CN109471105A - A kind of compressed sensing Inverse Synthetic Aperture Radar maneuvering target deviates the fast imaging method of grid - Google Patents
A kind of compressed sensing Inverse Synthetic Aperture Radar maneuvering target deviates the fast imaging method of grid Download PDFInfo
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- CN109471105A CN109471105A CN201811360874.2A CN201811360874A CN109471105A CN 109471105 A CN109471105 A CN 109471105A CN 201811360874 A CN201811360874 A CN 201811360874A CN 109471105 A CN109471105 A CN 109471105A
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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
- G01S13/9021—SAR image post-processing techniques
- G01S13/9029—SAR image post-processing techniques specially adapted for moving target detection within a single SAR image or within multiple SAR images taken at the same time
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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
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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
- G01S13/9004—SAR image acquisition techniques
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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
- 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
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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- Electromagnetism (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention discloses the fast imaging methods that a kind of compressed sensing Inverse Synthetic Aperture Radar maneuvering target deviates grid, comprising: handles Inverse Synthetic Aperture Radar echo, obtains the Range Profile of one group of distance unit composition；Rarefaction representation is carried out to signal in the 1st distance unit using compressed sensing restructing algorithm, obtains the frequency and frequency modulation rate initial value of K strong scattering point；Consider that the actual frequency of strong scattering point and frequency modulation rate generally deviate preset frequency grid and adjust frequency grid, converts the minimization problem that Combined estimator deviates grid error and sparse coefficient for the imaging that maneuvering target deviates grid；Sparse coefficient, frequency departure and tune frequency departure are obtained by iteratively solving two minimum variance problems；The signal of each distance unit is repeated the above, the sparse coefficient obtained in all distance unit is combined to obtain final Inverse Synthetic Aperture Radar image.This method can quickly obtain the compressed sensing of high quality against synthetic aperture maneuvering target radar image.
Description
Technical field
The present invention relates to inverse synthetic aperture radar imaging methods, more particularly to a kind of compressed sensing Inverse Synthetic Aperture Radar
Deviate the imaging method of grid.
Background technique
In compressed sensing based inverse synthetic aperture radar imaging because can not know in advance frequency in signal at
Part, so that is, continuous frequency is separated into frequency grid using the Fourier basis functions for presetting frequency grid, it is believed that strong
Scattering point is all on grid center.However, strong scattering point may be on grid center.In this way, preset dictionary with
There is mismatches for actual dictionary, this will reduce imaging performance significantly.Here it is deviate grid problem.
In order to solve this problem, most straightforward approach is exactly to refine grid, but this will increase the correlation of basic function, no
Conducive to reliably reconstruction signal.Have scholar propose based on nuclear norm optimization and local optimum method, but they to scattering point it
Between minimum range require.Most methods are to solve to deviate grid by the bias of Combined estimator grid and sparse solution at present
The problem of lattice, can be solved using bayes method, matching pursuit algorithm and the convex searching algorithm of alternating.However, they
Calculation amount is all bigger.Computation burden can be reduced using first order Taylor approximation, but the calculation amount of existing method is still very big.
The imaging method that some compressed sensing Inverse Synthetic Aperture Radar deviate grid is had proposed in field at present.But it
Calculation amount it is all bigger, and they both for target movement be steady situation.And under actual conditions, radar target
It is in maneuvering condition mostly.When target maneuver, deviate reduction and the position for adjusting frequency grid to will lead to strong scattering point amplitude
Mistake, so that image quality be made to be decreased obviously.It can be eliminated therefore, it is necessary to one kind and deviate the inverse synthesis of compressed sensing that grid influences
Aperture radar maneuvering target imaging method.
Summary of the invention
Goal of the invention: in order to overcome the above-mentioned deficiencies of the prior art, calculating when maneuvering target deviates grid imaging is reduced
Amount, the present invention provides the fast imaging methods that a kind of compressed sensing Inverse Synthetic Aperture Radar maneuvering target deviates grid.
