Dimensionality reduction processing method for space-time joint forward-looking imaging of airborne array radar

Abstract

The application discloses a dimension reduction processing method for space-time joint forward-looking imaging of an airborne array radar, constructs a forward-looking imaging geometric model of the airborne array radar, receives a three-dimensional echo matrix in range, azimuth and channel, then transforms data in a single coherent processing time interval into a frequency domain and compensates Doppler phase for the echo matrix, then truncates spectral effective information to obtain snapshot data after dimension reduction. Then the newly obtained space-time snapshot is applied to space-time adaptive iterative super-resolution imaging, a space-time super-resolution spectrum curve corresponding to a space-time snapshot of a range-azimuth unit is estimated, and according to a movement speed of an aircraft and antenna scanning parameters, the super-resolution spectrum curve of each range-azimuth unit is subjected to spectrum accumulation, and finally a two-dimensional forward-looking image is obtained. The application effectively compresses space-time data by truncating echo effective information in a Doppler domain, significantly reduces operation complexity, and meanwhile maintains imaging quality.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, and relates to airborne radar forward-looking imaging signal processing technology, specifically to a dimensionality reduction processing method for space-time joint forward-looking imaging of airborne array radar. Background Technology

[0002] Radar (Radio Detection and Ranging), as a long-range detection tool, has played an indispensable role in military, civilian, and scientific research fields since its inception. With the continuous advancement of radar technology, forward-looking radar imaging technology has gradually become a research hotspot in recent years. It overcomes the problem of imaging failure in the forward-looking area of ​​traditional imaging algorithms such as SAR or DBS, and can form accurate two-dimensional or three-dimensional images of radar forward-looking area echoes.

[0003] Currently, there are many technologies applied to radar forward-looking imaging, including monopulse imaging, bistatic SAR forward-looking imaging, and array radar super-resolution imaging. Existing research focuses on spatiotemporal two-dimensional super-resolution forward-looking imaging algorithms in array radar super-resolution imaging. This algorithm estimates the spatial spectrum using a single spatiotemporal snapshot of each range-azimuth cell, and then performs incoherent spectrum accumulation to form a two-dimensional forward-looking image. However, because this algorithm uses a spatiotemporal joint processing method, the system's degrees of freedom are the product of the degrees of freedom of individual domains, resulting in a large number. This high number of degrees of freedom directly leads to a sharp increase in the computational load of the algorithm, making real-time processing of radar signals quite difficult.

[0004] Although numerous classical dimensionality reduction and rank reduction algorithms and theories for Space-Time Adaptive Processing (STAP) have been proposed in the field of array signal processing, such as the 3DT algorithm, these algorithms are difficult to directly apply to existing super-resolution forward-looking imaging technology for array radar. Currently, for the problems of large data volume and complex computation in real-time radar signal processing, a common approach is to downsample and pre-filter the echo data in the azimuth direction. However, directly downsampling the data in the azimuth direction will sacrifice some resolution, affecting the final imaging effect. Summary of the Invention

[0005] Purpose of the invention: This invention provides a dimensionality reduction method for space-time joint forward-looking imaging of airborne array radar. The method achieves dimensionality reduction by truncating the effective information of the echo spectrum, which greatly reduces the computational load of the algorithm and improves the computational speed.

[0006] Technical Solution: The present invention provides a dimensionality reduction processing method for space-time joint forward-looking imaging of airborne array radar, comprising the following steps:

[0007] (1) Construct a forward-looking imaging geometric model of an airborne array radar, use an airborne forward-looking array radar to acquire multi-channel echoes, the radar operates in step scanning mode, transmits several coherent pulses to the same azimuth at each coherent pulse interval, and samples the echoes to obtain range-pulse-array three-dimensional echo data.

[0008] (2) Perform pulse-by-pulse processing and phase compensation on the range-pulse-array three-dimensional echo data, transform the signal to the Doppler frequency domain, then perform dimensionality reduction processing on the data in the frequency domain to extract the effective information of the echo, then transform it to the time domain and update the guidance vector related parameters;

[0009] (3) Construct the space-time snapshot signal corresponding to each range-azimuth unit based on the multi-channel data after pulse compression; calculate the space-time guidance vector corresponding to each azimuth angle and form a space-time guidance vector matrix;

[0010] (4) Processing each range-azimuth cell, establishing a cost function based on the least squares criterion, and initializing the scattering coefficients. By iteratively updating the echo autocorrelation matrix until the algorithm converges, the super-resolution spectral curve corresponding to the space-time snapshot of the range-azimuth cell is calculated.

