CN109116352A - A kind of circle sweeps ISAR mode ship super-resolution imaging method - Google Patents
A kind of circle sweeps ISAR mode ship super-resolution imaging method Download PDFInfo
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Abstract
The invention discloses a kind of circles to sweep ISAR mode ship super-resolution imaging method, belongs to Radar Technology field, includes the following steps: that the echo-signal swept under ISAR mode will be justified, be divided into M data frame, handled frame by frame；To than the m-th data frame, Range compress is carried out, selects the sub- echo of the ship target of m frame；To the sub- echo of the ship target of m frame, the pretreatment including translational compensation and rotation compensation is carried out；Using Burg algorithm, to the sub- echo of the ship target of m frame, Data Extrapolation is carried out in orientation；The data externally postponed carry out stochastical sampling in orientation；To the data after sampling, compressed sensing calculating is carried out in orientation, obtains the sparse coefficient matrix of current data frame；Constant false alarm rate detection is carried out to the sparse coefficient matrix after compressed sensing, obtains the range-Dopler domain super-resolution image of m frame.
Description
Technical field
The invention belongs to Radar Technology fields, and in particular to a kind of circle sweeps ISAR (Inverse Synthetic
Aperture Radar, Inverse Synthetic Aperture Radar) mode ship super-resolution imaging method.
Background technique
Circle sweeps a kind of Novel work mode that ISAR mode is airborne ocean surveillance radar, it passes through the quick circumference of antenna
Scanning ensure that system have biggish overlay area, can during antenna scanning to multiple targets in overlay area according to
Secondary imaging can also obtain the image sequence of same target different perspectives in multiframe scanning process.But then, antenna is fast
Speed scanning causes the integration time of target short, reduces the DOPPLER RESOLUTION of system.It is proposed that a kind of Data Extrapolation is felt with compression
Know that the circle combined sweeps ISAR mode ship super-resolution imaging method.This method is for returning after translational compensation, rotation compensation
Wave carries out Data Extrapolation by Burg algorithm in orientation first, and the data then externally postponed are adopted at random in orientation
Sample generates range Doppler area image using compression sensing method later.Finally, the image to generation carries out CFAR
(Constant False Alarm Rate, constant false alarm rate) detection, for improving the letter miscellaneous noise ratio of image.This method combines
The advantages of two methods of Data Extrapolation and compressed sensing, while improving DOPPLER RESOLUTION, obtain image secondary lobe also
It is preferable to inhibit.It is miscellaneous in DOPPLER RESOLUTION promotion, Sidelobe Suppression, letter that the emulation experiment carried out demonstrates proposed algorithm
It makes an uproar than the validity of improvement etc..
In airborne ocean surveillance radar, naval target detection, MMTI (Maritime Moving need to be usually set
Target Identification, marine moving-target identification), naval target tracking, distance is to imaging, ISAR (Inverse
Synthetic Aperture Radar, Inverse Synthetic Aperture Radar) etc. multiple-working modes, realize inspection to targets such as ships
The functions such as survey, tracking, imaging, classification and identification.In traditional ISAR mode, usually it is imaged just for single target,
To specific objective imaging it is previous as known the prior informations such as target position by other modes, consequently facilitating wave beam is referred to
To adjusting to target region.It is a kind of novel operating mode that circle, which sweeps ISAR mode, it is swept by the quick circumference of antenna
The system of ensure that is retouched with biggish overlay area, can during antenna scanning to multiple targets in overlay area successively
Imaging.Using the mode, the image sequence of same target different perspectives can be also obtained in multiframe scanning process, is conducive to target
Classification and identification.However, the integration time that the quick scanning of antenna also results in target is short, the Doppler for reducing system is differentiated
Rate.How to realize that the super-resolution imaging of target is that circle sweeps critical issue urgently to be resolved in ISAR imaging technique.
For the super-resolution imaging for realizing ISAR system, currently used method is generally divided into following several classes: Data Extrapolation,
Improved nonlinear filtering, power Spectral Estimation, compressed sensing imaging.In Data Extrapolation class method, using linear prediction model
Radar observation data are fitted, Data Extrapolation are carried out using Burg scheduling algorithm, to improve the resolution ratio of system.Changing
Into nonlinear filtering class method in, by system impulse response function carry out Sidelobe Suppression weaken strong scatterer to surrounding
Energy leakage, while signal extrapolation is realized by the bandwidth expansion operation of iteration, it is finally reached and proposes high-resolution purpose.Power
Power estimation class method is divided into parameter Estimation type and two kinds of non-parametric estmation type again.In parameter Estimation type method, assumes initially that and be
System meets certain mathematical model, then converts the Parameter Estimation Problem in selected mathematical model, exemplary process packet for problem
It includes the method based on multiple signal classification (MUltiple SIgnal Classification, MUSIC), be based on invariable rotary skill
Art (Estimation of Signal Parameter via Rotational Invariance Techniques,
ESPRIT method, method based on Relax algorithm) etc..In non-parametric estmation type method, then without carrying out signal model vacation
If exemplary process includes method based on Capon algorithm, based on sinusoidal signal amplitude-phase estimates (Amplitude and
Phase Estimation of a Sinusoid, APES) method etc..In compressed sensing imaging method, by actual time
Wave signal regards as the subset of high-resolution echo-signal, has the characteristics that sparsity in airspace using target scattering point, will surpass
Resolution imaging problem is converted into sparse Problems of Reconstruction and is solved.
Summary of the invention
For the above-mentioned technical problems in the prior art, the invention proposes a kind of circles to sweep ISAR mode ship oversubscription
Resolution imaging method, design rationally, overcome the deficiencies in the prior art, have good effect.
