CN104950306A - Method for realizing angular super-resolution imaging of forward-looking sea surface targets in sea clutter background - Google Patents
Method for realizing angular super-resolution imaging of forward-looking sea surface targets in sea clutter background Download PDFInfo
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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
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to a design of a forward-looking sea surface target angle super-resolution imaging method under a sea clutter background.
Background
The high-resolution imaging of the forward-looking sea area of the airborne platform has great application requirements in the fields of sea detection and imaging, sea surface target search and rescue, ship formation identification, ship attack and the like. However, due to the fact that the doppler bandwidth generated by the movement of the target and the airborne platform in the forward-looking area is too narrow, the high-resolution imaging of the target position in the forward-looking area cannot be achieved by utilizing the synthetic aperture radar technology (SAR) and the doppler beam sharpening method (DBS). Therefore, airborne radars usually use a scanning sampling method to obtain real beam echo signals in the front view area. Since the radar transmission signal is a chirp modulated signal (LFM), a high resolution in the range dimension is obtained using a pulse compression technique. For the azimuth dimension of the echo signal, due to the limitation of the antenna size, it is difficult to obtain the azimuth resolution matched with the target range resolution, and the application of the radar working mode is seriously influenced. Therefore, the azimuth radar angular resolution must be significantly improved by means of signal processing.
Because the scanning radar azimuth signal can be regarded as convolution of an antenna directional diagram and a target scattering coefficient, reconstruction of a target scene can be achieved through a deconvolution method, and the purpose of super-resolution of a real beam azimuth angle is achieved. In the document "B.Clark.Anefficient implementation of the algorithm 'clean', Astronomy and Astrophysics, vol.89, p.377, 1980", a clean algorithm is proposed that can improve both the distance and azimuth dimensional resolution. However, this method cannot suppress side lobe enhancement, and when a plurality of targets are present in the same beam, super-resolution performance is significantly degraded.
In the literature, "Jinchen Guan, Jianyu Yang and Yulin Huang, maximum a spatial-based angular super resolution for Scanning Radar imaging. ieee transport optics ON iterative ELECTRONIC system vol.50, No.3july 2014", an angular super-resolution method based ON the maximum posterior criterion is proposed, which assumes that both noise and target in echo signals follow independent poisson distribution, but these assumptions are not suitable for target angular super-resolution imaging under sea clutter background, and applying the method to airborne sea surface target angular super-resolution imaging causes the occurrence of target dislocation and noise amplification, and seriously affects imaging quality.
Disclosure of Invention
The invention aims to solve the problems of target dislocation, noise amplification and the like in the existing airborne forward-looking sea surface target angle super-resolution imaging technology, and provides a forward-looking sea surface target angle super-resolution imaging method under a sea clutter background.
The technical scheme of the invention is as follows: a forward-looking sea surface target angle super-resolution imaging method under a sea clutter background comprises the following steps:
s1, establishing a motion geometric model of a forward-looking scanning radar echo signal according to the geometric relation between the airborne radar and the target;
s2, performing distance-direction pulse compression on the echo signals;
s3, performing distance walking correction on the echo signal after pulse compression;
s4, rearranging the echo signals after the distance walk correction into a product form of an orientation target vector and a convolution measurement matrix according to the distance dimension according to the orientation echo characteristics to construct an orientation convolution model;
s5, according to the orientation convolution model, by using the statistical characteristics of noise and target distribution, establishing a maximum posterior target function under a Bayes framework and deducing an iterative expression to realize convolution inversion;
s6, calculating clutter statistic parameters and regularization parameters;
and S7, substituting the clutter statistical parameters and the regularization parameters into the iterative expression in the step S5, restoring the original imaging scene, and realizing super-resolution imaging of the sea surface target angle by the forward-looking radar.
