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

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 will be 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

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a SAR weak maneuvering target imaging method based on adaptive phase tracking. Background Art

[0002] 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, as well as in military fields such as battlefield reconnaissance, military target movement monitoring, and precision strike. Compared with optical imaging technology, it has the advantages of providing imaging results of observation scenes all day, all weather and at long distances. In addition, SAR imaging technology can not only obtain the electromagnetic scattering characteristics and high-resolution two-dimensional images of stationary objects, but also achieve focused imaging of moving targets through the selection and compensation of reference functions.

[0003] SAR imaging is to load the radar onto a mobile platform and move it along a pre-set route. This direction is called the azimuth direction, and the direction perpendicular to it is called the range direction. During the movement of the antenna in the azimuth direction, a large aperture antenna can be synthesized equivalently, thereby achieving the purpose of increasing the azimuth resolution, completing the coherent accumulation of echoes at various positions in the scene, and finally obtaining the scene image. The SAR echoes collected in different azimuths are coherently accumulated through matched filtering technology. In order to focus on the scene, the instantaneous slant range relationship between the radar and the imaging scene needs to be accurately known. This slant range relationship is reflected in the SAR echo as range movement and Doppler phase movement. The so-called range movement is the movement of the instantaneous slant range from the radar to each scattering point in the scene across the range unit in different azimuths; the so-called Doppler phase movement is the movement of the azimuth across the velocity unit caused by the change in the relative position relationship between the radar and the scattering point.

[0004] When SAR images a static scene, the motion trajectory of the radar platform can be accurately measured by inertial navigation and other equipment, and the instantaneous slant range or phase relationship between the radar and each scattering point in the imaging scene can be accurately calculated. At this time, phase-compensated coherent accumulation imaging can be performed using the classical imaging method. However, when there is a moving target in the scene, due to the non-cooperativeness and random movement of the moving target, its motion parameters are unknown, and the instantaneous slant range and its corresponding phase can no longer be accurately obtained. Direct processing using the static target imaging algorithm will cause image defocus, blur or azimuth offset. If the moving target parameters can be estimated from the SAR echo, and phase compensation can be performed to eliminate the influence caused by the target motion, then the compensated echo can be equivalent to a static target, and then a good focusing result of the moving target can be obtained by processing the static target SAR imaging method. Therefore, the key to the quality of the imaging result lies in whether the motion parameters of the moving target can be accurately estimated and compensated.

[0005] For conventional moving targets, generally only the estimation and compensation of low-order motion parameters (2nd order and below, such as velocity and acceleration) need to be considered to achieve a good imaging effect. However, with the development of radar technology and the update of practical application requirements, the imaging of maneuvering targets with complex motion characteristics has received close attention. For example, in modern military warfare, in order to evade detection and attack, the movement of some targets is complex and changeable. When imaging such targets, the phase error caused by the high-order motion parameters (3rd order and above) brought by the maneuver of the target cannot be ignored. If it is not compensated, the imaging result will be defocused. It is worth noting that in addition to the maneuver of the imaged target itself, which will bring non-negligible high-order phase, when the conventional moving target moves on the terrain with drastic fluctuations, it will also produce high-order phase in the SAR echo; when the synthetic aperture time is long, the traditional approximate model of uniform or uniformly accelerated motion of the target is no longer valid, which is equivalent to the target maneuvering, and the high-order phase also needs to be considered. It can be seen that in SAR moving target imaging, there are a large number of scenarios where the estimation and compensation of high-order phase parameters need to be considered. In addition, such targets with complex motion characteristics are often small in size and have weak radar echoes. This invention refers to such targets as weak maneuvering targets. Therefore, in order to effectively complete tasks such as surveillance, reconnaissance and precision strike, it is necessary to conduct in-depth research on SAR weak maneuvering target imaging technology.

[0006] In order to obtain high-resolution imaging results of maneuvering targets, it is necessary to estimate and compensate for the range walk and Doppler frequency walk, that is, the high-order phase caused by the target maneuver. In recent decades, the methods proposed by relevant research institutes for estimating and compensating range walk and Doppler frequency walk can be mainly divided into two categories: the first category only considers low-order phase models, that is, the second-order and lower phase models composed of velocity and acceleration; while the second category considers high-order phase models, that is, the third-order and higher-order phase models. For the estimation and compensation of low-order model parameters, the mainstream methods are: (1) based on Keystone transform and its improved methods, including first-order Keystone transform (Keystone Transform, KT), second-order Keystone transform (Second-order Keystone Transform, SOKT) and Doppler Keystone transform. This type of method does not require any prior information on the target motion parameters and is widely used. (2) Radon Transform (RT) methods, such as Radon-Fourier transform (RFT), Radon fractional Fourier transform and Radon second-order Weibull distribution. (3) Time-frequency analysis methods, mainly including short-time Fourier transform, Weibull distribution, fuzzy function and fractional Fourier transform.