Technical solution: a kind of compressed sensing Inverse Synthetic Aperture Radar maneuvering target deviates the fast imaging method of grid, packet
Containing following steps:
S10, Inverse Synthetic Aperture Radar echo is handled, obtains the Range Profile of one group of distance unit composition；
S20, rarefaction representation is carried out to the signal in the 1st distance unit using compressed sensing restructing algorithm, obtained K strong
The frequency of scattering point and the initial value of frequency modulation rate；
S30, consider that the actual frequency of strong scattering point and frequency modulation rate generally deviate preset frequency grid and frequency modulation rate
Grid asks the minimum that the imaging that maneuvering target deviates grid is converted into Combined estimator deviation grid error and sparse coefficient
Topic；
S40, the sparse coefficient of joint minimization problem, frequency departure are obtained by iteratively solving two minimum variance problems
With tune frequency departure；
S50, the processing that S20-S40 is repeated to the signal of other each distance unit will finally be obtained in all distance unit
To sparse coefficient s be combined to obtain final Inverse Synthetic Aperture Radar image.
Preferably, Inverse Synthetic Aperture Radar echo is subjected to solution linear frequency modulation, Range compress, movement in the step S10
After compensation deals, one group of Range Profile being made of L distance unit is obtained.
Preferably, the step S20 include: assume the 1st distance unit in measuring signal be y, calculation matrix Ψ,
Basic function is the linear frequency modulation basic function Φ for presetting grid, carries out sparse table to signal using compressed sensing restructing algorithm
Show, obtains the initial frequency f=[f of K strong scattering point1,f2,…fi,…fK] and tune initial frequency γ=[γ1,γ2,…
γi,…γK], fiAnd γiIndicate the frequency and frequency modulation rate of i-th of strong scattering point.
Preferably, minimization problem indicates in the step S30 are as follows:
Wherein i is scattering point serial number, siIt is the coefficient of i-th of scattering point, symbol δ fiWith δ γiI-th of scattering point with from
Unknown bias between its nearest frequency grid and tune frequency grid, subject to indicate restrictive condition, ΔfAnd Δγ
It is frequency grid and the size for adjusting frequency grid, g (f respectivelyi+δfi,γi+δγi) it is that parameter is (f in recovery matrix G=Ψ Φi
+δfi,γi+δγi) column vector.
Preferably, sparse coefficient s=[s is solved in the step S401,s2,…si,…sK], frequency departure amount δ f=[δ
f1,δf2,…δfi,…δfK] and frequency modulation rate bias δ γ=[δ γ1,δγ2,…δγi,…δγK] include:
F first(1)It is initialized as f, γ(1)It is initialized as γ, obtains the initial estimation of sparse coefficientWherein subscript 1 indicates the 1st iteration；
Then the number of iterations is indicated with n, the iteration as the following formula since n=1, until meeting the condition of convergence:
(δf(n),δγ(n))=Re { ((P(n))HP(n))-1(P(n))Hy(n)}
f(n+1)=f(n)+δf(n)
γ(n+1)=γ(n)+δγ(n)
s(n+1)=((Q(n+1))HQ(n+1))-1(Q(n+1))Hy
Wherein Re expression takes real part, defines
WhereinWithIt respectively indicatesTo fi (n)WithPartial derivative,
Preferably, it is askingTo fi (n)Partial derivative when,It is askingIt is rightPartial derivative when,
Preferably, bias (δ f is updated in iteration(n),δγ(n)), frequency f(n+1), frequency modulation rate γ(n+1)With sparse coefficient s(n +1)When, the condition of convergence is surplus2 Norm minimums or some frequency bias |
fi (n+1)-fi| > Δf/ 2 or some frequency modulation rate bias
The utility model has the advantages that the existing method for solving the problems, such as to deviate grid in compressed sensing inverse synthetic aperture radar imaging
It is limited only to the case where target is smooth motion, the present invention breaches this limitation, realizes the compressed sensing of maneuvering target
Inverse Synthetic Aperture Radar deviates grid imaging, and algorithm is simple, and speed is fast.The compressed sensing Inverse Synthetic Aperture Radar machine of proposition
The imaging algorithm that moving-target deviates grid can be quickly obtained the radar image of high quality.
Detailed description of the invention
Fig. 1 is fast imaging method flow chart of the invention；
Fig. 2 is the imaging results based on original signal according to the embodiment of the present invention；
Fig. 3 is to be used based on 20% signal according to the embodiment of the present invention and carried out orientation imaging based on Fourier basis functions
Result；
Fig. 4 is to carry out orientation imaging using linear frequency modulation basic function based on 20% signal according to the embodiment of the present invention
As a result.
Specific embodiment
Technical solution of the present invention is described further with reference to the accompanying drawing.
In order to carry out compressed sensing imaging to Inverse Synthetic Aperture Radar maneuvering target, while eliminating departure freqency grid and tune
Influence of the frequency grid to image quality, the present invention propose that a kind of compressed sensing Inverse Synthetic Aperture Radar maneuvering target deviates grid
Fast imaging method.Referring to Fig.1, the present invention is described in more detail below, comprising the following steps:
(1) after Inverse Synthetic Aperture Radar echo being carried out solution linear frequency modulation, Range compress, motion compensation process, one is obtained
The Range Profile that group is made of L distance unit.
(2) assume that the measuring signal in the 1st distance unit is y, calculation matrix Ψ.For even-keel objective, each away from
From the signal in unit can regard as a series of the linear of sinusoidal signals and.But this model is no longer adapted to maneuvering target.It is right
It can be regarded as a series of linear frequency modulation letter unknown by frequencies and frequency modulation rate in the signal in maneuvering target, each distance unit
Number constitute.Therefore basic function is using the linear frequency modulation basic function Φ for presetting grid.It is more in line with due to being used in imaging
The linear frequency modulation basic function of maneuvering target signal characteristic, therefore image quality can be significantly improved.Sparse restructing algorithm can be used
(as orthogonal matching pursuit algorithm, base seek track algorithm, FOCUSS algorithm or sparse Bayesian algorithm) obtains strong scattering point
The initial value of frequency and frequency modulation rate.Since the computation complexity of orthogonal matching pursuit algorithm is low, orthogonal matching is used here
Tracing algorithm.Orthogonal matching pursuit algorithm uses the thought of iteration, first all atom projections, selection into basic function by signal
Inner product the maximum is as matched atoms；This projection value is eliminated from original signal again and obtains residual signals, continues projection residual errors signal
And most matched atoms are selected, this step is repeated until meeting specified criteria.The frequency and tune frequency parameter of matched atoms are as strong
The frequency and frequency modulation rate of scattering point can be obtained by the initial frequency f=[f of K strong scattering point in this way1,f2,…fi,…fK] and
Adjust initial frequency γ=[γ1,γ2,…γi,…γK], f hereiAnd γiIndicate the frequency and frequency modulation rate of i-th of strong scattering point.
(3) when target maneuver, needing the parameter of discretization not only to have frequency, there are also frequency modulation rates.Consider strong scattering dot frequency
Exist between the actual value and preset frequency grid and tune frequency grid of frequency modulation rate and deviate, preferably to match measurement
Value, i.e.,
Wherein i is scattering point serial number, siIt is the coefficient of i-th of scattering point, symbol δ fiWith δ γiIndicate that i-th of scattering point is real
Unknown bias between the frequency and frequency modulation rate and the frequency grid nearest from it and tune frequency grid on border.If scattering point is real
The frequency and frequency modulation rate on border are just fallen on preset grid, there is δ fi=0, δ γi=0；If not in preset grid
Inevitable between two adjacent grids on lattice, when among two grids, offset is maximum, is the one of grid size
Half, i.e., | δ fi|=Δf/ 2, | δ γi|=Δγ/ 2, other situation offsets are respectively less than the half of grid size, i.e., | δ fi| <
Δf/ 2, | δ γi| < Δγ/2.Subject to indicates restrictive condition, ΔfAnd ΔγIt is frequency grid and tune frequency grid respectively
Size, g (fi+δfi,γi+δγi) it is that parameter is (f in recovery matrix G=Ψ Φi+δfi,γi+δγi) column vector.
Joint above in order to obtain minimizes, and estimates sparse coefficient s=[s using following step1,s2,…si,…
sK], frequency departure δ f=[δ f1,δf2,…δfi,…δfK] and tune frequency departure δ γ=[δ γ1,δγ2,…δγi,…δγK]。
1. f first(1)It is initialized as f, γ(1)It is initialized as γ, obtains the initial estimation of sparse coefficientWherein subscript 1 indicates the 1st iteration.
2. indicating the number of iterations with n, the iteration as the following formula since n=1 works as surplus2
Stop iteration or the bias of some frequency when Norm minimum | fi (n+1)-fi| > Δf/ 2 or some frequency modulation rate deviation
AmountWhen stop iteration.