Further, step S1 is specifically:
setting the moving speed of the platform of the carrier as v, scanning the scene clockwise by the antenna, and setting the initial time at the distance unit R0Is located at the distribution target Pn(ii) a At time t, the platform and scene are at PnDistance of object at point, denoted as Rn(t); at this time, the history of the target-to-radar slope is approximately expressed as:
Rn(t)≈R0-vt (1)
setting the transmitted signal to be a chirp signalWherein rect (-) denotes a rectangular signal, which is defined asTau is the distance-direction time variable, T is the pulse time width, c is the speed of light, lambda is the wavelength, KrIs the frequency modulation slope;
the received echo is subjected to discrete processing, and the number of azimuth discretization sampling points of a single distance unit is set asWhere φ is the scan range, θbIf the antenna beam width is, γ is the scanning speed, and PRI is the pulse repetition period, then the discretized echo analysis expression is:
where t is the azimuthal time variable, σnIs the scattering function of the target at the nth sampling point in azimuth, thetanAn antenna pointing angle corresponding to the nth target; ω is a window function in the slow time domain, representing the modulation of the antenna pattern function in the azimuth direction.
Further, step S2 is specifically:
constructing a range-wise pulse compression reference signalWherein, taurefRepresenting a distance to a reference time;
will srefPerforming maximum autocorrelation operation on the echo signal data s (t, τ) to obtain a pulse-compressed echo signal:
where B is the transmit signal bandwidth.
Further, step S3 is specifically:
distance walk correction function construction according to echo distance courseWherein f isrIs the range frequency;
the distance walk correction function is related to s1(t, τ) to obtain the echo signal after the distance walk correction as:
further, step S4 is specifically:
two-dimensional echo signal s in formula (4)2(t, τ) rearranging according to the distance dimension order to obtain the following matrix vector product form:
where, s ═ s (1,1) … s (1,2), …, s (1, N), …, s (L, N)]TRearranging the measured values in all distance dimensions in the azimuth direction to obtain LN multiplied by 1-dimensional vectors, wherein the superscript T represents transposition operation, and L is the number of sampling points in the echo distance dimension of the scene; x ═ x (1,1), x (1,2), …, x (1, M), …, x (L, M)]TIs an LM x 1 dimensional vector obtained by rearranging the amplitudes of targets in each direction in an imaging scene according to the distance dimension sequence,the azimuth sample points for a single range cell,is the number of sample points for a single beam; n ═ N [ N (1,1), N (1,2), …, N (1, N), …, N (L, N)]TIs LN multiplied by 1 dimensional vector representing sea clutter amplitude characteristic, obeying Rayleigh distribution; a is a measurement matrix A formed by convolutionN×MA matrix of LNxLM dimensions formed, wherein AN×M＝[a1,a2,…aN]Convolution measurement matrix for real beam scanning antenna, AN×MExpressed as:
wherein,weighting coefficients for the antenna pattern;
as can be seen from equation (6), if the doppler additional phases of the rows are the same, the nth element of the echo vector s is represented as:
wherein h isniA weighted amplitude value representing the (n, i) th element of the convolution matrix a;
since the purpose of radar imaging is to recover target amplitude and position information within the imaged scene, the echo signal is expressed as:
|s|＝|A|x+n (8)
wherein, | · | is a modulo operation;
therefore, the real beam scanning radar front view super-resolution imaging is converted into: given s and A in equation (8), the inverse problem of x is solved.
Further, step S5 is specifically:
according to the Bayesian formula, the posterior probability of the echo data is expressed as:
wherein p (-) represents a probability density function;
the maximum a posteriori is to find the most suitable x satisfying the following formula:
wherein,maximum posterior solution for the target information; p (x/s), p (s/x) and p (x) respectively represent a posterior probability function, a likelihood probability function and target prior information;
the negative natural logarithm operation is performed on equation (10), converting the maximum a posteriori problem to:
assuming that clutter statistics in each discrete echo sampling point are independent, the likelihood probability function is:
wherein n is each pixel point of the discrete echo signal,σ2is a clutter statistical parameter of the rayleigh distribution;
because the foresight sea imaging is often applied to the localization and tracking of a small number of sea surface targets in a large imaging scene, the sea surface targets have sparse characteristics relative to an imaging area, and the target distribution is expressed as follows by adopting the laplace distribution:
wherein μ > 0 is a scale parameter of the Laplace distribution;
substituting equations (12) and (13) into equation (10) yields the maximum a posteriori probability function:
taking the natural logarithm of equation (14) yields:
λ ═ 1/μ is a regularization parameter, and is used for balancing sparsity and imaging quality of a target information restoration result;
to overcome l in the objective function1The problem that the norm is not differentiable at zero, using a technique of smooth estimation, equation (15) is approximated as:
wherein a non-negative constant approximating zero is taken;
performing gradient operation on equation (16) to obtain:
wherein, <math>
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since equation (17) is a non-linear function with respect to x, it cannot be directly orderedObtaining an optimal solution to the objective function, here using an iterative method, by first obtaining a solution to the objective functionOne simple solution of (a) is:
wherein, the iteration initial value is selected as x ═ ATA)-1ATs is the least square solution of formula (8), and the initial iteration value of w (x) is also formed by the initial value of x, and the iteration expression is expressed as:
wherein k +1 and k are iteration times,equation (19) is an expression form of the maximum a posteriori algorithm.
