A forward-looking 3D imaging technology for airborne radar based on a 2D super-resolution algorithm

Abstract

The present invention discloses a forward-looking three-dimensional imaging technology for an airborne radar based on a two-dimensional super-resolution algorithm. A planar array antenna is used to receive scattered echoes from targets in the area in front of the carrier aircraft. After pulse compression and range migration correction are performed, the observation area is gridded and azimuth-elevation echo modeling is completed. For each two-dimensional snapshot data, a weighted least squares criterion is used to construct a cost function with weights. The parameters are iteratively updated until the estimation results converge to obtain a single azimuth-elevation super-resolution spectrum. Two-dimensional spectrum incoherent accumulation is performed on several super-resolution spectra of the same range gate to obtain three-dimensional super-resolution data in polar coordinates. Finally, the polar coordinate data is transformed into a spatial rectangular coordinate system and plotted to obtain forward-looking three-dimensional super-resolution imaging. The present invention only requires a single snapshot to complete azimuth-elevation two-dimensional super-resolution, which overcomes the disadvantage that a moving platform cannot accumulate a large number of snapshots for the same observation target while further improving the imaging resolution.

Description

Technical Field

[0001] The present invention belongs to the field of radar imaging technology, and in particular relates to a forward-looking three-dimensional super-resolution imaging technology for airborne radar. Background Art

[0002] Thanks to its 24 / 7, all-weather capability, radar imaging technology has gained increasing attention across various fields. Compared to fixed-platform radars, airborne radars offer greater flexibility and can achieve imaging over a wider range. With the advancement of research, traditional two-dimensional range-azimuth information no longer meets practical application needs. In areas with high terrain volume, such as cities and valleys, the elevation dimension often contains crucial information. Consequently, three-dimensional radar imaging technology has become a research hotspot in recent years.

[0003] For radar 3D imaging, pulse compression can achieve range super-resolution, so research focuses on achieving super-resolution in both azimuth and elevation. Existing methods either achieve super-resolution in both azimuth and elevation simultaneously or by processing them separately. Common approaches include the 3D Range Stacking Algorithm (RSA), Interferometric SAR (InSAR), and Multi-Baseline SAR (MBSAR).

[0004] The 3D range stacking algorithm uses an antenna array to jointly process two-dimensional range and elevation signals. Pulse compression is also required before processing the range-elevation signal. Super-resolution in azimuth is achieved using SAR principles. For elevation, super-resolution of the two-dimensional range-elevation signal is achieved using a series of algorithms employing focused filters using the antenna array. Finally, 3D reconstruction is achieved using IFFT. This method achieves 3D super-resolution without requiring geometric correction or interpolation, but suffers from the drawback of high computational complexity.

[0005] The principles of InSAR-based 3D imaging technology are as follows: Azimuth resolution is achieved through synthetic aperture technology, while elevation super-resolution is achieved through InSAR. InSAR is a classic altimetry method that uses two antennas mounted at different locations, or a single antenna in two parallel flights, to observe the same ground target. Altitude measurement in elevation is achieved through interferometry based on the phase difference between the echoes received by the two antennas. However, when multiple targets of varying heights exist within the same range-elevation unit, this technology can only produce an average height for these multiple targets and cannot super-resolve each individual target.

[0006] Multi-baseline SAR (Multi-baseline SAR) 3D imaging technology addresses the shortcomings of InSAR. Multiple antennas are placed perpendicular to the radar's line of sight to receive echoes from the same ground area. Using multiple baselines, a synthetic aperture in elevation is constructed, and combined with an azimuth synthetic aperture, azimuth-elevation 2D SAR imaging is achieved. Compared to InSAR, MBSAR can achieve super-resolution of multiple targets at different altitudes within the same range-elevation unit. However, during flight, radar phase errors can affect 2D SAR imaging quality, leading to a decrease in the 3D quality of multi-baseline SAR.

[0007] Currently, most research on airborne radar 3D imaging technology is conducted within the SAR (Special Aperture Radar) framework, with relatively little research on forward-looking 3D imaging. For forward-looking imaging, the aircraft's flight direction and the radar beam coincide, resulting in a very small Doppler bandwidth. This makes methods such as Doppler beam sharpening (DBS) and synthetic aperture radar (SAR) that exploit Doppler bandwidth to improve azimuth resolution unsuitable. However, airborne radar forward-looking 3D imaging technology plays an irreplaceable role in military applications such as autonomous landing, missile guidance, and low-altitude flight. This makes the development of a high-resolution forward-looking 3D imaging algorithm crucial.

