阅读说明：本技术 基于BiSAR回波的相关运动误差补偿方法、系统及应用 (BiSAR echo-based correlation motion error compensation method, system and application ) 是由 周松 王庆庆 包敏 杨磊 于 2020-02-28 设计创作，主要内容包括：本发明属于雷达成像技术领域,公开了一种基于BiSAR回波的相关运动误差补偿方法、系统及应用,通过BiSAR信号建模和波数矢量分解,得到极坐标下图像频谱解析表示,找到运动误差引起的相位误差和非系统性距离单元徙动之间的相关性；采用联合估计和补偿的方法对相位误差进行粗估计。对回波信号进行FFBP成像处理,得到误差补偿前的极坐标下的SAR图像；将该图像变换至距离压缩-方位频域并对其进行相位误差粗估计,得到粗略的相位误差；利用粗估计得到的相位误差补偿NsRCM,再进行相位误差精估计和精补偿,最终改善图像聚焦质量。本发明大大降低了对高精度惯导测量系统的依赖,并且具有较高的处理效率和工程实用性。(The invention belongs to the technical field of radar imaging, and discloses a method, a system and an application for compensating a relevant motion error based on BiSAR echo.A BiSAR signal modeling and wave number vector decomposition are adopted to obtain an image frequency spectrum analysis representation under a polar coordinate, and the correlation between a phase error caused by the motion error and a non-systematic range unit migration is found; and performing coarse estimation on the phase error by adopting a joint estimation and compensation method. FFBP imaging processing is carried out on the echo signals to obtain SAR images under polar coordinates before error compensation; transforming the image to a distance compression-azimuth frequency domain and carrying out coarse phase error estimation on the image to obtain a coarse phase error; and compensating the NsRCM by using the phase error obtained by the rough estimation, and then performing fine estimation and fine compensation on the phase error to finally improve the image focusing quality. The invention greatly reduces the dependence on a high-precision inertial navigation measurement system and has higher processing efficiency and engineering practicability.)

1. A correlated motion error compensation method based on BiSAR echo is characterized in that the correlated motion error compensation method based on BiSAR echo comprises the following steps:

establishing a signal model, carrying out FFBP imaging processing on an original echo signal to obtain an SAR image under a polar coordinate before error compensation, carrying out azimuth fast Fourier transform on the SAR image to obtain an SAR image signal under a distance compression domain-azimuth frequency domain, and meanwhile, obtaining analytic expression of an image spectrum under the polar coordinate based on wave number vector decomposition;

finding the correlation between the azimuth phase error and the NsRCM by using the spectrum analysis expression, firstly obtaining a rough APE by using weighted phase gradient self-focusing initial estimation, and simultaneously compensating the APE and the NsRCM;

and step three, after the NsRCM is compensated, APE fine estimation and fine compensation are carried out, then the image signal under the compensated distance compression domain-azimuth frequency domain is subjected to azimuth inverse FFT to obtain an SAR image under a polar coordinate, and the SAR image is projected to a Cartesian coordinate system to obtain an SAR image with good focus.

2. The method of correlated motion error compensation based on bistar echoes of claim 1, wherein step one further comprises:

(1) the radar transmitting station and the receiving station are respectively arranged on different aircrafts, P_TRepresentation radarTransmitting station location, P_RIndicating a radar receiving station location; for any target point P in the scene₀The echo signal of (a) is represented as:

in the formula (I), the compound is shown in the specification,representing radar P_TTo P₀Is determined by the distance vector of (a),representing the corresponding wave number vector of the transmitted signal;representing radar P_RTo P₀Is determined by the distance vector of (a),representing the corresponding wave number vector of the transmitted signal; according to the BP algorithm, an image projected to a rectangular coordinate grid is represented as:

in the formula, α represents the scattering coefficient,representing radar P_TThe distance vector to an arbitrary grid P,representing radar P_RA distance vector to an arbitrary grid P, K represents a module value of a wave number vector of a transmitted signal, and t represents azimuth time; in the real situation, due to the motion error, the platform of the receiving station of the transmitting station deviates from the predetermined track, and the real tracks are C1 'and C2'; therein, theUnder the conditions, the projected rectangular coordinate grid results in an image represented as:

in the formula, Δ represents a motion error, and there are:

(2) let (a, theta)_⊥) Represents grid coordinates in an elliptical polar coordinate system, wherein a represents an elliptical long-axis distance and theta represents_⊥Representing an angle, while introducing K_rAnd K_r⊥ wave number vector, wherein K_rAnd K_r⊥ are perpendicular to each other, K_r⊥ along the tangent of the ellipse, and calculating all signal wave number vectors and distance vectors according to K_rAnd K_r⊥, and analyzing by using a principle of stationary phase point to obtain an image analysis expression of the image in a polar coordinate system:

in the formula:

K_afrequency domain variation, K, corresponding to a_r⊥ corresponds to theta_⊥Obtaining an analytical representation of the image in polar coordinates:

analyzing the correlation of APE and NsRCM based on spectral analysis representationAnd (c) polar coordinate image i (a, theta)_⊥) Performing azimuth FFT, and transforming to distance compression-azimuth frequency domain I (a, K)_Υ⊥)。

3. The method of correlated motion error compensation based on BiSAR echo as claimed in claim 1, wherein step two further comprises:

(1) obtaining the correlation between the APE and the NsRCM according to the analytic expression form of the image under the polar coordinate; in the analytic expression of the image in polar coordinates, the first exponential term is a phase error term, and the phase error expression is given according to the error term:

the error in the formula is represented by θ_tFunction of (c):

wherein the content of the first and second substances,

(2) to pairAt K_a＝K_a0And (3) performing first-order Taylor series expansion to obtain:

the second term in the equation is an NsRCM component that includes:

for the phase error obtained by the preliminary estimation, the two parts of the NsRCM component are then usedExpressed, as:

and

(3) the phase error roughly obtained by adopting the WPGA method for estimationAccording toConstructing an NsRCM compensation function:

and

4. the method of correlated motion error compensation based on BiSAR echo as claimed in claim 1, wherein step three further comprises:

(1) compensating for NsRCM and coarseThen, the WPGA is adopted to perform fine estimation and fine compensation on the phase error of the signal;

(2) performing azimuth IFFT processing on the image signal to obtain an image i (a, theta) under polar coordinates_⊥)；

(3) The image i (a, theta)_⊥) And projecting the image to a rectangular coordinate system to obtain i (x, y) and obtain an SAR image with good focusing quality.

5. A computer program product stored on a computer readable medium, comprising a computer readable program for providing a user input interface for implementing a BiSAR echo based correlated motion error compensation method as claimed in any of claims 1 to 4 when executed on an electronic device.

6. A computer readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the method for correlated motion error compensation based on BiSAR echoes according to any of claims 1 to 4.

7. A BiSAR processing system for implementing the BiSAR echo-based correlation motion error compensation method according to any one of claims 1 to 4, wherein the BiSAR processing system for BiSAR echo-based correlation motion error compensation comprises:

the signal model module is used for projecting the original echo signal to a polar coordinate grid;

the image signal acquisition module is used for performing azimuth FFT (fast Fourier transform) after the signal model module projects the original echo signal to the polar coordinate grid to obtain an image signal in a range compression domain-azimuth frequency domain;

the image frequency spectrum analysis and representation module is used for obtaining the image signal under the distance compression domain-azimuth frequency domain by the image signal obtaining module and then obtaining the analysis and representation of the image frequency spectrum under the polar coordinate based on the wave number vector decomposition;

the APE and NsRCM module is used for obtaining the correlation between the APE and the NsRCM after the image spectrum analysis and representation module obtains the analysis and representation of the image spectrum under the polar coordinate, firstly, the WPGA is used for preliminarily estimating the APE, and then, the APE and the NsRCM are compensated at the same time;

and the SAR image acquisition module under the polar coordinate is used for carrying out APE fine estimation and APE fine compensation after the APE and NsRCM modules compensate the NsRCM, and carrying out azimuth IFFT on the compensated image signal under the distance compression domain-azimuth frequency domain to obtain the SAR image under the polar coordinate.

And the focusing SAR image acquisition module is used for projecting the SAR image in the polar coordinate acquired by the SAR image acquisition module in the polar coordinate to a Cartesian coordinate system to acquire the SAR image with good focusing.

8. A military radar apparatus implementing the BiSAR echo-based correlation motion error compensation method of any one of claims 1 to 4.

9. A disaster monitoring and environment protection civil radar instrument implementing the BiSAR echo based correlation motion error compensation method of any claim 1 to 4.

10. A double-base station SAR system implementing the BiSAR echo-based correlation motion error compensation method of any claim 1 to 4.

Technical Field

The invention belongs to the technical field of radar imaging, and particularly relates to a method, a system and an application for compensating a BiSAR (BiSAR) related motion error based on an echo under a fast decomposed back projection (FFBP) processing framework.

Background

Synthetic Aperture Radar (SAR) has the characteristics of all-weather, all-time and long-distance effects, and is widely applied to military and civil fields such as missile guidance, earth observation, disaster monitoring, environment protection and the like, while bistatic SAR (bissar) is more flexibly configured and can obtain richer target scattering information, and in addition, due to the characteristic of hiding a receiving station, the survival capability of the bistatic SAR in a battlefield can be greatly improved, so that the application of the bissar is widely concerned all the time, and the research on the bissar is also a hotspot in recent years.

However, compared with the traditional single-base-station SAR imaging, the geometric configuration and the signal characteristic of the BiSAR are more complex, and the BiSAR signal does not satisfy the assumption of orientation invariance, which introduces difficulty to the application of the traditional frequency domain imaging algorithm, and the adoption of the time domain imaging algorithm has very important advantages. Under the actual airborne application condition, the imaging is influenced by the motion error of the platform airborne platform. Particularly, for some small-sized BiSAR systems, due to the limitation of load and cost, the system is difficult to configure with high-precision inertial navigation measurement equipment, and a self-focusing method is required to estimate and compensate motion errors from echo data, so that the aim of improving the image focusing quality is fulfilled.

However, most of the existing self-focusing error compensation methods are designed for the processing framework of the frequency domain imaging algorithm, and the self-focusing methods are difficult to be directly combined with the processing framework of the time domain fast imaging algorithm. Although the optimization and search-based autofocus error compensation method can be performed in the framework of time-domain fast imaging, the search processing itself has a large computation amount, and it is difficult to meet the efficiency requirement of real-time imaging. Therefore, for a processing framework of time domain fast imaging, designing an efficient self-focusing error compensation method is still a difficult problem of BiSAR imaging. Especially in the case of severe motion error, the problem of non-systematic range cell migration (NsRCM) caused by motion error also needs to be considered.

In summary, the problems of the prior art are as follows:

(1) in the airborne BiSAR, unknown motion errors are introduced due to factors such as airflow and instability of an airborne platform, and the errors seriously affect the focusing quality of BiSAR imaging.

(2) Aiming at the problem of motion error, high-precision inertial navigation equipment can be equipped to measure the motion error and perform error compensation, but the high-precision inertial navigation equipment is high in price, large in volume and even limited by import, so that the conventional BiSAR system is difficult to be equipped with the high-precision inertial navigation equipment and to perform error compensation by adopting a measuring method.

(3) Compared with the traditional frequency domain imaging algorithm, the time domain fast imaging algorithm has more advantages in processing BiSAR, and then the existing self-focusing error algorithm is usually combined with the frequency domain imaging processing and is difficult to be applied to the time domain fast imaging processing.

The difficulty of solving the technical problems is as follows: how to design an efficient self-focusing error compensation method under a processing frame of a time domain fast imaging algorithm, and simultaneously accurately compensating Azimuth Phase Error (APE) and NsRCM caused by motion error, and improving the focusing quality of Synthetic Aperture Radar (SAR) images.

The significance of solving the technical problems is as follows:

1. the invention provides a high-precision high-efficiency error compensation method, which solves the problem of motion errors in airborne BiSAR and ensures the focusing quality of BiSAR images.

2. The invention adopts a method based on echo data estimation, directly estimates errors from BiSAR echo data with high efficiency and carries out high-precision compensation, thereby not depending on high-precision inertial navigation equipment to measure the errors, reducing the dependence of the system on the high-precision inertial navigation equipment and greatly reducing the cost and the complexity of the BiSAR system.

3. The invention provides how to design the self-focusing error compensation under the processing framework of time domain fast imaging, and expands the application of the existing self-focusing method in the time domain fast imaging.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a method, a system and an application for compensating the relevant motion error based on a BiSAR echo, and particularly relates to an APE and NsRCM combined motion error compensation method based on BiSAR echo data under an FFBP processing framework.

The invention is realized in such a way that an arbitrary configuration bistatic SAR combined self-focusing error compensation method based on a fast decomposition back projection imaging algorithm framework comprises the following steps:

establishing a signal model, carrying out FFBP imaging processing on an original echo signal to obtain an SAR image under a polar coordinate before error compensation, carrying out Fast Fourier Transform (FFT) on the SAR image to obtain an SAR image signal under a distance compression domain-azimuth frequency domain, and meanwhile, obtaining analytic expression of an image frequency spectrum under the polar coordinate based on wave number vector decomposition;

finding the correlation between the APE and the NsRCM by using the spectrum analysis expression, firstly carrying out initial estimation by using weighted phase gradient auto-focusing (WPGA) to obtain a rough APE, and simultaneously compensating the APE and the NsRCM;

and step three, after the NsRCM is compensated, APE fine estimation and fine compensation are carried out, then azimuth inverse FFT (inverse FFT, IFFT) is carried out on the compensated image signal under the range compression domain-azimuth frequency domain to obtain an SAR image under a polar coordinate, and then the SAR image is projected to a Cartesian coordinate system to obtain the SAR image with good focusing.

Further, the step one further comprises:

(1) the radar transmitting station and the receiving station are respectively arranged on different aircrafts, P_TIndicating the position of the radar transmitting station, P_RIndicating a radar receiving station location; for any target point P in the scene₀The echo signal of (a) is represented as:

in the formula (I), the compound is shown in the specification,representing radar P_TTo P₀Is determined by the distance vector of (a),representing the corresponding wave number vector of the transmitted signal;representing radar P_RTo P₀Is determined by the distance vector of (a),representing the corresponding wave number vector of the transmitted signal; according to the BP algorithm, an image projected to a rectangular coordinate grid is represented as:

in the formula, α represents the scattering coefficient,representing radar P_TThe distance vector to an arbitrary grid P,representing radar P_RA distance vector to an arbitrary grid P, K represents a module value of a wave number vector of a transmitted signal, and t represents azimuth time; in the real situation, due to the motion error, the platform of the receiving station of the transmitting station deviates from the predetermined track, and the real tracks are C1 'and C2'; under this condition, the projected rectangular grid results in an image represented by:

in the formula, Δ represents a motion error, and there are:

(2) let (a, theta)_⊥) Represents grid coordinates in an elliptical polar coordinate system, wherein a represents an elliptical long-axis distance and theta represents_⊥Representing an angle, while introducing K_rAnd K_r⊥Wave number vector, wherein, K_rAnd K_r⊥Perpendicular to each other, K_r⊥Along the tangent direction of the ellipse; all signal wave number vectors and distance vectors are arranged according to K_rAnd K_r⊥The direction of the image is decomposed, and meanwhile, the image analysis expression of the image under a polar coordinate system is obtained by analyzing the principle of the stationary phase point:

in the formula:

K_afrequency domain variation, K, corresponding to a_r⊥Corresponds to theta_⊥Obtaining an analytical representation of the image in polar coordinates:

analyzing the correlation between the APE and the NsRCM based on the spectrum analysis expression, and converting the polar coordinate image i (a, theta)_⊥) Performing azimuth FFT, and transforming to distance compression-azimuth frequency domain I (a, K)_Υ⊥)。

Further, the second step is characterized by further comprising:

(1) obtaining the correlation between the APE and the NsRCM according to the analytic expression form of the image under the polar coordinate; in the analytic expression of the image in polar coordinates, the first exponential term is a phase error term, and the phase error expression is given according to the error term:

the error in the formula is represented by θ_tFunction of (c):

wherein the content of the first and second substances,

(2) to pairAt K_a＝K_a0And (3) performing first-order Taylor series expansion to obtain:

the second term in the equation is an NsRCM component that includes:

for the phase error obtained by the preliminary estimation, the two parts of the NsRCM component are then usedExpressed, as:

and

(3) estimated using the WPGA method, coarseThe obtained phase errorAccording toConstructing an NsRCM compensation function:

and

further, the third step further comprises:

(1) compensating for NsRCM and coarseThen, the WPGA is adopted to perform fine estimation and fine compensation on the phase error of the signal;

(2) performing azimuth IFFT processing on the image signal to obtain an image i (a, theta) under polar coordinates_⊥)；

(3) The image i (a, theta)_⊥) And projecting the image to a rectangular coordinate system to obtain i (x, y) and obtain an SAR image with good focusing quality.

It is another object of the present invention to provide a computer program product stored on a computer readable medium, comprising a computer readable program for providing a user input interface to implement the arbitrary configuration bistatic SAR combined autofocus error compensation method under the framework of the fast decomposition backprojection imaging algorithm when executed on an electronic device.

It is another object of the present invention to provide a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the arbitrary configuration bistatic SAR combined autofocus error compensation method under the framework of the fast decomposition backward projection-based imaging algorithm.

Another object of the present invention is to provide a BiSAR system based on a correlated motion error compensation method of a BiSAR echo, including:

the signal model module is used for projecting the original echo signal to a polar coordinate grid;

the image signal acquisition module is used for performing azimuth FFT (fast Fourier transform) after the signal model module projects the original echo signal to the polar coordinate grid to obtain an image signal in a range compression domain-azimuth frequency domain;

the image frequency spectrum analysis and representation module is used for obtaining the image signal under the distance compression domain-azimuth frequency domain by the image signal obtaining module and then obtaining the analysis and representation of the image frequency spectrum under the polar coordinate based on the wave number vector decomposition;

the APE and NsRCM module is used for obtaining the correlation between the APE and the NsRCM after the image spectrum analysis and representation module obtains the analysis and representation of the image spectrum under the polar coordinate, firstly, the WPGA is used for preliminarily estimating the APE, and then, the APE and the NsRCM are compensated at the same time;

the SAR image acquisition module under the polar coordinate is used for carrying out APE fine estimation and APE fine compensation after the APE and NsRCM modules compensate the NsRCM, and carrying out azimuth IFFT on the compensated image signal under the distance compression domain-azimuth frequency domain to obtain an SAR image under the polar coordinate;

and the focusing SAR image acquisition module is used for projecting the SAR image in the polar coordinate acquired by the SAR image acquisition module in the polar coordinate to a Cartesian coordinate system to acquire the SAR image with good focusing.

The invention also aims to provide a military radar instrument for implementing the arbitrary configuration bistatic SAR combined self-focusing error compensation method based on the fast decomposition back projection imaging algorithm framework.

The invention also aims to provide a disaster monitoring and environment protection civil radar instrument for implementing the arbitrary configuration bistatic SAR combined self-focusing error compensation method based on the fast decomposition backward projection imaging algorithm framework.

The invention also aims to provide a method for implementing the arbitrary configuration bistatic SAR (synthetic aperture radar) combined self-focusing error compensation based on the fast decomposition back projection imaging algorithm framework.

In summary, the advantages and positive effects of the invention are: the invention provides an APE and NsRCM combined motion error compensation method based on BiSAR echo data under an FFBP processing frame, and discloses an APE and NsRCM combined motion error compensation method based on echo data under an FFBP processing frame aiming at the motion error problem in airborne BiSAR imaging. Firstly, obtaining image spectrum analysis representation under polar coordinates through BiSAR signal modeling and wave number vector decomposition, and finding out correlation between phase errors APE and NsRCM caused by motion errors based on the image spectrum analysis representation; using the correlation, a method of joint estimation and compensation is adopted: in a distance compression-azimuth frequency domain, firstly, the phase error is roughly estimated, then, the phase error obtained by rough estimation is used for compensating the NsRCM, and finally, the phase error is estimated, so that the aim of improving the image focusing quality is fulfilled.

Compared with the prior art, the invention has the advantages that: the method can be well combined with a processing framework of a time domain fast imaging algorithm, can be suitable for airborne double-base-station SAR imaging of almost any configuration and any track and any signal mode, has higher processing efficiency while obtaining a better SAR image focusing result, and is beneficial to development of a real-time imaging system; in addition, the invention directly estimates the motion error from the echo and accurately compensates the APE and the NsRCM, thereby greatly reducing the dependence of the airborne BiSAR system on a high-precision inertial navigation measurement system, well reducing the cost and the complexity of the system and being beneficial to the engineering realization. And has higher processing efficiency and engineering practicability. Simulation results show that the method effectively solves the problem of motion error in airborne BiSAR data processing by a time domain fast imaging algorithm, greatly reduces the dependence on a high-precision inertial navigation measurement system, can obtain higher imaging processing efficiency while ensuring high-quality imaging results, and is beneficial to system development and engineering realization.

The invention greatly reduces the dependence on a high-precision inertial navigation measurement system and has higher processing efficiency and engineering practicability; meanwhile, the method effectively solves the problem of motion error in airborne BiSAR data processed by a time domain rapid imaging algorithm, and can obtain higher imaging processing efficiency.

Drawings

Fig. 1 is a flowchart of a bistatic SAR combined autofocus error compensation method of any configuration based on a fast decomposition back projection imaging algorithm framework according to an embodiment of the present invention.

Fig. 2 is a schematic diagram of a bistatic SAR combined self-focusing error compensation method based on an arbitrary configuration under a fast decomposition back projection imaging algorithm framework according to an embodiment of the present invention.

FIG. 3 is a diagram of a signal model provided by an embodiment of the present invention.

FIG. 4 is a point target and imaging geometry of a simulation setup provided by an embodiment of the present invention.

Fig. 5 is a diagram of the motion error of the transmitting base station in the X-Y plane according to the embodiment of the present invention. In the figure, a is the motion error in the X direction and b is the motion error in the Y direction.

Fig. 6 shows the motion error of the receiving base station in the X-Y plane according to the embodiment of the present invention, where a is the motion error in the X direction and b is the motion error in the Y direction.

FIG. 7 is a diagram of two NsRCM components that are calculated from an APE that is estimated by an embodiment of the present invention. In the figure, (a) is an estimated APE. Graph (b) shows two NsRCM components calculated by APE.

Fig. 8 is a diagram of a range migration correction for a point target according to an embodiment of the present invention. In the figure, a is the result without any NsRCM correction. Fig. b shows the result of correcting only the H1 portion of NsRCM. FIG. c is the result of the NsRCM calibration performed by the method of the present invention.

FIG. 9 shows the focus results of the center point and the edge point obtained without error compensation, and the point target is out of focus severely. In the figure, a is the result of focusing the center point, and b is the result of focusing the edge point.

Fig. 10 is a graph of the focusing results of the center point and the edge point obtained by performing error compensation according to the embodiment of the present invention, where a is the center point focusing result and b is the edge point focusing result, and the point target focusing quality is good.

Fig. 11 is a diagram of a bistatic SAR combined autofocus error compensation system of any configuration based on the framework of a fast decomposition back projection imaging algorithm according to an embodiment of the present invention. In the figure: 1. a signal model module; 2. an image signal acquisition module; 3. an image spectrum analysis and representation module; 4. APE and NsRCM modules; 5. an SAR image acquisition module under polar coordinates; 6. and a focusing SAR image acquisition module.

Fig. 12 is a comparison of the present invention method with a prior art method of non-linear scaling of orientation. In the figure, the dotted line represents the edge point orientation response function obtained by combining the orientation non-linear transformation with the self-focusing method, and the solid line represents the edge point orientation response function obtained by the invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

For the problem of motion error in airborne BiSAR imaging, the invention provides a relevant motion error compensation method based on BiSAR echo, and the invention is described in detail below by combining with the attached drawings.

As shown in fig. 1, an embodiment of the present invention provides a method for compensating joint motion error of APE and NsRCM based on echo data in an FFBP imaging processing framework, including the following steps:

s101, signal modeling and error modeling of the airborne bistatic SAR under the FFBP imaging framework.

S102, obtaining an analytic expression of an image frequency spectrum under polar coordinates based on wave number vector decomposition, finding out the correlation between the APE and the NsRCM, and simultaneously compensating the APE and the NsRCM by using the initially estimated APE.

S103, after the NsRCM is compensated, APE estimation and APE fine compensation are carried out, and an SAR image with good focusing is obtained.

In step S101, a signal model diagram of the airborne bistatic SAR under the FFBP imaging framework is shown in fig. 3. In FIG. 3, the radar transmitting station and the receiving station are respectively installed on different aircrafts, P_TIndicating the position of the radar transmitting station, P_RIndicating the radar receiving station location. In spite of movement errorsIn the poor case, the carrier moves according to the ideal trajectory C1, C2, as shown by the solid curve in the figure. For any target point P in the scene₀The echo signal of (a) may be expressed as:

in the above formula, R_T0Representing radar P_TTo P₀Distance vector of, K_TRepresenting the corresponding wave number vector of the transmitted signal. R_R0Representing radar P_RTo P₀Distance vector of, K_RRepresenting the corresponding wave number vector of the transmitted signal. According to the BP algorithm, the image projected onto the rectangular coordinate grid can be represented as:

in real conditions, the actual flight path of the aircraft is the dashed curve in fig. 3, C1 'and C2', due to factors such as airflow, and the projected rectangular grid can be represented as:

in the above formula, "Δ" represents a motion error, and there are:

then, a spectral analysis representation of the image in polar coordinates is obtained by introducing wavenumber vector decomposition, and APEs and NsRCM are analyzed accordingly. Since imaging under the FFBP framework is performed in polar coordinates, the spectral resolution derivation here is also performed in a polar coordinate system. By introducing K as shown in FIG. 3_rAnd K_r⊥Wave number vector, and all signal wave numbersVector sum distance vector in accordance with K_rAnd K_r⊥The direction of the image is decomposed, and meanwhile, the image analysis expression of the image under a polar coordinate system can be obtained by analyzing the principle of the stationary phase point:

in the above formula:

from the above two equations, an analytical representation of the image in polar coordinates can be obtained:

based on the spectrum analysis expression, the correlation between the APE and the NsRCM can be analyzed, and a combined self-focusing error compensation method is designed. Polar coordinate image i (a, theta)_⊥) Performing azimuth FFT, and transforming to distance compression-azimuth frequency domain I (a, K)_r⊥) The spectral expression is shown in the above formula.

In step S102, the correlation between the APE and the NsRCM is found based on the analytic expression form of the image in polar coordinates. According to the above equation, the first exponential term is the phase error term, and the phase error expression is given according to the error term:

the error in the above equation is represented as θ_tFunction of theta_tAs shown in fig. 3:

wherein the content of the first and second substances,

then, toAt K_a＝K_a0And (3) performing first-order Taylor series expansion to obtain:

the second term in the above equation is the NsRCM component, which can be written as a two-part representation:

order:for the preliminary estimated phase error, then two parts of the NsRCM component can be usedTo represent, as:

and

the correlation between APE and NsRCM is obtained in the above manner, and the correlation is based on the obtained correlation. The phase error roughly obtained by adopting the WPGA method for estimationThen according toConstructing an NsRCM compensation function:

and

in step S103, NsRCM and coarse are compensatedThen, the WPGA is adopted to perform fine estimation and fine compensation on the phase error of the signal, and then the image signal is subjected to the IFFT processing to obtain an image i (a, theta) under the polar coordinates_⊥) Finally, the image i (a, theta)_⊥) And projecting the image to a rectangular coordinate system to obtain i (x, y), and finally obtaining the SAR image with good focusing quality.

The invention is further described with reference to specific examples.