CN110515080B - Hypersonic mobile platform SAR imaging method based on radius angle interpolation - Google Patents
Hypersonic mobile platform SAR imaging method based on radius angle interpolation Download PDFInfo
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Abstract
The invention provides a hypersonic mobile platform SAR imaging method based on radius angle interpolation, which is used for solving the technical problem of poor focusing precision when a target scene with height fluctuation is imaged in the prior art. The implementation steps are as follows: constructing a hypersonic mobile platform model carrying an SAR imaging system; calculating the slope distance process expansion from the hypersonic maneuvering platform to any point A of the detection scene; calculating a fundamental frequency echo signal received by the SAR imaging system; distance pulse pressure processing is carried out on the fundamental frequency echo signals; performing consistent phase compensation on the distance frequency domain signal after the distance pulse pressure; and performing radius angle two-dimensional interpolation on the distance frequency domain signals after the consistent phase compensation. According to the invention, radius angle two-dimensional interpolation is carried out on the curved surface stretched at the slant range speed, and the residual phase after the consistent phase compensation is compensated, so that the focusing precision of SAR echo data is effectively improved, and the SAR echo data acquisition method is beneficial to acquiring a high-quality SAR image.
Description
Technical Field
The invention belongs to the technical field of radars, relates to a hypersonic maneuvering platform SAR imaging method, and particularly relates to a hypersonic maneuvering platform SAR imaging method based on radius angle interpolation, which can be used for performing synthetic aperture radar SAR imaging on a scene with height fluctuation on a hypersonic maneuvering platform.
Background
Synthetic Aperture Radar (SAR) imaging theory and Radar imaging technology have been developed in recent years and are widely used. The traditional SAR imaging algorithm mainly comprises a back projection algorithm, a range-Doppler algorithm, a wave number domain algorithm, a polar coordinate algorithm and the like. The hypersonic speed maneuvering platform carrying the SAR imaging system is an SAR imaging platform which flies in a near space with the height of 20 km-30 km and has the flying speed higher than Mach 5.
The indexes influencing the imaging result are mainly divided into two categories of imaging result focusing precision and imaging speed. The focusing accuracy of the imaging result is mainly influenced by factors such as the flying speed and the acceleration of the SAR imaging platform, the height fluctuation of a target scene, an imaging algorithm and the like.
Due to the high flight speed and acceleration of the hypersonic mobile platform, the SAR echo signals are subjected to very large range migration, and the distance direction and the azimuth direction are severely coupled. These problems make the conventional SAR imaging algorithms no longer suitable for hypersonic mobile platform SAR imaging.
For example: the invention discloses an invention patent with an authorization publication number CN 103454635B, which is named as a forward squint SAR imaging method based on a flat flight section of a hypersonic aircraft, and discloses a forward squint SAR imaging method based on a flat flight section of a hypersonic aircraft. The method can improve the SAR imaging focusing precision of the hypersonic flight vehicle in the uniform linear flight mode. However, the method does not consider the influence of acceleration on the focusing accuracy, only considers an ideal two-dimensional plane target scene, and does not consider the influence of height fluctuation of the target scene on the focusing accuracy, so that when the SAR imaging platform with acceleration images the target scene with height fluctuation, the target focusing is not accurate, and good imaging cannot be achieved.
