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

BiSAR echo-based correlation motion error compensation method, system and application Download PDF

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CN111443349B
CN111443349B CN202010127580.6A CN202010127580A CN111443349B CN 111443349 B CN111443349 B CN 111443349B CN 202010127580 A CN202010127580 A CN 202010127580A CN 111443349 B CN111443349 B CN 111443349B
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周松
王庆庆
包敏
杨磊
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Nanchang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G01S13/9058—Bistatic or multistatic SAR
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9011—SAR image acquisition techniques with frequency domain processing of the SAR signals in azimuth
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9017—SAR image acquisition techniques with time domain processing of the SAR signals in azimuth
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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    • G01—MEASURING; TESTING
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    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/35—Details of non-pulse systems
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    • G01S7/356—Receivers involving particularities of FFT processing

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Abstract

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, wherein image frequency spectrum analysis representation under polar coordinates is obtained through BiSAR signal modeling and wave number vector decomposition, and the correlation between a phase error and non-systematic range unit migration caused by the motion error 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.

Description

BiSAR echo-based correlation motion error compensation method, system and application
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 be configured 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 self-focusing error compensation method based on optimization and search can be carried out under the framework of time-domain fast imaging, the search processing of the method has large computation amount, and the efficiency requirement of real-time imaging is difficult to meet. 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:
(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 T Indicating the position of the radar transmitting station, P R Indicating a radar receiving station location; for any target point P in the scene 0 The echo signal of (a) is represented as:
Figure BDA0002394863560000031
in the formula (I), the compound is shown in the specification,
Figure BDA0002394863560000032
representing radar P T To P 0 Is determined by the distance vector of (a),
Figure BDA0002394863560000033
representing a corresponding wave number vector of the transmitted signal;
Figure BDA0002394863560000034
representing radar P R To P 0 Is determined by the distance vector of (a),
Figure BDA0002394863560000035
representing a corresponding wave number vector of the transmitted signal;according to the BP algorithm, an image projected to a rectangular coordinate grid is represented as:
Figure BDA0002394863560000036
wherein, alpha represents a scattering coefficient,
Figure BDA0002394863560000041
representing radar P T The distance vector to an arbitrary grid P,
Figure BDA0002394863560000042
representing radar P R A 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:
Figure BDA0002394863560000043
in the formula, Δ represents a motion error, and there are:
Figure BDA0002394863560000044
Figure BDA0002394863560000045
(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 r And K r⊥ Wave number vector, wherein, K r And 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 r And 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:
Figure BDA0002394863560000046
in the formula:
Figure BDA0002394863560000047
K a frequency domain variation, K, corresponding to a r⊥ Corresponds to theta ⊥ Obtaining an analytical representation of the image in polar coordinates:
Figure BDA0002394863560000051
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:
Figure BDA0002394863560000052
the error in the formula is represented by θ t Function of (c):
Figure BDA0002394863560000053
wherein the content of the first and second substances,
Figure BDA0002394863560000054
(2) for is to
Figure BDA0002394863560000055
At K a ＝K a0 Performing first-order Taylor series expansion to obtain:
Figure BDA0002394863560000056
the second term in the equation is an NsRCM component that includes:
Figure BDA0002394863560000057
Figure BDA0002394863560000058
for the phase error obtained by the preliminary estimation, the two parts of the NsRCM component are then used
Figure BDA0002394863560000059
Expressed, as:
Figure BDA0002394863560000061
and
Figure BDA0002394863560000062
(3) the phase error roughly obtained by adopting the WPGA method for estimation
Figure BDA0002394863560000063
According to
Figure BDA0002394863560000064
Construct the NsRCM patchA compensation function:
Figure BDA0002394863560000065
and
Figure BDA0002394863560000066
further, the third step further comprises:
(1) compensating for NsRCM and coarse
Figure BDA0002394863560000067
Then, 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; and by utilizing the correlation, adopting a joint estimation and compensation method: 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 joint self-focusing error compensation method of any configuration based on a fast decomposition backward 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 shows two NsRCM components that are calculated from the APE and are estimated by the 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 shows the result of the NsRCM correction performed by the method of the present invention.
Fig. 9 shows the focusing results of the center point and the edge point obtained without error compensation, and the point target is seriously defocused. 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 do not 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 T Indicating the position of the radar transmitting station, P R Indicating the radar receiving station location. The carrier moves according to the ideal track C1, C2, as shown by the solid curve in the figure, without considering the motion error. For any target point P in the scene 0 The echo signal of (a) may be expressed as:
Figure BDA0002394863560000101
in the above formula, R T0 Representing radar P T To P 0 Distance vector of, K T Representing the corresponding wave number vector of the transmitted signal. R R0 Representing radar P R To P 0 Distance vector of, K R Representing 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:
Figure BDA0002394863560000102
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:
Figure BDA0002394863560000111
in the above formula, "Δ" represents a motion error, and there are:
Figure BDA0002394863560000112
Figure BDA0002394863560000113
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 r And K r⊥ Wave number vector, and all signal wave number vector and distance vector are in accordance with K r And K r⊥ The direction of the image is decomposed, and the image can be obtained by analyzing the principle of stationary phase pointsImage analytic representation in polar coordinate system:
Figure BDA0002394863560000114
in the above formula:
Figure BDA0002394863560000115
from the above two equations, an analytical representation of the image in polar coordinates can be obtained:
Figure BDA0002394863560000116
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 from the analytic expression of the image in polar coordinates. The first exponential term is the phase error term according to the above equation, and the phase error expression is given according to the error term:
Figure BDA0002394863560000121
the error in the above equation is represented as θ t Function of theta t As shown in fig. 3:
Figure BDA0002394863560000122
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002394863560000123
then, to
Figure BDA0002394863560000124
At K a ＝K a0 And (3) performing first-order Taylor series expansion to obtain:
Figure BDA0002394863560000125
the second term in the above equation is the NsRCM component, which can be written as a two-part representation:
Figure BDA0002394863560000126
order:
Figure BDA0002394863560000127
for the preliminary estimated phase error, then two parts of the NsRCM component can be used
Figure BDA0002394863560000128
To represent, as:
Figure BDA0002394863560000129
and
Figure BDA00023948635600001210
the correlation between APE and NsRCM is obtained in the above manner, and the correlation is based on the obtained correlation. The WPGA method is adopted to estimate and roughly obtain the phase error
Figure BDA0002394863560000131
Then according to
Figure BDA0002394863560000132
Constructing NsRCM compensationThe function is:
Figure BDA0002394863560000133
and
Figure BDA0002394863560000134
in step S103, NsRCM and coarse are compensated
Figure BDA0002394863560000135
Then, 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.
Examples
Fig. 2 is a principle 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. The method specifically comprises the following steps:
step 1, establishing a signal model, projecting an original echo signal to a polar coordinate grid, performing azimuth FFT (fast Fourier transform) to obtain an image signal in a distance compression domain-azimuth frequency domain, and meanwhile, obtaining an analytic expression of an image frequency spectrum in the polar coordinate based on wave number vector decomposition.
And 2, finding the correlation between the APE and the NsRCM by using the spectrum analysis expression, primarily estimating the APE by using weighted phase gradient auto-focusing (WPGA), and then simultaneously compensating the APE and the NsRCM.
And 3, after compensating the NsRCM, carrying out APE (approximate position transform) fine estimation and APE fine compensation, carrying out orientation IFFT (inverse fast Fourier transform) on the image signal under the compensated distance compression domain-orientation frequency domain to obtain an SAR image under a polar coordinate, projecting the image to a Cartesian coordinate system, and finally obtaining the SAR image with good focus.
In step 1, as a preferred embodiment, according to fig. 3, the radar transmitting station and the receiving station are each installed on a different aircraft, P T Indicating the position of the radar transmitting station, P R Indicating a radar receiving station location; the echo signal for any target point P0 in the scene is represented as:
Figure BDA0002394863560000141
in the above formula, the first and second carbon atoms are,
Figure BDA0002394863560000142
representing radar P T To P 0 Is determined by the distance vector of (a),
Figure BDA0002394863560000143
representing the corresponding wave number vector of the transmitted signal;
Figure BDA0002394863560000144
representing radar P R To P 0 Is determined by the distance vector of (a),
Figure BDA0002394863560000145
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:
Figure BDA0002394863560000146
in the above formula, α represents a scattering coefficient,
Figure BDA0002394863560000147
representing radar P T Distance vector to arbitrary grid P.
Figure BDA0002394863560000148
Representing radar P R Distance vector to arbitrary grid P, K denotes the wave number vector of the transmitted signalThe magnitude of the quantity, t, represents azimuth time. According to fig. 3, in a real case, the platform of the receiving station of the transmitting station deviates from a predetermined track due to the presence of motion errors, the real track being C1 'and C2'. Under this condition, the projected rectangular grid results in an image represented by:
Figure BDA0002394863560000149
in the above formula, Δ represents a motion error, and there are:
Figure BDA00023948635600001410
Figure BDA00023948635600001411
(2) according to FIG. 3, let (a, θ) ⊥ ) 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 r And K r Vector of ^ wavenumber, where, K r And K r Perpendicular to each other, K r And the T is along the tangent direction of the ellipse. Then, all signal wave number vectors and distance vectors are arranged according to K r And K r And decomposing the direction of the T, and analyzing by using a stationary phase point principle to obtain an image analysis expression of the image under a polar coordinate system:
Figure BDA0002394863560000151
in the above formula:
Figure BDA0002394863560000152
K a frequency domain variation, K, corresponding to a r T corresponds to theta ⊥ The other variables refer to fig. 3.From the above two equations, an analytical representation of the image in polar coordinates is obtained:
Figure BDA0002394863560000153
based on the above formula spectrum analysis expression, the correlation between APE and NsRCM is analyzed, and the polar coordinate image i (a, theta) is obtained ⊥ ) Performing azimuth FFT, and transforming to distance compression-azimuth frequency domain I (a, K) Υ⊥ ) The spectral expression is shown in the above formula.
