CN113608215A - Wave number domain ArcSAR imaging method based on triangular sine equivalent resident phase point solution - Google Patents

Wave number domain ArcSAR imaging method based on triangular sine equivalent resident phase point solution Download PDF

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CN113608215A
CN113608215A CN202110684856.5A CN202110684856A CN113608215A CN 113608215 A CN113608215 A CN 113608215A CN 202110684856 A CN202110684856 A CN 202110684856A CN 113608215 A CN113608215 A CN 113608215A
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rotation angle
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张远
贾林靖
赵灵然
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North China University of Technology
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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
    • G01S13/9056—Scan SAR mode
    • 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
    • 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
    • G01S13/9019—Auto-focussing of the SAR signals

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Abstract

The invention belongs to the technical field of radar imaging, and discloses a wavenumber domain ArcSAR imaging method based on triangular sine equivalent resident phase point solving, which comprises the following steps: under the condition of not approximating the target slant distance, the echo data is implicitly replaced by using the principle of the resident phase, and a complete expression of the phase of the echo signal in a wave number domain is calculated and deduced; constructing a compensation function to realize phase error compensation according to the complete expression; and obtaining a polar coordinate focusing result through the inverse Fourier transform of the rotation angle direction, and obtaining a two-position space coordinate result through the interpolation of the polar coordinate-to-rectangular coordinate. The imaging method disclosed by the invention has the advantages that the residual error is small theoretically, the imaging method is suitable for the imaging of the near-distance and long-distance targets, the imaging precision is high, the algorithm time efficiency is close to the RDA, and the imaging precision and the time efficiency are considered.

Description

Wave number domain ArcSAR imaging method based on triangular sine equivalent resident phase point solution
Technical Field
The invention belongs to the field of ground arc orbit scanning synthetic aperture radars with large visual field observation capability, and particularly relates to a wave number domain ArcSAR imaging method based on triangular sine equivalent resident phase point solving.
Background
The GB-SAR adopts a synthetic aperture radar imaging principle, a system platform of the GB-SAR is statically placed on the ground, radar signals can be actively transmitted and received to an observed area, and scene imaging within a range of several kilometers can be generally realized by utilizing received echo signals. GB-SAR systems fall into two categories: linear rail systems and circular arc rail systems. The GB-SAR system based on the circular arc orbit is called ArcSAR.
The disclosed ArcSAR imaging algorithms can be divided into three categories. The first is the Backprojection (BPA) algorithm, whose basic principle is to add distance to the compressed echo signal coherently in the two-dimensional time domain according to the arc orbit. The BP algorithm is characterized in that coherent accumulation is carried out point by point, and the method is suitable for various complex skew distance geometries. However, due to the point-by-point coherent accumulation processing, under the conditions of large field of view, long distance and high resolution, the number of scene grids to be processed becomes very large, and the execution efficiency of the BP algorithm is low. The second type is a range-doppler algorithm (RDA), the basic principle is that the range direction is focused by using pulse compression, the azimuth direction is transformed into a frequency domain, the range direction and the azimuth direction coupling are eliminated in the range-doppler domain through range migration correction, and in the general derivation process, the slant range is approximate to a second-order term of a rotation angle. Due to the gradient approximation of the algorithm, the near target usually cannot be focused well (the near range depends on different system parameters), and in addition, the residual distance space-variant error cannot be removed. The third type of algorithm is a two-dimensional frequency domain algorithm (omega ka), and a known correlation algorithm transforms an echo signal into a two-dimensional frequency domain, and then eliminates coupling between a rotation direction and a distance direction through nonlinear mapping. However, because the target slant range item still exists in the two-dimensional frequency domain phase, the algorithm can only adopt the processing of performing Stolt interpolation on targets at different slant range positions respectively, which inevitably causes repeated calculation in the Stolt interpolation process, and greatly reduces the processing efficiency.
