A method for joint imaging of flying targets based on a spaceborne platform

Abstract

The application relates to a method for jointly imaging a flying target based on a spaceborne platform, and relates to the field of ISAR imaging, in particular to a method for jointly imaging a flying target based on a spaceborne platform. The application aims to solve the problem of reduced ISAR imaging quality in the process of imaging a flying target based on a spaceborne platform. The process comprises the following steps: 1, dividing the observation time; 2, constructing a signal model for imaging a flying target based on a spaceborne platform after the planar motion compensation in the imaging time period; 3, obtaining the optimal solution estimation value of the equivalent rotation speed and the optimal solution estimation value of the equivalent rotation acceleration; 4, constructing a phase compensation function, obtaining a focused ISAR image and completing calibration; 5, repeating steps 3 and 4 to obtain focused and calibrated ISAR images under different imaging time periods; and 6, performing image registration on the focused and calibrated ISAR images, and performing wavelet transformation on the registered images to realize image fusion.

Description

Technical Field

[0001] This invention relates to the field of ISAR imaging, and in particular to a method for joint imaging of flying targets by pulse and frame based on a spaceborne platform. Background Technology

[0002] Imaging of flying targets has always been a hot topic in the field of ISAR imaging. Traditional ground-based imaging platforms are limited by their location and geographical terrain, while airborne and shipborne imaging platforms are limited by their range, making it difficult to achieve continuous and stable detection. Therefore, satellite platforms equipped with ISAR are considered for imaging flying targets. However, during long observation periods, both the satellite platform and the airborne target move along their respective orbits. The complex motion between the platform and the target will cause the image projection surface to be non-stationary, resulting in rotational distance migration and two-dimensional spatial phase errors. In ISAR imaging models, phase errors are non-negligible. Currently, among ISAR compensation methods for complex motion situations, non-parametric methods show decreased performance when the target has high maneuverability; parametric methods treat the signal in each range cell as an independent part, ignoring the integrity of the target's rotational motion, thus reducing the accuracy of parameter estimation. At the same time, when detecting and imaging the target, some scattering points on the target are obscured, resulting in the loss of some scattering points during ISAR imaging. Summary of the Invention

[0003] The purpose of this invention is to solve the problem of reduced ISAR imaging quality caused by the complex relative motion between the target and the platform during the imaging of flying targets by existing spaceborne platforms, such as the migration of rotational distance, two-dimensional spatial phase error, and missing scattering points. Therefore, this invention proposes a joint inter-pulse and inter-frame ISAR imaging method based on a spaceborne platform.

[0004] The specific process of a method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform is as follows:

[0005] Step 1: Estimate the three-dimensional rotation angle of the flying target using narrowband tracking data, and calculate the target's equivalent rotational speed ω based on the three-dimensional rotation angle. e and equivalent rotational acceleration α e Based on the target's equivalent rotational speed ω e and equivalent rotational acceleration α e Calculate the distance traveled R due to rotation. Rot,p The observation time is divided based on the condition that the distance traveled does not exceed one distance unit.

[0006] Step 2: Using the results of dividing the observation time obtained in Step 1, construct a signal model of the spaceborne platform imaging the flying target after translational compensation within the imaging time period;

[0007] Step three: obtaining image entropy based on the signal model constructed in step two, and obtaining optimal solution estimation of parameter vector M, i.e., optimal solution estimation of equivalent rotation speed, by minimizing image entropy and optimal solution estimation of equivalent rotation acceleration

[0008] Step four: using the optimal solution estimation of equivalent rotation speed obtained in step three and optimal solution estimation of equivalent rotation acceleration constructing a phase compensation function, obtaining focused ISAR images, and completing ISAR image scaling

[0009] Step five: repeating step three and step four to obtain focused and scaled ISAR images in different imaging time periods; performing image registration on the focused and scaled ISAR images, and performing wavelet transform on the registered images to realize image fusion.

[0010] The present application has the following advantages:

[0011] The present application provides an imaging method based on a spaceborne ISAR, and relates to the field of ISAR imaging, in particular to a pulse-to-pulse and frame-to-frame joint ISAR imaging method based on a spaceborne platform. The present application mainly aims at the problems of non-stationary imaging planes caused by complex relative motion and missing of scattering points caused by target occlusion when a spaceborne platform images a flying target. The main content of the present application includes the following steps. Firstly, narrowband tracking data is used to divide imaging time periods in a long observation time, and a spaceborne ISAR signal model after imaging time period division is constructed, and a phase error model is further derived. Then, a parameter optimization algorithm based on minimum image entropy search is proposed. Further, a phase compensation function is constructed using the estimated motion parameters to obtain focused and scaled ISAR images in the current imaging time period. Finally, ISAR image fusion in different imaging time periods is performed to obtain a focused and complete ISAR image.

[0012] The present application proposes a pulse-to-pulse and frame-to-frame joint ISAR imaging method based on a spaceborne platform to solve the problems of rotation distance migration, two-dimensional spatial phase error, and missing of scattering points.

[0013] This invention proposes a joint inter-pulse and inter-frame imaging algorithm for flying targets based on a spaceborne platform. First, narrowband tracking data is used to divide the long observation time into imaging time periods, and a spaceborne ISAR signal model after the imaging time period division is constructed, further deriving the phase error model. Next, a parameter optimization algorithm based on minimum image entropy search is proposed, and a focused and calibrated ISAR image within the current imaging time period is obtained. Finally, ISAR images from different imaging time periods are fused to obtain a well-focused ISAR image with complete target information. Attached Figure Description

[0014] Figure 1 This is a flowchart of the present invention;

[0015] Figure 2 The images show the imaging results of different algorithms: (a) RD, (b) STFT, (c) DSA, (d) PGA, (e) IGCPF, and (f) the algorithm proposed in this invention.

[0016] Figure 3 Image calibration results for ISAR images;

[0017] Figure 4 The calibration results of ISAR images in different imaging time periods are shown in the figure. (a) Reference image, (b) Image to be fused.

[0018] Figure 5 The registration result of the images to be fused;

[0019] Figure 6 To merge images. Detailed Implementation

[0020] Specific Implementation Method 1: The specific process of this implementation method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform is as follows:

[0021] Step 1: Estimate the three-dimensional rotation angle of the flying target using narrowband tracking data, and calculate the target's equivalent rotational speed ω based on the three-dimensional rotation angle. e and equivalent rotational acceleration α e Based on the target's equivalent rotational speed ω e and equivalent rotational acceleration α e Calculate the distance traveled R due to rotation. Rot,p The long observation period was divided based on the condition that the distance traveled did not exceed one distance unit.

[0022] Step 2: Using the results of dividing the long observation time obtained in Step 1, construct a signal model of the spaceborne platform imaging the flying target after translational compensation within the imaging time period;

[0023] Step three: obtain image entropy based on the signal model constructed in step two, and obtain the optimal estimation of the parameter vector M, i.e. the optimal estimation of the equivalent rotation velocity and the optimal estimation of the equivalent rotation acceleration

[0024] Step four: use the optimal estimation of the equivalent rotation velocity and the optimal estimation of the equivalent rotation acceleration obtained in step three to construct a phase compensation function, obtain a focused ISAR image, and complete the scaling of the ISAR image

[0025] Step five: repeat steps three and four to obtain focused and scaled ISAR images at different imaging time periods; perform image registration on the focused and scaled ISAR images, and perform wavelet transform on the registered images to realize image fusion.

[0026] Specific implementation method two: the difference between this implementation method and the specific implementation method one is that: in step one, the three-dimensional rotation angle of the flight target is estimated using narrowband tracking data, the equivalent rotation velocity ω e and the equivalent rotation acceleration α e of the target are calculated based on the three-dimensional rotation angle of the flight target, the distance walk R Rot,p caused by rotation is calculated based on the equivalent rotation velocity ω e and the equivalent rotation acceleration α e of the target, and the long observation time is divided based on the condition that the distance walk does not exceed one distance unit; the specific process is as follows:

[0027] Step one: in order to realize effective tracking of the target, the radar system also has a narrowband ranging function, which can measure the position r r (t m ) of the target at each time in the radar coordinate system, t m is the azimuth time domain time, i.e. the slow time dimension; t m =mT r , T r represents the pulse repetition period, m is the mth accumulation pulse, m=0,1,…,M-1, and M is the number of accumulation pulses

[0028] The radar line-of-sight unit vector i los (t m ) is represented as

[0029]

[0030] Where, | |2 represents the second order norm

[0031] The velocity vector of the target is represented as

[0032]

[0033] wherein v n (t m ) represents the velocity of the target along the n-axis of the radar coordinate system, v u (t m ) represents the velocity of the target along the u-axis of the radar coordinate system, and v w (t m ) represents the velocity of the target along the w-axis of the radar coordinate system;

[0034] The origin of the radar coordinate system is located at the center of the radar, the u-axis of the radar coordinate system is parallel to the moving direction of the radar satellite platform, the w-axis of the radar coordinate system points to the direction away from the center of the earth, and the n-axis of the radar coordinate system is obtained by the right-hand rule;

[0035] The acceleration vector of the target is represented as

[0036]

[0037] wherein a n (t m ) represents the acceleration of the target along the n-axis of the radar coordinate system, a u (t m ) represents the acceleration of the target along the u-axis of the radar coordinate system, and a w (t m ) represents the acceleration of the target along the w-axis of the radar coordinate system;

[0038] The three-dimensional rotation angles are obtained based on the velocity vector of the target and the acceleration vector of the target, and the three-dimensional rotation angles are represented as

[0039]

[0040]

[0041]

[0042] wherein θ w (t m ) represents the rotation angle of the target around the w-axis of the radar coordinate system, θ u (t m ) represents the rotation angle of the target around the u-axis of the radar coordinate system, and θ n (t m ) represents the rotation angle of the target around the n-axis of the radar coordinate system, g is the gravity on the surface of the earth, and R(t m ) is the curvature radius of the turning of the target;

[0043]

[0044] Step one two: using the extended Kalman filter to process three-dimensional rotation angle θ w (t m ), θ u (t m ), θ n (t m ) to obtain accurate three-dimensional rotation angle

[0045] Based on the accurate three-dimensional rotation angle Obtain the rotation vector ω s (t m ), ω s (t m ) caused by target rotation, expressed as

[0046]

[0047] Where, T represents the transpose;

[0048] The rotation vector ω l (t m ) caused by the change of radar line-of-sight direction is expressed as

[0049]

[0050] Where, × represents the vector cross product;

[0051] Based on the rotation vector ω s (t m ) caused by target rotation and the rotation vector ω l (t m ) caused by the change of radar line-of-sight direction, obtain the actual rotation vector ω i (t m ), ω i (t m ) is expressed as

[0052] ω i (t m ) = ω l (t m ) + ω s (t m )

[0053] The equivalent rotation velocity vector ω(t m ) is the projection of the actual rotation vector ω i (t m ) perpendicular to the radar line-of-sight unit vector i los (t m ), calculated by the following formula

[0054]

[0055] ω e (t m )=||ω(t m )||2 represents t m The equivalent rotational velocity of the target on the radar projection plane at any given time, where ||2 represents the second norm of the vector;

[0056] The equivalent rotational acceleration of the target on the projection plane is expressed as:

[0057]

[0058] The equivalent rotation angle of the target during the imaging time is expressed as:

[0059]

[0060] Where t is time;

[0061] Then, during the imaging time, the change in distance between a certain scattering point P on the target and the radar caused by rotation is:

[0062] R Rot,p (t m )≈y P cos(θ R (t m ))+x P sin(θ R (t m ))

[0063] Among them, (x P ,y P () represents the coordinates of the scattering point P on the radar projection plane;

[0064] The condition for dividing the time period is: the distance migration of the scattering point within the time period is less than one range resolution unit, i.e.

[0065] R Rot,p (t m )≤Δr

[0066] Where Δr represents the range resolution unit, c represents the speed of light, and B represents the signal bandwidth;

[0067] If the above conditions are met, it can be assumed that the scattering point does not migrate during the imaging time period. Using this condition, the long observation time can be segmented. The total number of segments is Q, and the length of each segment is T. q ,q=1,2,...,Q.

[0068] The other steps and parameters are the same as in Specific Implementation Method 1.

[0069] Specific implementation three: the embodiment is different from specific implementation one or two: the step two utilizes the result of dividing the long observation time obtained in step one, and constructs a signal model S(f r ,t m ) of the imaging time period after the translation compensation of the space-borne platform imaging the flight target

[0070] Step two one, the target echo in the division time period is compensated for the translation motion, at this time the equivalent rotation speed in the target imaging time period is assumed to be ω e (an unknown quantity, to be estimated later), and the equivalent rotation acceleration in the target imaging time period is assumed to be α e (an unknown quantity, to be estimated later);

[0071] Then the rotation angle change of the scattering point P is represented as

[0072]

[0073] Where θ0 is the initial rotation angle of the scattering point P;

[0074] Step two two, the distance walk caused by the rotation motion is represented as

[0075]

[0076] The trigonometric functions of the above formula are approximated by using the Maclaurin formula, and are represented as

[0077]

[0078]

[0079] The distance walk caused by the rotation motion is simplified as

[0080]

[0081] Step two three, the received signal spectrum S(f r ,t m ) of the scattering point P after pulse compression received by the radar is

[0082]

[0083] Where,

[0084] · represents multiplication;

[0085] σ p is the scattering intensity of the scattering point p;

[0086] f r represents the fast time dimension frequency;

[0087] λ is the wavelength, λ = c / f c f c For carrier frequency;

[0088] j is the imaginary unit, j 2 =-1;

[0089] After time division, the rotational distance migration is negligible, therefore the received signal spectrum S(f r ,t m The fourth item in ) It can be ignored, S(f) r ,t m Simplify to S'(f) r ,t m );

[0090] S'(f r ,t m The signal is divided into two parts, one of which is a signal without phase error. The remaining portion is the phase error caused by rotational motion.

