Space target ISAR imaging and calibration integrated method based on joint estimation of translation-rotation parameters

Abstract

The application relates to the technical field of remote sensing and radar imaging, and relates to a space target ISAR imaging and scaling integrated method based on a translation-rotation parameter joint estimation.The application is used to solve the problem that the existing space target ISAR imaging is affected by motion compensation, and the scattering points of a space target are prone to moving across distance units in a long-time accumulation.The application performs distance compression on echo obtained by a ground-based radar, performs generalized Radon Fourier transformation on a one-dimensional distance image sequence, and further estimates phase coefficients of the echo signal; the effective rotation angular velocity module value of a space uniform rotation target and a compensation signal are calculated by using the estimated value; the echo signal is subjected to translation compensation by using the compensation signal, the compensated echo signal is converted from a Cartesian coordinate system to a polar coordinate system by using the effective rotation angular velocity, and interpolation is performed; the imaging result is obtained by performing distance and azimuth compression on the interpolation result, scaling is completed according to the effective rotation angular velocity, and the space target ISAR imaging and scaling integration are realized.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing and radar imaging technology. Background Technology

[0002] Inverse synthetic aperture radar (InSAR) possesses the capability to acquire target information at all times, in all weather conditions, and over long distances, finding wide application in the surveillance and identification of moving targets such as ships, aircraft, and space satellites. In recent years, with the rapid development of technology, the number of man-made objects in space has increased dramatically, necessitating more accurate space target monitoring technologies to ensure space security. Compared to radar imaging of ship and aircraft targets, the imaging environment for space targets is more challenging, characterized by a lower signal-to-noise ratio (SNR). Typically, obtaining a clear image of a target requires a high-precision motion compensation algorithm. However, in low SNR environments, existing motion compensation algorithms cannot achieve accurate compensation, affecting imaging performance. To improve the SNR of the output signal, long-term coherent accumulation of the echo signal is necessary. However, space targets move at high speeds, and under long-term accumulation conditions, range-to-cell (MTRC) drift can easily occur, causing image defocusing. Current methods for addressing the MTRC problem involve expanding the phase of the translationally compensated signal into a polynomial form and then compensating for the higher-order phase signals by parameter estimation. This expansion process is an approximation and has certain errors. It is also affected by translational compensation. Meanwhile, to obtain accurate target information, the target's size needs to be calibrated, and the signal processed after motion compensation. This process leads to error accumulation, affecting the calibration results. Therefore, the core of inverse synthetic aperture radar imaging of space targets lies in accurate motion compensation algorithms and correction of range cell movement.

[0003] In their paper "An Effective Translational Motion Compensation Approach for High-Resolution ISAR Imaging With Time-Varying Amplitude," Yang et al. proposed a motion compensation method based on time-varying amplitude. This algorithm achieves translational compensation based on the minimum mean square error criterion and an algorithm for extracting salient point energy. However, in low signal-to-noise ratio environments, the mean square error of the echo is significantly affected by noise, and the salient point energy may also be submerged by noise, reducing the compensation effect.

[0004] In their paper "Bistatic ISAR Imaging and Scaling Algorithm Based on the Estimation of Bistatic Factor and Effective Rotation Velocity," Wei Jin et al. proposed a bistatic ISAR imaging and calibration algorithm based on parameter estimation. By estimating the phase parameters of the translationally compensated signal before compensation imaging, this approach separates translational and rotational motion, leading to error accumulation.

[0005] In summary, existing ISAR imaging techniques for space targets suffer from problems such as the estimation of rotation parameters being affected by motion compensation, and the tendency for space target scattering points to move across distance cells over long periods of time. Summary of the Invention

[0006] This invention aims to address the problems in existing space target ISAR imaging where rotation parameter estimation is affected by motion compensation, and the tendency for space target scattering points to move across distance cells over long periods of time. It provides an integrated algorithm for space target ISAR imaging and calibration based on joint estimation of translational and rotational parameters under low signal-to-noise ratio conditions.

