A method for error calibration of ground-based stepped-frequency radar imaging system for space targets

Abstract

The present invention relates to a method for calibrating the system error of a ground-based stepped-frequency radar for imaging a space target, and belongs to the field of radar imaging technology. First, based on the characteristics of a stepped-frequency chirp radar and high-speed motion, a complex coupled error echo signal model of system error and motion error is established. Then, based on the influence of the error form on different processing steps, the error is decoupled into sub-band range imaging error, sub-band azimuth imaging error, and full-sub-band composite imaging error. Then, the gradient of the error is solved by the image entropy after sub-band range imaging, sub-band azimuth imaging, and full-sub-band composite imaging, and the error is solved respectively using an adaptive moment estimation method. Finally, the above steps are looped, and the error is calibrated iteratively multiple times to obtain a high-quality image.

Description

Technical Field

[0001] The invention relates to a method for calibrating an error of a ground-based stepped-frequency radar for a space target imaging system, and belongs to the technical field of radar imaging. Background Art

[0002] Ground-based radar is an effective means of detecting and imaging air and space targets. Improving resolution allows for more detailed target information, facilitating classification and identification. Achieving high resolution requires the radar to transmit wide-bandwidth signals. Transmitting instantaneous wide-bandwidth signals, according to the Nyquist sampling theorem, requires a higher sampling rate to match them. This poses a significant challenge to system hardware such as analog-to-digital conversion and direct digital synthesis. Frequency-stepped signals offer the advantages of instantaneous narrow bandwidth and synthetically wide bandwidth, and are widely used in radar applications.

[0003] The frequency-stepped chirp signal has the advantages of both frequency-stepped and chirp signals. On the one hand, it reduces the difficulty of the system in transmitting large-bandwidth signals through the form of carrier frequency stepping. On the other hand, each sub-pulse has a large time-bandwidth product, which balances the contradiction between effective range and range resolution.

[0004] However, the ambiguity of stepped-frequency frequency modulated signals makes grating lobes very likely to occur when acquiring high-resolution range images. Grating lobes can be suppressed in two main ways: first, by designing appropriate waveform parameters to avoid information loss and redundancy in the synthesized broadband; second, by correcting for various errors in the signal to achieve perfect coherent synthesis of multiple sub-band signals. The second point is more important for data processing.

[0005] Stepped-frequency radars require different local oscillators and sub-links to transmit different sub-pulses, making it difficult to achieve strict timing and phase consistency, leading to systematic errors. Internal calibration methods have limited applicability, and observations of space targets typically lack isolated strong points, necessitating the development of self-calibration techniques based on radar data.

[0006] Furthermore, stepped-frequency chirp radars synthesize a wide-bandwidth signal from multiple sub-pulses. This means that the burst repetition rate is smaller than the sub-pulse repetition rate. For high-speed space targets, not only must inter-burst motion errors be considered, but also the inter-sub-pulse and intra-sub-pulse motion errors caused by high-speed motion. However, limited research is currently underway on the coupled errors between system errors and target motion errors that occur in practical applications.

[0007] In summary, there is currently no algorithm that can calibrate this complex coupling error to obtain better images. It is necessary to study a technology for high-speed space target imaging and coupling error self-calibration based on minimum entropy stepped frequency chirp radar. Summary of the Invention

[0008] In view of this, the present invention proposes a method for calibrating the error of a ground-based stepped-frequency radar for a space target imaging system, which can obtain high-precision space target imaging results.

[0009] The technical solution of the present invention is:

[0010] A method for calibrating errors of a ground-based stepped-frequency radar imaging system for a space target, the method comprising the following steps:

[0011] The first step is to establish a coupling error echo signal model. The coupling error echo signal model includes four errors: system phase error, starting sampling distance error, intra-pulse quadratic phase error, and first-order and zero-order phase errors caused by motion.

[0012] In the second step, the four errors in the coupled error echo signal model established in the first step are decoupled into three errors, namely, the sub-band range imaging error, the sub-band azimuth imaging error, and the full sub-band composite imaging error.

[0013] In the third step, sub-band range imaging is performed on the space target echo data collected by the ground-based stepped-frequency radar, and the gradient of the image entropy after sub-band range imaging with respect to the sub-band range imaging error obtained in the second step is calculated. Then, the adaptive moment estimation method is used to solve the sub-band range imaging error according to the calculated gradient.