[0007] However, for SAR maneuvering target imaging, the above method that can only compensate for low-order phase parameters is not applicable. In order to solve this problem, some scholars have studied the compensation method of third-order phase parameters. For example, You Dong et al. from Xidian University proposed a ground maneuvering target imaging and motion parameters estimation method based on adaptive polynomial fourier transform (APFT) in 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. The proposed algorithm first estimates the range velocity from the range movement of the signal envelope through Hough transform after the range pulse pressure and the uniform range movement correction. Then, this range velocity is used to complete the range movement correction of the signal. Then, the additional range curvature is corrected by SOKT. Next, the second-order and third-order Doppler parameters of the moving target are estimated by APFT and the corresponding moving target motion parameters are obtained. Finally, the moving target can be precisely focused by constructing a phase compensation function through the estimated motion parameters. Similarly, Huang Penghui et al. proposed a maneuvering target parameter estimation and imaging algorithm based on generalized high-order ambiguity function (GHAF) in the 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.Similar to the method proposed by You Dong et al., Hough transform and SOKT are first used to compensate for range motion, and the signal of the target's range unit is modeled as a third-order polynomial phase signal (PPS); then GHAF is used to transform the PPS signal into the two-dimensional frequency domain to achieve two-dimensional coherent accumulation of the signal, and the second-order and third-order motion parameters of the target motion are estimated based on the peak position; finally, the parameters are used for compensation to obtain the focused imaging result. Furthermore, in order to reduce the signal-to-noise ratio threshold, Xu Jia et al. in the non-patent literature Radarmaneuvering target motion estimation based on generalized radon-fourier transform, IEEE Transactions on Signal Processing, vol. 60, no. 12, pp. 6190–6201, 2012., realized parameter estimation and compensated imaging by traversing and searching in a multidimensional parameter space under coherent accumulation. Although better results can be obtained under low signal-to-noise ratio, the computational efficiency is reduced because it needs to search parameters in three-dimensional space. The above methods have one thing in common, that is, they only consider the third-order phase model, while higher-order phase compensation is ignored. There are few studies on the estimation of higher-order phase parameters above the third order. The current mainstream method is to perform high-order phase compensation through the self-focusing strategy, such as Phase Gradient Autofocus (PGA) and Contrast Optimization Algorithm (COA), but these methods require a high signal-to-noise ratio point, otherwise the estimated phase error accuracy will deteriorate sharply.

[0008] When using synthetic aperture radar (SAR) to image ground moving targets, existing methods have been able to obtain high-resolution images of static scenes and conventional moving targets. However, for targets to be imaged that have complex motion characteristics and a small target radar cross section (RCS), they are referred to as weak maneuvering targets in the present invention. Compared with conventional moving targets, the motion of such targets is more complex and changeable and the echo signal-to-noise ratio (SNR) is lower, so when using SAR to image them, there are two problems: 1) In addition to considering the distance and Doppler movement caused by low-order parameters such as speed and acceleration, the influence of jerk and even higher-order motion parameters cannot be ignored, that is, high-order motion parameters need to be estimated and compensated during SAR imaging; 2) In order to obtain SAR focused imaging results for such targets, it is necessary to study and develop parameter estimation and imaging algorithms with better noise resistance. Therefore, how to effectively focus on weak maneuvering targets under low signal-to-noise ratio is a key technical problem to be solved.

[0009] When dealing with the SAR weak maneuvering target imaging problem, the existing technology has the main disadvantages of low parameter estimation accuracy and high signal-to-noise ratio requirements, and is unable to accurately focus and image the maneuvering target when the signal-to-noise ratio is low.

[0010] The disadvantage of low parameter estimation accuracy mainly comes from three aspects:

[0011] 1) Model mismatch, for example, a high-order model in practice is modeled as a low-order model and the parameters are estimated, which ultimately leads to poor parameter estimation accuracy due to model mismatch;

[0012] 2) Methods based on time-frequency analysis cannot obtain high resolution of time and frequency at the same time. When the parameter estimation value is finally obtained by analyzing the time-frequency relationship on the time-frequency plane, the resolution is not high, resulting in large parameter estimation errors;

[0013] 3) Error transfer: The core principle of using high-order fuzzy functions for parameter estimation is to reduce the order of the estimated high-order parameter values ​​to obtain the next-highest-order parameter values. Once the high-order parameter value is estimated inaccurately, the error will be transferred to the low-order estimation result, that is, there is an error transfer effect, which leads to low accuracy of the final parameter estimation.

[0014] The disadvantages of high signal-to-noise ratio requirements mainly come from two aspects:

[0015] 1) In parameter estimation, incoherent accumulation is performed, resulting in signal-to-noise ratio loss;

[0016] 2) The self-focusing algorithm needs to use a prominent point with a high signal-to-noise ratio as a reference for phase estimation compensation. Only when there are obvious strong scattering points in the scene can the phase estimation result be accurate, and can better focused imaging results be obtained. Summary of the invention

[0017] In order to solve the problem that the performance of existing high-resolution SAR imaging technology drops sharply when applied to weak maneuvering targets, it is hoped that the signal-to-noise ratio threshold requirement can be reduced while improving the parameter estimation accuracy, and finally realizing high-resolution imaging of maneuvering targets under low signal-to-noise ratio. In view of this, the present invention proposes a SAR weak maneuvering target imaging method based on adaptive phase tracking, which is suitable for fast focusing imaging of weak maneuvering targets under low SNR conditions.

[0018] The SAR weak maneuvering target imaging method based on adaptive phase tracking disclosed in the present invention comprises the following steps:

[0019] Obtain the SAR echo signal of the maneuvering target and build a radar echo signal model;

[0020] 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;

[0021] 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;

[0022] The phase of the signal of the distance unit where the maneuvering target is extracted is tracked, and the maneuvering target parameters are inverted using the phase obtained by tracking;

[0023] The phase compensation function is constructed using the inverted motion parameters to achieve SAR focused imaging of maneuvering targets.