[0011] (5) Based on the aircraft's speed and antenna scanning parameters, the super-resolution spectral curves of each range-azimuth unit are stitched together to achieve the accumulation of spectral curves in the range-azimuth domain, ultimately forming a range-azimuth imaging image.

[0012] Furthermore, the implementation process of step (1) is as follows:

[0013] The carrier aircraft travels at a speed v a The system flies at a constant speed, with the array antenna system fixed on the moving platform along the tangent to the flight path. The array antennas are evenly distributed at equal intervals, forming N... s There are 1 receiving channel with a channel spacing of d; the radar scans the area in front by stepping through a narrow beam; when the beam center points to a fixed azimuth angle θ, θ is the angle between the beam center and the aircraft speed; within one coherent pulse interval, the radar transmitter transmits N... p A coherent linear frequency modulated pulse is generated, and then the beam is pointed to the next azimuth angle and the operation is repeated. Finally, the different pulse echoes received by the same array element are sampled and then arranged in columns to obtain the original range-pulse two-dimensional echo matrix. The data received by multiple array elements are combined to obtain range-pulse-array three-dimensional echo data.

[0014] When the beam center points to the azimuth angle θ, N, composed of the phase difference between the target and the horizontal linear array, is... s ×1-dimensional spatial guidance vector:

[0015]

[0016] N is composed of the Doppler frequencies generated by the relative motion between the radar and the target. p ×1-dimensional time guidance vector:

[0017]

[0018] Therefore, N is formed by the two guiding vectors. s N p ×1-dimensional spacetime guidance vector:

[0019]

[0020] in, Represents the Kronecker product, where d is the channel spacing, λ is the signal wavelength, θ is the beam center pointing angle, and v a This refers to the speed of the aircraft.

[0021] Furthermore, the implementation process of step (2) is as follows:

[0022] Calculate the phase difference to be compensated for in each pulse of the echo, and compensate the spectrum to zero frequency. The phase difference to be compensated is:

[0023]

[0024] Among them, R l (t) represents the instantaneous slant range of the array radar reaching the center of the current pulse scene;

[0025] Perform FFT transformation on the data of a single CPI at each distance and plot the spectrum before and after compensation. Extract the spectrum of the center part of the spectrum and inversely transform the spectrum to the time domain. Perform the same operation on all distance gates and all channels to obtain the dimension-reduced echo matrix.

[0026] Further, the updated guidance vector parameters in step (2) are as follows:

[0027]

[0028] Where β is the angle of the beam center corresponding to the current pulse.

[0029] Furthermore, the implementation process of step (3) is as follows:

[0030] Assume there are K targets in the imaging area ahead, and their azimuth angles relative to the radar are θ1, θ2, ..., θ. K Within a single cyclic scan, the received data consists of range-pulse-array three-dimensional samples. For a given range-azimuth cell, the pulse-array sampled data constitutes a two-dimensional spatiotemporal snapshot.

[0031] y = Ax + N

[0032] Where x is the echo signal reflected from the target, N is additive white Gaussian noise, independent of the other components; A is an NM×K dimensional spacetime guidance vector matrix, A=[a(θ1),a(θ2),…,a(θ2)… K )],in a s (θ k ) is an M×1 dimensional spatial guidance vector composed of the phase differences between the target's arrival at the horizontal linear array; a t (θ k The vector is an N×1-dimensional time guidance vector composed of Doppler frequencies generated by the relative motion between the radar and the target. Represents the Kronecker product.

[0033] Furthermore, the implementation process of step (4) is as follows:

[0034] The scattering coefficient x of the target is accurately reconstructed, and an estimate of the scattering coefficient is obtained using the weighted least squares criterion:

[0035]

[0036] Wherein, the autocorrelation matrix of the echo is R = AP k A H +ρI, where ρ is the regularization coefficient.

