CN118011342A - Error calibration method for space target imaging system of foundation step frequency radar - Google Patents

Abstract

The invention relates to a method for calibrating errors of a space target imaging system by a ground-based step frequency radar, and belongs to the technical field of radar imaging. Firstly, a complex coupling error echo signal model of a system error and a motion error is established according to the characteristics of a stepping frequency chirp radar and high-speed motion. The errors are then decoupled into sub-band distance imaging errors, sub-band azimuth imaging errors, and full sub-band composite imaging errors, depending on the effect of the error pattern on the different processing steps. Then solving the gradient solution of the image entropy to the error after the sub-band distance imaging, the sub-band azimuth imaging and the full-sub-band synthetic imaging, and respectively solving the error by using an adaptive moment estimation method. And finally, carrying out cyclic processing on the steps, iterating the calibration error for a plurality of times, and obtaining a high-quality image.

Description

Error calibration method for space target imaging system of foundation step frequency radar

Technical Field

The invention relates to a method for calibrating errors of a space target imaging system by a ground-based step frequency radar, and belongs to the technical field of radar imaging.

Background

The ground-based radar is an effective means for detecting and imaging the space-sky targets, improves the resolution, can acquire more target detail information, and is convenient for classification and identification. Achieving high resolution requires the ability of the radar to transmit large bandwidth signals, and if instantaneous large bandwidth signals are transmitted, a higher sampling rate matching the nyquist sampling theorem needs to be achieved, which is a great challenge for system hardware such as analog-to-digital conversion and direct digital synthesis. The frequency stepping signal has the advantages of instantaneous narrow band and synthesized broadband, and has wide application in the radar field.

The frequency stepping chirp signal has the advantages of both frequency stepping and chirp signals, on one hand, the difficulty of transmitting a large-bandwidth signal by a system is reduced through a carrier frequency stepping mode, and on the other hand, each sub-pulse has a larger time-wide bandwidth product, so that the contradiction between the acting distance and the distance resolution is balanced.

But the fuzzy function property of the frequency modulation step frequency signal determines that grating lobes are very easy to generate when a high-resolution range profile is acquired. Grating lobes are inhibited in two main ways: firstly, proper waveform parameters are designed to avoid information loss and redundancy in a synthesized broadband, secondly, various errors in signals are corrected, so that perfect coherent synthesis of a plurality of subband signals is realized, and the second point is more important for data processing.

The step frequency radar transmits different sub-pulses by using different local oscillators and sub-links, so that time and phase are difficult to be strictly consistent, and therefore, systematic errors can exist. The internal scaling-based methods have limited applicability and often do not have isolated strong points for spatial target observations, thus requiring research into self-calibration techniques based on radar data.

Meanwhile, the stepping frequency chirp radar synthesizes a large bandwidth signal through a plurality of sub-pulses, namely the repetition frequency of burst is smaller than that of the sub-pulses, and for a space high-speed space target, not only the motion errors among burst are needed to be considered, but also the motion errors among sub-pulses and in the sub-pulses caused by high-speed motion are needed to be considered. But the coupling error of the system error and the target motion error existing in the practical application is less studied at the present stage.

In summary, no algorithm can calibrate the complex coupling error at present, so that a better image is obtained, and a technology for imaging a high-speed space target and self-calibrating the coupling error by using a stepping frequency chirp radar based on minimum entropy needs to be studied.

Disclosure of Invention

In view of the above, the invention provides a method for calibrating the error of a space target imaging system by a ground-based step frequency radar, which can acquire a high-precision space target imaging result.

The technical scheme of the invention is as follows:

a method for calibrating errors of a space target imaging system by a ground-based step frequency radar, comprising the steps of:

the method comprises the steps of firstly, establishing a coupling error echo signal model, wherein the coupling error echo signal model comprises four errors, and the four errors are respectively a system phase error, an initial sampling distance error, a secondary phase error in a pulse and a primary and zero phase error caused by motion;

Step two, the four errors in the coupling error echo signal model established in the step one are decoupled into three errors, wherein the three errors are respectively a sub-band distance imaging error, a sub-band azimuth imaging error and a full sub-band synthetic imaging error;