To achieve the goals above, the present invention adopts the following technical scheme:
A kind of circle sweeps ISAR mode ship super-resolution imaging method, includes the following steps:
Step 1: circle being swept into the echo-signal under ISAR mode, by TframeFor the period, be divided into M data frame, frame by frame into
Row processing；
Circle is swept in ISAR mode, when orientation m- frequency of distance domain ship echo-signal, as shown in formula (1):
Wherein, subscript m is the serial number of current data frame, m=0 ..., M-1, t expression orientation time, frIndicate distance to
Frequency,Rect () is rectangular function, TframeFor the period of data frame,
tm0For the interval time between the initial time and ship synthetic aperture central instant of than the m-th data frame, TintWhen for pulse accumulation
Between, f0For radar carrier frequency, BrFor radar signal bandwidth, C indicates the light velocity, Rm0(t) it indicates from the phase center of radar to ship
The vector of center of rotation, Rm0It (t) is Rm0(t) mould, r be from ship center of rotation to ship on certain scattering point vector, σ0(r)
It is long-pending for the normalization normalized radar backscatter cross section of the scattering point at r,For Rm0(t) unit vector；
Step 2: to than the m-th data frame, carrying out Range compress, select the sub- echo of the ship target of m frame；For ship
The selection of sub- echo can both carry out manually, and also can use signal detection algorithm and be automatically performed；
Step 3: to the sub- echo of the ship target of m frame, carrying out the pre- place including translational compensation and rotation compensation
Reason；
Step 4: Data Extrapolation being carried out in orientation to the sub- echo of the ship target of m frame using Burg algorithm；
Specifically comprise the following steps:
Step 4.1: signal being expressed as discrete form, if sm(iΔt,jΔfr) it is sm(t,fr) discrete form,
Wherein i=0 ..., L-1, j=0 ..., N-1, L and N be respectively orientation and distance to discrete points, Δ t and Δ frRespectively
It is orientation time and distance to the sampling interval of frequency；
Step 4.2: setting pm(i Δ t, j Δ τ) is to sm(iΔt,jΔfr) carry out the pretreatment such as translational compensation, rotation compensation
M- Distance Time domain signal when rear orientation, wherein Δ τ is sampling interval of the distance to the time；
Step 4.3: according to introduced symbol, extrapolating results are simplified, as shown in formula (2):
p′m(i ' Δ t, j Δ τ)=Burg [pm(i Δ t, j Δ τ)] m=0 ..., M-1i '=0 ..., L ' -1 (2)；
Wherein, p 'm(i ' Δ t, j Δ τ) is the signal after the extrapolation of Burg algorithm, and L ' is the orientation point postponed outside
Number；
Step 5: to the outer data postponed acquired in step 4, stochastical sampling is carried out in orientation；
Step 6: to the data after sampling acquired in step 5, compressed sensing calculating is carried out in orientation, is obtained current
The sparse coefficient matrix of data frame, the matrix are range-Dopler domain super-resolution image；
Stochastical sampling and compressed sensing calculation formula are as follows:
[p″mC]L″×N=[Φ]L″×L′·[p′mC]L′×N=[Φ]L″×L′·[Ψ]L′×L′·[IC]L′×N=[Θ]L″×L′·
[IC]L′×N(3)；
Wherein, L " for the orientation points after stochastical sampling and having L " < < L ', p 'mCFor p 'mThe square of (i ' Δ t, j Δ τ)
Formation formula, Φ are the corresponding calculation matrix of random sampling procedure, p "mCFor the matrix after stochastical sampling, Ψ is basic matrix, and Θ is sense
Know matrix, ICFor the coefficient matrix obtained after compressed sensing calculates；
Wherein, basic matrix Ψ uses following Fourier's basic matrix:
Wherein, to sparse coefficient matrix ICSolution, following optimization problem can be converted into:
Wherein, | | | |0Indicate l0Norm in the case where meeting certain constraint condition, while considering the influence of noise, will be upper
State optimization problem conversion are as follows:
Wherein, | | | |1Indicate l1Norm, | | | |2Indicate l2Norm, ε are constant relevant to noise level；If K table
Show degree of rarefication, then when Θ meets K rank RIP condition, andWhen, then by solving above-mentioned optimization problem, recover
Coefficient matrix IC；
Step 7: CFAR detection being carried out to the sparse coefficient matrix after step 6 compressed sensing, will be determined as clutter plus noise
The amplitude of pixel is set to 0, obtains range-Dopler domain super-resolution image of the m frame after clutter recognition；
The matrix I ' constituted for sea clutter and the corresponding sparse coefficient of noiseCIf its real and imaginary parts obeys zero
Value, variance areGaussian Profile, then its amplitude Rayleigh distributed:
Wherein, r is matrix I 'CThe corresponding stochastic variable of middle each element amplitude, f (r) are the probability density expression of r；
Relationship between CFAR threshold value and false-alarm probability are as follows:
Wherein, PfaIt is the false-alarm probability of setting, VTIt is threshold value to be solved, threshold value is calculated by formula (9):
Step 8: judging whether m is equal to M-1；
If: judging result is that m is equal to M-1, is terminated；
Or judging result is m not equal to M-1, then enables m=m+1, then execute step 2.
Advantageous effects brought by the present invention:
The invention proposes the circle that a kind of Data Extrapolation is combined with compressed sensing sweep ISAR mode ship super-resolution at
Image space method.For the echo after translational compensation, rotation compensation, Data Extrapolation is carried out by Burg algorithm in orientation first, so
The data externally postponed afterwards carry out stochastical sampling in orientation, generate range-Dopler domain figure using compression sensing method later
Picture.Finally, CFAR (Constant False Alarm Rate, constant false alarm rate) detection is carried out to the image of generation, for improving
The letter miscellaneous noise ratio of image.
Why the present invention selects to combine above-mentioned two classes method into the reason of realizing super-resolution processing: 1) outside data
Push away method has advantage, but the image side with higher generated using this method in terms of the raising multiple of DOPPLER RESOLUTION
Valve；2) compression sensing method has certain limitation in terms of the raising multiple of DOPPLER RESOLUTION, but it is in the secondary lobe of image
Aspect is inhibited to have a clear superiority；Therefore, both methods has preferable complementary；The present invention sweeps ISAR mode for circle and opens
A series of emulation experiment has been opened up, having in terms of DOPPLER RESOLUTION promotion, Sidelobe Suppression, letter miscellaneous noise ratio is demonstrated
Effect property, also shows the ability that same target different perspectives image sequence is obtained in multiframe scanning process；The present invention is equally applicable
In the super-resolution imaging of other type ISAR systems.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention.