[0008] Array radar is a new radar system with higher spatial degrees of freedom. Traditional array signal processing techniques are also applicable to forward-looking array radar imaging. Due to the limitations of its antenna size, real-aperture radar cannot achieve a sufficiently narrow beamwidth. Array radars use beamforming to achieve narrower beams, improving angular resolution. Furthermore, array signal processing techniques can further enhance angular information super-resolution. A common type of array signal processing technique is direction-of-arrival (DOA) estimation. Applying DOA estimation super-resolution algorithms to forward-looking two-dimensional imaging can achieve imaging results far superior to those achieved with real-beam methods. Theoretically, by placing a uniform planar array perpendicular to the aircraft's flight direction and performing two-dimensional estimation, super-resolution imaging in azimuth and elevation can be achieved, ultimately enabling forward-looking three-dimensional imaging. However, when applying classic spectral estimation algorithms such as the Capon algorithm and the MUSIC algorithm to two-dimensional spectral estimation, it has been found that the required snapshot accumulation is greater than that required by one-dimensional algorithms. During aircraft flight, the radar beam's dwell time on the observed scene is very short, which cannot meet the snapshot accumulation requirements of classic 2D spectral estimation algorithms. This makes classic 2D DOA estimation algorithms unsuitable for forward-looking 3D imaging. Applying planar array correlation processing technology to forward-looking 3D imaging urgently requires a novel algorithm that requires fewer snapshots. Summary of the Invention

[0009] Purpose of the invention: The technical problem to be solved by the present invention is to address the defects involved in the background technology and provide an airborne radar forward-looking three-dimensional imaging technology based on a two-dimensional super-resolution algorithm. It adopts a two-dimensional iterative adaptive algorithm and constructs an error function using the weighted least squares criterion. The predicted value is continuously approached to the true value through iteration. Only a single two-dimensional snapshot signal is required to complete two-dimensional super-resolution.

[0010] The present invention provides a forward-looking three-dimensional imaging technology based on two-dimensional super-resolution, comprising the following steps:

[0011] Step 1) The airborne radar uses a planar array to transmit multiple signals, and the beam is scanned along the azimuth direction to obtain four-dimensional echo data of range-pulse-pitch array-azimuth array;

[0012] Step 2) After pulse compression and range migration correction are performed on each range gate, grid division is performed. Each grid is assumed to contain a potential signal source, and a two-dimensional spatial steering vector is constructed for each azimuth-elevation grid. This leads to the construction of a steering vector matrix and echo model for the entire azimuth-elevation plane.

[0013] Step 3) Performing two-dimensional super-resolution processing on the spatial snapshot data of the two-dimensional array on a range-by-pulse basis: constructing an initial power matrix of the signal source for each two-dimensional snapshot data; constructing a cost function using the weighted least squares criterion, minimizing the cost function to obtain an expression for the signal source estimate, and replacing the weight matrix in the expression with the autocorrelation matrix of the signal source via the inversion lemma to reduce the amount of computation; then updating each parameter through continuous iteration until the obtained two-dimensional signal source estimate converges; and plotting the two-dimensional estimated signal, i.e., the azimuth-elevation two-dimensional super-resolution spectrum of a single snapshot.

[0014] Step 4) Perform the following processing on each range gate in turn: Based on the beam center at each snapshot sampling, perform two-dimensional spectrum incoherent accumulation on all super-resolution spectra of the same range gate to complete azimuth-elevation super-resolution of a single range gate;

[0015] Step 5) uses interpolation to perform coordinate transformation, transforms the polar coordinate data into spatial rectangular coordinates, and obtains forward-looking 3D super-resolution imaging by drawing a point cloud.

[0016] As a further optimization solution of the present invention for the airborne radar forward-looking three-dimensional imaging technology based on a two-dimensional super-resolution algorithm, the specific steps of step 1) are as follows:

[0017] A planar array is placed along a plane perpendicular to the aircraft's flight direction, with array elements spaced equally apart. A one-tweet-multiple-receiver mode is used to perform beam scanning in azimuth within the observation area. A single independent array element transmits a linear frequency modulation signal with an additional carrier frequency, and the entire two-dimensional planar array receives the echo. After beam scanning the observed area and demodulating the echo signal, four-dimensional echo data is obtained: range-pulse-elevation array-azimuth array.

