.5°, 0.5°, 1.5° and 2.5°, at a distance of 3.48 km. Figure 5 (b) shows the results of a real beam with a signal-to-noise ratio of 10 dB. After pulse compression and range offset correction, targets within the same range cell are difficult to distinguish. Figure 5 (c) in the figure represents the Iterative Adaptive Algorithm (IAA) method, in which false targets exist in the imaging results. Figure 5 (d) and Figure 5In the diagram, (e) represents the Sparse Iterative Covariance Estimation (SPICE) algorithm and the Sparse Learning Iterative Minimization (SLIM) algorithm, respectively. They have good super-resolution performance, but limited performance improvement and the presence of false targets. Figure 5 (f) in the figure represents the result of the proposed method, which can accurately recover the target and effectively suppress noise.

[0133] Furthermore, the effectiveness of the proposed method was further verified using two metrics: mean squared error (MSE) and structural similarity (SSIM). The evaluation metrics for different methods are shown in Table 4.

[0134] MSE is defined as:

[0135]

[0136] In the formula, and Sampling points representing distance and azimuth. This indicates the number of Monte Carlo experiments. and These represent the estimated and actual target scattering coefficients, respectively.

[0137] SSIM is defined as:

[0138]

[0139] In the formula, and Let be the mean and standard deviation of the vector sum, respectively. For vectors and The correlation coefficient.

[0140] As shown in Table 4, the MSE of the proposed method is significantly lower than that of other methods, while the SSIM is significantly improved, which verifies the estimation accuracy and effectiveness of the proposed method.

[0141] Table 4. Mean square error and structural similarity index of imaging results from each method

[0142] method MSE (dB) SSIM Real beam -37.0253 0.0591 IAA -63.6191 0.9697 SPICE -67.3389 0.9712 SLIM -68.0491 0.9737 The proposed method -74.5322 0.9901

[0143] Those skilled in the art can make relevant applications of the radar forward-looking super-resolution imaging method based on echo energy correction disclosed in this invention, and the relevant knowledge is still within the protection scope of this invention.

[0144] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A radar forward-looking super-resolution imaging method based on echo energy correction, characterized in that, Includes the following steps: Step 1: The radar transmits a linear frequency modulated signal toward the target area and performs pulse compression and range migration correction on the received echo signal to obtain the echo signal model; Step 2: Based on the echo energy correction-based velocity estimation method, set the velocity search interval, calculate the one-dimensional waveform entropy of the velocity search interval based on the obtained echo signal model, and iteratively converge the velocity search interval based on the one-dimensional waveform entropy until the convergence criterion is met to obtain the final estimated velocity. Step 3: Correct the Doppler phase matrix of the echo signal based on the echo energy correction speed, and update the echo signal model; Step 4: Based on the power-weighted sparse super-resolution algorithm, construct a power-weighted sparse constraint optimization problem according to the updated echo signal model and target power matrix, and solve iteratively to obtain the super-resolution imaging results.

2. The radar forward-looking super-resolution imaging method based on echo energy correction according to claim 1, characterized in that, The echo signal, within the same distance cell r, can be formally represented by the following formula: ； in ， ； In the formula, For noise vectors, The echo signal is represented as a fixed distance unit. The echo signal acquired at a time t. Indicates a fixed distance unit as Time A slow time The acquired echo signal, of which The distance between the radar and the target is At that time, the round-trip time of the corresponding radar electromagnetic wave signal, This indicates the position of the imaging point in the corresponding imaging scene in the ground coordinate system, and the superscript T indicates transpose; This indicates the distance between the radar and the target is... At different slow-time imaging points, the scattering coefficients Represents the distance along the axis. Location of each scattering point Represents angular dimension; Indicates the first The complex convolution matrix corresponding to each distance unit is constructed as follows: ； in, This is a conventional convolution matrix constructed based on the antenna pattern. This represents the dot product operation. The Doppler phase matrix is ​​constructed from the Doppler phases of the discretized echo signal.

3. The radar forward-looking super-resolution imaging method based on echo energy correction according to claim 2, characterized in that, Step 2 is described in detail below: Step 2.1: Acquire echo data , its origin The samples obtained from each directional dimension Composed of column vectors, with a dimension of ,in Represents a distance dimension sampling unit. Indicates the azimuth dimension sampling unit; Step 2.2: Set the speed search range. ,in As the lower limit of speed, Set the speed limit to [value]. , and iteration termination threshold ,in It is the speed measured by the inertial navigation system; Step 2.3: Calculate the velocities respectively. and One-dimensional waveform entropy of the distance migration correction result: ； ； in, , For speed and The corrected one-dimensional waveform entropy, Represents a one-dimensional waveform entropy function. This represents the inverse fast Fourier transform. This represents the Fast Fourier Transform, where j represents the imaginary unit. Indicates the frequency of the radar's transmitted signal. This indicates the angle of view of the radar beam center line of sight relative to the frontal side view direction. The speed of light; Step 2.4: If Then shrink the search interval, and then: like The contraction interval is as follows: ； And update the calculation ;in Indicates the shrinkage ratio; like The contraction interval is as follows: ； And update the calculation Iteration continues until the convergence criterion is met. If so, the speed search will terminate; Step 2.5: Output the estimated speed : If the iteration terminates, ,but Conversely, .

4. The radar forward-looking super-resolution imaging method based on echo energy correction according to claim 3, characterized in that, The one-dimensional waveform entropy function is as follows: ； ； in, This represents the normalized probability density of the signal. express Norm, G is a discrete signal, and , The length of the signal. The first vector of the discrete signal G represents the first vector. One signal.

5. The radar forward-looking super-resolution imaging method based on echo energy correction according to claim 4, characterized in that, The Doppler phase matrix is ​​used to estimate velocity correction, as expressed by the following formula: ； in The corrected Doppler phase matrix; The wavelength of the electromagnetic waves emitted by radar. The pitch angle, It is the initial slant range of the target. For the 1st, ..., A slow-time sampling moment, for The oblique angle of view corresponding to the moment; let The echo signal model is updated as follows: ； Where y represents the echo signal and s represents the scattering coefficient.

6. The radar forward-looking super-resolution imaging method based on echo energy correction according to claim 5, characterized in that, Step 4 is as follows: Based on the updated echo signal model, let ； In the formula, Indicates echo signal The autocorrelation matrix, It is an echo signal The conjugate transpose of . It is a matrix The conjugate transpose of . It is a matrix No. column vectors, This means diagonalizing a vector into a diagonal matrix. Represents the target power matrix. The diagonal vector representing the target power matrix The There are 1 element; then the following sparse constraint criterion is constructed: ； in Indicates the weighting factor. The first one represents the target The power is then minimized iteratively to achieve monotonically decreasing and globally convergent results, yielding the final super-resolution imaging solution. ； in This indicates that the target is being updated. One power, Indicates the first During the iteration, for the ... An estimated value for the power. express The conjugate transpose of . Indicates the first The estimated echo covariance matrix is ​​obtained in the next iteration.

7. The radar forward-looking super-resolution imaging method based on echo energy correction according to claim 6, characterized in that, No. The target power for the next iteration can be expressed as: 。

Images