CN116299458B

CN116299458B - A SAR Weak Maneuvering Target Imaging Method Based on Adaptive Phase Tracking

Info

Publication number: CN116299458B
Application number: CN202310327067.5A
Authority: CN
Inventors: 宋勇平; 杜华贵; 黄晓涛; 范崇祎; 王建; 姜南; 曹春
Original assignee: National University of Defense Technology
Current assignee: National University of Defense Technology
Priority date: 2023-03-30
Filing date: 2023-03-30
Publication date: 2025-03-21
Anticipated expiration: 2043-03-30
Also published as: CN116299458A

Abstract

The present invention discloses a SAR weak maneuvering target imaging method based on adaptive phase tracking, comprising the steps of: constructing a radar echo signal model; performing pulse compression on the SAR echo signal, and correcting the range curvature by SOKT, and correcting the range movement by estimating the first-order motion parameter by Hough transform; the energy of the maneuvering target signal after the range movement correction will be concentrated in a distance unit, which is modeled as a PPS signal; extracting the signal of the distance unit where the maneuvering target is located for phase tracking, and inverting the maneuvering target parameters by using the phase obtained by tracking; constructing a phase compensation function by using the estimated motion parameters to achieve focused imaging. The present invention can be used for SAR weak maneuvering target imaging; the parameter estimation has high accuracy and small calculation amount; and focused imaging can be performed at low SNR.

Description

SAR weak maneuvering target imaging method based on self-adaptive phase tracking

Technical Field

The invention belongs to the technical field of radar signal processing, and particularly relates to a SAR weak maneuvering target imaging method based on self-adaptive phase tracking.

Background

In recent decades, SAR imaging technology has been widely used and studied in civil fields such as ocean observation, farmland mapping, land detection and ground deformation monitoring, and in military fields such as battlefield reconnaissance, military target motion monitoring, accurate striking, and the like. Compared with the optical imaging technology, the method has the advantage of providing imaging results of the observation scene all the time, all the weather and long distance. In addition, the SAR imaging technology not only can acquire electromagnetic scattering characteristics and high-resolution two-dimensional images of stationary ground objects, but also can realize focusing imaging of moving targets through selection and compensation of reference functions.

SAR imaging is to load a radar on a mobile platform and move along a preset route, wherein the direction is called an azimuth direction, and the direction perpendicular to the azimuth direction is called a range direction. The large aperture antenna can be equivalently synthesized in the process of moving the antenna along the azimuth direction, so that the purpose of increasing the azimuth resolution is achieved, the coherent accumulation of echoes of all positions in the scene is completed, and finally the scene image is obtained. SAR echoes acquired in different azimuth directions are coherently accumulated through a matched filtering technology, and in order to be able to focus a scene, the instantaneous skew relation between the radar and an imaging scene needs to be accurately known, and the skew relation is reflected in the SAR echoes to cause distance walk and Doppler phase walk. The distance walking is the movement of a span unit when the instantaneous slant distance of each scattering point in a radar scene is generated under different directions, and the Doppler phase walking is the movement of the direction to a speed-crossing unit caused by the change of the relative position relation between the radar and the scattering point.

When SAR images a static scene, the motion track of a radar platform can be accurately measured through inertial navigation and other equipment, the instantaneous slant distance or phase relation between the radar and each scattering point in the imaging scene can be accurately calculated, and at the moment, phase compensation coherent accumulation imaging can be carried out through a classical imaging method. However, when a moving object exists in a scene, due to the non-cooperative property and the motion randomness of the moving object, the motion parameters of the moving object are unknown, the instantaneous pitch and the corresponding phase thereof can not be accurately acquired any more, and the image defocusing, blurring or azimuth offset can be caused by directly processing by using a static object imaging algorithm. If the moving target parameters can be estimated from the SAR echo, and the phase compensation is performed to eliminate the influence caused by the target motion, the compensated echo can be equivalent to a stationary target, and then a good focusing result of the moving target can be obtained through the processing of the stationary target SAR imaging method. Therefore, the key to the merits of the imaging results is whether the motion parameters of the moving object can be accurately estimated and compensated.

For conventional moving targets, only the estimation and compensation of low-order motion parameters (2 nd order and below, such as speed and acceleration) are generally considered, so that a better imaging effect can be achieved. However, with the development of radar technology and the update of practical application demands, the imaging of maneuvering targets with complex motion characteristics is receiving close attention, for example, in modern military war, some targets have complex and variable motion in order to avoid reconnaissance and striking. In imaging such targets, the phase error caused by the higher order motion parameters (3 rd order and above) due to the maneuvering of the target is not negligible, if no compensation is performed, the imaging result will be defocused. It is worth to say that, besides the non-negligible higher-order phase brought by the maneuver of the target to be imaged, when the conventional moving target moves on the terrain with severe fluctuation, the higher-order phase is also generated in the SAR echo, and when the synthetic aperture time is long, the conventional target uniform speed or uniform acceleration motion approximation model is not established any more, and is equivalent to the maneuver of the target, and the higher-order phase also needs to be considered. It can be seen that in SAR moving object imaging, there are a large number of scenarios in which estimation and compensation of higher-order phase parameters are to be considered. In addition, such targets with complex motion characteristics tend to be smaller in size and weaker in radar returns, and the present invention refers to such targets as weak maneuvering targets. Therefore, in order to effectively complete tasks such as monitoring, investigation, accurate striking and the like, intensive research on the SAR weak maneuvering target imaging technology is necessary.

In order to obtain high resolution imaging results of a maneuver target, the range walk and the Doppler frequency walk, i.e. the higher order phase brought by the maneuver of the target, need to be estimated and compensated. In recent decades, the methods proposed by related researches on distance walking and Doppler frequency walking estimation and compensation can be mainly divided into two types, namely, a first type only considers a low-order phase model, namely, a phase model of 2 steps and below formed by speed and acceleration, and a second type considers a high-order phase model, namely, a phase model of 3 steps and higher. For estimation and compensation of low-order model parameters, the main stream method mainly comprises (1) a first-order Keystone transformation (Keystone Transform, KT), a Second-order Keystone transformation (Second-order Keystone Transform, SOKT), a Doppler Keystone transformation and the like based on Keystone transformation and an improved class method thereof. Such methods are widely used without any prior information on the motion parameters of the object. (2) Radon Transform (RT) type methods, such as Radon fourier Transform (Radon-Fourier Transform, RFT), radon fractional fourier Transform, radon second order weibull distribution, and the like. (3) a time-frequency analysis method. Mainly comprises short-time Fourier transform, weibull distribution, fuzzy function, fractional Fourier transform and the like.