[0018] As a further optimization solution of the present invention for the airborne radar forward-looking three-dimensional imaging technology based on a two-dimensional super-resolution algorithm, the specific steps of step 2) are as follows:

[0019] Step 2.1), perform Fourier transform on the range direction, and perform pulse compression and range migration correction in the range frequency domain;

[0020] Step 2.2), for the azimuth-elevation plane, assume that each azimuth-elevation grid in the observation area has a potential signal source, and divide the azimuth-elevation plane of a single range gate as follows: the azimuth angle is divided into I grids, and the corresponding angles are {θ1, θ2, ..., θ i ,…,θ I}; The pitch angle is divided into J grids, and the corresponding angles are The azimuth angle is θ i , the pitch angle is The steering vector corresponding to the signal source is: Where, is the steering vector of the horizontal array, is the steering vector of the vertical array, where 1≤i≤I,1≤j≤J, represents the Kronecker product;

[0021] In step 2.3), consider the entire azimuth-elevation plane and obtain the steering vector matrix A of the azimuth-elevation plane:

[0022] In step 2.4), assume that the noise in the space is additive white Gaussian noise e, then the echo model of the azimuth-elevation dimension is: y(n) = AX(n) + e(n); where y(n) is the array output at different snapshots, X(n) = [x 11 (n),x 12 (n),…x IJ (n)],x ij (n) is the position at azimuth angle θ i , pitch angle The scattering coefficient of the potential signal source at the grid, n = 1, 2…L is the number of snapshots.

[0023] As a further optimization solution of the present invention for the airborne radar forward-looking three-dimensional imaging technology based on a two-dimensional super-resolution algorithm, the specific steps of step 3) are as follows:

[0024] Step 3.1), process the spatial snapshot data of the two-dimensional array by range-pulse; initialize the power matrix P = diag ([p 11 ,p 12 ,…,p IJ ]), where the azimuth angle is θ i , the pitch angle is The initial power of the signal source is

[0025] Step 3.2) According to the weighted least squares criterion, the weighted sum of squared errors is taken as the cost function E: E = [y(n) - AX(n)] H W[y(n)-AX(n)], where W is the weight matrix, which satisfies W={E[e(n)*e(n) H ]} -1 Consider a single two-dimensional grid and find the minimum value by taking the derivative of the above formula with respect to X(n):

[0026] According to the weighted least squares criterion, W is the covariance matrix of interference and noise To simplify the calculation, the inverse matrix of the autocorrelation matrix of the echo signal is used. Instead, M1M2 is the number of elements in the planar array, and the above formula can be rewritten as: Where,

[0027] Step 3.3), in order to make the estimation more accurate, Iterate until The value of converges.

[0028] As a further optimization solution of the present invention for the airborne radar forward-looking three-dimensional imaging technology based on a two-dimensional super-resolution algorithm, the specific steps of step 4) are as follows:

[0029] Perform the following processing on each range gate to obtain range-azimuth-elevation three-dimensional super-resolution data:

[0030] At each snapshot, each received echo signal corresponds to a beam center in the azimuth direction. For the same range gate, each super-resolution spectrum processed in step 3) is shifted to the angle corresponding to the beam center. All super-resolution spectra are superimposed to obtain the range-elevation super-resolution for a single range gate.

[0031] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0032] This invention proposes a forward-looking 3D imaging technology for airborne radar based on a 2D super-resolution algorithm, addressing the drawback of forward-looking 2D imaging, which cannot obtain altitude information for a single range-azimuth unit. Furthermore, to address the drawback of airborne radar's low snapshot accumulation of the same observed area, the 2D iterative adaptive algorithm proposed in this invention only requires a single 2D snapshot signal to achieve azimuth-elevation 2D super-resolution, effectively reducing the amount of data processing. Finally, the forward-looking 3D imaging algorithm projects the elevation information in polar coordinates onto altitude information in a spatial rectangular coordinate system, addressing the inability to visualize altitude information in polar coordinates. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a forward-looking three-dimensional imaging model for airborne array radar;

[0034] Figure 2 is the azimuth-altitude imaging effect of the real beam method;

[0035] Figure 3 It is the azimuth-altitude imaging effect of the two-dimensional iterative adaptive method;

[0036] Figure 4 Point target imaging for real beam method;

[0037] Figure 5 Point target imaging of the method proposed in the invention;

[0038] Figure 6 Scenario simulation for the real beam method;

[0039] Figure 7 This is a scenario simulation of the method proposed in this invention. DETAILED DESCRIPTION

[0040] The following is a detailed description of an airborne radar forward-looking three-dimensional imaging technology based on a two-dimensional super-resolution algorithm according to the present invention.