[0007] An integrated method for ISAR imaging and calibration of space targets based on joint estimation of translational and rotational parameters includes:

[0008] Range compression is performed on the echoes acquired by the ground-based radar to obtain a one-dimensional range image sequence of a spatially rotating target at a constant speed. The echoes acquired by the ground-based radar are the reflected echoes from the scattering points of the spatially rotating target at a constant speed.

[0009] A generalized Radon Fourier transform is performed on the one-dimensional range image sequence of the uniformly rotating target in space to estimate the phase coefficients of the echo signal.

[0010] The magnitude of the effective rotational angular velocity and the compensation signal of a uniformly rotating target in space are calculated using the estimated values ​​of the phase coefficients of each order of the echo signal.

[0011] The compensation signal is used to perform translational compensation on the echo signal acquired by the ground-based radar. The effective rotational angular velocity is used to transform the compensated echo signal from the Cartesian coordinate system to the polar coordinate system. The transformed signal is then interpolated using Sinc interpolation.

[0012] The interpolation results are compressed in terms of distance and azimuth to obtain the imaging results of a uniformly rotating target in space. The calibration of the uniformly rotating target in space is completed based on the effective rotation angular velocity, realizing the integration of ISAR imaging and calibration of space targets.

[0013] Furthermore, the aforementioned one-dimensional range image sequence of a uniformly rotating target in space... The expression is:

[0014]

[0015] Where i = 1, 2, ..., N, N is the number of scattering points on the uniformly rotating target in space, σ i Let B be the scattering coefficient of the i-th scattering point, and let B be the bandwidth of the echo signal at the scattering point. Let c be the speed of light and t be the time delay variable. m For the direction of slow time, T obs The observation duration is denoted by rect(·), the rectangular window function is denoted by sinc(·), the sigma function is denoted by j, the imaginary unit is λ, the carrier wavelength is λ, and a0, a1 and a2 are the zeroth, first and second order phase coefficients, respectively.

[0016] Furthermore, the generalized Radon Fourier transform is performed on the one-dimensional range image sequence of the uniformly rotating target in space to estimate the phase coefficients of the echo signal, including:

[0017] Perform a generalized Radon Fourier transform on the one-dimensional range image sequence of the uniformly rotating target in space:

[0018]

[0019] Among them, s GRFT (a0, a1, a2) represents the result of the generalized Radon Fourier transform, R i (t m f represents the distance between the i-th scattering point on the uniformly rotating target and the radar. c Indicates the center frequency of the transmitted signal;

[0020] Take s GRFT The peak value of (a0, a1, a2) is used as an estimate of the phase coefficients of the echo signal.

[0021]

[0022] Furthermore, the estimated values ​​of each phase coefficient of the echo signal are obtained by using the particle swarm optimization method, and the fitness function of the particle swarm optimization is the result of the generalized Radon Fourier transform.

[0023] Furthermore, the expressions for the zeroth-order, first-order, and second-order phase coefficients a0, a1, and a2 are as follows:

[0024] a0=R0+x i ,

[0025] a1=v+yi ω e ,

[0026]

[0027] Among them, (x i ,y i Ri represents the coordinates of the i-th scattering point on a uniformly rotating target in space, and R0 represents the coordinates of the i-th scattering point on the uniformly rotating target in space at time ti. m = 0, the distance between the radar and its center of rotation, v and α represent the translational velocity and translational acceleration of the uniformly rotating target in space, respectively, ω e This represents the effective rotational angular velocity of a target rotating uniformly in space.

[0028] Furthermore, the above-mentioned calculation of the magnitude of the effective rotational angular velocity of a uniformly rotating target in space using the estimated values ​​of the phase coefficients of each order of the echo signal includes:

[0029] Take the estimated second-order phase coefficients of any two scattering points p and q on a uniformly rotating target in space. and

[0030] Where, x p and x q Let p and q represent the x-coordinates, α and ω, respectively. e These represent the translational acceleration and effective rotational angular velocity of a target rotating uniformly in space, respectively.

