SAR (Synthetic Aperture Radar) anti-radio frequency interference method based on low-rank decomposition and matrix filling

Abstract

The invention discloses an SAR (Synthetic Aperture Radar) anti-radio-frequency interference method based on low-rank decomposition and matrix filling, which comprises the following steps: firstly, carrying out echo preprocessing, converting the echo into a time-frequency domain, removing interference by utilizing a one-dimensional wave trap, then converting the echo into a distance frequency domain, dividing the echo into vectors according to pulses, then converting the pulse vectors into a matrix to be recovered through Toeplitz, then initializing parameters, and finally recovering the matrix to be recovered. The method comprises the following steps of: acquiring a matrix, initializing the matrix by using singular value decomposition, performing iteration by using an alternating direction multiplier method to recover a decomposed matrix factor, reconstructing an obtained estimation matrix into vectors after an iteration termination condition is reached, reshaping all the vectors into an echo matrix, and finally imaging a target by using a backward projection method. The method provided by the invention solves the limitation of the existing SAR anti-radio-frequency interference method, and has the advantages of high imaging quality, high operation speed and suitability for a multi-interference scene.

Description

Technical Field

[0001] The present invention belongs to the technical field of broadband radar anti-interference, and in particular relates to a SAR anti-radio frequency interference method based on low-rank decomposition and matrix filling. Background Art

[0002] Synthetic Aperture Radar (SAR) is an advanced radar imaging technology that is widely used in geological exploration, environmental monitoring, weather forecasting and other fields. Its unique imaging principle enables SAR to obtain high-resolution ground images under any weather conditions, day and night, and has irreplaceable advantages, especially in complex terrain and low-visibility environments. Therefore, the application of SAR in disaster monitoring and ground detection has become increasingly important.

[0003] However, with the development of science and technology, radio frequency interference (RFI) has become one of the main challenges affecting SAR performance. Radio frequency interference usually refers to interference signals generated by other electronic devices and communication systems. These signals can cover or blur the received signals of the SAR system, thereby affecting its image quality and detection capabilities. Especially in complex environments, interference may cause information loss or misjudgment, thereby weakening the overall effectiveness of the SAR system. Effectively dealing with interference signals can not only ensure the stable operation of the SAR system in harsh electromagnetic environments, but also improve its target recognition and imaging accuracy in complex scenes. Especially in the field of security prevention, SAR is an important reconnaissance and surveillance tool, and the strength of its anti-interference ability is directly related to the success of the mission. Therefore, studying and improving the anti-RF interference capability of SAR has become one of the focuses of current radar technology research.

[0004] However, some current SAR anti-interference methods have certain defects. Non-parametric interference suppression methods characterize the received signal into a 1D range-frequency domain or a 2D range-time-frequency domain, and use the difference in intensity characteristics between the interference signal and the true echo signal to construct an adaptive filter or use signal subspace projection to filter out interference. However, this method loses spectral information and lacks constraints on the true echo, which reduces the resolution of imaging. The parameterized model is suitable for isolated single-type interference, and can estimate the isolated interference parameters at each azimuth sampling time (single pulse), but it estimates the interference model parameters by iterative pulse-by-pulse, and the computational complexity is high. Therefore, it is a key issue to propose a SAR anti-RF interference method with fast computational speed and spectrum information retention. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a SAR anti-RF interference method based on low-rank decomposition and matrix filling.

[0006] The technical solution adopted by the present invention is: a SAR anti-RF interference method based on low-rank decomposition and matrix filling, and the specific steps are as follows:

[0007] S1. Preprocess the received echo and transform it into time-frequency domain through short-time Fourier transform to obtain time-frequency spectrum;

[0008] The received echo is pulse compressed to obtain the echo matrix S after pulse compression. Then the matrix S is short-time Fourier transformed to obtain the time-frequency spectrum S tf , the expression is as follows:

[0009] S tf =STFT{S}

[0010] Among them, STFT stands for short-time Fourier transform; S tf Represents the time spectrum.

[0011] S2, based on step S1, using a one-dimensional notch filter in the time-frequency domain to remove the interfered time-frequency spectrum, and transforming the notched time-frequency spectrum back to the range-frequency domain to obtain a spectrum with missing components;

[0012] First, the time spectrum S tf Input the adaptive one-dimensional notch filter for filtering, the expression is as follows:

[0013]

[0014] in, represents the time-frequency spectrum after notching, ANF 1 Represents an adaptive one-dimensional notch filter.