However, for SAR maneuvering target imaging, the above-described method that can only compensate for low-order phase parameters is not applicable. To solve this problem, some scholars have studied a compensation method for the 3-order phase parameter. For example, the non-patent literature SAR ground maneuvering targets imaging and motion parameters estimation based on the adaptive polynomial fourier transform,IEEE Geoscience and Remote Sensing Letters,vol.19,pp.1–5,2020 discloses a ground maneuvering target imaging and 3-order motion parameter estimation method based on an adaptive polynomial fourier transform (Adaptive Polynomial Fourier Transform, APFT) in the university of western electronic technology, winter et al. The algorithm firstly estimates the distance velocity from the distance walk of the signal envelope through Hough transformation after the distance pulse pressure and the uniform distance walk are corrected. This distance is then used to complete the distance walk correction of the signal to speed. Further, the additional distance curvature is corrected by SOKT. Next, second and third order doppler parameters of the moving object are estimated by APFT and corresponding moving object motion parameters are obtained. Finally, the moving target can construct a phase compensation function through the estimated motion parameters to realize accurate focusing. Similarly, huang Penghui et al in non-patent literature Ground maneuvering target imaging and high-order motion parameter estimation based on second-order keystone and generalized hough-haf transform,IEEE Transactions on Geoscience and Remote Sensing,vol.55,no.1,pp.320–335,2016 propose a maneuvering target parameter estimation and imaging algorithm based on Generalized High-order blur function (GHAF). Similar to the method proposed by winter et al, the distance walk compensation is firstly carried out by utilizing Hough transformation and SOKT, the signal of the distance unit where the target is positioned is modeled as a 3-order polynomial phase signal (Polynomial PHASE SIGNAL, PPS), then the PPS signal is transformed into a two-dimensional frequency domain by utilizing GHAF, the two-dimensional coherent accumulation of the signal is realized, the second-order and 3-order motion parameters of the target motion are estimated according to the peak position, and finally the focusing imaging result can be obtained by utilizing the parameters for compensation. Still further, to reduce the threshold of the signal-to-noise ratio, xu Jia et al in non-patent document Radar maneuvering target motion estimation based on generalized radon-fourier transform,IEEE Transactions on Signal Processing,vol.60,no.12,pp.6190–6201,2012. implement parameter estimation and compensation imaging by traversing searches in a multidimensional parameter space under coherent accumulation, which, although yielding better results at low signal-to-noise ratios, reduces computational efficiency due to the need to perform parameter searches in three dimensions. the above methods have in common that only 3-order phase models are considered, while higher-order phase compensation is neglected. Less research is directed to higher-order phase parameter estimation above 3 rd order, and currently the main method is to perform higher-order phase compensation through a self-focusing strategy, such as phase gradient self-focusing (PHASE GRADIENT Autofocus, PGA) and contrast optimization algorithm (Contrast Optimization Algorithm, COA), but such methods require special display points with high signal-to-noise ratio, otherwise the estimated phase error accuracy is severely deteriorated.

When imaging a ground moving object by using a synthetic aperture radar (SYNTHETIC APERTURE RADAR, SAR), the existing method can well acquire high-resolution images of a static scene and a conventional moving object. However, for such targets that have complex motion characteristics and small radar cross-sectional areas (Radar Cross Section, RCS) of the target, they are referred to herein as weak maneuvering targets. Compared with a conventional moving target, the target has more complex and changeable motion and lower echo Signal-to-noise Ratio (SNR), so that when the SAR is used for imaging, the SAR focusing imaging method has the problems that 1) in addition to distance and Doppler walk caused by low-order parameters such as speed, acceleration and the like, the influence of even higher-order motion parameters of jerk is not negligible, namely, the estimation and compensation of the higher-order motion parameters are required during SAR imaging, and 2) in order to obtain SAR focusing imaging results of the target, parameter estimation and imaging algorithms with better anti-noise performance are required to be researched and developed. Therefore, how to effectively focus weak maneuvering targets under low signal-to-noise ratio is a key technical problem to be solved.

In the prior art, when the problem of weak maneuvering target imaging of SAR is solved, the defects of low parameter estimation precision and high signal-to-noise ratio requirement mainly exist, and precise focusing imaging can not be performed on the maneuvering target under the condition of low signal-to-noise ratio.

The disadvantage of low accuracy of parameter estimation mainly comes from three aspects:

1) Model mismatch results in, for example, modeling a high-order model in practice as a low-order model and estimating parameters, and finally, parameter estimation accuracy is poor due to model mismatch;

2) Based on a time-frequency analysis method, the high resolution of time and frequency cannot be obtained at the same time, and when a parameter estimation value is finally obtained by analyzing a time-frequency relation on a time-frequency surface, the resolution is not high, so that a parameter estimation error is large;

3) The core principle of carrying out parameter estimation by using a high-order fuzzy function is to carry out order reduction by using the high-order parameter value obtained by estimation to obtain a second high-order parameter value, and once the high-order parameter value is estimated inaccurately, the error is transferred to a low-order estimation result, namely, an error transfer effect exists, so that the final parameter estimation precision is low.

The disadvantage of high signal-to-noise ratio requirements derives mainly from two aspects:

1) When the parameters are estimated, incoherent accumulation is carried out, so that signal-to-noise ratio loss is caused;

2) Based on the self-focusing algorithm, the special display point with high signal-to-noise ratio is needed to be used as a reference for phase estimation compensation, and the phase estimation result is accurate only when obvious strong scattering points exist in a scene, so that the focusing imaging result can be further and better obtained.

Disclosure of Invention

In order to solve the problem that the performance is drastically reduced when the existing high-resolution SAR imaging technology is applied to a weak maneuvering target, the signal-to-noise ratio threshold requirement is reduced while the parameter estimation precision is expected to be improved, and maneuvering target resolution imaging under low signal-to-noise ratio is finally realized. In view of the above, the invention provides an SAR weak maneuvering target imaging method based on adaptive phase tracking, which is suitable for the fast focusing imaging of the weak maneuvering target under the condition of low SNR.