[0031] Will and Subtraction:

[0032]

[0033] because Then the magnitude of the effective angular velocity of a uniformly rotating target in space is |ω e |:

[0034]

[0035] in, and These represent the estimated zero-order phase coefficients of scattering points p and q, respectively.

[0036] Furthermore, the calculation of the compensation signal using the estimated values ​​of the phase coefficients of the echo signal includes:

[0037] The compensation signal s is calculated according to the following formula. p ′(f,t m ):

[0038]

[0039] Where f is the fast time Frequency domain representation, Here is the estimated first-order phase coefficient of the scattering point p, where c is the speed of light, and t is the value of the first-order phase coefficient. m This refers to the slow time for the location.

[0040] Furthermore, the echo signal s(f,t) acquired by the ground-based radar after translational compensation m The representation of ) is:

[0041]

[0042] Where i = 1, 2, ..., N, N is the number of scattering points on the uniformly rotating target in space, σ i Let be the scattering coefficient of the i-th scattering point, rect(·) be the rectangular window function, and f be the fast time... The frequency domain representation, where B is the echo signal bandwidth, t m For the direction of slow time, T obs Let c be the observation duration, and c be the speed of light. i ,y i ) represents the coordinates of the i-th scattering point on a uniformly rotating target in space, where j is the imaginary unit, and θ(t) m ) is the rotation angle during the observation time.

[0043] Furthermore, the above-mentioned transformation of the compensated echo signal from the Cartesian coordinate system to the polar coordinate system using the effective rotational angular velocity includes:

[0044] Let the radial wavenumber of the echo signal

[0045] Let the range wavenumber k of the echo signal x =k r cosθ(t m ),

[0046] Let the azimuth wavenumber k of the echo signal y =k r sinθ(t m ),

[0047] The expression for the compensated echo signal s(k) in polar coordinates x ,k y )for:

[0048]

[0049] Where K(k) x ,k y A represents the sampling area of ​​the echo signal. i This represents the amplitude of the i-th scattering point.

[0050] Furthermore, the above-mentioned interpolation of the converted signal using Sinc interpolation includes:

[0051] Let the distance of the interpolated echo signal

[0052] Let the azimuth wavenumber of the interpolated echo signal be...

[0053] Interpolated signal Represented as:

[0054]

[0055] Among them, A′ i This represents the amplitude of the i-th scattering point after interpolation. This represents the rectangular region of the echo signal after the difference.

[0056] The present invention has the following beneficial effects:

[0057] 1. This invention enables high-precision motion compensation in low signal-to-noise ratio environments when the one-dimensional range image of a spatial target is submerged in noise.

[0058] 2. This invention eliminates the movement of space targets across distance cells caused by high rotation speed and long accumulation time, thus improving the imaging effect of space targets, especially in low signal-to-noise ratio environments.

[0059] 3. It realizes an integrated imaging calibration process, eliminating the need for multiple separate compensation calculations, reducing error accumulation, and improving calibration accuracy.

[0060] This invention breaks down the ISAR imaging problem of space targets into two key steps. The first step is motion compensation in low signal-to-noise ratio environments. The GRFT algorithm is used to achieve high-precision estimation of the echo signal phase coefficients. The estimated signal parameters are then used to perform translational compensation and determine the corresponding effective rotational angular velocity. Based on this, the echo data is converted to polar coordinates, and then the echo data region is re-interpolated to remove range and azimuth coupling. Finally, an integrated imaging and calibration operation is performed, ultimately obtaining a focused and calibrated ISAR image of the space target. Attached Figure Description

[0061] Figure 1 This is a flowchart of an integrated ISAR imaging and calibration method for space targets based on joint estimation of translational rotation parameters;

[0062] Figure 2 This is a geometric model diagram of a ground-based inverse synthetic aperture radar and a space target;

[0063] Figure 3 This is a diagram illustrating the interpolation process in polar coordinates.

