CN104950305B - A kind of real beam scanning radar angle super-resolution imaging method based on sparse constraint - Google Patents

Abstract

The invention discloses a kind of real beam scanning radar angle super-resolution imaging method based on sparse constraint, comprise the following steps：S1, echo modeling, the geometrical relationship based on real beam scanning radar and target set up the echo data model of scanning radar；S2, enter to echo data row distance to pulse compression, realize distance to high-resolution；S3, the convolution model that the echo data after pulse compression is expressed as to antenna beam and the scattering coefficient of observation scene；S4, set up maximum a posteriori object function according to the obtained convolution models of S3, derive maximum a posteriori solution；S5, go out by the method precise restoration of adaptive iteration original object distribution.The present invention characterizes noise performance using rayleigh distributed, and react target distribution characteristic using sparse constraint, noise influence on RT is inhibited while inverting target distribution, so that angle superresolution processing result more approaches realistic objective distribution, real beam scanning radar angle super-resolution imaging is realized.

Description

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

Technical Field

The invention belongs to the technical field of radar imaging, and particularly relates to a real beam scanning radar angle super-resolution imaging method based on sparse constraint.

Background

The high-resolution imaging of the real beam scanning radar has great application value in the fields of ship navigation, tower monitoring, remote early warning and the like, and meanwhile, the imaging mode has the advantages of small volume, low cost and the like, so that the imaging mode has wide application prospect. Real beam scanning radar successively irradiates an imaging area at a fixed scanning speed, and two-dimensional echo information of the radar action area is obtained by transmitting a linear frequency modulation signal (LFM) and receiving an echo signalNumber (n). Since the transmit signal dimension is an LFM signal, high range resolution can be achieved by using pulse compression techniques. In azimuth, the real beam azimuth resolution is given byAnd determining, wherein λ is radar wavelength, D represents antenna aperture size, and although the real beam azimuth resolution is far lower than the range resolution, the limitation of the antenna wavelength and the aperture can be broken through by a signal processing method, the azimuth resolution is remarkably improved, and real beam radar angle super-resolution imaging is realized.

The document "Ly C, Dropkin H, manual a z. extension of the MUSIC algorithm-wave (mmw) real-beam radar scanning anti-radar, aerosense 2002" proposes to use the MUSIC algorithm in spectral estimation to achieve scanning radar azimuthal super-resolution imaging according to the echo characteristics of real-beam scanning radar, but this method requires a fast enough beat number to accurately estimate the covariance matrix of the noise, which is difficult to achieve in practical mechanical scanning radar applications, and at the same time the angular super-resolution performance of this method is severely degraded in the context of coherent sources.

Documents "y.zhang, w.li, y.huang, and j.yang.angular super resolution for real beam radar with iterative adaptive algorithm. in Geoscience and RemoteSensing Symposium (igars), 2013IEEE international.ieee,2013:3100 and 3103" propose an adaptive iterative angle super-resolution method based on real beam scanning radar, which is based on weighted minimum weighted two-times criterion, overcomes the limit of fast beat number and can significantly improve the azimuth resolution, but the method has too much computational complexity, occupies a large amount of system resources and seriously affects the real-time performance of imaging, and is difficult to be popularized to practical applications.

The documents "Huang Y, Zha Y, Zhang Y, et al.real-beam scanning radar azimuth-resolution, geoscience and Remote sensing symposium (IGARSS),2014IEEE, 2014:3081 and 3084" establish the real beam scanning radar azimuth echoes as convolution models of antenna patterns and target scattering coefficients, and reconstruct a target scene through a deconvolution algorithm, thereby realizing the real beam radar angular resolution. However, the assumed noise-compliant poisson distribution characteristic of the method does not accord with the actual radar imaging characteristic, so that the imaging performance of the algorithm is reduced sharply at a low signal-to-noise ratio.

Disclosure of Invention

The invention aims to overcome the defects of the prior art, provides a real beam scanning radar angle super-resolution imaging method which uses Rayleigh distribution to represent clutter characteristics, utilizes sparse constraint to reflect target distribution characteristics, suppresses the influence of noise on an imaging result while inverting target distribution, improves the estimation precision of Rayleigh distribution statistical parameters and realizes real beam scanning radar angle super-resolution imaging based on sparse constraint.

