CN107193002B - A kind of one-dimensional range profile high-resolution imaging method can inhibit wideband phase noise - Google Patents

A kind of one-dimensional range profile high-resolution imaging method can inhibit wideband phase noise Download PDF

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CN107193002B
CN107193002B CN201710364405.7A CN201710364405A CN107193002B CN 107193002 B CN107193002 B CN 107193002B CN 201710364405 A CN201710364405 A CN 201710364405A CN 107193002 B CN107193002 B CN 107193002B
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CN107193002A (en
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张庆
颜铭江
邢玲
卢铭迪
杨悦
丛迅超
万群
黄忠涛
龙柯宇
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Sichuan Hongchuang Electronic Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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  • Radar, Positioning & Navigation (AREA)
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Abstract

The invention belongs to Radar Technology fields, are related to a kind of one-dimensional range profile high-resolution imaging method that can inhibit wideband phase noise.Method of the invention is main are as follows: firstly, carrying out oversampled discrete processing in the bandwidth of wideband radar transmitting signal to radar echo signal, constructing the one-dimensional range profile imaging model based on phase recovery；Secondly, non-convex problem is imaged in the one-dimensional range profile based on phase recovery and is converted to the convex problem restored based on auto-correlation using Fourier's base characteristic of observing matrix；Augmented Lagrangian Functions are constructed, the function is calculated relative to the derivative of auto-correlation vector and to enable it is zero, obtain the iterative equation about auto-correlation vector；Iterative processing is executed, stops when residual error is less than reservation threshold or the number of iterations is greater than maximum number of iterations, obtains optimal auto-correlation vector；Finally, solving corresponding scattering coefficient vector to the method for the auto-correlation vector Ke Ermoge love spectral factorization found out under minimum phase criterion.

Description

A kind of one-dimensional range profile high-resolution imaging method can inhibit wideband phase noise
Technical field
The invention belongs to Radar Technology field, be related to a kind of one-dimensional range profile high-resolution that can inhibit wideband phase noise at Image space method.
Background technique
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, and it is vertical to reflect target To fine structure, have great importance to target detection, tracking and identification, have in practice in engineering and important apply valence 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 indicated by the synthesis of local scattering properties, locally scattering is commonly known as equivalent scattering center for these.It is theoretical herein On the basis of, with the continuous development of Radar Technology, lot of documents proposes to obtain by pulse compression technique using big bandwidth signal The target scattering center high-resolution upward in distance by radar is obtained, to realize the one-dimensional range profile high-resolution of target scattering center Imaging.The present invention emits broadband signal using wideband radar, emits delay and amplitude modulating action of the signal Jing Guo observed object 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 It can be by the serious shadow of random phase noise in broadband signal with factors, the target echo that wideband radar receives such as atmospheric interference It rings, and then one-dimensional range profile generation is caused seriously to defocus, it is difficult to obtain high-resolution performance.
Summary of the invention
It is to be solved by this invention, aiming at the above problem, propose it is a kind of can inhibit wideband phase noise it is one-dimensional away from From image height resolution imaging method, target scene is observed using the broadband signal that wideband radar emits, utilizes observing matrix Fourier's base characteristic and phase retrieval problem architectural characteristic, to returning while establishing one-dimensional range profile imaging problem hidden convexity Phase noise of the wave number in is effectively inhibited, 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 can inhibit wideband phase noise, which is characterized in that including following Step:
The one-dimensional range profile imaging model that S1, building are interfered containing phase noise:
In the bandwidth of wideband radar transmitting signal, oversampled discrete processing is carried out to radar echo signal, building contains The one-dimensional range profile imaging model of phase noise interference, shown in following formula 1:
lr=Ψ Ds+n (formula 1)
In formula 1, lrIndicate echo vector, Ψ indicates phase noise matrix, and D indicates observing matrix, s be scattering coefficient to Amount, n is noise vector；
S2, it the one-dimensional range profile based on phase recovery is imaged to non-convex problem is converted to and convex being asked based on what auto-correlation was restored Topic:
Phase recovery is mainly that the amplitude information for utilizing linearly to measure restores echo signal, and the present invention utilizes observation square Fourier's base characteristic of battle array D constructs the one-dimensional range profile based on phase recovery and is imaged shown in the non-following formula 2 of convex problem:
H=| Ψ Ds |2+ e (formula 2)
In formula 2, h indicates that measurement vector, e indicate noise vector；
In order to restore vector s from vector h, the present invention considers that least square cost constructs phase retrieval problem, because this A problem is non-convex, therefore can obtain unique solution without algorithm, in order to solve this problem, most using minimum phase criterion The one-dimensional range profile based on phase recovery is imaged with auto-correlation formula under minimum phase criterion for smallization minimum mean-square error Non- convex problem is expressed as shown in following formula 3:
In formula 3, r is the auto-correlation vector of scattering coefficient vector, and E=diag { [1,2 ..., 2] } is diagonal matrix；
S3, optimal auto-correlation vector r is obtained:
Augmented Lagrangian Functions are constructed, the function is calculated relative to the derivative of auto-correlation vector and to enable it is zero, obtain Iterative equation about auto-correlation vector；
Reservation threshold ε and maximum number of iterations 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 the number of iterations is greater than maximum number of iterations T Only, optimal auto-correlation vector r is obtained；
S4, scattering coefficient vector is obtained:
Corresponding scattering coefficient vector is solved by auto-correlation vector r using Ke Ermoge love spectral factorization method.
The total technical solution of the present invention, firstly, being carried out in the bandwidth of wideband radar transmitting signal to radar echo signal Oversampled discreteization processing, constructs the one-dimensional range profile imaging model based on phase recovery；Secondly, using in Fu of observing matrix One-dimensional range profile based on phase recovery is imaged non-convex problem and is converted to the convex problem restored based on auto-correlation by phyllopodium characteristic； Augmented Lagrangian Functions are constructed, the function is calculated relative to the derivative of auto-correlation vector and to enable it is zero, are obtained about from phase Close the iterative equation of vector；Iterative processing is executed, until residual error is less than reservation threshold or the number of iterations greater than maximum number of iterations When stop, obtaining optimal auto-correlation vector；Finally, under minimum phase criterion, to the auto-correlation vector Ke Ermo found out The method of dagger-axe love spectral factorization solves corresponding scattering coefficient vector.
Further, step S1 method particularly includes:
Assuming that then one-dimensional distance is expressed as 4 institute of formula to scattering center model there are N number of ideal scattering point in scene Show:
In formula 4, lrIndicate echo-signal, k representation space frequency, σpIndicate the scattering coefficient of p-th of scattering point, △ R (xp) indicate p-th of scattering point to scene center distance,Indicate the phase noise in p-th of scattering point echo；
The echo of single scattering center is carried out to the oversampled discreteization processing of frequency, frequency over-sampling points are M, then return Wave vector lr=[lr1,lr2,…,lrN], scattering coefficient vector is expressed as 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, with auto-correlation formula that the one-dimensional range profile imaging based on phase recovery is non-convex in the step S2 The formula 2 of problem is expressed as formula 3 method particularly includes:
The auto-correlation vector of scattering coefficient is expressed asVector form isIt enablesR=[r is enabled after eliminating redundancy0,r1,…,rN-1], then haveWherein { [1,2 ..., 2] } E=diag.
Bound term in formula 3 is that r is limited autocorrelation sequence, and the necessary and sufficient condition that r is limited autocorrelation sequence is r Discrete time Fourier transform be more than or equal to 0, i.e.,Exist respectively to R (w)
Point is sampled, this operation is equivalent to matrix vector multiplication FLS, wherein FLBe L point it is discrete when Between the preceding N of Fourier transformation arrange shown in following formula (5)
In formula 5, φ=e-j2π/L。
The beneficial effects of the present invention are: the present invention combines alternating multiplier method and Ke Ermoge love spectral factorization method to broadband One-dimensional range profile imaging is carried out while phase noise is inhibited, and is divided first containing the target echo that phase noise interferes One-dimensional range profile based on phase recovery is imaged non-convex problem using Fourier's base characteristic of observing matrix and is converted to by analysis modeling Based on the convex problem that auto-correlation is restored, solved to obtain optimal auto-correlation vector using alternately multiplier method.Then, in minimum Under phase criterion, corresponding scattering coefficient vector is solved by auto-correlation vector using Ke Ermoge love spectral factorization method.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 Battle array is inhibited using the method that transposition is multiplied, and since calculation matrix is over-sampling, and the present invention is not needed to target field Scape carry out sparse prior it is assumed that therefore have preferable noiseproof feature, to reflection target longitudinal direction fine structure, target detection, Tracking and identification have great importance.
Detailed description of the invention
Fig. 1 is radar imagery geometrized structure graph；
Fig. 2 is the spectrogram using auto-correlation vector of the invention；
Fig. 3 is the high-resolution lattice image differently obtained in simulating, verifying, and (a) is tradition SDA method, (b) For method of the invention.
Specific embodiment
With reference to the accompanying drawings and examples, the technical schemes of the invention are described in detail:
The radar geometry that the present invention uses is as shown in Figure 1, wherein wideband radar constantly emits and connects to target scene Pulse is received, specific implementation step of the invention is as follows:
Step 1, the one-dimensional range profile imaging model interfered containing phase noise is constructed:
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 ideal scattering point, transmitting signal form scattering idea echo, target echo is after by the delay of each scattering point and amplitude modulation 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 indicated, N is the number of ideal scattering center in target scene, σpIndicate scene midpoint p Scattering coefficient, k is spatial frequency,For phase noise；
1.2) number that ideal scattering center is arranged 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, constructs one-dimensional range profile imaging mould when having N number of scattering center in target scene 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 Indicate noise vector；
Step 2, phase recovery mainly restores original signal from the amplitude information that linearly converts, according to observation square Fourier's base characteristic of battle array D constructs the one-dimensional range profile based on phase recovery and rebuilds non-convex problem.The present invention is proposed with minimum phase One-dimensional range profile based on phase recovery is rebuild non-convex problem weight with auto-correlation formula by the criterion of minimizing minimum mean-square error in position Structure is the convex problem restored based on auto-correlation, and solves auto-correlation vector using alternately multiplier method:
2.1) phase recovery mainly restores original signal from the amplitude information that linearly converts, and utilizes observing matrix Fourier's base characteristic, one-dimensional range profile based on phase recovery is imaged non-convex problem and can state are as follows:
H=| Ψ Ds |2+e
Wherein, h indicate measurement vector, e indicate noise vector, give as follows measurement vector most preceding 4 and 4 last values:
956344.768958355
969469.536257930
984190.736648139
993031.439383133
……
981176.583440932
960831.851019310
952150.404583882
956344.768958355
2.2) non-convex problem reformulation is imaged in the one-dimensional range profile based on phase recovery is convex asking of being restored based on auto-correlation Inscribe model.The discrete fourier sampling number L=20N of r is set first, and is existed respectively to itPoint Discrete sampling is carried out, then can obtain sampling matrix FL:
2.4) iteration factor λ=0, ρ=0 are set, and reservation threshold is ε=1e-5, maximum number of iterations 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 the number of iterations Stop when maximum number of iterations 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, gives auto-correlation vector r as follows 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 generating 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 there is 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) is indicated Amplitude response, β (w) indicate phase response；
3.3) assume that knowing that the amplitude response of auto-correlation vector Fourier transformation and phase response meet wishes by minimum phase The relationship of your Bert transformation, it can obtain β (w) by carrying out Hilbert transform to α (w)；
3.4) it can be obtained by the auto-correlation vector acquired in step 2:
Wherein,Expression takes corresponding real part,Expression takes corresponding imaginary part, and sgn (w) indicates sign function；
3.5) minimum for generating auto-correlation vector in step 2 can be acquired by the relationship between auto-correlation vector sum scattering coefficient Phase scattering coefficient vector:
Effect of the invention can be illustrated by following emulation experiments:
The present invention handles the echo data of simulating scenes, right while inhibition to phase noise in echo Target scene carries out one-dimensional range profile High resolution reconstruction.Centre carrier frequency in the present invention are as follows: f0=9GHz, signal bandwidth are as follows: B =1.0GHz, scene size are as follows: N=200 pixel, over-sampling points are as follows: M=20N, auto-correlation sampling number are as follows: L=20N, with Machine phase noise obedience is uniformly distributed: [- π/4, π/4], additive gaussian white noise are as follows: SNR=20dB.It is 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 indicates original one-dimensional range profile, circles mark curve It indicates 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 as a 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 algorithm cannot 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.Table 1 lists the reconstruction performance of the different next algorithms of signal-to-noise ratio, and present invention primarily contemplates following Reconstruction performance: 1) mean square error (RMSE) is rebuild:Wherein D indicates that observing matrix, s indicate original and dissipate Coefficient vector is penetrated,Indicate the scattering coefficient vector rebuild；2) target background ratio (TBR):Wherein ΩtIndicate the supported collection of target,Indicate the supplementary set of object support collection,Indicate background element number.As can be seen that compared with SDA algorithm, propose algorithm can obtain better target background ratio and Residual error, table 1 show the reconstruction performance parameter comparison of each algorithm under different signal-to-noise ratio.
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 that can inhibit wideband phase noise, which is characterized in that including following step It is rapid:
The one-dimensional range profile imaging model that S1, building are interfered containing phase noise:
In the bandwidth of wideband radar transmitting signal, oversampled discrete processing is carried out to radar echo signal, building is based on phase The one-dimensional range profile imaging model of bit recovery, shown in following formula 1:
lr=Ψ Ds+n (formula 1)
In formula 1, lrIndicate that echo vector, Ψ indicate that phase noise matrix, D indicate observing matrix, 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 be converted to based on auto-correlation restore convex problem:
Using Fourier's base characteristic of observing matrix D, it is as follows to construct the non-convex problem of one-dimensional range profile imaging based on phase recovery Shown in formula 2:
H=| Ψ Ds |2+ e (formula 2)
In formula 2, h indicates that measurement vector, e indicate 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 following formula 3:
In formula 3, r is the auto-correlation vector of scattering coefficient vector, and E=diag { [1,2 ..., 2] } is diagonal matrix；Table Show and takes corresponding real part；
S3, optimal auto-correlation vector r is obtained:
Construct Augmented Lagrangian Functions, calculate the function relative to the derivative of auto-correlation vector and to enable it be zero, obtain about The iterative equation of auto-correlation vector；
Reservation threshold ε and maximum number of iterations 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 the number of iterations is greater than maximum number of iterations T, Obtain optimal auto-correlation vector r；
S4, scattering coefficient vector is obtained:
Corresponding scattering coefficient vector is solved by auto-correlation vector r using Ke Ermoge love spectral factorization method.
2. a kind of one-dimensional range profile high-resolution imaging method that can inhibit wideband phase noise according to claim 1, It is characterized in that, step S1's method particularly includes:
Assuming that then one-dimensional distance is expressed as shown in formula 4 to scattering center model there are N number of ideal scattering point in scene:
In formula 4, lrIndicate echo vector, k representation space frequency, σpIndicate the scattering coefficient of p-th of scattering point, Δ R (xp) table Show p-th of scattering point to scene center distance,Indicate the phase noise in p-th of scattering point echo；
The echo of single scattering center is carried out to the oversampled discreteization processing of frequency, frequency over-sampling points are M, then echo to Measure lr=[lr1,lr2,…,lrN], scattering coefficient vector is expressed as 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 that can inhibit wideband phase noise according to claim 2, It is characterized in that, the one-dimensional range profile based on phase recovery is imaged in the step S2 with auto-correlation formula the formula of non-convex problem 2 are expressed as formula 3 method particularly includes:
The auto-correlation vector of scattering coefficient is expressed asVector form isIt enablesR=[r is enabled after eliminating redundancy0,r1,…,rN-1], then haveWherein { [1,2 ..., 2] } E=diag.
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