The invention discloses an SAR weak maneuvering target imaging method based on self-adaptive phase tracking, which comprises the following steps:

acquiring SAR echo signals of a maneuvering target, and constructing a radar echo signal model;

Pulse compression is carried out on SAR echo signals, distance bending is corrected through SOKT, and distance walking is corrected through estimating first-order motion parameters through Hough transformation;

the energy of the maneuvering target signal after distance walking correction is gathered in a distance unit, and the signal in the distance unit is modeled as a PPS signal and extracted;

Carrying out phase tracking on the extracted signals of the distance unit where the maneuvering target is located, and inverting maneuvering target parameters by utilizing the tracked phases;

And constructing a phase compensation function by using the motion parameters obtained by inversion, and realizing SAR focusing imaging of the maneuvering target.

The beneficial effects of the invention are as follows:

1) The SAR echo modeling method is suitable for SAR weak maneuvering target imaging, mainly because SAR echo modeling is carried out aiming at complex motion characteristics of maneuvering targets, non-negligible high-order motion parameters are considered, and an estimation method of the high-order parameters is provided in a targeted manner.

2) The parameter estimation method based on phase tracking can estimate parameters of each order simultaneously, avoids estimation errors caused by error transfer effect, realizes phase tracking by adopting EKF with smaller calculated amount, and improves calculation efficiency.

3) The method can perform focusing imaging under low SNR, mainly because the covariance matrix self-adaption and feedback correction iteration when the phase is tracked through EKF reduce the signal-to-noise ratio threshold of motion parameter estimation.

Drawings

FIG. 1 is a flow chart of an SAR weak maneuvering target imaging method based on adaptive phase tracking;

FIG. 2 is a geometric model diagram of a SAR observation maneuvering target;

FIG. 3 is a graph of an approximate error analysis of instantaneous pitch spread out at different orders;

FIG. 4 (a) is a graph of the results of motor target pulse compression;

FIG. 4 (b) is a graph showing the result of SOKT after the distance bending correction;

FIG. 4 (c) is a graph showing the result of the Hough transform after distance walk correction;

FIG. 5 is a graph of the result of phase tracking of a maneuver target signal using an adaptive EKF;

FIG. 6 is a diagram of motion parameter estimates and errors obtained by inversion using phase tracking results;

FIG. 7 (a) is a graph of imaging results after 2 nd order parameter estimation and compensation;

FIG. 7 (b) is a graph of imaging results after estimating and compensating the 3 rd order phase parameter using GHAF;

FIG. 7 (c) is a graph of the imaging result after compensating the high order phase using the PGA algorithm;

FIG. 7 (d) is a graph of the imaging results of the algorithm of the present invention;

FIG. 7 (e) is a graph of the results of ideal imaging of a simulated maneuvering target;

Fig. 8 is a graph of imaging results of the method at different pulse pressure SNRs, snr= -5dB in fig. 8 (a), snr= -3dB in fig. 8 (b), snr= -1dB in fig. 8 (c), snr=1 dB in fig. 8 (d), snr=3 dB in fig. 8 (e), and snr=5 dB in fig. 8 (f).

Detailed Description

The invention is further described below with reference to the accompanying drawings, without limiting the invention in any way, and any alterations or substitutions based on the teachings of the invention are intended to fall within the scope of the invention.

The basic idea of the technical scheme is that after a weak maneuvering target SAR echo signal is obtained, the motion parameters of the weak maneuvering target are estimated, so that the moving target can be equivalent to a cooperative target, and then the estimated motion parameters are utilized to determine the phase relation between the target and the moving radar platform, so that a compensation function is constructed to perform focusing imaging of the moving target. In this way, the accuracy of the SAR echo model, how to estimate the moving object parameters in particular, whether to effectively estimate at low signal-to-noise ratio, and whether to obtain higher-order parameter estimates, will directly affect the imaging result.

The detailed technical scheme of the invention is realized by a flow chart shown in figure 1. After a radar system obtains SAR echo signals of a maneuvering target, firstly, pulse compression is carried out on the signals, distance bending is corrected through SOKT, first-order motion parameters are estimated through Hough transformation to correct distance walking, the energy of maneuvering target signals after distance walking correction are gathered in a distance unit, the signals in the distance unit are modeled as PPS signals, secondly, signals of the distance unit where the maneuvering target is located are extracted, phase tracking is carried out on the signals, and the tracked phases are utilized to reverse maneuvering target parameters. The invention adopts the self-adaptive EKF with smaller calculation amount to complete the phase tracking of the PPS signal. The method mainly comprises the steps of constructing and solving a phase and amplitude state equation, an observation equation and a binary state space equation. In the process of carrying out iterative solution on the phase through the self-adaptive EKF, the value of the covariance matrix can be adjusted according to the self-adaptive iteration of echo data. After the phase value is obtained, the motion parameters of each order can be inverted at the same time, so that the error transfer effect is effectively avoided. And finally, constructing a phase compensation function by using the estimated motion parameter value, so that SAR focusing imaging of the maneuvering target can be realized.

The invention will be described in more detail below with reference to the following derivation and formulation.

In order to facilitate the description of the technical details of the method of the invention, the invention first constructs a radar echo signal of a SAR maneuvering target. Without loss of generality, for positive side view stripe SAR imaging, the imaging geometry in the two-dimensional diagonal plane is shown in FIG. 2. Assuming that the motion speed of the radar platform is V, the synthetic aperture time is T _a. The initial position coordinates of the maneuvering target are (0, R ₀), the speed and the acceleration along the track direction are v _a,a_a and the speed and the acceleration along the distance direction are v _r,a_r respectively, and the target moves from P ₀ to P ₁ in the observation time. Assume that the closest and instantaneous offsets between the platform and the target are denoted as R ₀ and R (t _a), respectively, where t _a represents the azimuth slow time.

Assuming that the radar emits a Linear Frequency-Modulated (LFM) signal, the pulse pressure of the echo signal of the moving target can be expressed as follows in a two-dimensional time domain:

Where δ _s is the complex reflection coefficient of the target after pulse compression. t _r denotes distance-wise fast time, w _a (·) denotes azimuth-wise time window function, and w _a(t_a)＝rect(t_a/T_a). In addition, c represents the speed of light, λ represents the wavelength, and B _r represents the bandwidth of the transmitted signal. From the geometry of FIG. 2, the instantaneous range expression between the radar platform and the moving target can be derived and expanded into a higher order polynomial model using the Taylor approximation as follows.

