Accelerated forward-looking sar imaging method based on spectrum regularization and spectrum fusion

Abstract

The application discloses an accelerated trajectory forward-looking squinted SAR imaging method based on spectrum regularization and spectrum fusion, and comprises the following steps: a uniform polar coordinate system is established according to a uniform accelerated motion trajectory and a generated synthetic aperture length, and echo signals are obtained in the polar coordinate system. When the echo signals are processed, the distance direction and the azimuth direction are processed in different dimensions: in the distance direction, the echo signals are matched filtered to obtain pulse compression signals; in the azimuth direction, sub-apertures are first divided, sub-aperture imaging is performed by using a BP algorithm and is transformed into a wave number domain, then the wave number spectrum of the sub-images is corrected by shifting, the corrected wave number spectrum of the sub-images is transformed into a distance frequency domain through distance direction Fourier transform, the tilt spectrum of the transformed sub-images is regularized by using a correction function in the distance frequency domain, the wave number spectrum of the regularized sub-images is obtained, and finally the wave number spectrum of the sub-images is fused and spliced to realize accurate focusing by converting from the wave number domain to a two-dimensional time domain.

Description

Technical Field

[0001] This invention belongs to the field of SAR imaging technology, specifically relating to an accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion. Background Technology

[0002] Radar, with its all-weather, all-day imaging capabilities, plays a vital role in both military and civilian fields, and SAR (Synthetic Aperture Radar) is increasingly being deployed on various platforms. However, when the platform trajectory model is no longer a uniform straight line but involves acceleration, existing imaging algorithms become inapplicable, necessitating the development of algorithms suitable for non-uniform straight-line trajectories to accommodate the changing imaging model. Research on imaging algorithms based on non-uniform straight-line models is of great significance for the rapid detection and engagement of targets.

[0003] SAR imaging algorithms can be divided into frequency domain algorithms and time domain algorithms. Frequency domain algorithms include the Range Doppler Algorithm (RDA), Chirp Scaling Algorithm (CSA), Range Migration Algorithm (RMA), and Polar Format Algorithm (PFA), among others. With the introduction of uniform acceleration, the platform's flight velocity changes over time, and the imaging model is no longer a simple uniform linear model. The presence of acceleration leads to spatial variation in the azimuth direction and intensifies the two-dimensional coupling between the range and azimuth directions of the spectrum. When applying frequency domain algorithms for imaging, numerous approximations are used, making it difficult to guarantee the accuracy of image focusing.

[0004] Temporal algorithms include the Back-Projection Algorithm (BPA), the Fast Back-Projection Algorithm (FBPA), the Fast Factorized Back-Projection Algorithm (FFBPA), and the Accelerated Factorized Back-Projection Algorithm (AFBPA), which were developed based on BPA to improve efficiency. These existing algorithms are all suitable for uniform linear trajectories. When both the synthetic aperture time and acceleration are small, the acceleration has little effect on imaging. However, when the acceleration is large or the synthetic aperture time is long, the uniform linear model is not suitable for processing accelerated trajectories, and the image often becomes difficult to focus, requiring algorithm improvements.

[0005] The HS_AFBP algorithm proposed in the article “Focusing High-Squint Synthetic Aperture Radar Data Based on Factorized Back-Projection and Precise Spectrum Fusion[J].Remote Sens,2019,11(24)” is based on the imaging algorithm research of uniform linear trajectory, but it is not applicable to the imaging of models with acceleration, and the focusing effect is not ideal. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides an accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion. The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] An accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion includes:

[0008] Based on the uniformly accelerated motion trajectory of the SAR-equipped moving platform and the generated synthetic aperture length, a unified polar coordinate system is established. Under the polar coordinate system, the expression for the instantaneous squint distance of the radar to any point target P in the polar coordinate system is calculated. Based on the expression for the instantaneous squint distance, the expression for the corresponding echo signal is obtained.

[0009] The echo signal is matched and filtered using a first preset formula to obtain an expression for the pulse compression signal;

[0010] The synthetic aperture in the azimuth direction of the pulse compression signal is divided into sub-apertures of equal length. The sub-apertures are then imaged using the BP algorithm to obtain the wavenumber spectrum of the sub-image corresponding to each sub-aperture. The wavenumber spectrum of the sub-image is then corrected by shifting.

[0011] The wavenumber spectrum of the corrected sub-image is transformed to the range frequency domain by using the range-to-Fourier transform. The wavenumber spectrum of the tilt spectrum of the transformed sub-image is then regularized using the correction function in the range frequency domain to obtain the wavenumber spectrum of the regularized sub-image.

[0012] The wavenumber spectra of the regularized sub-images are fused and stitched together to obtain the full aperture wavenumber spectrum;

[0013] The full aperture wavenumber spectrum is subjected to range-direction inverse Fourier transform and azimuth-direction Fourier transform to obtain a full aperture SAR image.