Of the three types of algorithms described above, BPA imaging accuracy is the best, but imaging time efficiency is the lowest. RDA imaging accuracy is affected by the slope distance approximation, however imaging time efficiency is highest. The disclosed omega KA algorithm adopts approximate processing in the process of deriving a two-dimensional frequency domain expression, and the main difficulty is that a trigonometric function related to a rotation angle exists in a target slope distance, and a wavenumber domain expression cannot be explicitly derived, so an effective wavenumber domain phase compensation method cannot be found.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a wave number domain ArcSAR imaging method based on triangular sine equivalent resident phase point solving, so as to give consideration to both imaging precision and time efficiency and have small residual error.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a wave number domain ArcSAR imaging method based on triangular sine equivalent dwell phase point solving comprises the following steps:
step S1, under the condition of not approximating the target slant range, the echo data is implicitly replaced by using the principle of resident phase, and a complete expression of the phase of the echo signal in the wavenumber domain is calculated and deduced;
step S2, according to the complete expression, a compensation function is reconstructed to realize phase error compensation;
and step S3, obtaining a polar coordinate focusing result through the inverse Fourier transform of the rotation angle direction, and obtaining a two-position space coordinate result through the interpolation of the polar coordinate-to-rectangular coordinate.
Further, the step S1 specifically includes:
step S11, deskewing echo data to obtain a preliminary expression of a signal model, constructing a primary compensation function of the distance wave number, and multiplying the preliminary expression and the primary compensation function to obtain a final expression of the model;
step S12, Fourier transform is carried out on the expression of the final model along the direction of the rotation angle, the signal phase is calculated, and the radar rotation angle is differentiated to obtain a resident phase point;
step S13, forming an equation formula according to the position relation among the radar, the target and the rotation center, and obtaining the difference between the rotation angle of the radar and the rotation angle of the target point;
and step S14, the calculated difference between the radar rotation angle and the target point rotation angle is brought into a signal phase formula to obtain a complete expression of the wavenumber domain.
Further, the preliminary expression of the signal model obtained by deskewing the echo signal is as follows:
Figure BDA0003124151240000031
wherein s represents the radar position, p represents the target position, R represents the distance from the target to the radar, the radar makes a circular motion by taking a point o as the center of a circle, and the length of the rotating arm is Rso，rpoIs the target-to-point o distance, θpIs the angle between op and ox; wa(θs) Is the signal amplitude, W, in the direction of the scan angler(kr) Is the signal amplitude, r, along the distancecIs a reference slope distance used in declivity, and is a known parameter, thetasIs the radar rotation angle, krIs the range wavenumber, exp represents the target phase;
the first order compensation function for the constructed distance wavenumber is:
s1＝exp{j[-2πkr·rc]} (2)；
the constructor in the formula (2) is utilized to compensate and eliminate r in the formula (1)cA modulation term;
the final expression formed is:
Figure BDA0003124151240000032
Figure BDA0003124151240000041
further, fourier transform is performed on the above equation (3) in the rotation angle direction, and a signal phase expression is obtained by using the dwell phase principle:
Figure BDA0003124151240000042
to publicTheta in the formula (4)sTaking the derivative and solving the dwell phase point to obtain the following expression:
Figure BDA0003124151240000043
calculating kθExpression (c):
Figure BDA0003124151240000044
further, from a triangle formed by the radar s, the target p, and the rotation center o in the ArcSA system, the following equation is derived:
Figure BDA0003124151240000045
calculated using equation (7):
Figure BDA0003124151240000046
Figure BDA0003124151240000047
substituting (9) into (6) yields:
kθ＝-kr·rso·sinφ (10)
substituting the formula (10) into the formula (9) to obtain an expression of the difference between the radar rotation angle and the target point rotation angle:
Figure BDA0003124151240000048
further, substituting equation (11) into equation (4) yields the following wavenumber domain complete phase expression:
Figure BDA0003124151240000051
the compound is obtained by the simplification of the process,
Figure BDA0003124151240000052
the relationship between the rotation angle wave number and the distance wave number domain signal is expressed as:
SS1(kθ,kr)＝Wa(θs)·Wr(kr)·exp{j·Φ}。
further, in SS1On the basis of the above, the following expression is obtained by compensating the rotation adjustment phase error:
Figure BDA0003124151240000053
further, performing inverse fourier transform on the compensated rotation angle wave number and distance wave number domain signals to obtain the following expression:
Figure BDA0003124151240000054
and then performing inverse Fourier transform on the second phase term in the formula (16) along the angular wave number direction to obtain a focusing result, wherein the expression is as follows:
Figure BDA0003124151240000055
in another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, which, when being executed by a processor, carries out the operational steps of the method according to the first aspect.