Fig. 2 is that DOPPLER RESOLUTION when handling only with compressed sensing improves multiple limit schematic diagram.
Fig. 3 difference on the frequency between target is greater than the compression sensing method DOPPLER RESOLUTION limit, is less than original Doppler resolution
Imaging results schematic diagram in the case of rate；Wherein, (a) is the result schematic diagram of direct FFT；It (b) is to utilize Burg algorithm logarithm
The FFT result schematic diagram after 3 times of expansions is carried out according to amount；(c) result schematic diagram to be obtained using compression sensing method.
Fig. 4 difference on the frequency between target is less than the compression sensing method DOPPLER RESOLUTION limit, postpones Doppler point greater than outer
Imaging results schematic diagram in the case of resolution；Wherein, figure (a) is the result schematic diagram of direct FFT；Figure (b) is to be calculated using Burg
Method carries out the FFT result schematic diagram after 3 times of expansions to data volume；Figure (c) is that the result obtained using compression sensing method is illustrated
Figure.
Fig. 5 is the amplitude spectrum schematic diagram of signal when being utilized respectively three kinds of FFT, Burg extrapolation, compressed sensing methods.
Fig. 6 is geometrical relationship schematic diagram used in emulation.
Fig. 7 is ship scattering point position view.
Fig. 8 be in signal not in the case where Noise and clutter the 0th frame imaging results schematic diagram；Wherein, figure (a) is both
Without Data Extrapolation, also without the range Doppler image under compressed sensing calculated case；Scheming (b) is only to carry out outside data
It pushes away but without the range Doppler image under compressed sensing calculated case；Figure (c) is without Data Extrapolation, is only pressed
Range Doppler image in the case of contracting perceptual computing；Figure (d) is not only to carry out Data Extrapolation but also carry out compressed sensing calculated case
Under range Doppler image.
Fig. 9 be in signal not in the case where Noise and clutter the 0th frame image point target impulse response schematic diagram；Its
In, figure (a) is the point target impulse response schematic diagram after direct FFT；Scheming (b) is the point target pulse sound for only carrying out Data Extrapolation
Answer schematic diagram；Scheming (c) is the point target impulse response schematic diagram for only carrying out compressed sensing calculating；Figure (d) is both to carry out outside data
Push away, again carry out compressed sensing point target impulse response schematic diagram.
Figure 10 be signal in containing noise and clutter in the case where the 0th frame imaging results schematic diagram；Wherein, figure (a) is
Both without Data Extrapolation or without the range Doppler image under compressed sensing calculated case；Figure (b) is only to carry out data
It extrapolates but without the range Doppler image under compressed sensing calculated case；Figure (c) is without Data Extrapolation, only carries out
Range Doppler image under compressed sensing calculated case；Figure (d) is not only to carry out Data Extrapolation but also carry out compressed sensing calculating feelings
Range Doppler image under condition；Scheming (e) is that the result schematic diagram after CFAR detection is carried out to figure (d).
Figure 11 is the imaging results schematic diagram of the multiple data frames obtained using the method for the present invention；Wherein, figure (a) is the 0th
Frame is ultimately imaged result schematic diagram；Figure (b) is ultimately imaged result schematic diagram for the 1st frame；Scheme (c) be the 2nd frame it is final at
As result schematic diagram；Figure (d) is ultimately imaged result schematic diagram for the 3rd frame；Figure (e) is that the result that is ultimately imaged of the 4th frame is illustrated
Figure.
Specific embodiment
With reference to the accompanying drawing and specific embodiment invention is further described in detail:
A kind of circle sweeps ISAR mode ship super-resolution imaging method, and process is as shown in Figure 1, include the following steps:
Step 1: circle being swept into the echo-signal under ISAR mode, by TframeFor the period, be divided into M data frame, frame by frame into
Row processing；
Circle is swept in ISAR mode, when orientation m- frequency of distance domain ship echo-signal, as shown in formula (1):
Wherein, subscript m is the serial number of current data frame, m=0 ..., M-1, t expression orientation time, frIndicate distance to
Frequency,Rect () is rectangular function, TframeFor the period of data frame,
tm0For the interval time between the initial time and ship synthetic aperture central instant of than the m-th data frame, TintWhen for pulse accumulation
Between, f0For radar carrier frequency, BrFor radar signal bandwidth, C indicates the light velocity, Rm0(t) it indicates from the phase center of radar to ship
The vector of center of rotation, Rm0It (t) is Rm0(t) mould, r be from ship center of rotation to ship on certain scattering point vector, σ0(r)
It is long-pending for the normalization normalized radar backscatter cross section of the scattering point at r,For Rm0(t) unit vector；
Step 2: to than the m-th data frame, carrying out Range compress, select the sub- echo of the ship target of m frame；For ship
The selection of sub- echo can both carry out manually, and also can use signal detection algorithm and be automatically performed；
Step 3: to the sub- echo of the ship target of m frame, carrying out the pre- place including translational compensation and rotation compensation
Reason；
Step 4: Data Extrapolation being carried out in orientation to the sub- echo of the ship target of m frame using Burg algorithm；
Specifically comprise the following steps:
Step 4.1: signal being expressed as discrete form, if sm(iΔt,jΔfr) it is sm(t,fr) discrete form,
Wherein i=0 ..., L-1, j=0 ..., N-1, L and N be respectively orientation and distance to discrete points, Δ t and Δ frRespectively
It is orientation time and distance to the sampling interval of frequency；
Step 4.2: setting pm(i Δ t, j Δ τ) is to sm(iΔt,jΔfr) carry out the pretreatment such as translational compensation, rotation compensation
M- Distance Time domain signal when rear orientation, wherein Δ τ is sampling interval of the distance to the time；
Step 4.3: according to introduced symbol, extrapolating results are simplified, as shown in formula (2):
p′m(i ' Δ t, j Δ τ)=Burg [pm(i Δ t, j Δ τ)] m=0 ..., M-1i '=0 ..., L ' -1 (2)；
Wherein, p 'm(i ' Δ t, j Δ τ) is the signal after the extrapolation of Burg algorithm, and L ' is the orientation point postponed outside