[0014] The fourth step is to perform sub-band azimuth imaging on the data after sub-band range imaging, and calculate the gradient of the image entropy after sub-band azimuth imaging with respect to the sub-band azimuth imaging error obtained in the second step. Then, the adaptive moment estimation method is used to solve the sub-band azimuth imaging error based on the calculated gradient.

[0015] In the fifth step, full sub-band synthetic imaging is performed on the data after sub-band azimuth imaging, and the gradient of the image entropy after full sub-band synthetic imaging with respect to the full sub-band synthetic imaging error obtained in the second step is calculated. Then, the full sub-band synthetic imaging error is solved based on the calculated gradient using the adaptive moment estimation method.

[0016] Step 6: Repeat steps 3 to 5 until the image is focused and the final image is obtained.

[0017] In the first step, the coupling error echo signal model established is:

[0018]

[0019] Among them, A q (·) is the amplitude error, is the system phase error of sampling number n, is the starting sampling distance error of sampling number n, is the quadratic phase error within the pulse with sampling number n, The first and zero-order phase errors caused by the motion of sampling number n; is the fast frequency, t n is the slow time with sampling number n, n = 1, 2, 3, ..., N, N is the number of azimuth sampling;

[0020] In the second step, the sub-band range imaging error is:

[0021]

[0022] in, is the amplitude error, For The relevant polynomial coefficients;

[0023] The sub-band azimuth imaging error is:

[0024]

[0025] Among them, f q is the carrier frequency of the qth sub-pulse; q = 1, 2, 3, ..., Q, Q is the total number of sub-bands; p = 1, 2, 3, ..., P, P is the polynomial order of the error; For t n The relevant polynomial coefficients;

[0026] The full sub-band composite imaging error is:

[0027]

[0028] in, is a constant amplitude error, p = 0 or 1, For The relevant polynomial coefficients;

[0029] In the third step, the formula for obtaining the gradient is:

[0030]

[0031]

[0032] Among them, X 1,q is the image after sub-band range imaging, En(X 1,q ) is the image entropy of the image after sub-band range imaging, is the error parameter, is the error parameter, S(X 1,q ) is the total energy of the image after sub-band range imaging, t q is the azimuth sampling time corresponding to the qth sub-pulse, For fast time, x 1,q It is the sub-element of the image after sub-band range imaging; is the inverse Fourier transform, is the data before sub-band range imaging;

[0033] In the fourth step, the formula for obtaining the gradient is:

[0034]

[0035] Among them, X 2,q is the image after sub-band azimuth imaging, En(X 2,q ) is the image entropy of the image after sub-band azimuth imaging, S(X 2,q ) is the total energy of the image after sub-band azimuth imaging, is the azimuth slow frequency, x 2,q is the sub-element of the image after sub-band azimuth imaging, is the Fourier transform, is the data before sub-band azimuth imaging;

[0036] In the fifth step, the formula for obtaining the gradient is:

[0037]

[0038]

[0039] Among them, X 3,q is the image after full sub-band synthesis imaging, En(X 3,q ) is the image entropy of the image after full sub-band synthesis imaging, S(X 3,q ) is the total energy of the image after full sub-band synthesis imaging, This is the data before full sub-band synthesis imaging;

[0040] The update formula of the adaptive moment estimation method is:

[0041]

[0042] Where e is the parameter to be estimated, H(e) is the gradient, m1 and m2 are the first-order and second-order moment estimates, respectively, k is the number of iterations, β1, β2 and α are adjustable parameters, and ε>0.

[0043] Beneficial effects

[0044] This invention accurately models the coupling error between a stepped-frequency radar system and high-speed moving targets, enabling high-resolution imaging of high-speed space targets. The invention decomposes the coupling error into sub-band range imaging error, sub-band azimuth imaging error, and full-sub-band composite imaging error. The gradient of the entropy with respect to the error is calculated in a step-by-step manner. This error is then calculated and compensated using an adaptive moment estimation method, achieving self-calibration of the coupling error. Frequency-stepped signals offer the advantages of instantaneous narrowband and synthetic wideband, enabling high-resolution imaging of space targets and have been widely used in the radar field. However, the echoes from frequency-stepped-frequency observations of space targets contain errors resulting from the coupling of systematic errors and errors from the target's high-speed motion, making imaging difficult using traditional methods. Therefore, this invention proposes a minimum entropy-based technique for high-speed space target imaging and coupling error self-calibration using a stepped-frequency chirp radar. First, based on the characteristics of stepped-frequency chirp radar and high-speed motion, a complex coupling error echo signal model of systematic and motion errors is established. Then, based on the influence of the error forms on different processing steps, the error is decoupled into sub-band range imaging error, sub-band azimuth imaging error, and full-sub-band composite imaging error. The gradient of the image entropy with respect to the error after sub-band range imaging, sub-band azimuth imaging, and full-sub-band composite imaging is then calculated, and the error is solved using an adaptive moment estimation method. Finally, the above steps are looped through multiple iterations to calibrate the error and obtain high-quality images. The proposed method aims to provide a robust high-resolution imaging algorithm for high-speed space targets using stepped-rate chirp radar, with potential applications in fields such as ground-based radar observation of space targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is the frequency domain representation of the error;