The invention aims to realize the following technical scheme, and discloses a real beam scanning radar angle super-resolution imaging method based on sparse constraint, which comprises the following steps of:

s1, echo modeling, namely establishing an echo data model of the scanning radar based on the geometrical relationship between the real beam scanning radar and the target;

s2, performing range-direction pulse compression on the echo data to realize high resolution of range direction;

s3, representing the echo data after pulse compression as a convolution model of the antenna beam and the scattering coefficient of the observation scene;

s4, establishing a maximum posterior objective function according to the convolution model obtained in the S3, and deducing a maximum posterior solution;

s5, accurately restoring the original target distribution by a self-adaptive iteration method, and comprising the following substeps:

s51, calculating an iteration initial value: obtaining iteration initial values of two parameters, namely a solution of an objective function and a Rayleigh distribution statistical parameter by using a TIKHONOV regularization method and a maximum likelihood estimation method;

s52, constructing an iterative expression according to the maximum posterior solution obtained in S4;

s53, substituting the iteration initial value into the iteration expression to obtain a new maximum posterior solution;

s54, bringing the maximum posterior solution obtained in the step S53 into a statistical parameter calculation formula of Rayleigh distribution, and updating a Rayleigh distribution statistical parameter value;

s55, substituting the maximum posterior solution obtained in S53 and the Rayleigh distribution statistical parameter value obtained in S54 into an iterative expression to obtain a new maximum posterior solution again;

and S56, repeating the steps S54 and S55 until the result of the iterative expression is compared with the result of the last iterative expression and the iterative convergence condition is met, and recording the result of the iterative expression as the real beam scanning radar angle super-resolution imaging result.

Further, the specific implementation method of step S1 is as follows: radar view angle at height HScanning-psi imaging areas in a clockwise sequence; at the initial moment, the initial slant distance between the radar antenna and the target at the central position of the scene is r₀Let the corresponding coordinates of each target point in the scene be (x)_i,y_i) The azimuth angle between each target and the radar is theta_iThe slant distance between each target and the radar is r_i；

Setting the transmitted signal to be a chirp signalWherein rect (-) denotes a rectangular signal, which is defined asTau is the distance fast time variable, T is the emission pulse duration, c is the speed of light, lambda is the wavelength, K_rIs the frequency modulation slope; is composed ofEnsuring that the theory is consistent with the actual verification condition, and performing discrete processing on the received wave; the discretized echo analytic expression is as follows:

wherein, Ω is the target scene range, θ is the antenna beam width, f (x)_i,y_i) Is a point (x)_i,y_i) A scattering function of the target; omega is the antenna scanning speed, T_βIs the dwell time of the target at the 3dB antenna beamwidth.

Further, the specific implementation method of step S2 includes the following sub-steps:

s21, constructing a distance-direction pulse pressure reference signal:

wherein,representing a distance to a reference time;

s22, mixing S_refAnd echo dataPerforming maximum autocorrelation operation to obtain a pulse-compressed two-dimensional signal as follows:

where B is the transmit signal bandwidth.

Further, the specific implementation method of step S3 is as follows: the convolution model of the echo signal is represented as:

where, s ═ s (1, 1), s (1, 2), …, s (N, 1), …, s (N, M)]^TThe vector is NM × 1 dimension vector, which is the result of rearranging the measured values of all the echo signals after pulse compression in the azimuth direction according to the sequence of distance units, and the superscript T represents transposition operation;

f＝[f(1，1)，f(1，2)，…,f(N，1)，…，f(N，M)]^Ta vector of dimension NM × 1, which is the result of rearranging the amplitudes of all unknown objects in the imaging region in the azimuthal direction in range-unit order;

n＝[n(1，1)，n(1，2)，…,n(N，1)，…，n(N，M)]^Ta vector of NM × 1 dimension, representing clutter and interference signal components, subject to statistically independent Rayleigh distributions;

h is matrix of NM × NM dimension, and matrix H is measured by convolution_M×NIs formed of (I) a compound of formula (I) wherein H_M×N＝[h₁,h₂,…,h_M]。

Further, the specific implementation method of step S4 is as follows: on the basis of a Bayes formula, a maximum posterior probability deconvolution super-resolution method is deduced by combining the given noise statistical characteristics and sparse target distribution prior information, so that convolution inversion is realized, and the method specifically comprises the following substeps:

s41, regarding the formula (3), the posterior probability of the echo data is expressed as follows by using the bayesian formula:

wherein p (-) represents a probability density function; according to the maximum a posteriori criterion, the deconvolution problem is transformed into the solution of the optimal solution f so that it satisfies:

wherein,maximum a posteriori estimation for the objective function; p (f/s), p (s/f) and p (f) respectively represent the posterior probability, the likelihood probability and the prior probability of the target of the echo data;

s42, assuming that the clutter or interference signal of each sampling point in the real beam scanning radar echo signal obeys the statistically independent rayleigh distribution, the likelihood probability is expressed as:

where i is each discrete point target,

σ²is a statistical parameter in the rayleigh distribution;

s43, selecting sparse characteristics as regularization constraint terms, wherein the probability density of target scattering sparseness is as follows:

wherein q is more than 0 and less than or equal to 1; when q is 1, p (f) · varies as exp (-2| | f | | non-calculation)₁) Is a laplace distribution; when q → 1, the probability of the target is

S44, obtaining the maximum posterior objective function according to the expressions (6) and (7) as follows:

taking the negative natural logarithm of formula (8) to obtain:

obtaining the gradient operation of the formula (9) with respect to f to obtain:

wherein, (.)^TDenotes a transpose operation, P ═ diag { P₁，…，p_NM}，p_i＝|f_i|^2-q；

S45, since equation (10) is a non-linear function, the result of approximating the original scene can only be obtained by an iterative method, and equation (10) is set to zero, so that the maximum a posteriori solution for f is obtained as:

further, the step S51 is specifically implemented by the following steps:

s511, calculating the rough estimation result of the original scene by using a TIKHONOV regularization method, wherein the rough estimation result comprises the following steps:

f＝(H^TH+βI)^-1H^Ts (12)

wherein, beta is a regularization parameter, and I is an NM multiplied by NM dimension unit diagonal matrix;

s512, estimating Rayleigh distribution statistical parameters by utilizing a maximum likelihood estimation method, firstly, aiming atClutter vector g ═ g in NM dimension subject to independent Rayleigh distribution₁，…，g_i](i 1, …, NM), the log of the joint likelihood function of the vector yields:

taking the derivative of equation (13) with respect to σ and letting the result be zero, yields:

therefore, then σ²The maximum likelihood estimate of (c) is:

for real beam scanning radar imaging, g_i＝s_i-(Hf)_iTherefore, using the TIKHONOV regularization calculation in combination with equation (15) to calculate the statistical parameters for the rayleigh distribution is:

further, the iterative expression constructed in step S52 is:

wherein the iteration initial value is the result of the calculation of formula (12) and the formula (12) is substituted into the formula (16), k +1 and k are the number of iterations, P_k＝diag{(p₁)_k，…，(p_NM)_k}，(p_i)_k＝|(f_i)_k|^2-q。

Further, the convergence condition in step S56 is:

||f_k+1-f_k||²＜ (18)

wherein f is_k+1、f_kThe two adjacent iteration results are preset threshold values.

The invention has the beneficial effects that: the method is characterized in that the clutter characteristic is represented by Rayleigh distribution, the target distribution characteristic is reflected by sparse constraint, the influence of noise on an imaging result is suppressed while target distribution is inverted, in addition, in the iterative processing, the estimation precision of Rayleigh distribution statistical parameters is improved by using a self-adaptive method, so that the angle super-resolution processing result is closer to the actual target distribution, and finally the real-beam scanning radar angle super-resolution imaging is realized.

Drawings

FIG. 1 is a flow chart of an imaging method of the present invention;

FIG. 2 is a diagram of a real beam scanning radar imaging mode in accordance with an embodiment of the present invention;

FIG. 3 is a diagram of the radar antenna pattern of the present embodiment;

FIG. 4 is a simulation scenario diagram of the present embodiment;

fig. 5 is a diagram of an echo profile in a clutter scene (SCR ═ 25 dB);

fig. 6 is a diagram of the final scanning radar imaging result after the processing of the embodiment.

Detailed Description

The technical solution of the present invention is further described below with reference to the accompanying drawings, but the present invention is not limited to the following.

As shown in fig. 1, a real beam scanning radar angle super-resolution imaging method based on sparsity constraint includes the following steps:

s1, echo modeling, namely establishing an echo data model of the scanning radar based on the geometrical relationship between the real beam scanning radar and the target; the specific implementation method comprises the following steps: radar view angle at height HScanning-psi imaging areas in a clockwise sequence; at the initial moment, the initial slant distance between the radar antenna and the target at the central position of the scene is r₀Let the corresponding coordinates of each target point in the scene be (x)_i,y_i) The azimuth angle between each target and the radar is theta_iThe slant distance between each target and the radar is r_i；

Setting the transmitted signal to be a chirp signalWherein rect (-) denotes a rectangular signal, which is defined asTau is the distance fast time variable, T is the emission pulse duration, c is the speed of light, lambda is the wavelength, K_rIs the frequency modulation slope; in order to ensure that the theory is consistent with the actual verification condition, the received echo is subjected to discrete processing; the discretized echo analytic expression is as follows:

wherein, Ω is the target scene range, θ is the antenna beam width, f (x)_i,y_i) Is a point (x)_i,y_i) A scattering function of the target; omega is the antenna scanning speed, T_βIs the dwell time of the target at the 3dB antenna beamwidth. This embodiment uses forward looking scanning radar imaging motionGeometric mode, as shown in fig. 2, the scanning radar imaging parameters are shown in table one.

Tabulated scanning radar system parameters

Parameter(s)	Symbol	Numerical value
			Carrier frequency	fc	10GHz
Transmission signal time width	T	10μs
			Bandwidth of transmitted signal	B	50MHz
Pulse sampling frequency	PRF	1500Hz
			Scanning speed of antenna	ω	60°/s
Antenna beam width	θ	2.5°
			Scanning range	Φ	-12°～12°
Scanning radar range	R0	10km

S2, performing range-direction pulse compression on the echo data to realize high resolution of range direction; the specific implementation method comprises the following substeps:

s21, constructing a distance-direction pulse pressure reference signal:

wherein,representing a distance to a reference time;

s22, mixing S_refAnd echo dataPerforming maximum autocorrelation operation to obtain a pulse-compressed two-dimensional signal as follows:

where B is the transmit signal bandwidth.

S3, representing the echo data after pulse compression as a convolution model of the antenna beam and the scattering coefficient of the observation scene; the specific implementation method comprises the following steps: the convolution model of the echo signal is represented as:

where, s ═ s (1, 1), s (1, 2), …, s (N, 1), …, s (N, M)]^TThe vector is NM × 1 dimension vector, which is the result of rearranging the measured values of all the echo signals after pulse compression in the azimuth direction according to the sequence of distance units, and the superscript T represents transposition operation;

f＝[f(1，1)，f(1，2)，…,f(N，1)，…，f(N，M)]^Ta vector of dimension NM × 1, which is the result of rearranging the amplitudes of all unknown objects in the imaging region in the azimuthal direction in range-unit order;

n＝[n(1，1)，n(1，2)，…,n(N，1)，…，n(N，M)]^Ta vector of NM × 1 dimension, representing clutter and interference signal components, subject to statistically independent Rayleigh distributions;

h is matrix of NM × NM dimension, and matrix H is measured by convolution_M×NIs formed of (I) a compound of formula (I) wherein H_M×N＝[h₁,h₂,…,h_M]。

S4, establishing a maximum posterior objective function according to the convolution model obtained in the S3, and deducing a maximum posterior solution; the specific implementation method comprises the following steps: on the basis of a Bayes formula, a maximum posterior probability deconvolution super-resolution method is deduced by combining the given noise statistical characteristics and sparse target distribution prior information, so that convolution inversion is realized, and the method specifically comprises the following substeps:

s41, regarding the formula (3), the posterior probability of the echo data is expressed as follows by using the bayesian formula:

wherein p (-) represents a probability density function; according to the maximum a posteriori criterion, the deconvolution problem is transformed into the solution of the optimal solution f so that it satisfies:

wherein,maximum a posteriori estimation for the objective function; p (f/s), p (s/f) and p (f) respectively represent the posterior probability, the likelihood probability and the prior probability of the target of the echo data;

s42, assuming that the clutter or interference signal of each sampling point in the real beam scanning radar echo signal obeys the statistically independent rayleigh distribution, the likelihood probability is expressed as:

where i is each discrete point target,

σ²is a statistical parameter in the rayleigh distribution;

s43, selecting sparse characteristics as regularization constraint terms, wherein the probability density of target scattering sparseness is as follows:

wherein q is more than 0 and less than or equal to 1; when q is 1, p (f) · varies as exp (-2| | f | | non-calculation)₁) Is a laplace distribution; when q → 1, the probability of the target is

S44, obtaining the maximum posterior objective function according to the expressions (6) and (7) as follows:

taking the negative natural logarithm of formula (8) to obtain:

obtaining the gradient operation of the formula (9) with respect to f to obtain:

wherein, (.)^TDenotes a transpose operation, P ═ diag { P₁，…，p_NM}，p_i＝|f_i|^2-q；

S45, since equation (10) is a non-linear function, the result of approximating the original scene can only be obtained by an iterative method, and equation (10) is set to zero, so that the maximum a posteriori solution for f is obtained as:

s5, accurately restoring the original target distribution by a self-adaptive iteration method, and comprising the following substeps:

s51, calculating an iteration initial value: obtaining iteration initial values of two parameters, namely a solution of an objective function and a Rayleigh distribution statistical parameter by using a TIKHONOV regularization method and a maximum likelihood estimation method; the specific implementation comprises the following steps:

s511, calculating the rough estimation result of the original scene by using a TIKHONOV regularization method, wherein the rough estimation result comprises the following steps:

f＝(H^TH+βI)^-1H^Ts (12)

wherein, beta is a regularization parameter, and I is an NM multiplied by NM dimension unit diagonal matrix;

s512, estimating the statistical parameters of the rayleigh distribution by the maximum likelihood estimation method, first, with respect to a clutter vector g ═ g [ g ] of one NM dimension, which follows the independent rayleigh distribution₁，…，g_i](i 1, …, NM), the log of the joint likelihood function of the vector yields:

taking the derivative of equation (13) with respect to σ and letting the result be zero, yields:

therefore, then σ²The maximum likelihood estimate of (c) is:

for real beam scanning radar imaging, g_i＝s_i-(Hf)_iTherefore, using the TIKHONOV regularization calculation in combination with equation (15) to calculate the statistical parameters for the rayleigh distribution is:

s52, constructing an iterative expression according to the maximum posterior solution obtained in S4:

wherein the iteration initial value is the result of the calculation of formula (12) and the formula (12) is substituted into the formula (16), k +1 and k are the number of iterations, P_k＝diag{(p₁)_k，…，(p_NM)_k}，(p_i)_k＝|(f_i)_k|^2-q。

S53, substituting the iteration initial value into the iteration expression to obtain a new maximum posterior solution;

s54, bringing the maximum posterior solution obtained in the step S53 into a statistical parameter calculation formula of Rayleigh distribution, and updating a Rayleigh distribution statistical parameter value;

s55, substituting the maximum posterior solution obtained in S53 and the Rayleigh distribution statistical parameter value obtained in S54 into an iterative expression to obtain a new maximum posterior solution again;

s56, repeating the steps S54 and S55 until the result of the iterative expression is compared with the result of the last iterative expression, and when the iterative convergence condition is met, recording that the result of the iterative expression is the real beam scanning radar angle super-resolution imaging result, wherein the convergence condition is as follows:

||f_k+1-f_k||²＜ (18)

wherein f is_k+1、f_kThe two adjacent iteration results are preset threshold values.

In this embodiment, the radar antenna pattern shown in fig. 3 is adopted, fig. 4 is a simulation scene diagram of this embodiment, fig. 5 is an echo profile diagram in a clutter scene (SCR ═ 25dB) of this embodiment, and fig. 6 is a final scanning radar imaging result diagram processed by this embodiment. As can be seen from the figure, the method provided by the invention can well recover the angle information of the target in the Rayleigh clutter background.

It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (4)

1. A real beam scanning radar angle super-resolution imaging method based on sparse constraint is characterized by comprising the following steps:

s1, echo modeling, namely establishing an echo data model of the scanning radar based on the geometrical relationship between the real beam scanning radar and the target; the specific implementation method comprises the following steps: radar view angle at height HScanning-psi imaging areas in a clockwise sequence; initial time, radar antenna andthe initial slope distance of the target at the central position of the scene is r₀Let the corresponding coordinates of each target point in the scene be (x)_i,y_i) The azimuth angle between each target and the radar is theta_iThe slant distance between each target and the radar is r_i；

Setting the transmitted signal to be a chirp signalWherein rect (-) denotes a rectangular signal, which is defined asTau is the distance fast time variable, T is the emission pulse duration, c is the speed of light, lambda is the wavelength, K_rIs the frequency modulation slope; in order to ensure that the theory is consistent with the actual verification condition, the received echo is subjected to discrete processing; the discretized echo analytic expression is as follows:

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

wherein, Ω is the target scene range, θ is the antenna beam width, f (x)_i,y_i) Is a point (x)_i,y_i) A scattering function of the target; omega is the antenna scanning speed, T_βIs the dwell time of the target at the 3dB antenna beamwidth;

s2, performing range-direction pulse compression on the echo data to realize high resolution of range direction; the specific implementation method comprises the following substeps:

s21, constructing a distance-direction pulse pressure reference signal:

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

wherein, tau_refRepresenting a distance to a reference time;

s22, mixing S_refPerforming maximum autocorrelation operation on the echo data s (θ, τ) to obtain a pulse-compressed two-dimensional signal:

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

wherein, B is the transmission signal bandwidth;

s3, representing the echo data after pulse compression as a convolution model of the antenna beam and the scattering coefficient of the observation scene; the specific implementation method comprises the following steps: the convolution model of the echo signal is represented as:

where, s ═ s (1, 1), s (1, 2), …, s (N, 1), …, s (N, M)]^TThe vector is NM × 1 dimension vector, which is the result of rearranging the measured values of all the echo signals after pulse compression in the azimuth direction according to the sequence of distance units, and the superscript T represents transposition operation;

f＝[f(1，1)，f(1，2)，…，f(N，1)，…，f(N，M)]^Ta vector of dimension NM × 1, which is the result of rearranging the amplitudes of all unknown objects in the imaging region in the azimuthal direction in range-unit order;

n＝[n(1，1)，n(1，2)，…，n(N，1)，…，n(N，M)]^Ta vector of NM × 1 dimension, representing clutter and interference signal components, subject to statistically independent Rayleigh distributions;

h is matrix of NM × NM dimension, and matrix H is measured by convolution_M×NIs formed of (I) a compound of formula (I) wherein H_M×N＝[h₁，h₂，...，h_M]；

S4, establishing a maximum posterior objective function according to the convolution model obtained in the S3, and deducing a maximum posterior solution; the specific implementation method comprises the following steps: on the basis of a Bayes formula, a maximum posterior probability deconvolution super-resolution method is deduced by combining the given noise statistical characteristics and sparse target distribution prior information, so that convolution inversion is realized, and the method specifically comprises the following substeps:

s41, regarding the formula (3), the posterior probability of the echo data is expressed as follows by using the bayesian formula:

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

wherein p (-) represents a probability density function; according to the maximum a posteriori criterion, the deconvolution problem is transformed into the solution of the optimal solution f so that it satisfies:

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

wherein,maximum a posteriori estimation for the objective function; p (f/s), p (s/f) and p (f) respectively represent the posterior probability, the likelihood probability and the prior probability of the target of the echo data;

s42, assuming that the clutter or interference signal of each sampling point in the real beam scanning radar echo signal obeys the statistically independent rayleigh distribution, the likelihood probability is expressed as:

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

where i is each discrete point target,

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

σ²is a statistical parameter in the rayleigh distribution;

s43, selecting sparse characteristics as regularization constraint terms, wherein the probability density of target scattering sparseness is as follows:

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

wherein q is more than 0 and less than or equal to 1; when q is 1, p (f) · varies as exp (-2| | f | | non-calculation)₁) Is a laplace distribution; when q → 1, the probability of the target is

S44, obtaining the maximum posterior objective function according to the expressions (6) and (7) as follows:

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

taking the negative natural logarithm of formula (8) to obtain:

obtaining the gradient operation of the formula (9) with respect to f to obtain:

wherein, (.)^TDenotes a transpose operation, P ═ diag { P₁，…，p_NM}，p_i＝|f_i|^2-q；

S45, since equation (10) is a non-linear function, the result of approximating the original scene can only be obtained by an iterative method, and equation (10) is set to zero, so that the maximum a posteriori solution for f is obtained as:

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

s5, accurately restoring the original target distribution by a self-adaptive iteration method, and comprising the following substeps:

s51, calculating an iteration initial value: obtaining iteration initial values of two parameters, namely a solution of an objective function and a Rayleigh distribution statistical parameter by using a TIKHONOV regularization method and a maximum likelihood estimation method;

s52, constructing an iterative expression according to the maximum posterior solution obtained in S4;

s53, substituting the iteration initial value into the iteration expression to obtain a new maximum posterior solution;

s54, bringing the maximum posterior solution obtained in the step S53 into a statistical parameter calculation formula of Rayleigh distribution, and updating a Rayleigh distribution statistical parameter value;

s55, substituting the maximum posterior solution obtained in S53 and the Rayleigh distribution statistical parameter value obtained in S54 into an iterative expression to obtain a new maximum posterior solution again;

and S56, repeating the steps S54 and S55 until the result of the iterative expression is compared with the result of the last iterative expression and the iterative convergence condition is met, and recording the result of the iterative expression as the real beam scanning radar angle super-resolution imaging result.

2. The real beam scanning radar angle super-resolution imaging method according to claim 1, wherein the step S51 is implemented by the steps of:

s511, calculating the rough estimation result of the original scene by using a TIKHONOV regularization method, wherein the rough estimation result comprises the following steps:

f＝(H^TH+βI)^-1H^Ts (12)

wherein, beta is a regularization parameter, and I is an NM multiplied by NM dimension unit diagonal matrix;

s512, estimating the statistical parameters of the rayleigh distribution by the maximum likelihood estimation method, first, with respect to a clutter vector g ═ g [ g ] of one NM dimension, which follows the independent rayleigh distribution₁，…，g_i](i 1, …, NM), the log of the joint likelihood function of the vector yields:

$\mathrm{\γ}(g,\mathrm{\σ})=NM{\mathrm{ln\σ}}^2-\underset{i=1}{\overset{NM}{\Σ}}{g}_i+\underset{i=1}{\overset{NM}{\Σ}}\frac{{\left(g_i\right)}^2}{2{\mathrm{\σ}}^2}---\left(13\right)$

taking the derivative of equation (13) with respect to σ and letting the result be zero, yields:

$\frac{\∂\left(\mathrm{\γ}\right(g,\mathrm{\σ}\left)\right)}{\∂\mathrm{\σ}}=\frac{2NM}{\mathrm{\σ}}-\frac{1}{{\mathrm{\σ}}^3}\underset{i=1}{\overset{NM}{\Σ}}{\left(g_i\right)}^2=0---\left(14\right)$

therefore, then σ²The maximum likelihood estimate of (c) is:

${\mathrm{\σ}}^2=\frac{\underset{i=1}{\overset{NM}{\Σ}}{\left(g_i\right)}^2}{2NM}---\left(15\right)$

for real beam scanning radar imaging, g_i＝s_i-(Hf)_iTherefore, using the TIKHONOV regularization calculation in combination with equation (15) to calculate the statistical parameters for the rayleigh distribution is:

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

3. the real beam scanning radar angle super-resolution imaging method according to claim 2, wherein the iterative expression constructed in the step S52 is:

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

where v is the initial value of the iteration of equation (12) and the result of substituting equation (12) into equation (16), k +1 and k are the number of iterations, P_k＝diag{(p₁)_k，…，(p_NM)_k}，(pi)k＝|(f_i)k|^2q。

4. The real beam scanning radar angle super-resolution imaging method according to claim 3, wherein the convergence condition in step S56 is:

||f_k+1-f_k||²＜ (18)

wherein f is_k+1、f_kThe two adjacent iteration results are preset threshold values.