A time-frequency synchronization error compensation method for bistatic SAR based on maximum contrast method

Abstract

A method for compensating for time-frequency synchronization errors in a bistatic SAR based on a maximum contrast method relates to an airborne bistatic SAR imaging method. The purpose of the present invention is to solve the problem of target imaging defocus caused by time-frequency synchronization errors in airborne bistatic SAR. The process is as follows: first, a bistatic SAR system is used to record echo signals of scene targets, a transmitter transmits an LFM signal, which is received by a receiver after being reflected by the scene target, and target echo data is obtained; second, range frequency domain data is obtained; third, echo data after matched filtering is obtained; fourth, echo data after range migration correction is obtained; fifth, echo data after azimuth compression is obtained; sixth, two-dimensional image contrast is obtained for the echo data after azimuth compression; seventh, the correction factor E1 and the compression factor E2 are used as variables, and a particle swarm optimization algorithm is used to obtain the echo data corresponding to the maximum value of the two-dimensional image contrast and compensated for the time-frequency synchronization error as the final target image. The present invention is used in the field of target imaging.

Description

Technical Field

[0001] The invention relates to an airborne bistatic SAR imaging method. Background Art

[0002] Bistatic forward-looking synthetic aperture radar (SAR) systems, by separating the transmitter and receiver on two separate platforms, can achieve imaging of the area ahead of the receiver, something not possible with monostatic SAR systems. However, the unique configuration of bistatic SAR also introduces new challenges, such as synchronization errors between the transmitter and receiver. Because the transceiver platforms use different clock and frequency sources to trigger the transmission and reception of linear frequency modulation (LFM) signals, bistatic SAR systems inevitably experience errors in time and frequency synchronization when recording target echoes. This leads to phase errors in the echo data, ultimately degrading target imaging quality and even making the target image defocused and difficult to identify. Therefore, it is necessary to study time-frequency synchronization error compensation algorithms to eliminate phase errors and achieve target image refocusing. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem of target imaging defocus caused by time-frequency synchronization error in airborne bistatic SAR, and to propose a bistatic SAR time-frequency synchronization error compensation method based on the maximum contrast method.

[0004] A method for compensating time-frequency synchronization errors of bistatic SAR based on the maximum contrast method is as follows:

[0005] Step 1: Use a bistatic SAR system to record the scene target echo signal. The transmitter transmits an LFM signal, which is reflected by the scene target and received by the receiver to obtain the target echo data d(τ,η);

[0006] Where τ is the distance-to-fast time, and the length of the distance-to-fast time is N τ ; η is the azimuth slow time, the length of the azimuth slow time is N η , the target echo data d(τ,η) is an N τ ×N η A two-dimensional matrix; LFM signal is a linear frequency modulation signal;

[0007] Step 2: Perform range-wise fast Fourier transform on the target echo data d(τ,η) to obtain the range-wise frequency domain data D1(f τ ,η);

[0008] where f τ is the distance frequency;

[0009] Step 3: Construct distance reference function d refr (τ), for the reference function d refr (τ) is processed by fast Fourier transform in the distance direction and then conjugated to obtain Drefr (f τ ), the distance in step 2 is converted to the frequency domain data D1(f τ ,η) multiplied by the function D refr (f τ ), and obtain the echo data D2(f τ ,η);

[0010] Step 4: Based on the distance to frequency domain data D1(f τ ,η) construct distance migration correction function F c (f τ ,η), in the distance migration correction function F c (f τ ,η) is multiplied by the correction factor E1 to obtain the range migration correction function F c (f τ ,η;E1), the initial value of the correction factor E1 is set to 1;

[0011] The echo data D2(f τ ,η) multiplied by the distance migration correction function F c (f τ ,η; E1), and then perform range inverse Fourier transform (IFFT) processing to obtain the echo data D3 (τ,η) after range migration correction;

[0012] Step 5: Perform azimuth fast Fourier transform on the target echo data d(τ,η) to obtain azimuth frequency domain data D1(τ,f η ); Based on the azimuth frequency domain data D1(τ,f η ) Construct azimuth compression function F a (τ,f η ), in the azimuth compression function F a (τ,f η ) is multiplied by the compression factor E2 to obtain the azimuth compression function F a (τ,f η ; E2), the initial value of the compression factor E2 is set to 1;