Where b _m denotes the coefficient of the M-th order polynomial after instantaneous pitch expansion, and M denotes the highest order expanded. In most studies, only the estimation and compensation of the third order and the following parameters (b ₁,b₂,b₃), i.e., M.ltoreq.3, are considered. Whereas for maneuver targets, the higher order parameters cannot be ignored, i.e., b ₄ and higher order parameters may need to be considered. In actual SAR imaging, the order M of taylor approximation expansion is determined jointly by the synthetic aperture time, the moving object parameters, and the imaging resolution Δρ _r. On the one hand, the instantaneous skew expansion approximation error DeltaR (t _a) should not span the range resolution unit in order to accomplish range walk correction, and on the other hand, the residual phase error needs to be guaranteed in order to achieve coherent accumulation imagingNot exceeding pi/4. The choice of M should be such that:

In actual operation, since the motion parameters of the non-cooperative targets are unknown, b _m in the above equation is unknown, so that the value of M cannot be accurately calculated. According to the reference, under the condition of low-medium resolution or short synthetic aperture time, the imaging requirement can be met by the fact that the instantaneous slope expansion order is not more than 3 orders, so that the existing moving target SAR imaging algorithm mainly aims at expansion researches of motion models with 3 orders and below. However, in high resolution imaging or imaging of a maneuvering target, the value of M must be appropriately increased.

The SAR echo model construction method aims at the characteristic that a weak maneuvering target has complex and changeable movements. Different from the conventional moving target SAR echo, the Taylor expansion of a higher order is needed to be considered for the instantaneous pitch, and then a higher order phase is introduced, wherein the value of the higher order phase is generally larger than pi/4 required by imaging performance, if the existing imaging method is directly utilized, only the estimation and compensation of low order motion parameters are considered, and Doppler walk caused by the higher order motion parameters is ignored, so that the moving target can not be focused naturally.

In imaging, whether the high-order expansion of the instantaneous skew is needed, namely whether the compensation of the high-order phase error is needed to be considered or not, mainly whether the high-order phase error is larger than pi/4 needed by imaging or not, namely whether the instantaneous skew expansion error is larger than lambda/16 or not. To illustrate the difference in signal model between maneuver targets and conventional maneuver targets, FIG. 3 shows the instantaneous pitch approximation error for a maneuver target at different expansion orders. It can be seen that at least 4 orders need to be considered to achieve focus imaging requirements, i.e. higher order phase parameters need to be considered. Therefore, the SAR echo model provided by the invention considers the high-order phase parameter so as to meet the requirement of focusing imaging.

After obtaining the maneuvering target SAR echo signal, the imaging method of the invention firstly needs to perform pulse compression and moving target signal extraction on the echo, and performs distance walking correction on the extracted moving target signal to correct the target signal to a distance unit. The step of correcting the distance walking comprises (1) carrying out SOKT correction distance bending on the signals after pulse pressure;

Since the envelope after pulse pressure is insensitive to the approximation error of instantaneous slope expansion, the distance curvature caused by 2 nd order and above parameters can be corrected by SOKT. Specifically:

Assuming that the instantaneous skew is required to be unfolded to M-order (in general, M is less than or equal to 4) according to resolution requirements, synthetic aperture time and prior parameters of a moving target, performing FFT on a two-dimensional time domain signal after pulse compression along a fast time dimension to obtain a distance frequency domain-azimuth time domain echo signal, wherein the distance frequency domain-azimuth time domain echo signal is as follows:

where W _r(f_r) represents the frequency domain form of the distance-to-time domain window function W _r(t_r), and f _r represents the distance-to-frequency. At higher SNRs, correction of range walk is performed using envelope alignment, however, at lower SNRs, generalized Keystone transforms can effectively correct range walk when moving target parameters are unknown. In this context SOKT is first used to correct distance curvature. SOKT has the expression:

substituting the formula (5) into the formula (4), and performing distance IFFT transformation, the two-dimensional time domain echo signal after SOKT is:

As can be seen from equation (6), the distance curvature is corrected. However, distance walks still exist, but the distance walks become half of the original. Next, the distance walk is corrected.

(2) Estimating first-order motion parameters by using Hough transformation to finish distance walk correction;

from the literature, hough can effectively detect straight lines in a two-dimensional plane. The invention utilizes Hough transformation to detect the distance walking curve in the t _r-η_a plane to obtain the slope of the straight line, and the estimated value of the first-order motion parameter can be estimated according to the slope value of the distance walking curve And finally, constructing a distance walking compensation factor according to the estimated value, so as to realize distance walking correction.

The echo expression after finishing the distance walk correction is:

After distance walking correction is completed, motion parameters of each order need to be estimated, and the invention provides a parameter estimation method based on self-adaptive phase tracking, wherein the parameter estimation method based on the self-adaptive phase tracking comprises the following steps:

(1) Extracting signals of a distance unit where the maneuvering target is located and constructing the signals into high-order PPS signals;

as can be seen from equation (7), after the distance walk correction, the maneuvering target echo is concentrated in a distance unit, and the echo in the distance unit is extracted and modeled as a high-order PPS signal, as follows:

the signal is sampled discretized and the noise term is considered, and the method comprises the following steps:

s(k)=A(k)·exp{jφ(k)}+n(k) (9)

Where k=1, 2, the contents of N _a, representing the SAR azimuthal sampling index, N _a represents the number of sampling points in the azimuth direction. n (k) is complex zero mean gaussian white noise with variance δ ². A (k) is the amplitude sampling value after pulse pressure, phi (k) is a polynomial phase function representing the doppler characteristics of the maneuvering target, specifically:

Where T _s is the azimuth sampling interval and ts=1/PRF, PRF is the pulse repetition frequency of SAR azimuth sampling.

(2) Constructing a phase state equation required by phase tracking aiming at the phase;

Assume that Values representing 3 consecutive phase sampling points are as follows:

from the expression of phi (k), the curvature between adjacent sample points of the polynomial phase curve is generally smoother. It should be noted that smoothing here refers to the phase values at adjacent sampling points being approximately equal. Thus:

φ(k-1)-2φ(k)+φ(k+1)≈0 (12)

combining (11) and (12), it is possible to obtain:

wherein B= [0,1,0;0, 1;0, -1,2].

On the other hand, the invention adopts a local polynomial to express the phase value when the sampling point sequence is k, and adopts a second-order local polynomial to carry out phase fitting in order to balance the relation between the calculation efficiency and the estimation accuracy, namely:

φ(k)=c^k-1(kT_s)²+c^k(kT_s)+c^k+1 (14)

according to (14), a vector of values of successive 3 phase sampling points Can be expressed as:

Wherein, In combination with (13) and (15), it is known that:

M_kc_k＝BM_k-1c_k-1 (16)

Thus, the phase state equation composed of the second order local polynomial phase coefficient vector ck, multiplied by the inverse of Mk at both ends of equation (16), can be expressed as:

c_k＝F_k-1c_k-1 (17)

Wherein the method comprises the steps of Representing the state transfer matrix.