Further, step S6 is specifically:
taking a single distance unit signal without target distribution in a two-dimensional echo signal, and setting a sea clutter amplitude sampling sequence f with the dimension of N1，…，fNAfter the rayleigh distribution is subjected to logarithmic operation, the following expression is obtained:
the gradient of equation (20) with respect to σ is found to be:
the clutter statistic parameter σ is obtained from the formula (21)2The maximum likelihood solution of (c) is:
then, a discrepanacy principle is adopted to select lambda, namely, the method selects the (| | y-Ax (lambda) | torrid cells2≈E[||n||2]λ when is the regularization parameter.
The invention has the beneficial effects that: according to the convolution characteristic of the azimuth dimension echo of the scanning radar, the echo signals of the scanning radar are rearranged into a product form of an azimuth dimension target vector and a convolution measurement matrix according to a distance dimension sequence. And constructing a maximum posterior target function for solving the original scene distribution on the basis of a Bayes formula according to the characteristics that the sea clutter obeys Rayleigh distribution and the sea surface target obeys Laplace, constructing an iterative equation by using the obtained maximum posterior solution, and performing reverse work on the original sea surface target distribution to realize angle super-resolution imaging. The method uses Rayleigh distribution to represent sea clutter characteristics, uses Laplace distribution to represent target characteristics, and deduces an iterative expression of a convolution inversion problem under Bayes criterion, so as to realize reconstruction of an original imaging scene and obtain an azimuth high-resolution image of a forward-looking sea surface target.
Drawings
Fig. 1 is a flow chart of a forward-looking sea surface target angle super-resolution imaging method under a sea clutter background provided by the invention.
Fig. 2 is a scene diagram of an original sea surface target under a simulated sea clutter background.
FIG. 3 is an azimuth dimension real beam map after pulse compression and range walk correction.
Fig. 4 is a scanning radar antenna pattern.
FIG. 5 is a schematic diagram of a sea surface target angle super-resolution imaging result processed by the method of the present invention.
Detailed Description
The embodiments of the present invention will be further described with reference to the accompanying drawings.
For the convenience of describing the contents of the present invention, the following terms are first explained:
(1) radar angle super resolution
The radar angle super-resolution means that the radar breaks through the inherent resolution limit of an imaging system by a signal processing method to achieve high resolution capability in the direction.
(2) Real beam scanning radar
A real beam scanning radar is a radar which transmits antenna beams in a mechanical rotation mode, so that the beams uniformly or non-uniformly scan scene targets in the direction.
(3) Sea clutter
In the field of radar, the echo signals reflected from the sea surface are referred to as sea clutter, which is determined by the waves, the wind speed, the direction and duration of the waves relative to the radar beam, and the presence of peaks, ebb tides and pollution that affect surface tension.
(4) Rayleigh distribution
The rayleigh distribution probability density function is:
wherein σ2V is more than or equal to 0 as a statistical parameter.
The invention provides a forward-looking sea surface target angle super-resolution imaging method under a sea clutter background, which comprises the following steps as shown in figure 1:
and S1, establishing a motion geometric model of the forward-looking scanning radar echo signal according to the geometric relation between the airborne radar and the target.
