Spatial target ISAR imaging and calibration integration method based on translation and rotation parameter joint estimation

Abstract

The invention discloses a space target ISAR imaging and calibration integration method based on translation and rotation parameter joint estimation, and relates to the technical field of remote sensing and radar imaging. The method aims to solve the problems that in existing space target ISAR imaging, rotation parameter estimation is affected by motion compensation, and space target scattering points are likely to walk over a distance unit under long-time accumulation. According to the method, distance compression is performed on echoes acquired by a ground-based radar, generalized Radon Fourier transform is performed after a one-dimensional distance image sequence is acquired, and then phase coefficients of all orders of echo signals are estimated; calculating a module value and a compensation signal of an effective rotation angular velocity of the spatial uniform-speed rotation target by using the estimated value; carrying out translation compensation on the echo signal by using the compensation signal, converting the compensated echo signal from a Cartesian coordinate system to a polar coordinate system by using the effective rotation angular velocity, and carrying out interpolation; and performing distance and orientation compression on the interpolation result to obtain an imaging result, and completing calibration according to the effective rotation angular velocity to realize integration of space target ISAR imaging and calibration.

Description

Technical Field

[0001] The present invention belongs to the technical field of remote sensing and radar imaging. Background Art

[0002] Inverse synthetic aperture radar (ISAR) has the ability to obtain target information all day and all weather at long distances, and is widely used in the field of surveillance and identification of moving targets such as ships, aircraft, and space satellites. In recent years, with the development of technology, the number of artificial objects in space has increased rapidly, and more accurate space target monitoring technology is needed to ensure space safety. Compared with the radar imaging of ship targets and aircraft targets, the imaging environment of space targets is relatively harsh, that is, the signal-to-noise ratio is low. Usually, to obtain a clear image of the target, a high-precision motion compensation algorithm is required. However, in a low signal-to-noise ratio environment, the existing motion compensation algorithms cannot achieve precise compensation, which affects the imaging effect. To improve the signal-to-noise ratio of the output signal, long-time coherent integration of the echo signal is required. However, the motion speed of space targets is relatively fast, and range cell migration (MTRC) is likely to occur under the condition of long-time integration, resulting in image defocusing. For the problem of range cell migration of scatterers, the existing method is to expand the signal phase after translational motion compensation into a polynomial form, estimate the parameters of the high-order phase signal and then compensate. This expansion process is an approximate process with certain errors. At the same time, it is also affected by translational motion compensation. At the same time, to obtain accurate information of the target, the size of the target needs to be calibrated, and the signal is processed after motion compensation, resulting in error accumulation and affecting the calibration effect. Therefore, the core of inverse synthetic aperture radar imaging of space targets lies in accurate motion compensation algorithms and correction of range cell migration.

[0003] Yang et al. proposed a motion compensation method based on time-varying amplitude in the literature "An Effective Translational Motion Compensation Approach for High-Resolution ISAR Imaging With Time-Varying Amplitude". This algorithm realizes translational motion compensation based on the least mean square error criterion and the algorithm for extracting the energy of prominent points. However, in a low signal-to-noise ratio environment, the mean square error of the echo is greatly affected by noise, and the energy of prominent points may also be submerged by noise, reducing the compensation effect.

[0004] Wei Jin et al. proposed a bistatic ISAR imaging and calibration algorithm based on parameter estimation in the literature "Bistatic ISAR Imaging and Scaling Algorithm Based on the Estimation of Bistatic Factor and Effective Rotation Velocity". By estimating the phase parameters of the signal after translational compensation and then compensating for imaging, this processing method separates the translational and rotational motions, resulting in error accumulation.

[0005] In summary, in the existing space target ISAR imaging technology, there are problems that the estimation of rotational parameters is affected by motion compensation, and the scatter points of space targets are prone to range cell migration under long-term accumulation. Summary of the Invention

[0006] The present invention is to solve the problems that in the existing space target ISAR imaging, the estimation of rotational parameters is affected by motion compensation, and the scatter points of space targets are prone to range cell migration under long-term accumulation. Now, an integrated algorithm for space target ISAR imaging and calibration based on the joint estimation of translational and rotational parameters under low signal-to-noise ratio is provided.