(3) Constructing an amplitude state equation for the amplitude;

Similarly to the construction of the phase state equation, for the amplitude a (k) varying with the slow time sampling point k, it can be considered as a slow variation as well, and the amplitude is represented by a second order local polynomial as well, the amplitude state equation composed of the second order local polynomial amplitude coefficient vector p _k can be represented as:

p_k＝F_k-1p_k-1 (18)

p_k＝[p_k-1,p_k,p_k+1]^T,A(k)＝p_k-1(kT_s)²+p_k(kT_s)+p_k+1,, among others, are known from A _k＝[A(k-1),A(k),A(k+1)]^T and A _k＝M_kp_k.

(4) Constructing an observation equation required by phase tracking according to the extracted maneuvering target echo signals;

Because of And A _k represent sampling points of 3 continuous amplitudes and phases respectively, the proposed method splits the observed data into a real part and an imaginary part to construct an observation equation, and the observation equation is known according to the formula (9):

Where s _k represents the continuous 3 sample points of the moving object signal s (η _a) after pulse compression and distance walking, i.e. s _k＝[s(k-1),s(k),s(k+1)]^T.v_r (k) and v _i (k) represent the real and imaginary sample points of the complex gaussian white noise, respectively. As indicated by the symbol H, hadamard product.

Will A _k＝M_kp_k andSubstituting into equation (19), the observation equation is:

y_k＝h¹(p_k)⊙h²(c_k)+v_k (20)

Wherein the method comprises the steps of In addition, v _k＝[v_r(k);v_i(k)]^T.

(5) And constructing a binary state space equation.

The amplitude a (k) in equation (9) is unknown in SAR imaging due to the weighting of the signal by the radar antenna pattern. On the other hand, since the motion parameters of the moving object are unknown, the phase Φ (k) is also unknown. In the method, the motion target parameter estimation is performed by utilizing the tracking thought, so that the following state space equation is constructed in order to realize tracking, to sum up, and in consideration of the influence of noise in practice:

Where w1 and w2 represent phase and amplitude noise, respectively, and Q1 and Q2 represent their corresponding noise covariance matrices. v _k denotes the observation noise and R denotes the corresponding covariance matrix. Unlike conventional state space equations, since the phase and amplitude are unknown at the same time and jointly determine the observed quantity, the state space equation constructed contains two linear state equations and one nonlinear observation equation, and is referred to as a binary state space equation.

(6) Solving the binary state space model to obtain a phase estimation value;

The alternating direction multiplier method (ALTERNATING DIRECTION METHOD OF MULTIPLIERS, ADMM) can effectively solve the problem that two state equations exist in the model, and the Extended Kalman filter (Extended KALMAN FILTER, EKF) can effectively process nonlinear observation equations. Therefore, tracking is performed on the constructed binary state space equation by using the EKF to obtain a tracking value of the phase coefficient, namely, a tracking value of the phase. In order to stably solve the binary state space equation, the invention combines ADMM and EKF and provides a phase tracking method of adaptive amplitude-phase alternating iteration. Specifically, the self-adaptive solving process of the binary state space equation by using the proposed method is as follows:

inputting a signal s (k) of a distance unit where the moving target is located after pulse pressure and distance walking correction.

Initialization parameter value c ₁,P1₁,Q1₁;p₁,P2₁,Q2₁, R

1.Fork=2:N_a-1

2. Extracting data s _k：s_k＝[s(k-1),s(k),s(k+1)]^T;

3. Calculating y _k：y_k＝[real(s_k);imag(s_k)]^T;

4. Calculation M _k-1、M_k and F _k-1:

5. Predicted phase state vector c _k|k-1 and amplitude state vector p _k|k-1:

6. State covariance matrices P1 _k|k-1 and P _2k|k-1 of predicted phases and amplitudes:

7. Alternately calculating Jacobian matrices H1 _k and H2 _k;

8. Kalman gains K1 _k and K2 _k for calculating amplitude and phase:

9. And (3) carrying out amplitude prediction:

10. Updating phase state vectors And an amplitude state vector:

11. Adaptively updating the phase state noise covariance matrix Q1 _k and the amplitude noise covariance matrix Q2 _k:

Wherein, D _k＝(1-b)/(1-b^k), (0 < b < 1), b being a forgetting factor.

12. Updating covariance matrices of phase and amplitude P1 _k and P2 _k:

P1_k＝(I-K1_kH1_k)P1_k|k-1;P2_k＝(I-K2_kH2_k)P2_k|k-1

13. Calculation of

14.End For

15. Obtaining an instantaneous phase vector:

output of instantaneous phase estimate

(7) Inverting the motion parameters of the maneuvering target;

at the time of obtaining the phase estimation value Then, as shown in equation (10), the motion parameter estimation value is:

Wherein the method comprises the steps of Representing an estimated value of the motion parameter,And ψ represents a polynomial phase base matrix, and the specific form is as follows:

After motion parameter estimation is completed, a phase compensation function needs to be constructed to carry out focusing imaging on a weak maneuvering target, and the focusing imaging steps are as follows:

(1) Constructing a phase compensation function based on the motion parameter estimation value;

the phase compensation function is constructed as follows:

(2) Performing phase compensation;

Multiplying the phase compensation function in (23) with (7) to obtain:

Wherein the method comprises the steps of Representing the residual phase due to parameter estimation errors, which are negligible when the parameter estimation is accurate.

(3) Focusing and imaging;

finally, s ₄(t_r,η_a) is subjected to FFT along the azimuth direction, so that a moving target focusing imaging result in a plane can be obtained, and the expression is as follows:

Thus, the focusing imaging of the SAR weak maneuvering target is completed.

The most core technology of the invention is to realize simultaneous estimation of high-order parameters under low signal-to-noise ratio by utilizing the self-adaptive phase tracking thought, thereby avoiding estimation errors caused by error transfer effect, reducing the signal-to-noise ratio threshold of motion parameter estimation by covariance matrix self-adaptation and feedback correction iteration during EKF phase tracking. The method mainly comprises the steps of firstly extracting echo signals of a distance unit where a maneuvering target is located and modeling the echo signals into PPS signals, secondly constructing a phase state equation by using a second-order local polynomial according to the phase of the signals, constructing an amplitude state equation according to the amplitude of change, and then constructing an observation equation by using the measured maneuvering target echo signals. Thus, a binary state space equation of the EKF tracking model consisting of two state equations and one observation equation can be obtained. And finally, carrying out alternate iterative solution on the binary state space equation to obtain an estimated value of the phase, and further carrying out inversion to obtain a parameter estimated value of the moving target.