[0015] Then the notched time-frequency spectrum is inversely transformed into the short-time Fourier transform, and the expression is as follows:

[0016]

[0017] in, represents the echo after notching, and ISTFT represents inverse short-time Fourier transform.

[0018] Then perform distance Fourier transform on the echo after notching, and the expression is as follows:

[0019]

[0020] in, Represents the spectrum after notching, FFT ran represents the Fourier transform of distance.

[0021] S3, based on step S2, reshape each azimuth pulse of the spectrum into a Toeplitz matrix;

[0022] The spectrum matrix Divided into N pulse vectors along the azimuth direction Pulse vector The expression is as follows:

[0023]

[0024] Wherein, M represents the length of the pulse vector.

[0025] Then define the Toeplitz transformation operator Γ: The expression is as follows:

[0026]

[0027] in, represents the complex field, n 1 and n 2 They represent the number of rows and columns of the transformed matrix respectively; h is a hyperparameter that changes the shape of the transformed Toeplitz matrix by adjusting its size.

[0028] Finally, the Toeplitz transform operator Γ is applied to the N pulse vectors to obtain the low-rank matrix The expression is as follows:

[0029]

[0030] S4, based on step S3, using a method based on low-rank decomposition filling matrix to restore all Toeplitz matrices;

[0031] S41, initializing parameters, using singular value decomposition to initialize two matrix factors, and performing matrix completion recovery on all low-rank matrices obtained in step S3;

[0032] Initialize the parameters first, including: regularization parameter α, scaling factor β, penalty factor ρ 0 , dimension parameter d, number of iterations k=0 and maximum number of iterations K.

[0033] Among them, the superscript of the matrix represents the number of iterations, and the penalty factor ρ 0 Indicates its initial value.

[0034] Reinitialize the matrix, that is, use singular value decomposition to initialize the two matrix factors, and then Perform singular value decomposition And A 0 =U(:,1:d)S(1:d,1:d) 1 / 2 ,Z 0 =zero(d,n 2 ),Y 0 =0,

[0035] The superscript H indicates the conjugate transpose; the matrices A and Z indicate the Decomposition of, Y represents the Lagrange multiplier matrix, zero represents the generated zero matrix, Represents the variable restored at each iteration The initial value of

[0036] S42, based on step S41, iteratively updating the optimization matrix and parameters;

[0037] (1) Update Z k+1 ;

[0038] By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression:

[0039]

[0040] Where I represents the identity matrix.

[0041] (2) Update A k+1 ;

[0042] By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression:

[0043]

[0044] (3) Update

[0045] By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression:

[0046]

[0047] (4) Update the Lagrange multiplier Y k+1 ;

[0048]

[0049] (5) Update the penalty factor ρ k+1 ;

[0050] ρ k+1 =βρ k

[0051] S43, determine whether the iteration termination condition is met, when k = K, output As If the recovery result is obtained, the process goes to step S44, otherwise the process returns to step S42, where k=k+1 and the iteration continues;

[0052] S44, traverse the azimuth direction, for each constructed Toeplitz matrix The optimization recovery of steps S41 to S43 is performed to obtain N restored spectrum matrices.

[0053] The superscript n represents the recovery result of each pulse.

[0054] S5, based on step S4, reshape all the recovered Toeplitz matrices into pulse vectors, and splice them to obtain a complete spectrum;

[0055] For each recovered spectrum matrix Reconstruct into a pulse vector according to the first row and the first column, and then concatenate and reshape into the recovered spectrum matrix S according to the pulse order F , and use the range inverse fast Fourier transform to transform the spectrum matrix into the echo matrix ζ est , the expression is as follows:

[0056] ζ est =IFFT ran {S F}

[0057] Among them, IFFT ran Represents the inverse fast Fourier transform of distance.

[0058] S6. Based on step S5, the echo matrix ζ est The target is imaged using the back-projection method;

[0059] First, the scene is gridded and the imaging area is divided into multiple grids. Each pixel in the final generated SAR image corresponds to a grid unit.

[0060] Then, at each azimuth moment, the distance between the radar and each grid point is calculated, and the round-trip delay is determined. From the data obtained at the current azimuth moment, the corresponding distance data is found based on the round-trip delay. This data is the signal received by the grid point at this azimuth moment.

[0061] Finally, coherent stacking is performed, and the data at each azimuth time is phase corrected and then stacked to finally generate a SAR image.

[0062] Beneficial effects of the present invention: The method of the present invention first pre-processes the echo matrix and transforms it to the time-frequency domain through short-time Fourier transform, filters the time-frequency spectrum through one-dimensional adaptive notch and transforms it to the range frequency domain, divides the spectrum of the range frequency domain into vectors according to pulses, reshapes it into a Toeplitz matrix and restores it based on the method of low-rank decomposition, reconstructs the restored matrix into vectors after reaching the iteration termination condition, and reshapes all vectors into echo matrices, and finally uses the back-projection method to image the target. The method of the present invention solves the limitations of existing SAR anti-RF interference methods, has the advantages of high imaging quality, fast calculation speed, and is suitable for multi-interference scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 The present invention is a flowchart of a SAR anti-radio frequency interference method based on low-rank decomposition and matrix filling.

[0064] Figure 2 It is a time-frequency diagram under multi-source interference in an embodiment of the present invention.

[0065] Figure 3 This is a spectrum diagram of the interference time-frequency diagram transformed into the range frequency domain after notching in an embodiment of the present invention.

[0066] Figure 4 It is a schematic diagram of the result of restoring the damaged spectrum graph in an embodiment of the present invention.

[0067] Figure 5 It is a schematic diagram of the result of direct imaging of multi-source interference in an embodiment of the present invention.

[0068] Figure 6 It is a schematic diagram of the imaging result after one-dimensional notch filtering with multi-source interference in an embodiment of the present invention.

[0069] Figure 7 This is a schematic diagram of the imaging result after multi-source interference one-dimensional notch and spectrum recovery using low-rank decomposition and matrix filling in an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The method of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0071] like Figure 1 As shown, a flow chart of a SAR anti-RF interference method based on low-rank decomposition and matrix filling of the present invention, the specific steps are as follows:

[0072] S1. Preprocess the received echo and transform it to the time-frequency domain through short-time Fourier transform (STFT) to obtain the time-frequency spectrum;

[0073] The received echo is pulse compressed to obtain the echo matrix S after pulse compression. Then the matrix S is short-time Fourier transformed to obtain the time-frequency spectrum S tf , the expression is as follows:

[0074] S tf =STFT{S}

[0075] Among them, STFT stands for short-time Fourier transform; S tf In this embodiment, the time-frequency diagram of the simulation under multi-source radio frequency interference is as follows Figure 2 shown.

[0076] S2, based on step S1, using a one-dimensional notch filter in the time-frequency domain to remove the interfered time-frequency spectrum, and transforming the notched time-frequency spectrum back to the range-frequency domain to obtain a spectrum with missing components;

[0077] In this embodiment, a one-dimensional notch is performed on the multi-source radio frequency interference in the time-frequency domain, and then transformed into a spectrum in the range-frequency domain as shown in FIG. Figure 3 As shown, it can be observed that the spectral components are lost.

[0078] First, the time spectrum S tf Input the adaptive one-dimensional notch filter for filtering, the expression is as follows:

[0079]

[0080] in, represents the time-frequency spectrum after notching, ANF 1 Represents an adaptive one-dimensional notch filter.

[0081] Then the notched time-frequency spectrum is inversely transformed into the short-time Fourier transform, and the expression is as follows:

[0082]

[0083] in, represents the echo after notching, and ISTFT represents inverse short-time Fourier transform.

[0084] Then perform distance Fourier transform on the echo after notching, and the expression is as follows:

[0085]

[0086] in, Represents the spectrum after notching, FFT ran represents the Fourier transform of distance.

[0087] S3, based on step S2, reshape each azimuth pulse of the spectrum into a Toeplitz matrix;

[0088] The spectrum matrix Divided into N pulse vectors along the azimuth direction Pulse vector The expression is as follows:

[0089]

[0090] Wherein, M represents the length of the pulse vector.

[0091] Then define the Toeplitz transformation operator Γ: The expression is as follows:

[0092]

[0093] in, represents the complex field, n 1 and n 2 They represent the number of rows and columns of the transformed matrix respectively; h is a hyperparameter that changes the shape of the transformed Toeplitz matrix by adjusting its size.

[0094] Finally, the Toeplitz transform operator Γ is applied to the N pulse vectors to obtain the low-rank matrix The expression is as follows:

[0095]

[0096] S4, based on step S3, using a method based on low-rank decomposition filling matrix to restore all Toeplitz matrices;

[0097] S41, initialization parameters, use singular value decomposition to initialize two matrix factors, and perform matrix completion recovery on all low-rank matrices obtained in step S3 (first restore );

[0098] Initialize the parameters first, including: regularization parameter α, scaling factor β, penalty factor ρ 0 , dimension parameter d, number of iterations k=0 and maximum number of iterations K.

[0099] Among them, the superscript of the matrix represents the number of iterations, and the penalty factor ρ 0 Indicates its initial value.

[0100] Reinitialize the matrix, that is, use singular value decomposition to initialize the two matrix factors, and then Perform singular value decomposition And A 0 =U(:,1:d)S(1:d,1:d) 1 / 2 ,Z 0 =zero(d,n 2 ),Y 0 =0,

[0101] The superscript H indicates the conjugate transpose; the matrices A and Z indicate the Decomposition of, Y represents the Lagrange multiplier matrix, zero represents the generated zero matrix, Represents the variable restored at each iteration The initial value of

[0102] S42, based on step S41, iteratively updating the optimization matrix and parameters;

[0103] (1) Update Z k+1 ;

[0104] By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression:

[0105]

[0106] Where I represents the identity matrix.

[0107] (2) Update A k+1 ;

[0108] By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression:

[0109]

[0110] (3) Update

[0111] By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression:

[0112]

[0113] (4) Update the Lagrange multiplier Y k+1 ;

[0114]

[0115] (5) Update the penalty factor ρ k+1 ;

[0116] ρ k+1 =βρ k

[0117] S43, determine whether the iteration termination condition is met, when k = K, output As If the recovery result is obtained, the process goes to step S44, otherwise the process returns to step S42, where k=k+1 and the iteration continues;

[0118] S44, traverse the azimuth direction, for each constructed Toeplitz matrix The optimization recovery of steps S41 to S43 is performed to obtain N restored spectrum matrices.

[0119] The superscript n represents the recovery result of each pulse.

[0120] S5, based on step S4, reshape all the recovered Toeplitz matrices into pulse vectors, and splice them to obtain a complete spectrum;

[0121] For each recovered spectrum matrix Reconstruct into a pulse vector according to the first row and the first column, and then concatenate and reshape into the recovered spectrum matrix S according to the pulse order F , and use the range inverse fast Fourier transform to transform the spectrum matrix into the echo matrix ζ est , the expression is as follows:

[0122] ζ est =IFFT ran {S F}

[0123] Among them, IFFT ran represents the inverse fast Fourier transform of distance.

[0124] All the recovered matrices are reshaped into pulse vectors and concatenated to obtain the complete spectrum, such as Figure 4 As shown in Figure 2, the spectral components are well restored, which is beneficial to the subsequent imaging process.

[0125] S6. Based on step S5, the echo matrix ζ est The target is imaged using the back projection method (BP).

[0126] First, the scene is gridded and the imaging area is divided into multiple grids. Each pixel in the final generated SAR image corresponds to a grid unit.

[0127] Then, at each azimuth moment (i.e., the moment when the radar transmits a pulse), the distance between the radar and each grid point is calculated, and the round-trip delay is determined. From the data obtained at the current azimuth moment, the corresponding distance data is found based on the round-trip delay. This data is the signal received by the grid point at this azimuth moment.

[0128] Finally, coherent stacking is performed, and the data at each azimuth time is phase corrected and then stacked to finally generate a SAR image.

[0129] The simulation results of this embodiment are as follows Figure 5 , Figure 6 , Figure 7shown. Figure 5 This is the result of direct imaging of echo BP containing multi-source RF interference. Figure 6 These are the results of imaging after multiple one-dimensional frequency notching. Figure 7 It is the result of imaging after spectrum restoration by the method of the present invention. It can be seen from the simulation result diagram that the method of the present invention can well remove interference under multi-source RF interference, accurately restore the spectrum, and then perform BP imaging, the side lobes are suppressed to a low level, the point target is well focused, and the imaging effect is significantly improved.

[0130] In summary, the method of the present invention pre-processes the received echo, and performs one-dimensional notch filtering in the time-frequency domain to remove interference, and then reconstructs each azimuth pulse into a Toeplitz matrix in the range-frequency domain, and uses a method based on low-rank decomposition to restore them separately, and reshapes multiple restored matrices into vectors in order and splices them into matrices, and finally performs back-projection imaging. The method of the present invention solves the limitations of existing SAR anti-RF interference methods, and has the advantages of high imaging quality, fast computing speed, and applicability to multi-interference scenarios.