[0014] In one embodiment of the present invention, a unified polar coordinate system is established based on the uniformly accelerated motion trajectory of the SAR-equipped motion platform and the generated synthetic aperture length. An expression for the instantaneous squint distance of the radar to any point target P in the polar coordinate system is calculated under the polar coordinate system. Based on the expression for the instantaneous squint distance, an expression for the corresponding echo signal is obtained, including:

[0015] Based on the expression of the uniformly accelerated motion trajectory of the motion platform equipped with SAR A unified polar coordinate system (r, θ) is established in the imaging plane, with the length L of the generated synthetic aperture, and the origin of the polar coordinate system located at the center point O of the synthetic aperture; where V represents the initial velocity, a represents the acceleration, and t represents the acceleration. m Indicates slow time;

[0016] In the polar coordinate system, t is calculated according to the second preset formula. m At any given moment, the radar reaches any point P(r) in the polar coordinate system. p ,θ p The expression for the instantaneous strabismus distance R(X; r) p ,α p ); where the second preset formula is r p α represents the distance from point target P to the center O of the synthetic aperture. p =sinθ p θ p The beam angle of view representing the point target P;

[0017] According to the third preset formula and the expression for the instantaneous strabismus distance R(X; r p ,α p The expression S for the echo signal is calculated. r (τ,X); where the third preset formula is Δt represents the two-way time delay, Δt = 2R(X; r p ,α p ) / c, where c represents the speed of light, rect() represents a rectangular window function, τ represents fast time, and T p f represents the pulse width. c γ represents the carrier frequency, exp() represents the frequency modulation frequency, and exp() represents the exponential function.

[0018] In one embodiment of the present invention, the first preset formula includes:

[0019]

[0020] Among them, S M(τ,X) represents the expression for the pulse compression signal, sinc represents the sinc function, expressed by sinc(q) = sin(πq) / πq, and K rc K represents the distance wavenumber. rc = 4π / λ, where λ represents the wavelength corresponding to the carrier frequency.

[0021] In one embodiment of the present invention, the synthetic aperture in the azimuth direction of the pulse compression signal is divided into sub-apertures of equal length, including:

[0022] For the pulse compression signal S M In the azimuth direction (τ,X), the synthetic aperture of length L is divided into N segments of equal length l. sub Sub-aperture, where l = L / N sub Let K be the number of pulses included in each sub-aperture, and t be the time point corresponding to the center of the u-th sub-aperture. u The time point corresponding to each pulse of the sub-aperture is t. k +t u ,

[0023] In one embodiment of the present invention, the step of performing sub-aperture imaging using the BP algorithm on the divided sub-apertures to obtain the wavenumber spectrum of the sub-image corresponding to each sub-aperture includes:

[0024] For the neighboring pixels of a grid point (r, α) in the sub-aperture, the impulse response function I of the sub-image is calculated using the fourth preset formula. u (r, α); where the fourth preset formula is x u Let x be the center of the u-th sub-aperture, x∈[-l / 2,l / 2], α=sinθ, ΔR(X;r p ,α) is the difference between the distance of the radar to any target point and the distance of the radar to any pixel point, and the expression for the difference of distances is ΔR(X; r p ,α)=R(X;r p ,α p )-R(X;r p ,α);

[0025] The difference in distance ΔR(X; r) p Based on the second-order Taylor expansion, the distance difference ΔR′(X; r) is obtained after processing. p ,α);

[0026] Based on the difference in distance after processing ΔR′(X;r p The impulse response function I of the sub-image (α) uSimplifying (r, α) yields the impulse response function I′ of the simplified sub-image. u (r,α);

[0027] Based on the impulse response function I′ of the simplified sub-image u (r, α), the azimuth angular domain wavenumber spectrum variable K is obtained using the fifth preset formula. a The expression is used to obtain the wavenumber spectrum center K using the sixth preset formula. au The expression is used to obtain the wavenumber spectral width ΔK using the seventh preset formula. a The expression; wherein, the fifth preset formula is The sixth preset formula is: The seventh preset formula is: t u Indicates the center time of the sub-aperture;

[0028] According to the azimuth angular domain wavenumber spectrum variable K a The wavenumber spectrum center K au and the wavenumber spectral width ΔK a The impulse response function I′ of the simplified sub-image u Rewriting (r, α) yields the impulse response function I″ of the rewritten sub-image. u (r,α); where, Δα=α-α p ;

[0029] Impulse response function I″ of the rewritten sub-image u The wavenumber spectrum I of the sub-image is obtained by performing an inverse Fourier transform on (r, α). u (K α );in,

[0030] In one embodiment of the present invention, the distance difference ΔR(X; r) p Based on the second-order Taylor expansion, the distance difference ΔR′(X; r) is obtained after processing. p ,α), including:

[0031] The difference in distance ΔR(X; r) p Perform a second Taylor expansion on α) and substitute it into the expression for the uniformly accelerated motion trajectory. We obtain ΔR″(X;r) p The expression for α); where,

[0032]

[0033] Let ΔR″(X;r) p t in ,α) m=t k +t u We obtain ΔR″′(X;r p The expression for α);

[0034] Let ΔR″′(X;r p ,α) proceed with t k The polynomial expansion and combination of variables yields ΔR″″(X; r p The expression for α);

[0035] Analyze the ΔR″″(X;r) p The higher-order phase error QPE of α) is used to adjust the ΔR″″(X;r) based on the higher-order phase error QPE. p The distance difference ΔR′(X; r) is obtained by simplifying α). p ,α).

