CN107193002A - A kind of one-dimensional range profile high-resolution imaging method for suppressing wideband phase noise - Google Patents
A kind of one-dimensional range profile high-resolution imaging method for suppressing wideband phase noise Download PDFInfo
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- 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
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Abstract
The invention belongs to Radar Technology field, it is related to a kind of one-dimensional range profile high-resolution imaging method for suppressing wideband phase noise.The present invention method be mainly：First, in the bandwidth of wideband radar transmission signal, oversampled discrete processing is carried out to radar echo signal, the one-dimensional range profile imaging model based on phase recovery is built；Secondly, using Fourier's base characteristic of observing matrix, the one-dimensional range profile based on phase recovery is imaged non-convex problem and is converted to the convex problem based on auto-correlation recovery；Augmented Lagrangian Functions are constructed, the function is calculated relative to the derivative of auto-correlation vector and makes it be zero, obtain the iterative equation on auto-correlation vector；Iterative processing is performed, is stopped when residual error is less than reservation threshold or iterations is more than maximum iteration, optimal auto-correlation vector is obtained；Finally, under minimum phase criterion, the method for the auto-correlation vector Ke Ermoge love spectral factorizations to obtaining solves corresponding scattering coefficient vector.
Description
Technical field
The invention belongs to Radar Technology field, be related to a kind of one-dimensional range profile high-resolution for suppressing wideband phase noise into
Image space method.
Background technology
Radar High Range Resolution (High Resolution Range Profiles, HRRP) is that target reflectivity characteristics exist
One Dimensional Projection on radar line of sight, contains the features such as number, distribution and the radical length of target scattering point, reflects target and indulges
To fine structure, have great importance to target detection, tracking and identification, engineering in practice have important application valency
Value.
According to electromagnetic theory, when the electric size of target scattering body is much larger than wavelength, the high-frequency electromagnetic scattering properties of target
It can be represented by the synthesis of local scattering properties, these locally scatter and are commonly known as equivalent scattering center.It is theoretical herein
On the basis of, with continuing to develop for Radar Technology, lot of documents proposes, by pulse compression technique, to obtain using big bandwidth signal
Target scattering center is obtained in the upward high-resolution of distance by radar, so as to realize the one-dimensional range profile high-resolution of target scattering center
Imaging.The present invention launches broadband signal, delay and amplitude modulation(PAM) effect of the transmission signal Jing Guo observed object using wideband radar
Afterwards, the reflection echo of target is obtained, and then carries out one-dimensional range profile high-resolution imaging.However, due to radio wave propagation, systematic error
With the factor such as atmospheric interference, the target echo that wideband radar is received can by random phase noise in broadband signal serious shadow
Ring, and then cause one-dimensional range profile to occur seriously to defocus, it is difficult to obtain high-resolution performance.
The content of the invention
It is to be solved by this invention, aiming above mentioned problem, propose it is a kind of suppress wideband phase noise it is one-dimensional away from
From image height resolution imaging method, the broadband signal launched using wideband radar is observed to target scene, utilizes observing matrix
Fourier's base characteristic and phase retrieval problem architectural characteristic, to returning while setting up one-dimensional range profile imaging problem hidden convexity
Phase noise of the wave number in is effectively suppressed, and then realizes one-dimensional range profile high-resolution imaging.