Disclosure of Invention
The invention aims to provide a hypersonic mobile platform SAR imaging method based on radius angle interpolation aiming at the defects of the prior art, and the method is used for solving the technical problem that the focusing precision is poor when a target scene with high fluctuation is imaged in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) Constructing a hypersonic mobile platform model carrying an SAR imaging system:
suppose a hypersonic mobile platform carrying a SAR imaging system is (0, H) in an xOyz coordinate system z ) For the initial coordinate to move along the y-axis with a curved trajectory, (0, H z ) The initial slope distance to any point A of the detection scene is r A Reference slope distance to the detection scene reference point C is r C The azimuth time of the hypersonic mobile platform carrying the SAR imaging system is eta, the initial speed is v, and the acceleration is a, v and r A And r C Are respectively theta and theta c The slope distance process from the hypersonic mobile platform carrying the SAR imaging system to A is
The reference slope history to the reference point C of the detection scene is
The SAR imaging system has a distance time t r The transmitted signal is s (t) r ,η)；
(2) Calculate | r A (η) | expansion:
slope distance process | r from hypersonic mobile platform carrying SAR imaging system to any point A of detection scene A (eta) is subjected to vector Taylor expansion to obtain | r A (η) | expansion:
|r A (η)|＝|r C (η)|+ζ ρ (η)·Δρ+ζ θ (η)·Δθ
wherein the initial slope distance r A The module value of (a) and the reference slope distance r C The difference of the modulus values of (a) is Δ ρ, Δ ρ = | r A |-|r C |，ζ ρ (η) is an expansion coefficient of Δ ρ, and a cosine value of the initial angle θ is equal to the reference angle θ c Has a difference of Δ θ, Δ θ = cos θ -cos θ C ，ζ θ (η) is the expansion coefficient of Δ θ;
(3) Calculating a fundamental frequency echo signal s received by the SAR imaging system 1 (t r ,η)：
Will | r A Expansion of (eta) I into the transmit signal s (t) of the SAR imaging system r Eta) to obtain an echo signal s received by the SAR imaging system 0 (t r Eta) and to s 0 (t r Eta) to obtain a base frequency echo signal s received by the SAR imaging system 1 (t r ,η)；
(4) To s 1 (t r Eta) distance pulse pressure treatment:
(4b) For the fundamental frequency echo signal s received by the SAR imaging system 1 (t r Eta) Fourier transform to obtain s 1 (t r Eta) range-frequency-domain echo signal s 2 (f r ,η)；
(4b) Pulse pressure function H by distance 1 For range frequency domain echo signal s 2 (f r Eta) distance pulse pressure to obtain distance frequency domain echo signal s 3 (K r ,η)；
(5) To s 3 (K r η) performing uniform phase compensation:
(5a) Construction of a coherent phase compensation function H 2 (K r ,η)：
H 2 (K r ,η)＝exp(jK r |r C (η))；
(5b) By a uniform phase compensation function H 2 (K r Eta) distance frequency domain signal s after distance pulse pressure 3 (K r Eta) are conformedBit compensation is carried out to obtain a distance frequency domain signal s after consistent phase compensation 4 (K r ,η)；
(6) To s 4 (K r Eta) performing a two-dimensional interpolation of radius and angle:
(6a) Respectively calculating distance frequency domain signals s after consistent phase compensation 4 (K r Eta) radius wave number K ρ Sum angle wave number K θ ：
(6b) For radius wave number K ρ Sum angle wavenumber K θ Respectively carrying out interpolation on the sinc kernel functions h (eta) to obtain a product containing a uniform radius wave number K' ρ And a uniform angle wave number K' θ Radius angle signal s 5 (K' ρ ,K' θ )；
(6c) For the radius angle signal s 5 (K' ρ ,K' θ ) Performing two-dimensional inverse Fourier transform to obtain SAR focused image S 6 (t r ,η)。
Compared with the prior art, the invention has the following advantages:
the method comprises the steps of carrying out vector Taylor expansion on the slope distance process of the hypersonic maneuvering platform carrying the SAR imaging system, considering the influence of the acceleration of the platform on the slope distance process, carrying out consistent phase compensation on echo signals according to the expansion of the slope distance process, and then carrying out radius angle two-dimensional interpolation on the echo signals after the consistent phase compensation on a curved surface formed by the slope distance and the velocity, so that the defect of poor focusing accuracy of target imaging with high fluctuation caused by interpolation on an ideal two-dimensional plane in the prior art is overcome, and the technical problem of poor focusing accuracy of the target scene with high fluctuation in the prior art can be solved.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a ground scene layout diagram adopted in the simulation experiment of the present invention;
fig. 3 is a contour simulation diagram of imaging results of different point targets in a ground scene according to the present invention and the prior art.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the present invention includes the following steps.
Step 1) constructing a hypersonic mobile platform model carrying an SAR imaging system:
suppose a hypersonic mobile platform carrying a SAR imaging system is (0, H) in an xOyz coordinate system z ) For the initial coordinate along the y-axis as a curved path, (0, H z ) The initial slope distance to any point A of the detection scene is r A Reference slope distance to detection scene reference point C is r C The azimuth time of the hypersonic mobile platform carrying the SAR imaging system is eta, the initial speed is v, and the acceleration is a, v and r A And r C Are respectively theta and theta c The slope distance process from the hypersonic mobile platform carrying the SAR imaging system to A is
The reference slope history to the reference point C of the detection scene is
The SAR imaging system has a distance time t r The transmitted signal is s (t) r ,η)；
In this embodiment, the Z-axis coordinate H of the initial coordinate z =20km, initial velocity v = (800, 1500, -500) m/s, acceleration a = (20, 50, -20) m/s 2 Reference slope distance r C ＝(10,40,-20)km；
Step 2) calculating | r A (η) | expansion:
due to the course of the skew distance
Is in vector representation form, is not beneficial to carrying out consistent phase compensation and interpolation on signals subsequently, so that the superposition is goodSlope distance process | r from hypersonic mobile platform carrying SAR imaging system to any point A of detection scene A (eta) carries out vector Taylor expansion to obtain r A (η) | expansion:
|r A (η)|＝|r C (η)|+ζ ρ (η)·Δρ+ζ θ (η)·Δθ
wherein the initial slope distance r A The module value of (a) and the reference slope distance r C The difference of the modulus values of (a) is Δ ρ, Δ ρ = | r A |-|r C |，ζ ρ (η) is an expansion coefficient of Δ ρ, and a cosine value of the initial angle θ is equal to the reference angle θ c Has a difference of Δ θ, Δ θ = cos θ -cos θ C ，ζ θ (η) is the expansion coefficient of Δ θ;
step 3) calculating a fundamental frequency echo signal s received by the SAR imaging system 1 (t r ,η)：
Will | r A Expansion of (eta) I into the transmit signal s (t) of the SAR imaging system r Eta) to obtain an echo signal s received by the SAR imaging system 0 (t r Eta) due to the echo signal s 0 (t r Eta) is in a high frequency band, inconvenient for signal processing, so that for s 0 (t r Eta) down-conversion, i.e. by converting the echo signal s 0 (t r Eta) and a down conversion function H down ＝exp(-j2πf c Eta) multiplication, wherein f c For transmitting the carrier frequency of the signal, the echo signal s 0 (t r Eta) to the baseband to obtain a fundamental echo signal s received by the SAR imaging system 1 (t r ,η)；
Step 4) for s 1 (t r Eta) distance pulse pressure treatment:
because the scene target SAR imaging platform has relative motion in a synthetic aperture time and the echo energy of the scene target is scattered on different distance units, a fundamental frequency echo signal s needs to be processed 1 (t r Eta) distance pulse pressure processing is carried out, and echo energy is focused on a distance unit corresponding to a target;
step 4 a) according to the following calculation formula, the fundamental frequency echo signal s received by the SAR imaging system 1 (t r Eta) Fourier transform to obtain s 1 (t r Eta) distance frequency domain echo signal s 2 (f r ,η)：
S 2 (f r ,η)＝∫S 1 (t r ,η)exp(-j2πf r t r )dt r
Wherein S is 2 (f r Eta) represents a distance frequency of f r Range frequency domain echo signal with azimuth time η |, [ integral ] dt r Representing the distance to time t r Performing an integration operation, S 1 (t r Eta) represents the SAR imaging system received distance time as t r The azimuth time is η, exp (-) represents an exponential operation with a natural constant e as the base, j represents an imaginary unit symbol, and
pi represents the circumference ratio;
step 4 b) by distance pulse pressure function H according to the following calculation formula 1 For range frequency domain echo signal s 2 (f r Eta) distance pulse pressure;
S 3 (K r ,η)＝S 2 (f r ,η)·H 1 (f r )
wherein S is 3 (K r Eta) represents the distance wave number K after the distance pulse pressure r Frequency domain echo signal with azimuth time η, H 1 (f r ) Representing a distance frequency of f r The distance of (a) to the pulse pressure function,
gamma denotes the SAR imaging system emission signal s (t) r η) distance tuning frequency;
step 5) for s 3 (K r η) consistent phase compensation:
due to the distance frequency domain signal s after the distance pulse pressure 3 (K r Eta) phase, reference point slope history | r C The phase corresponding to (eta) is space-invariant, and a consistent phase compensation function can be directly constructed to compensate the phaseSo as to obtain the distance frequency domain signal s after the distance pulse pressure 3 (K r Eta) performing uniform phase compensation;
