CN111443349B - BiSAR echo-based correlation motion error compensation method, system and application - Google Patents

Abstract

The invention belongs to the technical field of radar imaging, and discloses a method, system and application for compensation of relative motion error based on BiSAR echo. The correlation between the phase error and the non-systematic range cell migration; the method of joint estimation and compensation is used to make a rough estimation of the phase error. Perform FFBP imaging processing on the echo signal to obtain the SAR image in polar coordinates before error compensation; transform the image into the range compression-azimuth frequency domain and perform a rough estimation of the phase error to obtain a rough phase error; use the rough estimation The obtained phase error compensates NsRCM, and then the phase error is finely estimated and compensated, and finally the image focus quality is improved. The invention greatly reduces the dependence on the high-precision inertial navigation measurement system, and has high processing efficiency and engineering practicability.

Description

Correlation motion error compensation method, system and application based on BiSAR echo

technical field

The invention belongs to the technical field of radar imaging, and in particular relates to a method, system and application of BiSAR-based motion error compensation based on echoes under the framework of fast factorized back projection (FFBP) processing.

Background technique

Synthetic aperture radar (SAR) has the characteristics of all-weather, all-day and long-distance action, and has a wide range of applications in military and civilian fields such as missile guidance, earth observation, disaster monitoring and environmental protection. The configuration of (bistatic SAR, BiSAR) is more flexible and can obtain richer target scattering information. In addition, due to the concealed characteristics of its receiving station, it can greatly improve its survivability in the battlefield. Therefore, BiSAR applications have been widely used. Attention, the research on BiSAR has also been a hot spot in recent years.

However, compared with traditional single-station SAR imaging, BiSAR has more complex geometry and signal characteristics, and the BiSAR signal itself no longer satisfies the assumption of azimuth invariance, which brings difficulties to the application of traditional frequency domain imaging algorithms, and Processing with time-domain imaging algorithms has very important advantages. Under the actual airborne application conditions, the influence of the motion error of the platform on the imaging is due to the platform. Especially for some small BiSAR systems, due to the limitation of load and cost, it is difficult to configure high-precision inertial navigation measurement equipment for the system itself. It is necessary to use the self-focusing method to estimate and compensate the motion error from the echo data to improve the image focusing quality. the goal of.

However, most of the existing self-focusing error compensation methods are designed for the processing framework of frequency-domain imaging algorithms, and it is difficult for such self-focusing methods to directly combine with the processing framework of time-domain fast imaging algorithms. Although the self-focusing error compensation method based on optimization and search can be carried out in the framework of fast imaging in the time domain, the search processing itself has a large amount of computation, and it is difficult to meet the efficiency requirements of real-time imaging. Therefore, designing an efficient self-focusing error compensation method for the processing framework of fast time-domain imaging is still a difficult problem for BiSAR imaging. Especially when the motion error is relatively severe, the problem of nonsystematic range cell migration (NsRCM) caused by the motion error also needs to be considered.

To sum up, the problems existing in the prior art are:

(1) In airborne BiSAR, unknown motion errors will be introduced due to factors such as airflow and the instability of the airborne platform, which seriously affect the focusing quality of BiSAR imaging.

(2) For the problem of motion error, high-precision inertial navigation equipment can be equipped to measure motion error and perform error compensation. However, high-precision inertial navigation equipment is expensive, bulky, and even restricted by imports, so it is difficult for the existing BiSAR system to be equipped with high-precision inertial navigation equipment. The precision inertial navigation equipment is difficult to use the measurement method for error compensation.

(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, which is difficult to be used in the time domain fast imaging processing. application.

The difficulty of solving the above technical problems: how to design an efficient self-focusing error compensation method under the processing framework of the time-domain fast imaging algorithm, while accurately compensating the azimuthal phase error (APE) and NsRCM caused by the motion error, and improving the synthetic aperture Radar (synthetic aperture radar, SAR) image focus quality.

The significance of solving the above technical problems:

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

2. The present invention adopts a method based on echo data estimation to efficiently estimate errors directly from BiSAR echo data and perform high-precision compensation, so as to no longer rely on high-precision inertial navigation equipment to measure the errors, thus reducing the system's accuracy to high precision. The reliance on inertial navigation equipment greatly reduces the cost and complexity of the BiSAR system.

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

SUMMARY OF THE INVENTION

In view of the problems existing in the prior art, the present invention provides a BiSAR echo-based relative motion error compensation method, system and application, and specifically relates to an APE and NsRCM joint motion error based on BiSAR echo data under the FFBP processing framework compensation method.