Thirdly, carrying out sub-band distance imaging on the space target echo data acquired by the foundation step frequency radar, solving the gradient of the sub-band distance imaging error obtained in the second step by the image entropy after the sub-band distance imaging, and then solving the sub-band distance imaging error according to the solved gradient by using an adaptive moment estimation method;

fourth, carrying out sub-band azimuth imaging on the data after sub-band distance imaging, solving the gradient of the image entropy after sub-band azimuth imaging on the sub-band azimuth imaging error obtained in the second step, and then solving the sub-band azimuth imaging error according to the solved gradient by using an adaptive moment estimation method;

fifthly, carrying out full-subband synthesis imaging on the data after subband azimuth imaging, solving the gradient of the image entropy after full-subband synthesis imaging on the full-subband synthesis imaging error obtained in the second step, and then solving the full-subband synthesis imaging error according to the solved gradient by using a self-adaptive moment estimation method;

And sixthly, repeating the third step to the fifth step until the image is focused, and obtaining a final image.

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

wherein A _q (·) is the amplitude error, For a systematic phase error with sample number n,/>For a starting sampling distance error with a sampling number n,/>Is the secondary phase error in the pulse with the sampling sequence number of n,/>A primary phase error and a zero phase error brought by the motion with the sampling sequence number of n; /(I)For fast frequency, t _n is slow time with sampling sequence number N, n=1, 2,3, …, N is azimuth sampling number;

In the second step, the subband distance imaging error is:

Wherein, For amplitude error,/>Is AND/>Related polynomial coefficients;

The subband azimuth imaging error is:

wherein f _q is the carrier frequency of the q-th sub-pulse; q=1, 2,3, …, Q is the total number of subbands; p=1, 2,3, …, P is the polynomial order of the error; Is a polynomial coefficient related to t _n;

The full subband synthesis imaging error is:

Wherein, For constant amplitude error, p=0 or 1,/>Is AND/>Related polynomial coefficients;

in the third step, the formula for obtaining the gradient is as follows:

Wherein X _1,q is the sub-band distance imaged image, en (X _1,q) is the image entropy of the sub-band distance imaged image, Is an error parameter,/>S (X _1,q) is the total energy of the image after sub-band distance imaging, t _q is the azimuth sampling time corresponding to the qth sub-pulse, and is used as an error parameterFor fast time, x _1,q is the subelement of the image after sub-band distance imaging; is inverse Fourier transform,/> Data before imaging for a subband distance;

in the fourth step, the formula for obtaining the gradient is:

Wherein 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, For slow azimuth frequency, x _2,q is a subelement of the image after subband azimuth imaging,/>Is Fourier transform,/>Data prior to imaging for the subband azimuth;

in the fifth step, the formula for obtaining the gradient is:

Wherein X _3,q is the full-subband synthesized imaged image, en (X _3,q) is the image entropy of the full-subband synthesized imaged image, S (X _3,q) is the total energy of the full-subband synthesized imaged image, Synthesizing data before imaging for the full sub-band;

The updating formula of the self-adaptive moment estimation method is as follows:

Wherein e is a parameter to be estimated, H (e) is a gradient, m ₁ and m ₂ are first-order and second-order moment estimates, k is the number of iterations, β ₁、β₂ and α are adjustable parameters, ε >0.

Advantageous effects

According to the invention, the coupling error of the step frequency radar system and the high-speed moving target is accurately modeled, and high-resolution imaging of the high-speed space target can be realized. The coupling error is decomposed into the sub-band distance imaging error, the sub-band azimuth imaging error and the full-sub-band composite imaging error, the gradient of entropy to the error in each step is obtained in a step solving mode, the error is obtained and compensated by combining the self-adaptive moment estimation method, and the self-calibration of the coupling error is realized. The frequency stepping signal has the advantages of instantaneous narrow band and synthesized broadband, can image space target in a resolved way, and has wide application in the radar field. But frequency-modulated step-wise frequency observation. However, the echo in the observation of the space target by the frequency stepping radar contains errors formed by coupling a systematic error and a high-speed motion error of the target, and the traditional method is difficult to image. Therefore, the invention provides a stepping frequency chirp radar based on minimum entropy for high-speed space target imaging and coupling error self-calibration technology. Firstly, a complex coupling error echo signal model of a system error and a motion error is established according to the characteristics of a stepping frequency chirp radar and high-speed motion. The errors are then decoupled into sub-band distance imaging errors, sub-band azimuth imaging errors, and full sub-band composite imaging errors, depending on the effect of the error pattern on the different processing steps. Then solving the gradient solution of the image entropy to the error after the sub-band distance imaging, the sub-band azimuth imaging and the full-sub-band synthetic imaging, and respectively solving the error by using an adaptive moment estimation method. And finally, carrying out cyclic processing on the steps, iterating the calibration error for a plurality of times, and obtaining a high-quality image. The method aims at providing a robust step frequency chirp radar high-resolution imaging algorithm for a high-speed space target, and is expected to be applied to the fields of space target observation and the like of foundation radars.