[0131] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A SAR anti-RF interference method based on low-rank decomposition and matrix filling, the specific steps are as follows: S1. Preprocess the received echo and transform it into time-frequency domain through short-time Fourier transform to obtain time-frequency spectrum; The received echo is pulse compressed to obtain the echo matrix S after pulse compression; then the matrix S is short-time Fourier transformed to obtain the time-frequency spectrum S tf , the expression is as follows: S tf =STFT{S} in, STFT stands for Short Time Fourier Transform; S tf Represents time-frequency spectrum; S2, based on step S1, using a one-dimensional notch filter in the time-frequency domain to remove the interfered time-frequency spectrum, and transforming the notched time-frequency spectrum back to the range-frequency domain to obtain a spectrum with missing components; First, the time spectrum S tf Input the adaptive one-dimensional notch filter for filtering, the expression is as follows: in, represents the time-frequency spectrum after notching, and ANF1 represents the adaptive one-dimensional notch filter; Then the notched time-frequency spectrum is inversely transformed into the short-time Fourier transform, and the expression is as follows: in, represents the echo after notching, ISTFT represents the inverse short-time Fourier transform; Then perform distance Fourier transform on the echo after notching, and the expression is as follows: in, Represents the spectrum after notching, FFT ran represents the distance to Fourier transform; S3, based on step S2, reshape each azimuth pulse of the spectrum into a Toeplitz matrix; The spectrum matrix Divided into N pulse vectors along the azimuth direction Pulse vector The expression is as follows: Where M represents the length of the pulse vector; Then define the Toeplitz transformation operator Γ: The expression is as follows: in, represents the complex field, n1 and n2 represent the number of rows and columns of the transformed matrix respectively; h is a hyperparameter, and the shape of the transformed Toeplitz matrix is ​​changed by adjusting its size; Finally, the Toeplitz transform operator Γ is applied to the N pulse vectors to obtain the low-rank matrix The expression is as follows: S4, based on step S3, using a method based on low-rank decomposition filling matrix to restore all Toeplitz matrices; S41, initializing parameters, using singular value decomposition to initialize two matrix factors, and performing matrix completion recovery on all low-rank matrices obtained in step S3; Initialize the parameters first, including: regularization parameter α, scaling factor β, penalty factor ρ 0 , dimension parameter d, number of iterations k = 0 and maximum number of iterations K; Among them, the superscript of the matrix represents the number of iterations, and the penalty factor ρ 0 Indicates its initial value; Reinitialize the matrix, that is, use singular value decomposition to initialize two matrix factors, and then Perform singular value decomposition And A 0 =U(:,1:d)S(1:d,1:d) 1 / 2 ,Z 0 =zero(d,n2),Y 0 =0, The superscript H indicates the conjugate transpose; the matrices A and Z indicate the Decomposition of, Y represents the Lagrange multiplier matrix, zero represents the generated zero matrix, Represents the variable restored at each iteration The initial value of S42, based on step S41, iteratively updating the optimization matrix and parameters; (1) Update Z k+1 ; By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression: Where I represents the identity matrix; (2) Update A k+1 ; By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression: (3) Update By taking the partial derivative of the augmented Lagrangian function equal to zero, we can get the following expression: (4) Update the Lagrange multiplier Y k+1 ; (5) Update the penalty factor ρ k+1 ; r k+1 =water k S43, determine whether the iteration termination condition is met, when k = K, output As If the recovery result is obtained, the process goes to step S44, otherwise the process returns to step S42, where k=k+1 and the iteration continues; S44, traverse the azimuth direction, for each constructed Toeplitz matrix The optimization recovery of steps S41 to S43 is performed to obtain N restored spectrum matrices. Wherein, the superscript n represents the recovery result of each pulse; S5, based on step S4, reshape all the recovered Toeplitz matrices into pulse vectors, and splice them to obtain a complete spectrum; For each recovered spectrum matrix Reconstruct into a pulse vector according to the first row and the first column, and then concatenate and reshape into the recovered spectrum matrix S according to the pulse order F , and use the range inverse fast Fourier transform to transform the spectrum matrix into the echo matrix ζ est , the expression is as follows: g est =IFFT ran {S F } Among them, IFFT ran represents the inverse fast Fourier transform of distance; S6. Based on step S5, the echo matrix ζ est The target is imaged using the back-projection method; First, the scene is gridded, and the imaging area is divided into multiple grids. Each pixel point in the final generated SAR image corresponds to a grid unit. Then, at each azimuth time, the distance between the radar and each grid point is calculated, and the round-trip delay is determined. From the data obtained at the current azimuth time, the corresponding distance data is found according to the round-trip delay. This data is the signal received by the grid point at this azimuth time. Finally, coherent stacking is performed, and the data at each azimuth time is phase corrected and then stacked to finally generate a SAR image.

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