A method for fast imaging of moving targets based on KT transform

Abstract

The application discloses a kind of moving target fast imaging method based on KT conversion, this method includes: radar receives moving target echo signal;Moving target echo signal is handled, distance compression, consistent compensation, slow time inversion;Utilize KT conversion to echo signal distance azimuth decoupling, again do fast fourier transform in azimuth direction, obtain estimated first term coefficient;Utilize estimated first term coefficient to do go after compensation echo signal walk, again utilize SOKT conversion to do correction, extract after correction echo signal do mWVD conversion, obtain estimated doppler frequency modulation;Again utilize doppler frequency modulation to do azimuth focusing processing after correction echo signal, obtain focused echo signal, obtain moving target imaging result.The application significantly improves the efficiency of moving target imaging, and can guarantee good real-time effect.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing and relates to a moving target fast imaging method based on KT transformation. Background Art

[0002] Synthetic aperture imaging (SAR) technology can capture high-resolution images of static scenes, offering advantages such as all-day, all-weather, and high-resolution imaging. However, for moving targets on land and sea surfaces, such as vehicles speeding on roads, highly maneuverable weapons and equipment on the battlefield, and fast-moving speedboats on the sea, their motion parameters are unknown. Directly using the motion parameters of the static scene for phase matching cannot accurately compensate for their range and Doppler shifts, resulting in defocused and misaligned images due to mismatched matching functions. These moving targets are considered high-value and high-threat, making their detection and imaging crucial for battlefield situation assessment, traffic monitoring, and maritime counter-terrorism.

[0003] However, traditional moving target imaging methods for phase estimation mostly include search-based estimation methods, and the search accuracy is closely related to the size of the step, resulting in extremely high computational complexity and high time consumption of such methods, which is not conducive to the implementation of the algorithm.

[0004] Patent CN 113109810 A discloses a SAR moving target imaging method and system based on LVD. This solution includes steps such as range compression of echo signals, range curvature correction, range walk correction, Doppler frequency parameter estimation using the LVD method, and azimuth signal compression imaging. However, this method only considers the range curvature caused by platform motion when compensating for range curvature, while ignoring the range curvature caused by target motion. This results in inadequate motion compensation, especially in the case of strabismus, where range-azimuth coupling is more severe. Furthermore, this method uses a spatial search method using Radon transform to estimate range walk, which is slow and leads to poor imaging efficiency. Summary of the Invention

[0005] The present invention aims to solve the technical problem of poor efficiency in moving target imaging. The present invention provides a method for fast moving target imaging based on KT transform. The technical solution adopted is:

[0006] A moving target rapid imaging method based on KT transform comprises the following steps:

[0007] S1, radar receives the echo signal of the moving target;

[0008] S2. performing range compression processing on the moving target echo signal to obtain a compressed echo signal;

[0009] S3, making consistent compensation on the compressed echo signal to obtain a compensated echo signal;

[0010] S4, making slow-time inversion processing on the compensated echo signal to obtain an inverted echo signal;

[0011] S5, decoupling the inverted echo signal in range and azimuth by using KT transform to obtain a decoupled echo signal;

[0012] S6, making fast Fourier transform on the decoupled echo signal in the azimuth direction to obtain an estimated first-order coefficient;

[0013] S7, making a walk-off processing on the compensated echo signal by using the estimated first-order coefficient to obtain a walk-off echo signal;

[0014] S8, making correction on the walk-off echo signal by using SOKT transform to obtain a corrected echo signal;

[0015] S9, extracting the corrected echo signal to make mWVD transform to obtain an estimated Doppler frequency;

[0016] S10, making azimuth focusing processing on the corrected echo signal by using the Doppler frequency to obtain a focused echo signal, and obtaining a moving target imaging result.