The embodiment of the invention adopts a forward-looking scanning radar imaging motion geometric mode, and the imaging parameters of the scanning radar are shown in the following table:
| parameter(s) | Symbol | Numerical value |
| Carrier frequency | fc | 10GHz |
| Pulse width of transmitted signal | T | 10μs |
| Bandwidth of transmitted signal | B | 30MHz |
| Pulse sampling frequency | PRF | 1000Hz |
| Scanning speed of antenna | γ | 30°/s |
| Antenna beam width | θb | 2.5° |
| Scanning range | φ | -3°～3° |
| Speed of movement of the platform | v | 100m/s |
| Scanning radar range | R0 | 3km |
The moving speed v of the platform of the carrier is 100m/s, the antenna scans the scene clockwise, and the initial time is in a distance unit R0Distribute the target P3 km awayn(ii) a At time t, the platform and scene are at PnDistance of object at point, denoted as Rn(t) the history of the target-to-radar slope is expressed asFor slope history Rn(t) expansion by Taylor series at t-0 givesIn practical application, the slant distance history can be simplified to R due to long action distance, small imaging sector and high scanning speedn(t)≈R0-vtcosθn. And because the azimuth angle of the radar forward-looking imaging is usually less than 10 degrees, cos thetan1. Thus, the slope history between a target to a radar can be approximated as:
Rn(t)≈R0-vt (1)
setting the transmitted signal to be a chirp signalWherein rect (-) denotes a rectangular signal, which is defined asTau is the distance variable, T is the pulse time width, in the embodiment of the invention, T is 10 mus, c is the speed of light, lambda is the wavelength,Kris the chirp rate.
In order to ensure that the theory is consistent with the actual verification condition, the received wave is subjected to discrete processing, and the number of the azimuth discretization sampling points of a single distance unit is set asWhere φ is the scan range, θbIs the antenna beam width, gamma is the scanning speed, PRI is the pulse repetition period, in the embodiment of the invention, phi is-3 to 3 degrees, thetab＝2.5°，γ＝30°/s，PRI＝10-3s。
Then the discretized echo analytic expression is:
where t is the azimuthal time variable, σnIs the scattering function of the target at the nth sampling point in azimuth, thetanAn antenna pointing angle corresponding to the nth target; ω is a window function in the slow time domain, representing the modulation of the antenna pattern function in the azimuth direction.
The original imaging scene under the sea clutter background adopted in the step is shown in fig. 2, and for simulating a real sea surface scene, sea clutter with a signal-to-clutter ratio of 15dB is added into data s (t, τ).
And S2, performing distance direction pulse compression on the echo signals.
Constructing a range-wise pulse compression reference signalWherein, taurefIndicating the distance to the reference time.
Will srefPerforming maximum autocorrelation operation on the echo signal data s (t, τ) to obtain a pulse-compressed echo signal:
where B is a transmission signal bandwidth, in the embodiment of the present invention, B is 30 MHz.
And S3, performing distance walking correction on the echo signals after pulse compression.
From the analysis in the first step, the slope distance history between the point (x, y) in the imaging area omega and the airborne radar platform is approximate to Rn(t)≈R0Vt, thus constructing a range walk correction function from the echo range historyWherein f isrIs the range frequency.
The distance walk correction function is related to s1(t, τ) to obtain the echo signal after the distance walk correction as:
the pulse-compressed and range walk corrected azimuth-dimensional real beam image is shown in fig. 3.
And S4, rearranging the echo signals after the distance walk correction into a product form of an orientation target vector and a convolution measurement matrix according to the distance dimension according to the orientation echo characteristics, and constructing an orientation convolution model.
Because the distance dimension high resolution is realized by the pulse compression technology and the method of the invention carries out super resolution processing on the azimuth dimension signal, the two-dimensional echo signal s in the formula (4) is processed2(t, τ) rearranging according to the distance dimension order to obtain the following matrix vector product form:
where, s ═ s (1,1) … s (1,2), …, s (1, N), …, s (L, N)]TThe method is a vector of LN multiplied by 1 dimension after rearranging the measured values in all the distance dimensions in the azimuth direction, the superscript T represents transposition operation, and L is the sampling point number of the echo distance dimension of the scene.
x＝[x(1，1)，x(1，2)，…，x(1，M)，…，x(L，M)]TIs an LM x 1 dimensional vector obtained by rearranging the amplitudes of targets in each direction in an imaging scene according to the distance dimension sequence,the azimuth sample points for a single range cell,is the number of sample points for a single beam.
n＝[n(1，1)，n(1，2)，…，n(1，N)，…，n(L，N)]TThe vector is a LN × 1-dimensional vector representing the amplitude characteristic of the sea clutter, and follows Rayleigh distribution.