The present invention is implemented in this way, a method for compensating for any configuration dual-base SAR joint self-focusing error based on the framework of a fast decomposition back projection imaging algorithm includes:

Step 1, establish a signal model, perform FFBP imaging processing on the original echo signal, obtain a SAR image in polar coordinates before error compensation, and then perform an azimuth fast Fourier transform (fast Fourier transform, FFT) on the SAR image to obtain The SAR image signal in the range compression domain-azimuth frequency domain, and at the same time, the analytical representation of the image spectrum in polar coordinates is obtained based on the wavenumber vector decomposition;

Step 2: Find the correlation between APE and NsRCM by using the above spectrum analysis representation, first use weighted phase gradient autofocusing (WPGA) to preliminarily estimate to obtain a rough APE, and compensate APE and NsRCM at the same time;

Step 3: After compensating NsRCM, perform APE fine estimation and fine compensation, and then perform azimuth inverse FFT (inverse FFT, IFFT) on the compensated image signal in the range compression domain-azimuth frequency domain to obtain the SAR image in polar coordinates , and then project the SAR image to the Cartesian coordinate system to obtain a well-focused SAR image.

Further, step one further includes:

(1) The radar transmitting station and the receiving station are respectively installed on different aircraft, P _T represents the position of the radar transmitting station, and _PR represents the position of the radar receiving station; the echo signal to any target point P ₀ in the scene is expressed as:

表示雷达P_T到P₀的距离矢量，

表示发射信号对应的波数矢量；

表示雷达P_R到P₀的距离矢量，

表示发射信号对应的波数矢量；按照BP算法，投影到直角坐标网格得到的图像表示为：In the formula,

represents the distance vector from radar P _T to P ₀ ,

represents the wavenumber vector corresponding to the transmitted signal;

represents the distance vector from radar P _R to P ₀ ,

represents the wavenumber vector corresponding to the transmitted signal; according to the BP algorithm, the image obtained by projecting to the rectangular coordinate grid is expressed as:

表示雷达P_T到任意网格P的距离矢量，

表示雷达P_R到任意网格P的距离矢量，K表示发射信号波数矢量的模值，t表示方位向时间；在真实情况下，由于存在运动误差，发射站接收站的平台偏离预定的航迹，真实的航迹为C1’和C2’；在此条件下，投影得到的直角坐标网格得到的图像表示为：where α is the scattering coefficient,

represents the distance vector from radar P _T to any grid P,

Represents the distance vector from the radar P _R to any grid P, K represents the modulo value of the wavenumber vector of the transmitted signal, and t represents the azimuth time; in the real case, due to the motion error, the platform of the transmitting station and the receiving station deviates from the predetermined track. , the real tracks are C1' and C2'; under this condition, the image obtained from the projected Cartesian grid is expressed as:

In the formula, Δ represents the motion error, and has:

(2) Let (a, θ _⊥ ) represent the grid coordinates in the ellipse polar coordinate system, where a represents the long wheelbase of the ellipse, θ _⊥ represents the angle, and at the same time, K _r and K r _⊥ wavenumber vectors are introduced, where K _r and K _r⊥ are perpendicular to each other, and K _{r⊥ is} along the tangent direction of the ellipse; all signal wavenumber vectors and distance vectors are decomposed according to the directions of K _r and K _r⊥ , and at the same time, the principle of stationary phase point is used to obtain the image in polar coordinates. The image analysis representation under the system:

where:

_{Ka corresponds to the frequency domain variable of a, K r⊥ corresponds} to the frequency domain variable of θ _⊥ , and the analytical representation of the image in polar coordinates is obtained:

Based on the spectral analysis representation, the correlation between APE and NsRCM is analyzed, and the polar coordinate image i(a, θ _⊥ ) is subjected to azimuth FFT and transformed into range compression-azimuth frequency domain I(a,K _Υ⊥ ).

Further, it is characterized in that step 2 further comprises:

(1) According to the analytical representation of the image in polar coordinates, the relationship between APE and NsRCM is obtained; in the analytical representation of the image in polar coordinates, the first exponential term is the phase error term, and according to the error term, The phase error expression is:

The error in the formula is expressed as a function of θ _t :

in,

在K_a＝K_a0处做一阶泰勒级数展开，得到：(2 pairs

Do the first-order Taylor series expansion at _{Ka = Ka0 ,} and get:

The second term in the formula is the NsRCM component, which includes:

为初步估计得到的相位误差，然后NsRCM分量中的两个部分用

表示，为：

The phase error obtained for the initial estimation, then the two parts of the NsRCM component are given by

Expressed as:

and

根据

构造NsRCM补偿函数：(3) Using the WPGA method to estimate the roughly obtained phase error

according to

Construct the NsRCM compensation function:

and

Further, step 3 further includes:

后，再采用WPGA对信号做相位误差精估计和精补偿；(1) Compensate NsRCM and rough

After that, WPGA is used to accurately estimate and compensate the phase error of the signal;

(2) Perform azimuth IFFT processing on the image signal to obtain the image i(a, θ _⊥ ) in polar coordinates;

(3) Project the image i(a, θ _⊥ ) into a rectangular coordinate system to obtain i(x, y), and obtain a SAR image with good focusing quality.