[0064] Figure 4 A model diagram of the scattering points of a space target;

[0065] Figure 5 (a) is the imaging result of the distance Doppler algorithm based on motion compensation and image entropy at a signal-to-noise ratio of 0dB.

[0066] Figure 5 (b) is the imaging result of motion compensation and range Doppler algorithm based on image entropy at a signal-to-noise ratio of -20dB;

[0067] Figure 6 (a) is the imaging result of the method of the present invention at a signal-to-noise ratio of 0dB;

[0068] Figure 6 (b) is the imaging result of the method of the present invention at a signal-to-noise ratio of -20dB;

[0069] Figure 7 (a) An imaging result diagram of the method of the present invention based on measured data;

[0070] Figure 7 (b) is the imaging result of the distance Doppler algorithm based on motion compensation and image entropy of the measured data. Detailed Implementation

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0072] Reference Figures 1 to 3 This embodiment describes a method for integrated imaging and calibration of space targets based on joint estimation of translational and rotational parameters in a low signal-to-noise ratio environment. Its focus is on estimating the motion parameters of the space target and performing high-resolution imaging of the movement of scattering points across distance cells. Specifically, it includes:

[0073] Step 1: The ground-based radar acquires the reflected echo from the scattering point of the uniformly rotating target in space, and performs range compression on the scattering point echo to obtain a one-dimensional range image sequence of the uniformly rotating target in space.

[0074] according to Figure 2 The geometric model of the ground-based inverse synthetic aperture radar and the space target shown represents the i-th scattering point (x) on the target rotating at a constant speed.i ,y i The distance between the radar and the radar is expressed as:

[0075]

[0076] Among them, R i (t m ) represents the i-th scattering point (x) on a uniformly rotating target. i ,y i The distance between the radar and R T (t m ) represents the translational component, R R (t m The distance from the target scattering point to the center of rotation is projected onto the radar line of sight, representing the rotation component. m This indicates the azimuth time, i.e., the time between different pulses; (x i ,y i θ(t) represents the two-dimensional coordinates of any scattering point in the target's local coordinate system; m The angle () represents the target's rotation relative to the radar, i.e., the angle at which the target rotates around the center of rotation.

[0077] For a spatially stationary target, the translational component R T (t m ) and rotation angle θ(t) m They are represented as follows:

[0078]

[0079] θ(t m )=ω e t m ,

[0080] Where R0 represents the target at t m =At time 0, the distance between the radar and the center of rotation, v represents the translational velocity, α represents the target's translational acceleration, and ω e This indicates the effective rotational angular velocity.

[0081] Rotation angle θ(t) m The Taylor expansion of ) is:

[0082]

[0083] Then equation (1) can be rewritten as:

[0084]

[0085] The radar transmits a chirp signal, which is a scattered point echo signal after range compression. The expression for (i.e., the one-dimensional range image sequence of a target rotating uniformly in space) is:

[0086]

[0087] Where i = 1, 2, ..., N, N is the number of scattering points on the uniformly rotating target in space, σ i Let B be the scattering coefficient of the i-th scattering point, and T be the bandwidth of the echo signal at the scattering point. obs The observation duration is denoted by rect(·), where rect(·) is the rectangular window function, sinc(·) is the sigma function, j is the imaginary unit, and λ is the carrier wavelength. Here, c is the speed of light, and a0, a1, and a2 are phase coefficients;

[0088]

[0089] Step 2: Perform a generalized Radon Fourier Transform (GRFT) on the one-dimensional range image sequence of the uniformly rotating target in space to estimate the phase coefficients of the echo signal. During the estimation process, Particle Swarm Optimization (PSO) is employed, using the GRFT results of the one-dimensional range image sequence as the fitness function to accelerate the parameter estimation process while improving the accuracy of parameter estimation.