[0046] Figure 2 is the time domain representation of the error;

[0047] Figure 3 This is the flow chart of the coupling error self-calibration algorithm;

[0048] Figure 4 This is a satellite dot matrix simulation diagram, where Figure 4 (a) is the simulation point target, Figure 4 (b) is the imaging result without error correction. Figure 4 (c) is the imaging result after only performing average range correction. Figure 4 (d) is the uncorrected sub-band error imaging result, Figure 4 (e) is the imaging result of this method;

[0049] Figure 5 This is a graph showing how entropy changes with the processing flow. DETAILED DESCRIPTION

[0050] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] Example

[0052] Each frame of the frequency-stepped chirp signal consists of a group of Q sub-pulses with linear carrier frequency jumps. Assuming that the starting carrier frequency is f0 and the step size is Δf, the carrier frequency of the qth sub-pulse is f q =f0+qΔf, q=0,1,...,Q-1, with f q The expression of the transmitted signal with carrier frequency is:

[0053]

[0054] here For quick time, is the chirp baseband signal, T pulse is the pulse width, γ is the frequency modulation slope, rect(·) is the rectangular window function, and the sub-pulse bandwidth Since the spectra of different sub-pulses overlap, the maximum synthesized bandwidth that can be obtained for a frame of signal is B=B0+(Q-1)Δf.

[0055] If the target delay corresponding to the n=gQ+q sub-pulse in azimuth is is the frame index, t n =nT PRT , T PRT is the repetition time of the sub-pulse. n =f q , then the received echo is

[0056]

[0057] σ is the complex scattering intensity of the target. After matched filtering, its spectrum is

[0058]

[0059] Here (·) * It is a conjugate operator. It can be seen that after the matched filtering, only the first-order phase and the zero-order phase remain. The coupling error between the target motion and the system error is explained below.

[0060] Error Modeling: In actual radar systems, the nonideal characteristics of components such as amplifiers and filters lead to distortion in the radar system's amplitude-frequency and phase-frequency characteristics. This error can be modeled as a polynomial. Furthermore, because the system operates in frequency-hopping mode, the local oscillator and link used to transmit sub-pulses of different carrier frequencies vary, resulting in channel characteristics that are dependent on the carrier frequency index q. Furthermore, the actual and nominal values ​​of the frequency sources of the radar system's transmit and trigger signals may differ. Consequently, there will be an error between the designed value and the actual start sampling time, which is a linear and constant phase error.

[0061] For motion error, due to high-speed moving targets, motion will introduce phase into the pulse. Assuming the direction away from the radar is positive, since the target motion is usually continuously changing, the echo form becomes:

[0062]

[0063] Here is the scaling factor caused by high-speed motion, The reason for the approximation is that the intra-pulse changes caused by target motion are small during the radar observation time, so the same value can be used for intra-pulse phase compensation. The spectrum after matched filtering is

[0064]

[0065] Since the speed is changing, both ρ and time delay τ are related to the slow time t n High-speed motion can cause spectral shifts and amplitude scaling, but these are usually negligible. The secondary phase of f will cause HRRP waveform distortion and affect the quality of two-dimensional imaging. Therefore, it is the main compensation quantity for the intra-pulse error. The second and third terms are related to f q The first and zero-order phase errors will not cause waveform distortion.

[0066] After the above analysis, the system error of the step frequency and the motion error of the target will form a complex coupling error, which is expressed as

[0067]

[0068] Where A q (·) is the amplitude error, They represent the system phase error, the initial sampling distance error, the quadratic phase error within the pulse, and the first and zeroth order phase errors caused by motion, respectively.