A is a matrix of dimension LNXLM constructed from the radar antenna pattern shown in FIG. 4, and is formed by the convolution matrix AN×MIn which A isN×M＝[a1,a2,…aN]Convolution measurement matrix for real beam scanning antenna, AN×MExpressed as:
wherein,weighting coefficients for the antenna pattern.
As can be seen from equation (6), the doppler additional phase of each row is the same, and the nth element of the echo vector s can be expressed as:
wherein h isniRepresenting the weighted amplitude values of the (n, i) th element of the convolution matrix a.
Since the purpose of radar imaging is to recover object amplitude and position information within the imaged scene, the echo signal can be written as:
|s|＝|A|x+n (8)
where | is a modulo operation.
Therefore, real beam scanning radar front view super-resolution imaging can be converted into: given s and A in equation (8), the inverse problem of x is solved.
And S5, establishing a maximum posterior target function and deducing an iterative expression under a Bayes framework by using the statistical characteristics of noise and target distribution according to the orientation convolution model, thereby realizing convolution inversion.
According to the bayesian formula, the posterior probability of echo data can be expressed as:
where p (-) represents a probability density function.
The maximum a posteriori is to find the most suitable x satisfying the following formula:
wherein,maximum posterior solution for the target information; p (x/s), p (s/x) and p (x) respectively represent a posterior probability function, a likelihood probability function and target prior information.
For computational convenience, the negative natural logarithm operation is performed on equation (10), converting the maximum a posteriori problem to:
the invention aims at the super-resolution imaging of a sea surface scene target and needs to consider the amplitude distribution characteristic of the actual sea clutter. Therefore, we use the rayleigh distribution to represent the amplitude distribution of the sea clutter. Assuming that clutter statistics in each discrete echo sampling point are independent, the likelihood probability function is:
wherein n is each pixel point of the discrete echo signal,σ2is a clutter statistical parameter of the rayleigh distribution.
Because the foresight sea imaging is often applied to the localization and tracking of a small number of sea surface targets in a large imaging scene, the sea surface targets have sparse characteristics relative to an imaging area, and the target distribution is expressed as follows by adopting the laplace distribution:
where μ > 0 is a scale parameter of the Laplace distribution.
Substituting equations (12) and (13) into equation (10) yields the maximum a posteriori probability function:
taking the natural logarithm of equation (14) yields:
where λ ═ 1/μ is a regularization parameter used to balance sparseness and imaging quality of the target information restoration result.
To overcome l in the objective function1The problem that the norm is not differentiable at zero, using a technique of smooth estimation, equation (15) is approximated as:
where a non-negative constant approximating zero is taken.
By performing a gradient operation on equation (16), we can obtain:
wherein, <math>
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since equation (17) is a non-linear function with respect to x, it cannot be directly orderedObtaining an optimal solution to the objective function, here using an iterative method, by first obtaining a solution to the objective functionOne simple solution of (a) is:
wherein, the iteration initial value is selected as x ═ ATA)-1ATs is the least square solution of formula (8), and the initial iteration value of w (x) is also formed by the initial value of x, and the iterative expression can be expressed as:
wherein k +1 and k are iteration times,the iterative initial value of x is determined by calculating the least squares solution x ═ ATA)-1ATs is obtained, and the diagonal matrix is obtained by using the iteration initial valueThe initial value of iteration of (a) in the present embodiment is 0.01. Equation (19) is an expression form of the maximum a posteriori algorithm.
And S6, calculating clutter statistical parameters and regularization parameters.
Taking a single distance unit signal without target distribution in a two-dimensional echo signal, and setting a sea clutter amplitude sampling sequence f with the dimension of N1，…，fNAfter the rayleigh distribution is subjected to logarithmic operation, the following expression can be written:
the gradient of equation (20) with respect to σ is found to be:
the clutter statistic parameter σ is obtained from the formula (21)2The maximum likelihood solution of (c) is:
in the embodiment of the invention, a tenth distance unit without target distribution in an original scene is taken, and the maximum likelihood parameter estimation method is used for calculating the sigma2The maximum likelihood solution of (c) is:
then, a discrepanacy principle is adopted to select lambda, namely, the method selects the (| | y-Ax (lambda) | torrid cells2≈E[||n||2]λ when is the regularization parameter. In the present embodiment, λ is 0.65.
And S7, substituting the clutter statistical parameters and the regularization parameters into a formula (19), and iteratively calculating the restoration result of the original imaging scene to realize the super-resolution imaging of the sea surface target angle by the forward-looking radar. Fig. 5 is a final result obtained by the present invention, and it can be seen from the graph that the angle information of the target is well recovered in the background of the sea clutter by the method provided by the present invention.
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 (7)
1. A forward-looking sea surface target angle super-resolution imaging method under a sea clutter background is characterized by comprising the following steps:
s1, establishing a motion geometric model of a forward-looking scanning radar echo signal according to the geometric relation between the airborne radar and the target;
s2, performing distance-direction pulse compression on the echo signals;
s3, performing distance walking correction on the echo signal after pulse compression;
s4, rearranging the echo signals after the distance walk correction into a product form of an orientation target vector and a convolution measurement matrix according to the distance dimension according to the orientation echo characteristics to construct an orientation convolution model;
s5, according to the orientation convolution model, by using the statistical characteristics of noise and target distribution, establishing a maximum posterior target function under a Bayes framework and deducing an iterative expression to realize convolution inversion;
s6, calculating clutter statistic parameters and regularization parameters;
and S7, substituting the clutter statistical parameters and the regularization parameters into the iterative expression in the step S5, restoring the original imaging scene, and realizing super-resolution imaging of the sea surface target angle by the forward-looking radar.
2. The method according to claim 1, wherein the step S1 is specifically performed by:
setting the moving speed of the platform of the carrier as v, scanning the scene clockwise by the antenna, and setting the initial time at the distance unit R0Is located at the distribution target Pn(ii) a At time t, the platform and scene are at PnDistance of object at point, denoted as Rn(t); at this time, the history of the target-to-radar slope is approximately expressed as:
Rn(t)≈R0-vt (1)
setting the transmitted signal to be a chirp signalWherein rect (-) denotes a rectangular signal, which is defined asTau is the distance-direction time variable, T is the pulse time width, c is the speed of light, lambda is the wavelength, KrIs the frequency modulation slope;
the received echo is subjected to discrete processing, and the number of azimuth discretization sampling points of a single distance unit is set asWhereinPhi is the scanning range, thetabIf the antenna beam width is, γ is the scanning speed, and PRI is the pulse repetition period, then the discretized echo analysis expression is:
where t is the azimuthal time variable, σnIs the scattering function of the target at the nth sampling point in azimuth, thetanAn antenna pointing angle corresponding to the nth target; ω is a window function in the slow time domain, representing the modulation of the antenna pattern function in the azimuth direction.
3. The method according to claim 2, wherein the step S2 is specifically performed by:
constructing a range-wise pulse compression reference signalWherein, taurefRepresenting a distance to a reference time;
will srefPerforming maximum autocorrelation operation on the echo signal data s (t, τ) to obtain a pulse-compressed echo signal:
where B is the transmit signal bandwidth.