Drawings

FIG. 1 is a frequency domain representation of an error;

FIG. 2 is a time domain representation of an error;

FIG. 3 is a flow chart of a coupling error self-calibration algorithm;

FIG. 4 is a satellite lattice simulation diagram, wherein FIG. 4 (a) is a simulation point target, FIG. 4 (b) is an imaging result without error correction, FIG. 4 (c) is an imaging result with only average distance correction, FIG. 4 (d) is an uncorrected subband error imaging result, and FIG. 4 (e) is an imaging result of the method;

fig. 5 is a graph of entropy as a function of process flow.

Detailed Description

The invention is further described below with reference to the drawings and examples.

Examples

Each frame of the frequency stepping chirp signal is composed of a group of Q sub-pulses with carrier frequency linearly hopped, assuming that the initial carrier frequency is f ₀ and the stepping amount is Δf, the carrier frequency of the Q sub-pulse is f _q＝f₀ +qΔf, q=0, 1.

Here, theFor fast time,/>For chirp baseband signal, T _pulse is pulse width, gamma is frequency modulation slope, rect (& gt) is rectangular window function, sub-pulse bandwidth/>Because of the overlapping frequency spectra of the different sub-pulses, the maximum resulting bandwidth available for a frame of signal is b=b ₀ + (Q-1) Δf.

If the target time delay corresponding to the n=gQ+q sub-pulses in the azimuth direction isFor frame index, t _n＝nT_PRT,T_PRT is the repetition time of the sub-pulse. Because of f _n＝f_q, the received echo is

Sigma is the complex scattering intensity of the target. The frequency spectrum after matched filtering is

Here (-) ^* is a conjugate operator, and the visible signal only remains once phase and zero phase after matched filtering, and the coupling error of the target motion and the system error is described below.

Error modeling: in practical radar systems, the error can be modeled as a polynomial due to the distortion of the amplitude and phase frequency characteristics of the radar system caused by the non-ideal characteristics of the components such as amplifiers, filters, etc. Meanwhile, because the system works in a frequency hopping mode, local oscillators and links adopted when sub-pulses of different carrier frequencies are transmitted are different, the channel characteristics of the system are related to a carrier frequency index q, and meanwhile, errors exist between the actual value and the nominal value of a frequency source of a transmission and trigger signal of the radar system, so that errors exist between a design value and the actual initial sampling time, and the errors are primary and constant phase errors.

For motion errors, motion can introduce phase within the pulses due to high speed moving objects. Setting the direction away from the radar positive, the echo form becomes:

Here, the For scaling factors caused by high-speed motion,/>The approximate reason is that the pulse internal change caused by the target motion is not large in the radar observation time, the same value can be used for pulse internal phase compensation, and the spectrum after matching and filtering is that

Since the speed is variable, both p and the time delay τ here are related to the slow time t _n. High speed motion causes spectral shifting and amplitude scaling, but is typically negligible.The second phase of (2) will cause HRRP waveform distortion, which will further affect the two-dimensional imaging quality. It is therefore the amount by which the intra-pulse error is mainly compensated, and the second and third terms are related to f _q, the first and zero order phase errors do not lead to waveform distortion.

Through the above analysis, the systematic error of the step frequency and the motion error of the target form a complex coupling error, which is expressed as

Wherein A _q (·) is the amplitude error,Respectively representing the system phase error, the initial sampling distance error, the secondary phase error in the pulse and the primary and zero phase errors caused by motion.

Fig. 1 shows a phase frequency and amplitude frequency diagram of a wideband synthesis with two sub-pulses. In fig. 1 (a), the ideal phase splice result should be continuous and have the same slope, not including second and higher order phase errors. The first sub-pulse is subject to phase errors including second and higher orders, which are non-linear in phase, and the second sub-pulse includes first and zero order component phase errors, with a change in phase slope, and a phase jump at the time of splicing. The first sub-pulse amplitude spectrum in fig. 1 (b) is ideal, while the second sub-pulse polynomial amplitude error, therefore, does not allow wideband synthesis.