[0013] Perform azimuth FFT on the echo data D3(τ,η) corrected for range migration in step 4 to obtain A, which is then multiplied by the azimuth compression function F a (τ,f η E2) to obtain B, and finally perform azimuth IFFT processing on B to obtain the echo data D4 (τ, η) after azimuth compression;

[0014] where f η is the azimuth frequency;

[0015] Step 6: Calculate the two-dimensional image contrast C(τ,η) for the echo data D4(τ,η) after azimuth compression in step 5;

[0016] Step 7: Using the correction factor E1 and compression factor E2 as variables, the particle swarm optimization (PSO) algorithm is used to obtain the D corresponding to the maximum value of the two-dimensional image contrast C. out (τ,η) is taken as the final target image.

[0017] The beneficial effects of the present invention are:

[0018] In a bistatic SAR system configuration, time-frequency synchronization errors between the transmitting and receiving platforms are unavoidable. In addition to the range drift caused by platform motion, time synchronization errors also produce additional range drift in the target echo, affecting the effectiveness of range drift correction. Frequency synchronization errors, on the other hand, can cause phase errors in the signal echo, shifting the Doppler center frequency and Doppler modulation slope, ultimately rendering conventional SAR imaging algorithms ineffective. To achieve high-quality imaging of scene targets using a bistatic SAR system, it is necessary to compensate for the time-frequency synchronization errors present in the bistatic configuration. This is based on the two-dimensional compression and drift correction processing of the target echo data. To this end, the present invention proposes a bistatic SAR time-frequency synchronization error compensation method based on the maximum contrast method.

[0019] In a bistatic SAR system imaging model of a scene target, such as the bistatic SAR system imaging model of a ship target provided by the present invention, the time-frequency synchronization error existing in the bistatic configuration causes the conventional SAR imaging algorithm to still have the phenomenon of migration across range units in the range compression image after range migration correction, and the image after azimuth compression is severely defocused, the imaging quality is very poor, and the ship target is difficult to identify; while the bistatic SAR time-frequency synchronization error compensation method based on the maximum contrast method can effectively eliminate the influence of the time-frequency synchronization error on target imaging by estimating the correction factor and the compression factor to compensate for the range migration correction function and the azimuth compression function, and the phenomenon of migration across range units in the range compression image of the ship target is greatly improved, while the azimuth compression effect is significantly improved, and the ship target can be imaged with high quality. In summary, the bistatic SAR time-frequency synchronization error compensation method based on the maximum contrast method can effectively eliminate the influence of the time-frequency synchronization error of the bistatic SAR system, and the effect of correcting the range migration and azimuth compression of the echo signal is better than that of the conventional SAR imaging algorithm that does not compensate for the time-frequency synchronization error. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is the imaging model diagram of the ship target by the airborne bistatic SAR used in the present invention, where P is the ship target, T is the transmitter, R is the receiver, O is the origin of the coordinate system, XYZ is the rectangular coordinate system with the center of the scene as the origin, and α Tis the downward viewing angle of the transmitter beam;

[0021] Figure 2 This is the original echo data image captured by the bistatic SAR system;

[0022] Figure 3a is the range-compressed image without correcting the range migration,

[0023] Figure 3b It is the range-compressed image after range migration correction using conventional SAR imaging algorithms;

[0024] Figure 4a is the range-compressed image without correction for range migration;

[0025] Figure 4b The range compression image after range migration correction by the algorithm of the present invention;

[0026] Figure 5 This is the target imaging image of the conventional SAR imaging algorithm;

[0027] Figure 6 This is the target imaging diagram of the algorithm of the present invention. DETAILED DESCRIPTION

[0028] Specific implementation method 1: Combination Figure 1 This embodiment describes a method for compensating time-frequency synchronization errors of a bistatic SAR based on a maximum contrast method. The specific process is as follows:

[0029] Both the transmitter and the receiver fly at a constant speed along the positive direction of the X-axis, and the target is directly in front of the receiver.