(δf(n),δγ(n))=Re { ((P(n))HP(n))-1(P(n))Hy(n)} (1)
f(n+1)=f(n)+δf(n)
γ(n+1)=γ(n)+δγ(n)
s(n+1)=((Q(n+1))HQ(n+1))-1(Q(n+1))Hy (2)
Wherein subscript n, n+1 indicates the number of iterations, and Re expression takes real part, takes
WhereinThe present invention will be motor-driven
The deviation grid imaging problem of target is converted into two minimum variance problem formulas (1) and formula (2), is simply easy to solve.With it is orthogonal
Matching pursuit algorithm is compared, and the increased calculation amount of the method for the present invention is calculating formula (1), formula (2) and formula (3).If N-dimensional signal
Degree of rarefication is K, and the dimension of measured value is M.Because of P(n)And Q(n)Dimension be M × K, y(n)Dimension with y is M × 1, so formula
(1) and the computation complexity of formula (2) is Ο (MK2).If to P(n)And Q(n)QR decomposition is carried out, complexity can further decrease
For Ο (MK).Due to there is 2K component in formula (3), each component needs M multiplication, therefore the computation complexity of formula (3) is Ο
(2MK).Here K is the degree of rarefication of signal, is worth smaller.As it can be seen that the computation complexity of the method for the present invention is lower, can quickly ask
Solution.
(4) if distance unit number is less than L, distance unit number adds 1, repeats step (2)~(3).If distance unit number
Equal to L, it is exactly final Inverse Synthetic Aperture Radar image that the sparse coefficient s obtained in all distance unit, which is combined,.
Effect of the invention is verified with an example below.By the present invention be used for the direction dimensions of one-dimensional ISAR emulation data at
Picture, steps are as follows:
(1) the signal z: signal length 320 in a distance unit is generated, is made of 4 linear FM signals, amplitude
It is randomly generated from multiple unit circle, frequency is randomly selected 0 between 320Hz, and frequency modulation rate is respectively 30,40,50 and 60, sampling
Frequency is 320Hz.Size is used to be observed for the calculation matrix Ψ of 64 × 320 gaussian random matrix, obtaining dimension is 64
Measured value y.White Gaussian noise, which is added, makes the signal-to-noise ratio of signal be 25dB.Basic function Φ use size for 320 × 320 from
Linear frequency modulation basic matrix is dissipated, adjusts initial frequency to take 0, frequency grid size deltaf1 is taken, frequency modulation rate grid size ΔγTake 1.Using just
Matching pursuit algorithm is handed over to obtain the sparse coefficient of 4 linear frequency modulation ingredients, initial frequency f=[f1,f2,f3,f4] and frequency modulation rate at the beginning of
Value γ=[γ1,γ2,γ3,γ4]。
(2) consider to exist between the actual frequency of 4 linear frequency modulation ingredients and frequency modulation rate and corresponding initial value and deviate, with more preferable
Ground matches measured value, i.e.,
Joint above in order to obtain minimizes, and estimates sparse coefficient s=[s using following step1,s2,s3,s4], frequency
Rate deviates δ f=[δ f1,δf2,δf3,δf4] and tune frequency departure δ γ=[δ γ1,δγ2,δγ3,δγ4]。
1. f first(1)It is initialized as f, γ(1)It is initialized as γ, obtains the initial estimation of sparse coefficientWherein subscript 1 indicates the 1st iteration.
2. indicating the number of iterations with n, the iteration as the following formula since n=1 works as surplus2
Stop iteration or the bias of some frequency when Norm minimum | fi (n+1)-fi| the bias of > 1/2 or some frequency modulation rate
(δf(n),δγ(n))=Re { ((P(n))HP(n))-1(P(n))Hy(n)} (1)
f(n+1)=f(n)+δf(n)
γ(n+1)=γ(n)+δγ(n)
s(n+1)=((Q(n+1))HQ(n+1))-1(Q(n+1))Hy (2)
Wherein subscript n, n+1 indicates the number of iterations, and Re expression takes real part, takes
Wherein
Fig. 2 is the imaging results based on original signal, and Fig. 3 and Fig. 4 are the signals based on 20%, is respectively adopted based in Fu
The orthogonal matching pursuit algorithm and the present invention of phyllopodium function carry out the result of orientation imaging.It can be seen that since the present invention adopts
With linear frequency modulation basic function, and solve the problems, such as to deviate grid, therefore compared with existing algorithm, the present invention has been obtained more
Accurate imaging results.