[0024] The beneficial effects of the present invention are as follows:

[0025] 1) It is suitable for SAR imaging of weak maneuvering targets. This is mainly because the SAR echo modeling is carried out based on the complex motion characteristics of the maneuvering target, the non-negligible high-order motion parameters are taken into account, and a targeted estimation method for the high-order parameters is proposed.

[0026] 2) The parameter estimation has high accuracy and low computational complexity. This is mainly because a high-order motion model is taken into account, which is closer to the actual situation. In addition, the parameter estimation method based on phase tracking can estimate parameters of each order at the same time, avoiding the estimation error caused by the error propagation effect, and adopts the EKF with low computational complexity to realize phase tracking, thereby improving computational efficiency.

[0027] 3) Capable of focusing imaging at low SNR; this is mainly because the covariance matrix adaptation and feedback correction iteration during EKF phase tracking reduce the signal-to-noise ratio threshold of motion parameter estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of the SAR weak maneuvering target imaging method based on adaptive phase tracking of the present invention;

[0029] Figure 2 The geometric model diagram of SAR observing maneuvering targets;

[0030] Figure 3 This is the approximate error analysis diagram of the instantaneous slant distance at different orders;

[0031] Figure 4 (a) is the pulse compression result diagram of the maneuvering target;

[0032] Figure 4 (b) is the result image after SOKT distance bending correction;

[0033] Figure 4 (c) is the result after Hough transform is used to correct the distance movement;

[0034] Figure 5 This is the result of phase tracking of maneuvering target signal using adaptive EKF;

[0035] Figure 6 The motion parameter estimation and error map obtained by inverting the phase tracking results;

[0036] Figure 7 (a) is the imaging result after second-order parameter estimation and compensation;

[0037] Figure 7 (b) is the imaging result after estimating and compensating the third-order phase parameters using GHAF;

[0038] Figure 7 (c) is the imaging result after compensating the high-order phase using the PGA algorithm;

[0039] Figure 7 (d) is an imaging result diagram of the algorithm described in the present invention;

[0040] Figure 7 (e) is the ideal imaging result diagram of the simulated maneuvering target;

[0041] Figure 8 Graphs showing imaging results of the method under different pulse pressure SNRs; Figure 8 (a) SNR = -5dB; Figure 8 (b) SNR = -3dB; Figure 8 (c) SNR = -1dB; Figure 8 (d) SNR = 1 dB; Figure 8 (e) SNR = 3dB; Figure 8 In (f), SNR = 5dB. DETAILED DESCRIPTION

[0042] The present invention is further described below in conjunction with the accompanying drawings, but the present invention is not limited in any way. Any changes or substitutions made based on the teachings of the present invention belong to the protection scope of the present invention.

[0043] The basic idea of ​​the technical solution described in the present invention is that after obtaining the SAR echo signal of a weak maneuvering target, the motion parameters of the weak maneuvering target are estimated first, so that the moving target can be equivalent to a cooperative target, and then the estimated motion parameters are used to determine the phase relationship between the target and the moving radar platform, thereby constructing a compensation function to perform focused imaging of the moving target. In this way, the accuracy of the SAR echo model, how to estimate the parameters of the moving target, whether it can be effectively estimated under low signal-to-noise ratio, and whether the high-order parameter estimation values ​​can be obtained will directly affect the imaging results.

[0044] The detailed technical solution of the present invention is implemented in the flowchart as shown in FIG. Figure 1 As shown. When the radar system obtains the SAR echo signal of a maneuvering target, first, pulse compression is performed on it, and the range curvature is corrected by SOKT, and the first-order motion parameters are estimated by Hough transform to correct the range movement. The energy of the maneuvering target signal after the range movement correction will be concentrated in a distance unit. The signal in the distance unit is modeled as a PPS signal in the present invention; secondly, the signal of the distance unit where the maneuvering target is located is extracted, and the phase of the signal is tracked, and the maneuvering target parameters are inverted by the phase obtained by tracking. The present invention uses an adaptive EKF with a small amount of calculation to complete the phase tracking of the PPS signal. The method mainly includes the steps of constructing and solving the phase and amplitude state equations, the observation equation and the binary state space equation. In the process of iteratively solving the phase by the adaptive EKF, the value of the covariance matrix can be adaptively iteratively adjusted according to the echo data. Compared with the existing method, the method of the present invention has better stability and can effectively track the phase at low SNR. After the phase value is obtained, the motion parameters of each order can be inverted at the same time, effectively avoiding the error transmission effect. Finally, the phase compensation function is constructed using the estimated motion parameter value, and the SAR focusing imaging of the maneuvering target can be achieved.

[0045] Next, the present invention will explain in more detail the specific technical implementation scheme of the present invention in combination with derivation and formula.

[0046] In order to facilitate the description of the technical details of the method of the present invention, the present invention first constructs the radar echo signal of the SAR maneuvering target. Without loss of generality, for the positive side-view strip SAR imaging, the imaging geometry in the two-dimensional slant range plane is as follows: Figure 2 Assume that the speed of the radar platform is V and the synthetic aperture time is T a The initial position coordinates of the maneuvering target are (0, R0), and the velocity and acceleration along the track are v a , a a , the velocity and acceleration along the distance direction are v r , a r , the target moves from P0 to P1 during the observation time. Assume that the closest slant distance and instantaneous slant distance between the platform and the target are expressed as R0 and R(t a ), where t a Indicates slow time of direction.