[0030] Step 1: Use a bistatic SAR system to record the scene target echo signal. The transmitter transmits an LFM signal, which is reflected by the scene target and received by the receiver to obtain the target echo data d(τ,η);

[0031] Where τ is the distance-to-fast time, and the length of the distance-to-fast time is N τ ; η is the azimuth slow time, the length of the azimuth slow time is N η , the target echo data d(τ,η) is an N τ ×N η A two-dimensional matrix; LFM signal is a linear frequency modulation signal;

[0032] The target is a ship target;

[0033] Step 2: Perform range-direction fast Fourier transform (FFT) on the target echo data d(τ,η) to obtain the range-direction frequency domain data D1(f τ ,η);

[0034] where f τis the distance frequency;

[0035] Step 3: Construct distance reference function d refr (τ), for the reference function d refr (τ) is processed by fast Fourier transform (FFT) in the distance direction and then conjugated to obtain D refr (f τ ), the distance in step 2 is converted to the frequency domain data D1(f τ ,η) multiplied by the function D refr (f τ ), and obtain the echo data D2(f τ ,η);

[0036] Step 4: Based on the distance to frequency domain data D1(f τ ,η) construct distance migration correction function F c (f τ ,η), in the distance migration correction function F c (f τ ,η) is multiplied by the correction factor E1 to obtain the range migration correction function F c (f τ ,η; E1), used to compensate for the distance migration caused by the time-frequency synchronization error; the initial value of the correction factor E1 is set to 1;

[0037] The echo data D2(f τ ,η) multiplied by the distance migration correction function F c (f τ ,η; E1), and then perform range inverse Fourier transform (IFFT) processing to obtain the echo data D3 (τ,η) after range migration correction;

[0038] Step 5: Perform azimuth fast Fourier transform (FFT) on the target echo data d(τ,η) to obtain azimuth frequency domain data D1(τ,f η ); Based on the azimuth frequency domain data D1(τ,f η ) Construct azimuth compression function F a (τ,f η ), in the azimuth compression function F a (τ,f η ) is multiplied by the compression factor E2 to obtain the azimuth compression function F a (τ,f η ; E2), used to compensate for the azimuth compression defocus caused by the time-frequency synchronization error; the initial value of the compression factor E2 is set to 1;

[0039] Perform azimuth FFT on the echo data D3(τ,η) corrected for range migration in step 4 to obtain A, which is then multiplied by the azimuth compression function Fa (τ,f η E2) to obtain B, and finally perform azimuth IFFT processing on B to obtain the echo data D4 (τ, η) after azimuth compression;

[0040] where f η is the azimuth frequency;

[0041] Step 6: Calculate the two-dimensional image contrast C(τ,η) for the echo data D4(τ,η) after azimuth compression in step 5;

[0042] Step 7: Using the correction factor E1 and compression factor E2 as variables, the particle swarm optimization (PSO) algorithm is used to obtain the D corresponding to the maximum value of the two-dimensional image contrast C. out (τ,η) is taken as the final target image.

[0043] Specific embodiment 2: The difference between this embodiment and specific embodiment 1 is that the distance reference function d is constructed in step 3. refr (τ), for the reference function d refr (τ) is processed by fast Fourier transform (FFT) in the distance direction and then conjugated to obtain D refr (f τ ), the distance in step 2 is converted to the frequency domain data D1(f τ ,η) multiplied by the function D refr (f τ ), and obtain the echo data D2(f τ ,η);

[0044] The specific process is:

[0045] Construct distance reference function d refr (τ), the expression is

[0046] d refr (τ)=exp(jπK τ τ 2 ) (1)

[0047] where exp(·) represents the power of e, j represents an imaginary number and K τ is the frequency modulation slope of the LFM signal;

[0048] For the reference function d refr (τ) performs a distance-direction fast Fourier transform (FFT) and then takes the conjugate to obtain D refr (f τ ), the expression is

[0049] D refr (f τ )=[FFT τ(d refr (τ))] * (2)

[0050] Where FFT τ (·) represents the distance reference function d refr (τ) is processed by FFT, [·] * Indicates conjugate.

[0051] Other steps and parameters are the same as those in the first embodiment.