Compared with the prior art, the wave number domain ArcSAR imaging method based on the solution of the triangular sine equivalent dwell phase point has the following technical effects:
1. the target slope distance of the invention adopts a hyperbolic form, and no approximation in any form is carried out, including the rotation angle direction processing and the series expansion approximation of the rotation angle, so that compared with the prior various algorithms, the target slope distance of the invention has small residual error in theory and is suitable for near and far distance target imaging.
2. The method does not have a large-scale interpolation process unlike BPA, and the main operation is to compensate the phase error in a two-dimensional wavenumber domain, so the time efficiency of the algorithm is close to RDA (remote data acquisition) and far higher than BPA (Business reporting architecture), the accuracy of the algorithm is close to BP (Back propagation) algorithm, and the method is the best method considering both imaging accuracy and time efficiency in the existing ArcSAR imaging algorithm.
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Fig. 1 is a schematic scanning geometry diagram of an ArcSAR system in an embodiment of the present invention.
Fig. 2 is a schematic flow chart of a wave number domain ArcSAR imaging method based on a triangular sine equivalent dwell phase point solution in the embodiment of the present invention.
Fig. 3 is a schematic diagram of a simulated lattice target layout in the embodiment of the present invention.
Fig. 4 is a diagram of imaging effects of the method in an embodiment of the invention.
Fig. 5(a) and 5(b) are response comparison graphs of P1 observation points taken from the tangential and radial directions, respectively, according to the embodiment of the present invention.
Fig. 6(a) and 6(b) are response comparison graphs of P2 observation points taken from the tangential and radial directions, respectively, according to the embodiment of the present invention.
Fig. 7(a) and 7(b) are response comparison graphs of P3 observation points taken from the tangential and radial directions, respectively, according to the embodiment of the present invention.
Fig. 8 is an experimental scene diagram of the 24GHz ArcSAR system selected in the embodiment of the present invention.
Fig. 9(a), 9(b), and 9(c) are schematic diagrams illustrating comparison of the imaging results of the ArcSAR imaging algorithm, the BPA algorithm, and the RDA algorithm selected in the embodiment of the present invention, respectively.
Fig. 10(a) and 10(b) are schematic diagrams showing a comparison between the tangential direction of the response (a) and the radial direction of the response (b) of the corner reflector in the embodiment of the present invention.
Fig. 11 is an experimental scene diagram of a 17GHz ArcSAR system selected in the embodiment of the present invention.
Fig. 12(a) and 12(b) are schematic diagrams illustrating comparison of imaging results of the selected ArcSAR imaging algorithm and the BPA algorithm according to the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to the accompanying drawings, but the present invention is not limited thereto.
Referring to fig. 1, fig. 1 is a schematic diagram of a scanning geometry of an ArcSAR system according to an embodiment of the present invention. Where s denotes the radar position, p denotes the target position, and R denotes the target-to-radar distance. The radar makes circular motion by taking a point o as a circle center, and the length of a rotating arm is rsoThe target-to-point o distance is rpo,θpIs the angle between op and ox.