[0017] In one embodiment of the present application, the step S2 comprises:

[0018] S21: performing fast Fourier transform on the received two-dimensional time-domain moving target echo signal in the range dimension to obtain an echo signal with the range dimension being a frequency domain and the azimuth dimension being a time domain;

[0019] The moving target echo signal is represented as:

[0020]

[0021] Wherein, rect(·) represents a window function, t represents a fast time variable, t a represents an azimuth slow time variable, T p is a pulse width, λ represents a wavelength of a transmitted signal, τ represents a delay time of a received signal, c represents a light speed, μ is a range bandwidth, exp represents an exponential operation with a natural constant e as a base, R(t a ) is an instantaneous slant range;

[0022] The echo signal with the range dimension being a frequency domain and the azimuth dimension being a time domain is represented as:

[0023]

[0024] Wherein, f r is a range frequency variable, fc is the carrier frequency;

[0025] S22: In the range frequency domain, azimuth time domain, multiply the echo signal by the range compression function to obtain the compressed echo signal, and calculate the slant range R(t a ) at t a = 0, expand the Taylor formula and retain the second-order term, which is expressed as:

[0026]

[0027] Among them, H rcom is the distance compression function, which is expressed as R s is the reference slant distance, which represents the distance between the beam center and the platform, are the phase first-order coefficient and phase second-order coefficient respectively, θ0 is the oblique angle, v represents the platform speed, v x 、v y Represents the velocity component of the target.

[0028] In one embodiment of the present invention, step S3 includes:

[0029] S31: In the squint mode, the compressed echo signal has range-azimuth coupling. The compressed echo signal is first uniformly corrected for range movement and range curvature, and a uniform compensation function is constructed, which is expressed as:

[0030]

[0031] Among them, H un is the consistent compensation function, ρ 10 =-vsinθ0, are the distance travel and distance bending coefficients caused by platform motion, respectively;

[0032] S32: Compare the consistent compensation function with s2(f r ,t a ) are multiplied to obtain a compensated echo signal, which is expressed as:

[0033]

[0034] Where c1 = ρ1 - ρ 10 , c2=ρ2-ρ 20 .

[0035] In one embodiment of the present invention, step S4 includes:

[0036] S41: Using a time reversal conversion method, the compensated echo signal is converted, which is expressed as:

[0037]

[0038] in, represents the slow time-reversal conjugate transform;

[0039] S42: With s3(f r ,t a ) are multiplied to obtain an inverted echo signal, which is expressed as:

[0040]

[0041] In one embodiment of the present invention, step S5 includes:

[0042] Perform KT transformation on the inverted echo signal to achieve range-azimuth decoupling. The transformation method is expressed as:

[0043]

[0044] Among them, τ a is the transformed slow time variable;

[0045] The decoupled echo signal is obtained, and the decoupled echo signal is expressed as:

[0046]

[0047] In one embodiment of the present invention, step S6 includes:

[0048] S61: Performing azimuth fast Fourier transform on the decoupled echo signal, expressed as:

[0049]

[0050] Among them, δ(·) is the impulse function, and the impulse appears at Department;

[0051] S62: Obtain the estimated linear coefficient based on the position of the impulse function peak, expressed as:

[0052]

[0053] Among them, the peak(·) function represents the position of the impulse function peak, represents the estimated linear coefficient.

[0054] In one embodiment of the present invention, step S7 includes:

[0055] S71: Construct the anti-walking function, expressed as:

[0056]

[0057] Among them, H LRC is the distance travel function, used to correct the phase first-order term;

[0058] S72: The walking function H LRC and the compensated echo signal s3(f r ,t a ) are multiplied to obtain the echo signal after removing the movement, and the echo signal after removing the movement is expressed as:

[0059]

[0060] In one embodiment of the present invention, step S8 includes:

[0061] S81: Use SOKT transformation to correct the distance curvature term, expressed as:

[0062]

[0063] Among them, η a is the new slow time variable;

[0064] S82: Obtain a corrected echo signal, which is expressed as:

[0065]

[0066] In one embodiment of the present invention, step S9 includes:

[0067] S91: Perform inverse fast Fourier transform of the distance, extract the distance row after migration correction, and perform the inverse fast Fourier transform of the distance to the one-dimensional signal s p (η a ) performs mWVD transformation, which is expressed as:

[0068]

[0069] Among them, t0 is a fixed delay, take

[0070] S92: Slow-time inverse Fourier transform to obtain an estimate of the Doppler frequency modulation rate

[0071] In one embodiment of the present invention, step S10 includes:

[0072] S101: Fast Fourier transform along the azimuth direction to transfer to the range, time domain, azimuth and frequency domain;

[0073] S102: Using the Doppler frequency modulation, construct an azimuth pulse pressure function, which is expressed as:

[0074]

[0075] S103: Multiply the azimuth pulse pressure function by the corrected echo signal to obtain a focused echo signal. The focused echo signal is expressed as:

[0076]

[0077] S104: Perform inverse fast Fourier transform along the azimuth direction, convert to range time domain and azimuth time domain, and obtain a focused image.

