CN105652271A - Super-resolution processing method for augmented Lagrangian real-beam radar angle - Google Patents

Abstract

The invention discloses a super-resolution processing method for an augmented Lagrangian real-beam radar angle. Firstly a linear FM signal is transmitted in real-beam scanning, thereby obtaining a two-dimensional echo signal in a radar irradiation area. Then distance-direction high resolution is realized through distance-direction matched filtering. Then a signal model of an azimuth echo is constructed according to a scanning imaging process of a radar antenna. Then according to a principle of minimizing noise power influence, a deconvolution problem is converted to a constraint optimization problem. Furthermore solving of an objective function is realized by means of an augmented Lagrangian method, and an objective scattering coefficient is obtained through iterative inversion, thereby realizing super-resolution for the azimuth of a scanning radar. The super-resolution processing method settles a problem of low azimuth resolution in a real-beam scanning radar imaging mode.

Description

A kind of augmentation Lagrange real Beam radar angle super-resolution processing method

Technical field

The invention belongs to radar detection field, it is specifically related to real beam scanning radar angle super resolution technology.

Background technology

Radar as a kind of can round-the-clock, all weather operations imaging system, due to not by the impact of the factor such as weather, environment, in ocean and hydrologic observation, environment and disaster monitor and land/sea is followed the trail of and the dual-use field such as rescue has played indispensable effect.

Real beam scanning radar is a kind of conventional radar operation mode, successively irradiates imaging region by the mode of real aperture aerial mechanical scanning, obtains target scattering coefficient information. Therefore, high real Beam radar angular resolution, is conducive to the target in scanned radar detection region to scout, monitor, locate and identify that the application directions such as precise guidance, enemy and we's Target Recognition, target tracking and landform avoidance are had important meaning.

But, the position angle resolving power of real beam scanning radar is determined by antenna aperture, by manufacture craft and therefrom, existing real resolution of pore size cannot reach the demand of types of applications, and for real aperture imaging pattern, the technology such as traditional synthetic aperture imaging also cannot be utilized to improve position angle resolving power. Therefore, by setting up rational echo model, adopt signal processing algorithm to break through the restriction of real aperture, it is achieved position angle super-resolution has important application prospect.

For real beam scanning radar angle super-resolution, particularly how to improve the problem of position angle resolving power, general employing two kinds of methods.

It is just like document: Y.Zha, Y.Huang, J.Yang, 216J.Wu, Y.Zhang, andH.Yang, " Animprovedrichardson-lucyalgorithmforradarangularsuper-r esolution, " inRadarConference, 2014IEEE.IEEE, 2014, pp.0406 0410., propose the convolution inverting angle ultra-resolution method of a kind of improved maximum likelihood, it is mainly used in realizing the angle super-resolution of strong scattering target, but the method is mainly used in the angular resolution improving isolated strong scattering target, for point-spreading targets, the performance of the method will significantly decline.

Its two as document " F.Prez-Martnez; J.Garcia-Fominaya, andJ.Calvo-Gallego, " Ashift-and-convolutiontechniqueforhighresolutionradarima ges; " SensorsJournal, IEEE, vol.5, no.5, pp.1090 1098,2005., for the convolution model of scanned radar, it is proposed that a kind of method changing convolution.In distance to, under high-resolution prerequisite, utilizing this technology can obtain the profile information of target, but the method is only applicable to have the large-scale Ship Target of obvious profile, needs high range resolution to realize the resolution of different target at range unit simultaneously. But the method does not improve the azimuth resolution of target in essence. Therefore, the method cannot realize the resolution of the multiple target distribution within the scope of same wave beam. .

Summary of the invention

The present invention is the above-mentioned technical problem solved, a kind of augmentation Lagrange real Beam radar angle super-resolution processing method is proposed, the signal model of the procedure construction orientation echo according to radar scanner scanning imagery, minimum criteria is affected again according to noise power, deconvolution problem is converted into constrained optimization problem, and utilize solving of Augmented Lagrange method function to achieve the objective, and iterative inversion goes out target scattering coefficient, reaches the object of the position angle super-resolution realizing scanned radar.

The technical solution used in the present invention is: a kind of augmentation Lagrange real Beam radar angle super-resolution processing method, comprising:

S1, initialization system parameter;

S2, according to after radar emission signal and step S1 initialize system parameter generate two dimension echoed signal;

S3, the matrix that distributed by the two dimension target of discretize, echoed signal matrix are arranged as vector form according to each range unit order, obtain two dimension target distribution vector and echoed signal vector;

S4, the echoed signal vector obtained according to step S3, under the framework of canonical, introduce total variation operator, and establishing target function, utilizes Augmented Lagrange method to solve objective function, obtains scene objects distribution results.

Further, described step S2 specifically comprises step by step following:

S21, described radar emission signal are chirp signal;

S22, frequency domain construct distance to matched filter frequency matching function;

S23, the frequency matching function obtained according to step S22, carry out distance to processed compressed to the chirp signal of step S21, obtains two dimension echoed signal.

Further, described step S3 comprises:

S31, the two-dimentional echoed signal obtained by step S2 carry out discrete processes, obtain two dimension echoed signal convolution model;

S32, by image scene discrete region process, obtain two dimension matrix ��;

S33, to two dimension matrix �� carry out vector operation, obtain target distribution vector f=vec (��);

Noise signal n after S34, target distribution vector f=vec (��) obtained according to step S33 and vectorization, the two-dimentional echoed signal convolution model obtained by step S31 carries out vector operation, obtains echoed signal vector.

Further, described step S4 comprises:

S41, under the framework of canonical, introduce total variation operator, obtain constrained optimization problem according to the echoed signal vector that step S3 obtains,

$\begin{array}{cc}\underset{f}{\arg min}\mathrm{\λ}\left|\right|Lf|{|}_1& subjectto:\left|\right|g-Hf|{|}_2^2\≤\mathrm{\ϵ};\end{array}$

Wherein, | | | |₁Represent L₁Norm, | | | |₂Represent L₂Norm, �� is the parameter depending on noise variance, and �� >=0;

S42, introducing convex function ��₁(f)=�� | | Lf | |₁WithBy constrained optimization problem $\begin{array}{cc}\underset{f}{\arg min}\mathrm{\λ}\left|\right|Lf|{|}_1& subjectto:\left|\right|g-Hf|{|}_2^2\≤\mathrm{\ϵ}\end{array}$ It is converted into:

$\underset{f}{\arg min}\{{\mathrm{\θ}}_1\left(Lf\right)+{\mathrm{\θ}}_2\left(Hf\right)\};$

S43, introducing subsidiary variable $z=\left[\begin{array}{c}u\\ v\end{array}\right],$ ? $z=\left[\begin{array}{c}H\\ L\end{array}\right]$ Under f condition limits, will $\underset{f}{\arg min}\{{\mathrm{\θ}}_1\left(Lf\right)+{\mathrm{\θ}}_2\left(Hf\right)\}$ It is converted into:

$\begin{array}{cc}\underset{f}{\arg min}\{{\mathrm{\θ}}_1\left(v\right)+{\mathrm{\θ}}_2\left(u\right)\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f;\end{array}$

Wherein, u=Hf, v=Lf;

Then will $\begin{array}{cc}\underset{f}{\arg min}\{{\mathrm{\θ}}_1\left(v\right)+{\mathrm{\θ}}_2\left(u\right)\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f\end{array}$ It is converted into:

$\begin{array}{cc}\arg \underset{f,u,v}{min}\{E(f,u,v)=\mathrm{\λ}|\left|v\right|{|}_1+\frac{1}{2}\left|\right|g-u\left|{|}_2^2\right\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f;\end{array}$

S44, introducing function E (z) and z=Cf, obtain step S43

$\begin{array}{cc}\arg \underset{f,u,v}{min}\{E(f,u,v)=\mathrm{\λ}|\left|v\right|{|}_1+\frac{1}{2}\left|\right|g-u\left|{|}_2^2\right\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f\end{array}$ It is converted into:

$\begin{array}{cc}\underset{z}{\arg min}E\left(z\right)& subjectto:z=Cf;\end{array}$

Wherein, $C=\left[\begin{array}{c}H\\ L\end{array}\right];$

S45, employing Augmented Lagrange method, obtain step S44It is converted into and seeks the saddle point such as minor function:

$L_A(f,z,\mathrm{\γ})=E\left(z\right)+{\mathrm{\γ}}^T(z-Cf)+\frac{\mathrm{\μ}}{2}\left|\right|z-Cf|{|}_2^2$

Wherein,For Lagrange coefficient vector,It is two norms,For the vector arranged about the coherent element of u in Lagrange coefficient vector,For the vector arranged about the coherent element of v in Lagrange coefficient vector;

S46, iterative algorithm is utilized to calculate $L_A(f,z,\mathrm{\γ})=E\left(z\right)+{\mathrm{\γ}}^T(z-Cf)+\frac{\mathrm{\μ}}{2}\left|\right|z-Cf|{|}_2^2$ Saddle point, obtain super-resolution result.

Further, described step S46 also comprises: structure iterative loop, is brought in iterative loop by the result of each iteration, the iteration termination when root-mean-square error between twice iteration is less than 0.01, obtains the target distribution of accurate scene.

The useful effect of the present invention: a kind of augmentation Lagrange real Beam radar angle super-resolution processing method of the present invention, convolution model according to real wave beam, under the framework of canonical, set up objective function also introduce the total variation operator making angle super-resolution result more level and smooth, simultaneously, utilize Augmented Lagrange method to realize solving of constrained optimization problem, derive and calculate target scattering coefficient f_kLoop iteration solving equation, it is achieved real beam angle super-resolution. Thus solve conventional angular ultra-resolution method cannot the difficult problem of accurate recovery of realize target amplitude. The present invention not only overcomes the low problem of the real Beam radar angular resolution of tradition; And by introducing total variation operator under the framework of canonical, the precision of target scattering strength, positional information can be ensured when being processed by bearing signal; Introduce the parameter of noise variance simultaneously, avoid the noise scale-up problem in classical inverse convolution method; The method that the present invention proposes can be applied to the fields such as precise guidance, the knowledge of enemy and we's target, space exploration.

Accompanying drawing explanation

Fig. 1 is the inventive method FB(flow block);

Fig. 2 is the real beam scanning radar imaging system structure iron that the specific embodiment of the invention adopts;

Fig. 3 is target scene distribution schematic diagram in emulation experiment;

Fig. 4 is under different signal to noise ratio, the test-results of real beam scanning radar echo signal and use the present invention. The real beam scanning radar echo signal that wherein (a) (b) is respectively under signal to noise ratio 25dB and 15dB, the present invention that (c) and (d) is respectively under signal to noise ratio 25dB and 15dB proposes the result of algorithm.

As can be seen from Figure 4, method provided by the invention can significantly improve real beam scanning radar bearing angular resolution, it is achieved angle super-resolution. Imaging results is keeping having good effect in target location information and amplitude information.

Embodiment

Understand the technology contents of the present invention for ease of those skilled in the art, below in conjunction with accompanying drawing, content of the present invention is explained further.

Being illustrated in figure 1 the solution of the present invention schema, the technical scheme of the present invention is: a kind of augmentation Lagrange real Beam radar angle super-resolution processing method, comprising:

S1, radar imaging system parameter initialization, be specially: the real Beam radar imaging process according to Fig. 2, and the system emulation parameter of foundation shown in table 1, initialization system parameter.

Relate to real beam scanning radar imaging system parameter as follows: Texas tower radial motion speed, is designated as ��; Motion platform height, is designated as h; Radar scanner sweep velocity, is designated as ��; The radar scanner wave beam angle of pitch, is designated as; Texas tower starting position, be designated as (0,0, h), pulse repetition time, it is designated as PRI; Echoed signal orientation, to sampling number, is designated as N; Echoed signal distance is counted to echo samples, is designated as N_r; In initial moment antenna and scene, the oblique distance of target, is designated as R₀; The position angle of target opposed platforms, is designated as ��; Owing in motion platform scanning imagery process, podium level does not change, therefore cause, in analysis motion, the impact that height can be ignored when relative distance changes between platform and target.

In three-dimensional cartesian coordinate system as shown in Figure 2, taking xoy as horizontal plane, radar scanning direction comprises: the scanning direction up and down being perpendicular to xoy plane, and is parallel to the lateral probe movement direction of xoy plane.

The orientation time vector of scanned radar imaging region is designated as T_a=[-PRI N/2 ,-PRI (N/2-1) ..., PRI (N/2-1)]; Distance Time vector is designated as T_r=[-1/f_r��N_r/2,-1/f_r��(N_r/2-1),��,1/f_r��(N_r/ 2-1)], wherein, f_rFor distance is to sampling rate.

Table 1 system emulation parameter list

Parameter	Symbol	Numerical value
			Carrier frequency	fc	10GHz
Width when launching signal	T	2��s
			Transmitted signal bandwidth	B	40MHz
Podium level	h	1Km
			Pulse-repetition frequency	PRF	2000Hz
Antenna sweep velocity	��	60��/s
			Antenna beamwidth	��	3��
Sweep limit	��	-4 �㡫4 ��

The simulation imaging scene that this example adopts is as shown in Figure 3.

S2, echo data, along distance to pulse compression, achieve distance to high resolution by pulse compression technology, are specially: be that the system parameter after chirp signal and initialize generates two dimension echoed signal according to launching signal.

Radar emission signal is chirp signal, is designated as $s\left(t\right)=rect\left(\frac{t}{T}\right)\·\exp (j2{\mathrm{\πf}}_{c}t+{\mathrm{j\πk}}_f{t}^2);$

Wherein, rect () represents rectangle function, width when T represents transmit signal pulse, f_cRepresent carrier frequency, k_fRepresenting chirp rate, t represents that distance is to the fast time.

For distance R same in imaging region₀The different azimuth target at place, it is assumed that in scanning area, each orientation sampling point all has target to exist, and the location parameter of each sampling point is designated as ��=(��₁,��₂,����_N), range parameter is designated as f=(f₁,f₂,��,f_N), then target echo signal after coherent demodulation can represent and is:

$S(t,\mathrm{\τ})=\underset{n=1}{\overset{N_r}{\Σ}}{f}_n\·h({\mathrm{\θ}}_n,\mathrm{\τ})\·rect(t-\frac{2R_0}{c})\·\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_0)\·\exp \left(j\mathrm{\π}k{\[t-\frac{2R_0}{c}\]}^2\right)---\left(1\right)$

Wherein, h () is for orientation is to antenna pattern convolution function, and c is the light velocity, equals 3 �� 10⁸m/s��

Subsequently, distance is constructed to matched filter frequency matching function at frequency domainCarrying out distance to processed compressed according to this frequency matching function at echo S (t, ��) of frequency domain and formula (1), obtaining the two-dimensional time-domain signal after pulse compression is:

$s_2(t,\mathrm{\τ})\≈\underset{n=1}{\overset{N}{\Σ}}{f}_n\·h({\mathrm{\θ}}_n,\mathrm{\τ})\·\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_0)\·\sin c\[B(\mathrm{\τ}-\frac{2R_0}{c})\]---\left(2\right)$

S3, orientation, to echo modeling, are specially: according to radar system parameter and actual imaging scene structure two dimension target distribution matrix ��, echoed signal is carried out sliding-model control simultaneously and obtainFinally according to ��,Matrix and the vector expression-form of scanning imagery process is constructed with convolution matrix.

It is specially: the two-dimentional echoed signal s that step S2 is obtained₂(t, ��) carries out discrete processes, obtains two dimension echoed signal convolution model:

Wherein,Target is represented respectively in distance to position and orientation to angle information, N with ��_rWith N represent respectively scene distance to orientation to discrete sampling number,RepresentThe scattering coefficient of Place object,For two dimension convolution model, n_rRepresent scattering coefficientIn distance to positionSumming function subscript, and n_r=1,2,3 ..., N_r, n represents scattering coefficientIn orientation to the summing function subscript of angle, ��, and n=1,2,3 ..., N,Represent convolution.

In distance upwards, echoed signal is the convolution between the sinc function after target scattering coefficient and pulse compression, and in orientation upwards, echoed signal is the convolution between target scattering coefficient and antenna pattern, therefore, the two-dimensional imaging scene areas �� of discretize can represent and is:

Owing to pulse compression technology has achieved distance to high resolution, therefore, existing method is all improve orientation to angular resolution by signal processing, for the ease of process as, whole imaging process is write the form of matrix vector. First, image scene region two dimension matrix �� is carried out vector quantities operation, obtains target distribution vector f=vec (��):

Echoed signal being carried out vectorization, the discrete convolution equation obtained with reason, be echoed signal vector g, expression formula is as follows:

G=Hf+n (6)

Wherein,For carrying out the echoed signal after vectorization,For the noise signal after vector quantities operation, H is dimension is NN_r��NN_rMatrix, expression formula is such as formula shown in (7):

H_iFor antenna pattern andThe convolution imaging model of the imaging region of individual range unit, H_iThe convolution imaging process being respectively classified as between antenna with corresponding target, and, i=1,2,3 ... N_r, H_iExpression formula such as formula shown in (8):

Wherein,For the antenna pattern weighting coefficient of correspondence position.

S4, Augmented Lagrange method solve deconvolution problem, are specially: according to the echoed signal of formula (6) vector g, under the framework of canonical, introduce total variation operator | | Lf | |₁, convolution inverse problem is converted into the constrained optimization problem solving following formula,

$\begin{array}{cc}\underset{f}{\arg \min }\mathrm{\λ}\left|\right|Lf|{|}_1& subjectto:\left|\right|g-Hf|{|}_2^2\≤\mathrm{\ϵ}\end{array}---\left(9\right)$

Wherein,�� is regularization parameter, for balancing error term and penalty term, introduces total variation operator | | Lf | |₁Making to make result more level and smooth while improving azimuthal resolution, the noise scale-up problem in classical inverse convolution method, for depending on the parameter of noise variance, is avoided in �� >=0.

Formula (9) of equal value can be converted into the unconstrained optimization problem of following formula

$\underset{f}{\arg \min }\mathrm{\λ}\left|\right|Lf|{|}_1+\frac{1}{2}||g-Hf|{|}_2^2---\left(10\right)$

Introduce convex function ${\mathrm{\θ}}_1\left(f\right)=\mathrm{\λ}\left|\right|Lf|{|}_1,{\mathrm{\θ}}_2\left(Hf\right)=\frac{1}{2}||g-Hf|{|}_2^2,$ Formula (10) unconstrained optimization problem is converted into

$\underset{f}{\arg \min }\{{\mathrm{\θ}}_1\left(Lf\right)+{\mathrm{\θ}}_2\left(Hf\right)\}---\left(11\right)$

Introduce subsidiary variable again $z=\left[\begin{array}{c}u\\ v\end{array}\right],$ ? $z=\left[\begin{array}{c}H\\ L\end{array}\right]f$ Under condition limits, formula (11) equivalence is converted into

$\begin{array}{cc}\underset{f,z}{\arg min}\{{\mathrm{\θ}}_1\left(v\right)+{\mathrm{\θ}}_2\left(u\right)\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f\end{array}---\left(12\right)$

Wherein, u=Hf, v=Lf. Formula (12) is expressed from the next

$\begin{array}{cc}\arg \underset{f,u,v}{min}\{E(f,u,v)=\mathrm{\λ}|\left|v\right|{|}_1+\frac{1}{2}\left|\right|g-u\left|{|}_2^2\right\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f\end{array}---\left(13\right)$

Introduce function E (z) and z=Cf, $C=\left[\begin{array}{c}H\\ L\end{array}\right],$ Optimization problem in formula (13) is converted into

$\begin{array}{cc}\underset{z}{\arg min}E\left(z\right)& subjectto:z=Cf\end{array}---\left(14\right)$

The problems referred to above are converted into and seek the saddle point such as minor function by recycling Augmented Lagrange method

$L_A(f,z,\mathrm{\γ})=E\left(z\right)+{\mathrm{\γ}}^T(z-Cf)+\frac{\mathrm{\μ}}{2}\left|\right|z-Cf|{|}_2^2---\left(15\right)$

Wherein,Represent Lagrange coefficient vector,It is two norms,For the vector arranged about the coherent element of u in Lagrange coefficient vector,For the vector arranged about the coherent element of v in Lagrange coefficient vector, in order to calculate simplicity, formula (15) can arrange and be

$L_A(f,z,\mathrm{\γ})=E\left(z\right)+\frac{\mathrm{\μ}}{2}\left|\right|z-Cf-\mathrm{\η}|{|}_2^2+const---\left(16\right)$

Wherein,For the new Lagrangian coefficient vector independent with f and z phase,For the vector that coherent element about u in new Lagrangian coefficient vector arranges,For the vector that coherent element about v in new Lagrangian coefficient vector arranges, constant

The saddle point of function shown in recycling iterative algorithm calculating formula (16), iterative computation formula is as follows

$f_{k+1}=\underset{f}{\arg \min }\left|\right|z_k-Cf-{\mathrm{\η}}_k|{|}_2^2---\left(17\right)$

$z_{k+1}=\underset{z}{\arg \min }E\left(z\right)+\frac{\mathrm{\μ}}{2}\left|\right|z-{\mathrm{Cf}}_{k+1}-{\mathrm{\η}}_k|{|}_2^2---\left(18\right)$

��_k+1=��_k-(z_k+1-Cf_k+1)(19)

Wherein, k and k+1 is iteration number of times, and formula (17) can be converted into as shown in the formula general equation

C^TCf=C^T(z_k+��_k)(20)

Formula (20) can equivalently be converted into again

(H^TH+L^TL) f=H^T[u_k+(��_u)_k]+[v_k+(��_v)_k](21)

Wherein, u_k=Hf_k, v_k=Lf_k��

Owing to H is BlockToeplitz matrix, utilizing priori conditions method of conjugate gradient, the efficient solution of formula (21) can be calculated by following formula

$f=F^{-1}\left\{\frac{F{\left(H\right)}^{T}F\[u_k+{\left({\mathrm{\η}}_u\right)}_k\]+F\[v_k+{\left({\mathrm{\η}}_v\right)}_k\]}{F{\left(H\right)}^{T}F\left(H\right)+F{\left(L\right)}^{T}F\left(L\right)}\right\}---\left(22\right)$

Wherein, F is Fourier transform operator.

Due to the special construction of E (z) He C, formula (18) can by being separated into following two formulas

$u_{k+1}=\underset{u}{\arg min}\left\{\frac{1}{2}\right||g-u|{|}_2^2+{\left({\mathrm{\γ}}_u^T\right)}_k(u-{\mathrm{Hf}}_{k+1})+\frac{\mathrm{\μ}}{2}\left|\right|u-{\mathrm{Hf}}_{k+1}\left|{|}_2^2\right\}---\left(23\right)$

$v_{k+1}=\underset{v}{\arg min}\left\{\mathrm{\λ}\right|\left|v\right|{|}_1+{\left({\mathrm{\γ}}_v^T\right)}_k(v-f_{k+1})+\frac{\mathrm{\μ}}{2}\left|\right|v-f_{k+1}\left|{|}_2^2\right\}---\left(24\right)$

Formula (23) is separate with formula (24). Its Chinese style (23) is for quadratic equation and there is closed solution, is shown below

u_k+1=(1+ ��)^-1[��Hf_k+1+g-(��_u)_k](25)

Formula (24) can be solved by shrinkage equation, as shown in the formula

$\begin{array}{c}{v}_{k+1}={\mathrm{shrink}}_{\frac{\mathrm{\λ}}{\mathrm{\μ}}}\[v_k-f_{k+1}-{\left({\mathrm{\η}}_v\right)}_k\]\\ =\frac{v_k-f_{k+1}-{\left({\mathrm{\η}}_v\right)}_k}{\left|\right|v_k-f_{k+1}-{\left({\mathrm{\η}}_v\right)}_k|{|}_2}\×\max \left\{\left|\right|v_k-f_{k+1}-{\left({\mathrm{\η}}_v\right)}_k|{|}_2-\frac{\mathrm{\λ}}{\mathrm{\μ}},0\right\}\end{array}---\left(26\right)$

Wherein, parameter ��_uWith parameter ��_vIteration renewal is carried out by following formula.

(��_u)_k+1=(��_u)_k-(u_k+1-Hf_k+1)(27)

(��_v)_k+1=(��_v)_k-(v_k+1-f_k+1)(28)

According to formula (17), (19), (23), (24), (27) and (28) structure iterative loop, and the result of each iteration is brought in iterative loop, convolution inversion result Step wise approximation is made to be really the target distribution of scene, specifically it is judged as: the iteration termination when root-mean-square error between twice iteration is less than 0.01, obtains the target distribution of accurate scene; Again result is remapped in original two dimensional echoed signal after processing. When different signal to noise ratio, the correspondence of result is along orientation to sectional view as shown in Figure 4, the real beam scanning radar echo signal that wherein (a) (b) is respectively under signal to noise ratio 25dB and 15dB, the present invention that (c) and (d) is respectively under signal to noise ratio 25dB and 15dB proposes the result of algorithm.

As can be seen from Figure 4, method provided by the invention can significantly improve real beam scanning radar bearing angular resolution, it is achieved angle super-resolution. Imaging results is keeping having good effect in target location information and amplitude information.

The innovative point of the present invention is at the convolution model according to real wave beam, under the framework of canonical, set up objective function also introduce the total variation operator making angle super-resolution result more level and smooth, meanwhile, utilize Augmented Lagrange method to realize solving of constrained optimization problem, derive and calculate target scattering coefficient f_kLoop iteration solving equation, it is achieved real beam angle super-resolution; Thus solve conventional angular ultra-resolution method cannot the difficult problem of accurate recovery of realize target amplitude.

The those of ordinary skill of this area, it will be appreciated that embodiment described here is the principle in order to help reader understanding the present invention, should be understood to that protection scope of the present invention is not limited to such special statement and embodiment. For a person skilled in the art, the present invention can have various modifications and variations. Within the spirit and principles in the present invention all, any amendment of doing, equivalent replacement, improvement etc., all should be included within the right of the present invention.

Claims (5)

1. an augmentation Lagrange real Beam radar angle super-resolution processing method, it is characterised in that, comprising:

S1, initialization system parameter;

S2, according to after radar emission signal and step S1 initialize system parameter generate two dimension echoed signal;

S3, the matrix that distributed by the two dimension target of discretize, echoed signal matrix are arranged as vector form according to each range unit order, obtain two dimension target distribution vector and echoed signal vector;

S4, the echoed signal vector obtained according to step S3, under the framework of canonical, introduce total variation operator, and establishing target function, utilizes Augmented Lagrange method to solve objective function, obtains scene objects distribution results.

2. a kind of augmentation Lagrange according to claim 1 real Beam radar angle super-resolution processing method, it is characterised in that, described step S2 specifically comprises step by step following:

S21, described radar emission signal are chirp signal;

S22, frequency domain construct distance to matched filter frequency matching function;

S23, the frequency matching function obtained according to step S22, carry out distance to processed compressed to the chirp signal of step S21, obtains two dimension echoed signal.

3. a kind of augmentation Lagrange according to claim 1 real Beam radar angle super-resolution processing method, it is characterised in that, described step S3 comprises:

S31, the two-dimentional echoed signal obtained by step S2 carry out discrete processes, obtain two dimension echoed signal convolution model;

S32, by image scene discrete region process, obtain two dimension matrix ��;

S33, to two dimension matrix �� carry out vector operation, obtain target distribution vector f=vec (��);

Noise signal n after S34, target distribution vector f=vec (��) obtained according to step S33 and vectorization, the two-dimentional echoed signal convolution model obtained by step S31 carries out vector operation, obtains echoed signal vector.

4. a kind of augmentation Lagrange according to claim 1 real Beam radar angle super-resolution processing method, it is characterised in that, described step S4 comprises:

S41, under the framework of canonical, introduce total variation operator, obtain constrained optimization problem according to the echoed signal vector that step S3 obtains,

$\begin{array}{cc}\underset{f}{\arg min}\mathrm{\λ}\left|\right|Lf|{|}_1& subjectto:\left|\right|g-Hf|{|}_2^2\≤\mathrm{\ϵ}\end{array};$

Wherein, | | | |₁Represent L₁Norm, | | | |₂Represent L₂Norm, �� is the parameter depending on noise variance, and �� >=0;

S42, introducing convex function ��₁(f)=�� | | Lf | |₁WithBy constrained optimization problem

$\begin{array}{cc}\underset{f}{\arg min}\mathrm{\λ}\left|\right|Lf|{|}_1& subjectto:\left|\right|g-Hf|{|}_2^2\≤\mathrm{\ϵ}\end{array}$ It is converted into:

$\underset{f}{\arg min}\{{\mathrm{\θ}}_1\left(Lf\right)+{\mathrm{\θ}}_2\left(Hf\right)\};$

S43, introducing subsidiary variable $z=\left[\begin{array}{c}u\\ v\end{array}\right],$ ? $z=\left[\begin{array}{c}H\\ L\end{array}\right]$ Under f condition limits, will $\underset{f}{\arg \min }\{{\mathrm{\θ}}_1\left(Lf\right)+{\mathrm{\θ}}_2\left(Hf\right)\}$ It is converted into:

$\begin{array}{cc}\underset{f,z}{\arg min}\{{\mathrm{\θ}}_1\left(v\right)+{\mathrm{\θ}}_2\left(u\right)\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f\end{array};$

Wherein, u=Hf, v=Lf;

Then will $\begin{array}{cc}\underset{f,z}{\arg min}\{{\mathrm{\θ}}_1\left(v\right)+{\mathrm{\θ}}_2\left(u\right)\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f\end{array}$ It is converted into:

$\begin{array}{cc}\arg \underset{f,u,v}{min}\{E(f,u,v)=\mathrm{\λ}|\left|v\right|{|}_1+\frac{1}{2}\left|\right|g-u\left|{|}_2^2\right\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f\end{array};$

S44, introducing function E (z) and z=Cf, obtain step S43

$\begin{array}{cc}\arg \underset{f,u,v}{min}\{E(f,u,v)=\mathrm{\λ}|\left|v\right|{|}_1+\frac{1}{2}\left|\right|g-u\left|{|}_2^2\right\}& subjectto:\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}H\\ F\end{array}\right]f\end{array}$ It is converted into:

$\begin{array}{cc}\underset{z}{\arg \min }E\left(z\right)& subjectto:z=Cf\end{array};$

Wherein, $C=\left[\begin{array}{c}H\\ L\end{array}\right];$

S45, employing Augmented Lagrange method, obtain step S44Subjectto:z=Cf is converted into and seeks the saddle point such as minor function:

$L_A(f,z,\mathrm{\γ})=E\left(z\right)+{\mathrm{\γ}}^T(z-Cf)+\frac{\mathrm{\μ}}{2}\left|\right|z-Cf|{|}_2^2$

Wherein,For Lagrange coefficient vector,It is two norms,For the vector arranged about the coherent element of u in Lagrange coefficient vector,For the vector arranged about the coherent element of v in Lagrange coefficient vector;

S46, iterative algorithm is utilized to calculate $L_A(f,z,\mathrm{\γ})=E\left(z\right)+{\mathrm{\γ}}^T(z-Cf)+\frac{\mathrm{\μ}}{2}\left|\right|z-Cf|{|}_2^2$ Saddle point, obtain super-resolution result.

5. a kind of augmentation Lagrange according to claim 4 real Beam radar angle super-resolution processing method, it is characterized in that, described step S46 also comprises: structure iterative loop, the result of each iteration is brought in iterative loop, iteration termination when root-mean-square error between twice iteration is less than 0.01, obtains the target distribution of accurate scene.