[0052] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the step four is based on the distance to frequency domain data D1 (f τ ,η) construct distance migration correction function F c (f τ ,η), in the distance migration correction function F c (f τ ,η) is multiplied by the correction factor E1 to obtain the range migration correction function F c (f τ ,η; E1), used to compensate for the distance migration caused by the time-frequency synchronization error; the initial value of the correction factor E1 is set to 1;

[0053] The echo data D2(f τ ,η) multiplied by the distance migration correction function F c (f τ ,η; E1), and then perform range inverse Fourier transform (IFFT) processing to obtain the echo data D3 (τ,η) after range migration correction;

[0054] The specific process is:

[0055] Based on the distance frequency domain data D1(f τ ,η) construct distance migration correction function F c (f τ ,η),F c (f τ ,η) is expressed as:

[0056]

[0057] In the range migration correction function F c (f τ ,η) is multiplied by the correction factor E1 to obtain the range migration correction function F c (f τ ,η;E1), the expression is:

[0058]

[0059] Where c is the speed of light, c = 3 × 10 8 m / s; V T and V R are the speeds of the transmitter and receiver, θ T and θ R are the oblique viewing angles of the transmitter and receiver, respectively.

[0060] Other steps and parameters are the same as those in the first or second embodiment.

[0061] Specific embodiment 4: The difference between this embodiment and any one of the specific embodiments 1 to 3 is that in step 5, the target echo data d(τ,η) is processed by azimuth fast Fourier transform (FFT) to obtain azimuth frequency domain data D1(τ,f η ); Based on the azimuth frequency domain data D1(τ,f η ) Construct azimuth compression function F a (τ,f η ), in the azimuth compression function F a (τ,f η ) is multiplied by the compression factor E2 to obtain the azimuth compression function F a (τ,f η ; E2), used to compensate for the azimuth compression defocus caused by the time-frequency synchronization error; the initial value of the compression factor E2 is set to 1;

[0062] Perform azimuth FFT on the echo data D3(τ,η) corrected for range migration in step 4 to obtain A, which is then multiplied by the azimuth compression function F a (τ,f η E2) to obtain B, and finally perform azimuth IFFT processing on B to obtain the echo data D4 (τ, η) after azimuth compression;

[0063] where f η is the azimuth frequency;

[0064] The specific process is:

[0065] Based on the azimuth frequency domain data D1(τ,f η ) Construct azimuth compression function F a (τ,f η ), F a (τ,f η ) is expressed as:

[0066]

[0067] where f ηs is the maximum value of the azimuth frequency and f ηs =(V T cosθT +V R cosθ R ) / λ; R0 is the sum of the slant distances from the transmitter and receiver to the target center at the start time; λ represents the wavelength of the LFM signal;

[0068] The azimuthal compression function F a (τ,f η ) is multiplied by the compression factor E2 to obtain the azimuth compression function F a (τ,f η ; E2), F a (τ,f η ; E2) expression is:

[0069]

[0070] The other steps and parameters are the same as those in the first to third embodiments.

[0071] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that in step 6, the two-dimensional image contrast C(τ,η) is obtained from the echo data D4(τ,η) after azimuth compression in step 5. The specific process is as follows:

[0072] The expression of two-dimensional image contrast C is:

[0073]

[0074] Where M(·) represents the arithmetic formula for calculating the mean (D4(τ,η) is an N τ Row N η Column two-dimensional matrix, find the average value of the two-dimensional matrix, specifically N τ ×N η The data are summed up first and then divided by N τ ×N η ); |·| is the absolute value symbol.

[0075] The other steps and parameters are the same as those in the first to fourth embodiments.

[0076] Specific embodiment 6: This embodiment is different from the specific embodiments 1 to 5 in that in step 7, the correction factor E1 and the compression factor E2 are used as variables, and the particle swarm optimization (PSO) algorithm is used to obtain the D corresponding to the maximum value of the two-dimensional image contrast C. out (τ,η) is taken as the final target image; the specific process is:

[0077] The expression of the PSO algorithm is

[0078]

[0079] Where n represents the number of iterations, n = 1, 2, ..., N, N is the maximum number of iterations; m represents the current particle index, m = 1, 2, ..., M, M is the total number of particles;

[0080] It represents the parameter value estimated by the mth particle at the nth iteration, denoted as represents the correction factor E1 obtained by the mth particle in the nth iteration, represents the compression factor E2 obtained by the mth particle in the nth iteration, represents the change in the parameter value estimated by the mth particle at the nth iteration;