[0069] Figure 1 Shown are the phase-frequency and amplitude-frequency diagrams of broadband synthesis using two sub-pulses. Figure 1 In (a), the ideal phase splicing result should be continuous and have the same slope, without second-order or higher-order phase errors. However, the first sub-pulse contains second-order and higher-order phase errors, resulting in phase nonlinearity. The second sub-pulse contains first-order and zero-order phase errors, resulting in a variable phase slope and a phase jump during splicing. Figure 1 In (b), the amplitude spectrum of the first sub-pulse is ideal, while the second sub-pulse has polynomial amplitude errors, so broadband synthesis cannot be achieved.

[0070] Figure 2The ideal one-dimensional range image and the one-dimensional range image with errors are shown. Figure 2 In (a), the dotted line and the solid line represent the one-dimensional range image of a low-resolution single sub-band with no error and the one-dimensional range image of the perfect synthesis of two sub-bands, respectively. It can be seen that the main lobe of the dotted line is narrower, indicating that broadband synthesis can improve the resolution. Figure 2 (b) is the one-dimensional range image of the first subband when there is an error. Even-order phase errors of the second order and above will cause symmetrical sidelobe rises, while odd-order phase errors will cause sidelobe asymmetry. Figure 2 (c) is the one-dimensional range image of the second subband when there is an error. The amplitude error causes symmetrical distortion of the sidelobes, and the primary phase error causes the peak position to shift. Figure 2 (d) Figure 2 (b) and Figure 2 (c) The one-dimensional range image obtained by synthesizing the two sub-band spectra is obviously different from Figure 2 The high-resolution one-dimensional range image in (a) exhibits significant phase differences. It can also be seen that regular grating lobes appear at specific locations. This is due to the ambiguity function of the stepped-rate chirp signal. Therefore, the key to achieving ideal imaging results with stepped-rate chirp signals lies in correcting these various errors.

[0071] Error decoupling and self-calibration: According to the previous description, the relationship between the qth sub-band echo signal with error and the two-dimensional image is modeled as

[0072] Y q =E q ⊙AX q B+N

[0073] Where A and B are the distance Fourier transform matrix and the azimuth inverse Fourier transform matrix respectively, and Y q and X q are the echo and image respectively, ⊙ is the Hadamard product operator, N is the noise, E q is the coupling error, expressed as

[0074]

[0075] It is worth mentioning that X q After two-dimensional accumulation, it has a higher signal-to-noise ratio. The use of stepped frequency chirp signals to achieve high-resolution range can be considered as obtaining a larger bandwidth by splicing multiple sub-band spectra to achieve high-resolution imaging, that is, Here (·) H is the Hermite operator.

[0076] Image entropy is an important indicator for image quality evaluation. The smaller its value, the better the image quality. It is defined as

[0077]

[0078] The total energy of the image is is a constant. The imaging problem can be modeled as

[0079]

[0080] The computational cost of the search-based method has an exponential relationship with the number of parameters. Therefore, it is necessary to decouple the errors and simplify the number of parameter calculations each time.

[0081] Sub-band range imaging error: within each sub-band The second and above phase errors and the first and above amplitude errors will affect the waveform distortion after pulse compression. These errors do not change with t n All data of each sub-band can be used for error estimation and correction, that is, the optimization problem is:

[0082]

[0083] Sub-band azimuth imaging error

[0084] Both target motion and system errors can cause This coupling error is difficult to solve directly. Although there are many similar envelope alignment methods commonly used in ISAR, on the one hand, these methods are simpler to model the error than the coupling error model considered in this paper. On the other hand, the compensation accuracy of envelope alignment is difficult to achieve the phase accuracy required for synthesizing high-resolution images of stepped frequency chirp radar. Two-dimensional images have a higher signal-to-noise ratio and better entropy performance. In addition, each subband has more precise error calibration requirements in two-dimensional imaging. Therefore, the objective function can be modeled as

[0085]

[0086] Here Contains t n The error of the change,

[0087]

[0088] Full subband synthetic imaging error: still exists after the first two steps of error correction The non-time-varying first-order and zero-order phases of the θ are directly synthesized into high-resolution images, which will affect the accumulated gain, cause the appearance of grating lobes and image degradation. This error is called synthetic imaging error. Therefore, the optimization problem can be modeled as

[0089]

[0090] Here Since the time-varying error has been corrected before, only the time-invariant The first-order and zero-order phases can therefore be simplified. The error estimated in this step is expressed as

[0091]

[0092]

[0093] It is worth mentioning that It can be regarded as a time-invariant error, that is, it is contained in Inside.

[0094] After three steps of error decoupling, the final error estimation result can be obtained as

[0095]

[0096] The motion error and system error modeled previously are included and decoupled in three different processing steps. The image after the three-step correction is represented as

[0097]

[0098] In order to obtain the decoupled error and compensate it, the most direct method is to perform parameter traversal search. Although the proposed decoupling method can reduce the parameter dimension, it still requires a large amount of calculation. Obviously, it is not realistic to directly solve the analytical solution. Therefore, this paper uses the Adam algorithm with a faster convergence rate to solve it. The gradient is expressed as follows

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] For each of the three steps, the solution can be completed using adaptive moment estimation (Adam). The update formula of Adam is

[0105]

[0106] Where e is the parameter to be estimated, m1 and m2 are the first-order and second-order moment estimates respectively, k is the number of iterations, β1, β2 and α are adjustable parameters, ε>0, Adam applies the momentum method and can adaptively adjust the gradient descent rate.

[0107] Figure 3 The corresponding relationship between the decoupling error and the correction algorithm is shown in the figure, and an intuitive image is also presented.

[0108] 1) Sub-band pulse compression error estimation: This step utilizes the influence of the quadratic and higher phase-frequency responses and the primary and higher amplitude responses on pulse compression. Each sub-band is processed uniformly to correct the consistent time-invariant errors within the sub-band. After this step, the undistorted range image of all sub-bands is obtained.

[0109] 2) Sub-band 2D imaging error estimation: This step exploits the impact of time-varying motion errors on each sub-band data and simultaneously corrects the time-varying envelope and phase errors shared by all sub-bands through sub-band 2D imaging. After this step, a distortion-free low-resolution 2D image is obtained for each sub-band.

[0110] 3) Synthesis Error Correction: This step exploits the effect of residual error on wideband synthesis, or coherent accumulation. Entropy, as an image evaluation metric, can also measure the effectiveness of accumulation. Lower entropy values ​​indicate better accumulation of multiple sub-band images. After this step, a high-resolution 2D image is obtained.

[0111] It's worth noting that the proposed technique also works with stepped-rate chirp radar data, which only has a few frames. Even if target motion prevents the formation of a synthetic aperture, entropy can still measure the coherent accumulation effect, thereby enabling self-calibration of coupling errors. Furthermore, the error model is also applicable to other forms, such as sinusoidal errors, which can also be addressed using this technique.

[0112] Example

[0113] Using computer simulation, a satellite electron system consisting of 64 points was set up. Figure 4 (a). Motion parameters were set so that the rotation could form a synthetic aperture, enabling two-dimensional imaging. Additive white Gaussian noise was added to the image to maintain a signal-to-noise ratio of 0 dB. The simulated radar parameters are shown in Table 1.

[0114] Table 1 Simulation experiment parameters

[0115] Radar parameters Numerical unit Starting center frequency 3.5 GHz bandwidth 250 MHz Frequency step 200 MHz Number of subbands 4 indivual Pulse repetition frequency 800 Hz Pulse width 6.25 us Target distance 482 Km Target speed 1400 m / s acceleration 100 <![CDATA[m / s 2 ]]>

[0116] Table 2 Evaluation of simulation experiment test results

[0117] Figure No. Figure 4 (c) Figure 4 (c) Figure 4 (d) Figure 4 (e) entropy 5.3103 5.6782 5.7091 4.5182

[0118] Figure 4 (b) Uncorrected sub-band error, obvious range grating lobe, Figure 4 (c) Only simple average range image correction is performed, and the motion compensation accuracy is difficult to meet the requirements of spectrum synthesis, resulting in image quality degradation. Figure 4(d) The error between the uncalibrated sub-bands causes the main lobe to be broadened in the range direction of the image. Figure 4 (e) is the algorithm proposed in this paper. It can be seen that each point target is well focused. At the same time, in Table 2, Figure 4 The entropy value of (e) is the smallest.

[0119] The algorithm proposed in this paper is a step-by-step error decoupling, so Figure 4 The entropy value is calculated in the process of (e), and the curve is drawn as follows Figure 5 As shown in the figure, pulse compression error calibration is first performed, reducing the entropy of the sub-band range image after pulse compression. Two-dimensional imaging is then performed. As the motion error is calibrated during iteration, the entropy decreases. It can be seen that motion error typically causes large changes in entropy. Image synthesis is then performed, where the error is calibrated and the entropy is further reduced. After three steps of error estimation and calibration based on minimum entropy, better imaging results are ultimately achieved.

[0120] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets, characterized in that The steps of the method include: The first step is to establish a coupling error echo signal model. The coupling error echo signal model includes four errors: system phase error, starting sampling distance error, intra-pulse quadratic phase error, and first-order and zero-order phase errors caused by motion. In the second step, the four errors in the coupled error echo signal model established in the first step are decoupled into three errors, namely, the sub-band range imaging error, the sub-band azimuth imaging error, and the full sub-band composite imaging error. In the third step, sub-band range imaging is performed on the space target echo data collected by the ground-based stepped-frequency radar, and the gradient of the image entropy after sub-band range imaging with respect to the sub-band range imaging error obtained in the second step is calculated. Then, the adaptive moment estimation method is used to solve the sub-band range imaging error according to the calculated gradient. The fourth step is to perform sub-band azimuth imaging on the data after sub-band range imaging, and calculate the gradient of the image entropy after sub-band azimuth imaging with respect to the sub-band azimuth imaging error obtained in the second step. Then, the adaptive moment estimation method is used to solve the sub-band azimuth imaging error based on the calculated gradient. In the fifth step, full sub-band synthetic imaging is performed on the data after sub-band azimuth imaging, and the gradient of the image entropy after full sub-band synthetic imaging with respect to the full sub-band synthetic imaging error obtained in the second step is calculated. Then, the full sub-band synthetic imaging error is solved based on the calculated gradient using the adaptive moment estimation method. Step 6: Repeat steps 3 to 5 until the image is focused and the final image is obtained.

2. The method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets according to claim 1, characterized in that: In the first step, the coupling error echo signal model established is: Among them, A q (·) is the amplitude error, is the system phase error of sampling number n, is the starting sampling distance error of sampling number n, is the quadratic phase error within the pulse with sampling number n, The first and zero-order phase errors caused by the motion of sampling number n; is the fast frequency, t n is the slow time with sampling number n, n = 1, 2, 3, ..., N, and N is the number of azimuth sampling.

3. The method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets according to claim 1 or 2, characterized in that: In the second step, the sub-band range imaging error is: in, is the amplitude error, For The associated polynomial coefficients.

4. The method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets according to claim 3, characterized in that: The sub-band azimuth imaging error is: Among them, f q is the carrier frequency of the qth sub-pulse; q = 1, 2, 3, ..., Q, Q is the total number of sub-bands; p = 1, 2, 3, ..., P, P is the polynomial order of the error; For t n The associated polynomial coefficients.

5. The method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets according to claim 4, characterized in that: The full sub-band synthetic imaging error is: in, is a constant amplitude error, p = 0 or 1, For The associated polynomial coefficients.

6. The method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets according to claim 1, characterized in that: In the third step, the formula for obtaining the gradient is: Among them, X 1,q is the image after sub-band range imaging, En(X 1,q ) is the image entropy of the image after sub-band range imaging, is the error parameter, is the error parameter, S(X 1,q ) is the total energy of the image after sub-band range imaging, t q is the azimuth sampling time corresponding to the qth sub-pulse, For fast time, x 1,q It is the sub-element of the image after sub-band range imaging; is the inverse Fourier transform, is the data before sub-band range imaging.

7. The method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets according to claim 6, characterized in that: In the fourth step, the formula for obtaining the gradient is: Among them, X 2,q is the image after sub-band azimuth imaging, En(X 2,q ) is the image entropy of the image after sub-band azimuth imaging, S(X 2,q ) is the total energy of the image after sub-band azimuth imaging, is the azimuth slow frequency, x 2,q is the sub-element of the image after sub-band azimuth imaging, is the Fourier transform, It is the data before sub-band azimuth imaging.

8. The method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets according to claim 7, characterized in that: In the fifth step, the formula for obtaining the gradient is: Among them, X 3,q is the image after full sub-band synthesis imaging, En(X 3,q ) is the image entropy of the image after full sub-band synthesis imaging, S(X 3,q ) is the total energy of the image after full sub-band synthesis imaging, This is the data before full sub-band synthetic imaging.

9. The method for calibrating the error of a ground-based stepped-frequency radar imaging system for space targets according to claim 1, characterized in that: The update formula of the adaptive moment estimation method is: Where e is the parameter to be estimated, H(e) is the gradient, m1 and m2 are the first-order and second-order moment estimates, respectively, k is the number of iterations, β1, β2 and α are adjustable parameters, and ε>0.

Images