Number；
Step 5: to the outer data postponed acquired in step 4, stochastical sampling is carried out in orientation；
Step 6: to the data after sampling acquired in step 5, compressed sensing calculating is carried out in orientation, is obtained current
The sparse coefficient matrix of data frame, the matrix are range-Dopler domain super-resolution image；
Stochastical sampling and compressed sensing calculation formula are as follows:
[p″mC]L″×N=[Φ]L″×L′·[p′mC]L′×N=[Φ]L″×L′·[Ψ]L′×L′·[IC]L′×N=[Θ]L″×L′·
[IC]L′×N(3)；
Wherein, L " for the orientation points after stochastical sampling and having L " < < L ', p 'mCFor p 'mThe square of (i ' Δ t, j Δ τ)
Formation formula, Φ are the corresponding calculation matrix of random sampling procedure, p "mCFor the matrix after stochastical sampling, Ψ is basic matrix, and Θ is sense
Know matrix, ICFor the coefficient matrix obtained after compressed sensing calculates；
Wherein, basic matrix Ψ uses following Fourier's basic matrix:
Wherein, to sparse coefficient matrix ICSolution, following optimization problem can be converted into:
Wherein, | | | |0Indicate l0Norm in the case where meeting certain constraint condition, while considering the influence of noise, will be upper
State optimization problem conversion are as follows:
Wherein, | | | |1Indicate l1Norm, | | | |2Indicate l2Norm, ε are constant relevant to noise level；If K table
Show degree of rarefication, then when Θ meets K rank RIP condition, andWhen, then by solving above-mentioned optimization problem, recover
Coefficient matrix IC；
Step 7: CFAR detection being carried out to the sparse coefficient matrix after step 6 compressed sensing, will be determined as clutter plus noise
The amplitude of pixel is set to 0, obtains range-Dopler domain super-resolution image of the m frame after clutter recognition；
The matrix I ' constituted for sea clutter and the corresponding sparse coefficient of noiseCIf its real and imaginary parts obeys zero
Value, variance areGaussian Profile, then its amplitude Rayleigh distributed:
Wherein, r is matrix I 'CThe corresponding stochastic variable of middle each element amplitude, f (r) are the probability density expression of r；
Relationship between CFAR threshold value and false-alarm probability are as follows:
Wherein, PfaIt is the false-alarm probability of setting, VTIt is threshold value to be solved, threshold value is calculated by formula (9):
Step 8: judging whether m is equal to M-1；
If: judging result is that m is equal to M-1, is terminated；
Or judging result is m not equal to M-1, then enables m=m+1, then execute step 2.
Data Extrapolation method is compared with compression sensing method
The application is to two methods of Data Extrapolation, compressed sensing in the improvement of DOPPLER RESOLUTION, the inhibition of image secondary lobe
Two aspects are compared, it is therefore an objective to be illustrated the method that present invention selection Data Extrapolation is combined with compressed sensing and be carried out super-resolution
The reason of processing.
When merely with Data Extrapolation method carry out super-resolution processing when, it is clear that the raising multiple of its DOPPLER RESOLUTION with
The data volume postponed outside is related.When believing that miscellaneous noise ratio is sufficiently high, it can approximatively think that the raising multiple of DOPPLER RESOLUTION is equal to
The ratio between data volume and original data volume for postponing outside.But it must be noted that when being unsatisfactory for the sufficiently high condition of letter miscellaneous noise ratio,
The raising multiple of DOPPLER RESOLUTION will be substantially reduced.The raising multiple of DOPPLER RESOLUTION and the data volume, letter that postpone outside are miscellaneous
The factors such as ratio, radar parameter of making an uproar are related, are difficult to establish accurate quantitative relationship, therefore the general method by experiment carries out
Measurement.
When carrying out super-resolution processing merely with compression sensing method, the raising multiple of DOPPLER RESOLUTION is available
RIC (Restricted Isometry Constant, limited equidistant constant) in RIP condition carries out quantitative analysis.So-called RIP
Condition refers to and meets following formula:
Wherein, β is the column vector that sparse coefficient is constituted, ΘcsTo perceive matrix, δK∈(0,1).RIC constant refers to satisfaction
The smallest δ of formula (10)K.The value of RIC embodies ΘcsCorrelation between middle column vector.The value of RIC is smaller, the phase between column vector
Closing property is smaller.In general, the precision of sparse reconstruction is higher when the value of RIC is less than 0.5.When merely with compression sensing method
When carrying out super-resolution processing, matrix Θ is perceivedcsIt is usually arranged as:
It is noted that perception matrix ΘcsLine number L be less than columns L ', be incomplete Fourier's basic matrix.Benefit
Θ can be assessed with characteristic value statistical methodcsCorrelation between middle column vector.When L ' is equal to L, ΘcsNot phase between middle column vector
It closes, corresponding RIC value is 0 at this time.When L ' is greater than L, with the increase of L ', RIC value is begun to ramp up.When RIC value rises to threshold
When value 0.5, at this moment L ' DOPPLER RESOLUTION corresponding with the ratio of L improves the limit of multiple.Characteristic value statistical method is first to Θcs
Column vector be normalized, then arbitrary extracting wherein K column column vector constitute matrix Θcs,K.As matrix ΘcsMeet K rank
When RIP condition, to matrixAfter carrying out Eigenvalues Decomposition, any feature value is all in the range of (1-RIC, 1+RIC)
It is interior.
Therefore, the limit that DOPPLER RESOLUTION improves multiple can be solved using monte carlo method according to These characteristics.If
Determine initial data points L and degree of rarefication K, enables L ' be incremented by since L+1, constantly calculated using monte carlo method different
L ' corresponding RIC stops calculating when RIC increases to 0.5, and the ratio between L ' at this moment and L are that DOPPLER RESOLUTION improves again
Several limiting values.The limiting value is related with K and L.Fig. 2 depicts L=32, and in the case of 48,64,80,96 five kinds, Doppler is differentiated
Rate improves the limiting value of multiple with the variation tendency of K.As can be seen from Figure 2, with the variation of L, the amplitude of curvilinear motion is little.