[0091]

[0092]

[0093] Wherein, S'(f r ,t m This indicates the spectrum of the received signal after ignoring the rotational distance migration. This indicates a signal with no phase error.

[0094] Step 24: For S'(f) r ,t m )and Performing a discrete inverse Fourier transform in the distance dimension yields...

[0095]

[0096]

[0097] Where s(k,n) represents the sum of S'(f) and S'(f) r ,t m The result after performing a discrete inverse Fourier transform in the distance dimension;

[0098] Indicates to The result after performing a discrete inverse Fourier transform in the distance dimension;

[0099] n represents t ms(k, n) = s(m, n), n = 0, 1,..., N - 1, N represents the number of pulses in a time period after time period division (m is the index before time period division, and the current n is the index after time period division) ;

[0100] k represents the distance dimension unit index, k = 0, 1,..., K - 1, K represents the number of distance units;

[0101] Step two, s(k, n) and performing a discrete inverse Fourier transform in the slow time dimension to obtain

[0102]

[0103]

[0104] wherein g(k, h) represents the result of performing a discrete inverse Fourier transform in the slow time dimension on s(k, n) ;

[0105] represents the result of performing a discrete inverse Fourier transform in the slow time dimension on

[0106] h represents the discrete sequence index after the discrete inverse Fourier transform in the slow time dimension, h = 0, 1,..., N - 1;

[0107] (k, h) represents the image domain pixel position;

[0108] (y P , ω1x p ) represents the position of the scattering point P in the image;

[0109] (y P , ω1x p ) is obtained through the distance resolution and the azimuth dimension resolution, and is represented as

[0110]

[0111]

[0112] Substitute the above formula into g(k, h) to obtain

[0113]

[0114] The other steps and parameters are the same as those in the first or second embodiment.

[0115] The fourth embodiment is different from any one of the first to third embodiments in that: in the step three, the image entropy is obtained based on the signal model constructed in the step two, and the optimal estimation value of the parameter vector M, i.e., the optimal estimation value of the equivalent rotation speed, is obtained by minimizing the image entropy.​ and the optimal estimation of the equivalent rotational acceleration

[0116] The specific process is as follows:

[0117] Step three, in order to obtain the focused ISAR image, the phase compensation term needs to be constructed to compensate the echo signal s(k, n), and the parameter vector required for compensation is defined as M = (ω e , α e );

[0118] The phase compensation term is expressed as

[0119]

[0120] The signal after phase compensation is expressed as

[0121]

[0122] The image entropy E g (M) is defined as a function of M, and is expressed as

[0123]

[0124]

[0125] Where S g is the image density; and 2 represents the square of the absolute value.

[0126] Step three, the optimal estimation of the parameter vector M, i.e. the optimal estimation of the equivalent rotational velocity and the optimal estimation of the equivalent rotational acceleration

[0127] The other steps and parameters are the same as one of the first to third embodiments.

[0128] The fifth embodiment is different from one of the first to fourth embodiments in that: in the step three, the optimal estimation of the parameter vector M, i.e. the optimal estimation of the equivalent rotational velocity and the optimal estimation of the equivalent rotational acceleration The specific process is as follows:

[0129] The optimization function is constructed and expressed as

[0130]

[0131] Wherein, represents the optimal estimation of the equivalent rotational velocity, an estimate of the equivalent rotation acceleration, an optimal solution estimate of the parameter vector M;

[0132] Taking the parameter vector M = (ω e , α e ) as the initial input value of the optimization function, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is used to find the optimal solution estimate of the equivalent rotation velocity and the optimal solution estimate of the equivalent rotation acceleration

[0133] Through the above analysis, the phase error estimation idea based on minimum entropy optimization is established. Through the minimization of image entropy, the optimal parameters can be obtained, and the phase compensation is realized by using the estimated parameters, thereby significantly improving the clarity of the image. In order to improve the calculation efficiency, the BFGS algorithm is used to find the optimal result, and the initial value of the optimization algorithm can be obtained from step one.

[0134] The other steps and parameters are the same as one of the first to fourth embodiments.

[0135] The sixth embodiment is different from the first to fifth embodiments in that: in step four, the optimal solution estimate of the equivalent rotation velocity and the optimal solution estimate of the equivalent rotation acceleration obtained in step three are used to construct a phase compensation function, obtain a focused ISAR image, and complete the scaling of the ISAR image.

[0136] The specific process is as follows:

[0137] Based on the optimal solution estimate of the equivalent rotation velocity and the optimal solution estimate of the equivalent rotation acceleration obtained in step three, a phase compensation function is constructed, and the phase compensation function is represented as

[0138]

[0139] Then, the focused ISAR image is represented as

[0140]

[0141] Among them, the transverse scaling factor δ a and the range dimension scaling factor δ r of the ISAR image are respectively represented as

[0142]

[0143]

[0144] Thus, the ISAR image with good focusing and scaling is obtained.

[0145] The other steps and parameters are the same as those in the first to fifth embodiments.

[0146] The seventh embodiment is different from one of the first to sixth embodiments in that: the steps three and four are repeated in the step five to obtain the ISAR images with good focusing and scaling in different imaging time periods; the ISAR images with good focusing and scaling are image-registered, and the registered images are wavelet-transformed to realize image fusion.

[0147] The specific process is as follows:

[0148] In the step five one, the ISAR images with good focusing and scaling in different imaging time periods are represented as RD q , q = 1, 2, …, Q.

[0149] In the step five two, the optimal solution estimate of the equivalent rotation speed corresponding to each imaging time period in the step three is represented as The optimal solution estimate of the equivalent rotation acceleration is represented as

[0150] The rotation angle of the target in each imaging time period is represented as

[0151]

[0152] The lateral scaling factor of the ISAR image in each imaging time period is represented as

[0153]

[0154] The distance dimension scaling factor of the ISAR image in each imaging time period is represented as

[0155]

[0156] In the step five three, image registration is performed, and the rotation angle of the ISAR image with good focusing and scaling obtained in the qth imaging time period with respect to the reference image obtained in the first imaging time period is represented as

[0157]

[0158] In the step five four, the rotation angle between the reference image and the image to be registered, and the two-dimensional resolution δ a,q , q = 1, 2, …, Q and δ r of the image are known, and the image to be registered RD qRD' is obtained by rotating interpolation of RD q RD' is obtained by rotating interpolation of RD

[0159] The reference image is a focused and scaled ISAR image RD1 obtained in the first imaging time period q RD' is obtained by rotating interpolation of RD

[0160] The to-be-registered images are focused and scaled ISAR images RD2, RD3,..., RDQ obtained in the second, third,..., and Qth imaging time periods q RD' is obtained by rotating interpolation of RD

[0161] Step five, wavelet transform is performed on the reference image RD1 and the registered image RD' q RD' is obtained by rotating interpolation of RD

[0162] The other steps and parameters are the same as those in the first to sixth embodiments.

[0163] The eighth embodiment is different from the first to seventh embodiments in that, in the step five, wavelet transform is performed on the reference image RD1 and the registered image RD' q RD' is obtained by rotating interpolation of RD

[0164] Step five, wavelet transform is performed on the reference image RD1 and the registered image RD' q RD' is obtained by rotating interpolation of RD

[0165] Step five, wavelet transform is performed on the reference image RD1 and the registered image RD'

[0166] Step five, wavelet transform is performed on the reference image RD1 and the registered image RD'

[0167] The other steps and parameters are the same as those in the first to seventh embodiments.

[0168] Simulation analysis:

[0169] A simulation is used to verify the effectiveness of the designed inter-pulse and inter-frame joint ISAR imaging method based on a spaceborne platform, and the results are described.

[0170] Simulation 1 is used to verify the effectiveness of the ISAR imaging focusing of the present application. The relative motion parameters and simulation signal parameters are shown in Table 1. The imaging results corresponding to different algorithms are shown in FIG. 1, wherein Figure 2 (a) to (d) in FIG. 1 are the imaging results of the first to fourth algorithms, respectively. Figure 2 (a) to (d) in FIG. 1 are the imaging results of the first to fourth algorithms, respectively. Figure 2Fig. f shows the imaging results of RD algorithm, short-time Fourier transform (STFT), distinct scattering point algorithm (DSA), phase gradient autofocus (PGA), iterative generalized cubic phase function (IGCPF) and the method of the present application, respectively, and the corresponding image entropy is shown in Table 2. Figure 2 It can be seen from Table 2 that after image focusing, the method of the present application can obtain the image with the highest focusing degree and the smallest image entropy.

[0171] Table 1 simulation parameters

[0172]

[0173]

[0174] Table 2 image entropy

[0175]

[0176] Simulation 2 is used to verify the effectiveness of the ISAR image scaling method of the present application. The simulation parameters are shown in Table 1. Figure 3 Fig. f shows the imaging results of RD algorithm, short-time Fourier transform (STFT), distinct scattering point algorithm (DSA), phase gradient autofocus (PGA), iterative generalized cubic phase function (IGCPF) and the method of the present application, respectively, and the corresponding image entropy is shown in Table 2.

[0177] Simulation 3 is used to verify the effectiveness of the ISAR image fusion method of the present application. Figure 4 Fig. f shows two target images to be fused, wherein Figure 4 Fig. f (a) is a reference image, Figure 4 Fig. f (b) is a to-be-fused image. Figure 5 Fig. f shows the result of image registration of the to-be-fused image. Figure 6 Fig. f is the image after fusion of the two images. It can be seen that the two images before fusion respectively lack the left wing and the right wing, and after image fusion, the missing scattering points are completed, verifying the effectiveness of the image fusion method of the present application.

[0178] The present application also has other various embodiments, and those skilled in the art can make various corresponding changes and modifications according to the present application without departing from the spirit and essence of the present application, and these corresponding changes and modifications shall all belong to the protection scope of the claims attached to the present application.

Claims

1. A method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform, characterized in that: The specific process of the method is as follows: Step 1: Estimate the three-dimensional rotation angle of the flying target using narrowband tracking data, and calculate the target's equivalent rotational speed ω based on the three-dimensional rotation angle. e and equivalent rotational acceleration α e Based on the target's equivalent rotational speed ω e and equivalent rotational acceleration α e Calculate the distance traveled R due to rotation. Rot,p The observation time is divided based on the condition that the distance traveled does not exceed one distance unit. Step 2: Using the results of dividing the observation time obtained in Step 1, construct a signal model of the spaceborne platform imaging the flying target after translational compensation within the imaging time period; Step 3: Based on the signal model constructed in Step 2, obtain the image entropy. Minimize the image entropy to obtain the optimal solution estimate of the parameter vector M, i.e., the optimal solution estimate of the equivalent rotational velocity. The optimal solution estimate of the equivalent rotational acceleration Step 4: Utilize the optimal solution estimate of the equivalent rotational velocity obtained in Step 3. The optimal solution estimate of the equivalent rotational acceleration Construct a phase compensation function to obtain a focused ISAR image and complete the ISAR image calibration; Step 5: Repeat steps 3 and 4 to obtain focused and calibrated ISAR images under different imaging time periods; perform image registration on the focused and calibrated ISAR images, and perform wavelet transform on the registered images to achieve image fusion.

2. The method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform according to claim 1, characterized in that: In step one, the three-dimensional rotation angle of the flying target is estimated using narrowband tracking data, and the equivalent rotational speed ω of the target is calculated based on the three-dimensional rotation angle. e and equivalent rotational acceleration α e Based on the target's equivalent rotational speed ω e and equivalent rotational acceleration α e Calculate the distance traveled R due to rotation. Rot,p The observation time is divided based on the condition that the distance traveled does not exceed one distance unit. The specific process is as follows: Step 11: The radar system measures the target's position r in the radar coordinate system at various times. r (t m ), t m The azimuth dimension is the time domain, i.e., the slow time dimension; t m =mT r T r This represents the pulse repetition period, where m is the mth accumulated pulse, m = 0, 1, ..., M-1, and M is the number of accumulated pulses; Radar line-of-sight unit vector i los (t m ) represents Where ||2 represents the second norm; The target's velocity vector is represented as Among them, v n (t m ) represents the velocity of the target along the n-axis of the radar coordinate system, v u (t m ) represents the target's velocity along the u-axis of the radar coordinate system, v w (t m () represents the velocity of the target along the w-axis of the radar coordinate system; The origin of the radar coordinate system is located at the center of the radar. The u-axis of the radar coordinate system is parallel to the direction of motion of the radar spacecraft platform. The w-axis of the radar coordinate system points away from the center of the Earth. The n-axis of the radar coordinate system is obtained by the right-hand rule. The target's acceleration vector is represented as Among them, a n (t m ) represents the target's acceleration along the n-axis of the radar coordinate system, a u (t m ) represents the target's acceleration along the u-axis of the radar coordinate system, a w (t m () represents the target's acceleration along the w-axis of the radar coordinate system; The three-dimensional rotation angle is obtained based on the target's velocity vector and acceleration vector, and is expressed as follows: Where, θ w (t m θ represents the rotation angle of the target around the w-axis of the radar coordinate system. u (t m θ represents the rotation angle of the target around the u-axis of the radar coordinate system. n (t m R(t) represents the rotation angle of the target around the n-axis of the radar coordinate system, g is the gravity at the Earth's surface, and R(t) is the rotation angle of the target around the n-axis of the radar coordinate system. m () represents the radius of curvature of the target turn; Steps 1 and 2: Using an extended Kalman filter to measure the three-dimensional rotation angle θ w (t m ), θ u (t m ), θ n (t m The process is performed to obtain the three-dimensional rotation angle. Based on three-dimensional rotation angle Obtain the rotation vector ω caused by the target rotation. s (t m ), ω s (t m ) represents Where T represents the transpose; Rotation vector ω caused by changes in radar line-of-sight direction l (t m ) represents Where × represents the cross product of vectors; Based on the rotation vector ω caused by the target rotation s (t m The rotation vector ω caused by the change in radar line-of-sight direction l (t m ), to obtain the actual rotation vector ω i (t m ), ω i (t m ) is represented as ω i (t m )=ω l (t m )+ω s (t m ) Equivalent rotational velocity vector ω(t) m ) is the actual rotation vector ω i (t m The unit vector i perpendicular to the radar line of sight los (t m The projection of ) is calculated using the following formula. ω e (t m )=‖ω(t m )||2 represents t m The equivalent rotational velocity of the target on the radar projection plane at any given time, ‖ ‖2 represents the second norm of the vector; The equivalent rotational acceleration of the target on the projection plane is expressed as: The equivalent rotation angle of the target during the imaging time is expressed as: Where t is time; During the imaging time, the change in distance between a scattering point P on the target and the radar caused by rotation is R. Rot,p (t m )≈y P cos(θ R (t m ))+x P sin(θ R (t m )) Among them, (x P ,y P () represents the coordinates of the scattering point P on the radar projection plane; The condition for dividing the time period is: the distance migration of the scattering point within the time period is less than one range resolution unit, i.e., R. Rot,p (t m )≤Δr Where Δr represents the range resolution unit, c represents the speed of light, and B represents the signal bandwidth; The total number of segments in the time period is Q, and the length of each time period after division is T. q ,q=1,2,...,Q.

3. The method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform according to claim 2, characterized in that: In step two, the results of dividing the observation time obtained in step one are used to construct a signal model of the spaceborne platform imaging the flying target after translational compensation within the imaging time period. The specific process is as follows: Step 2: Perform translational motion compensation on the target echo within the divided time period. The equivalent rotational velocity of the target within the imaging time period is assumed to be ω. e The equivalent rotational acceleration during the target imaging time period is denoted as α. e ; The change in the rotation angle of the scattering point P is expressed as: Where θ0 is the initial rotation angle of the scattering point P; Step 22: The distance traveled due to rotational motion is represented as follows: The trigonometric functions in the above equation can be approximated using the Maclaurin formula, and expressed as follows: The distance traveled due to rotational motion is simplified to Steps 2 and 3: The received signal spectrum S(f) after compression of the scattered point P pulse received by the radar. r ,t m )for in, • Indicates multiplication sign; σ p Let p be the scattering intensity at scattering point p; f r Indicates the frequency in the fast time dimension; λ is the wavelength, λ = c / f c f c For carrier frequency; j is the imaginary unit, j 2 =-1; Received signal spectrum S(f) r ,t m The fourth item in ) It can be ignored, S(f) r ,t m Simplify to S'(f) r ,t m ); S'(f r ,t m The signal is divided into two parts, one of which is a signal without phase error. The remaining portion is the phase error caused by rotational motion. Wherein, S'(f r ,t m This indicates the spectrum of the received signal after ignoring the rotational distance migration. This indicates a signal with no phase error. Step 24: For S'(f) r ,t m )and Performing a discrete inverse Fourier transform in the distance dimension yields... Where s(k,n) represents the sum of S'(f r ,t m The result after performing a discrete inverse Fourier transform in the distance dimension; Indicates to The result after performing a discrete inverse Fourier transform in the distance dimension; n represents t m The discrete form of the time interval is n = 0, 1, ..., N-1, where N represents the number of pulses within the time interval after the time interval is divided. k represents the index of the distance dimension cell, k = 0, 1, ..., K-1, where K represents the number of distance cells; Step 2.5: For s(k,n) and Performing a discrete inverse Fourier transform in the slow time dimension yields... Where g(k,h) represents the result of performing a discrete inverse Fourier transform on s(k,n) in the slow time dimension; Indicates to The result after performing a discrete inverse Fourier transform in the slow time dimension; h represents the index of the discrete sequence after the slow-time dimension discrete inverse Fourier transform, h = 0, 1, ..., N-1; (k,h) represents the pixel position in the image domain; (y P ,ω e x p () indicates the location of the scattering point P in the image; (y) is obtained through distance resolution and azimuth resolution. P ,ω e x p ), represented as Substituting the above equation into g(k,h) yields 4. The method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform according to claim 3, characterized in that: In step three, the image entropy is obtained based on the signal model constructed in step two. The optimal solution estimate of the parameter vector M, i.e., the optimal solution estimate of the equivalent rotation speed, is obtained by minimizing the image entropy. The optimal solution estimate of the equivalent rotational acceleration The specific process is as follows: Step 3:

1. Construct a phase compensation term to compensate the echo signal s(k,n). The parameter vector to be compensated is defined as M = (ω... e ,α e ); The phase compensation term is expressed as The signal after phase compensation is represented as follows: Image entropy E g (M) is defined as a function of M, expressed as Among them, S g Image density; | | 2 Represents the square of the absolute value; Step 3.2: Obtain the optimal solution estimate of the parameter vector M, i.e., the optimal solution estimate of the equivalent rotation speed, by minimizing the image entropy. The optimal solution estimate of the equivalent rotational acceleration 5. The method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform according to claim 4, characterized in that: In step three, the optimal solution estimate of the parameter vector M, i.e., the optimal solution estimate of the equivalent rotation speed, is obtained by minimizing the image entropy. The optimal solution estimate of the equivalent rotational acceleration The specific process is as follows: Construct the optimization function as follows: in, This represents the optimal solution estimate of the equivalent rotational velocity. This represents an estimate of the equivalent rotational acceleration. This represents the optimal solution estimate of the parameter vector M; The parameter vector M = (ω e ,α e Using the initial input value of the optimization function, the optimal estimate of the equivalent rotational velocity is found using the quasi-Newton method BFGS. The optimal solution estimate of the equivalent rotational acceleration 6. The method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform according to claim 5, characterized in that: In step four, the optimal solution estimate of the equivalent rotational velocity obtained in step three is used. The optimal solution estimate of the equivalent rotational acceleration Construct a phase compensation function to obtain a focused ISAR image and complete the ISAR image calibration; The specific process is as follows: The optimal solution estimate based on the equivalent rotational velocity obtained in step three. The optimal solution estimate of the equivalent rotational acceleration Construct a phase compensation function, which is expressed as follows: The focused ISAR image is represented as follows Among them, the horizontal scaling factor δ of the ISAR image a and distance dimension calibration factor δ r They are respectively represented as At this point, a focused and calibrated ISAR image has been obtained.

7. The method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform according to claim 6, characterized in that: In step five, steps three and four are repeated to obtain focused and calibrated ISAR images under different imaging time periods; image registration is performed on the focused and calibrated ISAR images, and wavelet transform is performed on the registered images to achieve image fusion; The specific process is as follows: Step 51: Focused and calibrated ISAR images under different imaging time periods are represented as RD. q ,q=1,2,...,Q; The optimal estimated value of the equivalent rotational velocity corresponding to each imaging time interval in steps five and three is expressed as follows: The optimal solution estimate of the equivalent rotational acceleration is expressed as: The rotation angle of the target within each imaging time period is expressed as: The lateral calibration factor of the ISAR image within each imaging time period is expressed as follows: The range dimension calibration factor of the ISAR image within each imaging time period is expressed as follows: Step 53: Using the focused and calibrated ISAR image obtained within the first imaging time period as the reference image, the rotation angle of the focused and calibrated ISAR image obtained within the q-th imaging time period relative to the reference image is expressed as: Step 54: Given the rotation angle between the reference image and the image to be registered, and δ a,q ,q=1,2,...,Q and δ r Based on the reference image RD1, the image to be registered is RD q Rotation interpolation is performed on q = 2, 3, ..., Q to obtain the registered image RD'. q ,q=2,3,...,Q; Step 5: Compare the reference image RD1 and the registered image RD' q Image fusion is achieved by performing wavelet transform on q = 2, 3, ..., Q.

8. The method for joint inter-pulse and inter-frame imaging of flying targets based on a spaceborne platform according to claim 7, characterized in that: In step five, the reference image RD1 and the registered image RD' are compared. q Image fusion is achieved by performing wavelet transform on q = 2, 3, ..., Q. The specific process is as follows: Step 551: Compare the reference image RD1 and the registered image RD' q Perform wavelet transform on q = 2, 3, ..., Q to decompose it into transform coefficients in different frequency domains; Step 552: Select the transformation coefficients according to the principle of taking the largest absolute value; Step 553: Perform inverse wavelet transform on the selected transform coefficients to obtain the fused image.

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