[0090] The scattered point echo signal after distance compression Perform a generalized Radon Fourier transform to estimate the echo signal. The phase coefficients of each order are expressed as follows:

[0091]

[0092] f c This indicates the center frequency of the transmitted signal.

[0093] The phase coefficients of the signal after compression of the echo distance from the spatial scattering point are estimated by performing a GRFT transform. Coefficients of various orders can be obtained. A peak value is generated when the estimated result matches the actual signal.

[0094]

[0095] Particle swarm optimization (PSO) is a widely used heuristic optimization algorithm that primarily relies on information exchange within the swarm to coordinate convergence towards the global optimum. The quality of this information is evaluated by the fitness function f(x). In each iteration, each particle updates its position in the parameter space by combining its historical best solution pbest with the current global optimum gbest. The update formula is:

[0096]

[0097] Where k represents the current iteration number, xi (k) and v i (k) represent the position and velocity of the i-th particle in the k-th iteration, respectively. i (k) represents the historical best position of the i-th particle, gbest(k) represents the historical best position of all current particles, w is the inertia factor, c1 and c2 are learning factors, and r1 and r2 are random numbers between [0,1].

[0098] Equation (6) is used as the fitness function, and The search space is used as the selection space for each particle, which combines the GRFT algorithm and PSO optimization, thus speeding up the search for parameters, improving the accuracy of parameter estimation, and reducing the time for parameter estimation.

[0099] Step 3: Based on the estimation results of the coefficients of each order of the phase signal, obtain the magnitude of the effective rotational angular velocity |ω| of the uniformly rotating target in space. e | and obtained through step two A compensation signal is generated to complete motion compensation.

[0100] Space targets are typically composed of multiple scattering points. Since the coordinates of each scattering point are different, their coefficients are different according to equation (5). Assuming that the two scattering points of the target are p and q, their second-order phase coefficients are expressed as follows:

[0101]

[0102] Subtracting the above equations, we get:

[0103]

[0104] in, Therefore, the effective rotational angular velocity can be expressed as:

[0105]

[0106] While the exact values ​​of the target's translational parameters cannot be accurately obtained from the estimated signal parameters of each order, the translational parameters of the same target should be identical. Therefore, motion compensation can be performed using the estimated phase coefficient of a specific scattering point. Converting the signal to the fast time-frequency domain, the compensation signal can be expressed as:

[0107]

[0108] Where f represents fast time The frequency domain representation of the signal can be achieved by multiplying the echo signal acquired by the ground-based radar with the compensation signal, thus realizing translational compensation. However, it should be noted that this compensation method will change the target's rotation center, i.e., change it to rotation center p, but it will not affect the subsequent imaging results.

[0109] Step 4: Based on the effective rotational angular velocity obtained in Step 3, the translationally compensated echo signal is transformed from the Cartesian coordinate system to the polar coordinate system, and the coordinate position after the format transformation is re-interpolated by Sinc interpolation.

[0110] The echo signal acquired by ground-based radar, after translational compensation, can be expressed as:

[0111]

[0112] Where Tp is the signal duration; T obs ΔR represents the observation duration; rect(·) is the rectangular window function; ΔR p (t m ) is the projection of the distance from point p to the radar, excluding the translation term, onto the radar's line-of-sight direction, and ΔR is given. p (t m )=x p cosθ(t m )+y p sinθ(t m );θ(t m )=ω e t m It is the rotation angle during the observation period.

[0113] The frequency range of a signal can be expressed as f0 is the center frequency of the signal. The echo signal after translational compensation is represented as follows:

[0114]

[0115] Observing the above formula, we can see that f and t m There is nonlinear coupling between them, which can affect the image quality when the imaging angle is too large.

[0116] The signal is then converted to polar coordinate format.