[0081] a is the inertia factor, which represents the weight ratio of historical values; b1 and b2 are the local learning factor and the global learning factor respectively; Ra() is a random number between 0 and 1;

[0082] is the historical optimal solution of the mth particle at the nth iteration, gb n represents the historical optimal solution among all particles in the nth iteration, that is The best one among the corresponding M particles;

[0083] Set the M×N parameter values middle Substitute into the distance migration correction function F c (f τ ,η;E1) phase term, we get M×N updated range migration correction functions F c (f τ ,η;E1);

[0084] Set the M×N parameter values middle Substitute into the distance migration correction function F a (τ,f η E2) phase term, get M × N updated range migration correction function F a (τ,f η ; E2);

[0085] The echo data D2(f τ ,η) multiplied by the updated distance migration correction function F c (f τ ,η;E1) get D;

[0086] Perform distance IFFT on D to obtain E;

[0087] Perform azimuth FFT on E to obtain F;

[0088] Multiply F by the updated distance migration correction function F c (f τ ,η;E1) corresponds to the updated azimuth compression function F a (τ,f η ; E2) (corresponding to the same particle and the same iteration) to obtain G;

[0089] Perform azimuth IFFT processing on G to obtain echo data D that compensates for time-frequency synchronization errors out (τ,η), D out (τ,η) replaces D4(τ,η) and brings it into the expression of two-dimensional image contrast C to obtain M×N two-dimensional image contrast C. Take the D corresponding to the maximum value of the two-dimensional image contrast C out (τ,η) is taken as the final target image.

[0090] The other steps and parameters are the same as those in the first to fifth embodiments.

[0091] Specific embodiment 7: This embodiment differs from any one of specific embodiments 1 to 6 in that the echo data D used to compensate for the time-frequency synchronization error out The expression of (τ,η) is:

[0092]

[0093] in Represents the distance frequency f of the data τ Perform IFFT processing; FFT η (·) indicates FFT processing of the slow time η of the data; Indicates the azimuth frequency f of the data η Perform IFFT processing.

[0094] The other steps and parameters are the same as those in the first to sixth embodiments.

[0095] The following examples are used to verify the beneficial effects of the present invention:

[0096] Example 1:

[0097] The airborne SAR moving target imaging method based on Doppler parameter estimation in this embodiment is specifically prepared according to the following steps:

[0098] A parametric model is now provided:

[0099] Table 1 Basic parameter values ​​of the time-frequency synchronization error compensation method for bistatic SAR based on the maximum contrast method

[0100]

[0101] The simulation results of bistatic SAR for ship targets are as follows: Figure 2 、 3a , 3b, 4a, 4b, 5, 6; Figure 2 Record the original echo data of the ship target for the bistatic SAR system; Figure 3a 、 3b This is a comparison chart of range migration correction of conventional SAR imaging algorithms; Figure 4a 、 4b This is a comparison chart of the distance migration correction of the algorithm of the present invention; Figure 5 This is the target imaging image of the conventional SAR imaging algorithm; Figure 6 This is the target imaging diagram of the algorithm of the present invention. Figure 3a 、 3b and Figure 4a 、 4b The comparison results show that the method of the present invention can effectively correct the additional range migration phenomenon caused by the time-frequency synchronization error. Figure 5 and Figure 6 The comparison results show that the method of the present invention can effectively compensate for the time-frequency synchronization error, significantly improve the azimuth compression effect, and clearly image the ship target.