Another object of the present invention is to provide a computer program product stored on a computer-readable medium, including a computer-readable program that, when executed on an electronic device, provides a user input interface to implement the fast decomposition-based backward projection An arbitrary configuration dual-base SAR joint autofocus error compensation method under the imaging algorithm framework.

Another object of the present invention is to provide a computer-readable storage medium storing instructions, which, when the instructions are executed on a computer, cause the computer to execute the arbitrary configuration binary image based on the framework of the fast decomposition back-projection imaging algorithm. A joint self-focusing error compensation method based on SAR.

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

A signal model module for projecting raw echo signals to a polar grid;

The image signal acquisition module is used to perform azimuth FFT after the signal model module projects the original echo signal to the polar coordinate grid to obtain the image signal in the range compression domain-azimuth frequency domain;

The image spectrum analysis and representation module is used for the image signal acquisition module to obtain the image signal in the range compression domain-azimuth frequency domain, and then obtain the analytical representation of the image spectrum in polar coordinates based on wavenumber vector decomposition;

The APE and NsRCM modules are used to obtain the correlation between APE and NsRCM after obtaining the analytical representation of the image spectrum in polar coordinates using the image spectrum analysis and representation module. First, use WPGA to initially estimate APE, and then compensate for APE and NsRCM at the same time;

The SAR image acquisition module in polar coordinates is used for the APE and NsRCM modules to compensate NsRCM, and then perform APE fine estimation and APE fine compensation, and perform azimuth IFFT on the image signal in the range compression domain-azimuth frequency domain after compensation to obtain polar coordinates. SAR image in coordinates;

The focused SAR image acquisition module is used for projecting the SAR image in polar coordinates obtained by the SAR image acquisition module in polar coordinates to the Cartesian coordinate system to obtain a well-focused SAR image.

Another object of the present invention is to provide a military radar instrument that implements the combined self-focusing error compensation method for bistatic SAR with any configuration under the framework of the fast decomposition back-projection imaging algorithm.

Another object of the present invention is to provide a civil radar instrument for disaster monitoring and environmental protection that implements the arbitrary configuration dual-base SAR combined self-focusing error compensation method under the framework of the fast decomposition back projection imaging algorithm.

Another object of the present invention is to provide a method for implementing the joint self-focusing error compensation method for dual-base SAR with arbitrary configuration under the framework of the fast decomposition back-projection imaging algorithm.

To sum up, the advantages and positive effects of the present invention are as follows: the present invention provides a joint motion error compensation method of APE and NsRCM based on BiSAR echo data under the framework of FFBP processing, aiming at the motion error problem in airborne BiSAR imaging, A joint motion error compensation method of APE and NsRCM based on echo data under the framework of FFBP processing is disclosed. First, through BiSAR signal modeling and wavenumber vector decomposition, the analytical representation of the image spectrum in polar coordinates is obtained, and based on this, the correlation between the phase error APE and NsRCM caused by the motion error is found; Method: In the range compression-azimuth frequency domain, the phase error is first estimated roughly, then the phase error obtained by the rough estimation is used to compensate the NsRCM, and finally the phase error is estimated to improve the image focus quality.

Compared with the prior art, the advantages of the present invention further include: the present invention can be well combined with the processing framework of the time-domain fast imaging algorithm, and can be applied to the airborne dual-base station SAR with almost any configuration, any trajectory, and any signal mode. Imaging, while obtaining better SAR image focusing results, it also has high processing efficiency, which is beneficial to the development of real-time imaging systems; in addition, because the present invention directly estimates motion errors from echoes and performs accurate APE and NsRCM The compensation greatly reduces the dependence of the airborne BiSAR system on the high-precision inertial navigation measurement system, which can well reduce the cost and complexity of the system, which is beneficial to engineering implementation. And it has high processing efficiency and engineering practicability. The simulation results show that the present invention effectively solves the problem of motion error in the processing of airborne BiSAR data by the time-domain fast imaging algorithm, greatly reduces the dependence on the high-precision inertial navigation measurement system, and can ensure high-quality imaging results at the same time. Obtaining high imaging processing efficiency is beneficial to system development and engineering implementation.

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

Description of drawings

FIG. 1 is a flowchart of a method for compensating for a dual-base SAR joint autofocus error with an arbitrary configuration under the framework of a fast decomposition back-projection imaging algorithm provided by an embodiment of the present invention.

FIG. 2 is a schematic diagram of a combined self-focusing error compensation method for an arbitrary configuration dual-base SAR under the framework of a fast decomposition back projection imaging algorithm provided by an embodiment of the present invention.

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

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

FIG. 5 is a motion error diagram of a transmitting base station in an X-Y plane according to an embodiment of the present invention. Figure a is the motion error in the X direction, and Figure 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 an embodiment of the present invention, where a is the motion error in the X direction, and FIG. b is the motion error in the Y direction.