With the increase of degree of rarefication K, the limiting value that DOPPLER RESOLUTION improves multiple constantly declines.When K is greater than 5, Doppler is differentiated
Rate improves the limiting value of multiple at 1.2 times or less.In general, it is carried out at super-resolution when merely with compression sensing method
When reason, especially in the biggish situation of degree of rarefication, the raising leeway of DOPPLER RESOLUTION is smaller.This is mainly due to working as, columns is bright
When showing greater than line number, matrix Θ is perceivedcsCaused by the correlation of column vector is not strong.It should be noted that when permitted RIC threshold value
When being set greater than 0.5, DOPPLER RESOLUTION improve multiple limiting value will be greater than it is that Fig. 2 is provided as a result, but this will significantly drop
The precision of low sparse reconstruction.
Below by an example, compression sensing method is verified in the limit that DOPPLER RESOLUTION improves multiple,
And it is compared with the imaging results of direct FFT, Data Extrapolation method.Equipped with 1 data matrix, distance is to unit number
86, the orientation sampling interval is 0.01s, orientation original unit number is 20.It is two single-frequency void in 43rd distance unit
The superposition of exponential signal, frequency are respectively 10.2Hz and 14.6Hz, and the amplitude of two signals is equal.Letter in other distance unit
It number is zero.Data matrix is respectively completed: 1) orientation FFT；2) data volume is extended for after 3 times carrying out again using Burg algorithm
Orientation FFT；3) orientation compressed sensing calculates.Before implementing FFT operation, data have been carried out with 16 times of zero padding.Carry out
During compressed sensing calculates, matrix Θ is perceivedcsLine number L be set as 20, columns L ' is set as 33.Fig. 3 is 3 kinds of operations
Operation result schematic diagram.Since orientation time span is 0.2s in original signal, corresponding original DOPPLER RESOLUTION is
5Hz, therefore 2 targets directly can not be told using FFT, this is verified in figure (a).3 times of extrapolations are carried out to data
Afterwards, DOPPLER RESOLUTION approximation rises to original 3 times (5/3 ≈ 1.7Hz), therefore can tell 2 targets, this is scheming
(b) it is verified in.Conclusion according to fig. 2 is counted in the case where degree of rarefication is 2 using the method for compressed sensing
When calculation, the limiting value that DOPPLER RESOLUTION improves multiple is about 1.7, and DOPPLER RESOLUTION at this time is about 3Hz, therefore can also be with
Tell 2 targets.Figure (c) demonstrates above-mentioned conclusion, and 2 targets have obtained preferable differentiation, and the orientation position of target
Section corresponding to frequency with actual signal coincide.
Next setting the 43rd distance unit in two single-frequency imaginary exponent signals frequency be respectively 10.2Hz and
12.7Hz.During carrying out compressed sensing calculating, matrix Θ is perceivedcsLine number L be still set as 20, columns L ' is set as
50.In this case, the limit of the difference on the frequency between two targets already less than compression sensing method DOPPLER RESOLUTION in this example
Value 3Hz.After repeating above-mentioned operation, operation result shown in Fig. 4 has been obtained.Figure (a) cannot still be differentiated, scheme (b) still
It may be implemented to differentiate.Although can tell 2 targets from figure (c), wherein the orientation position of 1 target and reality are believed
Number frequency corresponding to section misfit, there is mistake in the result of reconstruction.This just because of the difference on the frequency between two targets
Through the limiting value 3Hz for being less than compression sensing method DOPPLER RESOLUTION in this example.
For radar imaging system, realizing is very important to effective inhibition of image secondary lobe, commonly uses by peak value
Valve than with integral secondary lobe than equal index characterizations system to the inhibition level of image secondary lobe.When the secondary lobe of image is relatively high, will make
At occur at the secondary lobe position of strong target false target, weak signal target by surrounding strong target cover phenomena such as, seriously affect image
Quality.For classical FFT method, the inhibition that secondary lobe is realized in windowing process is generallyd use.Frequently with window type include the Chinese
Bright window, Hanning window, Caesar's window etc..But after adding window image main lobe will broaden, cause the reduction of image resolution ratio.When only with number
When carrying out super-resolution processing according to the method for extrapolation, the resolution ratio of image can be improved with the increase of data volume, but other
Valve ratio can't be improved.When carrying out super-resolution processing only with compression sensing method, due to solving sparse coefficient
During without carrying out FFT operation, image secondary lobe will be obviously reduced.
Below by 1 examples comparative FFT, Burg extrapolation, the peak sidelobe ratio of three kinds of methods of compressed sensing.
Equipped with the single-frequency imaginary exponent signal that 1 duration is 0.2s, frequency is 10.2Hz, to signal with 0.01s when
Between be spaced and sampled.Collected discrete signal is respectively completed: 1) direct FFT；2) data volume is expanded using Burg algorithm
Fill be 3 times after carry out FFT again；3) compressed sensing calculates.Before implementing FFT operation, data have been carried out with 16 times of zero padding.Into
During row compressed sensing calculates, matrix Θ is perceivedcsLine number L be set as 20, columns L ' is set as 33.Fig. 5 illustrates 3 kinds
The frequency spectrum calculated result of operation.Solid line is direct FFT operation as a result, its azimuth resolution is poor, peak sidelobe ratio about-
13dB.Dotted line is the calculated result carried out after Data Extrapolation using Burg algorithm, and azimuth resolution significantly improves, but peak side-lobe
Than being still -13dB.Dotted line is the calculating knot obtained using compression sensing method (in the legend of Fig. 5, being simplified shown as " CS ")
Fruit, it is seen that peak sidelobe ratio is lower than -40dB.It should be noted that being calculated when using compression sensing method
When, the minimum frequency difference between the size and actual signal frequency and all base signal frequencies of peak sidelobe ratio is related.In general,
When this minimum frequency difference is smaller, peak sidelobe ratio is lower.In the case where having, it is possible that without traditional side
At this moment the case where valve, can carry out quantitatively evaluating with unit amplitude peak ratio is closed on.Here so-called " closes on unit amplitude peak
Than " refer to: in frequency cells where the maximum signal amplitudes and target in other units where target near frequency cells
The ratio between signal amplitude.