[0041] Step 1: Using an airborne planar array radar, the array is placed perpendicular to the aircraft's flight direction, with elements spaced evenly apart. Operating in a one-transmit-multiple-receive mode, individual elements transmit linear frequency-modulated signals with a carrier frequency added, and the entire two-dimensional planar array receives the echoes. The beam scans along the azimuth direction, transmitting and receiving multiple pulses angle by angle in the azimuth direction. After receiving and demodulating the echo signals, a four-dimensional echo signal is generated: range-pulse-elevation-array-azimuth array.

[0042] Step 2: Super-resolution can be achieved in the range direction by pulse compression, so the present invention focuses on the echo modeling in the azimuth-elevation direction. Figure 1 As shown, the aircraft moves along the y-axis at a speed of v aFly at a constant speed, and the beam scans along the azimuth direction. Place a planar array along a plane perpendicular to the flight direction, with the array element spacing d. (λ is the wavelength.) The array elements are arranged in an M1×M2 array, where M1 is the number of elements in each horizontal row and M2 is the number of elements in each vertical column.

[0043] During reception, the azimuth-elevation grid of each range gate needs to be scanned, assuming that each azimuth-elevation cell contains a potential signal source. The azimuth observation range is divided into I parts, and the elevation observation range is divided into J parts. The corresponding angles are {θ1,θ2,…,θ i ,…,θ I}、 Taking the first element in the upper right corner as the reference element, the azimuth angle is θ i , the pitch angle is The steering vector of the M1 array elements in the horizontal direction corresponding to the signal source can be written as:

[0044]

[0045] The steering vectors of the M2 array elements in the vertical direction are:

[0046]

[0047] Then the azimuth angle is θ i , the pitch angle is The steering vector matrix corresponding to the signal source can be written as:

[0048]

[0049] in is the Kronecker product, is a vector of size M1M2×1.

[0050] In actual received signals, noise is inevitable. Assuming the interference noise is Gaussian white noise e(n), after expanding the two-dimensional snapshot signal of size M1×M2 into a one-dimensional vector of size M1M2×1, the array output corresponding to the snapshot of the signal source can be written as: Where n=1,2…L is the number of snapshots. ij (n) is the nth snapshot with an azimuth angle of θ i , the pitch angle is The backscatter coefficient of the signal source, where 1≤i≤I,1≤j≤J.

[0051] For all potential signal sources, the total steering vector matrix can be written as:

[0052] Then the total output of the array can be written as: y(n) = AX(n) + e(n). In the formula, X(n) = [x 11 (n),x 12 (n),…x IJ (n)] T .

[0053] Step 3: The iterative adaptive method is a parameter-free spectrum estimation algorithm that uses the weighted least squares criterion to construct a cost function and iterates to continuously approximate the estimated value to the true value. The two-dimensional iterative adaptive algorithm is an extension of the one-dimensional algorithm. Its detailed steps are as follows:

[0054] Define a power matrix P = diag([p 11 ,p 12 ,…,p IJ ]). The matrix stores the diagonal elements p ij The azimuth angle is θ i , the pitch angle is The power of the potential signal source.

[0055] According to the weighted least squares criterion, the weighted sum of squared errors is used as the cost function: E = [y(n) - AX(n)] H W[y(n)-AX(n)]=y H Wy-X H A H Wy-y H WAX+X H A H WAX

[0056] Taking the derivative of the above formula with respect to X(n), the minimum value can be obtained:

[0057] The azimuth angle is θ i , the pitch angle is The estimated value of the potential signal source scattering coefficient. According to the weighted least squares criterion, the weighting matrix W can be constructed by the covariance matrix V of the noise and interference, which satisfies W = V -1 , where is the autocorrelation matrix of the echo signal, which satisfies: In the actual calculation process, each angle needs to be calculated once for each iteration. This will greatly increase the computational complexity of the algorithm. The matrix inversion lemma states that Can be Instead. Thus we get:

[0058] Through the above formula, the spectrum estimation of the signal source at the corresponding position is completed. However, the result obtained by a single estimation often has a large error. In order to make the estimated value closer to the true value, it is necessary to repeat the above process. Let l represent the number of iterations, and calculate the previous estimated value by The power of this iteration is updated (l) , and then update the echo autocorrelation matrix and estimated value to obtain and Through multiple iterations convergence.