[0078] Beneficial effects of the present invention:

[0079] The present invention uses a fast moving target imaging method based on the KT (keystone transform) to first perform consistent compensation processing for stationary scenes and moving targets in the range-frequency domain based on platform parameters. It then extracts single moving target echo information from the SAR image, uses slow time reversal, the KT transform, and the SOKT (second-order KT) transform to perform range migration processing. Finally, it extracts echo signals falling into the same range unit and performs azimuth focusing processing to obtain a two-dimensional, high-resolution moving target image. This method is suitable for squint imaging and eliminates the need for search estimation, significantly improving the efficiency of moving target imaging and providing an excellent solution for fast moving target imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is a flow chart of a moving target rapid imaging method based on KT transform provided by an embodiment of the present invention;

[0081] Figure 2 is a result diagram after consistent compensation provided by an embodiment of the present invention;

[0082] Figure 3 This is a result diagram of estimating the linear coefficient provided by an embodiment of the present invention;

[0083] Figure 4 This is a result image after removing the movement provided by an embodiment of the present invention;

[0084] Figure 5 This is a result diagram after SOKT provided by an embodiment of the present invention;

[0085] Figure 6 Result diagram of mWVD estimation phase quadratic term coefficient provided by an embodiment of the present invention;

[0086] Figure 7 is a focusing result diagram after azimuth processing provided by an embodiment of the present invention;

[0087] Figure 8 for Figure 7 Refined cross-section of the target in focus. DETAILED DESCRIPTION

[0088] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0089] The present invention provides a method for fast imaging of moving targets based on KT transformation. Figure 1 The moving target rapid imaging method based on KT transform includes the following steps:

[0090] S1, radar receives the echo signal of the moving target;

[0091] S2. Perform range compression processing on the moving target echo signal to obtain a compressed echo signal;

[0092] S3. performing consistent compensation on the compressed echo signal to obtain a compensated echo signal;

[0093] S4, performing slow time inversion processing on the compensated echo signal to obtain an inverted echo signal;

[0094] S5. Decouple the range and azimuth of the inverted echo signal using KT transformation to obtain a decoupled echo signal;

[0095] S6. Performing a fast Fourier transform in azimuth on the decoupled echo signal to obtain an estimated linear term coefficient;

[0096] S7. Using the estimated linear coefficient, the compensated echo signal is subjected to a motion reduction process to obtain a motion-reduced echo signal.

[0097] S8. Correcting the echo signal after removing the movement using a Second-Order Keystone Transform (SOKT) to obtain a corrected echo signal;

[0098] S9, extracting the corrected echo signal and performing mWVD transformation to obtain the estimated Doppler modulation rate;

[0099] S10. Perform azimuth focusing processing on the corrected echo signal using Doppler frequency modulation to obtain a focused echo signal and a moving target imaging result.

[0100] The KT transform-based moving target rapid imaging method of the present invention is applicable to squint imaging and does not require search estimation, thereby significantly improving the efficiency of moving target imaging and providing a good solution for moving target rapid imaging.

[0101] In one embodiment of the present invention, the moving target echo signal is expressed as:

[0102]

[0103] In formula (1), rect(·) represents the window function, t represents the fast time variable, and ta denotes the azimuth slow time variable, T p denotes the pulse width, lambda denotes the wavelength of the transmitted signal, tau denotes the time delay of the received signal, c denotes the speed of light, mu denotes the range bandwidth, exp denotes the exponential operation with the natural constant e as the base, R(t a ) denotes the instantaneous slant range.

[0104] In the model establishment, the echo model adopted by the application fully considers the squint condition, has strong adaptability, and can more accurately reflect the complex situation in actual application.

[0105] The step S2 of the application comprises:

[0106] S21: performing distance dimension fast Fourier transform on the received two-dimensional time domain moving target echo signal to obtain an echo signal with the distance dimension being the frequency domain and the azimuth dimension being the time domain.

[0107] The echo signal with the distance dimension being the frequency domain and the azimuth dimension being the time domain is expressed as:

[0108]

[0109] In formula (2), f r is a distance frequency variable, f c is a carrier frequency.

[0110] S22: in the distance frequency domain and the azimuth time domain, the echo signal is multiplied by a range compression function to obtain a compressed echo signal, and Taylor formula expansion is performed on the slant range R(t a ) at t a =0, and the second-order term is retained, and is expressed as:

[0111]

[0112] In formula (3), H rcom is a range compression function, the range compression function is expressed as R s is a reference slant range, indicating the distance between the beam center and the platform, are a phase first-order term coefficient and a phase second-order term coefficient respectively, theta0 is a squint angle, v indicates a platform speed, v x and v y indicate speed components of the target.

[0113] The step S3 of the application comprises:

[0114] S31: in the squint mode, the range compressed echo signal has a significant range migration problem, in which the platform causes a large part, and the compressed echo signal is first uniformly corrected for range migration and range curvature to construct a consistent compensation function, which is expressed as:

[0115]

[0116] In formula (4), H un is the consistent compensation function, ρ 10 =-vsinθ0, are the distance travel and distance bending coefficients caused by platform motion, respectively.

[0117] S32: Combine the consistent compensation function with s2(f r ,t a ) is multiplied to obtain the compensated echo signal, which can eliminate the influence of platform motion and effectively narrow the range of subsequent phase coefficient estimation.

[0118] The echo signal after compensation is expressed as:

[0119]

[0120] In formula (5), c1=ρ1-ρ 10 , c2=ρ2-ρ 20 .

[0121] Step S4 of the present invention includes:

[0122] S41: Based on the equidistant scattering sampling characteristics of the target signal in the slow time domain, a time reversal transformation (TRT) method without losing signal sampling data is used to compensate the echo signal conversion, which is expressed as:

[0123]

[0124] In formula (6), represents the slow time-reversal conjugate transform.

[0125] S42: With s3(f r ,t a ) are multiplied to obtain the inverted echo signal, which is expressed as:

[0126]

[0127] The slow time reversal processing utilizes the discrete equal interval characteristics of slow time and the phase parity to eliminate the influence of the phase quadratic term without any estimation processing, which is more efficient than other algorithms.

[0128] The present invention first uses platform motion information to perform consistent compensation on the echo, and then uses slow time reversal and KT transform to perform residual compensation for target motion, thereby achieving more refined phase compensation. As can be seen from formula (7), only the first-order phase term remains in the signal, which makes it easier to estimate the coefficient of the first-order term.

[0129] The step S5 of the present application comprises:

[0130] The echo signal after inversion is subjected to a KT (keystone) transformation to realize decoupling of the range and azimuth, and the transformation mode is represented as:

[0131]

[0132] In the formula (8), τ a is the slow time variable after transformation.

[0133] The echo signal after decoupling is obtained, and the echo signal after decoupling is represented as:

[0134]

[0135] It can be seen from the formula (9) that the phase only remains the slow time item (i.e. the azimuth direction) at this time, and there is no phase coupled with the range direction (f r , t r ), that is, the range migration item is eliminated.

[0136] The step S6 of the present application comprises:

[0137] S61: The echo signal after decoupling is subjected to a fast Fourier transformation in the azimuth direction, and is represented as:

[0138]

[0139] In the formula (10), δ(·) is an impulse function, and the impulse appears at .

[0140] S62: The estimated linear item coefficient is obtained according to the position of the peak value of the impulse function, and is represented as:

[0141]

[0142] In the formula (11), the peak(·) function represents the position of the peak value of the impulse function, represents the estimated linear item coefficient, and the position of the maximum value of the echo matrix can be obtained.

[0143] The step S7 of the present application comprises:

[0144] S71: The de-migration function is constructed, and is represented as:

[0145]

[0146] In the formula (12), H LRC is the range migration function, and is used to correct the linear item of the phase.

[0147] S72: The de-migration function HLRC and the compensated echo signal s3(f r ,t a ) are multiplied to obtain the echo signal after removing the movement. The echo signal after removing the movement is expressed as:

[0148]

[0149] Here, the estimated linear coefficients are used to perform range motion correction on the original uniformly compensated signal. The ultimate goal of the above slow time reversal and KT transform is to estimate the linear coefficients of the phase. Therefore, this algorithm can perform both KT and SOKT transforms simultaneously without affecting each other.

