CN103487802B - Scanning radar angle super-resolution imaging method - Google Patents

Abstract

The invention discloses a scanning radar angle super-resolution imaging method. The scanning radar angle super-resolution imaging method comprises the following steps that a backward model for real beam scanning radar angle super-resolution imaging is established according to the Bayesian theory, the likelihood function relationship between a target and an echo and prior information of the target are respectively expressed through the Poisson distribution and the Laplace distribution in the model, radar angle super-resolution imaging is expressed as a posterior probability problem existing between the target and the echo, finally, according to the convex optimization theory, based on the nonlinear optimization method and approximate treatment, the target information corresponding to the maximum posterior probability is solved, and radar angle super-resolution imaging is achieved through target information reconstruction. By the adoption of the scanning radar angle super-resolution imaging method, super resolution of multiple targets in a real beam can be achieved.

Description

Scanning radar angle super-resolution imaging method

Technical field

The invention belongs to radar imaging technology field, particularly Airborne Pulse Doppler Radar forward sight scan angle super-resolution imaging method.

Technical background

Radar has the ability of round-the-clock, all weather operations, plays an important role in civil and military fields such as earth observation, aircraft lands, target identifications.

Scanning radar refers to that radar beam even or non-homogeneous scanning in orientation is detected region, the time order and function relation of target in scene is skimmed over by radar antenna wave beam, to the process of echoed signal, obtaining the scattered information of target on dimensional orientation, reaching the super-resolution imaging to being detected region.Because scanning radar is only by changing radar beam radiation modality over the ground, the method for signal transacting is utilized to realize radar angle super-resolution imaging.Thus, the radar of this mode of operation has broad application prospects in dual-use field.Such as, automatically accurate spacecrafts rendezvous, the unmanned plane independent landing etc. of spacecraft.Scanning radar angle super-resolution imaging be echo data Accurate Reconstruction to aiming field and recover high-frequency information realize, this reconstruct is the ill-conditioning problem in mathematical meaning, does not realize said process by simple inversion operation.Therefore, realize scanning radar angle super-resolution imaging and first ill-conditioning problem will be changed into good state problem, and realize the Exact Solution of good state problem on this basis, final antenna parameter of breaking through is to the restriction of radar image angular resolution.

The angular resolution of antenna wherein, λ represents radar wavelength, and D represents antenna aperture size, λ and D is same unit.It can thus be appreciated that radar antenna angular resolution is subject to the restriction of ripple and antenna aperture parameter, therefore need to adopt corresponding signal processing method, break through the systematic parameter that relates in above-mentioned formula to the restriction of radar angular resolution, realize angle super-resolution imaging.The method of radar angular resolution is improved under document " Miller C S.Enhanced angle resolution in scanning beam systems [C] Aerospace Applications Conference; 1995.Proceedings.; 1995IEEE.IEEE; 1995:333-341 " proposes beam scanning, the method at least uses the data of two passages, Deconvolution Method is adopted to improve radar angular resolution at frequency domain, deconvolution problem pathosis inherently, can affect the performance of algorithm greatly; In document " Richardson W H.Bayesian-based iterative method of image restoration [J] .JOSA; 1972; 62 (1): 55-59 ", a kind of Deconvolution Method based on bayesian theory is proposed, when the method is used for realizing scanning radar imaging, better for single-point target effect; During for Area Objects imaging, because adopt ignorant distribution to describe target prior imformation, noise can be caused to amplify, cause the phenomenons such as angular resolution is low, target location skew, amplitude distortion, false target, do not improve the angular resolution of radar.These phenomenons bring adverse influence all can to the detection of target, location, identification.

Summary of the invention

The present invention is directed to the technological deficiency of the method existence introduced in background technology, propose a kind of new Deconvolution Method.The method breaches the restriction of radar antenna parameter to radar image angular resolution, solves the problem that radar image angular resolution that existing angle super-resolution imaging method causes because of pathosis is low, achieves scanning radar angle super-resolution imaging.

Detailed content of the present invention for convenience of description, first provides the definition of following term:

Term 1: radar angle super-resolution

Radar angle super-resolution refers to the method by signal transacting, breaks through radar antenna system parameter to the restriction of radar image angular resolution.

Term 2: scanning radar

Scanning radar, refers to the mode by mechanical rotation, makes radar beam in orientation, uniformly or non-uniformly scan a kind of radar of ground, ocean or extraterrestrial target.

Term 3: convex optimization

Convex optimization is optimum theory, refers to and meets simultaneously: objective function is convex function; Bound variable integrates the constrained optimization problem as convex set.

Term 4: likelihood function

Likelihood function is a kind of function about parameter in statistical model, the change of functional value during reflection Parameters variation.If sample space Θ obeys distribution represent solve for parameter, X ₁, X ₂... X _nthe sample from Θ, x ₁, x ₂... x _nx ₁, X ₂... X _nobserved reading, then the joint distribution of sample be called likelihood function.

The invention provides a kind of scanning radar angle super-resolution imaging method, concrete steps are as follows:

Step one: echo data distance is to pulse compression

It is as follows that echo data distance relates to radar imaging system parameter to pulse compression: Texas tower movement velocity, is designated as V; The radar antenna wave beam angle of pitch, is designated as θ; Transmit carrier frequency, is designated as f _c; Texas tower initial position, be designated as (0,0, z), pulse-recurrence time, be designated as PRI; Scene echoes distance, to sampling number, is designated as N _r; Imaging scene echoes orientation, to sampling number, is designated as N _a; Be positioned at the distance of (x, y) place target in t Texas tower and scene, be designated as R (x, y, t); wherein, R ₀for the oblique distance of target in initial time antenna and scene, for the position angle of target.In order to theory narrative is corresponding with actual verification, the present invention carries out discrete processes at will adjust the distance time and orientation time.

The orientation time arrow of scanning radar imaging region is designated as T _a=[-PRIN _a/ 2 ,-PRI (N _a/ 2-1) ..., PRI (N _a/ 2-1)]; Distance Time vector T _r=[-1/f _sn _r/ 2 ,-1/f _s(N _r/ 2-1) ..., 1/f _s(N _r/ 2-1)], wherein f _sfor distance is to sampling rate.Radar emission signal is designated as wherein, rect () represents rectangular function, T _pwide during expression transponder pulse, f _crepresent carrier frequency, k represents chirp rate, and τ represents fast time variable.The echo of imaging region Ω can be expressed as to transmit and add the result of noise with the convolution of target.For imaging region Ω, the analytical expression of echo can be write as:

$g_1(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\∫\∫}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_{a_0}}{T_{\mathrm{\β}}}\right)\·s(\mathrm{\τ}-\frac{2\·R(x,y,t)}{c})\mathrm{dxdy}+N_1(\mathrm{\τ},\mathrm{\η})---\left(1\right)$

Wherein, Ω represents imaging region; (x, y) represents the position of target in scene; F (x, y) represents point (x, y) place target scattering function; η represents slow time variable; ω _arepresent slow time domain window function, represent the modulation of orientation to antenna radiation pattern function; represent antenna azimuth initial time; T _βrepresent that target is at 3dB antenna beamwidth residence time; C represents propagation velocity of electromagnetic wave; N ₁(τ, η) represents the noise in echo.

(1) is expressed as following discrete form:

$g_2(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_{a_0}}{T_{\mathrm{\β}}}\right)\·s(\mathrm{\τ}-\frac{2\·R(x,y,t)}{c})+N_2(\mathrm{\τ},\mathrm{\η})---\left(2\right)$

Wherein, ∑ represents summation operation, N ₂(τ, η) represents N in (1) formula ₁(τ, η) form after discrete processes.According to distance to reference time τ _refwith the chirp rate k that transmits, structure distance is to pulse pressure reference signal again by s _refwith echo data g ₂(τ, η) carries out maximum auto-correlation computation, realizes echoed signal in distance to pulse compression.Signal after pulse compression can be expressed as:

$\begin{array}{c}{g}_3(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_{{\mathrm{\α}}_0}}{T_{\mathrm{\β}}}\right)\·\exp \{-j4\mathrm{\π}{f}_c\frac{R(x,y,t)}{c}\}\\ \·\sin c\left\{B\right[\mathrm{\τ}-\frac{2\·R(x,y,t)}{c}\left]\right\}+N_3(\mathrm{\τ},\mathrm{\η})\end{array}---\left(3\right)$

Wherein, B represents transmitted signal bandwidth, N ₃(τ, η) represents data g ₂(τ, η) noise after pulse pressure process;

Step 2: Range Walk Correction,

The distance of point (x, y) in imaging scene areas Ω between moment t and Texas tower is due to the variable that distance R (x, y, t) is about the time, being operated in that this step completes mathematically is characterized by: eliminate the impact of time variable t on Texas tower and target range function.

At t=0 place, Taylor series once item expansion is carried out to R (x, y, t).Again because θ with less, so cos θ ≈ 1.The distance function of Texas tower and target can be expressed as: R (x, y, t) ≈ R ₀-Vt.Realize Range Walk Correction, need to obtain Texas tower speed V, time t by inertial navigation equipment.On this basis, to data g ₃(τ, η) carries out change of scale and to move the range migration caused to eliminate Texas tower, can obtain:

$\begin{array}{c}{g}_4(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_{{\mathrm{\α}}_0}}{T_{\mathrm{\β}}}\right)\·\exp \{-j4\mathrm{\π}{f}_c\frac{R(x,y,t)}{c}\}\\ \·\sin c\left\{B\right[\mathrm{\τ}-\frac{2\·R_0}{c}\left]\right\}+N_3(\mathrm{\τ},\mathrm{\η})\end{array}---\left(4\right)$

Step 3: scanning radar angle super-resolution modeling,

Orientation is to the acquisition of signal echo data, and the convolution results being expressed as antenna and target by forward model adds noise.Be designated as:

g＝Hf+n (5)

Wherein, vector implication is: with each behavior unit according to lexicographic order by g ₄be arranged in a row vector, then carrying out matrix transpose operation, to form a length be N _rn _acolumn vector, g _i(i=1,2 ..., N _rn _a) be expressed as arranging according to lexicographic order as scene objects, the echo data of i-th processing unit, () ^trepresent and transposed transform is carried out to bracket interior element, g ₄represent data g in (4) formula ₄(τ, η) matrix after discrete processes.The present invention, when processing echo data, supposes g _i(i=1,2 ... N _rn _a) obey independent same distribution.

Matrix H represents radar directional pattern information matrix.According to the sampling number to antenna main lobe of system parameter setting, radar directional pattern information matrix H is arranged in following manner.

Wherein, represent at orientation time arrow T _athe sampled point of a middle jth moment antenna.

F is expressed as picture scene information, arranges line by line according to lexicographic order, then entering matrix transpose operation, to form a length be N _rn _acolumn vector, be designated as f _i(i=1,2 ... N _rn _a) obey independent same distribution; represent the noise vector in data, n _i(i=1,2 ... N _rn _a) between meet independent same distribution.

The present invention sets up the rear to model of scanning radar angle super-resolution imaging under bayesian theory, under the prerequisite of the statistical nature of known g, H and noise n, solve f.

The data directly related with target in echo in orientation have sparse feature, and the research object in view of Poisson distribution function is for the lower small probability event of large sample experiment.Therefore, Poisson distribution is used to describe the likelihood function relation of target and echo data here, that is,

$p\left(g\right|f)=\underset{k=1}{\overset{N_r\·N_a}{\mathrm{\Π}}}p\left(g_k\right|f_k)=\underset{k=1}{\overset{N_r\·N_a}{\mathrm{\Π}}}\{\frac{{\left[{\left(\mathrm{Hf}\right)}_k\right]}^{g_k}}{\left(g_k\right)!}\·\exp [-{\left(\mathrm{Hf}\right)}_k\left]\right\}---\left(6\right)$

Wherein, represent and bracket interior element is carried out from 1 to N _rn _aproduct calculation, (Hf) _krepresent that antenna array H is to target f in scene _k(k=1,2 ... N _rn _a) response, ()! Represent and continued product computing is carried out to bracket interior element.

Under bayesian theory, another remarkable advantage of modeling has merged prior imformation.Therefore, probability of use distribution function is also needed to characterize the prior imformation of target to model after the scanning radar angle super-resolution imaging in the present invention.Due to openness relative to imaging background of target, this model adopts the prior imformation of laplacian distribution function representation target.That is,

$p\left(f\right)=\underset{k=1}{\overset{N_r\·N_a}{\mathrm{\Π}}}\frac{1}{2\mathrm{\β}\·}\exp (-\frac{\left|f_k\right|}{\mathrm{\β}})---\left(7\right)$

Wherein, β represents scale parameter, || represent signed magnitude arithmetic(al).

P (g|f) and p (f) is substituted into total probability formula p (f|g) ∝ p (g|f) p (f), ∝ and represent proportional relation, and f corresponding when asking posterior probability maximum _mAP, by negative log-transformation, will f be solved _mAPchange into the globally optimal solution of following objective functions.Be minimum value about variable f due to what solve, eliminating the variable irrelevant with f can obtain,

$f_{\mathrm{MAP}}=\underset{f}{\arg \min }\{g\·\ln \left(\mathrm{Hf}\right)-\mathrm{Hf}+{\mathrm{\λ}}_r\·{\left|\right|f\left|\right|}_1\}---\left(8\right)$

Wherein, λ _rrepresent regular parameter, the weight of this Parametric Representation likelihood and priori, || || ₁represent the l under Euclidean distance meaning ₁norm;

Step 4: scanning radar angle super-resolution imaging,

On the basis of completing steps triangle super-resolution modeling, this step will realize solving of (8).Non-linear and containing non-differentiability because (8) have about f || f|| ₁, so traditional method based on gradient cannot realize f _mAP.For these difficult points, first this step adopts following approximate processing:

${\left|\right|f\left|\right|}_1\≈\underset{i=1}{\overset{N_r\·N_a}{\mathrm{\Σ}}}\sqrt{{\left|\left(f_i\right)\right|}^2+\mathrm{\ϵ}}---\left(9\right)$

Wherein, ε >0 represents a very little number, and its effect prevents from occurring in iterative process that can find out, " very little number " here to those skilled in the art, its implication is clearly except zero.

(9) brought into (8) and carry out abbreviation, can obtain:

$f_{\mathrm{MAP}}=\underset{f}{\arg \min }\{g\·\ln \left(\mathrm{Hf}\right)-\mathrm{Hf}+{\mathrm{\λ}}_r\·\left(\underset{i=1}{\overset{N_r\·N_a}{\mathrm{\Σ}}}\sqrt{{\left|\left(f_i\right)\right|}^2+\mathrm{\ϵ}}\right)\}---\left(10\right)$

About variable f, gradient is asked to objective function in (10), can obtain:

$\▿\left(f\right)={\left(H\right)}^T\·\left(\frac{g}{H\·f}\right)-{\left(H\right)}^T\·I+{\mathrm{\λ}}_r\·\mathrm{\Λ}\left(f\right)\·f---\left(11\right)$

Wherein, diag () represents that generation main diagonal element is the diagonal matrix of vector in bracket successively.

Make (11) to equal zero and operation is normalized to aerial information matrix rows, that is, (H) ^ti=I.Here I represents that element is a column vector of numerical value 1 entirely, and if do not illustrated, after this, the meaning that I represents as previously mentioned, can obtain:

${\left(H\right)}^T\·\left(\frac{g}{H\·f}\right)+{\mathrm{\λ}}_r\·\mathrm{\Λ}\left(f\right)\·f=I---\left(12\right)$

On the basis of (12), this step constructs following iterative process:

$f_{n+1}=f_n\·[{\left(H\right)}^T\·\left(\frac{g}{H\·f_n}\right)+{\mathrm{\λ}}_r\·\mathrm{\Λ}\left(f_n\right)\·f_n]---\left(13\right)$

Wherein, f _nand f _n+1represent n-th time and (n+1)th iteration result respectively.When iterations equals the number of times preset, iteration terminates, using the result of iteration as scanning radar angle super-resolution imaging result.

Beneficial effect of the present invention: the present invention sets up the rear to model of radar angle super-resolution imaging under Bayesian frame, under Bayesian frame, an advantage of Modling model is the prior imformation that effectively can merge target, rear set up to model time, use the likelihood function relation of Poisson distribution function representation target and echo.The present invention is openness relative to what distribute under imaging background according to target, adopt the prior imformation of laplacian distribution function representation target scattering, by backward model, radar angle super-resolution imaging precise translation is become maximum a posteriori probability problem, by realize posterior probability maximum time target information reconstruct, complete radar angle super-resolution imaging.

Method of the present invention when realizing radar angle super-resolution first for objective function in containing l ₁the function item approximate processing of norm, makes objective function meet differentiability; Secondly, method of the present invention use convex optimum theory to construct global minimum that nonlinear multiplicative iterative manner realizes non-linear objective function solves, reconstruct target information realizes radar angle super-resolution imaging.Feature of the present invention is to use non-linear objective function to describe linear radar angle super-resolution model, and uses nonlinear optimization method to construct efficient nonlinear iteration mode to solve.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) that the invention provides method.

Fig. 2 is the scanning radar imaging system structural drawing that the specific embodiment of the invention adopts.

Fig. 3 is the simulation objectives scene that the present invention adopts when specifically implementing.

Fig. 4 is the sectional view from SNR=20dB white Gaussian noise to target echo corresponding when adding in orientation.

Fig. 5 is the scanning radar angle superresolution processing result that enforcement the inventive method obtains.

Embodiment

The present invention adopts emulation experiment to come feasibility and the validity of the radar angle ultra-resolution method that proving institute is put forward.Of the present invention in steps, conclusion all on Matlab2012 emulation platform checking correct, below provide the concrete Detailed operating procedures implementing the inventive method.

Owing to adopting the likelihood function relation of Poisson distribution function representation target and echo, objective function is made mathematically to show as nonlinear function; Use the prior imformation of laplacian distribution function representation target, make again the l containing non-differentiability in objective function ₁norm, makes the linear algorithm based on gradient cannot the solving of function to achieve the objective global minimum.Solution of the present invention is Solve problems radar angle super-resolution imaging being mathematically characterized by maximum a posteriori probability.First, the rear to model of radar angle super-resolution imaging is set up under bayesian theory, Poisson distribution function and laplacian distribution is used to describe the likelihood function of target and echo and the prior imformation of target respectively in this model, radar angle super-resolution imaging is expressed as the posterior probability of target and echo, then negative log-transformation is carried out to posterior probability, finally use convex optimization method to solve global minimum to the objective function after conversion.

Idiographic flow as shown in Figure 1, comprises the steps:

Step one: echo data distance is to pulse compression

The present embodiment is for scanning radar imaging geometry pattern as shown in Figure 2.The correlation parameter that imaging relates to is as follows: Texas tower is with height z, along X-axis positive dirction flying speed V.With flying height dimension, ground composition 3 d space coordinate system, as shown in Figure 2, scanning radar imaging parameters is as shown in table 1.

Table 1

As shown in Figure 3, the target amplitude of setting is respectively from left to right for the amplitude of the target adopted in this implementation step and positional information: 1,0.8,0.8,0.9,1,0.7.The difference of simulation objectives in amplitude be in order to embody method of the present invention there are differences in processing target amplitude time, can effectively keep target amplitude information; As shown in the figure, the setting of target location is the resolution determined in order to ensure radar antenna parameter when cannot distinguish target, embodies the angle super-resolution performance that method provided by the invention has in the setting of target location.Arrange the target that amplitude is different in scene, be used for verifying that method provided by the invention is in processing target amplitude difference hour angle superresolution processing effect.

According to the simulation parameter that table 1 provides, Distance Time vector is:

T _r=[-1/f _sn _r/ 2 ,-1/f _s(N _r/ 2-1) ..., 1/f _s(N _r/ 2-1)], wherein, f _sfor distance is to sampling rate, N _rfor target echo distance is to sampling number; Orientation time arrow is T _a=[-PRIN _a/ 2 ,-PRI (N _a/ 2-1) ..., PRI (N _a/ 2-1)]; Wherein PRI is the transmit signal pulse repetition time, N _afor target echo orientation is to sampling number.According to simulation parameter, under Matlab 2012 emulation platform, generate echo, be designated as g ₂(τ, η).

According to radar emission signal chirp rate k and distance to reference time τ _refstructure distance is to pulse pressure reference signal to echo data g ₂(τ, η) carries out pulse compression.Data after pulse compression are designated as g ₃(τ, η), analytical form is as follows:

$\begin{array}{c}{g}_3(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_0}{T_{\mathrm{\β}}}\right)\·\exp \{-j4\mathrm{\π}{f}_c\frac{R(x,y,t)}{c}\}\\ \·\sin c\left\{B\right[\mathrm{\τ}-\frac{2\·R(x,y,t)}{c}\left]\right\}+N_3(\mathrm{\τ},\mathrm{\η})\end{array}$

Step 2: Range Walk Correction,

The operation of completing steps two, obtains data g ₃(τ, η), due to g ₃containing the function R (x, y, t) about time variable t in (τ, η).The task that this operation steps will complete mathematically is presented as: eliminate time variable t to data g ₃the impact of (τ, η).Taylor series expansion is carried out to oblique distance distance history R (x, y, t) of radar and target.Because θ with less, so cos θ ≈ 1; So R (x, y, t) ≈ R ₀-Vt.On this basis to g ₃(τ, η) carries out change of scale.Obtain

$\begin{array}{c}{g}_4(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{{\mathrm{\η}}_0}_{}}{T_{\mathrm{\β}}}\right)\·\exp \{-j4\mathrm{\π}{f}_c\frac{R(x,y,t)}{c}\}\\ \·\sin c\left\{B\right[\mathrm{\τ}-\frac{2\·R_0}{c}\left]\right\}+N_3(\mathrm{\τ},\mathrm{\η})\end{array}$

As can be seen from the above equation, sinc function part no longer by the impact of time variable t, thus completes range migration correction.

In order to simulate the existence of noise in actual imaging process, at data g ₄add SNR=20dB white Gaussian noise in (τ, η), accordingly result as shown in Figure 4, cannot draw the position of target, amplitude, information of number from Fig. 4.

Step 3: scanning radar angle super-resolution modeling,

First by data g in this step ₄the acquisition process of (τ, η) is expressed as matrix and vectorial linear operation form g=Hf+n.The posterior probability p (f|g) of target and echo is expressed as prior imformation p (f) and likelihood function p (g|f) without approximate.Again through negative log-transformation, scanning radar angle super-resolution imaging problem is changed into and solves $f_{\mathrm{MAP}}=\underset{f}{\arg \min }\{g\·\ln \left(\mathrm{Hf}\right)+\ln (g!)-\mathrm{Hf}+{\mathrm{\λ}}_r\·{\left|\right|f\left|\right|}_1\}.$

Step 4: scanning radar angle super-resolution imaging,

This step is by convex Optimization Method $f_{\mathrm{MAP}}=\underset{f}{\arg \min }\{g\·\ln \left(\mathrm{Hf}\right)+\ln (g!)-\mathrm{Hf}+{\mathrm{\λ}}_r\·{\left|\right|f\left|\right|}_1\},$ Finally realize scanning radar angle super-resolution imaging.First, right || f|| ₁carry out approximate processing to obtain this step operates, and chooses ε=10 ^-8; Structure then, multiplicative iterative rules is constructed: $f_{n+1}=f_n\·[{\left(H\right)}^T\·\left(\frac{g}{H\·f_n}\right)+{\mathrm{\λ}}_r\·\mathrm{\Λ}\left(f_n\right)].$

Here through the interative computation of 50 times, using the result of iteration as scanning radar angle super-resolution imaging result, specifically as shown in Figure 5.

Can be found out by the result of Fig. 5, the method that the present invention proposes can break through the restriction of antenna system parameter to radar image resolution, can realize scanning radar angle super-resolution, the result of superresolution processing can be recovered accurately for the amplitude of target, position, quantity information.This area engineering technical personnel can make relevant application according to radar angle disclosed by the invention ultra-resolution method, and relevant knowledge is still within scope.

Claims (1)

1. a scanning radar angle super-resolution imaging method, concrete steps are as follows:

Step one: echo data distance to pulse compression,

It is as follows that echo data distance relates to radar imaging system parameter to pulse compression: Texas tower movement velocity, is designated as V; The radar antenna wave beam angle of pitch, is designated as θ; Transmit carrier frequency, is designated as f _c; Texas tower initial position, is designated as that (0,0, z), wherein, z is Texas tower height; Pulse-recurrence time, be designated as PRI; Scene echoes distance, to sampling number, is designated as N _r; Imaging scene echoes orientation, to sampling number, is designated as N _a; Be positioned at the distance of (x, y) place target in t Texas tower and scene, be designated as R (x, y, t); wherein, R ₀for the oblique distance of target in initial time antenna and scene, for the position angle of target;

The orientation time arrow of scanning radar imaging region is designated as T _a=[-PRIN _a/ 2 ,-PRI (N _a/ 2-1) ..., PRI (N _a/ 2-1)]; Distance Time vector T _r=[-1/f _sn _r/ 2 ,-1/f _s(N _r/ 2-1) ..., 1/f _s(N _r/ 2-1)], wherein, f _sfor distance is to sampling rate, radar emission signal is designated as wherein, rect () represents rectangular function, T _pwide during expression transponder pulse, f _crepresent carrier frequency, k represents chirp rate, and τ represents fast time variable;

The echo of imaging region Ω can be expressed as to transmit and add the result of noise with the convolution of target, and for imaging region Ω, the analytical expression of echo can be write as:

$g_1(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\∫\∫}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_{a_0}}{T_{\mathrm{\β}}}\right)\·s(\mathrm{\τ}-\frac{2\·R(x,y,t)}{c})\mathrm{dxdy}+N_1(\mathrm{\τ},\mathrm{\η})---\left(1\right)$

Wherein, Ω represents imaging region; (x, y) represents the position of target in scene; F (x, y) represents point (x, y) place target scattering function; η represents slow time variable; ω _arepresent slow time domain window function, represent the modulation of orientation to antenna radiation pattern function; represent antenna azimuth initial time; T _βrepresent that target is at 3dB antenna beamwidth residence time; C represents propagation velocity of electromagnetic wave; N ₁(τ, η) represents the noise in echo;

(1) is expressed as following discrete form:

$g_2(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_{{\mathrm{\α}}_0}}{T_{\mathrm{\β}}}\right)\·s(\mathrm{\τ}-\frac{2\·R(x,y,t)}{c})+N_2(\mathrm{\τ},\mathrm{\η})---\left(2\right)$

Wherein, ∑ represents summation operation, N ₂(τ, η) represents N in (1) formula ₁(τ, η) form after discrete processes, according to distance to reference time τ _refwith the chirp rate k that transmits, structure distance is to pulse pressure reference signal again by s _refwith echo data g ₂(τ, η) carries out maximum auto-correlation computation, realizes echoed signal in distance to pulse compression, and the signal after pulse compression can be expressed as:

$\begin{array}{c}{g}_3(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_{{\mathrm{\α}}_0}}{T_{\mathrm{\β}}}\right)\·\exp \{-j4\mathrm{\π}{f}_c\frac{R(x,y,t)}{c}\}\\ \·\sin c\left\{B\right[\mathrm{\τ}-\frac{2\·R(x,y,t)}{c}\left]\right\}+N_3(\mathrm{\τ},\mathrm{\η})\end{array}---\left(3\right)$

Wherein, B represents transmitted signal bandwidth, N ₃(τ, η) represents data g ₂(τ, η) noise after pulse pressure process;

Step 2: Range Walk Correction,

Carry out Taylor series once item expansion to R (x, y, t) at t=0 place, the distance function of Texas tower and target can be expressed as: R (x, y, t) ≈ R ₀-Vt, to data g ₃(τ, η) carries out change of scale and to move the range migration caused to eliminate Texas tower, can obtain:

$\begin{array}{c}{g}_4(\mathrm{\τ},\mathrm{\η})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x,y)\·{\mathrm{\ω}}_a\left(\frac{\mathrm{\η}-{\mathrm{\η}}_{{\mathrm{\α}}_0}}{T_{\mathrm{\β}}}\right)\·\exp \{-j4\mathrm{\π}{f}_c\frac{R(x,y,t)}{c}\}\\ \·\sin c\left\{B\right[\mathrm{\τ}-\frac{2\·R_0}{c}\left]\right\}+N_3(\mathrm{\τ},\mathrm{\η})\end{array}---\left(4\right)$

Step 3: scanning radar angle super-resolution modeling,

Orientation is to the acquisition of signal echo data, and the convolution results being expressed as antenna and target by forward model adds noise, is designated as:

g＝Hf+n (5)

Wherein, vector concrete meaning is: with each behavior unit according to lexicographic order by g ₄be arranged in a row vector, then carrying out matrix transpose operation, to form a length be N _rn _acolumn vector, g _i(i=1,2 ..., N _rn _a) be expressed as arranging according to lexicographic order as scene objects, the echo data of i-th processing unit, () ^trepresent and transposed transform is carried out to bracket interior element, g ₄represent data g in (4) formula ₄(τ, η) matrix after discrete processes;

According to the sampling number to antenna main lobe of system parameter setting, radar directional pattern information matrix H is arranged in following manner:

Wherein, represent at orientation time arrow T _athe sampled point of a middle jth moment antenna;

F is expressed as picture scene information, arranges line by line according to lexicographic order, then entering matrix transpose operation, to form a length be N _rn _acolumn vector, be designated as f _i(i=1,2 ... N _rn _a) obey independent same distribution; represent the noise vector in data, n _i(i=1,2 ... N _rn _a) between meet independent same distribution;

Under bayesian theory, set up the rear to model of scanning radar angle super-resolution imaging, under the prerequisite of the statistical nature of known g, H and noise n, solve f,

Poisson distribution is used to describe the likelihood function relation of target and echo data, that is,

$p\left(g\right|f)=\underset{k=1}{\overset{N_r\·N_a}{\mathrm{\Π}}}p\left(g_k\right|f_k)=\underset{k=1}{\overset{N_r\·N_a}{\mathrm{\Π}}}\{\frac{{\left[{\left(\mathrm{Hf}\right)}_k\right]}^{g_k}}{\left(g_k\right)!}\·\exp [-{\left(\mathrm{Hf}\right)}_k\left]\right\}---\left(6\right)$

Wherein, represent and bracket interior element is carried out from 1 to N _rn _aproduct calculation, (Hf) _krepresent that radar directional pattern information matrix H is to target f in scene _k(k=1,2 ... N _rn _a) response, ()! Represent and continued product computing is carried out to bracket interior element;

Adopt the prior imformation of laplacian distribution function representation target, that is,

$p\left(f\right)=\underset{k=1}{\overset{N_r\·N_a}{\mathrm{\Π}}}\frac{1}{2\mathrm{\β}\·}\exp (-\frac{\left|f_k\right|}{\mathrm{\β}})---\left(7\right)$

Wherein, β represents scale parameter, || represent signed magnitude arithmetic(al);

P (g|f) and p (f) is substituted into total probability formula p (f|g) ∝ p (g|f) p (f), ∝ and represent proportional relation, and f corresponding when asking posterior probability maximum _mAP, by negative log-transformation, will f be solved _mAPchange into the globally optimal solution of following objective functions; Be minimum value about variable f due to what solve, eliminating the variable irrelevant with f can obtain,

$f_{\mathrm{MAP}}=\underset{f}{\arg \min }\{g\·\ln \left(\mathrm{Hf}\right)-\mathrm{Hf}+{\mathrm{\λ}}_r\·{\left|\right|f\left|\right|}_1\}---\left(8\right)$

Wherein, λ _rrepresent regular parameter, the weight of this Parametric Representation likelihood and priori, || ₁represent the l under Euclidean distance meaning ₁norm;

Step 4: scanning radar angle super-resolution imaging,

Adopt following approximate processing:

${\left|\right|f\left|\right|}_1\≈\underset{i=1}{\overset{N_r\·N_a}{\mathrm{\Σ}}}\sqrt{{\left|\left(f_i\right)\right|}^2+\mathrm{\ϵ}}---\left(9\right)$

Wherein, ε >0 represents a very little number, (9) is brought into (8) and carries out abbreviation, can obtain:

About variable f, gradient is asked to objective function in (10), can obtain:

$\▿\left(f\right)={\left(H\right)}^T\·\left(\frac{g}{H\·f}\right)-{\left(H\right)}^T\·I+{\mathrm{\λ}}_r\·\mathrm{\Λ}\left(f\right)\·f---\left(11\right)$

Wherein, diag () represents that generation main diagonal element is the diagonal matrix of vector in bracket successively,

Make (11) to equal zero and operation is normalized to aerial information matrix rows, be i.e. (H) ^ti=I, I represent that element is a column vector of numerical value 1 entirely, can obtain:

${\left(H\right)}^T\·\left(\frac{g}{H\·f}\right)+{\mathrm{\λ}}_r\·\mathrm{\Λ}\left(f\right)\·f=I---\left(12\right)$

Construct following iterative process:

$f_{n+1}=f_n\·[{\left(H\right)}^T\·\left(\frac{g}{H\·f_n}\right)+{\mathrm{\λ}}_r\·\mathrm{\Λ}\left(f_n\right)\·f_n]---\left(13\right)$

Wherein, f _nand f _n+1represent n-th time and (n+1)th iteration result respectively, when iterations equals the number of times preset, iteration terminates, using the result of iteration as scanning radar angle super-resolution imaging result.