FIG. 7 shows two NsRCM components obtained by providing an estimated APE according to an embodiment of the present invention and calculated by the APE. Figure (a) is the estimated APE. Figure (b) shows the two NsRCM components calculated by APE.

FIG. 8 is the range migration correction of the point target provided by the embodiment of the present invention. In the figure, a is the result without any NsRCM correction. Figure b shows the results obtained by only correcting the H1 part of the NsRCM. Figure c is the result of NsRCM correction performed by the method of the present invention.

FIG. 9 is a focusing result of a center point and an edge point obtained without error compensation provided by an embodiment of the present invention, and the point target is severely defocused. Figure a is the center point focusing result, and Figure b is the edge point focusing result.

10 is a graph of the focusing results of the center point and the edge point obtained by performing error compensation according to an embodiment of the present invention. The focusing quality of the point target is good.

FIG. 11 is a diagram of an arbitrary configuration dual-base SAR joint autofocus error compensation system based on the framework of a fast decomposition back projection imaging algorithm provided by an embodiment of the present invention. In the figure: 1. Signal model module; 2. Image signal acquisition module; 3. Image spectrum analysis and representation module; 4. APE and NsRCM module; 5. SAR image acquisition module in polar coordinates; 6. Focused SAR image acquisition module.

FIG. 12 is a comparison between the method of the present invention and the existing method of nonlinear azimuth scaling. In the figure, the dotted line represents the azimuth response function of the edge point obtained by combining the nonlinear azimuth scaling with the autofocus method, and the solid line represents the azimuth response function of the edge point obtained by the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

For the problem of motion error in airborne BiSAR imaging, the present invention provides a relative motion error compensation method based on BiSAR echoes. The present invention is described in detail below with reference to the accompanying drawings.

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

S101, Signal modeling and error modeling of airborne bistatic SAR under FFBP imaging framework.

S102 , an analytical representation of the image spectrum in polar coordinates is obtained based on wavenumber vector decomposition, the correlation between APE and NsRCM is found, and the APE and NsRCM are simultaneously compensated by using the preliminary estimated APE.

S103 , after compensating the NsRCM, perform APE estimation and APE fine compensation to obtain a well-focused SAR image.

In step S101 , the signal model diagram of the airborne dual-base 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 _T represents the location of the radar transmitting station, and _PR represents the location of the radar receiving station. Without considering the motion error, the carrier plane moves according to the ideal track C1, C2, as shown by the solid curve in the figure. The echo signal for any target point P ₀ in the scene can be expressed as:

In the above formula, R _T0 represents the distance vector from the radar P _T to P ₀ , and K _T represents the wavenumber vector corresponding to the transmitted signal. R _R0 represents the distance vector from the radar P _R to P ₀ , and K _R represents the wave number vector corresponding to the transmitted signal. According to the BP algorithm, the image obtained by projecting to the rectangular coordinate grid can be expressed as:

In a real situation, due to the influence of airflow and other factors, the actual flight path of the carrier aircraft is the dotted curve in Figure 3, C1' and C2', and the image obtained by the projected rectangular coordinate grid can be expressed as:

In the above formula, "Δ" represents the motion error, and has:

Then, the spectral analysis representation of the image in polar coordinates is obtained by introducing wavenumber vector decomposition, and the APE and NsRCM are analyzed accordingly. Since the imaging under the FFBP framework is carried out in polar coordinates, the analytical derivation of the spectrum here is also carried out in polar coordinates. By introducing the K _r and K _r⊥ wavenumber vectors shown in Figure 3, and all the signal wavenumber vectors and distance vectors are decomposed according to the directions of K _r and K _r⊥ , and using the principle of stationary phase analysis, it can be obtained that the image in the polar The analytical representation of the image in the coordinate system:

In the above formula:

From the above two formulas, the analytical representation of the image in polar coordinates can be obtained:

Based on the above spectral analytical representation, the correlation between APE and NsRCM can be analyzed, and a joint self-focusing error compensation method can be designed. The polar coordinate image i(a, θ _⊥ ) is subjected to azimuth FFT and transformed to range compression-azimuth frequency domain I(a, K _r⊥ ), and its spectral expression is shown in the above formula.