In step 2, the relationship between APEs and nsrcms is found according to the analytic representation of the image in polar coordinates. The first exponential term is the phase error term according to the above equation, and the phase error expression is given according to the error term:
Figure BDA0002394863560000154
the error in the above equation is represented as θ t Function of theta t As shown in fig. 3:
Figure BDA0002394863560000155
wherein the content of the first and second substances,
Figure BDA0002394863560000156
then, for
Figure BDA0002394863560000161
At K a ＝K a0 And (3) performing first-order Taylor series expansion to obtain:
Figure BDA0002394863560000162
the second term in the above equation is the NsRCM component, which can be written as a two-part representation:
Figure BDA0002394863560000163
order:
Figure BDA0002394863560000164
for the preliminary estimated phase error, then two parts of the NsRCM component can be used
Figure BDA0002394863560000165
To represent, as:
Figure BDA0002394863560000166
and
Figure BDA0002394863560000167
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 estimation
Figure BDA0002394863560000168
Then according to
Figure BDA0002394863560000169
Constructing an NsRCM compensation function:
Figure BDA00023948635600001610
and
Figure BDA00023948635600001611
as a preferred embodiment, in step 3, NsRCM and coarse are compensated
Figure BDA00023948635600001612
Then, 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, θ) ⊥ ) 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 below in connection with simulation experiments.
Simulation experiment
Some parameters used in the simulation of the present invention are shown in table 1. The simulation used a point target setup and imaging geometry as shown in figure 4.
Table 1 simulation parameter settings
Figure BDA0002394863560000171
Namely: the wave band Ku, the bandwidth 200MHz, the pulse repetition frequency, 1000Hz, the base length 2000m, the distance RR about 600m, the distance RT about 2088 m, the velocity VT on the X-Y plane (0,80) m/s, the acceleration aT (-0.1,0.2) m/s2, the velocity VT on the X-Y plane (20, 60) m/s, the acceleration aT (0.2, -0.3) m/s 2.
The motion error of the added transmitting and receiving base stations is 5 and shown in fig. 6. The APEs estimated using WPGA are shown in fig. 7(a), and the two NsRCM components (corresponding to the H1 and H2 functions) calculated from the estimated APEs are shown in fig. 7 (b). Fig. 8(a) shows that the spot target is not corrected by any NsRCM, the influence of NsRCM is severe, energy is distributed to a plurality of range bins, and phase error estimation and high quality focusing are affected. Fig. 8(b) shows the NsRCM compensated for only the H1 portion, and the effect of NsRCM is still severe. Fig. 8(c) shows that by using the combined APE and NsRCM compensation method of the present invention, the NsRCM is well corrected, 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 was 100m × 100m, (X × Y), the run time was 6.7 minutes, which is much faster than 107.1 minutes for the conventional BP method. Compared with the traditional BP algorithm, the method has higher processing efficiency. Fig. 9 shows the imaging results of the center point and the edge point without any error compensation, and it can be seen from fig. 9 that the point target is greatly defocused. Fig. 10 shows the imaging results of the central point and the edge point obtained by the method of the present invention, and as can be seen from fig. 10, the present invention can obtain very good imaging results, the main lobe and the side lobe in the figure are clear, and the obtained azimuth resolution and range resolution are respectively: 0.32m and 0.77m, very close to the theoretical resolutions 0.30m and 0.75 m. Fig. 12 shows a comparison of imaging performance between the method of the present invention and an existing method for nonlinear scaling of azimuth, where in fig. 12, a dotted line represents an edge point azimuth response function obtained by combining the nonlinear scaling of azimuth with a self-focusing method, and a solid line represents an edge point azimuth response function obtained by the present invention.
The invention is further described below in connection with simulation results.
The invention discloses a method for compensating a relevant motion error based on BiSAR echo aiming at the problem of the motion error 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 the correlation between APE and NsRCM caused by motion error 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. The method greatly reduces the dependence on a high-precision inertial navigation measurement system by estimating and compensating errors from echo data, and has higher processing efficiency and engineering practicability. In the simulation test process, the feasibility and the effectiveness of the method provided by the invention are verified.
The invention is further described below with reference to a bistatic SAR (synthetic aperture radar) joint autofocus error compensation system of any configuration based on a fast decomposition back projection imaging algorithm framework.
As shown in fig. 11, the bistar processing system based on arbitrary configuration bistatic SAR combined autofocus error compensation under the fast decomposition back projection imaging algorithm framework provided by the embodiment of the present invention includes:
and the signal model module 1 is used for projecting the original echo signal to a polar coordinate grid.
And the image signal acquisition module 2 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.
And the image spectrum analysis and representation module 3 is used for obtaining the analysis and representation of the image spectrum under the polar coordinate based on the wave number vector decomposition after the image signal acquisition module obtains the image signal under the distance compression domain-azimuth frequency domain.
And the APE and NsRCM module 4 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 simultaneously.
And the SAR image acquisition module 5 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 6 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 an SAR image with good focusing.
In the above embodiments, all or part of the implementation may be realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, can be implemented in a computer program product that includes one or more computer instructions. When loaded or executed on a computer, cause the flow or functions according to embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., 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 of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (10)

