CN110286375A - The quick motion compensation process of LS high-order and system towards near real-time ISAR imaging - Google Patents
The quick motion compensation process of LS high-order and system towards near real-time ISAR imaging Download PDFInfo
- Publication number
- CN110286375A CN110286375A CN201910404901.XA CN201910404901A CN110286375A CN 110286375 A CN110286375 A CN 110286375A CN 201910404901 A CN201910404901 A CN 201910404901A CN 110286375 A CN110286375 A CN 110286375A
- Authority
- CN
- China
- Prior art keywords
- formula
- matrix
- order
- cross
- correlation function
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/904—SAR modes
- G01S13/9064—Inverse SAR [ISAR]
-
- 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
- G01S13/9094—Theoretical aspects
-
- 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
- G01S7/40—Means for monitoring or calibrating
Abstract
The present invention provides a kind of quick motion compensation process of LS high-order and system towards near real-time ISAR imaging, high order symmetry proposed by the present invention based on least square accumulates cross-correlation method, optimize the accumulation mode of classical cross-correlation method, using least square fitting, the deficiency of high order parameters cannot be estimated by compensating for existing cross-correlation method；High order parameters estimation and motion compensation are realized with low-down calculating cost, and are not necessarily to priori knowledge.The beneficial effects of the present invention are: the present invention realizes high order parameters estimation and motion compensation, optimize computation complexity, to meet the quick process demand of near real-time imaging, and the present invention is able to carry out blind processing, is not necessarily to prior estimate section, reduces emission system burden.
Description
Technical field
The present invention relates to the communication technology and radar signal processing fields, more particularly to the LS towards near real-time ISAR imaging
The quick motion compensation process of high-order and system.
Background technique
ISAR imaging is based primarily upon classical distance-Doppler (RD, Range-Doppler) principle, that is, utilizes distance dimension
Frequency diversity, the angle diversity of azimuth dimension, by two dimensional compaction handle obtain constitute each scattering point of target Two-dimensional Position confidence
Breath.Since the one-dimensional range profile that radial target motion will lead to echo is walked about with observation sequence generation, so as to cause next step
Azimuth Compression cannot make the scattering point alignment of same distance unit.
Based on when-the two-dimentional Combined Treatment of frequency distance-it is instantaneous-Doppler imaging method (RID, Range-
Instantaneous-Doppler it) can be very good to solve the problems, such as this in the way of T/F two dimension slicing, but when-
The method computation complexity of the two-dimentional Combined Treatment of frequency is very high, under general imaging system processing environment, cannot expire well
Sufficient fast imaging, target identification, the real-time demand of classification.
Traditional RD class imaging method operation cost is low, and imaging is very fast, usually before carrying out Azimuth Compression, first carries out
Motion compensation process based on parameter Estimation.Echo data is after translational compensation, the one-dimensional range profile envelope of each observation sequence
It is accurately aligned, then carries out subsequent orientation resolution, and then obtain clearly ISAR image (such as Fig. 1).Therefore, join
The precision of number estimation and the quality of motion compensation, directly affect the quality of imaging.Currently used parameter estimation algorithm, substantially may be used
To be divided into following three classes:
(1) one kind is the algorithm based on target scattering point, but according to the analysis of actual test data, in observation accumulated time
It is interior, it is difficult steadily to track interested point on the whole.Therefore, this algorithm is not very extensively in practical applications.
(2) second classes are the methods that range-aligned is realized based on the envelope similitude of adjacent echoes, and are realized simpler
Single, most widely used a kind of algorithm, classical method include global range-aligned algorithm, cross-correlation method (CCM), and accumulation is mutual
Correlation technique (ACCM) etc..CCM method is the basic algorithm being suggested earliest in mutual a kind of algorithm of similar processing, is had simply in fact
With the low advantage of, computation complexity.The implementation of CCM method is to choose some Range Profile (generally first) as ginseng
Range Profile is examined, obtains one group of cross-correlation function after doing cross correlation process respectively with other Range Profiles, it is then each mutual by being aligned
The peak value of function curve is closed to estimate the difference distance between each secondary echo, and then obtains the estimated value of the kinematic parameter of target.
ACCM improves CCM and obtains the mode of cross-correlation function, it with accumulation concept reinforce strong frequency stable in each secondary echo at
Point, inhibit random fast change disturbance, the accidental error of CCM method is significantly reduced with the complexity cost of very little, very
Estimation performance is improved in big degree.On implementation, each cumulative cross-correlation function of ACCM is by each
The Range Profile of reference takes multiple Range Profiles and reference image before it to carry out cross correlation process and adds up to obtain.
(3) third class is the algorithm based on Image entropy, and representative is minimum entropy algorithm (MEM), by certain
Corresponding parameters of target motion when in parameter area with fixed precision search Image entropy minimum.
Existing some technology and methods all have the advantages that respective, but there is also deficiencies simultaneously, specifically:
(1) for the estimation method based on strong scattering point class: analyzed from measured data, be difficult to find and track entirely at
As all very stable strong scattering point in accumulated time (CPI, Coherent Processing Interval), even same
The echo of a target, posture, which varies slightly, may make the strong scattering point in echo disappear, therefore the distance pair based on scattering point
Quasi- method hardly results in application among actual ISAR engineering practice.
(2) estimation method (such as MEM) calculated based on entropy: the advantages of such methods, which is to move high-order target, joins
Number (such as acceleration) is estimated, but generally requires the estimation interval for having a priori to the parameters of target motion.Such side
Face this require radar emission system to need alternate emission is wide, narrow-band impulse tests the speed, is imaged to realize, increase system burden, or
Person needs to obtain the complexity that estimation interval increases processing by additional method from echo data；On the other hand, first
If the accuracy for testing estimation interval influences the estimation performance of algorithm very big -- prior estimate section does not include that parameter is true
Value, then the estimated value that algorithm obtains is completely ineffective.