The technical scheme is that：
A kind of one-dimensional range profile high-resolution imaging method for suppressing wideband phase noise, it is characterised in that including following
Step：
S1, the one-dimensional range profile imaging model for building the interference containing phase noise：
In the bandwidth of wideband radar transmission signal, oversampled discrete processing is carried out to radar echo signal, structure contains
The one-dimensional range profile imaging model of phase noise interference, shown in equation below 1：
lr=Ψ Ds+n (formula 1)
In formula 1, lrRepresent echo vector, Ψ represents phase noise matrix, D represents observing matrix, s be scattering coefficient to
Amount, n is noise vector；
S2, the one-dimensional range profile based on phase recovery is imaged to non-convex problem be converted to and convex being asked based on what auto-correlation was recovered
Topic：
The amplitude information that phase recovery mainly uses linearly to measure recovers echo signal, and the present invention utilizes and observes square
Battle array D Fourier's base characteristic, constructs the one-dimensional range profile based on phase recovery and is imaged shown in non-convex problem equation below 2：
H=| Ψ Ds |2+ e (formula 2)
In formula 2, h represents measurement vector, and e represents noise vector；
In order to recover vector s from vectorial h, the present invention considers least square cost construction phase retrieval problem, because this
Individual problem is non-convex, therefore no algorithm can obtain unique solution, in order to solve this problem, using minimum phase criterion most
One-dimensional range profile based on phase recovery, under minimum phase criterion, is imaged by smallization minimum mean-square error with auto-correlation formula
Non- convex problem is expressed as shown in equation below 3：
In formula 3, r is the auto-correlation vector of scattering coefficient vector, and E=diag { [1,2 ..., 2] } is diagonal matrix；
The optimal auto-correlation vector r of S3, acquisition：
Augmented Lagrangian Functions are constructed, the function is calculated relative to the derivative of auto-correlation vector and makes it be zero, obtain
Iterative equation on auto-correlation vector；
Reservation threshold ε and maximum iteration T is set, auto-correlation vector r is solved from formula 3 using alternately multiplier method,
In an iterative process, stop when the residual error of auto-correlation vector is less than reservation threshold ε or iterations is more than maximum iteration T
Only, optimal auto-correlation vector r is obtained；
S4, acquisition scattering coefficient vector：
Corresponding scattering coefficient vector is solved by auto-correlation vector r using Ke Ermoge love spectral factorization methods.
The total technical scheme of the present invention, first, in the bandwidth of wideband radar transmission signal, is carried out to radar echo signal
Oversampled discreteization processing, builds the one-dimensional range profile imaging model based on phase recovery；Secondly, using in Fu of observing matrix
Phyllopodium characteristic, is imaged non-convex problem by the one-dimensional range profile based on phase recovery and is converted to the convex problem based on auto-correlation recovery；
Augmented Lagrangian Functions are constructed, the function is calculated relative to the derivative of auto-correlation vector and makes it be zero, obtain on from phase
Close the iterative equation of vector；Iterative processing is performed, until residual error is less than reservation threshold or iterations more than maximum iteration
When stop, obtaining optimal auto-correlation vector；Finally, under minimum phase criterion, to the auto-correlation vector Ke Ermo obtained
The method of dagger-axe love spectral factorization solves corresponding scattering coefficient vector.
Further, step S1 specific method is：
Assuming that there is N number of preferable scattering point in scene, then one-dimensional distance is expressed as the institute of formula 4 to scattering center model
Show：
In formula 4, lrRepresent echo-signal, k representation space frequencies, σpRepresent the scattering coefficient of p-th of scattering point, △ R
(xp) p-th of scattering point is represented to the distance of scene center,Represent the phase noise in p-th of scattering point echo；
The echo of single scattering center is entered to the oversampled discreteization processing of line frequency, frequency over-sampling points are M, then return
Wave vector lr=[lr1,lr2,…,lrN], scattering coefficient vector representation is s=[σ1,σ2,…,σN]T, phase noise matrix isObserving matrix is expressed as D=[d1,d2,…,dN], wherein di=
[d(f1),d(f2),…,d(fM)]T, and 0≤i≤N, d (fj)=exp {-j2 π k △ R (xj)},0≤j≤N。
Further, the one-dimensional range profile based on phase recovery is imaged non-convex with auto-correlation formula in the step S2
The specific method that the formula 2 of problem is expressed as formula 3 is：
The auto-correlation vector representation of scattering coefficient isVector form isOrderR=[r are made after eliminating redundancy0,r1,…,rN-1], then haveWherein E=diag [1,2 ..., 2] }.
