An airborne CSSAR ground acceleration target imaging method

Abstract

This invention discloses an airborne CSSAR ground acceleration target imaging method. The method first establishes a distance equation model based on Chebyshev polynomials; then, an expression for the target in the two-dimensional frequency domain is derived; the imaging process is then modeled as an optimization problem, and a differential evolution algorithm is used to achieve optimal estimation of the coefficients of the distance equation model; finally, based on the optimal solution obtained by the differential evolution algorithm, the target is focused through phase multiplication in the two-dimensional frequency domain. This invention can enrich the theoretical and methodological framework of SAR ground moving target indication (GMTI) based on aviation platforms, and help to overcome the difficult problem of efficient and high-quality imaging of ground acceleration targets in the SAR-GMTI field.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to an airborne CSSAR ground acceleration target imaging method. Background Art

[0002] Airborne circular stripmap synthetic aperture radar (CSSAR) is a new type of SAR that moves along a horizontal circle with its antenna pointing outside the circle. It has the advantages of short revisit time and large coverage, making it an ideal tool for air-to-ground wide-area reconnaissance and time-sensitive target surveillance.

[0003] SAR time-sensitive target surveillance, often involving the imaging of ground-moving targets, has been a research hotspot in recent years. A key parameter in SAR imaging is the target's range equation (i.e., the instantaneous distance between the radar and the target), which determines the target's azimuth phase modulation and range cell migration (RCM). The second-order Taylor approximate range equation model is a commonly used range equation model in SAR ground-moving target imaging. It can derive an accurate analytical two-dimensional spectrum of the target, thereby simplifying the design of imaging methods. However, its accuracy is insufficient when the azimuth resolution is high or the target has acceleration. Although the higher-order Taylor approximate range equation has high accuracy, the derivation of the accurate two-dimensional spectrum is challenging, which complicates the design of imaging methods.

[0004] Furthermore, due to the unknown target motion, SAR ground moving target imaging typically involves searching for target motion parameters or other equivalent parameters (such as Doppler parameters), target range equation coefficients, and target phase history coefficients. These searches incur a significant computational burden due to the inefficient traversal search methods typically used. Research on efficient, high-quality methods for imaging ground moving targets using airborne CSSAR is highly urgent. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the present invention provides an airborne CSSAR ground acceleration target imaging method. The method first establishes a distance equation model based on Chebyshev polynomials; then, an expression for the target in the two-dimensional frequency domain is derived; the imaging process is then modeled as an optimization problem, and a differential evolution algorithm is used to achieve optimal estimation of the coefficients of the distance equation model; finally, based on the optimal solution obtained by the differential evolution algorithm, the target is focused through phase multiplication in the two-dimensional frequency domain. This method can enrich the theoretical and methodological framework of SAR ground moving target indication (GMTI) based on aerial platforms, and help to overcome the difficult problem of efficient and high-quality imaging of ground acceleration targets in the SAR-GMTI field.

[0006] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0007] Step 1: Establish a distance equation model based on Chebyshev polynomials;

[0008] Step 2: Derive the expression of the target in the two-dimensional frequency domain;

[0009] Step 3: Model the imaging process as an optimization problem and use the differential evolution algorithm to achieve the optimal estimation of each coefficient of the distance equation model;

[0010] Step 4: Based on the optimal solution obtained by the differential evolution algorithm, the target is focused by phase multiplication in the two-dimensional frequency domain.

[0011] Furthermore, the step 1 is specifically as follows:

[0012] Step 1-1: The instantaneous slant range from the target to the radar is expressed as:

[0013]

[0014] Among them, r a is the motion radius of the radar platform, ω is the angular velocity of the radar platform, and h is the flight altitude; v x and v y are the initial velocities of the target along the x-axis and y-axis, a x and a y are the accelerations of the target along the x-axis and y-axis, t a is the azimuth slow time, r0 is t a =0 time point, the distance from the target to the origin of the coordinate system, θ0 is t a = azimuth of the target at time 0;

[0015] Step 1-2: First kind n-order Chebyshev polynomial sequence T n (x) is defined as:

[0016] T n (x)=cos(n·arccosx),|x|≤1 (2)

[0017] nth-order Chebyshev polynomial T n (x) has n zeros on [-1,1]:

[0018]

[0019] For the function interpolation on the interval [a, b], normalize it to get a new interpolation node:

[0020]

[0021] Where a represents the starting point of the interpolation interval, and b represents the end point of the interpolation interval;

[0022] Step 1-3: Define the time when the center of the radar beam passes through the target as t ac , the synthetic aperture time is T a , in [t ac -T a / 2,t ac +T a / 2], and the interpolation nodes are:

[0023]

[0024]

[0025]

[0026]

[0027] According to the Lagrange interpolation principle, the expression of the third-order Lagrange interpolation polynomial is obtained as follows:

[0028]

[0029] Replace x with t a , y0 is replaced by R(x0), y1 is replaced by R(x1), y2 is replaced by R(x2), y3 is replaced by R(x3), and the above formula can be further written as:

[0030]

[0031] Where,

[0032]

[0033]

[0034]

[0035]

[0036] Furthermore, the step 2 is specifically as follows:

[0037] Step 2-1: Assume that the signal transmitted by the radar is a linear frequency modulated pulse signal. The target echo signal after range compression and carrier frequency demodulation is expressed as:

[0038]

[0039] Among them, t r is the distance between the fastest time, p r(·) is the range compression impulse response function, c is the speed of light, ω(·) is the azimuth envelope, and λ is the wavelength;

[0040] Step 2-2: Perform a two-dimensional Fourier transform on equation (15) to obtain:

[0041]

[0042] Among them, f r is the distance frequency, f a is the baseband azimuth frequency, i.e., the Doppler frequency, f c is the carrier frequency, W r (·) is the distance frequency envelope, K r is the frequency modulation of the range pulse;

[0043] Step 2-3: Apply the stationary phase principle to obtain the stationary phase expression:

[0044]

[0045] Where M is the Doppler ambiguity number and PRF is the pulse repetition frequency.

[0046] Step 2-4: Use the series inversion method to obtain the expression of the stationary phase point:

[0047]

[0048] Where,

[0049]

[0050]

[0051] Substituting equation (18) into equation (16), we get the expression of the target signal in the two-dimensional frequency domain:

[0052] S(f r ,f a )=W r (f r )W a (f a )exp{jΘ(f r ,f a )} (twenty one)

[0053] Where,

[0054]

[0055] Among them, W a (·) is the azimuth frequency envelope;

[0056] Furthermore, the step 3 is specifically as follows:

[0057] Step 3-1: Construct a matched filter:

[0058]

[0059] Multiply Equation (23) by Equation (21), and perform a two-dimensional inverse Fourier transform on the result of the multiplication to obtain the target imaging result;

[0060] Step 3-2: The imaging process is modeled as the following optimization problem:

[0061]

[0062] Where,

[0063]

[0064] s(t r ,t a ;a1,a2,a3)=IDFT2{S(f r ,f a )·H(f r ,f a )} (26)

[0065] Where IDFT(·) represents the two-dimensional inverse Fourier transform, E(·) represents the spatial averaging operation, Contrast(·) is the image contrast, and are the estimated values ​​of a1, a2, and a3 respectively. 1,min and a 1,max are the minimum and maximum values ​​of a1, a 2,min and a 2,max are the minimum and maximum values ​​of a2, a 3,min and a 3,max are the minimum and maximum values ​​of a3 respectively;

[0066] Step 3-3: The solution to the optimization problem is the optimal estimate of the three parameters a1, a2, and a3; therefore, the focused SAR image is given by Equation (27):

[0067]

[0068] Step 3-4: Use differential evolution algorithm to solve the optimization problem of formula (24);

[0069] Step 3-4-1: First, establish a relationship model between the differential evolution algorithm and the optimization problem to be solved:

[0070]

[0071] Among them A i,Grepresents the i-th individual in the G-th generation population, where i = 1, 2, ..., N, and N is the population size. D represents the dimension of the search space, and j represents the number of parameters to be searched.