Fig. 2 is a flowchart of a wavenumber domain imaging method based on a triangular sine equivalent dwell phase point solution in the embodiment of the present invention. Firstly, under the condition of not approximating the target slant range, the stationary phase principle utilizes the sine theorem to carry out implicit substitution, and a complete expression of the phase of the echo signal in a wave number domain is deduced. Then, the target skew-independent phase error caused by rotation of the radial arm can be found from the complete two-dimensional wave number domain expression, and a compensation function can be constructed to realize consistent compensation. For target-related phase errors, the signal can be removed subtly after being transformed into the range-wavenumber domain. And finally, obtaining a polar coordinate focusing result through inverse Fourier transform of the direction of the rotation angle, and further obtaining a two-dimensional space coordinate result through polar coordinate to rectangular coordinate interpolation.
The specific imaging algorithm comprises the following steps:
and step S1, carrying out implicit replacement according to the resident phase principle without approximating the target slant range, and deducing a complete expression of the phase of the echo signal in the wavenumber domain. The method specifically comprises the following steps:
step S11: after receiving the echo data, removing the Residual Video Phase (RVP) error, performing the distance wave number replacement processing,
Figure BDA0003124151240000081
the preliminary expression for any signal model obtained after the deskew (Decirp) of the echo signal is
Figure BDA0003124151240000082
Wherein, Wa(θs) Is the signal amplitude, W, in the direction of the scan angler(kr) Is the signal amplitude, r, along the distancecIs a reference slope distance used in deskewing and is a known parameter. ThetasIs the radar rotation angle, krIs the distance direction wave number, within exp, the target phase is represented. The first order compensation function of the distance wave number is constructed as follows
s1＝exp{j[-2πkr·rc]} (2)
The constructor expressed by the formula (2) can compensate and eliminate r in the formula (1)cAnd modulating the item. Multiplying formula (2) by formula (1) to obtain
Figure BDA0003124151240000083
Step S12: fourier transform is carried out on the formula (3) along the direction of the rotation angle, and by utilizing the principle of dwell phase, the signal phase is written as follows:
Figure BDA0003124151240000084
to thetasDerivative and solve for the dwell phase point, as follows
Figure BDA0003124151240000091
So as to obtain the compound with the characteristics of,
Figure BDA0003124151240000092
step S13: from the triangle formed by the radar s, the target p, and the rotation center o in fig. 1, the following equation is not difficult to obtain
Figure BDA0003124151240000093
Obtained by the formula (7)
Figure BDA0003124151240000094
Figure BDA0003124151240000095
By substituting formula (9) for formula (6)
kθ＝-kr·rso·sinφ (10)
By substituting formula (10) for formula (9)
Figure BDA0003124151240000096
Step S14: formula (11) is substituted for formula (4) to obtain a complete phase expression of wave number domain
Figure BDA0003124151240000097
The compound is obtained by further simplification,
Figure BDA0003124151240000098
Figure BDA0003124151240000101
from the first two terms of equation (13), it can be seen that the phase does not contain rpoThe target tilt-independent phase error caused by the rotation of the swing arm will be described. The target skew-independent phase error caused by rotation of the radial arm can be found from the complete two-dimensional wave number domain expression, and a compensation function can be constructed to realize consistent compensation.
Wherein, the relational expression of the rotation angle wave number and the distance wave number domain signal is,
SS1(kθ,kr)＝Wa(θs)·Wr(kr)·exp{j·Φ} (14)
step S2: in SS1On the basis of (1), compensating for the rotational modulation phase error yields:
Figure BDA0003124151240000102
step S3: and obtaining a polar coordinate focusing result through the inverse Fourier transform of the direction of the rotation angle, and further obtaining a two-dimensional space coordinate result through the interpolation of converting the polar coordinate into the rectangular coordinate. The method specifically comprises the following steps:
in SS2On the basis, inverse Fourier transform is carried out along the distance direction, namely, the inverse Fourier transform is carried out on the formula (15) along the distance direction to obtain
Figure BDA0003124151240000103
In the formula (16), the first phase term is in rpoIs zero, and at other range bin locations, although not zero, this phase term has been practically completely eliminated because the magnitude of the ambiguity function δ r (·) greatly limits the phase term effect. The second phase term in equation (16) determines the angular position of the target, and the focusing result is obtained by performing inverse fourier transform in the angular wavenumber direction.