[0036] In one embodiment of the present invention, the expression for the higher-order phase error QPE includes:

[0037]

[0038] In one embodiment of the present invention, the correction of the wavenumber spectrum of the sub-image by shifting includes:

[0039] The center of the wavenumber spectrum of each sub-image is shifted from zero in the azimuth direction to the center K of the wavenumber spectrum. au This allows for the correction of the wavenumber spectrum of each sub-image.

[0040] In one embodiment of the present invention, the step of transforming the wavenumber spectrum of the corrected sub-image to the range frequency domain through a range-to-Fourier transform, and then performing wavenumber spectrum regularization on the tilt spectrum of the transformed sub-image using a correction function in the range frequency domain to obtain the regularized wavenumber spectrum of the sub-image, includes:

[0041] A range-to-Fourier transform is performed on the wavenumber spectrum of the corrected sub-image to achieve a transformation from the range time domain to the range frequency domain, thereby obtaining the wavenumber spectrum of the transformed sub-image.

[0042] The regularized range wavenumber K is obtained from the correction function in the range frequency domain. r Using the regularized distance wavenumber K r The distance wavenumber K in the wavenumber spectrum of the sub-image rc The replacement yields the wavenumber spectrum of the regularized sub-image; wherein the distance-frequency domain correction function includes:

[0043] K r =4π / λ i (λ i∈[-Nnrn / 2,Nnrn / 2-1] / Nnrn·F s ); Nnrn represents the distance vector number of the sub-image, F s This indicates the radar range sampling frequency.

[0044] The beneficial effects of this invention are:

[0045] The solution provided in this invention extends the uniform linear trajectory to a uniformly accelerated trajectory, enabling precise focusing under the uniformly accelerated trajectory. This facilitates faster target detection and engagement, achieving forward-looking SAR imaging under a uniformly accelerated trajectory. The presence of acceleration exacerbates the tilt of the sub-image wavenumber spectrum, leading to wavenumber spectrum folding and gaps and overlaps during full-aperture wavenumber spectrum stitching. By using the BP algorithm to perform sub-aperture imaging on the divided sub-apertures, the wavenumber spectrum of each sub-image corresponding to each sub-aperture is obtained. The wavenumber spectrum of the sub-image is then shifted to the spectral center, and the tilted spectrum of the obtained sub-image is regularized, allowing for effective fusion of the wavenumber spectra and achieving precise focusing. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating an accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion, provided in an embodiment of the present invention.

[0047] Figure 2 The geometry of a forward-looking SAR imaging method based on spectral regularization and spectral fusion based on accelerated trajectory forward-looking SAR imaging provided in an embodiment of the present invention is shown.

[0048] Figure 3 A unified polar coordinate schematic diagram of an accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion provided in an embodiment of the present invention;

[0049] Figure 4 This is a schematic diagram of sub-image wavenumber spectrum center correction for an accelerated trajectory forward squint SAR imaging method based on spectrum regularization and spectrum fusion, provided in an embodiment of the present invention.

[0050] Figure 5 A schematic diagram of sub-image tilt wavenumber spectrum regularization for an accelerated trajectory forward squint SAR imaging method based on spectrum regularization and spectrum fusion provided in an embodiment of the present invention.

[0051] Figures 6(a) to 6(b) A comparison of the full aperture wavenumber spectrum of an accelerated trajectory forward squint SAR imaging method based on spectral regularization and spectral fusion provided in an embodiment of the present invention.

[0052] Figures 7(a) to 7(h)A comparison of simulation results of an accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion provided in an embodiment of the present invention;

[0053] Figures 8(a) to 8(c) This is a comparison of the measured data imaging results of an accelerated trajectory forward squint SAR imaging method based on spectral regularization and spectral fusion provided in an embodiment of the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] This invention provides an accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion. Please refer to [link to relevant documentation]. Figure 1 The flowchart shown is for reference. Specifically, this accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion may include the following steps S1 to S6:

[0056] S1. Based on the uniformly accelerated motion trajectory of the SAR-equipped moving platform and the generated synthetic aperture length, a unified polar coordinate system is established. The expression for the instantaneous squint distance of the radar to any point target P in the polar coordinate system is calculated in the polar coordinate system. Based on the expression for the instantaneous squint distance, the expression for the corresponding echo signal is obtained.