[0072] Step 3-4-2: Population initialization;

[0073] Individuals in the population are randomly initialized within the specified minimum and maximum values, expressed as:

[0074]

[0075] where rand i,j [0,1] is a uniformly distributed random number between 0 and 1;

[0076] Step 3-4-3: mutation;

[0077] Randomly select three mutually different vectors from the population The mutation vector of the differential evolution algorithm is generated in the following way:

[0078]

[0079] Where F is the variation factor;

[0080] Step 3-4-4: Cross;

[0081] The cross vector is generated as follows:

[0082]

[0083] Where Cr is the crossover factor;

[0084] Step 3-4-5: Calculate the fitness function;

[0085] The contrast of the image focused by the parameters corresponding to an individual is selected as the fitness value of the individual, the image is obtained by formula (26), and the contrast is calculated by formula (25);

[0086] Step 3-4-6: Select;

[0087] The differential evolution algorithm follows the greedy criterion and starts from the experimental population U i,G The individuals are selected as individuals in the next generation population. The specific selection method is:

[0088]

[0089] If the new experimental vector U i,G The resulting objective function value is equal to or higher than the target vector A i,G , then it will be replaced by the corresponding target vector in the next generation, otherwise the target will remain in the population;

[0090] Step 3-4-7: Repeat steps 3-4-3 to 3-4-6 until the termination condition is met or the specified number of iterations is reached. The parameter corresponding to the maximum contrast value is the solution to the optimization problem to be solved.

[0091] Furthermore, the optimal solution obtained in step 4 according to the differential evolution algorithm is used to focus the target through formula (27).

[0092] Furthermore, the variation factor F∈[0.4,1].

[0093] The beneficial effects of the present invention are as follows:

[0094] The high-precision Chebyshev polynomial-based distance equation model and efficient parameter search method based on differential evolution proposed in this paper enable efficient, high-quality imaging of ground acceleration targets using airborne CSSAR. This invention can enrich the theoretical and methodological framework of SAR-GMTI for aviation platforms and help overcome the difficult problem of efficient, high-quality imaging of ground acceleration targets in the SAR-GMTI field. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 It is a schematic diagram of the process of the present invention.

[0096] Figure 2 Schematic diagram of the differential evolution algorithm of the present invention.

[0097] Figure 3 These are the imaging results of three targets according to an embodiment of the present invention, (a) T1, (b) T2, and (c) T3. DETAILED DESCRIPTION

[0098] The present invention will be further described below with reference to the accompanying drawings and examples.

[0099] This paper proposes an efficient, high-quality ground acceleration target imaging method for high-resolution airborne CSSAR. This method establishes a precise distance equation model based on Chebyshev polynomials. Based on this model, a two-dimensional frequency domain signal model of the target is derived. Through phase multiplication in the two-dimensional frequency domain, target focusing is achieved efficiently. Furthermore, a differential evolution optimization algorithm is used to efficiently and accurately search for parameters in the distance equation model.

[0100] An airborne CSSAR ground acceleration target imaging method comprises the following steps:

[0101] Step 1: Establish a distance equation model based on Chebyshev polynomials;

[0102] Step 1-1: The instantaneous slant range from the target to the radar is expressed as:

[0103]

[0104] Among them, r a is the motion radius of the radar platform, ω is the angular velocity of the radar platform, and h is the flight altitude; v x and v y are the initial velocities of the target along the x-axis and y-axis, a x and a y are the accelerations of the target along the x-axis and y-axis, t a is the azimuth slow time, r0 is t a =0 time point, the distance from the target to the origin of the coordinate system, θ0 is t a = azimuth of the target at time 0;

[0105] Step 1-2: First kind n-order Chebyshev polynomial sequence T n (x) is defined as:

[0106] T n (x)=cos(n·arccosx),|x|≤1 (2)

[0107] nth-order Chebyshev polynomial T n (x) has n zeros on [-1,1]:

[0108]

[0109] For function interpolation on the general interval [a, b], it is necessary to normalize it to obtain a new interpolation node

[0110]

[0111] Step 1-3: Define the time when the center of the radar beam passes through the target as t ac , the synthetic aperture time is T a , in [t ac -T a / 2,t ac +T a / 2], and the interpolation nodes are:

[0112]

[0113]

[0114]

[0115]

[0116] According to the Lagrange interpolation principle, the expression of the third-order Lagrange interpolation polynomial is obtained as follows:

[0117]

[0118] Replace x with t a , y0 is replaced by R(x0), y1 is replaced by R(x1), y2 is replaced by R(x2), y3 is replaced by R(x3), and the above formula can be further written as:

[0119]

[0120] Where,

[0121]

[0122]

[0123]

[0124]

[0125] Step 2: Derive the expression of the target in the two-dimensional frequency domain;

[0126] Step 2-1: Assume that the signal transmitted by the radar is a linear frequency modulated pulse signal. The target echo signal after range compression and carrier frequency demodulation is expressed as:

[0127]

[0128] Among them, t r is the distance between the fastest time, p r (·) is the range compression impulse response function, c is the speed of light, ω(·) is the azimuth envelope, and λ is the wavelength. For simplicity, the constant amplitude term of the target echo signal is ignored.