Figure BDA0003124151240000104
By the method in this example, the radar parameters shown in table 1 below were run.
TABLE 1 Radar parameters
System carrier frequency f0＝24GHz
Pulse width of transmission Tp＝20us
Range of scanning angles θ1＝0°θ2＝360°
Azimuth beam-3 dB width 50°
Bandwidth of transmitted pulse 1GHz
Sampling frequency 60MHz
Referring to FIG. 3, a 4m dot matrix object is set, and P is selected1、P2、P3As a point of view. The target in the ArcSAR system has invariable focusing characteristics under the same distance and different angles, so the three targets have the universality of analysis.
Table 2 shows the effect of comparing the target response with the other two methods.
TABLE 2 comparison of point target responses for different methods
Figure BDA0003124151240000111
The imaging results of this method are shown in fig. 4. The same echo was then processed using BPA and RDA, respectively, and the three imaging algorithms were quality analyzed. The resolution analysis is performed along the tangential and radial directions of the object, here exactly in the Y and X directions of the coordinate axes. Fig. 5, 6, 7 are tangential and radial target response results for the three algorithms, respectively. Table 2 shows the (σ) ratiox,σy) m and (PLSRX, PLSRy) dB measures the results of the point target responses. From the above, it can be seen that with the method of the present invention, the overall point target response is closer to the BPA result, and the imaging accuracy is higher than the RDA.
In addition, time consuming tests were performed in the same computing environment. The azimuth point of the test echo data is 7200, and the distance point is 1024. The data is complex data, that is, contains a real part and an imaginary part. The data type is a double precision floating point number. Thus, the total data amount is 118 megabytes. The imaging scene size is 30 meters by 30 meters with a sampling interval of 0.05 meters. Table 3 shows the time consumption of the three algorithms. It can be seen that the time efficiency of the process of the invention is the same as RDA and much higher than BPA.
TABLE 3 calculation times for different methods
Figure BDA0003124151240000112
The imaging method of the invention is compared and verified by specific actual scene data.
The first actual data experiment was from a scanning acquisition of the motion field by the 24ghz arcsar system. The scene is shown in fig. 8. The radius of rotation of the radar system is 1 meter. There are two corner reflectors 23 meters away from the radar. The radar bandwidth is 1GHz and the angular beam of-3 dB width is 42 degrees. The algorithms in the embodiments of the present invention and the BPA and RDA algorithms are respectively adopted to perform imaging, and the effect graphs are shown in fig. 9(a) to 9 (c). Figure 10 shows the alignment of the three imaging methods. The reflection of the iron fence around the field can be clearly seen. We performed a mass analysis of one of the corner reflectors. The tangential and radial responses are shown in fig. 12(a) and 12(b), respectively. It can be seen that the target response of this algorithm is close to BPA, but better than RDA.
Therefore, compared with the conventional algorithm, the wave number domain ArcSAR imaging method based on the triangular sine equivalent resident phase point solving disclosed by the embodiment of the invention has the advantages that the residual error is small theoretically, the method is suitable for near-distance and long-distance target imaging, the imaging precision is high, the algorithm time efficiency is close to RDA, and both the imaging precision and the time efficiency are considered.
The foregoing description shows and describes several preferred embodiments of the invention, but as aforementioned, it is to be understood that the invention is not limited to the forms disclosed herein, but is not to be construed as excluding other embodiments and is capable of use in various other combinations, modifications, and environments and is capable of changes within the scope of the inventive concept as expressed herein, commensurate with the above teachings, or the skill or knowledge of the relevant art. And that modifications and variations may be made by those skilled in the art without departing from the spirit and scope of the invention except as it may be limited by the claims appended hereto.