In step S102, the relationship between APE and NsRCM is found according to the analytical representation of the image in polar coordinates. According to the above formula, the first exponential term is the phase error term, and the phase error expression is given according to this error term:

The error in the above equation is expressed as a function of θ _t , which _is shown in Figure 3:

in,

在K_a＝K_a0处做一阶泰勒级数展开，得到：Then, yes

Do the first-order Taylor series expansion at _{Ka = Ka0 ,} and get:

The second term in the above formula is the NsRCM component, which can be expressed in two parts:

为初步估计得到的相位误差，然后NsRCM分量中的两个部分可以用

来表示，为：make:

The phase error obtained for the initial estimation, then the two parts of the NsRCM component can be used

to represent, as:

and

然后根据

构造NsRCM补偿函数：The correlation between APE and NsRCM is obtained above, based on the correlation obtained above. Using the WPGA method to estimate, the roughly obtained phase error

then according to

Construct the NsRCM compensation function:

and

之后，再采用WPGA对信号做相位误差精估计和精补偿，然后将图像信号进行方位IFFT处理，得到在极坐标下的图像i(a，θ_⊥)，最后将该图像i(a，θ_⊥)投影到直角坐标系下得到i(x,y)，最终得到聚焦质量良好的SAR图像。In step S103, compensate the NsRCM and the rough

After that, WPGA is used to accurately estimate and compensate the phase error of the signal, and then the image signal is subjected to azimuth IFFT processing to obtain the image i(a, θ _⊥ ) in polar coordinates, and finally the image i(a, θ _⊥ ) is projected to the Cartesian coordinate system to obtain i(x,y), and finally a SAR image with good focusing quality is obtained.

The present invention will be further described below in conjunction with specific embodiments.

Example

FIG. 2 shows the principle of a combined self-focusing error compensation method for a dual-base SAR with any configuration under the framework of a fast decomposition back-projection imaging algorithm provided by an embodiment of the present invention. Specifically include:

Step 1, establish a signal model, project the original echo signal to the polar coordinate grid, and then perform azimuth FFT to obtain the image signal in the range compression domain-azimuth frequency domain. At the same time, based on the wavenumber vector decomposition, the image spectrum in polar coordinates is obtained Parse the representation.

Step 2: Find the correlation between APE and NsRCM by using the above spectrum analysis representation, first estimate APE by using weighted phase gradient autofocusing (WPGA), and then compensate APE and NsRCM at the same time.

Step 3: After compensating NsRCM, perform APE fine estimation and APE fine compensation, and then perform azimuth IFFT on the image signal in the compensated range compression domain-azimuth frequency domain to obtain the SAR image in polar coordinates, and then convert the image Projected to the Cartesian coordinate system, and finally a well-focused SAR image was obtained.

As a preferred embodiment, in step 1, according to Fig. 3, the radar transmitting station and the receiving station are installed on different aircraft respectively, P _T represents the position of the radar transmitting station, and _PR represents the position of the radar receiving station; for any target point in the scene The echo signal of P0 is expressed as:

表示雷达P_T到P₀的距离矢量，

表示发射信号对应的波数矢量；

表示雷达P_R到P₀的距离矢量，

表示发射信号对应的波数矢量；按照BP算法，投影到直角坐标网格得到的图像表示为：In the above formula,

represents the distance vector from radar P _T to P ₀ ,

represents the wavenumber vector corresponding to the transmitted signal;

represents the distance vector from radar P _R to P ₀ ,

represents the wavenumber vector corresponding to the transmitted signal; according to the BP algorithm, the image obtained by projecting to the rectangular coordinate grid is expressed as:

表示雷达P_T到任意网格P的距离矢量。

表示雷达P_R到任意网格P的距离矢量，K表示发射信号波数矢量的模值，t表示方位向时间。根据图3，在真实情况下，由于存在运动误差，发射站接收站的平台偏离预定的航迹，真实的航迹为C1’和C2’。在此条件下，投影得到的直角坐标网格得到的图像表示为：In the above formula, α represents the scattering coefficient,

represents the distance vector from radar P _T to any grid P.

Represents the distance vector from the radar P _R to any grid P, K represents the modulo value of the wavenumber vector of the transmitted signal, and t represents the azimuth time. According to Fig. 3, in the real situation, due to the motion error, the platform of the transmitting station and receiving station deviates from the predetermined track, and the real tracks are C1' and C2'. Under this condition, the image obtained from the projected Cartesian grid is expressed as:

In the above formula, Δ represents the motion error, and has:

(2) According to Figure 3, let (a, θ _⊥ ) represent the grid coordinates in the ellipse polar coordinate system, where a represents the long wheelbase of the ellipse, θ _⊥ represents the angle, and at the same time, K _r and K _r ⊥ wavenumber vectors are introduced , where K _r and K _r ⊥ are perpendicular to each other, and K _r ⊥ is along the tangent direction of the ellipse. Then, all signal wavenumber vectors and distance vectors are decomposed according to the directions of K _r and K _r ⊥, and at the same time, the principle of stationary phase is used to analyze the image analysis representation of the image in the polar coordinate system:

In the above formula:

Ka corresponds to the frequency domain variable of _a , K _r ⊥ corresponds to the frequency domain variable of θ _⊥ , and other variables refer to Figure 3. From the above two formulas, the analytical representation of the image in polar coordinates is obtained:

Based on the spectral analysis representation of the above formula, the correlation between APE and NsRCM is analyzed, and the polar coordinate image i(a, θ _⊥ ) is subjected to azimuth FFT and transformed into the range compression-azimuth frequency domain I(a, K _Υ⊥ ), and its spectral representation The formula is shown above.