4. The method according to claim 3, wherein the step S3 is specifically as follows:
distance walk correction function construction according to echo distance courseWherein f isrIs the range frequency;
the distance walk correction function is related to s1(t, τ) to obtain the echo signal after the distance walk correction as:
5. the method according to claim 4, wherein the step S4 is specifically as follows:
two-dimensional echo signal s in formula (4)2(t, τ) rearranging according to the distance dimension order to obtain the following matrix vector product form:
wherein s ═ s (1,1) … s (1,2), …, s (1, N), …,s(L,N)]TRearranging the measured values in all distance dimensions in the azimuth direction to obtain LN multiplied by 1-dimensional vectors, wherein the superscript T represents transposition operation, and L is the number of sampling points in the echo distance dimension of the scene; x ═ x (1,1), x (1,2), …, x (1, M), …, x (L, M)]TIs an LM x 1 dimensional vector obtained by rearranging the amplitudes of targets in each direction in an imaging scene according to the distance dimension sequence,the azimuth sample points for a single range cell,is the number of sample points for a single beam; n ═ N [ N (1,1), N (1,2), …, N (1, N), …, N (L, N)]TIs LN multiplied by 1 dimensional vector representing sea clutter amplitude characteristic, obeying Rayleigh distribution; a is a measurement matrix A formed by convolutionN×MA matrix of LNxLM dimensions formed, wherein AN×M＝[a1,a2,…aN]Convolution measurement matrix for real beam scanning antenna, AN×MExpressed as:
wherein,weighting coefficients for the antenna pattern;
as can be seen from equation (6), if the doppler additional phases of the rows are the same, the nth element of the echo vector s is represented as:
wherein h isniA weighted amplitude value representing the (n, i) th element of the convolution matrix a;
since the purpose of radar imaging is to recover target amplitude and position information within the imaged scene, the echo signal is expressed as:
|s|＝|A|x+n (8)
wherein, | · | is a modulo operation;
therefore, the real beam scanning radar front view super-resolution imaging is converted into: given s and A in equation (8), the inverse problem of x is solved.
6. The method according to claim 5, wherein the step S5 is specifically as follows:
according to the Bayesian formula, the posterior probability of the echo data is expressed as:
wherein p (-) represents a probability density function;
the maximum a posteriori is to find the most suitable x satisfying the following formula:
wherein,maximum posterior solution for the target information; p (x/s), p (s/x) and p (x) respectively represent a posterior probability function, a likelihood probability function and target prior information;
the negative natural logarithm operation is performed on equation (10), converting the maximum a posteriori problem to:
assuming that clutter statistics in each discrete echo sampling point are independent, the likelihood probability function is:
wherein n is each pixel point of the discrete echo signal,σ2is a clutter statistical parameter of the rayleigh distribution;
because the foresight sea imaging is often applied to the localization and tracking of a small number of sea surface targets in a large imaging scene, the sea surface targets have sparse characteristics relative to an imaging area, and the target distribution is expressed as follows by adopting the laplace distribution:
wherein μ > 0 is a scale parameter of the Laplace distribution;
substituting equations (12) and (13) into equation (10) yields the maximum a posteriori probability function:
taking the natural logarithm of equation (14) yields:
λ ═ 1/μ is a regularization parameter, and is used for balancing sparsity and imaging quality of a target information restoration result;
to overcome l in the objective function1The problem that the norm is not differentiable at zero, using a technique of smooth estimation, equation (15) is approximated as:
wherein a non-negative constant approximating zero is taken;
performing gradient operation on equation (16) to obtain:
wherein, <math>
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since equation (17) is a non-linear function with respect to x, it cannot be directly orderedObtaining an optimal solution to the objective function, here using an iterative method, by first obtaining a solution to the objective functionOne simple solution of (a) is:
wherein, the iteration initial value is selected as x ═ ATA)-1ATs is the least square solution of formula (8), and the initial iteration value of w (x) is also formed by the initial value of x, and the iteration expression is expressed as:
wherein k +1 and k are iteration times,equation (19) is an expression form of the maximum a posteriori algorithm.
7. The method according to claim 6, wherein the step S6 is specifically as follows:
taking a single distance unit signal without target distribution in a two-dimensional echo signal, and setting a sea clutter amplitude sampling sequence f with the dimension of N1，…，fNAfter the rayleigh distribution is subjected to logarithmic operation, the following expression is obtained:
the gradient of equation (20) with respect to σ is found to be:
the clutter statistic parameter σ is obtained from the formula (21)2The maximum likelihood solution of (c) is:
then, a discrepanacy principle is adopted to select lambda, namely, the method selects the (| | y-Ax (lambda) | torrid cells2≈E[||n||2]λ when is the regularization parameter.
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