[0057] Specifically, S1 is the step of establishing a uniformly accelerated signal model, which may include the following steps:

[0058] S11, based on the expression for the uniformly accelerated motion trajectory of the motion platform equipped with SAR. A unified polar coordinate system (r, θ) is established in the imaging plane, with the length L of the generated synthetic aperture, and the origin of the polar coordinate system located at the center point O of the synthetic aperture; where V represents the initial velocity, a represents the acceleration, and t represents the acceleration. m Indicates slow time;

[0059] A motion platform equipped with a SAR (Sensitive Aircraft SAR) performs uniformly accelerated level flight motion with an initial velocity V and acceleration a along the X-axis at a height H. The imaging geometry of the forward-looking SAR is shown below. Figure 2 As shown. A unified polar coordinate system is established in the imaging plane of the imaging geometry, with the origin of the polar coordinate system located at the center point O of the synthetic aperture. A schematic diagram of the unified polar coordinate system is shown below. Figure 3 As shown. In Figure 2 and Figure 3In this context, θ represents the angle of inclination, and r represents the center slant distance.

[0060] S12, in polar coordinates, t is calculated according to the second preset formula. m At any given moment, the radar reaches any point P(r) in the polar coordinate system. p ,θ p The expression for the instantaneous strabismus distance R(X; r) p ,α p ); where the second preset formula is r p α represents the distance from point target P to the center O of the synthetic aperture. p =sinθ p θ p The beam angle of view representing the point target P;

[0061] S13, according to the third preset formula and the expression for the instantaneous strabismus distance R(X; r p ,α p The expression S for the echo signal is calculated. r (τ,X); where...

[0062] The third preset formula is: Δt represents the two-way time delay, Δt = 2R(X; r p ,α p ) / c, where c represents the speed of light, rect() represents a rectangular window function, τ represents fast time, and T p f represents the pulse width. c γ represents the carrier frequency, exp() represents the frequency modulation frequency, and exp() represents the exponential function.

[0063] In S1, a unified polar coordinate system is first established. Under the polar coordinate system, the expression for the instantaneous oblique gaze distance of the radar to the grid point of the coordinate system under the uniform acceleration trajectory is derived. The echo signal is obtained based on the expression for the instantaneous oblique gaze distance and provided to S2 for processing.

[0064] In subsequent processing of the echo signal, the range and azimuth dimensions are processed separately.

[0065] S2, Use the first preset formula to perform matched filtering on the echo signal to obtain the expression of the pulse compression signal;

[0066] Specifically, the first preset formula may include:

[0067]

[0068] Among them, S M (τ,X) represents the expression for the pulse compression signal, sinc represents the sinc function, expressed by sinc(q) = sin(πq) / πq, and K rcK represents the distance wavenumber. rc = 4π / λ, where λ represents the wavelength corresponding to the carrier frequency.

[0069] In the distance direction, matched filtering of the echo signal yields the expression for the pulse compression signal.

[0070] S3, the synthetic aperture in the azimuth direction of the pulse compression signal is divided into sub-apertures of equal length, and the sub-apertures are imaged using the BP algorithm to obtain the wavenumber spectrum of the sub-image corresponding to each sub-aperture. The wavenumber spectrum of the sub-image is corrected by shifting.

[0071] Specifically, it may include the following steps:

[0072] S31, divide the synthetic aperture of the pulse compression signal into equal-length sub-apertures.

[0073] S31 may include:

[0074] For pulse compression signal S M In the azimuth direction (τ,X), the synthetic aperture of length L is divided into N segments of equal length l. sub Sub-aperture, where l = L / N sub Let K be the number of pulses included in each sub-aperture, and t be the time point corresponding to the center of the u-th sub-aperture. u The time point corresponding to each pulse of the sub-aperture is t. k +t u ,

[0075] When the trajectory is uniform, after dividing into sub-apertures, N sub Each sub-aperture has the same length. Each sub-aperture also contains the same number of pulses.

[0076] When there is acceleration, according to the characteristics of acceleration, the length of each sub-aperture is the same, but the number of pulses contained in each sub-aperture will gradually decrease.

[0077] S32, use the BP algorithm to perform sub-aperture imaging on the divided sub-apertures to obtain the wavenumber spectrum of the sub-image corresponding to each sub-aperture.

[0078] S32 may include:

[0079] S321, for the neighboring pixels of a certain grid point (r, α) in the sub-aperture, the IRF (Impulse Response Function) of the sub-image is calculated using the fourth preset formula. u (r,α);

[0080] The fourth preset formula is Where, x u Let x be the center of the u-th sub-aperture, x∈[-l / 2,l / 2], ΔR(X; r p α) represents the difference between the distance the radar reaches any point target and the distance the radar reaches any pixel.

[0081] The expression for the difference in distance is ΔR(X; r p ,α)=R(X;r p ,α p )-R(X;r p ,α);

[0082] The formula for calculating the initial impulse response function of a sub-image is derived from the neighboring pixels of a grid point (r, α) in the sub-aperture:

[0083]

[0084] By ignoring the amplitude information in the formula for calculating the initial impulse response function of the obtained sub-image and retaining only the phase information, the formula for calculating the initial impulse response function of the sub-image can be simplified to the impulse response function of the sub-image.