Different from the existing motion parameter estimation, the method utilizes the self-adaptive EKF to realize phase tracking and perform motion parameter inversion, and parameter estimation is not realized by the existing parameter searching method, the time-frequency analysis method or the high-order fuzzy function method, so that the problems of poor calculation efficiency and low parameter estimation precision are avoided. Specifically, the method of the invention has the computational complexity of O (M ²N_a).

In order to better illustrate the implementation steps and effects of the key technology, fig. 5 shows the phase tracking result, fig. 6 shows the parameter estimation value obtained after the phase inversion, and it can be seen that the parameters of the moving object can be accurately estimated.

Simulation description:

Simulation parameters (one)

The effects of the present invention can be illustrated by simulation using radar parameters and maneuvering target parameters as shown in tables 1 and 2 below. In addition, it should be noted that all effect graphs in the present invention are obtained through the simulation parameters.

Table 1 system simulation parameters

System index	Numerical value	System index	Numerical value
				Carrier frequency	5GHz	Distance to bandwidth	500MHz
Distance sampling rate	600MHz	PRF	2000Hz
				Pulse duration	0.2us	Radar platform speed	100m/s
Nearest diagonal distance	1000m	Accumulation time	2.5s

TABLE 2 maneuvering target parameters

Distance direction parameter	Numerical value	Azimuth parameter	Numerical value
				Initial coordinates	1000m	Initial coordinates	0m
Speed of speed	-10m/s	Speed of speed	10m/s
				Acceleration of	-2m/s²	Acceleration of	2m/s²

(II) simulation Contents

And 1, simulating and analyzing residual errors of the instantaneous skew under different expansion orders by adopting SAR imaging geometric relations, radar parameters and maneuvering target parameters in a table so as to better explain signal characteristics of the maneuvering target, namely, considering and compensating high-order movement parameters. As a result, referring to fig. 3, the horizontal axis represents azimuth time of SAR motion, i.e., slow time in seconds(s), and the vertical axis represents instantaneous pitch residual error in meters (m) at different orders. The dashed line at λ/16 represents a threshold value that enables good focusing, the dashed line marked with circles represents a2 nd order expansion error, the dashed line marked with triangles represents a 3 rd order expansion error, and the solid line marked with rectangles represents a 4 th order expansion error.

Simulation 2 simulation of distance walking correction by using Hough transformation and SOKT transformation. As a result, as shown in fig. 4, the horizontal axis in the figure represents azimuth slow time in seconds(s), and the vertical axis represents distance in meters (m). Fig. 4 (a) shows the result of the pulse compression of the maneuvering target, and a significant distance walk can be seen, and fig. 4 (b) shows the result of SOKT, and the target trajectory is a linear function of slow time, i.e. the distance walk still exists, after the distance bend correction. Fig. 4 (c) shows the result of HT estimation and compensation after distance walk, when the maneuvering target signal is focused substantially on one distance unit.

Simulation 3 whether focus imaging can be performed at low signal-to-noise ratio depends on the accuracy of parameter estimation at low signal-to-noise ratio. If the parameter estimation is accurate, the phase compensation function constructed by estimating the obtained motion parameters will be accurate, and after the phase compensation is performed, the residual phase error will not be greater than pi/4 any more, so that a good focusing imaging effect can be achieved theoretically. The invention extracts the signal of the distance unit where the maneuvering target is located, models the signal as a PPS signal, and performs phase tracking and inversion of the movement parameters by using the method. The results are shown in fig. 5 and 6. Fig. 5 shows a phase value obtained by tracking with an adaptive EKF, the horizontal axis shows an azimuth sampling point index, and the vertical axis shows a phase value in degrees (°). The solid line of the circular mark represents the theoretical value of the phase, and the broken line of the triangular mark represents the phase tracking result. It can be seen that the theoretical value is highly consistent with the phase tracking result. With this phase value, fig. 6 gives the result of the motion parameter estimation value, with the horizontal axis representing the motion parameter to be estimated, the left vertical axis representing the estimation value, and the right vertical axis representing the value of the estimation error. In the figure, a solid line marked with a circle represents an estimated value of each order motion parameter, a broken line marked with a triangle represents a theoretical value, and a broken line marked with a rectangle represents an estimated error result.

And 4, imaging the maneuvering target in the simulation by using the existing parameter estimation and imaging method, and comparing the maneuvering target with the imaging result in the invention. The existing method is mostly not considered for compensating the high-order phase, so that the existing method is ineffective for weak maneuvering target imaging. In addition, based on parameter estimation of self-focusing, the high-order phase compensation effect on the maneuvering target is not ideal under the condition of low signal-to-noise ratio, and in order to illustrate the effectiveness of the imaging method proposed by the invention, focusing effects of different imaging methods are shown in fig. 7. Fig. 7 (a) is an imaging result of estimating and compensating 2-order parameters, fig. 7 (b) is a result of estimating and compensating 3-order parameters by using Huang Penghui et al GHAF, both methods do not image the maneuvering target and have more obvious defocusing in azimuth because only low-order phase compensation is considered, and fig. 7 (c) is a result of estimating and compensating higher-order phases in fig. 7 (b) by using self-focusing PGA algorithm, but because of SNR, the azimuth is still defocused. Fig. 7 (d) shows the imaging result of the method according to the present invention, and fig. 7 (e) shows the ideal imaging result, and it can be seen that the imaging result of the proposed method substantially achieves the ideal effect. In the figure, the horizontal axes are all azimuth directions, and the vertical axes are all distance directions.

Simulation 5 to illustrate the low SNR threshold advantage of the method, the maneuver object was imaged with the method at different SNRs, the results are shown in fig. 8. It can be seen that at pulse pressure SNR as low as-5 dB, although clutter is generated, the focused maneuvering target is still visible, i.e., the method proves to be effective for imaging at low SNR. In addition, as the SNR increases, the target focusing effect becomes better.

The beneficial effects of the invention are as follows:

The word "preferred" is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as "preferred" is not necessarily to be construed as advantageous over other aspects or designs. Rather, use of the word "preferred" is intended to present concepts in a concrete fashion. The term "or" as used in this disclosure is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless specified otherwise or clear from the context, "X uses a or B" is intended to naturally include any of the permutations. That is, "X uses A or B" is satisfied in any of the foregoing examples if X uses A, X uses B, or X uses both A and B.