(3) method based on Range Profile cross correlation process: the advantages of such methods is to realize simple, can be very good to meet
The demand of near real-time imaging.However, on the one hand, due to including very diverse factor in the echo of practical flight target,
Especially under some more severe application environments, for example observation has the aircraft such as propeller aeroplane of internal disturbance component, or
It is in the lower imaging background of signal-to-noise ratio, the fluctuations of target scattering characteristics can very acutely, the multimodal envelope become fastly
Very influence the alignment precision of cross-correlation, these factors will cause biggish alignment error, at this time existing algorithm from precision or
Imaging requirements are no longer satisfied in terms of complexity, are analyzed as follows specific to each algorithm:
A) .CCM: the disadvantage is that alignment error and accidental error are very big.On the one hand, complex condition plus wave Range Profile envelope
Complexity causes alignment error very big；On the other hand, if there are biggish accidental errors for some Range Profile, entire
During cross correlation process and registration process, this accidental error can be constantly passed, under causing algorithm estimation performance serious
Drop.
B) .ACCM: although effectively enhancing strong frequency content stable in echo using the concept of accumulation, substantially reducing
Alignment error, while accidental error caused by individual Range Profiles is also improved, but be the failure to the angle from signal form in root
Alignment error is solved the problems, such as in sheet, in addition, still having biggish accumulation of phase error in accumulation.
On the other hand, this kind of algorithm can only generally estimate the first order motion parameter (i.e. speed) of target at present, and work as target
When observing progress acceleration-deceleration movement in residence time, this kind of algorithm accurately can not carry out high quality to nonuniform motion
Estimation and compensation.
Term is explained:
ISAR:(Inverse Synthetic Aperture Radar) Inverse Synthetic Aperture Radar.
RD:(Range-Doppler) distance-Doppler.
CCM:(Cross-Correlation Method) cross-correlation method.
ACCM:(Accumulated Cross-Correlation Method) accumulation cross-correlation method.
MEM:(Minimun Entropy Method) minimum entropy method
HSACM:(High-order Symmetric Accumulated Cross-Correlation Method) high-order
Symmetrical accumulation cross-correlation method.
Summary of the invention
The present invention provides a kind of quick motion compensation process of LS high-order towards near real-time ISAR imaging, comprising:
Step 1: discrete M × N echo matrix E is constructed by the base band echo-signal of targets, M be distance to hits or
Subpulse number, N are orientation hits, that is, echo times；
Step 2: to echo data EsThe one dimensional fourier transform for carrying out that length is N is tieed up according to distance, obtains each secondary echo
One-dimensional range profile { RPn}；
Step 3: determining best symmetrical cumulative length Q；
Step 4: calculating the expression formula of cross-correlation function, obtain the set of U cumulative cross-correlation function composition
Wherein U=N-2 (Q-1) indicates the length of symmetrical accumulation area；
Step 5: search for the peak value of each cumulative cross-correlation function, according to obtained each correlation function calculate corresponding difference away from
From { Δ rn1}；
Step 6: building time matrix Γ and apart from difference matrix Λ and corresponding least square relational expression, and solve minimum
Two multiply problem, calculate each rank kinematic parameter of target；
Step 7: to former echo data EsMultiplied by the compensation factor of formula formTo realize that order motion compensates:
In formula: ftEmit the instantaneous frequency of carrier wave for system；C is the light velocity in vacuum；viIt represents for describing target radial
Each rank kinetic parameter of movement, and i=1 ..., I, I are that the highest met under certain required precision describes order, such as v1Generation
Table single order radial motion speed, v2Represent the radial acceleration etc. of second order；T is time variable.
As a further improvement of the present invention, in the step 3, best symmetrical cumulative length Q is determined according to formula 10,
Formula 10 are as follows:
Wherein, Q is symmetrical cumulative length, and γ is build up factor, and N is echo total number.
As a further improvement of the present invention, in the step 6, the time matrix г and range difference in formula 19 are constructed
Sub-matrix Λ and corresponding least square relational expression, and least square problem is solved according to formula 20, calculate each rank of target
Kinematic parameter.
The invention also discloses a kind of quick motion compensating systems of LS high-order towards near real-time ISAR imaging, comprising:
Structural unit: for constructing discrete M × N echo matrix E by the base band echo-signal of targets, M be distance to
Hits or subpulse number, N are orientation hits, that is, echo times；
Converter unit: for echo data EsThe one dimensional fourier transform for carrying out that length is N is tieed up according to distance, is obtained each time
One-dimensional range profile { the RP of echon)；
Processing unit: for determining best symmetrical cumulative length Q；
Computing unit: for calculating the expression formula of cross-correlation function, the set of U cumulative cross-correlation function composition is obtainedWherein U=N-2 (Q-1) indicates the length of symmetrical accumulation area；
Search unit: it for searching for the peak value of each cumulative cross-correlation function, is calculated and is corresponded to according to obtained each correlation function
Difference distance { Δ rn1}；
Construction unit: for constructing time matrix Γ and apart from difference matrix Λ and corresponding least square relational expression,
And least square problem is solved, calculate each rank kinematic parameter of target；
Output unit: for former echo data EsMultiplied by the compensation factor of formula formTo realize that order motion is mended
It repays:
In formula: ftEmit the instantaneous frequency of carrier wave for system；C is the light velocity in vacuum；viIt represents for describing target radial
Each rank kinetic parameter of movement, and i=1 ..., I, I are that the highest met under certain required precision describes order, such as v1Generation
Table single order radial motion speed, v2Represent the radial acceleration etc. of second order；T is time variable.
The beneficial effects of the present invention are: the present invention realizes high order parameters estimation and motion compensation, optimize computation complexity, with
Meet the quick process demand of near real-time imaging, and the present invention is able to carry out blind processing, be not necessarily to prior estimate section, reduces transmitting
System burden.