[0150] Step S8 of the present invention includes:

[0151] S81: Use the SOKT transform (Second-Order Keystone Transform) to correct the range curvature term, expressed as:

[0152]

[0153] In formula (14), η a is the new slow time variable.

[0154] The SOKT transform is used to correct second-order range curvature. The traditional Keystone transform can only correct linear range movement. The SOKT transform achieves range curvature compensation through linear substitution without knowing the precise motion parameters of the moving target.

[0155] S82: Obtain a corrected echo signal, which is expressed as:

[0156]

[0157] Step S9 of the present invention includes:

[0158] S91: Perform inverse fast Fourier transform of the distance, extract the distance row after migration correction, and perform the inverse fast Fourier transform of the distance to the one-dimensional signal s p (η a ) performs mWVD transformation (Modified Wigner-Ville Distribution Transform), which is expressed as:

[0159]

[0160] In formula (16), t0 is a fixed delay,

[0161] The improved Wigner-Ville distribution transform consists of two WVD transform kernels, which can be regarded as the result of performing another WVD processing on the first-order WVD signal along the delay time variable; the improved Wigner-Ville distribution transform introduces an adjustable parameter, which can make the transform more flexible in adjusting the time-frequency resolution by changing the time delay τ0.

[0162] The present invention uses an improved mWVD function to estimate the Doppler modulation frequency to achieve two-dimensional refined imaging, which significantly improves the computational efficiency of the algorithm compared with traditional methods.

[0163] S92: Slow time dimension IFFT (slow time dimension inverse Fourier transform, slow time dimension = azimuth dimension) to obtain the estimated value of Doppler frequency modulation

[0164] Step S10 of the present invention includes:

[0165] S101: Fast Fourier transform along the azimuth direction to transfer to the range, time domain, azimuth and frequency domain.

[0166] S102: Using the Doppler frequency modulation, construct the azimuth pulse pressure function, which is expressed as:

[0167]

[0168] S103: Multiply the azimuth pulse pressure function by the corrected echo signal to obtain a focused echo signal. The focused echo signal is expressed as:

[0169]

[0170] S104: Perform inverse fast Fourier transform along the azimuth direction, convert to range time domain and azimuth time domain, and obtain a focused image.

[0171] The present invention's KT transform-based fast imaging method for moving targets uses slow time reversal and the KT transform to estimate the linear phase term. The estimated linear term coefficient is then used to compensate for the linear phase term of the uniformly compensated echo, achieving de-motion and Doppler center offset removal. The SOKT transform is then used to uniformly correct the range curvature term, effectively suppressing energy diffusion caused by range and Doppler migration. The present invention eliminates search steps and therefore has low computational complexity, significantly improving imaging efficiency and ensuring good real-time performance.

[0172] The effect of the moving target rapid imaging method based on KT transform of the present invention is described below through simulation experiments.

[0173] 1. The parameter settings of this example simulation experiment are shown in Table 1:

[0174] Table 1 Simulation test parameters

[0175]

[0176] 2. The target motion information of this simulation experiment is shown in Table 2:

[0177] Table 2 Target motion information table of simulation experiment

[0178] X-axis speed (m / s) Y-axis speed (m / s) Target 7 10

[0179] 3. Results of simulation test:

[0180] The results of the simulation test are shown in the attached Figure 2 -Attached Figure 8 . Figure 2 The result after consistent compensation is shown. Consistent compensation eliminates the range migration caused by platform motion. The remaining range migration in the figure is mainly caused by target motion. Figure 3 It is the result of azimuth-dimensional Fourier transform. A pulse will appear in the azimuth frequency domain. According to the position of the pulse, the first-order phase coefficient can be estimated. Figure 4 In order to use the estimated linear coefficient to correct the result after range migration, the echo phase only has the range bending term, so the migration is symmetrically distributed. Figure 5 is the result after SOKT transformation, at which time the range migration compensation is completed and the signals at all azimuth times fall into the same range unit; Figure 6 The result of extracting the range unit signal and performing mWVD transformation on it is obtained. The function of mWVD is to focus the one-dimensional linear frequency modulation signal into a pulse signal and obtain the Doppler modulation frequency according to the position of the pulse. Figure 7 The result of azimuth focusing processing on the signal is obtained by constructing the azimuth pulse pressure function using the estimated Doppler frequency modulation rate. Figure 8 for Figure 7 The refined cross-section of the target at the focal point shows good focusing effect and no coupling deformation.