Fig. 2 shows an ideal one-dimensional range profile and one-dimensional range profile with errors. In fig. 2 (a), the dashed line and the solid line represent a one-dimensional range profile of a single sub-band with low resolution and a one-dimensional range profile of perfect combination of two sub-bands without errors, respectively, and it can be seen that the main lobe of the dashed line is narrower, which indicates that the broadband combination can improve the resolution. Fig. 2 (b) shows a one-dimensional range profile of the first subband in the presence of errors, where even-order phase errors of second order and above cause symmetric sidelobes to rise, and odd-order phases cause sidelobes to be asymmetric. Fig. 2 (c) is a second subband one-dimensional range profile with errors, the amplitude error causes symmetrical distortion of the side lobes, and the primary phase error causes shift of the peak position. Fig. 2 (d) is a one-dimensional range profile obtained by synthesizing the two sub-band spectrums of fig. 2 (b) and fig. 2 (c), which is obviously far from the high-resolution one-dimensional range profile of fig. 2 (a) due to various errors, and it can be seen that a regular grating lobe appears at a specific position, which is determined by the fuzzy function property of the step frequency chirp signal. Therefore, the key to obtaining an ideal imaging result from the step frequency chirp signal is to correct various errors.

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

Y_q＝E_q⊙AX_qB+N

Wherein A and B are the distance Fourier transform and the azimuth inverse Fourier transform matrices, Y _q and X _q are the echo and the image, respectively, as indicated by Hadamard product operator, N is noise, E _q is coupling error, expressed as

It is worth noting that X _q has a higher signal-to-noise ratio after two-dimensional accumulation. The use of the step frequency chirp signal to achieve high resolution in the distance direction can be considered as obtaining a larger bandwidth by splicing a plurality of sub-band spectrums to achieve high resolution imaging, namelyHere (-) ^H is a Hermite operator.

The image entropy is an important image quality evaluation index, and the smaller the value, the better the image quality is, defined as

The total energy of the image isIs constant. The imaging problem can be modeled as

The calculation cost and the parameter amount of the search-based method have an exponential relation, so that error decoupling is carried out, and the parameter calculation amount of each time is necessary to be simplified.

Subband distance imaging error: in each sub-bandThe second and more phase errors of (a) and (b) the amplitude errors of (a) and (b) can influence waveform distortion after pulse pressure, and the errors do not change along with t _n, and all data of each sub-band can be used for error estimation and correction, namely, the optimization problem is that

Subband azimuth imaging errors

Both object motion and systematic errors can cause concernSuch coupling errors are difficult to solve directly, and although similar envelope alignment methods commonly used in ISAR are numerous, on the one hand these methods are simpler to model errors than the coupling error model considered herein, and on the other hand it is difficult to achieve the phase accuracy required for synthesizing high resolution images by means of envelope alignment compensation accuracy. While two-dimensional images have higher signal-to-noise ratios and better entropy performance, in addition, each subband has more accurate error calibration requirements in two-dimensional imaging, so the objective function can be modeled as

Here, the Containing errors varying with t _n, i.e

Full subband synthesis imaging error: is still present after the error correction of the first two stepsDirectly synthesizing the high resolution image affects the accumulation gain, causing grating lobes to appear and the image to degrade, an error known as a synthetic imaging error. The optimization problem can thus be modeled as

Here, theSince time-varying errors have been corrected before, only time-invariant/>First order and zero order phases, and therefore can be simplified. The error estimated at this step is expressed as

It is worth noting that the number of the parts,Can be regarded as a time-invariant error, i.e. contained in/>And (3) inner part.

Through three steps of error decoupling, a final error estimation result can be obtained as follows

Previously modeled motion errors and systematic errors are included and decoupling is achieved in three different processing steps. The three-step corrected image is represented as

In order to obtain the decoupled error and compensate it, the most straightforward approach is to perform a parameter traversal search, which, although the proposed decoupling approach can reduce the parameter dimension, still requires a large computational effort. It is clear that directly solving the analytical solution is not practical, so here the solution is performed using Adam algorithm with faster convergence rate, the gradient is represented as follows

For each of the three steps, the solution can be accomplished using adaptive moment estimation (Adam), whose updated formula is

Where e is a parameter to be estimated, m ₁ and m ₂ are first and second moment estimates, k is the number of iterations, β ₁、β₂ and α are adjustable parameters, ε >0, adam applies a momentum method, and the gradient descent rate can be adaptively adjusted.

The correspondence between the decoupled errors and the correction algorithm is shown in fig. 3, and also a visual image display is performed. This step

1) Sub-band pulse pressure error estimation: the method comprises the steps of uniformly processing each sub-band by utilizing the influence of secondary and more phase frequency responses and primary and more amplitude responses on pulse compression, correcting consistent time-invariant errors in the sub-bands, and obtaining undistorted range profiles of all the sub-bands after the processing;

2) Estimating a subband two-dimensional imaging error: the method comprises the steps of utilizing the influence of time-varying motion errors on each sub-band data, correcting time-varying envelope and phase errors shared by all sub-bands through sub-band two-dimensional imaging, and obtaining a low-resolution two-dimensional image without distortion of each sub-band after the processing;

3) And (3) correcting a synthetic error: the method utilizes the influence of residual errors on broadband synthesis, namely coherent accumulation, entropy is used as an evaluation standard of images, accumulation effect can be measured, entropy value is small, and more optimal accumulation of a plurality of sub-band images is realized. After this step, a high resolution two-dimensional image is obtained.

It is worth to say that the technology is also suitable for the step frequency chirp radar data with fewer frames, even if the target motion cannot form a synthetic aperture, the entropy can still measure the coherent accumulation effect, and then the coupling error self calibration is realized. Meanwhile, the error model is also applicable to other forms, such as sinusoidal errors, and the like, and can be solved by the technology.

Examples

A satellite electron containing 64 points was set using computer simulation as shown in fig. 4 (a). And the motion parameters are set, so that the rotation can form a synthetic aperture, and two-dimensional imaging can be performed. Meanwhile, additive Gaussian white noise is added into the image, so that the signal-to-noise ratio is kept at 0dB. The simulated radar parameters are shown in table 1.

Table 1 simulation experiment parameters

Radar parameters	Numerical value	Unit (B)
			Initial center frequency	3.5	GHz
Bandwidth of a communication device	250	MHz
			Frequency step size	200	MHz
Number of subbands	4	Personal (S)
			Pulse repetition frequency	800	Hz
Pulse width	6.25	us
			Target distance	482	Km
Target speed	1400	m/s
			Acceleration of	100	m/s2

Table 2 evaluation of test results of simulation experiments

Drawing figures	FIG. 4(c)	FIG. 4(c)	FIG. 4(d)	FIG. 4(e)
					Entropy of	5.3103	5.6782	5.7091	4.5182

The uncorrected intra-subband errors in fig. 4 (b) are obvious from the grating lobe, the motion compensation precision of fig. 4 (c) is difficult to meet the spectrum synthesis requirement by only performing simple average distance image correction, the image quality is degraded, the uncorrected inter-subband errors in fig. 4 (d) are generated, and the distance of the image is widened from the main lobe. Fig. 4 (e) is an algorithm presented herein, and it can be seen that each point target is well focused, while the entropy of fig. 4 (e) is minimal in table 2.

The algorithm presented here is step error decoupling, so the entropy calculation is performed for the process of fig. 4 (e), and the curve is depicted as in fig. 5. As shown in the figure, pulse compression error calibration is performed first, the entropy of the range profile after sub-band pulse pressure is reduced, then two-dimensional imaging is performed, and as the motion error is calibrated in iteration, the entropy is smaller and smaller, it can be seen that the motion error generally causes larger entropy change, then image synthesis is performed, and the error is calibrated in synthesis, and meanwhile, the entropy is further reduced. And through three steps of error estimation and calibration processing based on minimum entropy, a better imaging result is finally obtained.

In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. A method for calibrating errors of a space target imaging system by a ground-based step frequency radar is characterized by comprising the following steps:

the method comprises the steps of firstly, establishing a coupling error echo signal model, wherein the coupling error echo signal model comprises four errors, and the four errors are respectively a system phase error, an initial sampling distance error, a secondary phase error in a pulse and a primary and zero phase error caused by motion;

Step two, the four errors in the coupling error echo signal model established in the step one are decoupled into three errors, wherein the three errors are respectively a sub-band distance imaging error, a sub-band azimuth imaging error and a full sub-band synthetic imaging error;

Thirdly, carrying out sub-band distance imaging on the space target echo data acquired by the foundation step frequency radar, solving the gradient of the sub-band distance imaging error obtained in the second step by the image entropy after the sub-band distance imaging, and then solving the sub-band distance imaging error according to the solved gradient by using an adaptive moment estimation method;

fourth, carrying out sub-band azimuth imaging on the data after sub-band distance imaging, solving the gradient of the image entropy after sub-band azimuth imaging on the sub-band azimuth imaging error obtained in the second step, and then solving the sub-band azimuth imaging error according to the solved gradient by using an adaptive moment estimation method;

fifthly, carrying out full-subband synthesis imaging on the data after subband azimuth imaging, solving the gradient of the image entropy after full-subband synthesis imaging on the full-subband synthesis imaging error obtained in the second step, and then solving the full-subband synthesis imaging error according to the solved gradient by using a self-adaptive moment estimation method;

And sixthly, repeating the third step to the fifth step until the image is focused, and obtaining a final image.

2. The method for calibrating the error of a space target imaging system by using the ground-based step-frequency radar according to claim 1, wherein the method comprises the following steps:

in the first step, the established coupling error echo signal model is:

wherein A _q (·) is the amplitude error, For a systematic phase error with sample number n,/>For a starting sampling distance error with a sampling number n,/>Is the secondary phase error in the pulse with the sampling sequence number of n,/>A primary phase error and a zero phase error brought by the motion with the sampling sequence number of n; /(I)For fast frequency, t _n is the slow time with sample number N, n=1, 2,3, …, N is the azimuth sample number.

3. A method for calibrating error of a space target imaging system by using a ground-based step-frequency radar according to claim 1 or 2, wherein:

In the second step, the subband distance imaging error is:

Wherein, For amplitude error,/>Is AND/>The associated polynomial coefficients.

4. A method for calibrating an error of a space target imaging system by a ground-based step-frequency radar according to claim 3, wherein:

The subband azimuth imaging error is:

wherein f _q is the carrier frequency of the q-th sub-pulse; q=1, 2,3, …, Q is the total number of subbands; p=1, 2,3, …, P is the polynomial order of the error; Is the polynomial coefficient associated with t _n.

5. The method for calibrating the error of a space target imaging system by using the ground-based step-frequency radar according to claim 4, wherein the method comprises the following steps:

The full subband synthesis imaging error is:

Wherein, For constant amplitude error, p=0 or 1,/>Is AND/>The associated polynomial coefficients.

6. The method for calibrating the error of a space target imaging system by using the ground-based step-frequency radar according to claim 1, wherein the method comprises the following steps:

in the third step, the formula for obtaining the gradient is as follows:

Wherein X _1,q is the sub-band distance imaged image, en (X _1,q) is the image entropy of the sub-band distance imaged image, Is an error parameter,/>S (X _1,q) is the total energy of the image after sub-band distance imaging, t _q is the azimuth sampling time corresponding to the qth sub-pulse, and is used as an error parameterFor fast time, x _1,q is the subelement of the image after sub-band distance imaging; is inverse Fourier transform,/> Data before imaging for the subband distance.

7. The method for calibrating the error of a space target imaging system by using the ground-based step-frequency radar according to claim 6, wherein the method comprises the following steps:

in the fourth step, the formula for obtaining the gradient is:

Wherein 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, For slow azimuth frequencies, x _2,q is a sub-element of the image after sub-band azimuth imaging,Is Fourier transform,/>Data prior to imaging for the subband azimuth.

8. The method for calibrating the error of a space target imaging system by using the ground-based step-frequency radar according to claim 7, wherein the method comprises the following steps:

in the fifth step, the formula for obtaining the gradient is:

Wherein X _3,q is the full-subband synthesized imaged image, en (X _3,q) is the image entropy of the full-subband synthesized imaged image, S (X _3,q) is the total energy of the full-subband synthesized imaged image, The pre-imaging data is synthesized for the full sub-band.

9. The method for calibrating the error of a space target imaging system by using the ground-based step-frequency radar according to claim 1, wherein the method comprises the following steps:

The updating formula of the self-adaptive moment estimation method is as follows:

Wherein e is a parameter to be estimated, H (e) is a gradient, m ₁ and m ₂ are first-order and second-order moment estimates, k is the number of iterations, β ₁、β₂ and α are adjustable parameters, ε >0.