[0047] Assuming that the radar transmits a linear frequency modulated (LFM) signal, the echo signal of the moving target can be expressed in the two-dimensional time domain after pulse compression as follows:

[0048]

[0049] Among them, δ s is the complex reflection coefficient of the target after pulse compression. r Indicates the distance to fast time, w a (·) represents the azimuth 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. Figure 2 The geometric relationship between the radar platform and the moving target can be obtained, and the expression of the instantaneous slant range between the radar platform and the moving target can be expanded into a high-order polynomial model using Taylor approximation, as follows:.

[0050]

[0051] Among them, b m Represents the coefficient of the mth order polynomial after the instantaneous slant range is expanded, and M represents the highest order of expansion. In most studies, only the estimation and compensation of the third-order and lower parameters (b1, b2, b3) are considered, that is, M≤3. However, for maneuvering targets, high-order parameters cannot be ignored, that is, b4 and higher-order parameters may need to be considered. In actual SAR imaging, the order M of the Taylor approximation expansion is determined by the synthetic aperture time, the moving target parameters and the imaging resolution Δρ. rOn the one hand, in order to complete the distance movement correction, the instantaneous slant range expansion approximate error ΔR(t a ) should not span the range resolution unit; on the other hand, in order to achieve coherent accumulation imaging, it is necessary to ensure that the residual phase error No more than π / 4. The choice of M should satisfy:

[0052]

[0053] In actual operation, since the motion parameters of the non-cooperative target are unknown, b in the above formula will be m It is unknown, so the value of M cannot be accurately calculated. According to references, in the case of medium and low resolution or short synthetic aperture time, the instantaneous slant range expansion order usually does not exceed 3rd order to meet the imaging requirements, so the existing moving target SAR imaging algorithm is mainly studied for the 3rd order and below motion model. However, when imaging at high resolution or imaging maneuvering targets, the value of M must be appropriately increased.

[0054] The present invention constructs a SAR echo model for the complex and changeable motion characteristics of weak maneuvering targets. Different from the SAR echo of conventional moving targets, it is necessary to consider a higher-order Taylor expansion of the instantaneous slant range, followed by the introduction of a high-order phase, and the value of the high-order phase is usually greater than π / 4 required for imaging performance. If the existing imaging method is directly used, only the estimation and compensation of low-order motion parameters are considered, and the Doppler movement caused by high-order motion parameters is ignored, so the imaging of the maneuvering target naturally cannot be focused.

[0055] In imaging, whether it is necessary to perform high-order expansion of the instantaneous slant range, that is, whether it is necessary to consider the compensation of the high-order phase error, mainly depends on whether the high-order phase error is greater than π / 4 required for imaging, that is, whether the instantaneous slant range expansion error is greater than λ / 16. In order to illustrate the difference in signal model between maneuvering targets and conventional moving targets, Figure 3 The instantaneous slant range approximation error of a maneuvering target at different expansion orders is given. It can be seen that at least the fourth order needs to be considered to achieve the focused imaging requirements, that is, high-order phase parameters need to be considered. Therefore, the SAR echo model proposed in the present invention considers high-order phase parameters to achieve focused imaging requirements.

[0056] After obtaining the SAR echo signal of the maneuvering target as described above, the imaging method of the present invention first needs to perform pulse compression on the echo and extract the moving target signal, and perform range motion correction on the extracted moving target signal to correct the target signal to a range unit. The steps of range motion correction are: (1) performing SOKT correction on the signal after pulse compression to correct the range curvature;

[0057] Since the envelope after pulse compression is insensitive to the approximate error of instantaneous slant range expansion, it is considered that only SOKT can be used to correct the range curvature caused by 2nd order and above parameters. Specifically:

[0058] Assuming that the instantaneous slant range needs to be expanded to M orders (usually, M≤4) according to the resolution requirement, synthetic aperture time and prior parameters of the moving target, the two-dimensional time domain signal after pulse compression is FFT-ed along the fast time dimension to obtain the range frequency domain-azimuth time domain echo signal, as follows:

[0059]

[0060] Among them, W r (f r ) represents the distance time domain window function w r (t r ) in the frequency domain, f r represents the frequency in the range direction. When the SNR is high, envelope alignment is used to correct the range walk. However, when the SNR is low, the generalized Keystone transform can effectively correct the range walk when the moving target parameters are unknown. In this paper, SOKT is first used to correct the range curvature. The expression of SOKT is:

[0061]

[0062] Substituting (5) into (4) and performing range-oriented IFFT transformation, the two-dimensional time domain echo signal after SOKT is:

[0063]

[0064] From equation (6), we can see that the range curvature is corrected. However, the range movement still exists, but the amount of range movement is reduced to half of the original. Next, we correct the range movement.

[0065] (2) Using Hough transform to estimate the first-order motion parameters to complete distance walking correction;

[0066] According to the literature, Hough can effectively detect straight lines in a two-dimensional plane. r -η a The distance movement curve is detected in the plane to obtain the slope of the straight line. The estimated value of the first-order motion parameter can be estimated based on the slope value of the distance movement curve. Finally, distance movement correction can be achieved by constructing the distance movement compensation factor based on the estimated value.

[0067] The echo expression after distance movement correction is:

[0068]

[0069] After completing the distance walking correction, it is necessary to estimate the motion parameters of each order. The present invention proposes a parameter estimation method based on adaptive phase tracking. The steps of parameter estimation based on adaptive phase tracking are:

[0070] (1) Extract the signal of the distance unit where the maneuvering target is located and construct it into a high-order PPS signal;

[0071] It can be seen from formula (7) that after range movement correction, the echo of the maneuvering target is concentrated in one range unit. The echo in the range unit is extracted and modeled as a high-order PPS signal as follows:

[0072]

[0073] Discrete sampling of the signal and considering the noise term, we have:

[0074] s(k)=A(k)·exp{jφ(k)}+n(k) (9)

[0075] where k = 1, 2, ..., N a , represents the SAR azimuth sampling index, N a represents the number of sampling points in the azimuth direction. n(k) is the variance of δ 2 A(k) is the amplitude sampling value after pulse compression, and φ(k) is the polynomial phase function representing the Doppler characteristics of the maneuvering target. Specifically:

[0076]

[0077] Where T s is the azimuth sampling interval, and Ts=1 / PRF, PRF is the pulse repetition frequency of SAR azimuth sampling.

[0078] (2) Constructing the phase state equation required for phase tracking according to the phase;

[0079] Assumptions Represents the values ​​of 3 consecutive phase sampling points, as follows:

[0080]

[0081] From the expression of φ(k), we can see that the curvature between adjacent sampling points of the polynomial phase curve is usually smoother. It should be noted that the smoothness here means that the phase values ​​at adjacent sampling points are approximately equal. Therefore:

[0082] φ(k-1)-2φ(k)+φ(k+1)≈0 (12)

[0083] Combining (11) and (12), we can obtain:

[0084]

[0085] Where B = [0, 1, 0; 0, 0, 1; 0, -1, 2].

[0086] On the other hand, the present invention uses a local polynomial to represent the phase value when the sampling point sequence is k. In order to balance the relationship between calculation efficiency and estimation accuracy, a second-order local polynomial is used for phase fitting, that is,

[0087] φ(k)=c k-1 (kT s ) 2 +c k (kT s )+c k+1 (14)

[0088] According to (14), the vector consisting of the values ​​of three consecutive phase sampling points is It can be expressed as:

[0089]

[0090] in, Combining (13) and (15), we can see that:

[0091] M k c k =BM k-1 c k-1 (16)

[0092] 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 can be expressed as:

[0093] c k =F k-1 c k-1 (17)

[0094] in represents the state transfer matrix.

[0095] (3) Construct the amplitude state equation for the amplitude;

[0096] Similar to the construction of the phase state equation, the amplitude A(k) that changes with the slow time sampling point k can also be considered to be slowly varying, and the amplitude is also represented by a second-order local polynomial. Then the second-order local polynomial amplitude coefficient vector p k The amplitude state equation can be expressed as:

[0097] p k =F k-1 pk-1 (18)

[0098] where 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 , and we can also know that A k =[A(k-1), A(k), A(k+1)] T and A k =M k p k .

[0099] (4) Constructing the observation equation required for phase tracking based on the extracted maneuvering target echo signal;

[0100] because and A k Represent three consecutive sampling points of amplitude and phase respectively. The proposed method splits the observed data into real and imaginary parts to construct the observation equation. According to formula (9), it can be seen that:

[0101]

[0102] Among them, s k represents the moving target signal s(η) after pulse compression and distance movement a ), namely s k =[s(k-1),s(k),s(k+1)] T .v r (k) and v i (k) represents the real and imaginary sampling points of complex Gaussian white noise. ⊙ represents the Hadamard product.

[0103] A k =M k p k and Substituting into equation (19), we can get the observation equation:

[0104] y k =h 1 (p k )⊙h 2 (c k )+v k (20)

[0105] in In addition, vk =[v r (k); v i (k)] T .

[0106] (5) Construct a binary state space equation.

[0107] Due to the weighting effect of the radar antenna pattern on the signal, in SAR imaging, the amplitude A(k) in equation (9) is unknown. On the other hand, since the motion parameters of the moving target are unknown, the phase φ(k) is also unknown. The method described in the present invention uses the idea of ​​tracking to estimate the parameters of the moving target. In order to achieve tracking, in summary, and considering the influence of noise in practice, the following state space equation is constructed:

[0108]

[0109] Where w1 and w2 represent phase and amplitude noise respectively, and Q1 and Q2 represent their corresponding noise covariance matrices. k Represents the observation noise, and R represents the corresponding covariance matrix. Different from the conventional state space equation, since the phase and amplitude are unknown at the same time and jointly determine the observation quantity, the constructed state space equation includes two linear state equations and one nonlinear observation equation, which is called the binary state space equation in the present invention.

[0110] (6) Solving the binary state space model to obtain a phase estimate;

[0111] The Alternating Direction Method of Multipliers (ADMM) can effectively solve the problem of two state equations in the model; the Extended Kalman Filter (EKF) can effectively handle nonlinear observation equations. Therefore, by tracking the constructed binary state space equation using EKF, the tracking value of the phase coefficient is obtained, that is, the tracking value of the phase is obtained. In order to stably solve the above binary state space equation, the present invention combines ADMM with EKF and proposes an adaptive amplitude-phase alternating iterative phase tracking method. Specifically, the process of adaptively solving the binary state space equation using the proposed method is as follows:

[0112] Input: The signal s(k) of the distance unit where the moving target is located after pulse pressure and range movement correction.

[0113] Initialization parameter values: c1, P11, Q11; p1, P21, Q21; R

[0114] 1. Fork = 2: N a -1

[0115] 2. Extract data k :s k =[s(k-1),s(k),s(k+1)] T ;

[0116] 3. Calculate y k :y k =[real(s k );imag(s k )] T ;

[0117] 4. Calculate M k-1 、M k and F k-1 :

[0118] 5. Predict the phase state vector c k|k-1 and the amplitude state vector p k|k-1 :

[0119]

[0120] 6. Predict the state covariance matrix P1 of phase and amplitude k|k-1 and P 2k|k-1 :

[0121]

[0122] 7. Alternate calculation of the Jacobian matrix H1 k and H2 k ;

[0123] 8. Calculate the Kalman gain K1 of amplitude and phase k and K2 k :

[0124]

[0125] 9. Make amplitude prediction: 10. Update the phase state vector and the amplitude state vector :

[0126]

[0127] 11. Adaptively update the phase state noise covariance matrix Q1 k and the amplitude noise covariance matrix Q2 k :

[0128]

[0129] in, d k =(1-b) / (1-b k ), (0<b<1), b is the forgetting factor.

[0130] 12. Update the covariance matrix P1 of phase and amplitude k and P2 k :

[0131] P1 k =(I-K1 k H1 k )P1 k|k-1 ;P2 k =(I-K2 k H2 k )P2 k|k-1

[0132] 13. Calculation

[0133]

[0134] 14.End For

[0135] 15. Get the instantaneous phase vector:

[0136] Output: Instantaneous phase estimate

[0137] (7) Inversely reproduce the motion parameters of maneuvering targets;

[0138] Getting the phase estimate After that, according to formula (10), the estimated value of motion parameters is:

[0139]

[0140] in represents the estimated value of the motion parameters, Ψ represents the polynomial phase basis matrix, which is in the form of:

[0141]

[0142] After completing the motion parameter estimation, it is necessary to construct a phase compensation function to focus and image the weak maneuvering target. The steps of focusing and imaging are as follows:

[0143] (1) constructing a phase compensation function based on the estimated values ​​of motion parameters;

[0144] The constructed phase compensation function is as follows:

[0145]

[0146] (2) Perform phase compensation;

[0147] Multiplying the phase compensation function in (23) by (7) yields:

[0148]

[0149] in It represents the residual phase caused by the parameter estimation error. When the parameter estimation is accurate, the error can be ignored.

[0150] (3) Focus imaging;

[0151] Finally, for s4(t r , η a ) Perform FFT along the azimuth direction to obtain the focusing imaging result of the moving target in the plane, and the expression is as follows:

[0152]

[0153] At this point, the focused imaging of SAR weak maneuvering targets has been completed.

[0154] The core technology of the present invention is to use the idea based on adaptive phase tracking to realize simultaneous estimation of high-order parameters under low signal-to-noise ratio, which not only avoids the estimation error caused by the error transmission effect, but also reduces the signal-to-noise ratio threshold of motion parameter estimation through the adaptive covariance matrix and feedback correction iteration when EKF tracks the phase. Its technical details mainly include: first, the echo signal of the distance unit where the maneuvering target is located is extracted and modeled as a PPS signal; secondly, for the phase of the signal, a second-order local polynomial is used to construct a phase state equation, and similarly, an amplitude state equation is constructed for the changing amplitude; then, the measured maneuvering target echo signal is used to construct the observation equation. At this point, the binary state space equation of the EKF tracking model consisting of two state equations and one observation equation can be obtained. Finally, the binary state space equation is solved alternately and iteratively to obtain the estimated value of the phase, and then the parameter estimation value of the moving target can be inverted.

[0155] Different from the existing motion parameter estimation, the present invention uses adaptive EKF to achieve phase tracking and motion parameter inversion, instead of using the existing parameter search, time-frequency analysis or high-order fuzzy function methods to achieve parameter estimation, thus avoiding the problems of poor computational efficiency and low parameter estimation accuracy. Specifically, the computational complexity of the method described in the present invention is O(M 2 N a ).

[0156] In order to better explain the implementation steps and effects of this key technology, Figure 5 The phase tracking results are given. Figure 6The parameter estimates obtained after phase inversion are given, and it can be seen that the parameters of the dispatched target can be accurately estimated.

[0157] Simulation Description:

[0158] (I) Simulation parameters

[0159] The effect of the present invention can be explained by simulation, and the radar parameters and maneuvering target parameters used in the simulation are shown in Tables 1 and 2. It should also be noted that all the effect diagrams in the present invention are obtained by the simulation parameters.

[0160] Table 1 System simulation parameters

[0161] System indicators Numeric System indicators Numeric Carrier frequency 5GHz Distance bandwidth 500MHz Distance sampling rate 600MHz PRF 2000Hz Pulse duration 0.2us Radar platform speed 100m / s Minimum slope distance 1000m Accumulation time 2.5s

[0162] Table 2 Maneuvering target parameters

[0163] Distance Parameters Numeric Azimuth parameters Numeric Initial coordinates 1000m Initial coordinates 0m speed -10m / s speed 10m / s Acceleration <![CDATA[-2m / s 2 ]]> Acceleration <![CDATA[2m / s 2 ]]>

[0164] (II) Simulation content

[0165] Simulation 1: Using the SAR imaging geometry, radar parameters and maneuvering target parameters in the table, simulate and analyze the residual error under different expansion orders of instantaneous slant range to better illustrate the signal characteristics of maneuvering targets, that is, it is necessary to consider and compensate for high-order motion parameters. Figure 3 , the horizontal axis is the azimuth time of SAR movement, i.e., slow time, in seconds (s), and the vertical axis is the instantaneous slant range residual error at different orders, in meters (m). The dotted line at ±λ / 16 indicates the threshold value for good focusing, the dotted line marked with a circle indicates the 2nd-order expansion error, the dotted line marked with a triangle indicates the 3rd-order expansion error, and the solid line marked with a rectangle indicates the 4th-order expansion error.

[0166] Simulation 2: Simulation of distance walking correction using Hough transform and SOKT transform. The results are as follows Figure 4 As shown in the figure, the horizontal axis represents the azimuth slow time, in seconds (s), and the vertical axis represents the distance, in meters (m). Figure 4 (a) shows the result of pulse compression of a maneuvering target, where obvious range movement can be seen; Figure 4 (b) shows the result after SOKT. It can be seen that after the range curvature correction, the target trajectory is a linear function of the slow time, that is, the range movement still exists. Figure 4 (c) shows the result after HT estimation and compensation of range movement. At this time, the maneuvering target signal is basically focused on one range unit.

[0167] Simulation 3: Whether focusing imaging can be performed under low signal-to-noise ratio depends on the accuracy of parameter estimation under low signal-to-noise ratio. If the parameter estimation is accurate, the phase compensation function constructed by estimating the motion parameters will also be accurate. After phase compensation, the residual phase error will no longer be greater than π / 4, and theoretically a good focusing imaging effect can be achieved. The present invention extracts the signal of the distance unit where the maneuvering target is located, models it as a PPS signal, and uses the method to perform phase tracking and invert motion parameters. Results refer to Figure 5 and Figure 6 . Figure 5 It represents the phase value obtained by adaptive EKF tracking. The horizontal axis represents the azimuth sampling point index, and the vertical axis represents the phase value in degrees (°). The solid line marked with a circle represents the theoretical value of the phase, and the dotted line marked with a triangle represents the phase tracking result. It can be seen that the theoretical value is highly consistent with the phase tracking result. Using this phase value, Figure 6 The results of motion parameter estimation are given. The horizontal axis represents the motion parameter to be estimated, the left vertical axis represents the estimated value, and the right vertical axis represents the value of the estimation error. The solid lines marked with circles in the figure represent the estimated values ​​of motion parameters of each order, the dotted lines marked with triangles represent the theoretical values, and the dotted lines marked with rectangles represent the estimation error results.

[0168] Simulation 4: The maneuvering target in the simulation is imaged using the existing parameter estimation and imaging methods, and the imaging results are compared with those described in the present invention. Most existing methods do not consider the compensation of high-order phases, so they will fail to be used for imaging weak maneuvering targets. In addition, the high-order phase compensation effect of the maneuvering target based on the parameter estimation of autofocus is not ideal under low signal-to-noise ratio. In order to illustrate the effectiveness of the imaging method proposed in the present invention, Figure 7 The focusing effects of different imaging methods are given in Figure . Figure 7 (a) is the imaging result of estimating and compensating the second-order parameters; Figure 7 (b) is the result of using the GHAF proposed by Huang Penghui et al. to estimate the third-order parameters and compensate for the imaging. Since both methods only consider low-order phase compensation, they cannot image the maneuvering target, and the azimuth direction is significantly defocused. Figure 7 (c) is the use of the self-focusing PGA algorithm to Figure 7 The result in (b) performs a higher order phase estimate and compensates the image, but is still defocused in azimuth due to SNR reasons. Figure 7 (d) is the imaging result of the method of the present invention, Figure 7 (e) is the ideal imaging result. It can be seen that the imaging result of the proposed method basically achieves the ideal effect. The horizontal axis in the figure is the azimuth direction, and the vertical axis is the distance direction.

[0169] Simulation 5: In order to illustrate the advantage of the low signal-to-noise ratio threshold of the method, the method is used to image the maneuvering target at different SNRs. The results are shown in Figure 5. Figure 8 As shown. It can be seen that when the pulse pressure SNR is as low as -5dB, although clutter is generated, the maneuvering target can still be seen after focusing, which proves that the method can effectively perform imaging under low SNR. In addition, as the SNR increases, the target focusing effect becomes better and better.

[0170] The beneficial effects of the present invention are as follows:

[0171] 1) It is suitable for SAR imaging of weak maneuvering targets. This is mainly because the SAR echo modeling is carried out based on the complex motion characteristics of the maneuvering target, the non-negligible high-order motion parameters are taken into account, and a targeted estimation method for the high-order parameters is proposed.

[0172] 2) The parameter estimation has high accuracy and low computational complexity. This is mainly because a high-order motion model is taken into account, which is closer to the actual situation. In addition, the parameter estimation method based on phase tracking can estimate parameters of each order at the same time, avoiding the estimation error caused by the error propagation effect, and adopts the EKF with low computational complexity to realize phase tracking, thereby improving computational efficiency.

[0173] 3) Capable of focusing imaging at low SNR; this is mainly because the covariance matrix adaptation and feedback correction iteration during EKF phase tracking reduce the signal-to-noise ratio threshold of motion parameter estimation.

[0174] As used herein, the word "preferred" is intended to be used as an example, instance, or illustration. Any aspect or design described herein as "preferred" is not necessarily to be construed as being more advantageous than other aspects or designs. On the contrary, the use of the word "preferred" is intended to present concepts in a specific way. The term "or" as used in this application is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise specified or clear from the context, "X uses A or B" means any one of the naturally included permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0175] Moreover, although the present disclosure has been shown and described with respect to one or implementations, those skilled in the art will think of equivalent variations and modifications based on the reading and understanding of this specification and the accompanying drawings. The present disclosure includes all such modifications and variations, and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the above-mentioned components (such as elements, etc.), the terms used to describe such components are intended to correspond to any component (unless otherwise indicated) that performs the specified function of the component (such as it is functionally equivalent), even if the structure is not equivalent to the disclosed structure of the function in the exemplary implementation of the present disclosure shown herein. In addition, although the specific features of the present disclosure have been disclosed with respect to only one of several implementations, such features can be combined with one or other features of other implementations that may be desired and advantageous for a given or specific application. Moreover, insofar as the terms "including", "having", "containing" or their variations are used in specific embodiments or claims, such terms are intended to be included in a manner similar to the term "comprising".

[0176] The functional units in the embodiments of the present invention may be integrated into a processing module, or each unit may exist physically separately, or multiple or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium. The above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc. The above-mentioned devices or systems may execute the storage method in the corresponding method embodiment.

[0177] To sum up, the above embodiment is an implementation mode of the present invention, but the implementation mode of the present invention is not limited by the embodiment. Any other changes, modifications, substitutions, combinations, and simplifications that deviate from the spirit and principles of the present invention should be equivalent replacement methods and 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: The following steps are involved: 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 distance unit where the maneuvering target is extracted 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 range movement correction, the maneuvering target echo is concentrated in one 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, ..., N a , represents the SAR azimuth sampling index, N a represents the number of sampling points in the azimuth direction, and n(k) is the variance of δ 2 A(k) is the complex zero-mean Gaussian white noise, A(k) is the amplitude sampling value after pulse compression, φ(k) is the polynomial phase function representing the Doppler characteristics of the maneuvering target, specifically: Where T s is the azimuth sampling interval, and T s =1 / PRF, PRF is the pulse repetition frequency of SAR azimuth sampling, δ s is the target complex reflection coefficient; (2) Constructing the phase state equation required for phase tracking according to 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) Among them, 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 M k The inverse matrix of the second-order local polynomial phase coefficient vector c k The phase state equation 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 is represented by a second-order local polynomial. The second-order local polynomial amplitude coefficient vector p k The amplitude state equation is expressed as: p k =F k-1 p k-1 (18) where 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 , represents the second-order local polynomial of the amplitude; in addition, three consecutive amplitude sampling values ​​A k For: A k =[A(k-1), A(k), A(k+1)] T , and A k =M k p k ; (4) Constructing the observation equation required for phase tracking based on the extracted maneuvering target echo signal; because and A k Respectively represent three consecutive sampling points of amplitude and phase. The observation data is split into real and imaginary parts to construct the observation equation. According to formula (9), it can be seen that: Among them, s k represents the moving target signal s(η) after pulse compression and distance movement a ), namely s k =[s(k-1),s(k),s(k+1)] T , v r (k) and v i (k) represents the real and imaginary sampling points of complex Gaussian white noise, ⊙ represents the Hadamard product, A k =M k p k and Substituting into equation (19), the observation equation is: y k =h1(p k )⊙h2(c k )+v k (20) in In addition, v k =[v r (k); v i (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, and v k represents the observation noise, 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, for s4(t r , η a ) Perform FFT along the azimuth direction to obtain the focusing imaging result of the moving target in the plane. The expression is 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: c1, P11, Q11; p1, P21, Q21; R; Wherein c1 represents the initial value of the phase state vector, which is the value at the moment k=1, P11 represents the initial covariance matrix corresponding to c1, and Q11 represents the initial noise covariance matrix of the phase state equation; by analogy, p1 represents the initial value of the amplitude state vector, P21 represents the initial covariance matrix corresponding to p1, and Q21 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 and 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 real part operation, imag(·) is the imaginary part operation; 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: State covariance matrix P1 for predicted phase and amplitude k|k-1 and P2 k|k-1 : T stands for transpose; S7: Alternate calculation of the phase Jacobian matrix H1 k and the magnitude Jacobian matrix H2 k ; S8: Calculate the Kalman gain K1 of phase and amplitude 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 matrix P1 of phase and amplitude k and P2 k : 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 Indicates c k An estimated value of S14: Increase k by 1, and repeat steps S2-S13 until k equals N. a -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: Construct the radar echo signal model of SAR maneuvering target, including: The moving target echo signal after pulse compression is expressed in the two-dimensional time domain as: Among them, δ s is the complex reflection coefficient of the target after pulse compression, t r Indicates the distance to fast time, t a Indicates the azimuth slow time, T a is the synthetic aperture time, w a (·) represents the azimuth time window function, and w a (t a )=rect(t a / T a ), c represents the speed of light, λ represents the wavelength, B r represents the bandwidth of the transmitted signal, R(t a ) represents the instantaneous slant distance 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: Among them, b m 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 expansion, V is the movement 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 v a , a a , the velocity and acceleration along the distance direction are v r , a r , R0 is the shortest slant distance between the platform and the target; To meet the imaging focusing requirements, M has: Among them, ΔR(t a ) represents the instantaneous slant range Taylor approximation expansion error, Δρ r Indicates 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 distance walking 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: Among them, W r (f r ) represents the distance time domain window function w r (t r ) in the frequency domain, f r represents the distance frequency, f c Indicates 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; Using Hough transform at t r -η a The distance movement curve is detected in the plane 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:

Images