[0059] Simulations have shown that the two-dimensional iterative adaptive algorithm generally converges after about 10 iterations.

[0060] Step 4: Perform 2D iterative adaptive processing on a single 2D snapshot signal to obtain an azimuth-elevation super-resolution spectrum for a single range-pulse. During echo reception, each snapshot echo signal corresponds to a beam center. For a single range gate, each processed 2D super-resolution spectrum is spectrally shifted to the angle corresponding to its beam center. All shifted 2D spectra are superimposed to obtain 2D azimuth-elevation super-resolution for the single range gate. Repeating this process for each range gate sequentially yields 3D range-azimuth-elevation super-resolution.

[0061] Step 5: Because the pitch and actual height information in polar coordinates are inverted, it is impossible to plot the height information of the scene in polar coordinates. Use interpolation to transform the coordinates to a spatial rectangular coordinate system, plot the 3D data, and obtain the final 3D image of the forward-viewing area.

[0062] Finally, simulations are performed. The forward-looking 3D imaging results are compared with those of the windowed real beam method, and point target simulation and scene simulation of this method are given to verify the effectiveness of this method.

[0063] Assume that the height axis of the ground target is z, the direction of the aircraft's flight is y, and the direction perpendicular to yz is x. Set up 7 independent signal sources, whose position information is shown in Table 1, and the beam main lobe width is 4°. The azimuth-elevation super-resolution imaging results of the real beam method and the algorithm proposed in this invention are shown in Figures 1 and 2. Figure 2 、 Figure 3 shown. Figure 4 and Figure 5 The forward-looking 3D imaging results in the Cartesian coordinate system using the real beam method and the proposed algorithm are shown. It can be seen that when using real beam imaging, aliasing occurs in the azimuth-elevation direction of point targets, making it impossible to distinguish adjacent point targets within the same range gate. The proposed algorithm achieves super-resolution in both azimuth and elevation, effectively distinguishing multiple point targets within the same beam mainlobe and enabling alias-free reconstruction.

[0064] Table 1 Point target parameters

[0065]

[0066] To verify the effectiveness of the proposed method for scenario targets, two scenario targets are simulated. The parameters of the two scenarios are shown in Table 2.

[0067] Table 2 Scenario target parameters

[0068]

[0069] The forward-looking 3D imaging results of the real beam method and the forward-looking 3D imaging results of the method proposed in the present invention are shown as follows: Figure 6 、 Figure 7 As shown in the figure, real beam imaging results in a significant number of sidelobes, rendering the two scene objects indistinguishable. However, the proposed algorithm accurately reconstructs the two scene objects, achieving super-resolution in all three dimensions. The effectiveness of the proposed algorithm was demonstrated through point and area target simulations.

Claims

1. A forward-looking three-dimensional imaging method for airborne radar based on a two-dimensional super-resolution algorithm, characterized in that: The following steps are involved: Step 1) The airborne radar uses a planar array to transmit multiple signals, and the beam is scanned along the azimuth direction to obtain four-dimensional echo data of range-pulse-pitch array-azimuth array; Step 2) After pulse compression and range migration correction are performed on each range gate, grid division is performed. Each grid is assumed to contain a potential signal source, and a two-dimensional spatial steering vector is constructed for each azimuth-elevation grid. This leads to the construction of a steering vector matrix and echo model for the entire azimuth-elevation plane. Step 3) Performing two-dimensional super-resolution processing on the spatial snapshot data of the two-dimensional array on a range-by-pulse basis: constructing an initial power matrix of the signal source for each two-dimensional snapshot data; The cost function is constructed by weighted least squares criterion, and the expression of the source estimation value is obtained by minimizing the cost function; The weight matrix in this expression is replaced by the autocorrelation matrix of the signal source through the inversion lemma to reduce the computational complexity. The parameters are then updated through continuous iteration until the resulting two-dimensional source estimate converges. The two-dimensional estimated signal is plotted, i.e., the azimuth-elevation two-dimensional super-resolution spectrum of a single snapshot. Step 4) Perform the following processing on each range gate in turn: Based on the beam center at each snapshot sampling, perform two-dimensional spectrum incoherent accumulation on all super-resolution spectra of the same range gate to complete azimuth-elevation super-resolution of a single range gate; Step 5) uses interpolation to perform coordinate transformation, transforms the polar coordinate data into a spatial rectangular coordinate system, and obtains forward-looking three-dimensional super-resolution imaging by drawing a three-dimensional graph.

2. The airborne radar forward-looking 3D imaging method based on a 2D super-resolution algorithm according to claim 1, characterized in that: The specific steps of step 1) are as follows: A planar array is placed along a plane perpendicular to the aircraft's flight direction, with array elements spaced equidistant from each other. A one-tweet-multiple-receiver mode is used to perform beam scanning in azimuth within the observation area. A single independent array element transmits a linear frequency modulation signal with an additional carrier frequency, and the entire two-dimensional planar array receives the echo. After completing the beam scanning of the observed area and demodulating the echo signal, four-dimensional echo data of range-pulse-elevation array-azimuth array is obtained.

3. The airborne radar forward-looking 3D imaging method based on a 2D super-resolution algorithm according to claim 1, characterized in that: The specific steps of step 2) are as follows: Step 2.1), perform Fourier transform on the range direction, and perform pulse compression and range migration correction in the range frequency domain; Step 2.2), for the azimuth-elevation plane, assume that each azimuth-elevation grid in the observation area has a potential signal source, and divide the azimuth-elevation plane of a single range gate as follows: the azimuth angle is divided into I grids, and the corresponding angles are {θ1, θ2, ..., θ i ,…,θ I }; The pitch angle is divided into J grids, and the corresponding angles are Then the azimuth is θi i , the pitch angle is The steering vector corresponding to the signal source is: Where, is the steering vector of the horizontal array, is the steering vector of the vertical array, where 1≤i≤I,1≤j≤J, represents the Kronecker product; In step 2.3), consider the entire azimuth-elevation plane and obtain the steering vector matrix A of the azimuth-elevation plane: In step 2.4), assume that the noise in the space is additive white Gaussian noise e, then the echo model of the azimuth-elevation dimension is: y(n) = AX(n) + e(n); where y(n) is the array output at different snapshots, X(n) = [x 11 (n),x 12 (n),…x IJ (n)],x ij (n) is the position at azimuth angle θ i , pitch angle The scattering coefficient of the potential signal source at the grid, n = 1, 2…L is the number of snapshots.

4. The airborne radar forward-looking 3D imaging method based on a 2D super-resolution algorithm according to claim 3, characterized in that: The specific steps of step 3) are as follows: Step 3.1), process the spatial snapshot data of the two-dimensional array by range-pulse; initialize the power matrix P = diag ([p 11 ,p 12 ,…,p IJ ]), where the azimuth angle is θ i , the pitch angle is The initial power of the signal source is Step 3.2) According to the weighted least squares criterion, the weighted sum of squared errors is taken as the cost function E: E = [y(n) - AX(n)] H W[y(n)-AX(n)], where W is the weight matrix, W={E[e(n)*e(n) H ]} -1 Consider a single two-dimensional grid and find the minimum value by taking the derivative of the cost function E with respect to X(n): According to the weighted least squares criterion, W is the covariance matrix of interference and noise To simplify the calculation, the inverse matrix of the autocorrelation matrix of the echo signal is used. Instead of W, M1M2 is the number of elements in the planar array, and the above formula can be rewritten as: Where, Step 3.3), in order to make the estimation more accurate, Iterate until The value of converges.

5. The airborne radar forward-looking 3D imaging method based on a 2D super-resolution algorithm according to claim 1, characterized in that: The specific steps of step 4) are as follows: The following processing is performed on each range gate to obtain range-azimuth-elevation three-dimensional super-resolution data: At each snapshot, each received echo signal corresponds to a beam center in the azimuth direction. For the same range gate, each super-resolution spectrum processed in step 3) is shifted to the angle corresponding to the beam center. All super-resolution spectra are superimposed to obtain the range-elevation super-resolution for a single range gate.

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