[0102] The present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for compensating time-frequency synchronization errors in bistatic SAR based on the maximum contrast method, characterized by: The specific process of the method is: Step 1: Use a bistatic SAR system to record the scene target echo signal. The transmitter transmits an LFM signal, which is reflected by the scene target and received by the receiver to obtain the target echo data d(τ,η); Where τ is the distance-to-fast time, and the length of the distance-to-fast time is N τ ; η is the azimuth slow time, the length of the azimuth slow time is N η , the target echo data d(τ,η) is an N τ ×N η A two-dimensional matrix; LFM signal is a linear frequency modulation signal; Step 2: Perform range-wise fast Fourier transform on the target echo data d(τ,η) to obtain the range-wise frequency domain data D1(f τ ,η); where f τ is the distance frequency; Step 3: Construct distance reference function d refr (τ), for the reference function d refr (τ) is processed by fast Fourier transform in the distance direction and then conjugated to obtain D refr (f τ ), the distance in step 2 is converted to the frequency domain data D1(f τ ,η) multiplied by the function D refr (f τ ), and obtain the echo data D2(f τ ,η); Step 4: Based on the distance to frequency domain data D1(f τ ,η) construct distance migration correction function F c (f τ ,η), in the distance migration correction function F c (f τ ,η) is multiplied by the correction factor E1 to obtain the range migration correction function F c (f τ ,η;E1), the initial value of the correction factor E1 is set to 1; The echo data D2(f τ ,η) multiplied by the distance migration correction function F c (f τ ,η; E1), and then perform range inverse Fourier transform (IFFT) processing to obtain the echo data D3 (τ,η) after range migration correction; Step 5: Perform azimuth fast Fourier transform on the target echo data d(τ,η) to obtain azimuth frequency domain data D1(τ,f η ); Based on the azimuth frequency domain data D1(τ,f η ) Construct azimuth compression function F a (τ,f η ), in the azimuth compression function F a (τ,f η ) is multiplied by the compression factor E2 to obtain the azimuth compression function F a (τ,f η ; E2), the initial value of the compression factor E2 is set to 1; Perform azimuth FFT on the echo data D3(τ,η) corrected for range migration in step 4 to obtain A, which is then multiplied by the azimuth compression function F a (τ,f η E2) to obtain B, and finally perform azimuth IFFT processing on B to obtain the echo data D4 (τ, η) after azimuth compression; where f η is the azimuth frequency; Step 6: Calculate the two-dimensional image contrast C(τ,η) for the echo data D4(τ,η) after azimuth compression in step 5; Step 7: Using the correction factor E1 and compression factor E2 as variables, the particle swarm optimization (PSO) algorithm is used to obtain the D corresponding to the maximum value of the two-dimensional image contrast C. out (τ,η) is taken as the final target image.

2. The method for compensating time-frequency synchronization errors of bistatic SAR based on the maximum contrast method according to claim 1, wherein: In step 3, the distance reference function d is constructed. refr (τ), for the reference function d refr (τ) is processed by fast Fourier transform in the distance direction and then conjugated to obtain D refr (f τ ), the distance in step 2 is converted to the frequency domain data D1(f τ ,η) multiplied by the function D refr (f τ ), and obtain the echo data D2(f τ ,η); The specific process is: Construct distance reference function d refr (τ), the expression is d refr (τ)=exp(jπK τ t 2 ) (1) where exp(·) represents the power of e, j represents an imaginary number and K τ is the frequency modulation slope of the LFM signal; For the reference function d refr (τ) performs distance-direction fast Fourier transform and then obtains the conjugate D refr (f τ ), the expression is D refr (f τ )=[FFT τ (the refr (τ))] * (2) Where FFT τ (·) represents the distance reference function d refr (τ) is processed by FFT, [·] * Indicates conjugate.

3. The method for compensating time-frequency synchronization errors of bistatic SAR based on the maximum contrast method according to claim 2, wherein: In step 4, based on the distance frequency domain data D1 (f τ ,η) construct distance migration correction function F c (f τ ,η), in the distance migration correction function F c (f τ ,η) is multiplied by the correction factor E1 to obtain the range migration correction function F c (f τ ,η;E1), the initial value of the correction factor E1 is set to 1; The echo data D2(f τ ,η) multiplied by the distance migration correction function F c (f τ ,η; E1), and then perform range inverse Fourier transform (IFFT) processing to obtain the echo data D3 (τ,η) after range migration correction; The specific process is: Based on the distance frequency domain data D1(f τ ,η) construct distance migration correction function F c (f τ ,η),F c (f τ ,η) is expressed as: In the range migration correction function F c (f τ ,η) is multiplied by the correction factor E1 to obtain the range migration correction function F c (f τ ,η;E1), the expression is: Where c is the speed of light, c = 3 × 10 8 m / s; V T and V R are the speeds of the transmitter and receiver, θ T and θ R are the oblique viewing angles of the transmitter and receiver, respectively.