As a preferred embodiment, in step 2, the relationship between APE and NsRCM is found according to the analytical representation of the image in polar coordinates. According to the above formula, the first exponential term is the phase error term, and the phase error expression is given according to this error term:

The error in the above equation is expressed as a function of θ _t , which _is shown in Figure 3:

in,

在K_a＝K_a0处做一阶泰勒级数展开，得到：Then, yes

Do the first-order Taylor series expansion at _{Ka = Ka0 ,} and get:

The second term in the above formula is the NsRCM component, which can be expressed in two parts:

为初步估计得到的相位误差，然后NsRCM分量中的两个部分可以用

来表示，为：make:

The phase error obtained for the initial estimation, then the two parts of the NsRCM component can be used

to represent, as:

and

然后根据

构造NsRCM补偿函数：The correlation between APE and NsRCM is obtained above, based on the correlation obtained above. Using the WPGA method to estimate, the roughly obtained phase error

then according to

Construct the NsRCM compensation function:

and

之后，再采用WPGA对信号做相位误差精估计和精补偿，然后将图像信号进行方位IFFT处理，得到在极坐标下的图像i(a,θ_⊥)，最后将该图像i(a,θ_⊥)投影到直角坐标系下得到i(x,y)，最终得到聚焦质量良好的SAR图像。As a preferred embodiment, in step 3, the compensated NsRCM and the rough

After that, WPGA is used to accurately estimate and compensate the phase error of the signal, and then the image signal is subjected to azimuth IFFT processing to obtain the image i(a, θ _⊥ ) in polar coordinates, and finally the image i(a, θ _⊥ ) is projected to the Cartesian coordinate system to obtain i(x,y), and finally a SAR image with good focusing quality is obtained.

The present invention will be further described below in conjunction with simulation experiments.

Simulation

Some parameters used in the simulation of the present invention are shown in Table 1. The point target setup and imaging geometry used for the simulation are shown in Figure 4.

Table 1 Simulation parameter settings

Namely: band Ku, bandwidth 200MHz, pulse repetition frequency, 1000Hz, baseline length 2000m, distance RR about 600m, distance RT about 2088m, velocity VT=(0,80)m/s on X-Y plane, acceleration aT is ( -0.1,0.2)m/s2, the velocity VT=(-20,60)m/s on the X-Y plane, and the acceleration aT is (0.2,-0.3)m/s2.

The motion error of the added transmitting base station and receiving base station is 5 and shown in FIG. 6 . The APE estimated by WPGA is shown in Figure 7(a), and the two NsRCM components (corresponding to H1 and H2 functions) calculated from the estimated APE are shown in Figure 7(b). Figure 8(a) shows the point target without any NsRCM correction. The influence of NsRCM is serious, and the energy is distributed to multiple range units, which affects the phase error estimation and high-quality focusing. Figure 8(b) shows the NsRCM that only compensated for the H1 part. It can be seen that the influence of NsRCM is still serious. Figure 8(c) shows that the NsRCM is well corrected by using the combined APE and NsRCM compensation method of the present invention, which provides a guarantee for the subsequent high-quality SAR image focusing.

The imaging processing algorithm runs in Matlab environment, windows 1064 operating system, i79700cpu, 32GB memory. The imaging range is 100m×100m, (X×Y), and the running time is 6.7 minutes, which is much faster than the 107.1 minutes of the traditional BP method. It can be seen that the method of the present invention has higher processing efficiency than the traditional BP algorithm. Figure 9 shows the imaging results of the center point and edge point without any error compensation. It can be seen from Figure 9 that the point target is seriously defocused. Fig. 10 shows the imaging results of the center point and edge point obtained by the method of the present invention. It can be seen from Fig. 10 that the present invention can obtain very good imaging results. The resolutions are: 0.32m and 0.77m, which are very close to the theoretical resolutions of 0.30m and 0.75m. Figure 12 shows the imaging performance comparison between the method of the present invention and the existing azimuth nonlinear scaling method. In Figure 12, the dotted line represents the edge point azimuth response function obtained by combining the azimuth nonlinear scaling with the autofocus method, and the solid line represents the present invention. For the edge point azimuth response function obtained by the invention, since the azimuth nonlinear scaling operation will disturb the self-focusing error estimation, it is difficult to obtain good imaging results in the simulation experiment, but the method of the present invention can obtain very good imaging results, and the comparison further proves that Feasibility and effectiveness of the method of the present invention.

The present invention will be further described below in conjunction with the simulation effect.