Claims (9)

1. A wave number domain ArcSAR imaging method based on triangular sine equivalent dwell phase point solving is characterized by comprising the following steps:
step S1, under the condition of not approximating the target slant range, the echo data is implicitly replaced by using the principle of resident phase, and a complete expression of the phase of the echo signal in the wavenumber domain is calculated and deduced;
step S2, according to the complete expression, constructing a compensation function to realize phase error compensation;
and step S3, obtaining a polar coordinate focusing result through the inverse Fourier transform of the rotation angle direction, and obtaining a two-position space coordinate result through the interpolation of the polar coordinate-to-rectangular coordinate.
2. The imaging method according to claim 1, wherein the step S1 specifically includes:
step S11, deskewing echo data to obtain a preliminary expression of a signal model, constructing a first-order compensation function of a distance wave number, and multiplying the preliminary expression and the first-order compensation function to obtain a final expression of the model;
step S12, Fourier transform is carried out on the expression of the final model along the direction of the rotation angle, the signal phase is calculated, and the radar rotation angle is differentiated to obtain a resident phase point;
step S13, forming an equation formula according to the position relation among the radar, the target and the rotation center, and obtaining the difference between the rotation angle of the radar and the rotation angle of the target point;
and step S14, the calculated difference between the radar rotation angle and the target point rotation angle is brought into a signal phase formula to obtain a complete expression of the wavenumber domain.
3. The imaging method of claim 2, wherein deskewing the echo signals yields a preliminary expression for the signal model:
Figure FDA0003124151230000011
wherein s represents the radar position, p represents the target position, R represents the distance from the target to the radar, the radar makes a circular motion by taking a point o as the center of a circle, and the length of the rotating arm is Rso，rpoIs the target-to-point o distance, θpIs the angle between op and ox; wa(θs) Is the signal amplitude, W, in the direction of the scan angler(kr) Is the signal amplitude, r, along the distancecIs a reference slope distance used in declivity, and is a known parameter, thetasIs the radar rotation angle, krIs the range wavenumber, exp represents the target phase;
the first order compensation function for the constructed distance wavenumber is:
s1＝exp{j[-2πkr·rc]} (2)；
the constructor in the formula (2) is utilized to compensate and eliminate r in the formula (1)cA modulation term;
the final expression formed is:
Figure FDA0003124151230000021
4. the imaging method according to claim 3, wherein the fourier transform is performed on the above equation (3) in the rotation angle direction, and the signal phase expression is obtained by using the dwell phase principle:
Figure FDA0003124151230000022
for theta in formula (4)sTaking the derivative and solving the dwell phase point to obtain the following expression:
Figure FDA0003124151230000023
calculating kθExpression (c):
Figure FDA0003124151230000024
。
5. the imaging method according to claim 4, wherein the following equation is derived from a triangle formed by the radar s, the target p and the rotation center o in the ArcSAR system:
Figure FDA0003124151230000025
calculated using equation (7):
Figure FDA0003124151230000031
Figure FDA0003124151230000032
substituting (9) into (6) yields:
kθ＝-kr·rso·sinφ (10)
substituting the formula (10) into the formula (9) to obtain an expression of the difference between the radar rotation angle and the target point rotation angle:
Figure FDA0003124151230000033
6. the imaging method according to claim 5, characterized in that substituting equation (11) into equation (4) yields the following wavenumber domain complete phase expression:
Figure FDA0003124151230000034
the compound is obtained by the simplification of the process,
Figure FDA0003124151230000035
the relationship between the rotation angle wave number and the distance wave number domain signal is expressed as:
SS1(kθ,kr)＝Wa(θs)·Wr(kr)·exp{j·Φ}。
7. the imaging method of claim 6, wherein in SS1Based on the obtained compensation rotation adjustment phase errorThe following expression is obtained:
Figure FDA0003124151230000041
8. the imaging method according to claim 7, wherein performing inverse fourier transform on the compensated rotation angle wavenumber and distance wavenumber domain signals yields the following expression:
Figure FDA0003124151230000042
and then performing inverse Fourier transform on the second phase term in the formula (16) along the angular wave number direction to obtain a focusing result, wherein the expression is as follows:
Figure FDA0003124151230000043
9. a computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the operating steps of the method according to any one of claims 1 to 8.
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