4. The method for compensating time-frequency synchronization errors of bistatic SAR based on the maximum contrast method according to claim 3, wherein: In step 5, the target echo data d(τ,η) is processed by azimuth fast Fourier transform to obtain azimuth frequency domain data D1(τ,f η ); Based on the azimuth frequency domain data D1(τ,f η ) Construct azimuth compression function F a (τ,f η ), in the azimuth compression function F a (τ,f η ) is multiplied by the compression factor E2 to obtain the azimuth compression function F a (τ,f η ; E2), the initial value of the compression factor E2 is set to 1; Perform azimuth FFT on the echo data D3(τ,η) corrected for range migration in step 4 to obtain A, which is then multiplied by the azimuth compression function F a (τ,f η E2) to obtain B, and finally perform azimuth IFFT processing on B to obtain the echo data D4 (τ, η) after azimuth compression; where f η is the azimuth frequency; The specific process is: Based on the azimuth frequency domain data D1(τ,f η ) Construct azimuth compression function F a (τ,f η ), F a (τ,f η ) is expressed as: where f ηs is the maximum value of the azimuth frequency and f ηs =(V T cosθ T +V R cosθ R ) / λ; R0 is the sum of the slant distances from the transmitter and receiver to the target center at the start time; λ represents the wavelength of the LFM signal; The azimuthal compression function F a (τ,f η ) is multiplied by the compression factor E2 to obtain the azimuth compression function F a (τ,f η ; E2), F a (τ,f η ; E2) expression is:

5. The method for compensating time-frequency synchronization errors of bistatic SAR based on the maximum contrast method according to claim 4, wherein: In step 6, the two-dimensional image contrast C(τ,η) is obtained from the echo data D4(τ,η) after azimuth compression in step 5. The specific process is as follows: The expression of two-dimensional image contrast C is: Where M(·) represents the arithmetic formula for calculating the mean; |·| is the symbol for finding the absolute value.

6. The method for compensating time-frequency synchronization errors of bistatic SAR based on the maximum contrast method according to claim 5, characterized in that: In step 7, the correction factor E1 and the compression factor E2 are used as variables, and the particle swarm optimization (PSO) algorithm is used to obtain the D corresponding to the maximum value of the two-dimensional image contrast C. out (τ,η) is taken as the final target image; the specific process is: Where n represents the number of iterations, n = 1, 2, ..., N, N is the maximum number of iterations; m represents the current particle index, m = 1, 2, ..., M, M is the total number of particles; It represents the parameter value estimated by the mth particle at the nth iteration, denoted as represents the correction factor E1 obtained by the mth particle in the nth iteration, represents the compression factor E2 obtained by the mth particle in the nth iteration, represents the change in the parameter value estimated by the mth particle at the nth iteration; a is the inertia factor; b1 and b2 are the local learning factor and the global learning factor respectively; Ra() is a random number between 0 and 1; is the historical optimal solution of the mth particle at the nth iteration, gb n represents the historical optimal solution among all particles in the nth iteration; Set the M×N parameter values middle Substitute into the distance migration correction function F c (f τ ,η;E1) phase term, we get M×N updated range migration correction functions F c (f τ ,η;E1); Set the M×N parameter values middle Substitute into the distance migration correction function F a (τ,f η E2) phase term, get M × N updated range migration correction function F a (τ,f η ; E2); The echo data D2(f τ ,η) multiplied by the updated distance migration correction function F c (f τ ,η;E1) get D; Perform distance IFFT on D to obtain E; Perform azimuth FFT on E to obtain F; Multiply F by the updated distance migration correction function F c (f τ ,η;E1) corresponds to the updated azimuth compression function F a (τ,f η ; E2) obtain G; Perform azimuth IFFT processing on G to obtain echo data D that compensates for time-frequency synchronization errors out (τ,η), D out (τ,η) replaces D4(τ,η) and brings it into the expression of two-dimensional image contrast C to obtain M×N two-dimensional image contrast C. Take the D corresponding to the maximum value of the two-dimensional image contrast C out (τ,η) is taken as the final target image.

7. The method for compensating time-frequency synchronization errors of bistatic SAR based on the maximum contrast method according to claim 6, characterized in that: The echo data D that compensates for the time-frequency synchronization error out The expression of (τ,η) is: in Represents the distance frequency f of the data τ Perform IFFT processing; FFT η (·) indicates FFT processing of the slow time η of the data; Indicates the azimuth frequency f of the data η Perform IFFT processing.

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