Bound term in formula 3 is that r is limited autocorrelation sequence, and r is that the necessary and sufficient condition of limited autocorrelation sequence is r
Discrete time Fourier transform be more than or equal to 0, i.e.,R (w) is existed respectively
Point is sampled, and this computing is equivalent to matrix vector multiplication FLS, wherein FLIt is the discrete time of L points
Shown in the preceding N row equation below (5) of Fourier transformation
In formula 5, φ=e-j2π/L。
The beneficial effects of the invention are as follows：Present invention joint alternating multiplier method and Ke Ermoge love spectral factorization methods are to broadband
One-dimensional range profile imaging is carried out while phase noise is suppressed, first to being divided containing the target echo that phase noise is disturbed
Analysis modeling, is imaged non-convex problem by the one-dimensional range profile based on phase recovery using Fourier's base characteristic of observing matrix and is converted to
The convex problem recovered based on auto-correlation, is solved using alternately multiplier method progress and obtains optimal auto-correlation vector.Then, in minimum
Under phase criterion, corresponding scattering coefficient vector is solved by auto-correlation vector using Ke Ermoge love spectral factorization methods.This hair
The bright concrete form for not considering phase noise, but the structural advantage of secondary amplitude observation model is utilized, to phase noise square
The method that battle array is multiplied using transposition is suppressed, and because calculation matrix is over-sampling, and the present invention need not be to target field
Scape carries out sparse prior it is assumed that therefore having preferable noiseproof feature, the fine structure longitudinal to reflection target, target detection,
Tracking and identification have great importance.
Brief description of the drawings
Fig. 1 is radar imagery geometrized structure graph；
Fig. 2 is the spectrogram of the auto-correlation vector using the present invention；
Fig. 3 is the high-resolution lattice image differently obtained in simulating, verifying, and (a) is tradition SDA methods, (b)
For the method for the present invention.
Embodiment
With reference to the accompanying drawings and examples, technical scheme is described in detail：
The radar geometry that the present invention is used is as shown in figure 1, wherein wideband radar is constantly launched with connecing to target scene
Pulse is received, specific implementation step of the invention is as follows：
Step 1, the one-dimensional range profile imaging model disturbed containing phase noise is built：
1.1) wideband radar works in microwave band, and target length is much larger than wavelength, at this moment target can be approximately one group from
Scattered preferable scattering point, transmission signal is formed scattering idea echo by after the delay of each scattering point and amplitude modulation(PAM), and target echo is
Be each scattering idea echo and, it can thus be concluded that one-dimensional distance is to scattering center model：
Wherein lr(k) echo-signal is represented, N is the number of preferable scattering center in target scene, σpRepresent scene midpoint p
Scattering coefficient, k is spatial frequency,For phase noise；
1.2) number for setting preferable scattering center in the present invention is N=200, and spatial frequency sampling number is M, and is made
M=20N is obtained, vector form is denoted as, one-dimensional range profile imaging mould when having N number of scattering center in target scene is built
Type：
lr=Ψ Ds+n
Wherein, lrFor echo vector, Ψ is phase noise matrix, and s is scene scatters coefficient vector, and D is observing matrix, n
Represent noise vector；
Step 2, phase recovery recovers primary signal in being mainly the amplitude information converted from linearly, according to observation square
Battle array D Fourier's base characteristic, constructs the one-dimensional range profile based on phase recovery and rebuilds non-convex problem.The present invention is proposed with minimum phase
The criterion of minimizing minimum mean-square error in position, non-convex problem weight is rebuild with auto-correlation formula by the one-dimensional range profile based on phase recovery
Structure is the convex problem recovered based on auto-correlation, and solves auto-correlation vector using alternately multiplier method：
2.1) phase recovery recovers primary signal in being mainly the amplitude information converted from linearly, utilizes observing matrix
Fourier's base characteristic, one-dimensional range profile based on phase recovery is imaged non-convex problem and can be expressed as：
H=| Ψ Ds |2+e
Wherein, h represents measurement vector, and e represents noise vector, most preceding 4 as follows for giving measurement vector and
4 last values：
956344.768958355
969469.536257930
984190.736648139
993031.439383133
……
981176.583440932
960831.851019310
952150.404583882
956344.768958355
2.2) it is convex the asking based on auto-correlation recovery the one-dimensional range profile based on phase recovery to be imaged into non-convex problem reformulation
Inscribe model.R discrete fourier sampling number L=20N is set first, and it is existed respectivelyPoint
Discrete sampling is carried out, then can obtain sampling matrix FL：
2.4) iteration factor λ=0, ρ=0 is set, and reservation threshold is ε=1e-5, maximum iteration T=100, is introduced auxiliary
Help variableWhen the residual values of auto-correlation vector in iterative process are big less than reservation threshold ε=1e-5 or iterations
Stop when maximum iteration T=100, obtain optimal auto-correlation vector, specific iterative equation is as follows：
Wherein, Z is the auxiliary variable introduced, diagonal matrix E=diag { [1,2 ..., 2] }, rk+1Be in kth time iteration more
New auto-correlation vector, Zk+1It is the auxiliary variable updated in kth time iteration, λk+1It is the coefficient updated in kth time iteration.For
Obtained optimal auto-correlation vector is solved, Fig. 2 illustrates the spectrogram of auto-correlation vector, auto-correlation vector r has been given below most
4 preceding and 4 last values：
1000511.96176304+0.00000000000000i
477.932961976909+2.18140192724284e-10i
477.932961977524-1.22061440209938e-10i
500.277937547207-25.8125130313545i
……
477.932961972361-6.50920079632485e-09i
477.932961978081+8.29003513697613e-09i
477.932961967987-1.17880427427074e-08i
477.932961982636-1.59174930667994e-09i
Step 3：The auto-correlation vector obtained according to step 2 iteration, solves the minimum phase for producing this auto-correlation vector
Scattering coefficient vector：
3.1) discrete time Fourier transform is carried out to auto-correlation vector r, obtains the power spectrum R (w) of scattering coefficient vector,
And have R (w)=sH(w)s(w)；
3.2) by that 3.1) can obtain ln [R (w)]=2lns (w), and ln [R (w)]=α (w)+j β (w), wherein α (w) are represented
Amplitude response, β (w) represents phase response；
3.3) assume that the amplitude response and phase response that understand the vectorial Fourier transformation of auto-correlation meet uncommon by minimum phase
The relation of your Bert conversion, you can to obtain β (w) by carrying out Hilbert transform to α (w)；
3.4) the auto-correlation vector tried to achieve in step 2 can be obtained：
Wherein,Expression takes correspondence real part,Expression takes correspondence imaginary part, and sgn (w) represents sign function；
3.5) relation between auto-correlation vector sum scattering coefficient can try to achieve the minimum for producing auto-correlation vector in step 2
Phase scattering coefficient vector：
The effect of the present invention can be illustrated by following emulation experiments：
The present invention is handled the echo data of simulating scenes, right while suppression to phase noise in echo
Target scene carries out one-dimensional range profile High resolution reconstruction.Centre carrier frequency is in the present invention：f0=9GHz, signal bandwidth is：B
=1.0GHz, scene size is：N=200 pixels, over-sampling, which is counted, is：M=20N, auto-correlation sampling number is：L=20N, with
Machine phase noise is obeyed and is uniformly distributed：[- π/4, π/4], additive gaussian white noise is：SNR=20dB.Carried out using distinct methods
The result of one-dimensional range profile imaging is as shown in figure 3, figure culminant star labelled notation curve represents original one-dimensional range profile, circles mark curve
Represent to rebuild one-dimensional range profile.Fig. 3 (a), which shows, utilizes sparse driving self-focusing method (Sparsity-driven
Autofocus, SDA) carry out one-dimensional range profile imaging result, Fig. 3 (b) show using algorithm proposed by the present invention progress
The result of one-dimensional range profile imaging.It can be obtained from Fig. 3, when noise jamming containing random phase in radar return, SDA algorithms can not
One-dimensional range profile high-resolution imaging is carried out, and algorithm proposed by the present invention can carry out good imaging to one-dimensional range profile, obtain
High-resolution one-dimensional range profile.Form 1 lists the reconstruction performance of the different next algorithms of signal to noise ratio, and present invention primarily contemplates following heavy
Build performance：1) mean square error (RMSE) is rebuild：Wherein D represents observing matrix, and s represents raw scattered system
Number vector,Represent the scattering coefficient vector rebuild；2) target background ratio (TBR)：
Wherein ΩtThe supported collection of target is represented,The supplementary set of object support collection is represented,Represent background element number.As can be seen that
Compared with SDA algorithms, propose that algorithm can obtain more preferable target background ratio and residual error, table 1 shows each under different signal to noise ratio
The reconstruction performance parameter comparison of algorithm.
The reconstruction performance of each algorithm under the different signal to noise ratio of table 1
Claims (3)
1. a kind of one-dimensional range profile high-resolution imaging method for suppressing wideband phase noise, it is characterised in that including following step
Suddenly：
S1, the one-dimensional range profile imaging model for building the interference containing phase noise：
In the bandwidth of wideband radar transmission signal, oversampled discrete processing is carried out to radar echo signal, builds and is based on phase
The one-dimensional range profile imaging model of bit recovery, shown in equation below 1：
lr=Ψ Ds+n (formula 1)
In formula 1, lrEcho vector is represented, Ψ represents phase noise matrix, and D represents observing matrix, and s is scattering coefficient vector, n
It is noise vector；
S2, the one-dimensional range profile based on phase recovery is imaged non-convex problem is converted to the convex problem recovered based on auto-correlation：
Using observing matrix D Fourier's base characteristic, the non-convex problem of one-dimensional range profile imaging based on phase recovery is constructed as follows
Shown in formula 2：
H=| Ψ Ds |2+ e (formula 2)
In formula 2, h represents measurement vector, and e represents noise vector；
Using the criterion of minimizing minimum mean-square error of minimum phase, under minimum phase criterion, phase will be based on auto-correlation formula
The one-dimensional range profile of bit recovery is imaged non-convex problem and is expressed as shown in equation below 3：
In formula 3, r is the auto-correlation vector of scattering coefficient vector, and E=diag { [1,2 ..., 2] } is diagonal matrix；
The optimal auto-correlation vector r of S3, acquisition：
Construct Augmented Lagrangian Functions, calculate the function relative to auto-correlation vector derivative and make it be zero, obtain on
The iterative equation of auto-correlation vector；
Reservation threshold ε and maximum iteration T is set, auto-correlation vector r is solved from formula 3 using alternately multiplier method, repeatedly
During generation, stop when the residual error of auto-correlation vector is less than reservation threshold ε or iterations is more than maximum iteration T,
Obtain optimal auto-correlation vector r；
S4, acquisition scattering coefficient vector：
Corresponding scattering coefficient vector is solved by auto-correlation vector r using Ke Ermoge love spectral factorization methods.
2. a kind of one-dimensional range profile high-resolution imaging method for suppressing wideband phase noise according to claim 1, its
It is characterised by, step S1 specific method is：
Assuming that there is N number of preferable scattering point in scene, then one-dimensional distance is expressed as shown in formula 4 to scattering center model：
In formula 4, lrRepresent echo-signal, k representation space frequencies, σpRepresent the scattering coefficient of p-th of scattering point, Δ R (xp) table
Show p-th of scattering point to the distance of scene center,Represent the phase noise in p-th of scattering point echo；
By the echo of single scattering center enter line frequency oversampled discreteization processing, frequency over-sampling points be M, then echo to
Measure lr=[lr1,lr2,…,lrN], scattering coefficient vector representation is s=[σ1,σ2,…,σN]T, phase noise matrix isObserving matrix is expressed as D=[d1,d2,…,dN], wherein di=
[d(f1),d(f2),…,d(fM)]T, and 0≤i≤N, d (fj)=exp {-j2 π k Δ R (xj)},0≤j≤N。
3. a kind of one-dimensional range profile high-resolution imaging method for suppressing wideband phase noise according to claim 2, its
It is characterised by, the one-dimensional range profile based on phase recovery is imaged to the formula of non-convex problem in the step S2 with auto-correlation formula
2 specific methods for being expressed as formula 3 are：
The auto-correlation vector representation of scattering coefficient isVector form is
OrderR=[r are made after eliminating redundancy0,r1,…,rN-1], then haveWherein E=diag [1,
2,…,2]}。
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