step 5 a) constructing and constructing a consistent phase compensation function H according to the slope distance process expansion 2 (K r ,η)：
H 2 (K r ,η)＝exp(jK r |r C (η)|)；
Wherein, K r Represents the distance wave number, | r C (η) | represents the reference point slope distance course;
step 5 b) passing the uniform phase compensation function H according to the following calculation formula 2 (K r Eta) distance frequency domain signal s after distance pulse pressure 3 (K r Eta) performing uniform phase compensation;
S 4 (K r ,η)＝S 3 (K r ,η)·H 2 (K r ,η)
wherein S is 4 (K r Eta) represents a distance wave number K after uniform phase compensation r The azimuth time is a distance frequency domain echo signal of eta;
step 6) for s 4 (K r Eta) performing a two-dimensional interpolation of radius and angle:
after the consistent phase compensation, only the target of the reference point is well compensated, and the remaining phases of the other target points are not compensated, so that the distance frequency domain echo signal S after the consistent phase compensation needs to be compensated 4 (K r Eta) performing radius-angle two-dimensional interpolation, completing residual phase compensation while completing homogenization treatment of radius wave number and angle wave number, and obtaining a final focusing image;
step 6 a) calculating distance frequency domain signals s after consistent phase compensation respectively 4 (K r Eta) radius wave number K ρ Sum angle wave number K θ ：
Wherein, K r Represents the distance wave number, ζ ρ (η) is the pitchExpansion coefficient of Δ ρ, ζ, over the course θ (η) is the expansion coefficient of Δ θ in the course of the ramp;
step 6 b) of measuring the radial wavenumber K ρ Sum angle wave number K θ Respectively carrying out sinc kernel function h (eta) interpolation,
obtaining a mixture containing a uniform radius wavenumber K' ρ And a uniform angle wave number K' θ Radius angle signal s 5 (K' ρ ,K' θ )；
Step 6 c) of converting the radial angle signal s according to the following equation 5 (K' ρ ,K' θ ) Performing two-dimensional inverse Fourier transform to obtain SAR focusing image S 6 (t r ,η)；
S 6 (t r ,η)＝∫∫S 5 (K' ρ ,K' θ )exp(jK' ρ t r )exp(jK' θ η)dK' ρ dK' θ
Wherein S is 6 (t r Eta) represents the distance time t r SAR focused image with azimuth time η, S 5 (K' ρ ,K' θ ) Expressed in terms of radial wavenumber K ρ Sum angle wavenumber K θ Homogenized radius angle signal, K' ρ Denotes the interpolated radius wave number, K' θ Representing the interpolated angular wavenumber.
The technical effects of the invention are further explained by simulation experiments as follows:
1. simulation conditions and contents:
in the ground scene, 9 points are arranged according to a receiver coordinate system, the distance between the points is 0.5km, wherein the point C is the center point of the scene, the height is 0m, the points A and B are the edge points of the scene, the height of the point A is 20m, and the height of the point B is 100m, as shown in FIG. 2. On the same computer, a simulation experiment was performed using MATLAB R2017a, and the parameters used in the simulation experiment are shown in table 1:
table 1 simulation parameters schedule
The imaging result of the forward squint SAR imaging method based on the hypersonic aircraft flat flight section, which is the most practical method in the prior art, is shown in figure 3, wherein the abscissa is sampling in the azimuth direction, and the ordinate is sampling in the distance direction; fig. 3 (a) is a contour diagram of an imaging result of a scene edge point a using a prior art, fig. 3 (B) is a contour diagram of an imaging result of a scene center point C using a prior art, fig. 3 (C) is a contour diagram of an imaging result of a scene edge point B using a prior art, fig. 3 (d) is a contour diagram of an imaging result of a scene edge point a using the present invention, fig. 3 (e) is a contour diagram of an imaging result of a scene center point C using the present invention, and fig. 3 (f) is a contour diagram of an imaging result of a scene edge point B using the present invention;
meanwhile, in order to quantify the performance of the invention, two SAR images are obtained according to the invention and a front squint SAR imaging method based on a hypersonic aircraft flat flight section in the prior art, and the index parameters of the peak side lobe ratio and the integral side lobe ratio of a scene center point C point and a scene edge point A point and a scene edge point B point in the two SAR images are respectively calculated, wherein the index parameters are shown in a table 2:
TABLE 2
2. And (3) simulation result analysis:
comparing fig. 3 (a) and fig. 3 (d), it can be found that, for the scene edge point a with small height fluctuation, the azimuth direction main lobe and the side lobe of the contour map of the imaging result obtained by using the prior art have obvious aliasing, which indicates that the prior art has insufficient focusing precision for imaging the target with height fluctuation, while the main lobe and the side lobe of the contour map of the imaging result obtained by using the present invention are both obviously separated and present a good "cross" shape, which indicates that the present invention can improve the focusing precision for imaging the target with height fluctuation;
comparing fig. 3 (b) and fig. 3 (e), it can be found that, for the scene central point C without height fluctuation, the main lobe and the side lobe of the contour map of the imaging results obtained by using the prior art and the present invention are both obviously separated and present a good "cross" shape, which indicates that the present invention has good imaging focusing precision;
comparing fig. 3 (c) and fig. 3 (f), it can be found that, for the scene edge point B with large height fluctuation, the azimuth main lobe and the side lobe of the contour map of the imaging result obtained by using the prior art have serious aliasing and defocusing, which indicates that the prior art has insufficient focusing accuracy for the imaging of the target with height fluctuation, but the main lobe and the side lobe of the contour map of the imaging result obtained by using the present invention are both obviously separated and present a good "cross" shape, which indicates that the present invention can improve the focusing accuracy for the imaging of the target with height fluctuation;
referring to table 2, it can be found that the indexes of the scene edge points a and the scene edge points B obtained by using the prior art have deviations from the theoretical values, while the performance indexes of the scene edge points a and B obtained by the present invention are closer to the theoretical values, and the performance indexes of the central scene point C obtained by using the two methods are both closer to the theoretical values, which indicates that the prior art has poor focusing accuracy on scenes with high fluctuation, and the present invention has better focusing accuracy on scenes with high fluctuation.
Claims (6)
1. A hypersonic mobile platform SAR imaging method based on radius angle interpolation is characterized by comprising the following steps:
(1) Constructing a hypersonic mobile platform model carrying an SAR imaging system:
suppose a hypersonic mobile platform carrying a SAR imaging system is (0, H) in an xOyz coordinate system z ) For the initial coordinate along the y-axis as a curved path, (0, H z ) The initial slope distance to any point A of the detection scene is r A Reference slope distance to detection scene reference point C is r C The azimuth time of the hypersonic mobile platform carrying the SAR imaging system is eta, the initial speed is v, and the acceleration is a, v and r A And r C Are respectively theta and theta c The slope distance process from the hypersonic mobile platform carrying the SAR imaging system to A is
The reference slope distance process to the detection scene reference point C is
The SAR imaging system has a distance time t r The transmission signal is s (t) r ,η)；
(2) Calculate | r A (η) | expansion:
the slope distance process | r from the hypersonic mobile platform carrying the SAR imaging system to any point A of the detection scene A (eta) is subjected to vector Taylor expansion to obtain | r A (η) | expansion:
|r A (η)|＝|r C (η)|+ζ ρ (η)·Δρ+ζ θ (η)·Δθ
wherein the initial slope distance r A The module value of (a) and the reference slope distance r C The difference of the modulus values of (a) is Δ ρ, Δ ρ = | r A |-|r C |，ζ ρ (η) is an expansion coefficient of Δ ρ, and a cosine value of the initial angle θ is equal to the reference angle θ c Has a cosine value of Δ θ, Δ θ = cos θ -cos θ C ，ζ θ (η) is the expansion coefficient of Δ θ;
(3) Calculating a fundamental frequency echo signal s received by the SAR imaging system 1 (t r ,η)：
Will | r A Expansion of (eta) I into the transmit signal s (t) of the SAR imaging system r Eta) to obtain an echo signal s received by the SAR imaging system 0 (t r Eta) and to s 0 (t r Eta) to obtain a base frequency echo signal s received by the SAR imaging system 1 (t r ,η)；