To sum up analyze, when carrying out super-resolution processing only with compression sensing method, the raising of DOPPLER RESOLUTION
Multiple is relatively limited, but preferable to the Sidelobe Suppression of image.When signal-to-noise ratio is sufficiently high, only with the method for Data Extrapolation
Guarantee that higher resolution ratio improves multiple, but the secondary lobe of image is relatively high.For this purpose, the application combines two methods, it is first sharp
Data Extrapolation is carried out with Burg algorithm, then the data externally postponed are calculated using compression sensing method, to both can guarantee
Higher DOPPLER RESOLUTION improve multiple, again can the secondary lobe to image preferably inhibited.
Simulation result
The purpose of emulation experiment includes 3 aspects.First, verify the oversubscription of proposed Data Extrapolation combination compressed sensing
Resolution imaging method promotes in DOPPLER RESOLUTION, the validity in terms of image Sidelobe Suppression, and with only carry out Data Extrapolation, only
Performance comparison is carried out using the two methods of compressed sensing；Second, the brought letter miscellaneous noise ratio of verifying CFAR detection improves；The
Three, show that circle sweeps the ability that ISAR mode obtains same target different perspectives image sequence in multiframe scanning process.
Geometrical relationship used in emulation is as shown in fig. 6,3 coordinate systems defined herein: radar fix system Er, ship
Only with reference to coordinate system Esf, ship body coordinate system Esb.Radar fix system ErOrigin O be that radar platform exists with reference to the position at moment
The projection on sea level, x-axis direction are radar platform heading, and vertically upward, y-axis meets the right-hand rule to z-axis.Ship is with reference to seat
Mark system EsfThe definition of reference axis and radar fix system ErThe definition of reference axis is identical, and only origin O ' becomes ship and referring to
The center of rotation when moment.Ship body coordinate system EsbOrigin be also O ', ξ axis forward direction is directed toward fore, and η axis forward direction is directed toward ship
Larboard, ζ axis meet the right-hand rule.If vpIndicate platform speed, H indicates podium level, then in orientation moment t, radar platform
In coordinate system ErIn position be [vpt,0,H].It can be obtained after a series of coordinate transforms, certain is dissipated on orientation moment t, ship
Exit point s is in coordinate system ErIn position are as follows:
Wherein, [X0,Y0,Z0] be with reference to the moment when ship center of rotation in coordinate system ErIn position, vsx、vsy、vszPoint
Not Wei ship translational velocity x, y, z axis component,Scattering point s is in coordinate system E when for reference to the momentsbIn
Position, and have:
Wherein, θy0、θp0、θr0It is from coordinate system E respectivelysfIt rotates to coordinate system EsbCorresponding yaw, pitching, roll angle, θy
(t)、θp(t)、θr(t) when being orientation moment t respectively ship yaw, pitching, roll angle.It is dissipated according to radar platform and ship
Exit point s is in orientation moment t in coordinate system ErIn position, the instantaneous distance between the two can be calculated.WithIt is opposite respectively
In the wind angle and ship course angle of y-axis.
Table 1 is the parameters such as radar, ocean surface wind speed, wind direction of ocean surface used in emulation.Table 2 is each data frame collection process
The kinematic parameter of middle ship.Fig. 7 is ship scattering point position view.It is dissipated using the ship in the parameter and Fig. 7 in table 1, table 2
Exit point position sweeps ISAR to circle and has carried out analogue echoes.The echo simulated is superimposed by ship echo, noise, sea return
It arrives.
Major parameter used in the emulation of table 1
The kinematic parameter of ship in each data frame collection process of table 2
Wherein, the simulation process of sea return are as follows: random sea is generated by the sea PM spectrum model first, then utilizes electromagnetism
The method of scattering calculates the mirror reflection component and Bragg diffraction component of surface scattering unit, is finally added two kinds of components
To normalization backscattering coefficient and and then sea return is calculated.The calculation formula of the sea PM spectrum are as follows:
Wherein, K is wave number,For the angle with reference direction (y-axis in Fig. 6), g0For acceleration of gravity, U19.5For sea
Wind speed at the 19.5m of face overhead,For the angle of wind speed and reference direction.The formula on random sea is generated according to extra large spectrum model
Are as follows:
Wherein, z (r, t) is the time variations of sea surface level degree at r, LxAnd LyRespectively two-dimentional sea is in x-axis direction and y-axis
The length in direction, K=(Kx,Ky), G (K) is that zero-mean, variance 1, the two dimension for meeting Gaussian Profile answer random sequence, G*(-K)
It is conjugated for the backward of G (K).The specular components as caused by the big wave in seaAre as follows:
Wherein, θiFor incidence angle, SuAnd ScRespectively slope variance of the big wave in sea in contrary wind and cross-wind direction, φiFor
Angle between radar line of sight and wind direction, ε are sea relative dielectric constant.The Bragg diffraction as caused by small scale Rough Sea Surfaces point
AmountAre as follows:
Wherein, f (Zx′,Zy′) be under radar line of sight coordinate system the big wave slope in sea dimensional probability distribution function,For the Bragg diffraction coefficient under local coordinate.
In the case that Fig. 8 illustrates in the signal not Noise and clutter, obtained using several different disposal processes the 0th
The imaging results of frame.Wherein, figure (a) is both more without Data Extrapolation or without the distance under compressed sensing calculated case
General Le image, figure (b) are only to carry out Data Extrapolation but without the range Doppler image under compressed sensing calculated case, figure
(c) for without Data Extrapolation, only carry out compressed sensing calculated case under range Doppler image, figure (d) be both counted
According to extrapolation, again progress compressed sensing calculated case under range Doppler image.During only carrying out compressed sensing calculating,
The raising multiple of azimuth resolution is set as 1.3 times.From improvement of visual effect, the image quality for scheming (a) is relatively low, schemes (b)
It is placed in the middle with the image quality of figure (c), scheme the image quality highest of (d).To carry out quantitative analysis, from figure (a), figure (b), figure (c)
Point target analysis has been carried out with the scattering point (scattering point of origin position in corresponding diagram 7) for extracting the same position in figure (d).
(a), (b), (c), (d) of Fig. 9 gives the point target impulse response in the case of above-mentioned 4 kinds, DOPPLER RESOLUTION, peak side-lobe
Table 3 is listed in than, the calculated result of closing on unit amplitude peak ratio.Data in contrast table 3 can be concluded that Fig. 9 (a)
In the representative value that DOPPLER RESOLUTION is worst, peak sidelobe ratio is traditional FFT processing method；Compared to Fig. 9 (a), Fig. 9 (b)
In DOPPLER RESOLUTION be significantly improved, but the magnitude of peak sidelobe ratio is suitable；Compared to Fig. 9 (a), in Fig. 9 (c)
DOPPLER RESOLUTION is also improved, but effect is obviously not so good as Fig. 9 (b)；Compared to Fig. 9 (a), the Doppler in Fig. 9 (d) divides
Resolution is improved significantly, closes on unit amplitude peak ratio also below -30dB, and comprehensive performance is optimal.
DOPPLER RESOLUTION and peak sidelobe ratio under several different disposal processes of table 3
Followed by containing the emulation in the case of noise and clutter in signal.It, will to simulate lower letter miscellaneous noise ratio
Wind speed above sea at 19.5m has been set as 20m/s, and will be set as only more equivalent than normalizing except the RCS of scattering point at origin
The corresponding big 20dB of RCS value of noise coefficient value.The RCS of scattering point is set as 10 times of other scattering point RCS at origin.To guarantee
The value being arranged in the practical equivalent noise figure value and table 1 of analogue system is consistent, and peak power is calculated by following formula:
Wherein, k is Boltzmann constant, T0=290K, F are receiver noise factor, RmaxFor within the scope of beam with
The maximum distance of radar, laFor orientation antenna size, PRI is pulse repetition period, NE σ0To normalize equivalent noise figure,
ρazFor azimuth resolution, ρrgFor ground range resolution, G is antenna gain, TrFor pulse width, Kbeam=0.88.It substitutes into table 1
Relevant parameter, the peak power being calculated are about 1.2Kw.
Figure 10 is illustrated in the signal containing in the case where noise and clutter, the obtained using several different disposal processes
The imaging results of 0 frame.Wherein, figure (a) is both more without Data Extrapolation or without the distance under compressed sensing calculated case
General Le image, figure (b) are only to carry out Data Extrapolation but without the range Doppler image under compressed sensing calculated case, figure
(c) for without Data Extrapolation, only carry out compressed sensing calculated case under range Doppler image, figure (d) be both counted
According to extrapolation, again carry out compressed sensing calculated case under range Doppler image, figure (e) be to figure (d) progress CFAR detection after
Result.It can be seen that Data Extrapolation, the method that compressed sensing calculates after Figure 10 (b), (c) are compared with Figure 10 (a) respectively all
The letter miscellaneous noise ratio of image is set to have obtained certain improvement.The reason of above two method makes letter miscellaneous noise ratio obtain improvement is also aobvious
And it is clear to.When being handled using Data Extrapolation method, the data volume of orientation is increased, so that the pulse product of orientation
Tired number increases.When being handled using compression sensing method, due to the reduction of image sidelobe level, but also letter miscellaneous noise ratio obtains
To improvement.Obviously, when both methods to be used in combination with, the letter miscellaneous noise ratio of image can be made to obtain biggish improvement,
Figure (d) demonstrates above-mentioned conclusion.Figure (d) the upper left corner be to the non-ship scattering point region of certain in figure amplification display after as a result,
It can therefrom find that there are still have certain clutter/noise.Figure (e) is after carrying out CFAR detection to figure (d) as a result, letter miscellaneous noise ratio
It is further improved.All ship scattering points have been calculated separately for Figure 10 (d), Figure 10 (e) to carry out quantitative analysis
The mean power of the mean power of pixel and other pixels, to obtain respective letter miscellaneous noise ratio.Here letter miscellaneous noise ratio definition
For the ratio between average power signal and clutter/noise mean power.Have:
Wherein, EsIndicate signal energy, EsumIndicate gross energy, NsIndicate " signal pixels " number, NcnIndicate " clutter/make an uproar
Acoustic image element " number.Here " signal pixels " are defined as amplitude greater than the centesimal pixel of highest amplitude in image.Substitution formula
(23) it can be obtained after being calculated, figure (d) and the letter miscellaneous noise ratio for scheming (e) are respectively 13.3dB and 28.2dB, improve 14.9dB.
To show the ability for obtaining same target different perspectives image sequence in multiframe scanning process, 5 frames reality has been carried out altogether
It tests, image generated is shown in Figure 11.Wherein, Figure 11 (a) is identical with Figure 10 (e).Due to being acquired in the data of each frame
The kinematic parameter of Cheng Zhong, ship change, it can be seen that the top view of the obtained existing ship of image also has the side view of ship
Figure, there are also view is mixed, to be conducive to classify to ship and identified.
This paper presents the circles that a kind of Data Extrapolation is combined with compressed sensing to sweep ISAR mode ship super-resolution imaging
Method.Demonstrate the advantage and disadvantage of Data Extrapolation method and compression sensing method when carrying out super-resolution processing: 1) Data Extrapolation
Method is advantageous than in terms of in DOPPLER RESOLUTION improvement, but the secondary lobe of image is poor；2) compression sensing method is in Doppler
Resolution ratio improvement is more general than the ability of aspect, but has good image Sidelobe Suppression ability.Therefore, two methods are combined
Realize super-resolution processing.Burg extrapolation is carried out in orientation by elder generation and then carries out the process flow of compressed sensing calculating again,
DOPPLER RESOLUTION has obtained preferable promotion, while image secondary lobe has obtained preferable inhibition.Give sparse coefficient CFAR
The calculation formula of detection threshold value.It is detected by CFAR, the letter miscellaneous noise ratio of image is further improved.The emulation experiment carried out
Validity of present invention in terms of DOPPLER RESOLUTION promotion, Sidelobe Suppression, letter miscellaneous noise ratio is demonstrated, circle is also demonstrated
Sweep the ability that ISAR mode obtains same target different perspectives image sequence in multiframe scanning process.It should be noted that by
In the similitude of imaging mechanism, method proposed in this paper equally may extend to the super-resolution imaging of other type ISAR systems.
Certainly, the above description is not a limitation of the present invention, and the present invention is also not limited to the example above, this technology neck
The variations, modifications, additions or substitutions that the technical staff in domain is made within the essential scope of the present invention also should belong to of the invention
Protection scope.
Claims (1)
1. a kind of circle sweeps ISAR mode ship super-resolution imaging method, which comprises the steps of:
Step 1: circle being swept into the echo-signal under ISAR mode, by TframeFor the period, it is divided into M data frame, is located frame by frame
Reason；
Circle is swept in ISAR mode, when orientation m- frequency of distance domain ship echo-signal, as shown in formula (1):
Wherein, subscript m is the serial number of current data frame, m=0 ..., M-1, t expression orientation time, frIndicate distance to frequency,Rect () is rectangular function, TframeFor the period of data frame, tm0For
Interval time between the initial time and ship synthetic aperture central instant of than the m-th data frame, TintFor the pulse accumulation time,
f0For radar carrier frequency, BrFor radar signal bandwidth, C indicates the light velocity, Rm0(t) it indicates to turn from the phase center of radar to ship
The vector at dynamic center, Rm0It (t) is Rm0(t) mould, r be from ship center of rotation to ship on certain scattering point vector, σ0It (r) is position
The normalization normalized radar backscatter cross section product of scattering point at r,For Rm0(t) unit vector；
Step 2: to than the m-th data frame, carrying out Range compress, select the sub- echo of the ship target of m frame；Ship is returned
The selection of wave can both carry out manually, and also can use signal detection algorithm and be automatically performed；
Step 3: to the sub- echo of the ship target of m frame, carrying out the pretreatment including translational compensation and rotation compensation；
Step 4: Data Extrapolation being carried out in orientation to the sub- echo of the ship target of m frame using Burg algorithm；Specifically
Include the following steps:
Step 4.1: signal being expressed as discrete form, if sm(iΔt,jΔfr) it is sm(t,fr) discrete form, wherein i
=0 ..., L-1, j=0 ..., N-1, L and N be respectively orientation and distance to discrete points, Δ t and Δ frRespectively orientation
To time and distance to the sampling interval of frequency；
Step 4.2: setting pm(i Δ t, j Δ τ) is to sm(iΔt,jΔfr) to carry out translational compensation, rotation compensation etc. pretreated
M- Distance Time domain signal when orientation, wherein Δ τ is sampling interval of the distance to the time；
Step 4.3: according to introduced symbol, extrapolating results are simplified, as shown in formula (2):
p′m(i ' Δ t, j Δ τ)=Burg [pm(i Δ t, j Δ τ)] m=0 ..., M-1i '=0 ..., L ' -1 (2)；
Wherein, p 'm(i ' Δ t, j Δ τ) is the signal after the extrapolation of Burg algorithm, and L ' is the orientation points postponed outside；
Step 5: to the outer data postponed acquired in step 4, stochastical sampling is carried out in orientation；
Step 6: to the data after sampling acquired in step 5, compressed sensing calculating is carried out in orientation, obtains current data
The sparse coefficient matrix of frame, the matrix are range-Dopler domain super-resolution image；
Stochastical sampling and compressed sensing calculation formula are as follows:
[p″mC]L″×N=[Φ]L″×L′·[p′mC]L′×N=[Φ]L″×L′·[Ψ]L′×L′·[IC]L′×N=[Θ]L″×L′·
[IC]L′×N(3)；
Wherein, L " for the orientation points after stochastical sampling and having L " < < L ', p 'mCFor p 'mThe rectangular of (i ' Δ t, j Δ τ)
Formula, Φ are the corresponding calculation matrix of random sampling procedure, p "mCFor the matrix after stochastical sampling, Ψ is basic matrix, and Θ is perception square
Battle array, ICFor the coefficient matrix obtained after compressed sensing calculates；
Wherein, basic matrix Ψ uses following Fourier's basic matrix:
Wherein, to sparse coefficient matrix ICSolution, following optimization problem can be converted into:
Wherein, | | | |0Indicate l0Norm in the case where meeting certain constraint condition, while considering the influence of noise, will be above-mentioned excellent
The conversion of change problem are as follows:
Wherein, | | | |1Indicate l1Norm, | | | |2Indicate l2Norm, ε are constant relevant to noise level；If K indicates dilute
Dredge degree, then when Θ meets K rank RIP condition, andWhen, then by solving above-mentioned optimization problem, recover coefficient
Matrix IC；
Step 7: CFAR detection being carried out to the sparse coefficient matrix after step 6 compressed sensing, will be determined as clutter plus noise pixel
Amplitude be set to 0, obtain range-Dopler domain super-resolution image of the m frame after clutter recognition；
The matrix I ' constituted for sea clutter and the corresponding sparse coefficient of noiseCIf its real and imaginary parts obeys zero-mean, side
Difference isGaussian Profile, then its amplitude Rayleigh distributed:
Wherein, r is matrix I 'CThe corresponding stochastic variable of middle each element amplitude, f (r) are the probability density expression of r；
Relationship between CFAR threshold value and false-alarm probability are as follows:
Wherein, PfaIt is the false-alarm probability of setting, VTIt is threshold value to be solved, threshold value is calculated by formula (9):
Step 8: judging whether m is equal to M-1；
If: judging result is that m is equal to M-1, is terminated；
Or judging result is m not equal to M-1, then enables m=m+1, then execute step 2.
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