Aiming at the motion error problem in airborne BiSAR imaging, the invention discloses a relative motion error compensation method based on BiSAR echoes. First, through BiSAR signal modeling and wavenumber vector decomposition, the analytical representation of the image spectrum in polar coordinates is obtained, and based on this, the correlation between APE and NsRCM caused by motion error is found; using the correlation, a joint estimation and compensation method is used: That is, in the range compression-azimuth frequency domain, the phase error is first roughly estimated, then the phase error obtained by the rough estimation is used to compensate the NsRCM, and finally the phase error is estimated to improve the image focus quality. By estimating and compensating errors from echo data, the method greatly reduces the dependence on high-precision inertial navigation measurement systems, and has high processing efficiency and engineering practicability. In the simulation test process, the feasibility and effectiveness of the method proposed in the present invention are verified.

The present invention will be further described below in conjunction with an arbitrary configuration dual-base SAR joint self-focusing error compensation system based on the framework of the fast decomposition back projection imaging algorithm.

As shown in FIG. 11 , the BiSAR processing system provided by the embodiment of the present invention based on the framework of the fast decomposition back-projection imaging algorithm and the combined self-focusing error compensation of the bistatic SAR with any configuration includes:

Signal model module 1, used to project the original echo signal to a polar grid.

The image signal acquisition module 2 is used for performing azimuth FFT after the signal model module projects the original echo signal to the polar coordinate grid, to obtain the image signal in the range compression domain-azimuth frequency domain.

The image spectrum analysis and representation module 3 is used for the image signal acquisition module to obtain the image signal in the range compression domain-azimuth frequency domain, and then obtain the analytical representation of the image spectrum in polar coordinates based on wavenumber vector decomposition.

The APE and NsRCM module 4 is used to obtain the correlation of APE and NsRCM after obtaining the analytical representation of the image spectrum in polar coordinates by using the image spectrum analysis and representation module. First, use WPGA to initially estimate APE, and then compensate for APE and NsRCM at the same time.

The SAR image acquisition module 5 in polar coordinates is used for APE and NsRCM modules to compensate NsRCM, and then perform APE fine estimation and APE fine compensation, and perform azimuth IFFT on the image signal in the compensated range compression domain-azimuth frequency domain to obtain SAR image in polar coordinates.

The focused SAR image acquisition module 6 is used for projecting the SAR image in polar coordinates obtained by the SAR image acquisition module in polar coordinates to the Cartesian coordinate system to obtain a well-focused SAR image.

In the above-mentioned embodiments, it may be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented in whole or in part in the form of a computer program product, the computer program product includes one or more computer instructions. When the computer program instructions are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer may be a general purpose computer, special purpose computer, computer network, or other programmable device. The computer instructions may be stored in or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be downloaded from a website site, computer, server, or data center Transmission to another website site, computer, server, or data center by wireline (eg, coaxial cable, fiber optic, digital subscriber line (DSL), or wireless (eg, infrared, wireless, microwave, etc.)). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, a data center, etc. that includes one or more available mediums integrated. The usable media may be magnetic media (eg, floppy disks, hard disks, magnetic tapes), optical media (eg, DVD), or semiconductor media (eg, Solid State Disk (SSD)), and the like.

The above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

Claims (10)

1. a relative motion error compensation method based on BiSAR echo, is characterized in that, the described relative motion error compensation method based on BiSAR echo comprises: Step 1: Establish a signal model, perform FFBP imaging processing on the original echo signal, and obtain the SAR image in polar coordinates before error compensation, and then perform azimuth fast Fourier transform on the SAR image to obtain the range compression domain-azimuth frequency domain. At the same time, the analytical representation of the image spectrum in polar coordinates is obtained based on wavenumber vector decomposition; Step 2: Find the correlation between the azimuth phase error and the NsRCM by using the above spectrum analysis representation, first use the weighted phase gradient self-focusing preliminary estimation to obtain a rough APE, and compensate the APE and NsRCM at the same time; Step 3: After compensating NsRCM, perform APE fine estimation and fine compensation, and then perform azimuth inverse FFT on the compensated range compression domain-azimuth frequency domain image signal to obtain a SAR image in polar coordinates, and then project the SAR image. In the Cartesian coordinate system, a well-focused SAR image is obtained. 2. the relative motion error compensation method based on BiSAR echo as claimed in claim 1 is characterized in that, step 1 further comprises: (1) The radar transmitting station and the receiving station are respectively installed on different aircraft, P _T represents the position of the radar transmitting station, and _PR represents the position of the radar receiving station; the echo signal to any target point P ₀ in the scene is expressed as:

In the formula,

represents the distance vector from radar P _T to P ₀ ,

represents the wavenumber vector corresponding to the transmitted signal;

represents the distance vector from radar P _R to P ₀ ,

represents the wavenumber vector corresponding to the transmitted signal; according to the BP algorithm, the image obtained by projecting to the rectangular coordinate grid is expressed as:

where α is the scattering coefficient,

represents the distance vector from radar P _T to any grid P,

Represents the distance vector from the radar P _R to any grid P, K represents the modulo value of the wavenumber vector of the transmitted signal, and t represents the azimuth time; in the real case, due to the motion error, the platform of the transmitting station and the receiving station deviates from the predetermined track. , the real tracks are C1' and C2'; under this condition, the image obtained from the projected Cartesian grid is expressed as:

In the formula, Δ represents the motion error, and has:

(2) Let (a, θ _⊥ ) represent the grid coordinates in the ellipse polar coordinate system, where a represents the long wheelbase of the ellipse, θ _⊥ represents the angle, and at the same time, K _r and K _r ⊥ wavenumber vectors are introduced, where K _r and K _r ⊥ are perpendicular to each other, and K _r ⊥ is along the tangent direction of the ellipse; all signal wavenumber vectors and distance vectors are decomposed according to the directions of K _r and K _r ⊥, and at the same time, the principle of stationary phase point is used to obtain the image in polar coordinates. The image analysis representation under the system:

where:

Ka corresponds to the frequency domain variable of _a , K _r ⊥ corresponds to the frequency domain variable of θ _⊥ , and the analytical representation of the image in polar coordinates is obtained:

Based on the spectral analysis representation, the correlation between APE and NsRCM is analyzed, and the polar coordinate image i(a, θ _⊥ ) is subjected to azimuth FFT and transformed into range compression-azimuth frequency domain I(a,K _Υ⊥ ). 3. the relative motion error compensation method based on BiSAR echo as claimed in claim 1 is characterized in that, step 2 further comprises: (1) According to the analytical representation of the image in polar coordinates, the relationship between APE and NsRCM is obtained; in the analytical representation of the image in polar coordinates, the first exponential term is the phase error term, and according to the error term, The phase error expression is:

The error in the formula is expressed as a function of θ _t :

in,

(2 pairs

Do the first-order Taylor series expansion at _{Ka = Ka0 ,} and get:

The second term in the formula is the NsRCM component, which includes:

The phase error obtained for the initial estimation, then the two parts of the NsRCM component are used

Expressed as:

and

(3) Using the WPGA method to estimate, the roughly obtained phase error

according to

Construct the NsRCM compensation function:

and

4. the relative motion error compensation method based on BiSAR echo as claimed in claim 1 is characterized in that, step 3 further comprises: (1) Compensate NsRCM and rough

After that, WPGA is used to accurately estimate and compensate the phase error of the signal; (2) Perform azimuth IFFT processing on the image signal to obtain the image i(a, θ _⊥ ) in polar coordinates; (3) Project the image i(a, θ _⊥ ) into a rectangular coordinate system to obtain i(x, y), and obtain a 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 when executed on an electronic device to implement the BiSAR-based return according to any one of claims 1 to 4. Wave-dependent motion error compensation method. 6. A computer-readable storage medium storing instructions, which, when executed on a computer, cause the computer to execute the BiSAR echo-based relative motion error compensation method according to any one of claims 1 to 4. 7. A BiSAR processing system implementing the BiSAR echo-based relative motion error compensation method according to any one of claims 1 to 4, wherein the BiSAR echo-based BiSAR echo-based relative motion error compensation comprises: : A signal model module for projecting raw echo signals to a polar grid; The image signal acquisition module is used to perform azimuth FFT after the signal model module projects the original echo signal to the polar coordinate grid to obtain the image signal in the range compression domain-azimuth frequency domain; The image spectrum analysis and representation module is used for the image signal acquisition module to obtain the image signal in the range compression domain-azimuth frequency domain, and then obtain the analytical representation of the image spectrum in polar coordinates based on wavenumber vector decomposition; The APE and NsRCM modules are used to obtain the correlation between APE and NsRCM after obtaining the analytical representation of the image spectrum in polar coordinates using the image spectrum analysis and representation module. First, use WPGA to initially estimate APE, and then compensate for APE and NsRCM at the same time; The SAR image acquisition module in polar coordinates is used for the APE and NsRCM modules to compensate NsRCM, and then perform APE fine estimation and APE fine compensation, and perform azimuth IFFT on the image signal in the range compression domain-azimuth frequency domain after compensation to obtain polar coordinates. SAR image in coordinates; The focused SAR image acquisition module is used for projecting the SAR image in polar coordinates obtained by the SAR image acquisition module in polar coordinates to the Cartesian coordinate system to obtain a well-focused SAR image. 8. A military radar instrument implementing the BiSAR echo-based relative motion error compensation method according to any one of claims 1 to 4. 9 . A civil radar instrument for disaster monitoring and environmental protection that implements the BiSAR echo-based relative motion error compensation method according to any one of claims 1 to 4 . 10. A dual-base station SAR system implementing the BiSAR echo-based correlation motion error compensation method according to any one of claims 1 to 4.

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