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

[0008] Perform range compression on the echo obtained by the ground-based radar to obtain a sequence of one-dimensional range images of a space uniformly rotating target, where the echo obtained by the ground-based radar is the echo reflected by the scatter points of the space uniformly rotating target;

[0009] Perform a generalized Radon Fourier transform on the sequence of one-dimensional range images of the space uniformly rotating target, and then estimate the phase coefficients of each order of the echo signal;

[0010] Calculate the modulus value of the effective rotation angular velocity and the compensation signal of the space uniformly rotating target by using the estimated values of the phase coefficients of each order of the echo signal;

[0011] Perform translational compensation on the echo signal obtained by the ground-based radar by using the compensation signal, convert the compensated echo signal from the Cartesian coordinate system to the polar coordinate system by using the effective rotation angular velocity, and interpolate the converted signal by means of Sinc interpolation;

[0012] Perform range and azimuth compression on the interpolation result to obtain the imaging result of the space uniformly rotating target, and complete the calibration of the space uniformly rotating target according to the effective rotation angular velocity, realizing the integration of space target ISAR imaging and calibration.

[0013] Furthermore, the one-dimensional range image sequence of the above-mentioned 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 is the scattering coefficient of the i-th scattering point, B is the bandwidth of the echo signal of the scattering point, is the fast time delay variable, c is the speed of light, t m is the azimuth slow time, T obs is the observation duration, rect(·) is the rectangular window function, sinc(·) is the Sigmoid function, j is the imaginary unit, λ is the carrier wavelength, a0, a1 and a2 are the zero-order, first-order and second-order phase coefficients, respectively.

[0016] Furthermore, performing a generalized Radon Fourier transform on the one-dimensional range image sequence of the spatially uniformly rotating target to estimate the various order phase coefficients of the echo signal includes:

[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 generalized Radon Fourier transform result, R i (t m ) represents the distance between the i-th scattering point on the uniformly rotating target and the radar, f c Indicates the center frequency of the transmitted signal;

[0020] Take s GRFT The peak value of (a0, a1, a2) is used as the estimated value of each order phase coefficient of the echo signal

[0021]

[0022] Furthermore, a particle swarm optimization method is used to obtain estimated values of each order phase coefficient of the echo signal, and the fitness function of the particle swarm optimization is the result of the generalized Radon Fourier transform.

[0023] Furthermore, the expressions of the zero-order, first-order and second-order phase coefficients a0, a1 and a2 are:

[0024] a0=R0+x i ,

[0025] a1=v+yi ω e ,

[0026]

[0027] Among them, (x i , y i ) represents the coordinates of the i-th scatterer on the spatially uniformly rotating target, R0 represents the distance between the radar and the center of its rotation at t m = 0, v and α respectively represent the translational velocity and translational acceleration of the spatially uniformly rotating target, and ω e represents the effective rotational angular velocity of the spatially uniformly rotating target.

[0028] Furthermore, the above method for calculating the modulus of the effective rotational angular velocity of the spatially uniformly rotating target using the estimated values of the phase coefficients of each order of the echo signal includes:

[0029] Taking the estimated values of the second-order phase coefficients and

[0030] of any two scatterers p and q on the spatially uniformly rotating target p and x q respectively represent the abscissas of scatterers p and q, and α and ω e respectively represent the translational acceleration and effective rotational angular velocity of the spatially uniformly rotating target;

[0031] Subtracting from :

[0032]

[0033] Since then there is the modulus of the effective rotational angular velocity of the spatially uniformly rotating target |ω e |:

[0034]

[0035] Among them, and respectively represent the estimated values of the zero-order phase coefficients of scatterers p and q.

[0036] Furthermore, the above method for calculating the compensation signal using the estimated values of the phase coefficients of each order of the echo signal includes:

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

[0038]

[0039] where f is the fast time in the frequency domain, is the estimated value of the first-order phase coefficient of the scattering point p, c is the speed of light, and t m is the azimuth slow time.

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

[0041]

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

[0043] Furthermore, the above conversion 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 wave number of the echo signal

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

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

[0047] The expression s(k x , k y 5) of the compensated echo signal in the polar coordinate system is:

[0048]

[0049] where K(k x , k y ) represents the sampling region of the echo signal, and A i represents the amplitude of the i-th scattering point.

[0050] Furthermore, interpolating the converted signal by means of Sinc interpolation includes:

[0051] Let the range of the interpolated echo signal

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

[0053] The interpolated signal is expressed as:

[0054]

[0055] where A′ i represents the amplitude of the i-th scatterer after interpolation, represents the rectangular region of the echo signal after interpolation.

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

[0057] 1. The present invention realizes high-precision motion compensation when the one-dimensional range profile of a space target is submerged by noise in a low signal-to-noise ratio environment.

[0058] 2. The present invention eliminates the range cell migration of a space target caused by a relatively high rotation speed and a long accumulation time, improves the imaging effect of the space target, especially in a low signal-to-noise ratio environment.

[0059] 3. It realizes the integrated process of imaging and calibration, without separate calculations through multiple compensations, reduces error accumulation, and improves the accuracy of calibration.

[0060] The present invention splits the ISAR imaging problem of a space target into two important steps. First, motion compensation is performed in a low signal-to-noise ratio environment. The GRFT algorithm is used to complete the high-precision estimation of the phase coefficient of the echo signal, and translational compensation and the corresponding effective rotational angular velocity are obtained through the estimated signal parameters. On this basis, by converting the echo data into polar coordinate format, and then re-interpolating the echo data region to remove the range-azimuth coupling, and then realizing the integrated operation of imaging and calibration, and finally obtaining the focused and calibrated ISAR image of the space target. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a flowchart of the integrated method for ISAR imaging and calibration of a space target based on joint estimation of translational and rotational parameters;

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

[0063] Figure 3 It is a diagram of the interpolation process in polar coordinate format;

[0064] Figure 4 It is a diagram of the scattering point model of the space target;

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

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

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

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

[0069] Figure 7 (a) It is a diagram of the imaging result of the method of the present invention for measured data;

[0070] Figure 7 (b) It is a diagram of the imaging result of the range-Doppler algorithm with motion compensation and based on image entropy for measured data. Specific embodiments

[0071] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts belong to the scope of protection of the present invention. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0072] Refer to Figures 1 to 3 To specifically illustrate this embodiment, an integrated method for imaging and calibration of a space target based on the joint estimation of translational parameters and rotational parameters in a low signal-to-noise ratio environment described in this embodiment focuses on estimating the motion parameters of the space target and performing high-resolution imaging on the scatter point's cross-range cell migration. Specifically, it includes:

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

[0074] According to Figure 2 the geometric model of the ground-based inverse synthetic aperture radar and the space target shown, for the i-th scatter point (x on the uniformly rotating targeti , y i The distance between () and the radar is expressed as:

[0075]

[0076] where, R i (t m ) represents the distance between the i-th scatterer (x i , y i ) on the uniformly rotating target and the radar, R T (t m ) represents the translational component, and R R (t m ) represents the projection of the distance from the target scatterer to the center of rotation in the radar line-of-sight direction, representing the rotational component. t m represents the azimuth slow time, that is, the time between different pulses; (x i , y i ) represents the two-dimensional coordinates of any scatterer in the local coordinate system of the target; θ(t m ) represents the angle of rotation of the target relative to the radar, that is, the angle by which the target rotates around the center of rotation.

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

[0078]

[0079] θ(t m ) = ω e t m ,

[0080] where, R0 represents the distance between the radar and the center of rotation at t m = 0, v represents the translational velocity, α represents the translational acceleration of the target, and ω e represents the effective rotational angular velocity.

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

[0082]

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

[0084]

[0085] The signal transmitted by the radar is a Chirp signal, and the scattered point echo signal after range compression (i.e., the one-dimensional range profile sequence of a spatially uniformly rotating target) is expressed as:

[0086]

[0087] where \(i = 1, 2, \cdots, N\), \(N\) is the number of scattering points on the spatially uniformly rotating target, \(\sigma\) i is the scattering coefficient of the \(i\)-th scattering point, \(B\) is the bandwidth of the scattering point echo signal, \(T\) obs is the observation duration, \(rect(\cdot)\) is the rectangular window function, \(sinc(\cdot)\) is the sinc function, \(j\) is the imaginary unit, \(\lambda\) is the carrier wavelength, is the fast time delay variable, \(c\) is the speed of light, \(a_0\), \(a_1\) and \(a_2\) are phase coefficients;

[0088]

[0089] Step 2: Perform the Generalized Radon Fourier Transform (GRFT) on the one-dimensional range profile sequence of the spatially uniformly rotating target to estimate the phase coefficients of the echo signal. In the estimation process, the Particle Swarm Optimization (PSO) method is adopted, and the GRFT result of the one-dimensional range profile sequence is used as the fitness function to accelerate the parameter estimation process and improve the parameter estimation accuracy at the same time.

[0090] For the scattered point echo signal after range compression perform the Generalized Radon Fourier Transform, and then estimate the phase coefficients of the echo signal , and its expression is:

[0091]

[0092] \(f\) c represents the center frequency of the transmitted signal.

[0093] Estimate the phase coefficients of the signal after range compression of the spatial scattered point echo through the GRFT transform, and various order coefficients can be obtained. When the estimation result matches the actual signal, a peak will be generated:

[0094]

[0095] The particle swarm algorithm is a widely used heuristic optimization algorithm. It mainly coordinates all individuals to converge to the global optimal solution through information exchange in the group, and the quality of the information is evaluated by the fitness function \(f(x)\). In each iteration, the particle will update its position in the parameter space by combining its own historical best solution \(pbest\) and the current global best solution \(gbest\), and the update formula is:

[0096]

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

[0098] Equation (6) is used as the fitness function, and the search space of is used as the selection space for each particle. In this way, the GRFT algorithm and the PSO optimization method are combined, which not only speeds up the search for parameters but also improves the accuracy of parameter estimation and reduces the time of parameter estimation.

[0099] Step 3: Obtain the modulus |ω e | of the effective rotational angular velocity of the spatially uniformly rotating target based on the estimation results of the coefficients of each order of the phase signal, and form a compensation signal through Step 2 to complete motion compensation.

[0100] Spatial targets usually consist of multiple scattering points. Since the coordinates of each scattering point are different, according to Equation (5), the coefficients of each order are different. Assume that the two scattering points of the target are p and q respectively, and their second-order phase coefficients are expressed as follows:

[0101]

[0102] Subtracting the above equations gives:

[0103]

[0104] Among them, So the effective rotational angular velocity can be expressed as:

[0105]

[0106] The specific values of the translational parameters of the target cannot be accurately obtained from the estimated coefficients of each order of the signal. However, the translational parameters of the same target should be the same. Therefore, the phase coefficient of a certain scattering point estimated can be used for motion compensation. After converting the signal to the fast-time frequency domain, the compensation signal can be expressed as:

[0107]

[0108] Among them, f represents the fast time In the frequency domain representation, translational compensation can be achieved by multiplying the echo signal obtained by the ground-based radar with the compensation signal. However, it should be noted that this compensation method will change the rotation center of the target, that is, it will be changed to rotate around point p, but it has no impact on the subsequent imaging results.

[0109] Step 4: Based on the effective rotational angular velocity obtained in Step 3, convert the echo signal after translational compensation from the Cartesian coordinate system to the polar coordinate system, and re-interpolate the coordinate positions after format conversion by means of Sinc interpolation.

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

[0111]

[0112] where Tp is the signal time width; T obs is 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 after removing the translational term in the direction of the radar line of sight, and there is ΔR p (t m ) = x p cosθ(t m ) + y p sinθ(t m ); θ(t m ) = ω e t m is the rotation angle within the observation time.

[0113] The frequency range of the signal can be expressed as f0 is the center frequency of the signal, and the expression form of the echo signal after translational compensation is:

[0114]

[0115] Observing the above formula, it can be seen that there is a non-linear coupling between f and t m When the imaging angle is too large, it will affect the imaging quality.

[0116] Next, perform the conversion of the polar coordinate format for the signal.

[0117] Let the radial wavenumber of the echo signal Let the range wavenumber of the echo signal be k x = k r cosθ(t m ), let the azimuth wavenumber of the echo signal be k y = k r sinθ(t m ). Since ω ePrecisely known, the effective rotation angle θ(t m ) = ω e t m , and accordingly, the k x and k y of the signal at each moment can be determined. Then the signal after polar coordinate format conversion can be expressed as:

[0118]

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

[0120] Observing the above formula, it can be obtained that after polar coordinate format conversion, the non-linear time-frequency coupling in the signal phase is eliminated. However, at this time, the signal is non-uniformly distributed in the fan-shaped area. At this time, it is very difficult to display a clear two-dimensional image by two-dimensional compression. The signal needs to be re-uniformly interpolated into the rectangular area before two-dimensional compression can be used for signal imaging. The interpolation method uses the sinc interpolation method. First, interpolate the range beam. Assume that f(x) is the signal before interpolation and f′(x) is the signal after interpolation. Then the interpolation process can be expressed as:

[0121]

[0122] where is the interpolation kernel function. This interpolation method can accurately reconstruct the band-limited signal. After range interpolation, azimuth interpolation is completed in the same way.

[0123] The interpolation process of the signal is as Figure 3 shown in the figure. In the figure, θ = ω e T obs represents the total accumulation angle in the imaging process. Let the interpolated range and azimuth wavenumbers be denoted as and respectively. Then the interpolated signal can be expressed as:

[0124]

[0125] where A′ represents the amplitude of each scattering point after interpolation, represents the rectangular area after signal interpolation. The interpolated range beam is denoted as and the azimuth wavenumber is

[0126] Step Five: Perform range and azimuth compression based on the results obtained in Step Four to obtain the imaging result of the target. At the same time, complete the calibration of the space target according to the effective rotational angular velocity obtained in Step Three, and realize the integrated process of imaging and calibration.

[0127] The coupling relationship between the range and azimuth of the interpolated signal has been eliminated, and it has been evenly distributed within the rectangular region through interpolation. Perform a two-dimensional compression on the interpolated signal with respect to and . At this time, the energy of the compressed signal will be focused at (x i , y i ), and the imaging process is completed.

[0128] Perform resolution analysis on the imaging result after PFA interpolation. Its range and azimuth resolutions are respectively:

[0129]

[0130] For the interpolated data region and , they are respectively expressed as

[0131]

[0132] Substituting into the above formula, we can get

[0133]

[0134] Through calculation, it can be confirmed that this imaging algorithm can realize the integrated process of imaging calibration, and does not change the resolution of the imaging result. At the same time, it can solve the imaging problem of space targets under long-term accumulation.

[0135] To verify the beneficial effects of the present invention, the following simulation experiments are carried out:

[0136] The scatter point model used in the simulation is as Figure 4 shown. The distance between the center of the scatter point in the simulation and the radar is 460 Km. The effective rotational angular velocity ω e of the target is 0.0192 rad / s. The translational velocity and acceleration of the target are 128 m / s and 112 m / s 2 respectively. The transmission parameters of the radar system are shown in Table 1.

[0137] By calculation, the cumulative time of the signal can be obtained as T obs = 2000 / 250 = 8 s, and the rotational angle of the signal is θ = 0.0192 × 8 = 0.1536 rad ≈ 8.8°. To show the imaging effects at different signal-to-noise ratios and highlight the advantages of the present invention, two groups of experiments are set at signal-to-noise ratios of 0 dB and -20 dB respectively. Use image contrast as the fitness function to perform motion compensation and combine with the traditional range-Doppler algorithm to form an imaging algorithm. The results are as Figure 5 shown. By observation, it can be seen that serious blurring occurs in the traditional RD algorithm at low signal-to-noise ratios. When the signal-to-noise ratio is 0 dB, that isFigure 5 (a), the defocusing effect is also relatively obvious. When the signal-to-noise ratio is -20 dB, the imaging effect is very poor. Figure 6 (a) shows the imaging result of the present invention at a signal-to-noise ratio of 0 dB. Figure 6 (b) shows the imaging result of the present invention at a signal-to-noise ratio of -20 dB. It can be seen that the imaging quality is very good at both signal-to-noise ratios. The estimated values of the effective rotational angular velocity obtained by using GRFT for parameter estimation at signal-to-noise ratios of 0 dB and -20 dB are 0.0196 rad / s and 0.0183 rad / s respectively. The above results indicate that its estimation effect 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 embodiment, the real radar data of the International Space Station is used to verify the method of this embodiment in the ground experimental data of the Gaofen-3 satellite. The system emission parameters of the radar are shown in Table 2. Since there is no prior information on the motion parameters of the space station, the processing of the measured data can better reflect the practicality of the imaging algorithm. Through Figure 7 The imaging result of (a) shows that the algorithm proposed in this embodiment is successful. By comparing Figure 7 (a) and (b), it can be seen that the focusing effect of the result obtained from the measured data under the algorithm of this embodiment is better, and the focusing effect of the crossbar and some special display points is significantly better.

[0143] In summary, a space target inverse synthetic aperture radar imaging and calibration integration method based on joint estimation of translational and rotational parameters described in the present invention gives full play to the parameter estimation accuracy of the two-dimensional signal under long-term accumulation, solves the problems of motion compensation at low signal-to-noise ratio, range cell migration of space target scatterers, and error accumulation. The present invention uses the generalized Radon Fourier transform to estimate the parameters of the echo phase signal of the space target at low signal-to-noise ratio, obtains the effective rotational angular velocity of the target and the phase parameters of the compensation signal from the parameter estimation results through corresponding mathematical relationships, then compensates the signal, and combines the estimated effective rotational angular velocity to complete the polar coordinate format conversion of the signal, and then interpolates to perform the two-dimensional Fourier transform to complete the imaging process, and at the same time combines the estimated effective rotational angular velocity to complete the calibration process. The present invention can be applied to space target inverse synthetic aperture radar imaging and calibration at low signal-to-noise ratio.

[0144] Although the present 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 present invention. Accordingly, it should be understood that numerous modifications may be made to the exemplary embodiments, and other arrangements may be devised, without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in connection with a separate embodiment may 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 Including: Performing range compression on the echo obtained by the ground-based radar to obtain a sequence of one-dimensional range profiles of a spatially uniformly rotating target, where the echo obtained by the ground-based radar is the echo reflected by the scatterers of the spatially uniformly rotating target; Performing a generalized Radon Fourier transform on the sequence of one-dimensional range profiles of the spatially uniformly rotating target, and then estimating the phase coefficients of each order of the echo signal; Calculating the modulus of the effective rotational angular velocity of the spatially uniformly rotating target and the compensation signal by using the estimated values of the phase coefficients of each order of the echo signal; Performing translational compensation on the echo signal obtained by the ground-based radar by using the compensation signal, converting the compensated echo signal from the Cartesian coordinate system to the polar coordinate system by using the effective rotational angular velocity, and interpolating the converted signal by means of Sinc interpolation; Performing range and azimuth compression on the interpolation result to obtain the imaging result of the spatially uniformly rotating target, and completing the calibration of the spatially uniformly rotating target according to the effective rotational angular velocity, so as to realize the integration of ISAR imaging and calibration of space targets.

2. The integrated method for ISAR imaging and calibration of space targets based on the joint estimation of translational and rotational parameters according to claim 1, wherein, The one-dimensional range image sequence of the spatially uniformly rotating target has the following expression: where \(i = 1, 2, \cdots, N\), \(N\) is the number of scatterers on the spatially uniformly rotating target, \(\sigma\) i is the scattering coefficient of the \(i\)-th scatterer, \(B\) is the bandwidth of the scatterer echo signal, is the fast time delay variable, \(c\) is the speed of light, \(t\) m is the azimuth slow time, \(T\) obs is the observation duration, \(rect(\cdot)\) is the rectangular window function, \(sinc(\cdot)\) is the sinc function, \(j\) is the imaginary unit, \(\lambda\) is the carrier wavelength, and \(a_0\), \(a_1\), and \(a_2\) are the zero-order, first-order, and second-order phase coefficients, respectively.

3. The integrated method for spatial target ISAR imaging and calibration based on the joint estimation of translational and rotational parameters according to claim 2, characterized in that The performing a generalized Radon Fourier transform on the sequence of one-dimensional range profiles of the spatially uniformly rotating target, and then estimating the phase coefficients of each order of the echo signal, includes: Performing a generalized Radon Fourier transform on the sequence of one-dimensional range profiles of the spatially uniformly rotating target: Among them, s GRFT (a0, a1, a2) represents the result of the generalized Radon Fourier transform, and R i (t m ) represents the distance between the i-th scattering point on the uniformly rotating target and the radar, and f c represents the center frequency of the transmitted signal; Take s GRFT Take the peak value of (a0, a1, a2) as the estimated value of each order phase coefficient of the echo signal 4. The integrated method for ISAR imaging and calibration of space targets based on the joint estimation of translational and rotational parameters according to claim 3, characterized in that, Using a particle swarm optimization method to obtain the estimated values of the phase coefficients of each order of the echo signal, where the fitness function of the particle swarm optimization is the result of the generalized Radon Fourier transform.

5. The integrated method for space target ISAR imaging and calibration based on combined estimation of translational and rotational parameters according to claim 2, 3 or 4, characterized in that The expressions of the zero-order, first-order, and second-order phase coefficients a0, a1, and a2 are respectively: a0 = R0 + x i , a1 = v + y i ω e , Among them, (x i , y i ) represents the coordinates of the i-th scattering point on the spatially uniformly rotating target, R0 represents the distance between the radar and its rotation center at t m = 0, v and α respectively represent the translational velocity and translational acceleration of the spatially uniformly rotating target, and ω e represents the effective rotation angular velocity of the spatially uniformly rotating target.

6. The integrated method for spatial target ISAR imaging and calibration based on the joint estimation of translational and rotational parameters according to claim 1, characterized in that The calculating the modulus of the effective rotational angular velocity of the spatially uniformly rotating target by using the estimated values of the phase coefficients of each order of the echo signal, includes: Obtain the estimated values of the second-order phase coefficients of any two scattering points p and q on a spatially uniformly rotating target and where x p and x q represent the abscissas of the scattering points p and q respectively, and α and ω e represent the translational acceleration and the effective rotational angular velocity of the uniformly rotating target in space respectively; Subtract from : Since there is a modulus value |ω e | of the effective rotational angular velocity of the space-uniformly rotating target: Among them, and respectively represent the estimated values of the zero-order phase coefficients of the scattering points p and q.

7. The integrated method for ISAR imaging and calibration of space targets based on the joint estimation of translational and rotational parameters according to claim 6, characterized in that The calculating the compensation signal by using the estimated values of the phase coefficients of each order of the echo signal, includes: Calculate the compensation signal s according to the following formula p ′(f,t m ): where f is the fast time in the frequency domain, is the estimated value of the first-order phase coefficient of scatterer p, c is the speed of light, and t m is the azimuth slow time.

8. The integrated method for space target ISAR imaging and calibration based on the combined estimation of translational and rotational parameters according to claim 1, characterized in that The echo signal s(f, t m ) obtained by the ground-based radar after translational compensation is expressed as: where \(i = 1,2,\cdots,N\), \(N\) is the number of scatterers on the spatially uniformly rotating target, \(\sigma\) i is the scattering coefficient of the \(i\)-th scatterer, \(rect(\cdot)\) is the rectangular window function, \(f\) is the frequency-domain expression of the fast time , \(B\) is the bandwidth of the echo signal, \(t\) m is the azimuth slow time, \(T\) obs is the observation duration, \(c\) is the speed of light, \((x\) i , \(y\) i ) represents the coordinates of the \(i\)-th scatterer on the spatially uniformly rotating target, \(j\) is the imaginary unit, \(\theta(t\) m ) is the rotation angle within the observation time.

9. The integrated method for ISAR imaging and calibration of space targets based on the joint estimation of translational and rotational parameters according to claim 8, characterized in that, The converting the compensated echo signal from the Cartesian coordinate system to the polar coordinate system by using the effective rotational angular velocity, includes: Let the radial wave number of the echo signal Let the range wavenumber of the echo signal be k x = k r cosθ(t m ), Let the azimuth wavenumber of the echo signal be k y = k r sinθ(t m ), The expression of the compensated echo signal in the polar coordinate system s(k x , k y ) is as follows: Among them, K(k x ,k y ) represents the sampling region of the echo signal, and A i represents the amplitude of the i-th scattering point.

10. The integrated method for ISAR imaging and calibration of space targets based on the joint estimation of translational and rotational parameters according to claim 9, characterized in that The interpolating the converted signal by means of Sinc interpolation, includes: Let the range of the interpolated echo signal Let the azimuth wavenumber of the interpolated echo signal Interpolated signal is expressed as: Among them, A i ' represents the amplitude of the i-th scattered point after interpolation, represents the rectangular region of the echo signal after the difference.

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