Claims (10)
1. the fast imaging method that a kind of compressed sensing Inverse Synthetic Aperture Radar maneuvering target deviates grid, which is characterized in that should
Method comprises the steps of:
S10, Inverse Synthetic Aperture Radar echo is handled, obtains the Range Profile of one group of distance unit composition；
S20, rarefaction representation is carried out to the signal in the 1st distance unit using compressed sensing restructing algorithm, obtains K strong scattering
The frequency of point and the initial value of frequency modulation rate；
S30, consider that the actual frequency of strong scattering point and frequency modulation rate generally deviate preset frequency grid and adjust frequency grid,
The minimization problem that Combined estimator deviates grid error and sparse coefficient is converted by the imaging that maneuvering target deviates grid；
S40, sparse coefficient, frequency departure and the tune of joint minimization problem are obtained by iteratively solving two minimum variance problems
Frequency departure；
S50, the processing that S20-S40 is repeated to the signals of other each distance unit will finally be obtained in all distance unit
Sparse coefficient s is combined to obtain final Inverse Synthetic Aperture Radar image.
2. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 1 deviates grid
Method, which is characterized in that Inverse Synthetic Aperture Radar echo is subjected to solution linear frequency modulation, Range compress, movement benefit in the step S10
After repaying processing, one group of Range Profile being made of L distance unit is obtained.
3. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 1 deviates grid
Method, which is characterized in that the step S20 includes:
Assuming that measuring signal in the 1st distance unit is y, calculation matrix Ψ, basic function is preset grid linear
Frequency modulation basic function Φ carries out rarefaction representation to signal using compressed sensing restructing algorithm, obtains the initial frequency of K strong scattering point
F=[f1,f2,…fi,…fK] and tune initial frequency γ=[γ1,γ2,…γi,…γK], fiAnd γiIndicate i-th of strong scattering
The frequency and frequency modulation rate of point.
4. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 3 deviates grid
Method, which is characterized in that the compressed sensing restructing algorithm uses orthogonal matching pursuit algorithm.
5. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 3 deviates grid
Method, which is characterized in that minimization problem indicates in the step S30 are as follows:
Wherein i is scattering point serial number, siIt is the coefficient of i-th of scattering point, symbol δ fiWith δ γiI-th of scattering point with most from it
Unknown bias between close frequency grid and tune frequency grid, subject to indicate restrictive condition, ΔfAnd ΔγRespectively
It is frequency grid and the size for adjusting frequency grid, g (fi+δfi,γi+δγi) it is that parameter is (f in recovery matrix G=Ψ Φi+δ
fi,γi+δγi) column vector.
6. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 3 deviates grid
Method, which is characterized in that sparse coefficient s=[s is solved in the step S401,s2,…si,…sK], frequency departure amount δ f=[δ f1,
δf2,…δfi,…δfK] and frequency modulation rate bias δ γ=[δ γ1,δγ2,…δγi,…δγK] include:
F first(1)It is initialized as f, γ(1)It is initialized as γ, obtains the initial estimation of sparse coefficientWherein subscript 1 indicates the 1st iteration；
Then the number of iterations is indicated with n, the iteration as the following formula since n=1, until meeting the condition of convergence:
(δf(n),δγ(n))=Re { ((P(n))HP(n))-1(P(n))Hy(n)}
f(n+1)=f(n)+δf(n)
γ(n+1)=γ(n)+δγ(n)
s(n+1)=((Q(n+1))HQ(n+1))-1(Q(n+1))Hy
Wherein Re expression takes real part, defines
WhereinWithIt respectively indicatesTo fi (n)WithPartial derivative,
7. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 6 deviates grid
Method, it is characterised in that: askingTo fi (n)Partial derivative when,
8. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 6 deviates grid
Method, it is characterised in that: askingIt is rightPartial derivative when,
9. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 6 deviates grid
Method, it is characterised in that: in the step S40, update bias (δ f in iteration(n),δγ(n)), frequency f(n+1), frequency modulation rate
γ(n+1)With sparse coefficient s(n+1)When, the condition of convergence is surplus2 Norm minimums.
10. the fast imaging side that compressed sensing Inverse Synthetic Aperture Radar maneuvering target according to claim 6 deviates grid
Method, it is characterised in that: in the step S40, update bias (δ f in iteration(n),δγ(n)), frequency f(n+1), frequency modulation rate
γ(n+1)With sparse coefficient s(n+1)When, the condition of convergence is the bias of some frequency | fi (n+1)-fi| > Δf/ 2 or certain
The bias of a frequency modulation rate
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