Detailed description of the invention
Fig. 1 is the distance-Doppler schematic diagram of the ISAR imaging in background technique；
Fig. 2 is ISAR imaging system schematic diagram；
Fig. 3 is the symmetrical cumulative cross-correlation function method principle assumption diagram of optimization；
Fig. 4 a is the cross-correlation function figure in CCM method for parameter estimation；
Fig. 4 b is the unidirectional cumulative cross-correlation function figure in ACCM method for parameter estimation；
Fig. 4 c is the symmetrical cumulative cross-correlation function figure in method for parameter estimation HSACM of the invention；
Fig. 4 d is the corresponding difference distance disturbance curve graph of different modes cross-correlation function；
Fig. 5 is principle flow chart of the present invention for ISAR motion compensation and imaging；
Fig. 6 a is normalized mean squared error (NMSE) curve graph of first order parameter；
Fig. 6 b is normalized mean squared error (NMSE) curve graph of second order parameter；
Fig. 7 is the computation complexity curve graph of all kinds of estimation methods；
Fig. 8 a is ACCM method range-aligned figure (high-order compensation is insufficient)；
Fig. 8 b is MEM method range-aligned figure (compensation precision is lower)；
Fig. 8 c is MEM method range-aligned figure (compensation precision is higher)；
Fig. 8 d is the range-aligned figure that high-order compensation method of the present invention is realized；
Fig. 9 a is ACCM high-order compensation less than ISAR image graph；
Fig. 9 b is low precision MEM compensation ISAR image graph；
Fig. 9 c is high-precision MEM compensation ISAR image graph；
Fig. 9 d is HSACM compensation ISAR image graph.
Specific embodiment
The present invention quickly locates towards near real-time radar imagery application scenarios for high quality motion compensation and low complex degree
The application demand of reason solves Inverse Synthetic Aperture Radar (ISAR, Inverse Synthetic Aperture Radar) imaging
Deficiency existing for existing method for parameter estimation and problem in motion compensation link.
For deficiency existing for background technique, present invention aim to address parameter Estimations near real-time ISAR imaging
With the following problems in motion compensation link:
(1) high order parameters estimation and motion compensation are realized
(2) optimize computation complexity, to meet the quick process demand of near real-time imaging.
(3) blind processing is not necessarily to prior estimate section, reduces emission system burden.
The invention discloses a kind of quick motion compensation process of LS high-order towards near real-time ISAR imaging, in order to realize
The high-precision and low-complexity motion compensation of ISAR imaging, the invention proposes one kind to be based on least square (LS, Least-
Squares) core algorithm of the high order parameters estimation method (HSACM) being fitted as motion compensated schemes.The present invention is a kind of
Cross-correlation method for parameter estimation is derived from widely used first order parameter estimation method ACCM.Below to parameter proposed by the present invention
Estimation and motion compensated schemes from the signal model of application system, the technical principle of mentioned algorithm, concrete implementation scheme and
Several aspects such as the technical application of scheme are described in detail.
1. system signal model:
According to RD principle, the ISAR image of target is substantially projection of the target in distance-Doppler plane, and Fig. 2 is
ISAR imaging system schematic diagram.X-axis is distance to the direction i.e. radar line of sight (RLOS), and Y-axis is orientation, that is, target rotational tangent line
Direction, O are target phase center.Not consider initial phase and initial distance, observing mesh for far field low-angle convenient for discussing
Mark, fundamental frequency radar return can be expressed as
In formula, Pk(xk, yk) it is coordinate position of k-th of scattering point relative to target phase center, AkIt is strong for back scattering
Degree.ftEmit the instantaneous frequency of carrier wave, θ for systemtFor observation during by the geostrophic angle change of target.RtFor target phase
Instantaneous distance of the position center relative to radar.Without loss of generality, radial target motion can be described as follows by Taylor series:
Wherein Δ r is the offset of the instantaneous position as caused by radial target motion；viRepresent the i-th rank radial motion parameter, i.e. v1
For radial velocity, v2To use as a servant to acceleration.For cooperating observed object, radial motion is generally uniform motion, can be by single order
Parameter is described；For most of Non-synergic observed objects, then its radial component can accurately be described by second order parameter.
In actual Radar Signal Processing, continuous broadband signal generally pass through fast time dimension and slow time dimension into
Row sampling, forms the two-dimentional echo data of range-azimuth.Assuming that system emits N group step frequency in observation accumulated time
(SF, Step Frequency) signal, every group of signal include M sub- burst pulses.Subpulse carrier frequency is ft=f0+ m Δ f,
Middle f0For center carrier frequency, Δ f is step frequency.If the subpulse repetition time is Tr, and meet MTr≤TB.Then in fast time dimension
Degree hasSlow time dimension has t=mTr+nTB(m=0,1,2 ..., M-1；N=0, when 1,2 ..., N-1 is respectively speed
Between tie up index).Therefore available two-dimensional echo data is as follows:
Assuming that target is in the direction RLOS with first order motion parameter v1Uniform rotation, by distance-Doppler principle, ISAR is utilized
Fast time dimension frequency diversity, slow time dimension angle diversity realize two dimensional compaction, then the matrix form of echo-signal is
As can be seen that in fm~xk, θn~ykThe transformation of composition is in addition, there is a phase term as caused by radial motion
Wherein
The presence of phase term shown in formula (8) will lead to orientation and do when compressing apart from envelope with parameter υiTranslation is generated,
To make each scattering point in same distance unit that can not be aligned in the azimuth direction according to spike.Therefore it in ISAR imaging, needs
It to be translatable to each rank and carry out parameter Estimation, and then pass through motion compensation process, the compensation of phase term shown in (8) is fallen, is just conducive to
Imaging is further done, the two-dimentional ISAR image of following form is obtained
2. technical principle of the invention:
2.1. it symmetrically accumulates and complexity optimized:
In order to solve the problems, such as the transmitting of CCM method phase error and accumulation, accumulation is utilized in accumulation cross-correlation method ACCM
Concept, complete the estimations and alignment of ranging offset as carrying out cross-correlation so that current one-dimensional picture and preceding Z-1 are one-dimensional, Z is arteries and veins
Rush cumulative number.If each secondary echo Range Profile obtained through Range compress is { RPn, RPrefReference distance as (with first
A Range Profile is as reference).
Compared to CCM, although the method accumulated in ACCM can reinforce ingredient stable in spectrum component, what inhibition became fastly
Disturbance and noise contribution, largely improve the precision of range-aligned, still, what this unidirectional accumulation mode obtained
Total correlation function can accumulated phase error, and then the precision of influence range-aligned in a single direction.Therefore the present invention utilizes
The improved mode symmetrically accumulated generates correlation function, i.e., using the one-dimensional range profile when pre-echo as referring to, to before it
Cross correlation process is carried out in a manner of handling in pairs to one-dimensional range profile below, as shown in Figure 3.
In actual discrete data processing, the relationship of cross-correlation and convolution algorithm and the volume of time-frequency domain can use
Product theorem, quickly calculates the correlation function between each Range Profile with following formula
Cnr=| IFFT (FFT (| RPref|)·FFT(|RPn|)*)| (11)
In formula, FFT () and IFFT () respectively represent quick Fourier transformation and quickly inverse Fourier transformation.
Correspondingly, spreading to symmetrical accumulation cross correlation process of the invention, the accumulation correlation function to be calculated passes through folded
Add the Range Profile RP of referencenIt is obtained with the cross-correlation function of the symmetry number purpose Range Profile of its forward and backward, it may be assumed that
Wherein Q is symmetrical cumulative length.For the ease of discussing the performance of algorithm, symmetrical cumulative length Q=ceil is generally taken
{ mod (Z, 2) } i.e. Q is that the half of Z rounds up, so that the pulse accumulation number symmetrically accumulated is suitable with unidirectional accumulation.In order to beg for
By the determination of best accumulated length, it is as follows that we define a build up factor:
In formula, ρ=2Q/N indicates accumulation ratio；ι=L/ δcrIndicate that length is that the target of L samples required for orientation
Points, δcrIndicate the resolution ratio of orientation.Without loss of generality, with objective body long L=24m, δcr=0.375m is pervasive
Situation, available ι=64.
On the one hand, cumulative length is bigger, and stable ingredient can more be strengthened in echo, and estimated accuracy also can be better
Meet the requirement of motion compensation；And on the other hand, more Range Profiles, which participates in, carrys out (especially distance reference Range Profile in accumulation
Those of farther out echo), then system generates bigger range walk and rotation angle, and this will lead to it is common more single in imaging
First range walk (MTRC, Migration Through Resolution Cell) problem.In summary it considers, cumulative length
Generally it is preferred with 0.5~1 times that corresponds to sampling number in an azimuth discrimination unit.Therefore, the best model of build up factor γ
It encloses as 0.5~1, then optimal symmetrical cumulative length can be determined by following formula:
Compared to traditional accumulation mode that ACCM is used, the mode symmetrically accumulated that the present invention uses can offset current reference
Range Profile and the Range Profile of forward and backward do the positive and negative phase error generated when cross-correlation, i.e., realize simultaneously in range-aligned link
Phasing.Fig. 4 (a, b, c) illustrates the cross-correlation function that different accumulation modes generate, and the curve of Fig. 4 d then depicts respectively
The corresponding error of kind mode disturbs situation.
As can be seen that one group of cross-correlation function curve that CCM method obtains is noisy multimodal from Fig. 4 a, Fig. 4 b, Fig. 4 c
, and the interval of each peak of curve position does not have regularity, this nothing brings very big error suspected of range-aligned；And ACCM
The concept of accumulation is utilized in method, strengthens the stabilization component in adjacent echoes signal, and preferable regularity is presented in peak intervals,
Noise has also obtained a degree of inhibition, but because phase error is constantly accumulated, search peak position still has biggish
Error；The symmetrical accumulation mode that the present invention uses then in cross correlation process pairs of each time, eliminates the positive and negative phase of generation
Position error, one group of cross-correlation curve because obtained from all perform better in terms of inhibiting noise, peak value searching, reducing.
Disturbance curve shown in Fig. 4 d demonstrates accumulation method used in this programme and generates the smallest error disturbance.
Validity of the symmetrical accumulation mode in terms of reducing alignment error is demonstrated above, and on the other hand, in order to meet
The real-time of system imaging processing, it is contemplated that advanced optimizing the computation complexity of scheme.As seen from Figure 3, due to tired
Long-pending symmetry, the cross-correlation function C in the area Tu Zhong IIijAnd CjiThe mirror-symmetrical characteristic of opposite diagonal line element is presented.According to volume
The commutative properties of product operation, it is known that
Cij=Cji (15)
Therefore, when carrying out cross correlation process using symmetrical accumulation approach, the computation complexity of algorithm can be advanced optimized.
In Fig. 3 by taking Q=4 (i.e. Z=8) as an example, illustrate symmetrical accumulation cross correlation process optimizes structure.As can be seen that II in figure
The cross-correlation function C that area obtainsijAnd CjiThere is subscript symmetric relations.Therefore the cross-correlation function calculated needed for the area II only needs
Calculate trigonum thereon or lower trigonum.That is, the convolution algorithm amount that the area II integrally needs to carry out can subtract
Half.
Next we carry out quantitative analysis to the degree of optimization of computation complexity in the present invention.Table 1 lists in Fig. 3
Each sub-regions correspond to target expression formula under required convolutional calculation number and all subregion cross-correlation function.U=N- in table
2 (Q-1) indicate the length of symmetrical accumulation area, then have U=7 corresponding to SACR4~SACR10 in Fig. 3.II in tableuAnd IIdThen divide
It Biao Shi not upper trigonum and the lower area triangle in the II of the region Fig. 3.
The cross-correlation function table in each region of 1 corresponding diagram of table 3
So according to Fig. 3 and table 1, the calculating number for the cross-correlation function that can be reduced in our available area II is
The required convolution algorithm sum calculated is N when without optimizingS=(N-Z+2) (Z-2)=2U (Q-1) (17)
Therefore, after our available optimization computation complexities, the cross-correlation function total number of required calculating is Ncon=U2 (18)
The global optimization degree of so algorithm can be calculated as
Since symmetrical cumulative length Q is much smaller than length N, i.e. Q/ (4U) ≈ 0 of cross-correlation function, therefore utilize symmetrical accumulation
Mode carry out it is complexity optimized, can approximation obtain following optimization degree
Odep≈ 50% (20)
With N=256, parameter Estimation is carried out for γ=0.5, Q=4 and calculates cumulative cross-correlation function, ACCM method needs
62500 convolution algorithms are carried out to obtain participating in the cross-correlation function of accumulation, and are suggested plans with the present invention, operation times then may be used
It is reduced to 31384 times.CCM, accumulation mode used in ACCM and the present invention program are compared, computation complexity is shown in Table 2.
2 computation complexity of table
The estimation of 2.2 least square fitting solution high order parameters:
The kinematic parameter of target is included in the cross-correlation function that the above symmetrical accumulated process mode obtains, therefore for reality
We, which ask include in cross-correlation function apart from difference information modeling for least square, now is estimated to the high order parameters of target
Topic obtains the estimated value of parameter by solving LS problem.
Assuming that between the symmetrical cumulative cross-correlation function based on n-th of reference distance picture and the 1st reference distance picture away from
It is Δ r from offsetn1, then the mathematical relationship between each rank kinematic parameter and ranging offset can be released by formula (9):
It is abbreviated data matrix in above formulaRepresent time interval data；NoteJoin for required each rank
Matrix number；AndFor ranging offset matrix.Then formula (21) can be abbreviated as
Γ V=Λ (22)
Therefore, high order parameters estimation problem can be converted into the solution LS problem of solution matrix V:
Since in practical application scene, radial target motion generally can accurately be described by 2 rank kinematic parameters, i.e. I < <
N, Γ always sequency spectrum, therefore above LS problem can pass through and calculate the left pseudo inverse matrix of Γ and solve:
In formula,The left pseudo inverse matrix of representing matrix, ()HThe Hermitian transposition of representing matrix, ()-1Expression can
The inverse matrix of inverse matrix.By solving the above LS problem, it can be achieved that target order motion parameter Estimation and order motion compensation.
3. implementation of the invention:
To sum up, parameter Estimation proposed by the invention and motion compensated schemes are utilized symmetrical accumulation mode and generate cross-correlation
Then function realizes parameter Estimation by being modeled as least square problem, and then realizes the range-aligned and phase of motion compensation
Correction link.As shown in figure 5, concrete scheme of the invention is as follows:
Step 1: discrete M × N echo matrix E is constructed by the base band echo-signal of targets, M be distance to hits or
Subpulse number, N are orientation hits, that is, echo times；
Step 2: to echo data EsThe one dimensional fourier transform for carrying out that length is N is tieed up according to distance, obtains each secondary echo
One-dimensional range profile { RPn}；
Step 3: determining best symmetrical cumulative length Q according to formula 10；
Step 4: according to the expression formula for calculating cross-correlation function in table 1, obtaining the set of U cumulative cross-correlation function compositionWherein U=N-2 (Q-1) indicates the length of symmetrical accumulation area；
Step 5: search for the peak value of each cumulative cross-correlation function, according to obtained each correlation function calculate corresponding difference away from
From { Δ rn1}；
Step 6: building formula 19 in time matrix Γ and apart from difference matrix Λ and corresponding least square relationship
Formula, and least square problem is solved according to formula 20, calculate each rank kinematic parameter of target；
Step 7: to former echo data EsMultiplied by the compensation factor of formula formTo realize that order motion compensates:
In formula: ftEmit the instantaneous frequency of carrier wave for system；C is the light velocity in vacuum；viIt represents for describing target radial
Each rank kinetic parameter of movement, and i=1 ..., I, I are that the highest met under certain required precision describes order, such as v1Generation
Table single order radial motion speed, v2Represent the radial acceleration etc. of second order；T is time variable.
4. technical application of the invention:
High order parameters estimation method proposed by the present invention based on least square, can be used as towards near real-time imaging demand
Order motion compensation scheme quickly identifies for noncooperative target and provides the leading information of high quality with classification.First below from ginseng
The high order parameters estimation method mentioned in terms of the performance of number estimation and the operation cost of scheme to scheme is discussed.
Using classical first-order arithmetic CCM, ACCM and second order MEM method as representative comparison algorithm, Fig. 6 a and figure
6b gives normalized mean squared error (NMSE) curve of first order parameter and second order parameter, and it is complicated that Fig. 7 gives corresponding calculating
It writes music line.NMSE is defined as follows:
Wherein NmlRepresent Monte-Carlo number of experiment, XEst, iFor the sample observations estimated every time, XrealIt is estimation
The true value of parameter.RMSE is root-mean-square error.It can be seen from the figure that for the parameter Estimation of low order, the performance suggested plans
Best estimation performance, especially compared to MEM method, because the precision step-length being set in advance is not only restricted to, with SNR's
It increases, the evaluated error of generation tends to reduce；High order parameters are estimated, mentioned method and MEM method similar performance, but compares
Under, the computation complexity suggested plans is far smaller than MEM method.To sum up, the method for parameter estimation suggested plans has minimum
Evaluated error, while but also with the smallest operation cost, therefore it is balanced to show optimal performance-cost.
It being specifically applied in ISAR imaging, Fig. 8 a- Fig. 8 d and Fig. 9 a- Fig. 9 d is set forth via ACCM method,
Low precision and high-precision MEM method and HSACM method proposed by the invention carry out the Range compress result after motion compensation
With ISAR imaging results.Target, which is arranged, in simulation parameter has Secondary movement parameter.Table 3 gives operation time and the figure of each method
As entropy.It can be seen from the figure that Fig. 9 a) in do not estimated due to second order parameter, high-order compensation is insufficient, thus Range Profile does not have
Have and be aligned well, apparent ghost image is presented in the ISAR image of generation；Fig. 9 b) although in by MEM method to high-order join
Number is estimated, but because pursuing lower computation complexity, the estimated accuracy of setting is poor, causes compensation precision lower,
Obtained imaging results are also very undesirable.Fig. 9 c) it improves precision and obtains preferable range alignment and imaging results, but calculate
Complexity increases sharply, and takes the computer processing time of nearly ten seconds grades；Fig. 9 d) show pair with high-precision MEM homogenous quantities
Neat and imaging results, but only spend the calculating cost of Millisecond.Therefore, the present invention, which suggests plans, may be implemented in terms of very small
It calculates cost and reaches high order parameters estimation and high-precision motion compensation, be advantageous to the ISAR imaging of near real-time.
3 picture quality of table and calculating cost
| Corresponding method | Image entropy | Operation time (second) | |
| Fig. 9 a) | ACCM | 3.5334 | 0.0468 |
| Fig. 9 b) | MEM (low precision) | 3.3529 | 0.4309 |
| Fig. 9 c) | MEM (high-precision) | 2.6864 | 7.3808 |
| Fig. 9 d) | HSACM | 2.6668 | 0.0484 |
The invention also discloses a kind of quick motion compensating systems of LS high-order towards near real-time ISAR imaging, comprising:
Structural unit: for constructing discrete M × N echo matrix E by the base band echo-signal of targets, M be distance to
Hits or subpulse number, N are orientation hits, that is, echo times；
Converter unit: for echo data EsThe one dimensional fourier transform for carrying out that length is N is tieed up according to distance, is obtained each time
One-dimensional range profile { the RP of echon}；
Processing unit: for determining best symmetrical cumulative length Q；
Computing unit: for calculating the expression formula of cross-correlation function, the set of U cumulative cross-correlation function composition is obtainedWherein U=N-2 (Q-1) indicates the length of symmetrical accumulation area；
Search unit: it for searching for the peak value of each cumulative cross-correlation function, is calculated and is corresponded to according to obtained each correlation function
Difference distance { Δ rn1}；
Construction unit: for constructing time matrix Γ and apart from difference matrix Λ and corresponding least square relational expression,
And least square problem is solved, calculate each rank kinematic parameter of target；
Output unit: for former echo data EsMultiplied by the compensation factor of formula formTo realize that order motion is mended
It repays:
In formula: ftEmit the instantaneous frequency of carrier wave for system；C is the light velocity in vacuum；viIt represents for describing target radial
Each rank kinetic parameter of movement, and i=1 ..., I, I are that the highest met under certain required precision describes order, such as v1Generation
Table single order radial motion speed, v2Represent the radial acceleration etc. of second order；T is time variable.
In the processing unit, best symmetrical cumulative length Q, formula 10 are determined according to formula 10 are as follows:
Wherein, Q is symmetrical cumulative length, and γ is build up factor, and N is echo total number.
In the computing unit, according to the expression formula for calculating cross-correlation function in table 1, U accumulation cross-correlation letter is obtained
Array at setIts subscriptRange is Q~(N-Q+1).
In the construction unit, construct formula 19 in time matrix Γ and apart from difference matrix Λ and it is corresponding most
Small two multiply relational expression, and solve least square problem according to formula 20, calculate each rank kinematic parameter of target.
Order motion compensation scheme proposed by the invention belongs to the second class method of background technique from principle, i.e., sharp
With the correlation and difference distance of adjacent echoes, to estimate the kinematic parameter of target, and then motion compensation is realized.Most with the present invention
Similar implementation is the accumulation cross-correlation method (ACCM) being most widely used, but the solution of the present invention improves the tired of ACCM
Product mode, optimizes computation complexity, it is most important that, the deficiency of high order parameters cannot be estimated by compensating for such algorithm.
Asking for order motion parameter Estimation cannot be rapidly and efficiently carried out for generally existing in existing parameter estimation algorithm
Topic is realized the invention is intended to find a kind of fast higher order motion compensation process and obtains higher estimation with lower calculating cost
Precision, and then improve ISAR image quality.High order symmetry proposed by the present invention based on least square accumulates cross-correlation method
(HSACM, High-order Symmetric Accumulated Cross-Correlation Method), optimizes classics
The accumulation mode of cross-correlation method, using least square fitting, high order parameters cannot be estimated by compensating for existing cross-correlation method
It is insufficient；High order parameters estimation and motion compensation are realized with low-down calculating cost, and are not necessarily to priori knowledge.The present invention is preferable
Solves the equalization problem between high-accuracy compensation and computation complexity, to realize that the near real-time imaging of high-speed high-quality provides
Superior precondition.
Contribution and advantage of the invention is as follows:
(1) firstly, method proposed by the invention generates in such a way that symmetrical accumulation is instead of traditional unidirectional accumulation
Cross-correlation function.This symmetric mode can effectively cancel out positive phase and negative phase error, this is advantageous to Range Profile pair
Quasi- and phasing.
(2) further, since the convolution symmetry characteristic of cross-correlation function, the calculating cost suggested plans are optimized compared with ACCM
Half, this is highly beneficial for realizing near real-time imaging.
(3) parameter Estimation is formulated as solving least square (LS) problem by third, method proposed by the invention, thus
Realize high order parameters estimation.Its significance lies in that compensate for the algorithm based on Range Profile relevant treatment generally existing for proposed scheme
Estimation high order parameters in terms of defect.
(4) compared to MEM, method of the invention is a kind of blind processing method.That is, it is not necessary to which radar system replaces
Emit wide and narrow strip wave to obtain priori knowledge (i.e. the estimation range of parameter), and its computation complexity differs 2~3 with MEM method
A order of magnitude, far smaller than MEM can better meet real-time demand under the premise of reaching same compensation precision.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist
Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention
Protection scope.
Claims (8)
1. a kind of quick motion compensation process of LS high-order towards near real-time ISAR imaging characterized by comprising
Step 1: discrete M × N echo matrix E is constructed by the base band echo-signal of targets, M is distance to hits or subpulse
Number, N are orientation hits, that is, echo times；
Step 2: to echo data EsAccording to distance tie up carry out length be N one dimensional fourier transform, obtain each secondary echo it is one-dimensional away from
From as { RPn}；
Step 3: determining best symmetrical cumulative length Q；
Step 4: calculating the expression formula of cross-correlation function, obtain the set of U cumulative cross-correlation function compositionWherein
U=N-2 (Q-1) indicates the length of symmetrical accumulation area；
Step 5: searching for the peak value of each cumulative cross-correlation function, corresponding difference distance is calculated according to obtained each correlation function
{Δrn1}；
Step 6: building time matrix Γ and apart from difference matrix Λ and corresponding least square relational expression, and solve least square
Problem calculates each rank kinematic parameter of target；
Step 7: to former echo data EsMultiplied by the compensation factor of formula formTo realize that order motion compensates:
In formula: ftEmit the instantaneous frequency of carrier wave for system；C is the light velocity in vacuum；viIt represents for describing radial target motion
Each rank kinetic parameter, and i=1 ..., I, I are that the highest met under certain required precision describes order, such as v1Represent one
Rank radial motion speed, v2Represent the radial acceleration etc. of second order；T is time variable.
2. the quick motion compensation process of LS high-order according to claim 1, which is characterized in that in the step 3, foundation
Formula (10) determines best symmetrical cumulative length Q, formula (10) are as follows:
Wherein, Q is symmetrical cumulative length, and γ is build up factor, and N is echo total number.
3. the quick motion compensation process of LS high-order according to claim 1, which is characterized in that in the step 4, according to
The expression formula that cross-correlation function is calculated in table 1, obtains the set of U cumulative cross-correlation function compositionIts subscript
Range is Q~(N-Q+1)；
Table 1.
4. the quick motion compensation process of LS high-order according to claim 1, which is characterized in that in the step 6, building
Time matrix Γ in formula 19 and apart from difference matrix Λ and corresponding least square relational expression, and most according to 20 solution of formula
Small two multiply problem, calculate each rank kinematic parameter of target；
Formula 19:In formulaFor time interval matrix；Join for required each rank
Matrix number；For ranging offset matrix；
Formula 20:In formula,The left pseudo inverse matrix of representing matrix, ()HRepresenting matrix
Hermitian transposition, ()-1Indicate the inverse matrix of invertible matrix.
5. a kind of quick motion compensating system of LS high-order towards near real-time ISAR imaging characterized by comprising
Structural unit: for constructing discrete M × N echo matrix E by the base band echo-signal of targets, M is distance to hits
Or subpulse number, N are orientation hits, that is, echo times；
Converter unit: for echo data EsThe one dimensional fourier transform for carrying out that length is N is tieed up according to distance, obtains each secondary echo
One-dimensional range profile { RPn}；
Processing unit: for determining best symmetrical cumulative length Q；
Computing unit: for calculating the expression formula of cross-correlation function, the set of U cumulative cross-correlation function composition is obtainedWherein U=N-2 (Q-1) indicates the length of symmetrical accumulation area；
Search unit: for searching for the peak value of each cumulative cross-correlation function, corresponding difference is calculated according to obtained each correlation function
Divide distance { Δ rn1}；
Construction unit: it for constructing time matrix Γ and apart from difference matrix Λ and corresponding least square relational expression, and solves
Least square problem calculates each rank kinematic parameter of target；
Output unit: to former echo data EsMultiplied by the compensation factor of formula formTo realize that order motion compensates:
In formula: ftEmit the instantaneous frequency of carrier wave for system；C is the light velocity in vacuum；viIt represents for describing radial target motion
Each rank kinetic parameter, and i=1 ..., I, I are that the highest met under certain required precision describes order, such as v1Represent one
Rank radial motion speed, v2Represent the radial acceleration etc. of second order；T is time variable.
6. the quick motion compensating system of LS high-order according to claim 5, which is characterized in that in the processing unit,
Best symmetrical cumulative length Q, formula 10 are determined according to formula 10 are as follows:
Wherein, Q is symmetrical cumulative length, and γ is build up factor, and N is echo total number.
7. the quick motion compensating system of LS high-order according to claim 5, which is characterized in that in the computing unit,
According to the expression formula for calculating cross-correlation function in table 1, the set of U cumulative cross-correlation function composition is obtainedUnder it
MarkRange is Q~(N-Q+1)；
Table 1.
8. the quick motion compensating system of LS high-order according to claim 5, which is characterized in that in the construction unit,
Time matrix Γ in formula 19 is constructed and apart from difference matrix Λ and corresponding least square relational expression, and according to formula 20
Least square problem is solved, each rank kinematic parameter of target is calculated；
Formula 19:In formulaFor time interval matrix；For required each rank parameter square
Battle array；For ranging offset matrix；
Formula 20:In formula,The left pseudo inverse matrix of representing matrix, ()HRepresenting matrix
Hermitian transposition, ()-1Indicate the inverse matrix of invertible matrix.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910404901.XA CN110286375B (en) | 2019-05-16 | 2019-05-16 | LS high-order fast motion compensation method and system for near real-time ISAR imaging |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910404901.XA CN110286375B (en) | 2019-05-16 | 2019-05-16 | LS high-order fast motion compensation method and system for near real-time ISAR imaging |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110286375A true CN110286375A (en) | 2019-09-27 |
| CN110286375B CN110286375B (en) | 2021-06-08 |
Family
ID=68002354
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910404901.XA Active CN110286375B (en) | 2019-05-16 | 2019-05-16 | LS high-order fast motion compensation method and system for near real-time ISAR imaging |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110286375B (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114698204A (en) * | 2022-04-26 | 2022-07-01 | 星慧照明工程集团有限公司 | Wisdom street lamp control system |
| JP2022179328A (en) * | 2021-05-21 | 2022-12-02 | 株式会社東芝 | Method and device for improved range tracking to reverse synthesis opening radar |
| CN115825061A (en) * | 2022-11-21 | 2023-03-21 | 中国科学院力学研究所 | In-situ observation method for laser-induced ultrahigh-temperature ablation under high-speed airflow |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1727913A (en) * | 2004-07-26 | 2006-02-01 | 电子科技大学 | Method for compensating relative motion of mobile multiple objective for reverse synthetic aperture radar |
| CN103941255A (en) * | 2013-01-17 | 2014-07-23 | 南京航空航天大学 | ISAR motion compensation method based on design structuration Gram matrix |
| KR20160053520A (en) * | 2014-11-05 | 2016-05-13 | 국방과학연구소 | Efficient Method and Apparatus of Generating Inverse Synthetic Aperture Radar Image of Multiple Targets Using Flight Trajectory and Morphological Processing |
| KR101757885B1 (en) * | 2017-02-22 | 2017-07-13 | 엘아이지넥스원 주식회사 | Apparatus and method for compensating SAR image |
| CN109709552A (en) * | 2019-01-24 | 2019-05-03 | 南京信息职业技术学院 | A kind of low signal-to-noise ratio ISAR imaging moving compensation method |
-
2019
- 2019-05-16 CN CN201910404901.XA patent/CN110286375B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1727913A (en) * | 2004-07-26 | 2006-02-01 | 电子科技大学 | Method for compensating relative motion of mobile multiple objective for reverse synthetic aperture radar |
| CN103941255A (en) * | 2013-01-17 | 2014-07-23 | 南京航空航天大学 | ISAR motion compensation method based on design structuration Gram matrix |
| KR20160053520A (en) * | 2014-11-05 | 2016-05-13 | 국방과학연구소 | Efficient Method and Apparatus of Generating Inverse Synthetic Aperture Radar Image of Multiple Targets Using Flight Trajectory and Morphological Processing |
| KR101757885B1 (en) * | 2017-02-22 | 2017-07-13 | 엘아이지넥스원 주식회사 | Apparatus and method for compensating SAR image |
| CN109709552A (en) * | 2019-01-24 | 2019-05-03 | 南京信息职业技术学院 | A kind of low signal-to-noise ratio ISAR imaging moving compensation method |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2022179328A (en) * | 2021-05-21 | 2022-12-02 | 株式会社東芝 | Method and device for improved range tracking to reverse synthesis opening radar |
| JP7362810B2 (en) | 2021-05-21 | 2023-10-17 | 株式会社東芝 | Method and device for improved range tracking for retrosynthetic aperture radar |
| CN114698204A (en) * | 2022-04-26 | 2022-07-01 | 星慧照明工程集团有限公司 | Wisdom street lamp control system |
| CN115825061A (en) * | 2022-11-21 | 2023-03-21 | 中国科学院力学研究所 | In-situ observation method for laser-induced ultrahigh-temperature ablation under high-speed airflow |
| CN115825061B (en) * | 2022-11-21 | 2023-07-07 | 中国科学院力学研究所 | In-situ observation method for laser-induced ultra-high temperature ablation under high-speed airflow |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110286375B (en) | 2021-06-08 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Su et al. | High-speed multi-target detection with narrowband radar | |
| CN110286375A (en) | The quick motion compensation process of LS high-order and system towards near real-time ISAR imaging | |
| CN107229048B (en) | High-resolution wide-range SAR moving target speed estimation and imaging method | |
| CN106872974B (en) | High-precision motion target imaging method based on hypersonic platform Two-channels radar | |
| CN110907910B (en) | Distributed coherent radar moving target echo coherent synthesis method | |
| CN110095765A (en) | High-resolution Doppler's reconstructing method of frequency-agile radar | |
| CN103616687B (en) | The fitting of a polynomial ISAR envelope alignment method that piecewise linearity is estimated | |
| Huang et al. | Radar high speed small target detection based on keystone transform and linear canonical transform | |
| CN106501785B (en) | A kind of sane sparse recovery STAP methods and its system based on alternating direction multiplier method | |
| CN104698459B (en) | Stripe SAR (specific absorption resolution) compressed sensing and imaging method for missing data | |
| CN109856635A (en) | CSAR ground moving target refocusing imaging method | |
| CN104251991B (en) | A kind of fractional dimension threshold value iteration sparse microwave imaging method estimated based on degree of rarefication | |
| CN108535726A (en) | ISAR imaging methods based on power power Fourier transformation | |
| CN110146886A (en) | The method for quick estimating of non-homogeneous rotating target motion parameter | |
| CN106405552A (en) | WVD-PGA algorithm based SAR object focusing method | |
| CN106199600A (en) | The orientation Multichannel SAR formation method estimated based on Doppler | |
| CN108226928A (en) | Based on the inverse synthetic aperture radar imaging method for it is expected propagation algorithm | |
| CN115616518A (en) | Method for estimating weak target motion parameters and reconstructing high-resolution range profile of broadband radar | |
| CN109613507A (en) | A kind of detection method for high-order maneuvering target radar return | |
| CN112433210A (en) | Quick time domain imaging method for double-station forward-looking ground penetrating radar | |
| Yu et al. | Ground moving target motion parameter estimation using Radon modified Lv's distribution | |
| CN112327301B (en) | Parameterized translational compensation rapid method under low signal-to-noise ratio based on subaperture GRFT | |
| CN114545351A (en) | Maneuvering target coherent detection method and system based on range frequency axis inversion transformation and second-order WVD (WVD) | |
| CN103616669B (en) | In two-dimensional frequency, channel-equalization method is carried out to non-homogeneous scene | |
| CN107632302B (en) | Time domain weighted symmetric cumulative cross-correlation parameter estimation method for ISAR imaging |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |