CN104950306B - Method for realizing angular super-resolution imaging of forward-looking sea surface targets in sea clutter background - Google Patents

Abstract

The invention discloses a method for realizing angular super-resolution imaging of forward-looking sea surface targets in a sea clutter background. According to the convolution characteristic of azimuth dimension echoes of scanning radar, echo signals of the scanning radar are rearranged into a form of the product of an azimuth dimension target vector and a convolution measurement matrix in the distance dimension order. Then a maximum posterior target function for solving original scene distribution is constructed on the basis of the Bayes formula according to characteristics that sea clutter obeys Rayleigh distribution and the sea surface targets obey Laplace, original sea surface target distribution is inverted by the aid of an acquired maximum posterior deconstruction iterative equation, and angular super-resolution imaging is realized. According to the method, the Rayleigh distribution is used for representing sea clutter characteristics, the Laplace distribution is used for representing the target characteristics, an iteration expression of the convolution inversion problem is derived in the Bayes principle, reconstruction of original imaging scenes is realized, and azimuth high-definition pictures of the forward-looking sea surface targets are acquired.

Description

Forward sight sea-surface target angle super-resolution imaging method under a kind of sea clutter background

Technical field

The invention belongs to radar imaging technology field, and in particular to forward sight sea-surface target angle oversubscription under a kind of sea clutter background Distinguish the design of imaging method.

Background technology

The high-resolution imaging of airborne platform forward sight water area, is compiling to sea detection with imaging, sea-surface target search and rescue, naval vessel Team recognizes, has huge application demand to fields such as warship attacks.However, due to target in forward vision areas and airborne platform motion The doppler bandwidth of generation is narrow, it is impossible to real using Synthetic Aperture Radar Technique (SAR) and Doppler beam sharpening method (DBS) Target bearing high-resolution imaging in existing forward vision areas.Therefore, airborne radar generally obtains front-view area using the mode of scanning sample Real wave beam echo-signal in domain.Because radar emission signal is linear FM signal (LFM), obtained using pulse compression technique The high-resolution of distance dimension.For the azimuth dimension of echo-signal, due to being limited by antenna size, it is difficult to obtain and target range point The azimuth resolution that resolution matches, has had a strong impact on the application of the radar operation mode.Therefore, it is necessary to pass through at signal The mode of reason, is obviously improved orientation radar angular resolution.

Because scanning radar orientation signal can be regarded as the convolution of antenna radiation pattern and target scattering coefficient, therefore can To realize the reconstruct of target scene by the method for deconvolution, the purpose of real beam positional angle super-resolution is reached.In document “B.Clark.An efficient implementation of the algorithm‘clean’.Astronomy and Astrophysics, vol.89, p.377,1980 " in, it is proposed that one kind can be improved apart from peacekeeping azimuth dimension resolution simultaneously Clean algorithms.But, this method is unable to suppressed sidelobes enhancing, and when multiple targets are occurred in same wave beam, Super-resolution performance has and is decreased obviously.

Document " Jinchen Guan, Jianyu Yang and Yulin Huang.Maximum A Posteriori- Based Angular Superresolution for Scanning Radar Imaging.IEEE TRANSACTIONS ON In AEROSPACE AND ELECTRONIC SYSTEMS VOL.50, NO.3JULY 2014 ", it is proposed that after one kind is based on maximum The angle ultra-resolution method tested under criterion, noise and target obey independent Poisson distribution in the echo-signal that the method is assumed, so And these hypothesis are not suitable for the target angle super-resolution imaging under sea clutter background, Air-borne Forward-looking sea mesh is applied this method to In mark angle super-resolution imaging, the appearance that target displacement and noise amplify can be caused, have a strong impact on image quality.

The content of the invention

The invention aims to solve there is target in existing Air-borne Forward-looking sea-surface target angle super-resolution imaging technology A kind of the problems such as dislocation and noise amplify, it is proposed that forward sight sea-surface target angle super-resolution imaging method under sea clutter background.

The technical scheme is that：Forward sight sea-surface target angle super-resolution imaging method under a kind of sea clutter background, including Following steps：

S1, the kinematic geometry mould that forward sight scanning radar echo-signal is set up according to the geometrical relationship of airborne radar and target Type；

S2, echo-signal is entered row distance to pulse compression；

S3, Range Walk Correction is carried out to the echo-signal after pulse compression；

S4, according to orientation echoing characteristicss, by the echo-signal after Range Walk Correction according to the distance dimension side of being rearranged for Position object vector and the product form of convolution calculation matrix, build orientation convolution model；

S5, according to orientation convolution model, using noise and the statistical property of target distribution, set up most under Bayesian frame Big posteriority object function simultaneously derives iteration expression formula, realizes Deconvolution；

S6, ask for clutter statistical parameter and regularization parameter；

S7, clutter statistical parameter and regularization parameter are substituted in the iteration expression formula of step S5, restore original image field Scape, realizes forward-looking radar to sea-surface target angle super-resolution imaging.

Further, step S1 is specially：

If carrier aircraft platform movement velocity is v, antenna scans clockwise scene, initial time, in range cell R₀Place's distribution Target P_n；Elapsed time t, in carrier aircraft platform and scene P is located at_nThe distance of target, is designated as R at point_n(t)；Now, target is to thunder Oblique distance history approximate representation between soothing the liver is：

R_n(t)≈R₀-vt (1)

If transmission signal is linear FM signalWherein, rect () Rectangular signal is represented, it is defined asτ is distance to time variable, width when T is pulse, and c is the light velocity, λ is wavelength, K_rFor chirp rate；

Discrete processes are carried out to being received back to ripple, the orientation discrete sampling points for making single range cell areWherein, φ is sweep limitss, θ_bIt is antenna beamwidth, γ is scanning speed, and PRI is the pulse repetition period, Then discretization echo analytical expression is：

Wherein, t be orientation time variable, σ_nFor the scattering function of n-th sample point target of orientation, θ_nFor n-th The corresponding antenna pointing angle of target；ω is the window function of slow time domain, represents modulation of the antenna radiation pattern function in orientation.

Further, step S2 is specially：

Distance is built to pulse compression reference signalWherein, τ_refRepresent Distance is to the reference time；

By s_refMaximum auto-correlation computation is carried out with echo signal data s (t, τ), the echo-signal after pulse compression is obtained For：

Wherein, B is transmitted signal bandwidth.

Further, step S3 is specially：

Range Walk Correction function is constructed apart from course according to echoWherein, f_rIt is distance To frequency；

By Range Walk Correction function and s₁(t, τ) is multiplied, and obtaining the echo-signal after Range Walk Correction is：

Further, step S4 is specially：

By two-dimentional echo-signal s in formula (4)₂(t, τ) after rearranging apart from dimension order according to obtaining following matrix Vector product form：

Wherein, s=[s (and 1,1) ... s (1,2) ..., s (1, N) ..., s (L, N)]^TIt is by the measured value in all distance dimensions The vector of LN × 1 dimension after rearranging in orientation, subscript T represents transposition computing, and L is scene echoes distance dimension sampled point Number；X=[x (1,1), x (1,2) ..., x (1, M) ..., x (L, M)]^TIt is by distance by each orientation target amplitude in image scene Dimension order rearranged after LM × 1 dimension vector,For the orientation of single range cell Sampled point,It is the sampling number of single wave beam；N=[n (1,1), n (1,2) ..., n (1, N) ..., n (L, N) ]^TIt is to represent the vector that LN × 1 of sea clutter amplitude characteristic is tieed up, Rayleigh distributed；A is one by convolution calculation matrix A_N×MStructure Into LN × LM dimension matrix, wherein, A_N×M=[a₁,a₂,…a_N] be real beam scanning antennas convolution calculation matrix, A_N×MTable It is shown as：

Wherein,For antenna radiation pattern weight coefficient；

From formula (6), Doppler's additive phase of each row is identical, then the nth elements of echo vector s are represented For：

Wherein, h_niRepresent the weighted amplitude value of the individual element of convolution matrix A (n, i)；

Because the purpose of radar imagery is to restore target amplitude and positional information in image scene, therefore echo-signal It is expressed as：

| s |=| A | x+n (8)

Wherein, | | it is modulo operation；

Therefore, the front visual angle super-resolution imaging of real beam scanning radar is just converted into：S and A in given formula (8), solves x Inversion problem.

Further, step S5 is specially：

According to Bayesian formula, the posterior probability of echo data is expressed as：

Wherein, p () represents probability density function；

Maximum a posteriori is exactly to find most suitable x to meet following formula：

Wherein,For the maximum a posteriori solution of target information；P (x/s), p (s/x) and p (x) represent respectively posterior probability letter Number, likelihood probability function and target prior information；

Negative natural logrithm operation is carried out to formula (10), maximum a posteriori problem is converted to：

Assume the clutter statistical iteration in each discrete echo sampled point, then likelihood probability function is：

Wherein, n is each pixel of discrete echo signal,σ²It is the clutter statistics of rayleigh distributed Parameter；

Because forward sight is usually applied to the location tracking of a small amount of sea-surface target in big imaging scene to marine origin picture, therefore, sea Area Objects have sparse characteristic relative to imaging region, are expressed as target distribution using laplacian distribution：

Wherein, μ ＞ 0 are the scale parameters of laplacian distribution；

Formula (12) and (13) are substituted into into formula (10), maximum a posteriori probability function is obtained：

Natural logrithm is taken to formula (14), is obtained：

Wherein, λ=1/ μ is regularization parameter, for the openness and image quality of balancing objective information recovery result；

L in order to overcome object function₁The problem of norm non-differentiability at zero point, uses the smooth technology estimated by formula (15) it is approximately：

Wherein, ε takes the nonnegative constant for being similar to zero；

Gradient algorithm is carried out to formula (16), is obtained：

Wherein,

Because formula (17) is the nonlinear function with regard to x, it is impossible to directly makeObtain the optimum of object function Solution, here using the method for iteration, obtain first with regard toA simple solution be：

Wherein, iterative initial value selects to be x=(A^TA)^-1A^TS, is the least square solution of formula (8), while the iteration of W (x) Initial value is constituted also with the initial value of x, and iteration expression formula is expressed as：

Wherein, k+1 and k is iterationses,Formula (19) is maximum a posteriori The expression-form of algorithm.

Further, step S6 is specially：

The single range cell signal without target distribution in two-dimentional echo-signal is taken, if dimension is adopted for the sea clutter amplitude of N Sample sequence f₁..., f_N, rayleigh distributed carried out after logarithm operation, obtains following expression：

The derivation of equation (20) is obtained with regard to the gradient of σ：

Clutter statistical parameter σ is obtained by formula (21)²Maximum likelihood solution be：

Then λ is chosen using discrepancy principle, that is, chooses order | | y-Ax (λ) | |²≈E[||n||²] when λ is regularization parameter.

The invention has the beneficial effects as follows：The present invention will scan thunder according to the convolution property of the azimuth dimension echo of scanning radar Up to echo-signal by the product form that azimuth dimension object vector and convolution calculation matrix are rearranged for apart from dimension order.Further according to It is original that the characteristic of sea clutter Rayleigh distributed and sea-surface target obedience Laplce builds solution on the basis of Bayesian formula The maximum a posteriori object function of scene distribution, and iterative equation is built using the maximum a posteriori solution for obtaining, it is finally inversed by original sea Target distribution, realizes angle super-resolution imaging.The present invention characterizes sea clutter characteristic using rayleigh distributed, is characterized with laplacian distribution Target property, derives the iteration expression formula of Deconvolution problem under bayesian criterion, realizes the reconstruct of original image scene, Obtain the orientation high-definition picture of forward sight sea-surface target.

Description of the drawings

Forward sight sea-surface target angle super-resolution imaging method flow chart under a kind of sea clutter background that Fig. 1 is provided for the present invention.

Fig. 2 is to simulate the original sea-surface target scene graph under sea clutter background.

Fig. 3 is pulse compression and the reality beam pattern of the azimuth dimension after Range Walk Correction.

Fig. 4 is scanning radar antenna radiation pattern.

Fig. 5 is the sea-surface target angle super-resolution imaging result schematic diagram after the inventive method process.

Specific embodiment

Embodiments of the invention are further described below in conjunction with the accompanying drawings.

Present disclosure is described for convenience, and following term is explained first：

(1) radar angle super-resolution

Radar angle super-resolution refers to method of the radar by signal processing, breaks through the intrinsic resolution limit of imaging system, Reach the high resolution in orientation.

(2) real beam scanning radar

Real beam scanning radar, is a kind of transmitted antednna beam by way of mechanical rotation, makes wave beam equal in orientation Radar that is even or anisotropically scanning scene objects.

(3) sea clutter

Calling sea clutter from the echo-signal of sea surface reflection in field of radar, it be by wave, wind speed, wave relative to The direction of radar beam, the appearance of persistent period and unrestrained peak, ebb, flood tide and affect capillary pollution decision.

(4) rayleigh distributed

Rayleigh distributed probability density function is：

Wherein, σ²For statistical parameter, v >=0.

The invention provides forward sight sea-surface target angle super-resolution imaging method under a kind of sea clutter background, as shown in figure 1, bag Include following steps：

S1, the kinematic geometry mould that forward sight scanning radar echo-signal is set up according to the geometrical relationship of airborne radar and target Type.

The embodiment of the present invention adopts forward sight scanning radar imaging moving geometric mode, scanning radar imaging parameters such as following table institute Show：

Parameter	Symbol	Numerical value
			Carrier frequency	fc	10GHz
Width during transmission signal pulse	T	10μs
			Transmitted signal bandwidth	B	30MHz
Impulse sampling frequency	PRF	1000Hz
			Antenna scanning speed	γ	30°/s
Antenna beamwidth	θb	2.5°
			Sweep limitss	φ	- 3 °～3 °
Carrier aircraft platform movement velocity	v	100m/s
			Scanning radar operating distance	R0	3km

Carrier aircraft platform movement velocity v=100m/s, antenna scans clockwise scene, initial time, in range cell R₀= Distribution objectives P at 3km_n；Elapsed time t, in carrier aircraft platform and scene P is located at_nThe distance of target, is designated as R at point_n(t), target It is expressed as to the oblique distance history between radarTo oblique distance history R_nT () is at t=0 Taylor series expansion is carried out, can be obtainedIn practical application, due to making With distance it is remote, imaging sector is little, scanning speed is fast, oblique distance history can be reduced to R_n(t)≈R₀-vtcosθ_n.Again because radar The azimuth of forword-looking imaging is typically smaller than 10 °, therefore cos θ_n≈1.Therefore, target can be approximate to the oblique distance history between radar It is expressed as：

R_n(t)≈R₀-vt (1)

If transmission signal is for linear FM signalWherein, rect () represents rectangular signal, and it is defined asτ is distance to time variable, width when T is pulse, this In bright embodiment, T=10 μ s, c are the light velocity, and λ is wavelength, K_rFor chirp rate.

To ensure that theory is consistent with actual verification situation, discrete processes are carried out to being received back to ripple, made single range cell Orientation discrete sampling points beWherein, φ is sweep limitss, θ_bIt is antenna beamwidth, γ is to sweep Speed is retouched, PRI is the pulse repetition period, in the embodiment of the present invention, φ=- 3 °～3 °, θ_b=2.5 °, γ=30 °/s, PRI= 10^-3s。

Then discretization echo analytical expression is：

Wherein, t be orientation time variable, σ_nFor the scattering function of n-th sample point target of orientation, θ_nFor n-th The corresponding antenna pointing angle of target；ω is the window function of slow time domain, represents modulation of the antenna radiation pattern function in orientation.

Original image scene under the sea clutter background adopted in this step is as shown in Fig. 2 to simulate real sea field Scape, adds the sea clutter that signal to noise ratio is 15dB in data s (t, τ).

S2, echo-signal is entered row distance to pulse compression.

Distance is built to pulse compression reference signalWherein, τ_refRepresent Distance is to the reference time.

By s_refMaximum auto-correlation computation is carried out with echo signal data s (t, τ), the echo-signal after pulse compression is obtained For：

Wherein, B is transmitted signal bandwidth, in the embodiment of the present invention, B=30MHz.

S3, Range Walk Correction is carried out to the echo-signal after pulse compression.

Analyzed from step one, oblique distance history of the point in imaging region Ω between (x, y) and airborne radar platform is approximate For R_n(t)≈R₀- vt, therefore, Range Walk Correction function is constructed apart from course according to echo Wherein, f_rIt is distance to frequency.

By Range Walk Correction function and s₁(t, τ) is multiplied, and obtaining the echo-signal after Range Walk Correction is：

Azimuth dimension reality beam pattern picture after pulse compression and Range Walk Correction is as shown in Figure 3.

S4, according to orientation echoing characteristicss, by the echo-signal after Range Walk Correction according to the distance dimension side of being rearranged for Position object vector and the product form of convolution calculation matrix, build orientation convolution model.

Because distance dimension high-resolution is realized by pulse compression technique, and the inventive method is for azimuth dimension letter Number superresolution processing is carried out, therefore, by two-dimentional echo-signal s in formula (4)₂(t, τ) apart from dimension order according to rearranging After obtain following matrix-vector product form：

Wherein, s=[s (and 1,1) ... s (1,2) ..., s (1, N) ..., s (L, N)]^TIt is by the measured value in all distance dimensions The vector of LN × 1 dimension after rearranging in orientation, subscript T represents transposition computing, and L is scene echoes distance dimension sampled point Number.

X=[x (1,1), x (1,2) ..., x (1, M) ..., x (L, M)]^TBe by each orientation target amplitude in image scene by Apart from dimension order rearranged after LM × 1 dimension vector,For the side of single range cell Position to sampled point,It is the sampling number of single wave beam.

N=[n (1,1), n (1,2) ..., n (1, N) ..., n (L, N)]^TIt is LN × 1 dimension for representing sea clutter amplitude characteristic Vector, Rayleigh distributed.

A is the matrix of LN × LM dimension, and the radar directional pattern construction according to Fig. 4 is obtained, by convolution matrix A_N×MConstitute, wherein, A_N×M=[a₁,a₂,…a_N] be real beam scanning antennas convolution calculation matrix, A_N×MIt is expressed as：

Wherein,For antenna radiation pattern weight coefficient.

From formula (6), Doppler's additive phase of each row is identical, then the nth elements of echo vector s can be with It is expressed as：

Wherein, h_niRepresent the weighted amplitude value of the individual element of convolution matrix A (n, i).

Because the purpose of radar imagery is to restore target amplitude and positional information in image scene, therefore echo-signal Can be write as：

| s |=| A | x+n (8)

Wherein, | | it is modulo operation.

Therefore, the front visual angle super-resolution imaging of real beam scanning radar can be converted into：S and A in given formula (8), solves x Inversion problem.

S5, according to orientation convolution model, using noise and the statistical property of target distribution, set up most under Bayesian frame Big posteriority object function simultaneously derives iteration expression formula, realizes Deconvolution.

According to Bayesian formula, the posterior probability of echo data is represented by：

Wherein, p () represents probability density function.

Maximum a posteriori is exactly to find most suitable x to meet following formula：

Wherein,For the maximum a posteriori solution of target information；P (x/s), p (s/x) and p (x) represent respectively posterior probability letter Number, likelihood probability function and target prior information.

For convenience of calculation, negative natural logrithm operation is carried out to formula (10), maximum a posteriori problem is converted to：

The present invention be directed to Ocean Scenes target super-resolution imaging, needs the amplitude distribution characteristic for considering actual sea clutter. Therefore, we represent the amplitude distribution of sea clutter using rayleigh distributed.Assume the clutter statistics in each discrete echo sampled point Independent, then likelihood probability function is：

Wherein, n is each pixel of discrete echo signal,σ²It is the clutter statistics of rayleigh distributed Parameter.

Because forward sight is usually applied to the location tracking of a small amount of sea-surface target in big imaging scene to marine origin picture, therefore, sea Area Objects have sparse characteristic relative to imaging region, are expressed as target distribution using laplacian distribution：

Wherein, μ ＞ 0 are the scale parameters of laplacian distribution.

Formula (12) and (13) are substituted into into formula (10), maximum a posteriori probability function is obtained：

Natural logrithm is taken to formula (14), is obtained：

Wherein, λ=1/ μ is regularization parameter, for the openness and image quality of balancing objective information recovery result.

L in order to overcome object function₁The problem of norm non-differentiability at zero point, uses the smooth technology estimated by formula (15) it is approximately：

Wherein, ε takes the nonnegative constant for being similar to zero.

Gradient algorithm is carried out to formula (16), can be obtained：

Wherein,

Because formula (17) is the nonlinear function with regard to x, it is impossible to directly makeObtain the optimum of object function Solution, here using the method for iteration, obtain first with regard toA simple solution be：

Wherein, iterative initial value selects to be x=(A^TA)^-1A^TS, is the least square solution of formula (8), while the iteration of W (x) Initial value is constituted also with the initial value of x, and iteration expression formula can be expressed as：

Wherein, k+1 and k is iterationses,The iterative initial value of x is by calculating most A young waiter in a wineshop or an inn takes advantage of solution x=(A^TA)^-1A^TS is obtained, and obtains diagonal matrix using the iterative initial value Iterative initial value, in the embodiment of the present invention, ε=0.01.Formula (19) is the expression-form of maximum a posteriori algorithm.

S6, ask for clutter statistical parameter and regularization parameter.

The single range cell signal without target distribution in two-dimentional echo-signal is taken, if dimension is adopted for the sea clutter amplitude of N Sample sequence f₁..., f_N, rayleigh distributed carried out after logarithm operation, can be written as expression formula：

The derivation of equation (20) is obtained with regard to the gradient of σ：

Clutter statistical parameter σ can be obtained by formula (21)²Maximum likelihood solution be：

In the embodiment of the present invention, the without target distribution the tenth range cell in original scene is taken, use maximum likelihood parameter Method of estimation calculate with regard to σ²Maximum likelihood solution be：

Then λ is chosen using discrepancy principle, that is, chooses order | | y-Ax (λ) | |²≈E[||n||²] when λ is regularization parameter.In the embodiment of the present invention, λ=0.65.

S7, clutter statistical parameter and regularization parameter are substituted into into formula (19), iterate to calculate out answering for original image scene Former result, realizes forward-looking radar to sea-surface target angle super-resolution imaging.Fig. 5 is the final result that the present invention is obtained, can by diagram Know, the method provided by the present invention, under sea clutter background, the angle information of target has obtained good recovery.

One of ordinary skill in the art will be appreciated that embodiment described here is to aid in reader and understands this Bright principle, it should be understood that protection scope of the present invention is not limited to such especially statement and embodiment.This area It is each that those of ordinary skill can make various other without departing from essence of the invention according to these technologies enlightenment disclosed by the invention Plant concrete deformation and combine, these deformations and combination are still within the scope of the present invention.

Claims (2)

1. forward sight sea-surface target angle super-resolution imaging method under a kind of sea clutter background, it is characterised in that comprise the following steps：

S1, the kinematic geometry model that forward sight scanning radar echo-signal is set up according to the geometrical relationship of airborne radar and target；

Step S1 is specially：

If carrier aircraft platform movement velocity is v, antenna scans clockwise scene, initial time, in range cell R₀Place's distribution objectives P_n；Elapsed time t, in carrier aircraft platform and scene P is located at_nThe distance of target, is designated as R at point_n(t)；Now, target to radar it Between oblique distance history approximate representation be：

R_n(t)≈R₀-vt (1)

If transmission signal is linear FM signalWherein, rect () is represented Rectangular signal, it is defined asτ is distance to time variable, width when T is pulse, and c is the light velocity, and λ is Wavelength, K_rFor chirp rate；

Discrete processes are carried out to being received back to ripple, the orientation discrete sampling points for making single range cell areWherein, φ is sweep limitss, θ_bIt is antenna beamwidth, γ is scanning speed, and PRI is the pulse repetition period, Then discretization echo analytical expression is：

$s(t,\mathrm{\τ})=\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\σ}}_n\·\mathrm{\ω}({\mathrm{\θ}}_n,\mathrm{\τ})\·rect(\mathrm{\τ}-\frac{2R_n\left(t\right)}{c})\×\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_n(t\left)\right)\·\exp \left({\mathrm{j\πK}}_r{\[\mathrm{\τ}-\frac{2R_n\left(t\right)}{c}\]}^2\right)---\left(2\right)$

Wherein, t be orientation time variable, σ_nFor the scattering function of n-th sample point target of orientation, θ_nFor n-th target Corresponding antenna pointing angle；ω is the window function of slow time domain, represents modulation of the antenna radiation pattern function in orientation；

S2, echo-signal is entered row distance to pulse compression；

Step S2 is specially：

Distance is built to pulse compression reference signalWherein, τ_refRepresent distance to Reference time；

By s_refMaximum auto-correlation computation is carried out with echo signal data s (t, τ), obtaining the echo-signal after pulse compression is：

$s_1(t,\mathrm{\τ})=\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\σ}}_n\·\mathrm{\ω}({\mathrm{\θ}}_n,\mathrm{\τ})\·\exp \{-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_n\left(t\right)\}\×\sin c\{B\[\mathrm{\τ}-\frac{2\·R_n\left(t\right)}{c}\]\}---\left(3\right)$

Wherein, B is transmitted signal bandwidth；

S3, Range Walk Correction is carried out to the echo-signal after pulse compression；

Step S3 is specially：

Range Walk Correction function is constructed apart from course according to echoWherein, f_rIt is distance to frequency Rate；

By Range Walk Correction function and s₁(t, τ) is multiplied, and obtaining the echo-signal after Range Walk Correction is：

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

S4, according to orientation echoing characteristicss, the echo-signal after Range Walk Correction is rearranged for into orientation mesh according to distance dimension Mark vector and the product form of convolution calculation matrix, build orientation convolution model；

Step S4 is specially：

By two-dimentional echo-signal s in formula (4)₂(t, τ) after rearranging apart from dimension order according to obtaining following matrix-vector multiplication Product form：

Wherein, s=[s (and 1,1) ... s (1,2) ..., s (1, N) ..., s (L, N)]^TIt is in side by the measured value in all distance dimensions Position rearrange upwards after LN × 1 dimension vector, subscript T represents transposition computing, and L is scene echoes distance dimension sampling number；x =[x (1,1), x (1,2) ..., x (1, M) ..., x (L, M)]^TIt is that each orientation target amplitude in image scene is suitable by distance dimension Sequence rearranged after LM × 1 dimension vector,Orientation for single range cell is sampled Point,It is the sampling number of single wave beam；N=[n (1,1), n (1,2) ..., n (1, N) ..., n (L, N)]^TIt is table Show the vector of LN × 1 dimension of sea clutter amplitude characteristic, Rayleigh distributed；A is one by convolution calculation matrix A_N×MThe LN of composition The matrix of × LM dimensions, wherein, A_N×M=[a₁,a₂,…a_N] be real beam scanning antennas convolution calculation matrix, A_N×MIt is expressed as：

Wherein,For antenna radiation pattern weight coefficient；

From formula (6), Doppler's additive phase of each row is identical, then the nth elements of echo vector s are expressed as：

$s_n=e^{-j\frac{4\mathrm{\π}}{\mathrm{\λ}}v\·(n-1)\·PRI}\·\underset{i=1}{\overset{LM}{\Σ}}{h}_{ni}\·x_i---\left(7\right)$

Wherein, h_niRepresent the weighted amplitude value of the individual element of convolution matrix A (n, i)；

Because the purpose of radar imagery is that, in order to restore target amplitude and positional information in image scene, therefore echo-signal is represented For：

| s |=| A | x+n (8)

Wherein, | | it is modulo operation；

Therefore, the front visual angle super-resolution imaging of real beam scanning radar is just converted into：S and A in given formula (8), solves the anti-of x Drill problem；

S5, according to orientation convolution model, using noise and the statistical property of target distribution, under Bayesian frame set up maximum after Test object function and derive iteration expression formula, realize Deconvolution；

Step S5 is specially：

According to Bayesian formula, the posterior probability of echo data is expressed as：

$p(x/s)=\frac{p(s/x)p\left(x\right)}{p\left(s\right)}---\left(9\right)$

Wherein, p () represents probability density function；

Maximum a posteriori is exactly to find most suitable x to meet following formula：

$\hat{x}=\arg \underset{x}{max}p\left(x\right|s)=\arg \underset{x}{max}\[p\left(s\right|x)p\left(x\right)\]---\left(10\right)$

Wherein,For the maximum a posteriori solution of target information；P (x/s), p (s/x) and p (x) represent respectively posterior probability function, likelihood Probability function and target prior information；

Negative natural logrithm operation is carried out to formula (10), maximum a posteriori problem is converted to：

$\begin{array}{c}\hat{x}=\arg \underset{x}{\min }\[-ln\left(p\right(x|s\left)\right)\]\\ =\arg \underset{x}{\min }\[-ln\left(p\right(x|s\left)\right)-\ln \left(p\right(x\left)\right)\]\end{array}---\left(11\right)$

Assume the clutter statistical iteration in each discrete echo sampled point, then likelihood probability function is：

$p(s/x)=\underset{n=1}{\overset{LN}{\Π}}\frac{(s_n-{\left(Ax\right)}_n)}{{\mathrm{\σ}}^2}{e}^{\left(\frac{{(s_n-{\left(Ax\right)}_n)}^2}{2{\mathrm{\σ}}^2}\right)}---\left(12\right)$

Wherein, n is each pixel of discrete echo signal,σ²It is the clutter statistical parameter of rayleigh distributed；

Because forward sight is usually applied to the location tracking of a small amount of sea-surface target in big imaging scene to marine origin picture, therefore, sea mesh Mark has sparse characteristic relative to imaging region, is expressed as target distribution using laplacian distribution：

$p\left(x\right)\∝\underset{m=1}{\overset{LM}{\Π}}\frac{1}{2\mathrm{\μ}}{e}^{(-\frac{\left|x_m\right|}{\mathrm{\μ}})}---\left(13\right)$

Wherein, μ ＞ 0 are the scale parameters of laplacian distribution；

Formula (12) and (13) are substituted into into formula (10), maximum a posteriori probability function is obtained：

$\begin{array}{c}g\left(x\right)=\underset{x}{\max }\[p\left(x\right)p(s/x)\]\\ =\underset{m=1}{\overset{LM}{\Π}}\frac{1}{2\mathrm{\μ}}{e}^{(-\frac{\left|x_m\right|}{\mathrm{\μ}})}\·\underset{n=1}{\overset{LN}{\Π}}\frac{(s_n-{\left(Ax\right)}_n)}{{\mathrm{\σ}}^2}{e}^{(-\frac{{(s_n-{\left(Ax\right)}_n)}^2}{2{\mathrm{\σ}}^2})}\end{array}---\left(14\right)$

Natural logrithm is taken to formula (14), is obtained：

$\begin{array}{c}f\left(x\right)=-\ln g\left(x\right)=\mathrm{\λ}\left|\right|x|{|}_1\\ +\underset{n=1}{\overset{LN}{\Σ}}\[-ln(s_n-{\left(Ax\right)}_n)+{\mathrm{LNln\σ}}^2+\frac{{(s_n-{\left(Ax\right)}_n)}^2}{2{\mathrm{\σ}}^2}\]\end{array}---\left(15\right)$

Wherein, λ=1/ μ is regularization parameter, for the openness and image quality of balancing objective information recovery result；

L in order to overcome object function₁The problem of norm non-differentiability at zero point, uses the smooth technology estimated by formula (15) It is approximately：

$\begin{array}{c}f\left(x\right)\≈\underset{n=1}{\overset{LN}{\Σ}}=\[-ln(s_n-{\left(Ax\right)}_n)+{\mathrm{LNln\σ}}^2+\frac{{(s_n-{\left(Ax\right)}_n)}^2}{2{\mathrm{\σ}}^2}\]\\ +\mathrm{\λ}\underset{m=1}{\overset{LN}{\Σ}}\sqrt{|x_m{|}^2+\mathrm{\ϵ}}\end{array}---\left(16\right)$

Wherein, ε takes the nonnegative constant for being similar to zero；

Gradient algorithm is carried out to formula (16), is obtained：

$\▿\left(f\right(x\left)\right)=A^T\frac{1}{s-Ax}-\frac{1}{{\mathrm{\σ}}^2}{A}^T(s-Ax)+\mathrm{\λ}W\left(x\right)x---\left(17\right)$

Wherein,

Because formula (17) is the nonlinear function with regard to x, it is impossible to directly makeThe optimal solution of object function is obtained, this In using iteration method, obtain first with regard toA simple solution be：

$x={(A^{T}A+\mathrm{\λ}W(x\left)\right)}^{-1}(A^{T}s-{\mathrm{\σ}}^2{A}^T\frac{1}{s-Ax})---\left(18\right)$

Wherein, iterative initial value selects to be x=(A^TA)^-1A^TS, is the least square solution of formula (8), while the iterative initial value of W (x) is same Sample is constituted using the initial value of x, and iteration expression formula is expressed as：

$x_{k+1}={(A^{T}A+\mathrm{\λ}W(x_k\left)\right)}^{-1}(A^{T}s-{\mathrm{\σ}}^2{A}^T\frac{1}{s-{\mathrm{Ax}}_k})---\left(19\right)$

Wherein, k+1 and k is iterationses,Formula (19) is maximum a posteriori algorithm Expression-form；

S6, ask for clutter statistical parameter and regularization parameter；

S7, clutter statistical parameter and regularization parameter are substituted in the iteration expression formula of step S5, restore original image scene, it is real Existing forward-looking radar is to sea-surface target angle super-resolution imaging.

2. forward sight sea-surface target angle super-resolution imaging method under sea clutter background according to claim 1, it is characterised in that Step S6 is specially：

The single range cell signal without target distribution in two-dimentional echo-signal is taken, if dimension is the sea clutter amplitude sample sequence of N Row f₁..., f_N, rayleigh distributed carried out after logarithm operation, obtains following expression：

$\mathrm{\γ}(f,\mathrm{\σ})={\mathrm{Nln\σ}}^2-\underset{n=1}{\overset{N}{\Σ}}{f}_n+\underset{n=1}{\overset{N}{\Σ}}\frac{{\left(f_n\right)}^2}{2{\mathrm{\σ}}^2}---\left(20\right)$

The derivation of equation (20) is obtained with regard to the gradient of σ：

$\frac{\∂\left(\mathrm{\γ}\right(f,\mathrm{\σ}))}{\∂\mathrm{\σ}}=\frac{2N}{\mathrm{\σ}}-\frac{1}{{\mathrm{\σ}}^3}\underset{n=1}{\overset{N}{\Σ}}{\left(f_n\right)}^2=0---\left(21\right)$

Clutter statistical parameter σ is obtained by formula (21)²Maximum likelihood solution be：

${\mathrm{\σ}}^2=\frac{\underset{n=1}{\overset{N}{\Σ}}{\left(f_n\right)}^2}{2N}---\left(22\right)$

Then λ is chosen using discrepancy principle, that is, chooses order | | y-Ax (λ) | |²≈E[||n||²] when λ be Regularization parameter.