[0085] S322, for the distance difference ΔR(X; r) p Based on the second-order Taylor expansion, the distance difference ΔR′(X; r) is obtained after processing. p ,α);

[0086] S322 may include:

[0087] S3221, for the difference in distance ΔR(X; r) p Perform a second Taylor expansion on α) and substitute it into the expression for the trajectory of uniformly accelerated motion. We obtain ΔR″(X;r) p The expression for α); where,

[0088]

[0089] When the trajectory is uniform, after Taylor expansion, the trajectory is X = Vt. m The difference is that after adding acceleration to the trajectory, the expression for the uniformly accelerated motion trajectory of the platform is substituted into it. The trajectory difference caused by the introduced acceleration is analyzed using Taylor expansion:

[0090]

[0091]

[0092] Where, σ(X) 3 ) represents a higher-order term in the Taylor expansion, Δα = (α - α)p ).

[0093] S3222, let ΔR″(X;r p t in ,α) m =t k +t u We obtain ΔR″′(X;r p The expression for α);

[0094] slow time t m Represented as the time point t corresponding to the center of the u-th sub-aperture u The time point t corresponding to the k-th pulse within the u-th sub-aperture k The sum, through substitution, transforms the full-aperture slow time into the sub-aperture time variable t. u and t k We obtain ΔR″′(X;r p The expression for α):

[0095]

[0096] The distance difference under the acceleration trajectory is expressed as the time variable t of the sub-aperture. u and t k This is so that the wavenumber spectrum of the sub-image corresponding to the sub-aperture can be analyzed and processed subsequently.

[0097] S3223, ΔR″′(X;r p ,α) proceed with t k The polynomial expansion and combination of variables yields ΔR″″(X; r p The expression for ,α).

[0098]

[0099] S3224, Analysis of ΔR″″(X;r) p The higher-order phase error QPE of α) is used to determine the relationship between the higher-order phase error QPE and ΔR″″(X; r). p Simplifying α) yields the processed distance difference ΔR′(X;r) p ,α).

[0100] Due to the presence of acceleration, ΔR″″(X;r p The value of α is related to the initial velocity V, acceleration a, and sub-aperture center time t. u The first-order and higher-order terms are related. Different initial velocities, accelerations, and different synthesis aperture times will affect ΔR″″(X;r). p The values ​​of α and β have different effects. Therefore, higher-order terms due to acceleration cannot be ignored and need to be compensated for during imaging to achieve precise focusing.

[0101] Specifically, the expressions for higher-order phase errors QPE include:

[0102]

[0103] When the higher-order phase error QPE ≤ π / 4, it can be ignored.

[0104] When the angular sampling interval Δα < λ / 2l, the Nyquist sampling rate is satisfied, and the initial expression for the higher-order phase error is obtained. The simplified expression for the higher-order phase error QPE is obtained as follows:

[0105]

[0106] For the impulse response function of the sub-aperture corresponding to the sub-image, in engineering, it is necessary to satisfy the expression of the higher-order phase error QPE. At this time, the influence of the higher-order phase can be ignored.

[0107] The difference in distance ΔR′(X;r) after processing is obtained based on the higher-order phase error QPE. p ,α):

[0108]

[0109] S323, based on the processed distance difference ΔR′(X; r p The impulse response function I of the sub-image (α) u Simplifying (r, α) yields the impulse response function I′ of the simplified sub-image. u (r,α);

[0110] The difference in distance after processing is ΔR′(X;r p Substitute α) into the impulse response function I of the sub-image u In (r, α), the impulse response function I′ of the simplified sub-image is obtained. u The expression for (r, α) is:

[0111]

[0112] S324, based on the impulse response function I′ of the simplified sub-image u (r, α), the azimuth angular domain wavenumber spectrum variable K is obtained using the fifth preset formula. a The expression is used to obtain the wavenumber spectrum center K using the sixth preset formula. au The expression is used to obtain the wavenumber spectral width ΔK using the seventh preset formula. a The expression;

[0113] The fifth preset formula is: The sixth preset formula is The seventh preset formula is

[0114] t u Indicates the center time of the sub-aperture;

[0115] K a K au and ΔK a It is related to the sub-aperture center time, initial velocity, acceleration, and sub-aperture length.

[0116] By analyzing the acceleration, the definitions of the wavenumber spectrum center and wavenumber spectrum width under the acceleration trajectory were redefined, and the beamwidth and wavenumber spectrum center were expressed as functions of time. Subsequently, the fusion of the full aperture wavenumber spectrum can be achieved by shifting the wavenumber spectrum center.

[0117] S325, based on the azimuth angular domain wavenumber spectrum variable K a Wavenumber spectral center K au and wavenumber spectral width ΔK a Impulse response function I′ of the simplified sub-image u Rewriting (r, α) yields the impulse response function I″ of the rewritten sub-image. u (r,α);

[0118] in, Δα=α-α p ;

[0119] By relating the azimuth time domain to the angular wavenumber domain in the BP integral, the impulse response function I″ of the rewritten sub-image is obtained. u (r,α) indicates that the impulse response function of the wavenumber spectrum of the sub-image corresponding to the sub-aperture has a Fourier transform relationship with the wavenumber domain variables.

[0120] S326, the impulse response function I″ of the rewritten sub-image u The wavenumber spectrum I of the sub-image is obtained by performing an inverse Fourier transform on (r, α). u (K α );

[0121] in,

[0122] Specifically,

[0123] Where, ΔA u A represents the angular width of the unified polar coordinate system. cu It represents the angular center of the unified polar coordinate system.

[0124] S33, correcting the wavenumber spectrum of the sub-image by shifting, may include:

[0125] Shift the center of the wavenumber spectrum of each sub-image from zero in the azimuth direction to the center K of the wavenumber spectrum. au This achieves wavenumber spectrum correction for each sub-image. A schematic diagram of wavenumber spectrum center correction for each sub-image is shown below. Figure 4 As shown.

[0126] The wavenumber spectrum of the sub-image is corrected to obtain the corrected wavenumber spectrum of the sub-image, which is used for subsequent processing.

[0127] S4, transform the wavenumber spectrum of the corrected sub-image to the range frequency domain using a range-to-Fourier transform, and then perform wavenumber spectrum regularization on the tilt spectrum of the transformed sub-image using a correction function in the range frequency domain to obtain the regularized wavenumber spectrum of the sub-image, which may include:

[0128] S41, Perform a range-to-Fourier transform on the wavenumber spectrum of the corrected sub-image to achieve the transformation from the range time domain to the range frequency domain, and obtain the wavenumber spectrum of the transformed sub-image.

[0129] S42, the regularized range wavenumber K is obtained based on the range frequency domain correction function. r Using regularized distance wavenumber K r The distance wavenumber K in the wavenumber spectrum of the sub-image rc The replacement yields the wavenumber spectrum of the regularized sub-image; where the correction function in the range frequency domain includes:

[0130] K r =4π / λ i (λ i ∈[-Nnrn / 2,Nnrn / 2-1] / Nnrn·F s ); Nnrn represents the distance vector number of the sub-image, F s This indicates the radar range sampling frequency.

[0131] By using K r Replace K rc The wavenumber spectrum of the regularized sub-image is obtained. The correction process is as follows: Figure 5 As shown.

[0132] The presence of acceleration can cause a significant tilt in the wavenumber spectrum of the sub-image, leading to wavenumber spectrum folding and affecting the imaging results. Therefore, it is necessary to regularize the wavenumber spectrum of the sub-image before performing wavenumber spectrum fusion and stitching.

[0133] S5, the wavenumber spectra of the regularized sub-images are fused and stitched together to obtain the full aperture wavenumber spectrum.

[0134] Figure 6(a) shows the wavenumber spectrum after correction based on the existing algorithm. As can be seen from Figure 6(a), there are problems such as spectral overlap and spectral gaps during the stitching process. Figure 6(b) shows the wavenumber spectrum of the regularized sub-image provided by the embodiment of the present invention. As can be seen from Figure 6(b), the wavenumber spectra of the sub-image can be seamlessly and without overlap fused into a full aperture wavenumber spectrum.

[0135] S6. Perform range-direction inverse Fourier transform and azimuth-direction Fourier transform on the full aperture wavenumber spectrum to obtain the full aperture SAR image.

[0136] The obtained full aperture wavenumber spectrum is subjected to range-direction inverse Fourier transform and azimuth-direction Fourier transform to transform it into a two-dimensional time domain, thereby obtaining a full aperture SAR image.

[0137] Compared with the prior art, the present invention has the following advantages:

[0138] 1) It achieves imaging of forward-looking SAR on a uniformly accelerated trajectory. Compared with existing algorithms, extending the uniform linear trajectory to a uniformly accelerated trajectory enables precise focusing, which is beneficial for faster target detection and engagement.

[0139] 2) Tilted wavenumber spectrum regularization was performed. The presence of acceleration exacerbates the tilt of the sub-image wavenumber spectrum, causing wavenumber spectrum folding and resulting in gaps and overlaps when stitching full-aperture wavenumber spectra. Tilted wavenumber spectrum regularization enables effective fusion of wavenumber spectra, achieving precise focusing.

[0140] The embodiments of the present invention will be further illustrated below through simulation experiments and measured data processing experiments:

[0141] Simulation experiment:

[0142] Table 1 Simulation Parameters

[0143]

[0144] Simulation experiments were conducted in the X-band using the parameters listed in Table 1 to verify the effectiveness of the method described in this embodiment of the invention.

[0145] Figures 7(a) to 7(h)The figures show a comparison of simulation results for nine point targets under the same simulation conditions between the existing algorithm HS_AFBP and the method provided in this embodiment of the invention. Figure 7(a) shows the entire scene focused image of HS_AFBP, which clearly shows severe azimuth blur and poor target point resolution. Figure 7(b) shows the entire scene focused image of the method provided in this embodiment of the invention, which shows good target point focusing. The left images in Figures 7(c), 7(e), and 7(g) are the algorithm imaging images, while the right images in Figures 7(c), 7(e), and 7(g) are two-dimensional profile views comparing the three point targets P1, O, and P2 imaged by the method provided in this embodiment of the invention. Figures 7(d), 7(f), and 7(h) are comparison images of the range and azimuth directions of the two methods at the three target points. It is easily seen from the figures that when the radar has a large acceleration, the imaging of HS_AFBP is clearly unable to focus, especially in the azimuth direction; while the method provided in this embodiment of the invention can consistently achieve good focusing results.

[0146] The specific simulation target point imaging index analysis is shown in Table 2:

[0147] Table 2 Analysis of Simulated Target Point Imaging Indicators

[0148]

[0149]

[0150] Table 2 shows the simulation target point imaging index analysis results for PSLR (Peak Sidelobe Ratio), ISLR (Integrated Sidelobe Ratio), and IRW (Impulse Response Width, 3dB pulse width) of point targets after imaging using the HS_AFBP and the proposed algorithm. Table 2 shows that the imaging indices of the proposed method—PSLR, ISLR, and IRW—are close to the theoretical values, while the imaging indices of the HS_AFBP algorithm are significantly different. Through comparative experiments, the embodiments of this invention can achieve better forward-tilting SAR imaging with a uniform acceleration trajectory.

[0151] Experimental Data Processing:

[0152] Table 3 Measured Data Parameters Table

[0153]

[0154] The measured data in Table 3 were processed using the embodiments of the present invention, and the resulting imaging results are shown in Figure 8(a). The red box in the figure marks the angular reflection imaging. Figure 8(b) is a two-dimensional cross-sectional view of an angular reflection image formed by HS_AFBP and the present method. Figure 8(c) is a comparison of the angular reflection images of HS_AFBP and the present method in the range and azimuth directions. As can be seen from Figures 8(b) and 8(c), compared with HS_AFBP, the present method has better azimuth focusing effect, clearer target azimuth resolution, and lower sidelobes during imaging.

[0155] The results of the angular reflection imaging index analysis are shown in Table 4.

[0156] Table 4: Analysis of Corner Reverse Imaging Indicators

[0157]

[0158] As can be seen from Table 4, the imaging performance of this method is better than that of HS_AFBP and is closer to the theoretical value, which verifies the effectiveness of the embodiments of the present invention for uniform acceleration trajectories.

[0159] The solution provided in this invention extends the uniform linear trajectory to a uniformly accelerated trajectory, enabling precise focusing under the uniformly accelerated trajectory. This facilitates faster target detection and engagement, achieving forward-looking SAR imaging under a uniformly accelerated trajectory. The presence of acceleration exacerbates the tilt of the sub-image wavenumber spectrum, leading to wavenumber spectrum folding and gaps and overlaps during full-aperture wavenumber spectrum stitching. By using the BP algorithm to perform sub-aperture imaging on the divided sub-apertures, the wavenumber spectrum of each sub-aperture's corresponding sub-image is obtained. The wavenumber spectrum of the sub-image is then shifted to the spectral center, and the tilted spectrum in the obtained sub-image wavenumber spectrum is regularized, allowing for effective wavenumber spectrum fusion and achieving precise focusing.

[0160] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature.

[0161] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. An accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion, characterized in that, include: Based on the uniformly accelerated motion trajectory of the SAR-equipped moving platform and the generated synthetic aperture length, a unified polar coordinate system is established. Under the polar coordinate system, the expression for the instantaneous squint distance of the radar to any point target P in the polar coordinate system is calculated. Based on the expression for the instantaneous squint distance, the expression for the corresponding echo signal is obtained. The echo signal is matched and filtered using a first preset formula to obtain an expression for the pulse compression signal; The synthetic aperture in the azimuth direction of the pulse compression signal is divided into sub-apertures of equal length. The sub-apertures are then imaged using the BP algorithm to obtain the wavenumber spectrum of the sub-image corresponding to each sub-aperture. The wavenumber spectrum of the sub-image is then corrected by shifting. The wavenumber spectrum of the corrected sub-image is transformed to the range frequency domain by using the range-to-Fourier transform. The wavenumber spectrum of the tilt spectrum of the transformed sub-image is then regularized using the correction function in the range frequency domain to obtain the wavenumber spectrum of the regularized sub-image. The wavenumber spectra of the regularized sub-images are fused and stitched together to obtain the full aperture wavenumber spectrum; Perform range-direction inverse Fourier transform and azimuth-direction Fourier transform on the full aperture wavenumber spectrum to obtain a full aperture SAR image; The process of dividing the synthetic aperture in the azimuth direction of the pulse compression signal into equal-length sub-apertures includes: For the pulse compression signal In the azimuth direction, the length is The synthetic aperture is divided into those with equal lengths of Individual apertures, among which Let the number of pulses included in each sub-aperture be... , No. The time point corresponding to the center of each aperture is The time point corresponding to each pulse of the sub-aperture is obtained as follows: , ; Indicates a fast time. This represents the uniformly accelerated motion trajectory of a motion platform equipped with a SAR (Sensitive Radar System). Indicates the first Within each aperture The time points corresponding to each pulse; The process of performing sub-aperture imaging using the BP algorithm after dividing the sub-apertures to obtain the wavenumber spectrum of the sub-image corresponding to each sub-aperture includes: For a certain grid point in the sub-aperture The impulse response function of the sub-image is calculated using the fourth preset formula from the neighboring pixels. The fourth preset formula is: ; For the first The center of the sub-aperture, , , Indicates the distance wavenumber. , Indicates the wavelength corresponding to the carrier frequency. The distance from the radar to any target point is the difference between the distance from the radar to any pixel point, and the expression for this distance difference is: , This represents the distance from point target P to the center O of the synthetic aperture; The difference in distance The difference in distances is obtained by performing corresponding processing based on a second-order Taylor expansion. ; Based on the difference in distance after the processing Impulse response function of the sub-image The impulse response function of the simplified sub-image is obtained by simplification. ; Based on the impulse response function of the simplified sub-image The azimuth angular domain wavenumber spectrum variable is obtained using the fifth preset formula. The expression is used to obtain the wavenumber spectrum center using the sixth preset formula. The expression is used to obtain the wavenumber spectral width using the seventh preset formula. The expression; wherein, the fifth preset formula is The sixth preset formula is: The seventh preset formula is: ; According to the azimuth angular domain wavenumber spectrum variable The wavenumber spectrum center and the wavenumber spectral width Impulse response function of the simplified sub-image The impulse response function of the rewritten sub-image is obtained by rewriting the function. ;in, , ; Impulse response function of the rewritten sub-image The wavenumber spectrum of the sub-image is obtained by performing an inverse Fourier transform. ;in, ; Indicates the initial velocity. It represents acceleration.

2. The accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion according to claim 1, characterized in that, Based on the uniformly accelerated motion trajectory of the SAR-equipped moving platform and the generated synthetic aperture length, a unified polar coordinate system is established. Under this polar coordinate system, an expression for the instantaneous squint distance of the radar to any point target P in the polar coordinate system is calculated. Based on this instantaneous squint distance expression, the corresponding echo signal expression is obtained, including: Based on the expression of the uniformly accelerated motion trajectory of the motion platform equipped with SAR and the length of the generated synthetic aperture Establish a unified polar coordinate system within the imaging plane. The origin of the polar coordinate system is located at the center point O of the synthesized aperture; wherein, Indicates slow time; Calculate according to the second preset formula in the polar coordinate system. At any given moment, the radar reaches any target point in the polar coordinate system. The expression for the instantaneous strabismus distance Wherein, the second preset formula is: , , The beam angle of view representing the point target P; According to the third preset formula and the expression for the instantaneous strabismus distance The expression for the echo signal is calculated. The third preset formula is: ; Indicates the time delay for a two-way trip. , Represents the speed of light. Represents a rectangular window function. Indicates the pulse width. Indicates the carrier frequency. Indicates frequency modulation. This represents an exponential function.

3. The accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion according to claim 2, characterized in that, The first preset formula includes: ； in, The expression representing a pulse compression signal. express Function, by express.

4. The accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion according to claim 3, characterized in that, The difference in distance The difference in distances is obtained by performing corresponding processing based on a second-order Taylor expansion. ,include: The difference in distance Perform a second Taylor expansion and substitute the expression for the uniformly accelerated motion trajectory. ,get The expression; where, make In ,get The expression; Will To carry out Polynomial expansion and combination of variables yields The expression; Analysis of the above higher-order phase error According to the higher-order phase error Regarding the The difference in distance after simplification is obtained. .

5. The accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion according to claim 4, characterized in that, The higher-order phase error The expressions include: 。 6. The accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion according to claim 5, characterized in that, The correction of the wavenumber spectrum of the sub-image by shifting includes: The center of the wavenumber spectrum of each sub-image is shifted from zero in the azimuth direction to the center of the wavenumber spectrum. This allows for the correction of the wavenumber spectrum of each sub-image.

7. The accelerated trajectory forward-looking SAR imaging method based on spectral regularization and spectral fusion according to claim 6, characterized in that, The process of transforming the wavenumber spectrum of the corrected sub-image to the range frequency domain using a range-to-Fourier transform, and then performing wavenumber spectrum regularization on the tilt spectrum of the transformed sub-image using a correction function in the range frequency domain to obtain the regularized wavenumber spectrum of the sub-image includes: A range-to-Fourier transform is performed on the wavenumber spectrum of the corrected sub-image to achieve a transformation from the range time domain to the range frequency domain, thereby obtaining the wavenumber spectrum of the transformed sub-image. The regularized range wavenumber is obtained from the correction function in the range frequency domain. Using the regularized distance wavenumber The distance wavenumber in the wavenumber spectrum of the sub-image The replacement yields the wavenumber spectrum of the regularized sub-image; wherein the distance-frequency domain correction function includes: ; This represents the distance points of a sub-image. This indicates the radar range sampling frequency.

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