[0129] Step 2-2: Perform a two-dimensional Fourier transform on equation (15) to obtain:

[0130]

[0131] Among them, f r is the distance frequency, f a is the baseband azimuth frequency, i.e., the Doppler frequency, f c is the carrier frequency, W r (·) is the distance frequency envelope, K r is the frequency modulation of the range pulse;

[0132] Step 2-3: Apply the stationary phase principle to obtain the stationary phase expression:

[0133]

[0134] Where M is the Doppler ambiguity number and PRF is the pulse repetition frequency.

[0135] Step 2-4: Use the series inversion method to obtain the expression of the stationary phase point:

[0136]

[0137] Where,

[0138]

[0139]

[0140] Substituting equation (18) into equation (16), we get the expression of the target signal in the two-dimensional frequency domain:

[0141] S(f r ,f a )=W r (f r )W a (f a )exp{jΘ(f r ,f a )} (twenty one)

[0142] Where,

[0143]

[0144] Among them, W a (·) is the azimuth frequency envelope;

[0145] Step 3: Model the imaging process as an optimization problem and use the differential evolution algorithm to achieve the optimal estimation of each coefficient of the distance equation model;

[0146] Step 3-1: Observe equation (22) and only need to compensate for the last two exponential terms that do not contain f a The first power term can focus on the target and construct a matched filter:

[0147]

[0148] Multiplying Equation (23) with Equation (21) and performing a two-dimensional inverse Fourier transform on the result yields the target imaging result. It should be noted that, combining Equations (19), (20), and (23), it can be found that the coefficients a1, a2, and a3 of the target distance equation are unknown during the imaging process, so a three-dimensional parameter search is required. The target can only be accurately focused when the searched parameter values ​​completely match their true values, at which point the contrast of the target in the image domain reaches its maximum value.

[0149] Step 3-2: The imaging process is modeled as the following optimization problem:

[0150]

[0151] Where,

[0152]

[0153] s(t r ,t a ;a1,a2,a3)=IDFT2{S(f r ,f a )·H(f r ,f a )} (26)

[0154] Where IDFT(·) represents the two-dimensional inverse Fourier transform, E(·) represents the spatial averaging operation, Contrast(·) is the image contrast, and are the estimated values ​​of a1, a2, and a3 respectively. 1,min and a 1,max are the minimum and maximum values ​​of a1, a 2,min and a 2,max are the minimum and maximum values ​​of a2, a 3,min and a 3,max are the minimum and maximum values ​​of a3 respectively;

[0155] Step 3-3: From the above analysis, it can be seen that the solution to the optimization problem is the optimal estimate of the three parameters; therefore, the focused SAR image is given by Equation (27):

[0156]

[0157] Step 3-4: If Figure 2 , the differential evolution algorithm is used to solve the optimization problem of formula (24);

[0158] Step 3-4-1: First, establish a relationship model between the differential evolution algorithm and the optimization problem to be solved:

[0159]

[0160] Among them A i,G represents the i-th individual in the G-th generation population, where i = 1, 2, ..., N, and N is the population size. D represents the dimension of the search space, and j represents the number of parameters to be searched.

[0161] Step 3-4-2: Population initialization;

[0162] Individuals in the population are randomly initialized within the specified minimum and maximum values, expressed as:

[0163]

[0164] where rand i,j [0,1] is a uniformly distributed random number between 0 and 1;

[0165] Step 3-4-3: mutation;

[0166] Randomly select three mutually different vectors from the population The mutation vector of the differential evolution algorithm is generated in the following way:

[0167]

[0168] Where F is the variation factor, and F∈[0.4,1];

[0169] Step 3-4-4: Cross;

[0170] The cross vector is generated as follows:

[0171]

[0172] Where Cr is the crossover factor;

[0173] Step 3-4-5: Calculate the fitness function;

[0174] Since the optimization problem is based on maximizing the contrast of the target image, the contrast of the image focused by the parameters corresponding to a certain individual is selected as the fitness value of the individual. The image is obtained by formula (26), and the contrast is calculated by formula (25);

[0175] Step 3-4-6: Select;

[0176] The differential evolution algorithm follows the greedy criterion and starts from the experimental population U i,G The individuals are selected as individuals in the next generation population. The specific selection method is:

[0177]

[0178] If the new experimental vector U i,G The resulting objective function value is equal to or higher than the target vector A i,G , then it will be replaced by the corresponding target vector in the next generation, otherwise the target will remain in the population;

[0179] Step 3-4-7: Repeat steps 3-4-3 to 3-4-6 until the termination condition is met or the specified number of iterations is reached. The parameter corresponding to the maximum contrast value is the solution to the optimization problem to be solved;

[0180] Step 4: Based on the optimal solution obtained by the differential evolution algorithm, focus the target using formula (27). Specific embodiment:

[0182] The effects of the present invention are further illustrated by the following simulation experiments.

[0183] The parameters of the airborne multi-channel CSSAR system are shown in Table 1, and the target parameters are shown in Table 2. Imaging is performed using the distance equation obtained by zero-point interpolation of Chebyshev polynomials and the parameters searched by differential evolution. Figure 3 The imaging results of the three targets are given. Table 3 measures the quality parameters of each image, including Impulse Response Width (IRW), Integrated Side-Lobe Ratio (ISLR), and Peak Side-Lobe Ratio (PSLR). Figure 3 As can be seen from Table 3, all three targets are well focused. It can also be seen that the IRW spread in azimuth is less than 1% for all targets, while the IRW spread in range is zero.

[0184] Table 1 Airborne CSSAR-GMTI system parameters

[0185] System parameters Parameter value System parameters Parameter value Radar platform speed 125m / s Sampling frequency 180MHz Flight radius 2.3km Transmitted signal bandwidth 150MHz Radar platform height 8km Synthetic Aperture Time 2.4s carrier frequency 10GHz Pulse repetition frequency 1600Hz Scene center distance 20km

[0186] Table 2 Moving target parameters

[0187] T1 T2 T3 <![CDATA[v x (m / s)]]> -25 4 -26 <![CDATA[v y (m / s)]]> 22 -28 -9 <![CDATA[a x (m / s 2 )]]> 0.3 -0.9 0.8 <![CDATA[a y (m / s 2 )]]> -0.9 0.4 -0.7 <![CDATA[θ0(rad)]]> -0.03 -0.01 0.03 <![CDATA[r0(km)]]> 20.630 20.030 21.230

[0188] Table 3 Image quality parameters

[0189]

[0190]

Claims

1. An airborne CSSAR ground acceleration target imaging method, characterized in that: The following steps are involved: Step 1: Establish a distance equation model based on Chebyshev polynomials; Step 2: Derive the expression of the target in the two-dimensional frequency domain; Step 3: Model the imaging process as an optimization problem and use the differential evolution algorithm to achieve the optimal estimation of each coefficient of the distance equation model; Step 4: Based on the optimal solution obtained by the differential evolution algorithm, the target is focused by phase multiplication in the two-dimensional frequency domain.

2. The airborne CSSAR ground acceleration target imaging method according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: The instantaneous slant range from the target to the radar is expressed as: Among them, r a is the motion radius of the radar platform, ω is the angular velocity of the radar platform, and h is the flight altitude; v x and v y are the initial velocities of the target along the x-axis and y-axis, a x and a y are the accelerations of the target along the x-axis and y-axis, t a is the azimuth slow time, r0 is t a =0 time point, the distance from the target to the origin of the coordinate system, θ0 is t a = azimuth of the target at time 0; Step 1-2: First kind n-order Chebyshev polynomial sequence T n (x) is defined as: T n (x)=cos(n·arccosx),|x|≤1 (2) nth-order Chebyshev polynomial T n (x) has n zeros on [-1,1]: For the function interpolation on the interval [a, b], normalize it to get a new interpolation node: Where a represents the starting point of the interpolation interval, and b represents the end point of the interpolation interval; Step 1-3: Define the time when the center of the radar beam passes through the target as t ac , the synthetic aperture time is T a , in [t ac -T a / 2,t ac +T a / 2], and the interpolation nodes are: According to the Lagrange interpolation principle, the expression of the third-order Lagrange interpolation polynomial is obtained as follows: Replace x with t a , y0 is replaced by R(x0), y1 is replaced by R(x1), y2 is replaced by R(x2), y3 is replaced by R(x3), and the above formula can be further written as: Where, 3. The airborne CSSAR ground acceleration target imaging method according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2-1: Assume that the signal transmitted by the radar is a linear frequency modulated pulse signal. The target echo signal after range compression and carrier frequency demodulation is expressed as: Among them, t r is the distance between the fastest time, p r (·) is the range compression impulse response function, c is the speed of light, ω a (·) is the azimuthal envelope, λ is the wavelength; Step 2-2: Perform a two-dimensional Fourier transform on equation (15) to obtain: Among them, f r is the distance frequency, f a is the baseband azimuth frequency, i.e., the Doppler frequency, f c is the carrier frequency, W r (·) is the distance frequency envelope, K r is the frequency modulation of the range pulse; Step 2-3: Apply the stationary phase principle to obtain the stationary phase expression: Where M is the Doppler ambiguity number and PRF is the pulse repetition frequency; Step 2-4: Use the series inversion method to obtain the expression of the stationary phase point: Where, Substituting equation (18) into equation (16), we get the expression of the target signal in the two-dimensional frequency domain: S(f r ,f a )=W r (f r )W a (f a )exp{jΘ(f r ,f a )} (21) Where, Among them, W a (·) is the azimuth frequency envelope.

4. The airborne CSSAR ground acceleration target imaging method according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3-1: Construct a matched filter: Multiply Equation (23) by Equation (21), and perform a two-dimensional inverse Fourier transform on the result of the multiplication to obtain the target imaging result; Step 3-2: The imaging process is modeled as the following optimization problem: Where, s(t r ,t a ;a1,a2,a3)=IDFT2{S(f r ,f a )·H(f r ,f a )} (26) Where IDFT(·) represents the two-dimensional inverse Fourier transform, E(·) represents the spatial averaging operation, Contrast(·) is the image contrast, and are the estimated values ​​of a1, a2, and a3 respectively. 1,min and a 1,max are the minimum and maximum values ​​of a1, a 2,min and a 2,max are the minimum and maximum values ​​of a2, a 3,min and a 3,max are the minimum and maximum values ​​of a3 respectively; Step 3-3: The solution to the optimization problem is the optimal estimate of the three parameters a1, a2, and a3; therefore, the focused SAR image is given by Equation (27): Step 3-4: Use differential evolution algorithm to solve the optimization problem of formula (24); Step 3-4-1: First, establish a relationship model between the differential evolution algorithm and the optimization problem to be solved: Among them A i,G represents the i-th individual in the G-th generation population, where i = 1, 2, ..., N, and N is the population size. D represents the dimension of the search space, and j represents the number of parameters to be searched. Step 3-4-2: Population initialization; Individuals in the population are randomly initialized within the specified minimum and maximum values, expressed as: where rand i,j [0,1] is a uniformly distributed random number between 0 and 1; Step 3-4-3: mutation; Randomly select three mutually different vectors from the population The mutation vector of the differential evolution algorithm is generated in the following way: Where F is the variation factor; Step 3-4-4: Cross; The cross vector is generated as follows: Where Cr is the crossover factor; Step 3-4-5: Calculate the fitness function; The contrast of the image focused by the parameters corresponding to an individual is selected as the fitness value of the individual, the image is obtained by formula (26), and the contrast is calculated by formula (25); Step 3-4-6: Select; The differential evolution algorithm follows the greedy criterion and starts from the experimental population U i,G The individuals are selected as individuals in the next generation population. The specific selection method is: If the new experimental vector U i,G The resulting objective function value is equal to or higher than the target vector A i,G , then it will be replaced by the corresponding target vector in the next generation, otherwise the target will remain in the population; Step 3-4-7: Repeat steps 3-4-3 to 3-4-6 until the termination condition is met or the specified number of iterations is reached. The parameter corresponding to the maximum contrast value is the solution to the optimization problem to be solved.

5. The airborne CSSAR ground acceleration target imaging method according to claim 4, characterized in that: In step 4, the optimal solution obtained by the differential evolution algorithm is used to focus the target through formula (27).

6. The airborne CSSAR ground acceleration target imaging method according to claim 4, characterized in that: The variation factor F∈[0.4,1].

Images