[0181] By attaching Figure 2 -Attached Figure 8 It can be seen that the moving target rapid imaging method based on KT transform of the present invention has a good moving target focusing effect.

[0182] The algorithm proposed in this paper can be widely applied in airborne and missile-borne synthetic aperture radar (SAR) imaging systems, particularly in complex battlefield environments, to acquire and analyze the motion and position information of various military targets in real time. The algorithm can effectively focus on dynamic targets on the battlefield, including but not limited to tanks, armored vehicles, military trucks, aircraft carriers, warships, and other moving targets. This algorithm can refocus moving targets in SAR images, effectively imaging them while they are in motion, overcoming the blur and deviation caused by target motion, thereby obtaining clear and accurate images of the target.

[0183] At the same time, the present invention can not only improve the accuracy of parameter estimation of moving targets, but also maintain high-precision true positioning under high-speed moving targets, ensuring the real-time and reliability of battlefield situation perception, and providing an efficient solution for airborne and missile-borne SAR systems. It greatly enriches the functions and information acquisition capabilities of SAR systems, and is of great significance to military reconnaissance, target strikes, battlefield situation perception, monitoring of ocean ships, and detection of low-altitude targets.

[0184] Moreover, the present invention can monitor moving vehicles and pedestrians on the ground, better implement traffic control, monitor traffic flow and vehicle status on the road in real time, identify traffic violations such as speeding, running red lights, and driving against traffic, and provide real-time alerts. This plays an important role in urban traffic management and rapid response to traffic accidents. In terms of intelligent driving simulation, moving target imaging can provide automatic driving systems with all-time and all-weather perception capabilities, especially in bad weather or night driving conditions, to ensure the safety and stability of automatic driving vehicles. In automated logistics systems, moving target imaging can monitor the dynamic position of transportation tools (such as unmanned vehicles, robots, etc.), ensure the efficiency and safety of the cargo transportation process, and optimize the allocation of logistics resources. It can also be applied in disaster monitoring, marine research, and resource exploration to achieve efficient scheduling and save manpower and material resources.

[0185] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A moving target rapid imaging method based on KT transform, characterized in that: Including steps: S1, radar receives the echo signal of the moving target; S2. performing range compression processing on the moving target echo signal to obtain a compressed echo signal; S3. performing consistent compensation on the compressed echo signal to obtain a compensated echo signal; S4, performing slow time inversion processing on the compensated echo signal to obtain an inverted echo signal; S5. Decouple the range and azimuth of the inverted echo signal using KT transformation to obtain a decoupled echo signal; S6. Performing a fast Fourier transform in azimuth on the decoupled echo signal to obtain an estimated linear coefficient; S7. Using the estimated linear coefficient, perform a motion-removal process on the compensated echo signal to obtain a motion-removed echo signal; S8. Correcting the echo signal after removing the movement using SOKT transformation to obtain a corrected echo signal; S9, extracting the corrected echo signal and performing mWVD transformation to obtain an estimated Doppler frequency modulation rate; S10, performing azimuth focusing processing on the corrected echo signal using the Doppler frequency modulation to obtain a focused echo signal and obtain a moving target imaging result.