Moreover, although the disclosure has been shown and described with respect to one or more implementations, equivalent alterations and modifications will occur to others skilled in the art based upon a reading and understanding of this specification and the annexed drawings. The present disclosure includes all such modifications and alterations and is limited only by the scope of the following claims. In particular regard to the various functions performed by the above described components (e.g., elements, etc.), the terms used to describe such components are intended to correspond, unless otherwise indicated, to any component which performs the specified function of the described component (e.g., that is functionally equivalent), even though not structurally equivalent to the disclosed structure which performs the function in the herein illustrated exemplary implementations of the disclosure. Furthermore, while a particular feature of the disclosure may have been disclosed with respect to only one of several implementations, such feature may be combined with one or other features of the other implementations as may be desired and advantageous for a given or particular application. Moreover, to the extent that the terms "includes," has, "" contains, "or variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term" comprising.

The functional units in the embodiment of the invention can be integrated in one processing module, or each unit can exist alone physically, or a plurality of or more than one unit can be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product. The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like. The above-mentioned devices or systems may perform the storage methods in the corresponding method embodiments.

In summary, the foregoing embodiment is an implementation of the present invention, but the implementation of the present invention is not limited to the embodiment, and any other changes, modifications, substitutions, combinations, and simplifications made by the spirit and principles of the present invention should be equivalent to the substitution manner, and all the changes, modifications, substitutions, combinations, and simplifications are included in the protection scope of the present invention.

Claims

1. A SAR weak maneuvering target imaging method based on adaptive phase tracking, characterized in that it comprises the following steps:

Obtain the SAR echo signal of the maneuvering target and build a radar echo signal model;

Pulse compression is performed on the SAR echo signal, and range curvature is corrected by SOKT, and range walk is corrected by estimating the first-order motion parameters by Hough transform;

The signal energy of the maneuvering target after range movement correction will be concentrated in a range unit, and the signal in the range unit will be modeled as a PPS signal and extracted;

The phase of the signal of the extracted range unit of the maneuvering target is tracked, and the maneuvering target parameters are inverted using the phase obtained by tracking;

The phase compensation function is constructed using the motion parameters obtained by inversion to achieve SAR focused imaging of maneuvering targets.

The adaptive phase tracking method is used to estimate the motion parameters of each order. The specific steps are as follows:

(1) Extract the signal of the distance unit where the maneuvering target is located and construct it into a high-order PPS signal;

After the range movement correction, the maneuvering target echo is concentrated in a range unit. After the echo in the range unit is extracted, it is modeled as a high-order PPS signal as follows:

Discrete sampling of the signal and considering the noise term, we have:

s(k)＝A(k)·exp{jφ(k)}+n(k) (9)

Where k = 1, 2, ..., _Na , represents the SAR azimuth sampling index, _Na represents the number of sampling points in the azimuth, n(k) is a complex zero-mean Gaussian white noise with a variance of δ ² , A(k) is the amplitude sampling value after pulse compression, and φ(k) is a polynomial phase function representing the Doppler characteristics of a maneuvering target. Specifically:

Where _Ts is the sampling interval in azimuth, and _Ts = 1/PRF, PRF is the pulse repetition frequency of SAR azimuth sampling, _δs is the target complex reflection coefficient;

(2) Constructing the phase state equation required for phase tracking for the phase;

Represents the values of 3 consecutive phase sampling points, as follows:

From the expression of φ(k), we can see that the phase values between adjacent sampling points of the polynomial phase curve are approximately equal, so:

φ(k-1)-2φ(k)+φ(k+1)≈0 (12)

Combining (11) and (12), we get:

Where B = [0, 1, 0; 0, 0, 1; 0, -1, 2];

A local polynomial is used to represent the phase value when the sampling point sequence is k. In order to balance the relationship between computational efficiency and estimation accuracy, a second-order local polynomial is used for phase fitting, that is,

Φ(k)＝c _k-1 (kT _s ) ² +c _k (kT _s )+c _k+1 (14)

Where c _k is the coefficient of the local phase polynomial at time k;

According to (14), the vector consisting of the values of three consecutive phase sampling points is It is expressed as:

in For a certain k moment, it is a certain matrix; represents the phase state vector;

Combining (13) and (15), we can know that:

M _k c _k =BM _k-1 c _k-1 (16)

Therefore, both ends of equation (16) are multiplied by the inverse matrix of _Mk , and the phase state equation formed by the second-order local polynomial phase coefficient vector _ck is expressed as:

c _k =F _k-1 c _k-1 (17)

in represents the state transfer matrix;

(3) Construct the amplitude state equation for the amplitude;

The amplitude A(k) that changes with the slow time sampling point k is slowly varying, and the amplitude is represented by a second-order local polynomial. The amplitude state equation formed by the second-order local polynomial amplitude coefficient vector p _k is expressed as:

p _k =F _k-1 p _k-1 (18)

Wherein p _k =[p _k-1 ,p _k ,p _k+1 ] ^T ; A(k)=p _k-1 (kT _s ) ² +p _k (kT _s )+p _k+1 , representing a second-order local polynomial of the amplitude; in addition, three consecutive amplitude sampling values _Ak are: _Ak =[A(k-1), A(k), A(k+1)] ^T , and _Ak =M _k p _k ;

(4) Constructing the observation equation required for phase tracking based on the extracted maneuvering target echo signal;

because and _Ak represent three consecutive sampling points of amplitude and phase respectively. The observation data is split into real and imaginary parts to construct the observation equation. According to formula (9), we can know that:

Wherein, _sk represents three consecutive sampling points of the moving target signal s( _ηa ) after pulse compression and range movement, that is, _sk = [s(k-1), s(k), s(k+1)] ^T , v _r (k) and _vi (k) represent the real and imaginary sampling points of complex Gaussian white noise, respectively, ⊙ represents the Hadamard product,

Set _Ak = _Mk p _k and Substituting into equation (19), the observation equation is:

y _k ＝h ₁ (p _k )⊙h ₂ (c _k )+v _k (20)

in In addition, v _k =[v _r (k); _vi (k)] ^T ,

(5) Constructing the binary state space equation

Construct the following binary state space equation:

Where w1 and w2 represent phase and amplitude noise respectively, Q1 and Q2 represent their corresponding noise covariance matrices, v _k represents observation noise, and R represents the noise covariance matrix corresponding to the observation equation;