[0037] Furthermore, the estimation of the scattering coefficient employs an iterative method to continuously reduce the error between the estimated value and the true value. Specifically, the ground scattering coefficient is first initialized by setting the autocorrelation matrix R to the identity matrix, and then substituted into the scattering coefficient estimation formula to obtain... The initial estimate; then use the estimate The autocorrelation matrix of the echo signal is updated, and then substituted back into the scattering coefficient calculation formula to obtain a more accurate estimate of the ground scattering coefficient. This process is repeated until the algorithm converges, yielding the final scattering coefficient estimate.

[0038] Furthermore, the implementation process of step (5) is as follows:

[0039] The azimuth super-resolution spectral curves corresponding to each range-azimuth unit space-time snapshot obtained in step (4) are stitched together with the corresponding azimuth angles for the azimuth super-resolution spectral curves of different azimuth units at the same range gate, thus realizing the accumulation of spectral curves in the range-azimuth domain. The range-azimuth imaging results can be obtained by displaying the accumulated and stored data.

[0040] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are: The present invention does not rely on a large amount of independent and identically distributed snapshot data. It mainly achieves dimensionality reduction by truncating the effective information of the echo spectrum and establishing an objective function under the least squares criterion. The autocorrelation matrix of the array received signal is estimated by iterative method, which greatly reduces the computational load of the algorithm and improves the computational speed. Attached Figure Description

[0041] Figure 1 This is a flowchart of the present invention;

[0042] Figure 2 This is a schematic diagram of the forward-looking imaging geometric model of an airborne array radar.

[0043] Figure 3 The images show a comparison of the spectra before and after compensation, where (a) is the spectra before compensation and (b) is the spectra after compensation.

[0044] Figure 4 This is a flowchart of the dimensionality reduction process;

[0045] Figure 5 Schematic diagram of the snapshot model when empty;

[0046] Figure 6 This is a schematic diagram of azimuth super-resolution spectrum stitching;

[0047] Figure 7 Image of the real-beam imaging result for a point target;

[0048] Figure 8 Image of spatiotemporal iterative super-resolution imaging results for point targets;

[0049] Figure 9 A comparison of the azimuth profiles of point targets, including real-beam imaging and spatiotemporal imaging;

[0050] Figure 10 A comparison of the azimuth profiles of point targets, including both dimensionality-reduced and non-dimensionality-reduced spatiotemporal imaging.

[0051] Figure 11 For the target scene diagram;

[0052] Figure 12 The images show a comparison of the target scene imaging results, where (a) is the real beam imaging result and (b) is the dimension-reduced spatiotemporal joint imaging result. Detailed Implementation

[0053] The present invention will now be described in further detail with reference to the accompanying drawings.

[0054] like Figure 1 As shown, this invention proposes a dimensionality reduction processing method for space-time joint forward-looking imaging of airborne array radar, specifically including the following steps:

[0055] Step 1: Construct a forward-looking imaging model for an airborne array radar. An airborne forward-looking array radar is used to acquire multi-channel echoes. The radar operates in step-scan mode, transmitting several coherent pulses to the same azimuth at each coherent pulse interval. Echoes are sampled to obtain range-pulse-array three-dimensional echo data.

[0056] A horizontal array antenna receiving system along the azimuth direction is used to receive echo signals from multiple channels, thereby achieving spatial data sampling. The radar array operates in a step-scan mode; when the radar beam is aligned with a specific direction, it transmits continuous linear frequency modulated pulses according to the pulse repetition frequency (PRF) or interval (PRI) during a coherent pulse interval (CPI). During this process, the system receives the echoes of a series of coherent pulses, thereby collecting time-series sampled data.

[0057] The specific geometric model of forward-looking imaging for airborne array radar is as follows: Figure 2 As shown, the carrier aircraft travels at a speed v a The system flies at a constant speed, with the array antenna system fixed on the moving platform along the tangent to the flight path. The array antennas are evenly distributed at equal intervals, forming N... s There are 1 receiving channel with a channel spacing of d. The radar scans the area in front using a narrow beam in a step-by-step manner. When the beam center points to a fixed azimuth angle θ (θ is the angle between the beam center and the aircraft speed), the radar transmitter transmits N signals within one coherent pulse interval (CPI). p A coherent linear frequency modulated pulse (LFM) is generated, and then the beam is pointed to the next azimuth angle, repeating the operation. Finally, the different pulse echoes received by the same array element are sampled and arranged in columns to obtain the original range-pulse two-dimensional echo matrix. The data received by multiple array elements are combined to obtain range-pulse-array three-dimensional echo data.

[0058] When the beam center points to the azimuth angle θ, N, composed of the phase difference between the target and the horizontal linear array, is... s ×1-dimensional spatial guidance vector:

[0059]

[0060] N is composed of the Doppler frequencies generated by the relative motion between the radar and the target. p ×1-dimensional time guidance vector:

[0061]

[0062] Therefore, N is formed by the two guiding vectors. s N p ×1-dimensional spacetime guidance vector:

[0063]

[0064] in, Represents the Kronecker product, where d is the channel spacing, λ is the signal wavelength, θ is the beam center pointing angle, and v a This refers to the speed of the aircraft.

[0065] Step 2: Perform phase compensation on the range-pulse-array three-dimensional echo data, and then perform dimensionality reduction on the compensated data, specifically as follows: Figure 4 As shown.

[0066] Calculate the phase difference to be compensated for in each pulse of the echo, and compensate the spectrum to zero frequency. The phase difference to be compensated is:

[0067]

[0068] Among them, R l (t) represents the instantaneous slant range of the array radar reaching the center of the current pulse scene.

[0069] Perform FFT transformation on the data of individual CPIs at each distance and plot the spectrum before and after compensation, as shown below. Figure 3 As shown, it can be seen that the effective information of the echo spectrum is shifted to the vicinity of zero frequency.

[0070] Then, the spectrum at the center is extracted, and the spectrum is inversely transformed to the time domain. The same operation is performed on all range gates and all channels, finally yielding the dimension-reduced echo matrix.

[0071] Because phase compensation is required for the echo, N is needed due to the relative motion between the radar and the target. p The updated guidance vector is a 1×1 dimensional time guidance vector:

[0072]

[0073] Where β is the angle of the beam center corresponding to the current pulse.

[0074] Step 3: Construct the space-time snapshot signal corresponding to each range-azimuth unit based on the multi-channel data after pulse compression; calculate the space-time guidance vector corresponding to each azimuth angle to form a space-time guidance vector matrix.

[0075] Using data acquired by an airborne horizontal array radar system, pulse compression in the range dimension is performed. By selecting the two-dimensional received data generated by each array element in each range-azimuth cell, a spatiotemporal snapshot signal for the corresponding range-azimuth cell can be constructed. Subsequently, these spatiotemporal snapshot signals are superimposed, converting the original two-dimensional data matrix into a one-dimensional data vector, such as... Figure 5As shown. Then, for all azimuth angles within the imaging area, calculate the corresponding spatiotemporal guidance vector a(θ), and combine them to form the spatiotemporal guidance vector matrix A.

[0076] Assume there are K targets in the imaging area ahead, and their azimuth angles relative to the radar are θ1, θ2, ..., θ. K Within a single cyclic scan, the received data is a three-dimensional matrix of range-pulse-channel. For a given range-azimuth cell, the pulse-array sampling data constitutes a two-dimensional spatiotemporal snapshot:

[0077] y = Ax + N

[0078] Where A is N p N s ×K-dimensional spacetime guidance vector matrix, A=[a(θ1),a(θ2),…,a(θ)] K )],in x represents the echo signal reflected from the target, and N represents additive white Gaussian noise, independent of the other components.

[0079] Step 4: After receiving the space-time snapshot, the target distribution function after weighting the antenna pattern needs to be accurately reconstructed. Range-wise azimuth cell processing is used. Considering that when the beam points to a certain azimuth, the interference and noise in the echo are actually correlated, a weighted least squares criterion is used to establish the loss function:

[0080]

[0081] To minimize the sum of squared errors, expand the loss function and... By taking the derivative and setting it to zero, we can obtain an estimate of the scattering coefficient:

[0082]

[0083] The autocorrelation matrix of the echo is R = AP k A H +ρI does not rely on a large amount of snapshot data, but is obtained through iteration, where ρ is the regularization coefficient and I is the identity matrix.

[0084] When a precise estimate of x is required, an iterative method can be used to continuously reduce the error between the estimated value and the true value. The iterative process is established as follows:

[0085] First, the ground scattering coefficient is initialized by setting the autocorrelation matrix R to the identity matrix. Then, it is substituted into the scattering coefficient estimation formula to obtain... The initial estimate; then use the estimate The autocorrelation matrix of the echo signal is updated, and then substituted back into the scattering coefficient calculation formula to obtain a more accurate estimate of the ground scattering coefficient. This process is repeated until the algorithm converges, yielding the final scattering coefficient estimate.

[0086] Step 5: Based on the aircraft's speed and antenna scanning parameters (beam scanning range, beam scanning speed), stitch the spectral curves of each range-azimuth unit together to achieve the accumulation of spectral curves in the range-azimuth domain, ultimately forming a range-azimuth imaging image.

[0087] For each range-azimuth unit space-time snapshot obtained in step 4, the azimuth spectrum curves corresponding to the azimuth angles of different azimuth units for the same range gate are summed, as shown in the schematic diagram. Figure 6 As shown, displaying the accumulated and stored data yields the range and azimuth imaging results.

[0088] Next, point target simulation is performed. Three point targets are located at [2000m, -0.7°], [2000m, 1.2°], and [1900m, 1.2°], respectively, with the same amplitude and a dwell pulse count of 32. The 3dB width of the real beam is approximately 2.1 degrees. The real beam scanning imaging results are as follows... Figure 7 As shown, after real-beam imaging, two closely spaced targets at the same distance cannot be distinguished. However, after processing with the spatiotemporal adaptive iterative super-resolution algorithm, the three point targets are clearly visible, as shown in the imaging results. Figure 8 As shown. Figure 9 Comparison of azimuth profiles of real-beam imaging and dimension-reduced spatiotemporal imaging at the same distance gate (2000m). Figure 10 Comparison of dimensionality-reduced spatiotemporal imaging azimuth profiles were plotted for different spectral lengths, including 8, 16, and no truncation. It can be seen that truncation has little impact on the results but significantly reduces the computational load of the algorithm. Two targets with the same range gate were imaged at -0.7° and 1.2° respectively. This demonstrates that the algorithm can effectively distinguish multiple targets in the main lobe, providing feasibility for dimensionality reduction processing of forward-looking imaging for airborne radar.

[0089] Existing high-resolution complex images of airborne SAR are selected as the ground simulation scene for the forward-looking region to be imaged. The simulation scene is a ground building area, and the target scene image is shown below. Figure 11 As shown, radar forward-looking echo data is generated in this way, with a dwell pulse count of 64. During dimensionality reduction, the spectral truncation length is set to 16 and dimensionality reduction is performed before spatiotemporal joint imaging. Figure 12Figures (a) and (b) show the results of real beam imaging and dimension-reduced spatiotemporal imaging, respectively. It can be seen that the imaging effect is good, strong scattering points are clearly visible, and the contours of surface targets are distinct. This proves that the algorithm can effectively image forward-looking scenes while significantly reducing the amount of computation.

[0090] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A dimensionality reduction processing method for space-time joint forward-looking imaging of airborne array radar, characterized in that, Includes the following steps: (1) Construct a forward-looking imaging geometric model of an airborne array radar. Use an airborne forward-looking array radar to acquire multi-channel echoes. The radar operates in step scanning mode and transmits several coherent pulses to the same azimuth at each coherent pulse interval. Sample the echoes to obtain range-pulse-array three-dimensional echo data. (2) Perform pulse-by-pulse processing and phase compensation on the range-pulse-array three-dimensional echo data, transform the signal to the Doppler frequency domain, then perform dimensionality reduction processing on the data in the frequency domain to extract the effective information of the echo, then transform it to the time domain and update the guidance vector related parameters; (3) Construct the space-time snapshot signal corresponding to each range-azimuth unit based on the multi-channel data after pulse compression; Calculate the space-time guidance vector corresponding to each azimuth angle and construct the space-time guidance vector matrix; (4) Processing each range-azimuth cell, establishing a cost function based on the least squares criterion, and initializing the scattering coefficients. By iteratively updating the echo autocorrelation matrix until the algorithm converges, the super-resolution spectral curve corresponding to the space-time snapshot of the range-azimuth cell is calculated. (5) Based on the aircraft's speed and antenna scanning parameters, the super-resolution spectral curves of each range-azimuth unit are stitched together to achieve the accumulation of spectral curves in the range-azimuth domain, and finally form a range-azimuth imaging image. The implementation process of step (1) is as follows: The carrier aircraft travels at a speed v a The aircraft flies at a constant speed, and the array antenna system is fixed on the aircraft along the tangent to the flight path. The array antennas are evenly distributed at equal intervals, forming N... s There are one receiving channel with a channel spacing of d; the radar scans the area in front by stepping through a narrow beam. When the beam center points to a fixed azimuth angle hour, The angle between the beam center and the aircraft speed is given. Within one coherent pulse interval, the radar transmitter emits N... p A coherent linear frequency modulated pulse is generated, and then the beam is pointed to the next azimuth angle and the operation is repeated; finally, the different pulse echoes received by the same array element are sampled and then arranged in columns to obtain the original range-pulse two-dimensional echo matrix. Multiple array elements receive data and combine them to obtain range-pulse-array three-dimensional echo data; When the beam center points to the azimuth angle At that time, the phase difference between the target's arrival at the horizontal linear array constitutes... 3D space guiding vector: Composed of Doppler frequencies generated by the relative motion between the radar and the target 3D time-guided vector: Therefore, the two guiding vectors constitute Spacetime guidance vector: in, This represents the Kronecker product, where d is the channel spacing. For the signal wavelength, v is the beam center pointing angle. a For the speed of the carrier aircraft; The implementation process of step (2) is as follows: Calculate the phase difference to be compensated for in each pulse of the echo, and compensate the spectrum to zero frequency. The phase difference to be compensated is: in, The instantaneous slant range of the array radar reaching the center of the current pulse scene; Perform FFT transformation on the data of a single CPI at each distance and plot the spectrum before and after compensation. Extract the spectrum of the center part of the spectrum and inversely transform the spectrum to the time domain. Perform the same operation on all distance gates and all channels to obtain the dimension-reduced echo matrix.

2. The dimension reduction processing method for space-time joint forward-looking imaging of airborne array radar according to claim 1, characterized in that, The updated guidance vector parameters in step (2) are as follows: Where β is the angle of the beam center corresponding to the current pulse.

3. The dimension reduction processing method for space-time joint forward-looking imaging of airborne array radar according to claim 2, characterized in that, The implementation process of step (3) is as follows: Assume there are K targets in the imaging area ahead, and their azimuth angles relative to the radar are respectively... Within a single cyclic scan, the received data consists of range-pulse-array three-dimensional samples. For a given range-azimuth cell, the pulse-array sampled data constitutes a two-dimensional spatiotemporal snapshot. in, The target scattering coefficient, It is additive white Gaussian noise, independent of other components; for 3D spacetime guidance vector matrix, ,in ; Composed of the phase difference of the target arriving at the horizontal linear array 3D space guiding vector; Composed of Doppler frequencies generated by the relative motion between the radar and the target 3D time-guided vector, Represents the Kronecker product.

4. The dimension reduction processing method for space-time joint forward-looking imaging of airborne array radar according to claim 3, characterized in that, The implementation process of step (4) is as follows: Target scattering coefficient Accurate reconstruction is performed, and the weighted least squares criterion is used to obtain an estimate of the scattering coefficients: Among them, the autocorrelation matrix of the echo , It is the regularization coefficient.

5. The dimension reduction processing method for space-time joint forward-looking imaging of airborne array radar according to claim 4, characterized in that, The estimation of the scattering coefficient employs an iterative method to continuously reduce the error between the estimated and true values. Specifically, the ground scattering coefficient is first initialized, and the autocorrelation matrix is ​​set... Let the identity matrix be substituted into the scattering coefficient estimation formula to obtain... The initial estimate; then use the estimate The autocorrelation matrix of the echo signal is updated, and then substituted back into the scattering coefficient calculation formula to obtain a more accurate estimate of the ground scattering coefficient. This process is repeated until the algorithm converges, yielding the final scattering coefficient estimate. .

6. The dimension reduction processing method for space-time joint forward-looking imaging of airborne array radar according to claim 5, characterized in that, The implementation process of step (5) is as follows: The azimuth super-resolution spectral curves corresponding to each range-azimuth unit space-time snapshot obtained in step (4) are stitched together with the corresponding azimuth angles for the azimuth super-resolution spectral curves of different azimuth units at the same range gate, thus realizing the accumulation of spectral curves in the range-azimuth domain. The range-azimuth imaging results can be obtained by displaying the accumulated and stored data.

Images