(4) To s 1 (t r Eta) distance pulse pressure treatment:
(4a) For the fundamental frequency echo signal s received by the SAR imaging system 1 (t r Eta) to obtain s 1 (t r Eta) range-frequency-domain echo signal s 2 (f r Eta), wherein f r Represents a range frequency;
(4b) Pulse pressure function H by distance 1 For range frequency domain echo signal s 2 (f r Eta) distance pulse pressure to obtain distance frequency domain echo signal s 3 (K r Eta) in which K r Representing the distance wave number after the distance pulse pressure;
(5) To s 3 (K r η) consistent phase compensation:
(5a) Construction of a coherent phase compensation function H 2 (K r ,η)：
H 2 (K r ,η)＝exp(jK r |r C (η)|)；
(5b) By a uniform phase compensation function H 2 (K r Eta) distance frequency domain signal s after distance pulse pressure 3 (K r Eta) to obtain a distance frequency domain signal s after uniform phase compensation 4 (K r ,η)；
(6) To s 4 (K r Eta) two-dimensional interpolation of radius and angle:
(6a) Respectively calculating distance frequency domain signals s after consistent phase compensation 4 (K r Eta) radius wave number K ρ Sum angle wave number K θ ：
(6b) For radius wave number K ρ Sum angle wave number K θ Respectively carrying out interpolation on the sinc kernel functions h (eta) to obtain the product containing the uniform radius wave number K' ρ And uniform angle wave number K' θ Radius angle signal s 5 (K' ρ ,K' θ )；
(6c) For radius angle signal s 5 (K' ρ ,K' θ ) Performing two-dimensional inversionFourier transform to obtain SAR focused image s 6 (t r ,η)。
2. The hypersonic mobile platform SAR imaging method based on radius angle interpolation as claimed in claim 1, characterized in that: the step (4 a) of receiving the fundamental frequency echo signal s of the SAR imaging system 1 (t r Eta) performing a Fourier transform, the transform formula being:
s 2 (f r ,η)＝∫s 1 (t r ,η)exp(-j2πf r t r )dt r
wherein s is 2 (f r Eta) represents a distance frequency of f r Range frequency domain echo signal with azimuth time η |, [ integral ] dt r Representing the distance to time t r Performing an integration operation s 1 (t r Eta) represents the SAR imaging system received distance in time t r The azimuth time is η, exp (-) represents an exponential operation with a natural constant e as the base, j represents an imaginary unit symbol, and
and pi represents the circumferential ratio.
3. The SAR imaging method based on radius angle interpolation for hypersonic maneuvering platform is characterized in that the passing distance pulse pressure function H in the step (4 b) 1 For range frequency domain echo signal s 2 (f r Eta) distance pulse pressure is calculated according to the following formula:
s 3 (K r ,η)＝s 2 (f r ,η)·H 1 (f r )
wherein s is 3 (K r Eta) represents the distance wave number K after the distance pulse pressure r Frequency domain echo signal with azimuth time η, H 1 (f r ) Representing a distance frequency of f r The distance of (a) to the pulse pressure function,
gamma denotes the SAR imaging system emission signal s (t) r And η) distance tuning frequency.
4. The hypersonic maneuvering platform SAR imaging method based on radius angle interpolation as claimed in claim 1, characterized in that: passing the uniform phase compensation function H as described in step (5 b) 2 (K r Eta) distance frequency domain signal s after distance pulse pressure 3 (K r Eta) performing uniform phase compensation, wherein the calculation formula is as follows:
s 4 (K r ,η)＝s 3 (K r ,η)·H 2 (K r ,η)
wherein s is 4 (K r Eta) represents a distance wave number K after uniform phase compensation r And the azimuth time is eta.
5. The hypersonic maneuvering platform SAR imaging method based on radius angle interpolation as claimed in claim 1, characterized in that: the sinc kernel function h (η) in the step (6 b) has an expression as follows:
wherein h (η) represents a sinc kernel function with azimuth time η, and sin (·) represents taking a sine.
6. The hypersonic maneuvering platform SAR imaging method based on radius angle interpolation as claimed in claim 1, characterized in that: the radial angle signal s in step (6 c) 5 (K' ρ ,K' θ ) Performing two-dimensional inverse Fourier transform, wherein the transform formula is as follows:
s 6 (t r ,η)＝∫∫s 5 (K' ρ ,K' θ )exp(jK' ρ t r )exp(jK' θ η)dK' ρ dK' θ
wherein s is 6 (t r Eta) represents distance time t r SAR focused image with azimuth time eta, s 5 (K' ρ ,K' θ ) Expressed in terms of radial wavenumber K ρ Sum angle wave number K θ Homogenized radius angle signal, K' ρ Denotes the interpolated radius wave number, K' θ Representing the interpolated angular wavenumber.
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