A distance ambiguity suppression method combining sparse reconstruction and dual linear frequency modulation

Abstract

The invention discloses a distance ambiguity suppression method combining sparse reconstruction and dual linear frequency modulation, belonging to the field of synthetic aperture radar imaging technology; the steps are: constructing a SAR echo signal by alternately transmitting a linear frequency modulation signal with equal magnitude and opposite positive and negative range frequency modulation; performing range pulse compression, range migration correction and azimuth Fourier transform on the received SAR echo signal; constructing an observation matrix of the distance ambiguity signal; sparsely reconstructing and estimating the distance ambiguity signal through a cyclic iteration algorithm; subtracting the estimated ambiguity signal from the SAR echo signal; performing azimuth pulse compression and azimuth inverse Fourier transform on the processed SAR echo signal. The invention combines sparse reconstruction and dual linear frequency modulation technology, performs dual linear frequency modulation on the transmitted signal, uses a cyclic iteration algorithm to reconstruct the ambiguity zone, improves the distance ambiguity suppression effect, improves the accuracy of distance ambiguity suppression and improves the applicability of distance ambiguity suppression.

Description

Technical Field

[0001] The invention belongs to the technical field of synthetic aperture radar imaging, and in particular relates to a range ambiguity suppression method combining sparse reconstruction and dual linear frequency modulation. Background Art

[0002] Synthetic Aperture Radar (SAR) is a high-resolution imaging radar that can achieve two-dimensional high-resolution imaging of ground objects by emitting electromagnetic wave signals and processing the echoes when receiving them. It has attracted widespread attention because it can obtain high-resolution radar images similar to optical photography even under extremely low visibility weather conditions. At the same time, SAR radar also has the advantages of all-weather and all-day, and can overcome extreme weather to observe and image targets. In recent years, SAR radar range ambiguity suppression has become one of the research hotspots. Due to the sidelobe characteristics of the SAR antenna and its own pulse working system, the SAR radar may receive the echoes of the first few transmitted pulses when receiving, which will cause range ambiguity, thus affecting the imaging quality of the SAR image to a certain extent.

[0003] In order to solve the range ambiguity, it is generally suppressed through two aspects: SAR system design and SAR signal processing. In terms of system design, it is suppressed by designing the antenna receiving method and adopting orthogonal coding. For example, in the paper "Azimuth Phase Coding by Up and Down Chirp Modulation for Range Ambiguity Suppression" published by Xu Wei in 2019, by combining dual linear frequency modulation with azimuth phase coding, some ambiguity energy can be suppressed, but there is still ambiguity energy that cannot be completely removed. In terms of signal processing, it is suppressed by post-processing the echo image; for example, in the paper "A Range Ambiguity Suppression Method Combining Sparse Reconstruction and Matched Filtering" published by Qi Meng in 2022, it is shown that the range ambiguity signal can be reconstructed through sparse reconstruction, and the range ambiguity signal can be reconstructed by subtracting the total signal to achieve a good range ambiguity suppression effect. However, there is still some ambiguity energy. Summary of the invention

[0004] The object of the present invention is to provide a range ambiguity suppression method combining sparse reconstruction and bilinear frequency modulation to solve the problems raised in the above background technology.

[0005] The object of the present invention is achieved by: a distance ambiguity suppression method combining sparse reconstruction and dual linear frequency modulation, characterized in that the method comprises the following steps:

[0006] Step S1: constructing a SAR echo signal by alternately transmitting linear frequency modulation signals with equal magnitude and opposite positive and negative range modulation frequencies;

[0007] Step S2: construct a range-matched filter to perform range-direction pulse compression, range migration correction and azimuth Fourier transform on the received SAR echo signal;

[0008] Step S3: constructing the measurement matrix of the range fuzzy signal;

[0009] Step S4: sparsely reconstruct and estimate the range ambiguity signal through a cyclic iterative algorithm;

[0010] Step S5: subtract the estimated fuzzy signal from the SAR echo signal to remove the fuzzy energy;

[0011] Step S6: performing azimuth pulse compression and azimuth inverse Fourier transform on the processed SAR echo signal to obtain a useful SAR echo signal.

[0012] Preferably, in step S1, a SAR echo signal is constructed by alternately transmitting linear frequency modulation signals with equal magnitude and opposite positive and negative range modulation frequencies. The constructed SAR echo signal is expressed as:

[0013]

[0014]

[0015] Among them, s down (τ,t) is the distance ambiguity signal, s up (τ, t) is the range unambiguous signal, τ is the time in the range direction, t is the time in the azimuth direction, w a (t) represents the azimuth antenna pattern, R(t) is the azimuth time-varying distance between the radar and the target, λ is the wavelength, k r is the range modulation frequency, τ d (t) indicates the transmission time delay, τ p is the transmit pulse duration.

[0016] Preferably, in step S2, a range-matched filter is constructed, and the range-matched filter is expressed as:

[0017]

[0018] Where f is the range frequency, B r is the transmit pulse bandwidth and j is an imaginary unit.

[0019] Preferably, the range-direction pulse compression performed on the received SAR echo signal in step S2 is expressed as:

[0020]

[0021] Among them, τ is the time in range, t is the time in azimuth, and w a (t) represents the azimuth antenna pattern, R(t) is the azimuth time-varying distance between the radar and the target, λ is the wavelength, k r is the range modulation frequency, τ d (t) indicates the transmission time delay, τ p is the transmit pulse duration.

[0022] It is observed that the amplitude of the range-ambiguous signal is reduced compared to the useful signal after the pulse compression step. This is equivalent to suppressing the intensity by 3dB, while the duration of the signal is doubled, the distance linear frequency modulation still exists, and the modulation rate is halved to This step can prove that the dual linear frequency modulation signal can effectively suppress the energy of the range ambiguous signal.

[0023] Preferably, after the SAR echo signal received in step S2 is subjected to range migration correction and azimuth Fourier transform, the main image and its blurred image are represented as azimuth one-dimensional signals, and the azimuth one-dimensional signal expression is:

[0024]

[0025] Among them, f η Represents the azimuth frequency axis, R c and f dc They represent the imaging center time, the slant range and the Doppler center frequency at the reference zero time, λ represents the radar wavelength, σ represents the target backscattering cross-sectional area, and W a (·) represents the Doppler domain amplitude-frequency envelope, V r Indicates equivalent speed.

[0026] Preferably, in step S3, a measurement matrix of the range ambiguity signal is constructed, and the measurement matrix is ​​expressed as:

[0027]

[0028] in, Represents the echo signal of the mth discrete sampling point at the nth target;

[0029] The elements are:

[0030]

[0031]

[0032] Among them, f η|mrepresents the mth sampling point of the azimuth frequency axis, m = 1, 2, 3, ..., M; η c|n Represents the target vector X BI The moment when the center of the beam illuminates the nth target, n = 1, 2, 3, ..., N; Respectively represent the vector elements in the first distance fuzzy area at the near end and the far end.

[0033] Preferably, the step S4 performs sparse reconstruction on the range ambiguity signal through a cyclic iteration algorithm, and the specific operation is:

[0034] S4-1: input the observation matrix φ, the azimuth one-dimensional signal y, and the number of iterations K as parameters into the cyclic iterative algorithm;

[0035] S4-2: Residual r t When the number of iterations reaches K, the iteration is stopped and the estimated value of the vector x of the fuzzy signal is obtained.

[0036] S4-3: The column vector obtained each time The distance fuzzy signal matrix is ​​obtained by combination;

[0037] S4-4: Multiply the matrix of the distance ambiguity signal by the observation matrix to obtain the sparsely reconstructed distance ambiguity signal S BI .

[0038] Preferably, in step S5, the SAR echo signal minus the estimated fuzzy signal is expressed as:

[0039] S E =S MI +S BI +N noise

[0040] Among them, S MI Represents the main image echo signal, S BI Represents the echo signal in the fuzzy area, N noise represents the noise signal, S E Represents the total echo signal.

[0041] Preferably, the step S6 performs azimuth pulse compression on the processed SAR echo signal, and the azimuth matched filtering expression is:

[0042]

[0043] Among them, f η Represents the azimuth frequency axis, R c represents the slant range at the imaging center (reference zero time), λ represents the radar wavelength, V r Indicates equivalent speed.

[0044] Compared with the prior art, the present invention has the following improvements and advantages: 1. By combining the dual linear frequency modulation signal with the sparse reconstruction method, the blur energy is removed; the blur energy is suppressed by utilizing the characteristic of the dual linear frequency modulation signal to perform matched filtering in the distance direction to defocus the blur energy, thereby achieving a better distance blur suppression effect, improving the accuracy of distance blur suppression and expanding the applicability of distance blur suppression.

[0045] 2. By using a cyclic iterative algorithm to reconstruct the blurred area, the estimated blurred image is subtracted from the original echo image to achieve the purpose of suppressing distance blur. After processing, the suppressed image can be obtained by using matched filtering, so that the blur energy is further removed; further improving the accuracy of distance blur suppression. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The figure is an overall flow chart of the method of the present invention.

[0047] Figure 2 Schematic diagram of the geometric model of satellite-borne SAR signal transmission and reception.

[0048] Figure 3 Schematic diagram of the SAR echo image of a normal point target and two range-ambiguous targets from a positive side view.

[0049] Figure 4 Schematic diagram of the image after sparse reconstruction of a normal point target and two range blurred targets.

[0050] Figure 5 Schematic diagram of the echo image after dual linear frequency modulation of a normal point target and two range-ambiguous targets.

[0051] Figure 6 Schematic diagram of the echo image after sparse reconstruction and dual linear frequency modulation of a normal point target and two range-ambiguous targets.

[0052] Figure 7 Schematic diagram of the SAR echo image of a point target and 100 blurred targets in a positive side view.

[0053] Figure 8 Schematic diagram of the image after 100 blurred targets are suppressed using sparse reconstruction.

[0054] Fig. 9 Schematic diagram of SAR echo image using dual linear frequency modulation method to suppress 100 blurred targets.

[0055] Fig.10 Schematic diagram of SAR echo image with 100 blurred targets suppressed using dual linear frequency modulation method and sparse reconstruction.

[0056] Fig.11 Schematic diagram of SAR echo image of a rectangular target and 100 blurred targets under positive side view.

[0057] Fig.12 Schematic diagram of the image after 100 blurred targets are suppressed using sparse reconstruction.

[0058] Fig.13 Schematic diagram of SAR echo image using dual linear frequency modulation method to suppress 100 blurred targets.

[0059] Fig.14 Schematic diagram of SAR echo image with 100 blurred targets suppressed using dual linear frequency modulation method and sparse reconstruction. DETAILED DESCRIPTION

[0060] The present invention is further summarized below with reference to the accompanying drawings.

[0061] like Figure 1 As shown, a distance ambiguity suppression method combining sparse reconstruction and dual linear frequency modulation includes the following steps:

[0062] Step S1: constructing a SAR echo signal by alternately transmitting linear frequency modulation signals with equal magnitude and opposite positive and negative range modulation frequencies;

[0063] The specific steps of step S1 include: Figure 2 As shown in the figure, according to the satellite SAR signal acquisition model, assuming that the radar is running at a height of H from the ground and moves along the x-axis at a speed of v, when the radar receives the signal at X2, it will receive the signal reflected by the current pulse of X2 in the main image area and the signal reflected by the signal transmitted at X1 in the first fuzzy area. For the signal received at X2, the signal reflected by the signal transmitted at X1 in the first fuzzy area is the fuzzy signal. We assume that the signal transmitted at X1 is a negative frequency modulation signal, and the signal is expressed as:

[0064]

[0065] The signal transmitted at X2 is a positive frequency modulation signal, and the signal is expressed as:

[0066]

[0067] Where τ is the fast time, t is the azimuth time, and w a (t) represents the azimuth antenna pattern, R(t) is the azimuth time-varying distance between the radar and the target, λ is the wavelength, k r is the range modulation frequency, τ d (t) indicates the transmission time delay, τ p is the transmit pulse duration.

[0068] Step S2: construct a range-matched filter to perform range-direction pulse compression, range migration correction and azimuth Fourier transform on the received SAR echo signal;

[0069] The specific steps of step S2 include:

[0070] In order to effectively suppress the range ambiguity signal without affecting the useful signal, a range-direction matched filter is designed. The expression of the designed matched filter is:

[0071]

[0072] Where f is the range frequency, B r is the transmit pulse bandwidth and j is an imaginary unit.

[0073] For the range ambiguity signal s down (τ,t), the processed signal expression is

[0074]

[0075] For the useful signal s up (τ,t), the processed signal expression is:

[0076]

[0077] It is observed that the amplitude of the range-ambiguous signal is reduced compared to the useful signal after the pulse compression step. This is equivalent to suppressing the intensity by -3dB, while the duration of the signal is doubled, the range linear frequency modulation still exists, and the modulation rate is halved to

[0078] After range motion correction and azimuth Fourier transform, the main image and its blurred image can be expressed as azimuth one-dimensional signals. The signal expression is:

[0079] Main image and its blurred image:

[0080]

[0081] Among them, f η Represents the azimuth frequency axis, R c and f dc They represent the slant range and Doppler center frequency at the imaging center time (reference zero time), λ represents the radar wavelength, σ represents the target backscattering cross-sectional area, and W a (·) represents the Doppler domain amplitude-frequency envelope, V r Indicates equivalent speed.

[0082] Step S3: constructing the measurement matrix of the range fuzzy signal;

[0083] The observation matrix can be expressed as:

[0084]

[0085] in, Represents the echo signal of the mth discrete sampling point at the nth target.

[0086] The elements are:

[0087]

[0088]

[0089] Among them, f η|m represents the mth sampling point of the azimuth frequency axis, m = 1, 2, 3, ..., M; η c|n Represents the target vector X BI The moment when the center of the beam illuminates the nth target, n = 1, 2, 3, ..., N; Respectively represent the vector elements in the first distance fuzzy area at the near end and the far end.

[0090] Step S4: sparsely reconstruct and estimate the range ambiguity signal through a cyclic iterative algorithm;

[0091] The main image and its blurred image can be expressed as one-dimensional azimuth signals, so the OMP algorithm can be used to sparsely reconstruct the blurred image in one dimension. The specific steps of the OMP algorithm are:

[0092] Step (1): Input:

[0093] Step (1-1): M×N sensing matrix A=φψ;

[0094] Step (1-2): N×1 dimensional observation vector y;

[0095] Step (1-3): Signal sparsity K.

[0096] Step (2): Output:

[0097] Step (2-1): Estimation of signal sparse representation coefficients

[0098] Step (2-2): N×1 dimensional residual

[0099] Step (3): The OMP algorithm is specifically implemented as follows:

[0100] Step (3-1): Initialize r0 = y, t = 1;

[0101] Step (3-2): Find the index λ t , so that:

[0102] Step (3-3): Let Λ t =Λ t-1 ∪{λ t},

[0103] Step (3-4): Find y = A t θ t The least squares solution of :

[0104] Step (3-5): New residual

[0105] Step (3-6): t=t+1, if t≤K, return to step (3-2), otherwise stop iteration and go to step (3-7);

[0106] Steps (3-7) reconstructed In Λ t There are non-zero entries at the last iteration.

[0107] Among them, r t represents the residual, t represents the number of iterations, represents the empty set, Λ t represents the set of indices (column numbers) for t iterations, λ t Indicates the index (column number) found in the tth iteration, a j represents the jth column of matrix A, A t Indicates by index Λ t The selected set of columns of matrix A (a matrix of size M×t), θ t is a t×1 column vector, the symbol ∪ represents set union, and <·,·> represents the inner product of vectors.

[0108] Apply the OMP algorithm to SAR sparse imaging. The specific steps are as follows:

[0109] S4-1: input the observation matrix φ, the azimuth one-dimensional signal y, and the number of iterations K as parameters into the cyclic iterative algorithm;

[0110] S4-2: Residual r t When the number of iterations reaches K, the iteration is stopped and the estimated value of the vector x of the fuzzy signal is obtained.

[0111] S4-3: The column vector obtained each time The distance fuzzy signal matrix is ​​obtained by combination;

[0112] S4-4: Multiply the matrix of the distance ambiguity signal by the observation matrix to obtain the sparsely reconstructed distance ambiguity signal S BI .

[0113] Step S5: subtract the estimated fuzzy signal from the SAR echo signal to remove the fuzzy energy;

[0114] The SAR echo signal minus the estimated ambiguity signal is expressed as:

[0115] S E =S MI +S BI +N noise

[0116] Among them, S MI Represents the main image echo signal, S BI Indicates the echo signal in the fuzzy area, N noise represents the noise signal, S E Represents the total echo signal.

[0117] That is, the total signal received is composed of the main image and its blurred image. BI , using the total echo signal S E Subtract the blurred image S BI , the rest is the main image signal S MI .

[0118] Step S6: performing azimuth pulse compression and azimuth inverse Fourier transform on the processed SAR echo signal to obtain a useful SAR echo signal.

[0119] The obtained signal is subjected to azimuth matched filtering, and the expression of the matched filter is:

[0120]

[0121] Among them, f η Represents the azimuth frequency axis, R c represents the slant range at the imaging center (reference zero time), λ represents the radar wavelength, V r Indicates equivalent speed.

[0122] By performing an inverse Fourier transform on it in azimuth, we can obtain the imaging result after range blur suppression.

[0123] A point target experimental simulation is carried out on a range ambiguity suppression method combining sparse reconstruction and dual linear frequency modulation. The effect of range ambiguity energy removal is verified through point target experimental simulation.

[0124] Table 1 Radar simulation parameters

[0125] Radar parameters Numeric Radar carrier frequency (GHz) 9.6 Radar transmit signal bandwidth (MHz) 100 Pulse repetition frequency (Hz) 5000 Target center slant distance (km) 600 Platform flight speed (m / s) 7000 Synthetic aperture time (s) 0.7

[0126] This experiment will be divided into three cases. The first case is a point target and two point targets with blurred distances. The second case is a point target and 100 point targets with blurred distances. The third case is a rectangular target and 100 point targets with blurred distances. The simulation of the three cases is analyzed in detail below:

[0127] Figure 3 The original echo images are of a point target and two point targets with blurred range. The left, middle and right images are of a normal point target, a point target with blurred range and a point target with blurred range respectively. All three point targets use LFM signals. Figure 4 Yes Figure 3 After sparse reconstruction, the image is Figure 5 Yes Figure 3 After bilinear frequency modulation, the image Figure 6 The point target on the left is the image of a normal point target after sparse reconstruction, the target in the middle is the image of a distance blurred point target after bilinear frequency modulation and sparse reconstruction, and the point target on the right is the image after sparse reconstruction. It can be found that using the signal after bilinear frequency modulation as the transmitting signal can achieve better distance ambiguity suppression effect on the basis of sparse reconstruction.

[0128] Figure 7 The original echo images of a point target and 100 point targets with blurred range. The left side shows a normal point target, and the right side shows 100 point targets with blurred range. The point targets all use LFM signals as the transmitting signals. Figure 8 Yes Figure 7 After sparse reconstruction, the image is Fig. 9 Yes Figure 7 After bilinear frequency modulation, the image Fig.10 Yes Figure 7 Compare the images after dual linear frequency modulation and sparse reconstruction Figures 7 to 10 , it can be found that the range ambiguity suppression effect achieved by using the dual LFM system and sparse reconstruction is better than using either one alone.

[0129] Fig.11 It is the original echo image of the rectangular target and 100 point targets with blurred distance. The point targets all use LFM signals as the transmitting signals. Fig.12 Yes Fig.11 After sparse reconstruction, the image is Fig.13 Yes Fig.11 After bilinear frequency modulation, the image Fig.14 Yes Fig.11 Compare the images after dual linear frequency modulation and sparse reconstruction Figures 11 to 14 , it can be found that the range ambiguity suppression effect achieved by using the dual LFM system and sparse reconstruction is better than using either one alone.

[0130] Working principle: A distance ambiguity suppression method combining sparse reconstruction and dual linear frequency modulation, which uses dual linear frequency modulation signal as the transmitting signal, suppresses the ambiguity energy by using dual linear frequency modulation system, constructs the observation matrix of the distance ambiguity signal, and uses a cyclic iterative algorithm to sparsely reconstruct the azimuth one-dimensional signal of the distance ambiguity signal. The ambiguity energy is removed by subtracting the echo signal from the reconstructed signal. It can be seen from the imaging results that the use of dual linear frequency modulation system and sparse reconstruction can effectively suppress and remove the ambiguity energy, which proves the effectiveness of the algorithm.

[0131] The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A distance ambiguity suppression method combining sparse reconstruction and dual linear frequency modulation, characterized in that: The method comprises the following steps: Step S1: constructing a SAR echo signal by alternately transmitting linear frequency modulation signals with equal magnitude and opposite positive and negative range modulation frequencies; Step S2: construct a range-matched filter to perform range-direction pulse compression, range migration correction and azimuth Fourier transform on the received SAR echo signal; Step S3: constructing the measurement matrix of the range fuzzy signal; Step S4: sparsely reconstruct and estimate the range ambiguity signal through a cyclic iterative algorithm; Step S5: subtract the estimated fuzzy signal from the SAR echo signal to remove the fuzzy energy; Step S6: performing azimuth pulse compression and azimuth inverse Fourier transform on the processed SAR echo signal to obtain a useful SAR echo signal.

2. The method for suppressing range ambiguity by combining sparse reconstruction and dual linear frequency modulation according to claim 1, characterized in that: In step S1, a SAR echo signal is constructed by alternately transmitting linear frequency modulation signals with equal magnitude and opposite positive and negative range modulation frequencies. The constructed SAR echo signal is expressed as: Among them, s down (τ,t) is the distance ambiguity signal, s up (τ, t) is the range unambiguous signal, τ is the time in the range direction, t is the time in the azimuth direction, w a (t) represents the azimuth antenna pattern, R(t) is the azimuth time-varying distance between the radar and the target, λ is the wavelength, k r is the range modulation frequency, τ d (t) indicates the transmission time delay, τ p is the transmit pulse duration.

3. The method for suppressing range ambiguity by combining sparse reconstruction and dual linear frequency modulation according to claim 1, characterized in that: In step S2, a range-matched filter is constructed, and the range-matched filter is expressed as: Where f is the range frequency, B r is the transmit pulse bandwidth and j is an imaginary unit.

4. The method for suppressing range ambiguity by combining sparse reconstruction and dual linear frequency modulation according to claim 1, characterized in that: The range-direction pulse compression performed on the received SAR echo signal in step S2 is expressed as:

5. The method for suppressing range ambiguity by combining sparse reconstruction and dual linear frequency modulation according to claim 1, characterized in that: After the SAR echo signal received in step S2 is subjected to range migration correction and azimuth Fourier transform, the main image and its blurred image are represented as azimuth one-dimensional signals. The azimuth one-dimensional signal expression is: Among them, f η Represents the azimuth frequency axis, R c and f dc They represent the imaging center time, the slant range and the Doppler center frequency at the reference zero time, λ represents the radar wavelength, σ represents the target backscattering cross-sectional area, and W a (·) represents the Doppler domain amplitude-frequency envelope, V r Indicates equivalent speed.

6. The method for suppressing range ambiguity by combining sparse reconstruction and dual linear frequency modulation according to claim 1, characterized in that: In step S3, a measurement matrix of the range ambiguity signal is constructed, and the measurement matrix is ​​expressed as: in, Represents the echo signal of the mth discrete sampling point at the nth target; The elements are: Among them, f η|m represents the mth sampling point of the azimuth frequency axis, m = 1, 2, 3, ..., M; η c|n Represents the target vector X BI The moment when the center of the beam illuminates the nth target, n = 1, 2, 3, ..., N; Respectively represent the vector elements in the first distance fuzzy area at the near end and the far end.

7. The method for suppressing range ambiguity by combining sparse reconstruction and dual linear frequency modulation according to claim 6, characterized in that: The step S4 performs sparse reconstruction on the range ambiguity signal through a cyclic iteration algorithm, and the specific operation is as follows: S4-1: input the observation matrix φ, the azimuth one-dimensional signal y, and the number of iterations K as parameters into the cyclic iterative algorithm; S4-2: Residual r t When the number of iterations reaches K, the iteration is stopped and the estimated value of the vector x of the fuzzy signal is obtained. S4-3: The column vector obtained each time The distance fuzzy signal matrix is ​​obtained by combination; S4-4: Multiply the matrix of the distance ambiguity signal by the observation matrix to obtain the sparsely reconstructed distance ambiguity signal S BI .

8. The method for suppressing range ambiguity by combining sparse reconstruction and dual linear frequency modulation according to claim 1, characterized in that: In step S5, the SAR echo signal minus the estimated fuzzy signal is expressed as: S E =S MI +S BI +N noise Among them, S MI Represents the main image echo signal, S BI Represents the echo signal in the fuzzy area, N noise represents the noise signal, S E Represents the total echo signal.

9. The method for suppressing range ambiguity by combining sparse reconstruction and dual linear frequency modulation according to claim 1, characterized in that: The step S6 performs azimuth pulse compression on the processed SAR echo signal, and the azimuth matched filtering expression is: Among them, f η Represents the azimuth frequency axis, R c represents the slant range at the imaging center (reference zero time), λ represents the radar wavelength, V r Indicates equivalent speed.

Images