Since the phase and amplitude are unknown at the same time and jointly determine the observed quantity, the constructed state space equation contains two linear state equations and one nonlinear observation equation, that is, the binary state space equation;

(6) Solving the binary state space model to obtain a phase estimate;

The binary state space equation is stably solved by using an adaptive amplitude-phase alternating iteration phase tracking method combining ADMM and EKF algorithms, wherein the ADMM method is used to solve the problem of two state equations in the model, and the EKF is used to process nonlinear observation equations;

(7) Inverting the estimated parameter values of the maneuvering target through the phase estimated value;

Getting the phase estimate After that, the motion parameter estimation is:

in represents the estimated value of the motion parameters, Ψ represents the polynomial phase basis matrix, which is in the form of:

8) After obtaining the estimated values of the parameters of the maneuvering target, focusing imaging is achieved by constructing a phase compensation function, wherein the phase compensation function is constructed as follows:

Multiplying the phase compensation function in equation (23) with equation (7) yields:

in represents the residual phase due to parameter estimation error;

Finally, perform FFT on s ₄ (t _r , η _a ) along the azimuth direction to obtain the focusing imaging result of the moving target in the plane, which is expressed as follows:

The process of adaptive solution of binary state space equations using improved EKF is as follows:

S1: Get the signal s(k) of the distance unit where the moving target is located after pulse pressure and distance movement correction;

Initialization parameter values: c ₁ , P1 ₁ , Q1 ₁ ; p ₁ , P2 ₁ , Q2 ₁ ; R;

Wherein c ₁ represents the initial value of the phase state vector, the initial value is the value at the moment k=1, P1 ₁ represents the initial covariance matrix corresponding to c ₁ , Q1 ₁ represents the initial noise covariance matrix of the phase state equation; by analogy, p ₁ represents the initial value of the amplitude state vector, P2 ₁ represents the initial covariance matrix corresponding to p ₁ , Q2 ₁ represents the initial noise covariance matrix of the amplitude state equation; R represents the noise covariance matrix of the observation equation;

S2: Set k=2, extract data s _k : s _k =[s(k-1), s(k), s(k+1)] ^T ;

S3: Calculate y _k : y _k =[real(s _k );imag(s _k )] ^T ; real(·) is the operation of taking the real part, and imag(·) is the operation of taking the imaginary part;

S4: Calculate M _k-1 , M _k and F _k-1 :

S5: Predict the phase state vector c _k|k-1 and the amplitude state vector p _k|k-1 :

Where k|k-1 represents the prediction result of the next moment k based on the previous moment k-1;

S6: Predict the state covariance matrices P1 _k|k-1 and P2 _k|k-1 of phase and amplitude:

T stands for transpose;

S7: alternately calculating the phase Jacobian matrix H1 _k and the amplitude Jacobian matrix H2 _k ;

S8: Calculate the phase and amplitude Kalman gains K1 _k and K2 _k :

S9: Make amplitude prediction at time k:

S10: Update phase state vector and the amplitude state vector

S11: Adaptively update the phase state noise covariance matrix Q1 _k and the amplitude noise covariance matrix Q2 _k :

in, d _k =(1-b)/(1-b _k ), (0＜b＜1), b is the forgetting factor;

S12: Update the covariance matrices P1 _k and P2 _k of the phase and amplitude:

P1 _k = (I-K1 _k H1 _k )P1 _k|k-1 ; P2 _k = (I-K2 _k H2 _k )P2 _k|k-1

Where I is the identity matrix;

S13: Calculation

in represents the estimated value of c _k ;

S14: increase k by 1 in sequence, and repeat steps S2-S13 until k is equal to ^Na -1;

S15: Get the estimated value of the instantaneous phase vector φ

2. The SAR weak maneuvering target imaging method based on adaptive phase tracking according to claim 1 is characterized in that constructing a radar echo signal model of a SAR maneuvering target comprises:

The moving target echo signal after pulse compression is expressed in the two-dimensional time domain as:

Wherein, _δs is the complex reflection coefficient of the target after pulse compression, _tr represents the fast time in range, _ta represents the slow time in azimuth, _Ta is the synthetic aperture time, _wa (·) represents the time window function in azimuth, and _wa ( _ta )=rect( _ta / _Ta ), c represents the speed of light, λ represents the wavelength, _Br represents the bandwidth of the transmitted signal, and R( _ta ) represents the instantaneous slant range between the platform and the target;

The instantaneous slant range between the radar platform and the moving target is expanded into a high-order polynomial model using Taylor approximation, as follows:

Wherein, _bm represents the coefficient of the mth order polynomial after the instantaneous slant range is expanded, 1≤m≤M, and M represents the highest order of the expansion, V is the moving speed of the radar platform, the initial position coordinates of the maneuvering target are (0, _R0 ), and the speed and acceleration along the track direction are _va , _aa , respectively, and the speed and acceleration along the range direction are _vr , _ar , respectively, and _R0 is the closest slant range between the platform and the target;

To meet the imaging focus requirements, M has:

Where ΔR(t _a ) represents the instantaneous slant range Taylor approximation expansion error, Δρ _r represents the range resolution, represents the residual phase error.

3. The SAR weak maneuvering target imaging method based on adaptive phase tracking according to claim 2 is characterized in that the specific steps of the range movement correction are:

(1) Perform SOKT correction on the signal after pulse compression to correct the distance bending:

Only SOKT is used to correct the distance curvature caused by second-order and higher parameters, including:

According to the resolution requirements, synthetic aperture time and the prior parameters of the moving target, the instantaneous slant range is expanded to the Mth order, and the two-dimensional time domain signal after pulse compression is FFT along the fast time dimension to obtain the range frequency domain-azimuth time domain echo signal, as follows:

Wherein, W _r (f _r ) represents the frequency domain form of the range-direction time-domain window function w _r (t _r ), f _r represents the range-direction frequency, and f _c represents the radar carrier frequency;

The distance curvature is corrected by SOKT, the expression of which is:

Among them, η _a is the new slow time variable;

Substituting (5) into (4) and performing range-oriented IFFT transformation, the two-dimensional time domain echo signal after SOKT is:

(2) Using Hough transform to estimate the first-order motion parameters to complete distance walking correction;

The distance movement curve is detected in the t _r -η _a plane using Hough transform to obtain the slope of the straight line. The estimated value of the first-order motion parameter is estimated based on the slope value of the distance movement curve. Finally, the distance movement compensation factor is constructed according to the estimated value to achieve distance movement correction;

Finally, the echo expression after distance movement correction is: