CN104950305A - Real beam scanning radar angle super-resolution imaging method based on sparse constraint - Google Patents

Abstract

The invention discloses a real beam scanning radar angle super-resolution imaging method based on sparse constraint. The real beam scanning radar super-resolution imaging method comprises the following steps of S1 performing echo modeling, and establishing an echo data model of a scanning radar on the basis of a geometrical relationship of a real beam scanning radar and a target; S2 performing range pulse compression on echo data, so as to realize range high resolution; S3 expressing the echo data after pulse compression to a convolution model of scattering coefficients of an antenna beam and an observation scene; S4 establishing a maximum posterior objective function according to the convolution model obtained in the step S3, and deducing a maximum posterior solution; S5 precisely reducing original target distribution through an adaptive iteration method. According to the real beam scanning radar angle super-resolution imaging method, clutter characteristics are expressed by using rayleigh distribution, target distribution characteristics are reflected by utilizing the sparse constraint, target distribution is inverted, and additionally, the influence of noise on imaging results is inhibited, so that radar angle super resolution processing results are close to actual target distribution, and real beam scanning radar angle super-resolution imaging is realized.

Description

A kind of real beam scanning radar angle super-resolution imaging method based on sparse constraint

Technical field

The invention belongs to radar imaging technology field, it is in particular to a kind of real beam scanning radar angle super-resolution imaging method based on sparse constraint.

Background technology

The high-resolution imaging of real beam scanning radar, have huge using value in fields such as marine navigation, control tower monitoring and distant early warnings, this imaging pattern also has the advantage such as small size and low cost simultaneously, and therefore this imaging pattern is with a wide range of applications.Real beam scanning radar successively irradiates imaging region, by launching linear FM signal (LFM) and receiving echoed signal to obtain the two-dimentional echoed signal in acquisition radar coverage territory with scanning constant speed.Because the dimension that transmits is for LFM signal, therefore, distance can realize by using pulse compression technique to high-resolution.In orientation to, real beam positional angular resolution by determine, wherein, λ is radar wavelength, D represents antenna aperture size, although real beam positional angular resolution is far below range resolution, by the method for signal transacting, antenna wavelength and aperture restriction can be broken through, significantly improve azimuth resolution, realize real Beam radar angle super-resolution imaging.

Document " Ly C, Dropkin H, Manitius A Z.Extension of the music algorithm to millimeter-wave (mmw) real-beam radar scanning antennas.AeroSense 2002. " according to the MUSIC algorithm realization scanning radar orientation in the echoing characteristics proposition Power estimation of real beam scanning radar to super-resolution imaging, but the method needs enough fast umber of beats with the covariance matrix of accurate estimating noise, this mechanical scanning radar in reality is difficult to realization in applying, under coherent source background, the angle super-resolution performance of the method can degradation simultaneously.

Document " Y.Zhang, Y.Zhang, W.Li, Y.Huang, and J.Yang.Angular superresolution for real beam radar with iterative adaptive approach.in Geoscience and Remote Sensing Symposium (IGARSS), 2013IEEE International.IEEE, 2013:3100-3103 " propose a kind of adaptive iteration angle ultra-resolution method based on real beam scanning radar, the method takes advantage of criterion based on weighting minimum weight two, the method overcome the restriction of fast umber of beats and significantly can improve azimuth resolution, but the computation complexity of the method is excessive, a large amount of system resource can be taken and have a strong impact on the real-time of imaging, be difficult to be generalized in practical application.

Real beam scanning radar orientation is established as the convolution model of antenna radiation pattern and target scattering coefficient by document " Huang Y; Zha Y; Zhang Y; et al.Real-beam scanning radar angular super-resolution via sparse deconvolution.Geoscience and Remote Sensing Symposium (IGARSS); 2014IEEE International.IEEE; 2014:3081-3084. " to echo, and by deconvolution algorithm reconstructed object scene, realize real Beam radar angular resolution.But the noise of the method hypothesis obeys the not realistic radar imagery characteristic of Poisson distribution characteristic, and therefore under low signal-to-noise ratio, the imaging performance of this algorithm can sharply decline.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, a kind of rayleigh distributed that uses is provided to characterize noise performance, and utilize sparse constraint to react target distribution characteristic, noise influence on RT is inhibit while inverting target distribution, improve the estimated accuracy of rayleigh distributed statistical parameter, achieve the real beam scanning radar angle super-resolution imaging method based on sparse constraint.

The object of the invention is to be achieved through the following technical solutions, a kind of real beam scanning radar angle super-resolution imaging method based on sparse constraint, comprises the following steps:

S1, echo modeling, the geometric relationship based on real beam scanning radar and target sets up the echo data model of scanning radar;

S2, distance is carried out to pulse compression to echo data, realize distance to high resolving power;

S3, the echo data after pulse compression is expressed as antenna beam and the convolution model of scattering coefficient observing scene;

S4, the convolution model obtained according to S3 set up maximum a posteriori objective function, and maximum a posteriori solution of deriving;

S5, to be gone out original object distribution by the method precise restoration of adaptive iteration, comprise following sub-step:

S51, calculating iteration initial value: utilize TIKHONOV regularization method and maximum Likelihood to obtain the solution of objective function and the iteration initial value of these two parameters of rayleigh distributed statistical parameter;

S52, the maximum a posteriori solution structure iteration expression formula obtained according to S4;

S53, iteration initial value to be substituted in iteration expression formula, obtain new maximum a posteriori solution;

S54, the maximum a posteriori solution obtained by S53 are brought in the statistical parameter computing formula of rayleigh distributed, upgrade rayleigh distributed statistical parameter value;

The rayleigh distributed statistical parameter value that S55, the maximum a posteriori solution obtained by S53 and S54 obtain substitutes in iteration expression formula, regains new maximum a posteriori solution;

S56, repetition step S54 and S55, until the result of iteration expression formula is compared with the result of last iteration expression formula, when meeting iteration convergence condition, the result recording this iteration expression formula is real beam scanning radar angle super-resolution imaging result.

Further, the concrete methods of realizing of described step S1 is: radar sentences downwards angle of visibility in height H p-ψ ~ ψ imaging region presses clock-wise order scanning; Initial time, the initial oblique distance of radar antenna and scene center Place object is r ₀if each impact point respective coordinates is (x in scene _i, y _i), that the position angle between each target and radar is corresponding is θ _i, the oblique distance between each target and radar is r _i;

If transmit as linear FM signal wherein, rect () represents rectangular signal, and it is defined as τ be distance to fast time variable, T is the transponder pulse duration, and c is the light velocity, and λ is wavelength, K _rfor chirp rate; In order to ensure that theory and practice checking situation conforms to, docking is regained ripple and is carried out discrete processes; Echo analytical expression after discretize is:

$\begin{array}{c}s(\mathrm{\θ},\mathrm{\τ})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x_i,y_i)\·\mathrm{\ω}\left(\frac{\mathrm{\θ}-{\mathrm{\θ}}_i}{T_{\mathrm{\β}}}\right)\·\mathrm{rect}(\mathrm{\τ}-\frac{2r_i}{c})\\ \×\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{r}_i)\·\exp \left(\mathrm{j\π}{K}_r{[\mathrm{\τ}-\frac{{2r}_i}{c}]}^2\right)\end{array}---\left(1\right)$

Wherein, Ω is target scene domain, and θ is antenna beamwidth, f (x _i, y _i) be point (x _i, y _i) scattering function of place's target; ω is antenna scanning speed, T _βthe residence time of target in 3dB antenna beamwidth.

Further, the concrete methods of realizing of described step S2 comprises following sub-step:

S21, structure distance are to pulse pressure reference signal:

$s_{\mathrm{ref}}=\mathrm{rect}\left(\frac{{\mathrm{\τ}}_{\mathrm{ref}}}{T}\right)\·\exp \left\{\mathrm{j\π}{K}_r{\mathrm{\τ}}_{\mathrm{ref}}^2\right\}$

Wherein, represent that distance is to the reference time;

S22, by s _refwith echo data carry out maximum auto-correlation computation, obtaining the 2D signal after pulse compression is:

$s_1(\mathrm{\θ},\mathrm{\τ})=\underset{(x,y)\∈\mathrm{\Ω}}{\mathrm{\Σ}}f(x_i,y_i)\·\mathrm{\ω}\left(\frac{\mathrm{\θ}-{\mathrm{\θ}}_i}{T_{\mathrm{\β}}}\right)\·\sin c\left[B(\mathrm{\τ}-\frac{2r_i}{c})\right]\·\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{r}_i)---\left(2\right)$

Wherein, B is transmitted signal bandwidth.

Further, the concrete methods of realizing of described step S3 is: the convolution model of echoed signal is expressed as:

Wherein, s=[s (1,1), s (1,2) ..., s (N, 1) ..., s (N, M)] ^tfor the vector that NM × 1 is tieed up, be the result upwards rearranged in orientation by range unit order by the measured value of all pulse compression back echo signals, subscript T represents transpose operation;

F=[f (1,1), f (1,2) ..., f (N, 1) ..., f (N, M)] ^tfor the vector that NM × 1 is tieed up, be by the result that in orientation upwards rearrange of the amplitude of unknown objects all in imaging region by range unit order;

N=[n (1,1), n (1,2) ..., n (N, 1) ..., n (N, M)] ^t, be the vector that NM × 1 is tieed up, represent clutter and interference signal component, obey the rayleigh distributed of statistical iteration;

H is the matrix of NM × NM dimension, by convolution calculation matrix H _{m × N}form, wherein, H _{m × N}=[h ₁, h ₂..., h _m].

Further, the concrete methods of realizing of described step S4 is: on Bayesian formula basis, by given noise statistics, and in conjunction with sparse target distribution prior imformation, release maximum a posteriori probability deconvolution ultra-resolution method, realize Deconvolution, specifically comprise following sub-step:

S41, for formula (3), utilize Bayesian formula, the posterior probability of echo data be expressed as:

$p(f/s)=\frac{p(s/f)p\left(f\right)}{p\left(s\right)}---\left(4\right)$

Wherein, p () represents probability density function; According to maximum a posteriori criterion, deconvolution problem is converted into and solves optimum solution f it is met:

$\hat{f}=\arg \underset{f}{\max }p\left(f\right|s)=\arg \underset{f}{\max }\left[p\left(s\right|f)p\left(f\right)\right]---\left(5\right)$

Wherein, for the MAP estimation of objective function; P (f/s), p (s/f) and p (f) represent the prior probability of the posterior probability of echo data, likelihood probability and target respectively;

S42, the clutter establishing each sampled point in real beam scanning radar echoed signal or undesired signal obey the rayleigh distributed of statistical iteration, then likelihood probability is expressed as:

$p(s/f)=\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\Π}}}\frac{(s_i-{\left(\mathrm{Hf}\right)}_i)}{{\mathrm{\σ}}^2}{e}^{(-\frac{{(s_i-{\left(\mathrm{Hf}\right)}_i)}^2}{2{\mathrm{\σ}}^2})}---\left(6\right)$

Wherein, i is each discrete point target,

${\left(\mathrm{Hf}\right)}_i=\underset{j=1}{\overset{\mathrm{NM}}{\mathrm{\Σ}}}{h}_{\mathrm{ij}}{f}_j$

σ ²it is the statistical parameter in rayleigh distributed;

S43, selection sparse characteristic are as regularization constraint item, and the probability density that target scattering is sparse is:

$p\left(f\right)\∝\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\Π}}}\exp [-\frac{2}{q}({\left|f_i\right|}^q-1)]---\left(7\right)$

Wherein, 0 < q≤1; As q=1, p (f) ∝ exp (-2||f|| ₁) be laplacian distribution; When q → 1, the probability of target is $p\left(f\right)\&Proportional;\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}(1/{\left|f_i\right|}^2);$

S44, basis (6) formula and (7) formula obtain maximum a posteriori objective function and are:

$y\left(f\right)=p(s/f)p\left(f\right)=\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\frac{(s_i-{\left(\mathrm{Hf}\right)}_i)}{{\mathrm{\&sigma;}}^2}{e}^{(-\frac{{\left(s_i{\left(\mathrm{Hf}\right)}_i\right)}^2}{2{\mathrm{\&sigma;}}^2})}\&CenterDot;\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\exp [-\frac{2}{q}{\left(\right|f_i\left|\right)}^q-1]---\left(8\right)$

Negative natural logarithm is got to (8) formula, obtains:

(9) formula is asked about the gradient algorithm of f, to obtain:

Wherein, () ^trepresent matrix transpose operation, P=diag{p ₁..., p _nM, p _i=| f _i| ^2-q;

S45, because (10) formula is nonlinear function, therefore, can only obtain by the method for iteration the result approaching original scene, make (10) formula be zero, the maximum a posteriori solution obtained about f is:

$f={(H^{T}H+{\mathrm{\&sigma;}}^2{P}^{-1})}^{-1}(H^{T}s-{\mathrm{\&sigma;}}^2{H}^T\frac{1}{s-\mathrm{Hf}})---\left(11\right).$

Further, described step S51 specific implementation comprises the following steps:

S511, utilize TIKHONOV regularization method, calculating original scene rough estimate result is:

f＝(H ^TH+βI) ^-1H ^Ts (12)

Wherein, β is regularization parameter, and I is that NM × NM ties up unit diagonal matrix;

S512, maximum Likelihood is utilized to estimate rayleigh distributed statistical parameter, first, for the clutter vector g=[g of the obedience independent Rayleigh distribution of a NM dimension ₁..., g _i] (i=1 ..., NM), to the joint likelihood function of this vector take the logarithm process after, obtain:

$\mathrm{\&gamma;}(g,\mathrm{\&sigma;})=\mathrm{NM}{\ln \mathrm{\&sigma;}}^2-\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{g}_i+\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}\frac{{\left(g_i\right)}^2}{2{\mathrm{\&sigma;}}^2}---\left(13\right)$

Ask formula (13) about the derivative of σ, and make result be zero, obtain:

$\frac{\&PartialD;\left(\mathrm{\&gamma;}(g,\mathrm{\&sigma;})\right)}{\&PartialD;\mathrm{\&sigma;}}=\frac{2\mathrm{NM}}{\mathrm{\&sigma;}}-\frac{1}{{\mathrm{\&sigma;}}^3}\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{\left(g_i\right)}^2=0---\left(14\right)$

Therefore, then σ ²maximum likelihood estimator be:

${\mathrm{\&sigma;}}^2=\frac{\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{\left(g_i\right)}^2}{2\mathrm{NM}}---\left(15\right)$

For real beam scanning radar imaging, g _i=s _i-(Hf) _i, therefore utilize TIKHONOV regularization result of calculation and the statistical parameter that (15) formula that combines calculates about rayleigh distributed is:

${\mathrm{\&sigma;}}^2=\frac{\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}{(s_i-{\left(\mathrm{Hf}\right)}_i)}^2}{2\mathrm{NM}}---\left(16\right).$

Further, the iteration expression formula that described step S52 builds is:

$f_{k+1}={(H^{T}H+{\left({\mathrm{\&sigma;}}^2\right)}_k{\left(P_k\right)}^{-1})}^{-1}(H^{T}s-{\left({\mathrm{\&sigma;}}^2\right)}_k{H}^T\frac{1}{s-{\mathrm{Hf}}_k})---\left(17\right)$

Wherein, iteration initial value is the result that (12) formula and (16) formula of (12) formula being brought into calculate, k+1 and k is the number of times of iteration, P _k=diag{ (p ₁) _k..., (p _nM) _k, (p _i) _k=| (f _i) _k| ^2-q.

Further, the condition of convergence in described step S56 is:

||f _k+1-f _k|| ²＜ε (18)

Wherein, f _k+1, f _kfor adjacent twice iteration result, ε is the threshold value preset.

The invention has the beneficial effects as follows: use rayleigh distributed to characterize noise performance, and utilize sparse constraint to react target distribution characteristic, noise influence on RT is inhibit while inverting target distribution, in addition, in iterative processing, utilize adaptive method to improve the estimated accuracy of rayleigh distributed statistical parameter, make angle superresolution processing result more approach realistic objective distribution, finally achieve real beam scanning radar angle super-resolution imaging.

Accompanying drawing explanation

Fig. 1 is formation method process flow diagram of the present invention;

Fig. 2 is the real beam scanning radar imaging pattern figure of specific embodiments of the invention;

Fig. 3 is the radar directional pattern of the present embodiment;

Fig. 4 is the simulating scenes figure of the present embodiment;

Fig. 5 is (SCR=25dB) echo sectional view under the clutter scene of the present embodiment;

Fig. 6 is the final scanning radar imaging results figure after the present embodiment process.

Embodiment

Further illustrate technical scheme of the present invention below in conjunction with accompanying drawing, but the content that the present invention protects is not limited to the following stated.

As shown in Figure 1, a kind of real beam scanning radar angle super-resolution imaging method based on sparse constraint, comprises the following steps:

S1, echo modeling, the geometric relationship based on real beam scanning radar and target sets up the echo data model of scanning radar; Its concrete methods of realizing is: radar sentences downwards angle of visibility in height H p-ψ ~ ψ imaging region presses clock-wise order scanning; Initial time, the initial oblique distance of radar antenna and scene center Place object is r ₀if each impact point respective coordinates is (x in scene _i, y _i), that the position angle between each target and radar is corresponding is θ _i, the oblique distance between each target and radar is r _i;

If transmit as linear FM signal wherein, rect () represents rectangular signal, and it is defined as τ be distance to fast time variable, T is the transponder pulse duration, and c is the light velocity, and λ is wavelength, K _rfor chirp rate; In order to ensure that theory and practice checking situation conforms to, docking is regained ripple and is carried out discrete processes; Echo analytical expression after discretize is:

$\begin{array}{c}s(\mathrm{\&theta;},\mathrm{\&tau;})=\underset{(x,y)\&Element;\mathrm{\&Omega;}}{\mathrm{\&Sigma;}}f(x_i,y_i)\&CenterDot;\mathrm{\&omega;}\left(\frac{\mathrm{\&theta;}-{\mathrm{\&theta;}}_i}{T_{\mathrm{\&beta;}}}\right)\&CenterDot;\mathrm{rect}(\mathrm{\&tau;}-\frac{2r_i}{c})\\ \&times;\exp (-j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{r}_i)\&CenterDot;\exp \left(\mathrm{j\&pi;}{K}_r{[\mathrm{\&tau;}-\frac{{2r}_i}{c}]}^2\right)\end{array}---\left(1\right)$

Wherein, Ω is target scene domain, and θ is antenna beamwidth, f (x _i, y _i) be point (x _i, y _i) scattering function of place's target; ω is antenna scanning speed, T _βthe residence time of target in 3dB antenna beamwidth.The present embodiment adopts forward sight scanning radar imaging moving geometric mode, and as shown in Figure 2, scanning radar imaging parameters as shown in Table 1.

Table one scan radar system parameters

Parameter	Symbol	Numerical value
			Carrier frequency	f c	10GHz
Wide when transmitting	T	10μs
			Transmitted signal bandwidth	B	50MHz
Impulse sampling frequency	PRF	1500Hz
			Antenna scanning speed	ω	60°/s
Antenna beamwidth	θ	2.5°
			Sweep limit	Φ	-12°～12°
Scanning radar operating distance	R 0	10km

S2, distance is carried out to pulse compression to echo data, realize distance to high resolving power; Its concrete methods of realizing comprises following sub-step:

S21, structure distance are to pulse pressure reference signal:

$s_{\mathrm{ref}}=\mathrm{rect}\left(\frac{{\mathrm{\&tau;}}_{\mathrm{ref}}}{T}\right)\&CenterDot;\exp \left\{\mathrm{j\&pi;}{K}_r{\mathrm{\&tau;}}_{\mathrm{ref}}^2\right\}$

Wherein, represent that distance is to the reference time;

S22, by s _refwith echo data carry out maximum auto-correlation computation, obtaining the 2D signal after pulse compression is:

$s_1(\mathrm{\&theta;},\mathrm{\&tau;})=\underset{(x,y)\&Element;\mathrm{\&Omega;}}{\mathrm{\&Sigma;}}f(x_i,y_i)\&CenterDot;\mathrm{\&omega;}\left(\frac{\mathrm{\&theta;}-{\mathrm{\&theta;}}_i}{T_{\mathrm{\&beta;}}}\right)\&CenterDot;\sin c\left[B(\mathrm{\&tau;}-\frac{2r_i}{c})\right]\&CenterDot;\exp (-j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{r}_i)---\left(2\right)$

Wherein, B is transmitted signal bandwidth.

S3, the echo data after pulse compression is expressed as antenna beam and the convolution model of scattering coefficient observing scene; Its concrete methods of realizing is: the convolution model of echoed signal is expressed as:

Wherein, s=[s (1,1), s (1,2) ..., s (N, 1) ..., s (N, M)] ^tfor the vector that NM × 1 is tieed up, be the result upwards rearranged in orientation by range unit order by the measured value of all pulse compression back echo signals, subscript T represents transpose operation;

F=[f (1,1), f (1,2) ..., f (N, 1) ..., f (N, M)] ^tfor the vector that NM × 1 is tieed up, be by the result that in orientation upwards rearrange of the amplitude of unknown objects all in imaging region by range unit order;

N=[n (1,1), n (1,2) ..., n (N, 1) ..., n (N, M)] ^t, be the vector that NM × 1 is tieed up, represent clutter and interference signal component, obey the rayleigh distributed of statistical iteration;

H is the matrix of NM × NM dimension, by convolution calculation matrix H _{m × N}form, wherein, H _{m × N}=[h ₁, h ₂..., h _m].

S4, the convolution model obtained according to S3 set up maximum a posteriori objective function, and maximum a posteriori solution of deriving; Its concrete methods of realizing is: on Bayesian formula basis, by given noise statistics, and in conjunction with sparse target distribution prior imformation, releases maximum a posteriori probability deconvolution ultra-resolution method, realizes Deconvolution, specifically comprise following sub-step:

S41, for formula (3), utilize Bayesian formula, the posterior probability of echo data be expressed as:

$p(f/s)=\frac{p(s/f)p\left(f\right)}{p\left(s\right)}---\left(4\right)$

Wherein, p () represents probability density function; According to maximum a posteriori criterion, deconvolution problem is converted into and solves optimum solution f it is met:

$\hat{f}=\arg \underset{f}{\max }p\left(f\right|s)=\arg \underset{f}{\max }\left[p\left(s\right|f)p\left(f\right)\right]---\left(5\right)$

Wherein, for the MAP estimation of objective function; P (f/s), p (s/f) and p (f) represent the prior probability of the posterior probability of echo data, likelihood probability and target respectively;

S42, the clutter establishing each sampled point in real beam scanning radar echoed signal or undesired signal obey the rayleigh distributed of statistical iteration, then likelihood probability is expressed as:

$p(s/f)=\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\frac{(s_i-{\left(\mathrm{Hf}\right)}_i)}{{\mathrm{\&sigma;}}^2}{e}^{(-\frac{{(s_i-{\left(\mathrm{Hf}\right)}_i)}^2}{2{\mathrm{\&sigma;}}^2})}---\left(6\right)$

Wherein, i is each discrete point target,

${\left(\mathrm{Hf}\right)}_i=\underset{j=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}{f}_j$

σ ²it is the statistical parameter in rayleigh distributed;

S43, selection sparse characteristic are as regularization constraint item, and the probability density that target scattering is sparse is:

$p\left(f\right)\&Proportional;\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\exp [-\frac{2}{q}({\left|f_i\right|}^q-1)]---\left(7\right)$

Wherein, 0 < q≤1; As q=1, p (f) ∝ exp (-2||f|| ₁) be laplacian distribution; When q → 1, the probability of target is $p\left(f\right)\&Proportional;\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}(1/{\left|f_i\right|}^2);$

S44, basis (6) formula and (7) formula obtain maximum a posteriori objective function and are:

$y\left(f\right)=p(s/f)p\left(f\right)=\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\frac{(s_i-{\left(\mathrm{Hf}\right)}_i)}{{\mathrm{\&sigma;}}^2}{e}^{(-\frac{{\left(s_i{\left(\mathrm{Hf}\right)}_i\right)}^2}{2{\mathrm{\&sigma;}}^2})}\&CenterDot;\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\exp [-\frac{2}{q}{\left(\right|f_i\left|\right)}^q-1]---\left(8\right)$

Negative natural logarithm is got to (8) formula, obtains:

(9) formula is asked about the gradient algorithm of f, to obtain:

Wherein, () ^trepresent matrix transpose operation, P=diag{p ₁..., p _nM, p _i=| f _i| ^2-q;

S45, because (10) formula is nonlinear function, therefore, can only obtain by the method for iteration the result approaching original scene, make (10) formula be zero, the maximum a posteriori solution obtained about f is:

$f={(H^{T}H+{\mathrm{\&sigma;}}^2{P}^{-1})}^{-1}(H^{T}s-{\mathrm{\&sigma;}}^2{H}^T\frac{1}{s-\mathrm{Hf}})---\left(11\right).$

S5, to be gone out original object distribution by the method precise restoration of adaptive iteration, comprise following sub-step:

S51, calculating iteration initial value: utilize TIKHONOV regularization method and maximum Likelihood to obtain the solution of objective function and the iteration initial value of these two parameters of rayleigh distributed statistical parameter; Its specific implementation comprises the following steps:

S511, utilize TIKHONOV regularization method, calculating original scene rough estimate result is:

f＝(H ^TH+βI) ^-1H ^Ts (12)

Wherein, β is regularization parameter, and I is that NM × NM ties up unit diagonal matrix;

S512, maximum Likelihood is utilized to estimate rayleigh distributed statistical parameter, first, for the clutter vector g=[g of the obedience independent Rayleigh distribution of a NM dimension ₁..., g _i] (i=1 ..., NM), to the joint likelihood function of this vector take the logarithm process after, obtain:

$\mathrm{\&gamma;}(g,\mathrm{\&sigma;})=\mathrm{NM}{\ln \mathrm{\&sigma;}}^2-\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{g}_i+\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}\frac{{\left(g_i\right)}^2}{2{\mathrm{\&sigma;}}^2}---\left(13\right)$

Ask formula (13) about the derivative of σ, and make result be zero, obtain:

$\frac{\&PartialD;\left(\mathrm{\&gamma;}(g,\mathrm{\&sigma;})\right)}{\&PartialD;\mathrm{\&sigma;}}=\frac{2\mathrm{NM}}{\mathrm{\&sigma;}}-\frac{1}{{\mathrm{\&sigma;}}^3}\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{\left(g_i\right)}^2=0---\left(14\right)$

Therefore, then σ ²maximum likelihood estimator be:

${\mathrm{\&sigma;}}^2=\frac{\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{\left(g_i\right)}^2}{2\mathrm{NM}}---\left(15\right)$

For real beam scanning radar imaging, g _i=s _i-(Hf) _i, therefore utilize TIKHONOV regularization result of calculation and the statistical parameter that (15) formula that combines calculates about rayleigh distributed is:

${\mathrm{\&sigma;}}^2=\frac{\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}{(s_i-{\left(\mathrm{Hf}\right)}_i)}^2}{2\mathrm{NM}}---\left(16\right);$

S52, the maximum a posteriori solution structure iteration expression formula obtained according to S4:

$f_{k+1}={(H^{T}H+{\left({\mathrm{\&sigma;}}^2\right)}_k{\left(P_k\right)}^{-1})}^{-1}(H^{T}s-{\left({\mathrm{\&sigma;}}^2\right)}_k{H}^T\frac{1}{s-{\mathrm{Hf}}_k})---\left(17\right)$

Wherein, iteration initial value is the result that (12) formula and (16) formula of (12) formula being brought into calculate, k+1 and k is the number of times of iteration, P _k=diag{ (p ₁) _k..., (p _nM) _k, (p _i) _k=| (f _i) _k| ^2-q.

S53, iteration initial value to be substituted in iteration expression formula, obtain new maximum a posteriori solution;

S54, the maximum a posteriori solution obtained by S53 are brought in the statistical parameter computing formula of rayleigh distributed, upgrade rayleigh distributed statistical parameter value;

The rayleigh distributed statistical parameter value that S55, the maximum a posteriori solution obtained by S53 and S54 obtain substitutes in iteration expression formula, regains new maximum a posteriori solution;

S56, repetition step S54 and S55, until the result of iteration expression formula is compared with the result of last iteration expression formula, when meeting iteration convergence condition, the result recording this iteration expression formula is real beam scanning radar angle super-resolution imaging result, and the described condition of convergence is:

||f _k+1-f _k|| ²＜ε (18)

Wherein, f _k+1, f _kfor adjacent twice iteration result, ε is the threshold value preset.

The present embodiment adopts radar directional pattern as shown in Figure 3, Fig. 4 is the simulating scenes figure of the present embodiment, Fig. 5 is (SCR=25dB) echo sectional view under the clutter scene of the present embodiment, and Fig. 6 is the final scanning radar imaging results figure after the present embodiment process.As can be seen from the figure, by method provided by the invention, under Rayleigh Clutter background, the angle information of target obtains good recovery.

Those of ordinary skill in the art will appreciate that, embodiment described here is to help reader understanding's principle of the present invention, should be understood to that protection scope of the present invention is not limited to so special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combination of not departing from essence of the present invention according to these technology enlightenment disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (8)

1., based on a real beam scanning radar angle super-resolution imaging method for sparse constraint, it is characterized in that, comprise the following steps:

S1, echo modeling, the geometric relationship based on real beam scanning radar and target sets up the echo data model of scanning radar;

S2, distance is carried out to pulse compression to echo data, realize distance to high resolving power;

S3, the echo data after pulse compression is expressed as antenna beam and the convolution model of scattering coefficient observing scene;

S4, the convolution model obtained according to S3 set up maximum a posteriori objective function, and maximum a posteriori solution of deriving;

S5, to be gone out original object distribution by the method precise restoration of adaptive iteration, comprise following sub-step:

S51, calculating iteration initial value: utilize TIKHONOV regularization method and maximum Likelihood to obtain the solution of objective function and the iteration initial value of these two parameters of rayleigh distributed statistical parameter;

S52, the maximum a posteriori solution structure iteration expression formula obtained according to S4;

S53, iteration initial value to be substituted in iteration expression formula, obtain new maximum a posteriori solution;

S54, the maximum a posteriori solution obtained by S53 are brought in the statistical parameter computing formula of rayleigh distributed, upgrade rayleigh distributed statistical parameter value;

The rayleigh distributed statistical parameter value that S55, the maximum a posteriori solution obtained by S53 and S54 obtain substitutes in iteration expression formula, regains new maximum a posteriori solution;

S56, repetition step S54 and S55, until the result of iteration expression formula is compared with the result of last iteration expression formula, when meeting iteration convergence condition, the result recording this iteration expression formula is real beam scanning radar angle super-resolution imaging result.

2. real beam scanning radar angle according to claim 1 super-resolution imaging method, it is characterized in that, the concrete methods of realizing of described step S1 is: radar sentences downwards angle of visibility in height H p-ψ ~ ψ imaging region presses clock-wise order scanning; Initial time, the initial oblique distance of radar antenna and scene center Place object is r ₀if each impact point respective coordinates is (x in scene _i, y _i), that the position angle between each target and radar is corresponding is θ _i, the oblique distance between each target and radar is r _i;

If transmit as linear FM signal wherein, rect () represents rectangular signal, and it is defined as τ be distance to fast time variable, T is the transponder pulse duration, and c is the light velocity, and λ is wavelength, K _rfor chirp rate; In order to ensure that theory and practice checking situation conforms to, docking is regained ripple and is carried out discrete processes; Echo analytical expression after discretize is:

$\begin{array}{c}s(\mathrm{\&theta;},\mathrm{\&tau;})=\underset{(x,y)\&Element;\mathrm{\&Omega;}}{\mathrm{\&Sigma;}}f(x_i,y_i)\&CenterDot;\mathrm{\&omega;}\left(\frac{\mathrm{\&theta;}-{\mathrm{\&theta;}}_i}{T_{\mathrm{\&beta;}}}\right)\&CenterDot;\mathrm{rect}(\mathrm{\&tau;}-\frac{2r_i}{c})\\ \&times;\exp (-j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{r}_i)\&CenterDot;\exp \left(\mathrm{j\&pi;}{K}_r{[\mathrm{\&tau;}-\frac{2r_i}{c}]}^2\right)\end{array}---\left(1\right)$

Wherein, Ω is target scene domain, and θ is antenna beamwidth, f (x _i, y _i) be point (x _i, y _i) scattering function of place's target; ω is antenna scanning speed, T _βthe residence time of target in 3dB antenna beamwidth.

3. real beam scanning radar angle according to claim 2 super-resolution imaging method, it is characterized in that, the concrete methods of realizing of described step S2 comprises following sub-step:

S21, structure distance are to pulse pressure reference signal:

$s_{\mathrm{ref}}=\mathrm{rect}\left(\frac{{\mathrm{\&tau;}}_{\mathrm{ref}}}{T}\right)\&CenterDot;\exp \left\{\mathrm{j\&pi;}{K}_r{\mathrm{\&tau;}}_{\mathrm{ref}}^2\right\}$

Wherein, τ _refrepresent that distance is to the reference time;

S22, by s _refcarry out maximum auto-correlation computation with echo data s (θ, τ), obtaining the 2D signal after pulse compression is:

$s_1(\mathrm{\&theta;},\mathrm{\&tau;})=\underset{(x,y)\&Element;\mathrm{\&Omega;}}{\mathrm{\&Sigma;}}f(x_i,y_i)\&CenterDot;\mathrm{\&omega;}\left(\frac{\mathrm{\&theta;}-{\mathrm{\&theta;}}_i}{T_{\mathrm{\&beta;}}}\right)\&CenterDot;\sin c\left[B(\mathrm{\&tau;}-\frac{2r_i}{c})\right]\&CenterDot;\exp (-j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{r}_i)---\left(2\right)$

Wherein, B is transmitted signal bandwidth.

4. real beam scanning radar angle according to claim 3 super-resolution imaging method, it is characterized in that, the concrete methods of realizing of described step S3 is: the convolution model of echoed signal is expressed as:

Wherein, s=[s (1,1), s (1,2) ..., s (N, 1) ..., s (N, M)] ^tfor the vector that NM × 1 is tieed up, be the result upwards rearranged in orientation by range unit order by the measured value of all pulse compression back echo signals, subscript T represents transpose operation;

F=[f (1,1), f (1,2) ..., f (N, 1) ..., f (N, M)] ^tfor the vector that NM × 1 is tieed up, be by the result that in orientation upwards rearrange of the amplitude of unknown objects all in imaging region by range unit order;

N=[n (1,1), n (1,2) ..., n (N, 1) ..., n (N, M)] ^t, be the vector that NM × 1 is tieed up, represent clutter and interference signal component, obey the rayleigh distributed of statistical iteration;

H is the matrix of NM × NM dimension, by convolution calculation matrix H _{m × N}form, wherein, H _{m × N}=[h ₁, h ₂..., h _m].

5. real beam scanning radar angle according to claim 4 super-resolution imaging method, it is characterized in that, the concrete methods of realizing of described step S4 is: on Bayesian formula basis, by given noise statistics, and in conjunction with sparse target distribution prior imformation, release maximum a posteriori probability deconvolution ultra-resolution method, realize Deconvolution, specifically comprise following sub-step:

S41, for formula (3), utilize Bayesian formula, the posterior probability of echo data be expressed as:

$p(f/s)=\frac{p(s/f)p\left(f\right)}{p\left(s\right)}---\left(4\right)$

Wherein, p () represents probability density function; According to maximum a posteriori criterion, deconvolution problem is converted into and solves optimum solution f it is met:

$\hat{f}=\arg \underset{f}{\max }p\left(f\right|s)=\arg \underset{f}{\max }\left[p\left(s\right|f)p\left(f\right)\right]---\left(5\right)$

Wherein, for the MAP estimation of objective function; P (f/s), p (s/f) and p (f) represent the prior probability of the posterior probability of echo data, likelihood probability and target respectively;

S42, the clutter establishing each sampled point in real beam scanning radar echoed signal or undesired signal obey the rayleigh distributed of statistical iteration, then likelihood probability is expressed as:

$p(s/f)=\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\frac{(s_i-{\left(\mathrm{Hf}\right)}_i)}{{\mathrm{\&sigma;}}^2}{e}^{(-\frac{{(s_i-{\left(\mathrm{Hf}\right)}_i)}^2}{2{\mathrm{\&sigma;}}^2})}---\left(6\right)$

Wherein, i is each discrete point target,

${\left(\mathrm{Hf}\right)}_i=\underset{j=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}{f}_j$

σ ²it is the statistical parameter in rayleigh distributed;

S43, selection sparse characteristic are as regularization constraint item, and the probability density that target scattering is sparse is:

$p\left(f\right)\&Proportional;\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\exp [-\frac{2}{q}({\left|f_i\right|}^q-1)]---\left(7\right)$

Wherein, 0 < q≤1; As q=1, p (f) ∝ exp (-2||f|| ₁) be laplacian distribution; When q → 1, the probability of target is $p\left(f\right)\&Proportional;\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}(1/{\left|f_i\right|}^2);$

S44, basis (6) formula and (7) formula obtain maximum a posteriori objective function and are:

$y\left(f\right)=p(s/f)p\left(f\right)=\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\frac{(s_i-{\left(\mathrm{Hf}\right)}_i)}{{\mathrm{\&sigma;}}^2}{e}^{(-\frac{{(s_i-{\left(\mathrm{Hf}\right)}_i)}^2}{2{\mathrm{\&sigma;}}^2})}\&CenterDot;\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Pi;}}}\exp [-\frac{2}{q}{\left(\right|f_i\left|\right)}^q-1]---\left(8\right)$

Negative natural logarithm is got to (8) formula, obtains:

(9) formula is asked about the gradient algorithm of f, to obtain:

Wherein, () ^trepresent matrix transpose operation, P=diag{p ₁..., p _nM, p _i=| f _i| ^2-q;

S45, because (10) formula is nonlinear function, therefore, can only obtain by the method for iteration the result approaching original scene, make (10) formula be zero, the maximum a posteriori solution obtained about f is:

$f={(H^{T}H+{\mathrm{\&sigma;}}^2{P}^{-1})}^{-1}(H^{T}s-{\mathrm{\&sigma;}}^2{H}^T\frac{1}{s-\mathrm{Hf}})---\left(11\right).$

6. real beam scanning radar angle according to claim 5 super-resolution imaging method, it is characterized in that, described step S51 specific implementation comprises the following steps:

S511, utilize TIKHONOV regularization method, calculating original scene rough estimate result is:

f＝(H ^TH+βI) ^-1H ^Ts (12)

Wherein, β is regularization parameter, and I is that NM × NM ties up unit diagonal matrix;

S512, maximum Likelihood is utilized to estimate rayleigh distributed statistical parameter, first, for the clutter vector g=[g of the obedience independent Rayleigh distribution of a NM dimension ₁..., g _i] (i=1 ..., NM), to the joint likelihood function of this vector take the logarithm process after, obtain:

$\mathrm{\&gamma;}(g,\mathrm{\&sigma;})=\mathrm{NM}\ln {\mathrm{\&sigma;}}^2-\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{g}_i+\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}\frac{{\left(g_i\right)}^2}{2{\mathrm{\&sigma;}}^2}---\left(13\right)$

Ask formula (13) about the derivative of σ, and make result be zero, obtain:

$\frac{\&PartialD;\left(\mathrm{\&gamma;}(g,\mathrm{\&sigma;})\right)}{\&PartialD;\mathrm{\&sigma;}}=\frac{2\mathrm{NM}}{\mathrm{\&sigma;}}-\frac{1}{{\mathrm{\&sigma;}}^3}\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{\left(g_i\right)}^2=0---\left(14\right)$

Therefore, then σ ²maximum likelihood estimator be:

${\mathrm{\&sigma;}}^2=\frac{\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{\left(g_i\right)}^2}{2\mathrm{NM}}---\left(15\right)$

For real beam scanning radar imaging, g _i=s _i-(Hf) _i, therefore utilize TIKHONOV regularization result of calculation and the statistical parameter that (15) formula that combines calculates about rayleigh distributed is:

${\mathrm{\&sigma;}}^2=\frac{\underset{i=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{(s_i-{\left(\mathrm{Hf}\right)}_i)}^2}{2\mathrm{NM}}---\left(16\right).$

7. real beam scanning radar angle according to claim 5 super-resolution imaging method, is characterized in that, the iteration expression formula that described step S52 builds is:

$f_{k+1}={(H^{T}H+{\left({\mathrm{\&sigma;}}^2\right)}_k{\left(P_k\right)}^{-1})}^{-1}(H^{T}s-{\left({\mathrm{\&sigma;}}^2\right)}_k{H}^T\frac{1}{s-{\mathrm{Hf}}_k})---\left(17\right)$

Wherein, iteration initial value is the result that (12) formula and (16) formula of (12) formula being brought into calculate, k+1 and k is the number of times of iteration, P _k=diag{ (p ₁) _k..., (p _nM) _k, (p _i) _k=| (f _i) _k| ^2-q.

8. real beam scanning radar angle according to claim 7 super-resolution imaging method, it is characterized in that, the condition of convergence in described step S56 is:

||f _k+1-f _k|| ²＜ε (18)

Wherein, f _k+1, f _kfor adjacent twice iteration result, ε is the threshold value preset.