1. A relevant motion error compensation method based on BiSAR echo is characterized by comprising 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 T Indicating the position of the radar transmitting station, P R Indicating a radar receiving station location; for any target point P in the scene 0 The echo signal of (a) is represented as:
Figure FDA0002394863550000011
in the formula (I), the compound is shown in the specification,
Figure FDA0002394863550000012
representing radar P T To P 0 Is determined by the distance vector of (a),
Figure FDA0002394863550000013
representing the corresponding wave number vector of the transmitted signal;
Figure FDA0002394863550000014
representing radar P R To P 0 The distance vector of (a) is calculated,
Figure FDA0002394863550000015
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:
Figure FDA0002394863550000016
in the formula, alpha tableShowing the coefficient of the scattering of the light,
Figure FDA0002394863550000017
representing radar P T The distance vector to an arbitrary grid P,
Figure FDA0002394863550000018
representing radar P R A 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:
Figure FDA0002394863550000021
where Δ represents the motion error and there are:
Figure FDA0002394863550000022
Figure FDA0002394863550000023
(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 r And K r Vector of ^ wavenumber, where, K r And K r Perpendicular to each other, K r The T direction is along the tangent direction of the ellipse; all signal wave number vectors and distance vectors are arranged according to K r And K r And decomposing the direction of the T, and analyzing by using a stationary phase point principle to obtain an image analysis expression of the image under a polar coordinate system:
Figure FDA0002394863550000024
in the formula:
Figure FDA0002394863550000025
K a frequency domain variation, K, corresponding to a r T corresponds to theta ⊥ Obtaining an analytical representation of the image in polar coordinates:
Figure FDA0002394863550000026
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 range 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:
Figure FDA0002394863550000031
the error in the formula is represented by θ t Function of (c):
Figure FDA0002394863550000032
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0002394863550000033
(2) for is to
Figure FDA0002394863550000034
At K a ＝K a0 And (3) performing first-order Taylor series expansion to obtain:
Figure FDA0002394863550000035
the second term in the equation is an NsRCM component that includes:
Figure FDA0002394863550000036
Figure FDA0002394863550000037
for the phase error obtained by the preliminary estimation, the two parts of the NsRCM component are then used
Figure FDA0002394863550000038
Expressed, as:
Figure FDA0002394863550000039
and
Figure FDA0002394863550000041
(3) the phase error roughly obtained by adopting the WPGA method for estimation
Figure FDA0002394863550000042
According to
Figure FDA0002394863550000043
Constructing an NsRCM compensation function:
Figure FDA0002394863550000044
and
Figure FDA0002394863550000045
4. the method of claim 1, wherein step three further comprises:
(1) compensating for NsRCM and coarse
Figure FDA0002394863550000046
Then, 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;
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.
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.
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