2. The method for rapid imaging of moving targets based on KT transform according to claim 1, characterized in that: The step S2 comprises: S21: performing a range-dimensional fast Fourier transform on the received two-dimensional time-domain moving target echo signal to obtain an echo signal with a range dimension in the frequency domain and an azimuth dimension in the time domain; The moving target echo signal is expressed as: Where rect(·) represents the window function, t represents the fast time variable, and t a represents the azimuth slow time variable, T p is the pulse width, λ is the wavelength of the transmitted signal, τ is the delay time of the received signal, c is the speed of light, μ is the distance bandwidth, exp is the exponential operation with the natural constant e as the base, R(t a ) is the instantaneous slant distance; The echo signal with the distance dimension in the frequency domain and the azimuth dimension in the time domain is expressed as: Among them, f r is the distance frequency variable, f c is the carrier frequency; S22: In the range frequency domain, azimuth time domain, multiply the echo signal by the range compression function to obtain the compressed echo signal, and calculate the slant range R(t a ) at t a = 0, expand the Taylor formula and retain the second-order term, which is expressed as: Among them, H rcom is the distance compression function, which is expressed as R s is the reference slant distance, which represents the distance between the beam center and the platform, are the phase first-order coefficient and phase second-order coefficient respectively, θ0 is the oblique angle, v represents the platform speed, v x 、v y Represents the velocity component of the target.

3. The method for rapid imaging of moving targets based on KT transform according to claim 2, characterized in that: The step S3 comprises: S31: In the squint mode, the compressed echo signal has range-azimuth coupling. The compressed echo signal is first uniformly corrected for range movement and range curvature, and a uniform compensation function is constructed, which is expressed as: Among them, H un is the consistent compensation function, ρ 10 =-vsinθ0, are the distance travel and distance bending coefficients caused by platform motion, respectively; S32: Compare the consistent compensation function with s2(f r ,t a ) are multiplied to obtain a compensated echo signal, which is expressed as: Where, c1=ρ1-ρ 10 ,c2=ρ2-ρ 20 。 4. The method for rapid imaging of moving targets based on KT transform according to claim 3, characterized in that: The step S4 comprises: S41: Using a time reversal conversion method, the compensated echo signal is converted, which is expressed as: in, represents the slow time-reversal conjugate transform; S42: With s3(f r ,t a ) are multiplied to obtain an inverted echo signal, which is expressed as:

5. The method for fast imaging of moving targets based on KT transform according to claim 4, characterized in that: The step S5 comprises: Perform KT transformation on the inverted echo signal to achieve range-azimuth decoupling. The transformation method is expressed as: Among them, τ a is the transformed slow time variable; The decoupled echo signal is obtained, and the decoupled echo signal is expressed as:

6. The method for fast imaging of moving targets based on KT transform according to claim 5, characterized in that: The step S6 comprises: S61: Performing azimuth fast Fourier transform on the decoupled echo signal, expressed as: Among them, δ(·) is the impulse function, and the impulse appears at Department; S62: Obtain the estimated linear term coefficient according to the position of the impulse function peak, expressed as: Among them, the peak(·) function represents the position of the impulse function peak, represents the estimated linear coefficient.

7. The method for rapid imaging of moving targets based on KT transform according to claim 6, characterized in that: The step S7 comprises: S71: Construct the anti-walking function, expressed as: Among them, H LRC is the distance travel function, used to correct the phase first-order term; S72: The walking function H LRC and the compensated echo signal s3(f r ,t a ) are multiplied to obtain the echo signal after removing the movement, and the echo signal after removing the movement is expressed as:

8. The method for fast imaging of moving targets based on KT transform according to claim 7, characterized in that: The step S8 comprises: S81: Use SOKT transformation to correct the distance curvature term, expressed as: Among them, η a is the new slow time variable; S82: Obtain a corrected echo signal, which is expressed as:

9. The method for fast imaging of moving targets based on KT transform according to claim 8, characterized in that: The step S9 includes: S91: Perform inverse fast Fourier transform of the distance, extract the distance row after migration correction, and perform the inverse fast Fourier transform of the distance to the one-dimensional signal s p (η a ) performs mWVD transformation, which is expressed as: Among them, t0 is a fixed delay, take S92: Slow-time inverse Fourier transform to obtain an estimate of the Doppler frequency modulation rate 10. The method for fast imaging of moving targets based on KT transform according to claim 9, characterized in that: The step S10 includes: S101: Fast Fourier transform along the azimuth direction to transfer to the range, time domain, azimuth and frequency domain; S102: Using the Doppler frequency modulation, construct an azimuth pulse pressure function, which is expressed as: S103: Multiply the azimuth pulse pressure function by the corrected echo signal to obtain a focused echo signal, which is expressed as: S104: Perform inverse fast Fourier transform along the azimuth direction, convert to range time domain and azimuth time domain, and obtain a focused image.

Images