[0117] Let the radial wavenumber of the echo signal Let the range wavenumber k of the echo signal x =k r cosθ(t m Let the azimuth wavenumber k of the echo signal be... y =k r sinθ(t m ). Due to ω eWith precise knowledge, the effective rotation angle θ(t) of the target at each moment can be obtained. m )=ω e t m Accordingly, the k of the signal at each time point can be determined. x and k y The signal after polar coordinate transformation can be represented as:

[0118]

[0119] Where K(k) x ,k y ) represents the signal sampling area, A i This represents the amplitude corresponding to the i-th scattering point.

[0120] Observing the above formula, we can see that the nonlinear time-frequency coupling in the signal phase is eliminated after polar coordinate format conversion. However, at this point, the signal is not uniformly distributed within the fan-shaped region. Therefore, it is difficult to display a clear two-dimensional image using two-dimensional compression. The signal needs to be re-interpolated uniformly into a rectangular region before two-dimensional compression can be used for signal imaging. The interpolation method used is sinc interpolation. First, the range beam is interpolated. Assuming f(x) is the signal before interpolation and f′(x) is the signal after interpolation, the interpolation process can be expressed as:

[0121]

[0122] in This is the interpolation kernel function. This interpolation method can accurately reconstruct band-limited signals. Similarly, after distance interpolation, azimuth interpolation is completed.

[0123] The signal interpolation process is as follows: Figure 3 As shown in the figure, θ=ω e T obs Let represent the total accumulated angle during the imaging process. Let the interpolated range and azimuth wavenumbers be expressed as... and The interpolated signal can then be represented as:

[0124]

[0125] Where A′ represents the amplitude of each scattering point after interpolation. This represents the rectangular region after signal interpolation. The interpolated range beam is represented as follows. azimuth wave number is

[0126] Step 5: Based on the results obtained in Step 4, perform distance and orientation compression to obtain the target imaging result. At the same time, based on the effective rotational angular velocity obtained in Step 3, complete the calibration of the space target, realizing the integrated imaging and calibration process.

[0127] The coupling between the range and azimuth of the interpolated signal has been eliminated, and the signal has been evenly distributed within the rectangular region through interpolation. The interpolated signal is then subjected to... and Two-dimensional compression, at this time the compressed signal energy will be in (x i ,y i Focusing is achieved at () point, and the imaging process is completed.

[0128] Resolution analysis was performed on the imaging results after PFA interpolation, and the range and azimuth resolutions were as follows:

[0129]

[0130] For the interpolated data region and They are respectively represented as

[0131]

[0132] Substituting into the above equation, we can obtain

[0133]

[0134] Calculations have confirmed that this imaging algorithm can achieve an integrated imaging and calibration process without changing the resolution of the imaging results, and can also solve the imaging problem of space targets accumulated over a long period of time.

[0135] To verify the beneficial effects of the present invention, the following simulation experiments were conducted:

[0136] The scattering point model used in the simulation is as follows: Figure 4 As shown, the simulated scattering point center is 460 km away from the radar, and the target's effective rotational angular velocity ω e The velocity is 0.0192 rad / s, and the target's translational velocity and acceleration are 128 m / s² and 112 m / s², respectively. 2 The radar system's transmission parameters are shown in Table 1.

[0137] The cumulative time of the signal can be calculated as T. obs =2000 / 250=8s, the signal rotation angle is θ=0.0192×8=0.1536rad≈8.8°. To demonstrate the imaging effect under different signal-to-noise ratios and highlight the advantages of this invention, two sets of experiments were set with signal-to-noise ratios of 0dB and -20dB respectively. Image contrast was used as the fitness function for motion compensation, combined with the traditional range Doppler algorithm for imaging. The results are as follows. Figure 5 As shown, observation reveals that the traditional RD algorithm exhibits severe blurring at low signal-to-noise ratios (SNRs), particularly at an SNR of 0dB. Figure 5 (a) The defocusing effect is also quite obvious, and the imaging effect is very poor when the signal-to-noise ratio is -20dB. Figure 6 (a) represents the imaging result of the invention at a signal-to-noise ratio of 0 dB. Figure 6 (b) shows the imaging results of this invention at a signal-to-noise ratio of -20dB, demonstrating good imaging quality at both signal-to-noise ratios. The estimated effective rotational angular velocities obtained using GRFT parameter estimation at signal-to-noise ratios of 0dB and -20dB are 0.0196 rad / s and 0.0183 rad / s, respectively. These results indicate that the estimation is very close to the true value.

[0138] Table 1 System Simulation Parameters

[0139]

[0140] Table 2 System parameters of measured data

[0141]

[0142] To verify the practicality of this implementation method, real radar data from the International Space Station was used to verify the method based on ground-based experimental data from the Gaofen-3 satellite. The radar system transmission parameters are shown in Table 2. Since the motion parameters of the space station are unknown, processing the measured data better demonstrates the practicality of the imaging algorithm. Figure 7 The imaging results in (a) demonstrate that the algorithm proposed in this embodiment is successful. By comparison... Figure 7 (a) and (b) show that the measured data obtained under the algorithm of this implementation method have better focusing effect, and the focusing effect of the crossbeam and some special points is significantly better.

[0143] In summary, the integrated method for inverse synthetic aperture radar (INS) imaging and calibration of space targets based on joint estimation of translational and rotational parameters, as described in this invention, fully leverages the parameter estimation accuracy of two-dimensional signals accumulated over a long period, and solves the problems of motion compensation under low signal-to-noise ratio (SNR), the movement of space target scattering points across range cells, and error accumulation. This invention utilizes the generalized Radon Fourier transform to estimate the parameters of the echo phase signal of space targets under low SNR. From the parameter estimation results, the effective rotational angular velocity of the target and the phase parameters of the compensation signal are derived through corresponding mathematical relationships. Then, the signal is compensated, and combined with the estimated effective rotational angular velocity, the polar coordinate format of the signal is converted. Finally, interpolation is performed to perform a two-dimensional Fourier transform to complete the imaging process, while simultaneously using the estimated effective rotational angular velocity to complete the calibration process. This invention can be applied to inverse synthetic aperture radar (INS) imaging and calibration of space targets under low SNR conditions.

[0144] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. An integrated method for ISAR imaging and calibration of space targets based on joint estimation of translational and rotational parameters, characterized in that, include: Range compression is performed on the echoes acquired by the ground-based radar to obtain a one-dimensional range image sequence of a spatially rotating target at a constant speed. The echoes acquired by the ground-based radar are the reflected echoes from the scattering points of the spatially rotating target at a constant speed. A generalized Radon Fourier transform is performed on the one-dimensional range image sequence of the uniformly rotating target in space to estimate the phase coefficients of the echo signal. The magnitude of the effective rotational angular velocity and the compensation signal of a uniformly rotating target in space are calculated using the estimated values ​​of the phase coefficients of each order of the echo signal. The compensation signal is used to perform translational compensation on the echo signal acquired by the ground-based radar. The effective rotational angular velocity is used to transform the compensated echo signal from the Cartesian coordinate system to the polar coordinate system. The transformed signal is then interpolated using Sinc interpolation. The interpolation results are compressed in terms of distance and orientation to obtain the imaging results of a uniformly rotating target in space. The calibration of the uniformly rotating target in space is completed based on the effective rotation angular velocity, realizing the integration of ISAR imaging and calibration of space targets. The one-dimensional range image sequence of the uniformly rotating target in space The expression is: ， in, , The number of scattering points on a target rotating at a constant speed in space. For the first The scattering coefficient at each scattering point The bandwidth of the echo signal at the scattering point. For fast time delay variables, At the speed of light, For location, slow time, For the duration of observation, For rectangular window functions, For the Singer function, The imaginary unit, For carrier wavelength, , and These are the zeroth, first, and second order phase coefficients, respectively. The zeroth, first, and second order phase coefficients , and The expressions are as follows: ， ， ， in, The first point on the uniformly rotating target in space Coordinates of the scattering points Indicates a target rotating at a constant speed in space. The distance between the radar and its rotation center. and Let represent the translational velocity and translational acceleration of a uniformly rotating target in space, respectively. The effective rotational angular velocity of a uniformly rotating target in space; The calculation of the magnitude of the effective rotational angular velocity of a uniformly rotating target in space using estimated values ​​of the phase coefficients of the echo signal includes: Take any two scattering points on a target that rotates at a constant speed in space. and Second-order phase coefficient estimate and : ， ， in, and They represent the scattering points respectively. and x-coordinate and These represent the translational acceleration and effective rotational angular velocity of a target rotating uniformly in space, respectively. Will and Subtraction: ， because Then the magnitude of the effective angular velocity of the uniformly rotating target in space is... : ， in, and They represent the scattering points respectively. and The zeroth-order phase coefficient estimate; The calculation of the compensation signal using estimated values ​​of the phase coefficients of the echo signal includes: The compensation signal is calculated according to the following formula. : ， in, For the fastest time Frequency domain representation, For scattering points The estimated value of the first-order phase coefficient, At the speed of light, This refers to the slow time for the location.

2. The integrated method for ISAR imaging and calibration of space targets based on joint estimation of translational and rotational parameters as described in claim 1, characterized in that, The generalized Radon Fourier transform is performed on the one-dimensional range image sequence of the uniformly rotating target in space to estimate the phase coefficients of the echo signal, including: Perform a generalized Radon Fourier transform on the one-dimensional range image sequence of the uniformly rotating target in space: ， in, This represents the result of the generalized Radon Fourier transform. Indicates the first point on the uniformly rotating target. The distance between each scattering point and the radar Indicates the center frequency of the transmitted signal; Pick The peak value is used as an estimate of the phase coefficients of each order of the echo signal. : 。 3. The integrated method for ISAR imaging and calibration of space targets based on joint estimation of translational and rotational parameters according to claim 2, characterized in that, The estimated values ​​of each phase coefficient of the echo signal are obtained by using the particle swarm optimization method, and the fitness function of the particle swarm optimization is the result of the generalized Radon Fourier transform.

4. The integrated method for ISAR imaging and calibration of space targets based on joint estimation of translational and rotational parameters according to claim 1, characterized in that, Echo signal acquired by ground-based radar after translational compensation The representation of is: ， in, , The number of scattering points on a target rotating at a constant speed in space. For the first The scattering coefficient at each scattering point For rectangular window functions, For the fastest time Frequency domain representation, For echo signal bandwidth, For location, slow time, For the duration of observation, At the speed of light, The first point on the uniformly rotating target in space Coordinates of the scattering points It is the imaginary unit. It is the rotation angle during the observation period.

5. The integrated method for ISAR imaging and calibration of space targets based on joint estimation of translational and rotational parameters according to claim 4, characterized in that, The process of converting the compensated echo signal from Cartesian coordinates to polar coordinates using the effective rotational angular velocity includes: Let the radial wavenumber of the echo signal , Let the range wavenumber of the echo signal , Let the azimuth wavenumber of the echo signal , Expression of the compensated echo signal in polar coordinates for: ， in, Indicates the sampling area of ​​the echo signal. Indicates the first The amplitude of each scattering point.

6. The integrated method for ISAR imaging and calibration of space targets based on joint estimation of translational and rotational parameters according to claim 5, characterized in that, The process of interpolating the converted signal using Sinc interpolation includes: Let the distance of the interpolated echo signal , Let the azimuth wavenumber of the interpolated echo signal be... , Interpolated signal Represented as: ， in, Indicates the first interpolation step The amplitude of each scattering point This represents the rectangular region of the echo signal after the difference.

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