CN111856465B - Forward-looking sea surface target angle super-resolution method based on sparse constraint - Google Patents

Forward-looking sea surface target angle super-resolution method based on sparse constraint Download PDF

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CN111856465B
CN111856465B CN202010750115.8A CN202010750115A CN111856465B CN 111856465 B CN111856465 B CN 111856465B CN 202010750115 A CN202010750115 A CN 202010750115A CN 111856465 B CN111856465 B CN 111856465B
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CN111856465A (en
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杨海光
张寅�
康瑶
杨建宇
庹兴宇
张启平
黄钰林
张永超
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9094—Theoretical aspects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G01S13/9056—Scan SAR mode
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects

Abstract

The invention discloses a forward-looking sea surface target angle super-resolution method based on sparse constraint, which comprises the following steps of: s1, establishing a forward-looking imaging azimuth echo signal model; s2, establishing a target function based on the maximum posterior probability of the sea surface target; and S3, solving the objective function by using a Newton-Raphson method. According to the method, Weibull distribution more suitable for sea surface clutter characteristics is adopted to represent sea clutter characteristics, Laplace distribution is adopted to represent prior information of a sea surface target scattering coefficient, a target function is deduced based on a maximum posterior criterion, the target function is solved through a Newton-Raphson iteration method, an iteration solution of the target scattering coefficient is obtained, and sparse super-resolution imaging of the sea surface target is achieved. The method can obviously improve the azimuth resolution of the real-aperture scanning radar for imaging the forward-looking sea surface target, and provides an idea for a super-resolution imaging method of the airborne radar sea surface target.

Description

Forward-looking sea surface target angle super-resolution method based on sparse constraint
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to a forward-looking sea surface target angle super-resolution method based on sparse constraint.
Background
With the remarkable increase of human sea surface activities, the applications of sea surface environment monitoring, sea surface disaster rescue, fighter navigation and the like urgently need the aircrafts to realize high-resolution imaging of sea surface targets in forward-looking areas. The traditional synthetic aperture technology (SAR) and Doppler sharpening technology (DBS) can respectively realize high-resolution imaging of side view and oblique forward view, but the forward view area imaging has a blind area due to the limitation of an imaging mechanism. The real-aperture scanning radar can realize forward-looking area imaging, but the azimuth angle resolution is limited by the size of the antenna aperture, and the imaging performance is influenced by echo noise, so that the real-aperture scanning radar cannot meet the actual application requirement.
In recent years, a deconvolution-based super-resolution method is widely concerned, and the method can improve the azimuth resolution of the real-aperture scanning radar and break through the inherent limitation of the resolution. In documents "xiaoxing.zhu, and richard.bamler," Very high resolution space sar to morphology in urban environment, "IEEE Transactions on Geoscience and remove sensing, vol.48, No.12, pp.4296-4308, jun.2010," a singular value decomposition method is proposed based on the regularization theory, which can effectively suppress noise amplification, but can obtain a good suppression effect only in a high signal-to-noise ratio environment. To further maintain the robustness of super-resolution imaging, In the documents "y.zhang, y.huang, y.zha, and j.yang," super resolution imaging for forward-looking scanning radar with generated gaussian constraint, "Progress In electromagnetic research, vol.46, pp.1c10, dec.2016", a maximum posteriori based deconvolution method converts the azimuthal super-resolution process into a maximum posteriori estimation problem, which can effectively restore the ground target scene. However, the statistical characteristics of the noise of the ground imaging scene generally meet the Gaussian distribution or Poisson distribution, and the noise is greatly different from the noise of the sea imaging scene, so that the super-resolution method is not suitable for the sea environment.
Sea clutter characteristic studies are an important part of sea imaging. The main statistical models of sea clutter include lognormal distribution, Weibull distribution and K distribution. In addition, the difference between the characteristics of the Weibull distribution and the characteristics of the K distribution is small, but the calculation complexity of the K distribution is far greater than that of the Weibull distribution.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a sparse constraint-based foresight sea surface target angle super-resolution method which adopts Weibull distribution more suitable for sea surface clutter characteristics to represent sea clutter characteristics, adopts Laplace distribution to represent prior information of a scattering coefficient of a sea surface target, deduces a target function based on a maximum posterior criterion, solves the target function through a Newton-Raphson iteration method, and can obviously improve the azimuth resolution of real-aperture scanning radar to foresight sea surface target imaging.
The purpose of the invention is realized by the following technical scheme: a forward-looking sea surface target angle super-resolution method based on sparse constraint comprises the following steps:
s1, establishing a forward-looking imaging azimuth echo signal model;
s2, establishing a target function based on the maximum posterior probability of the sea surface target;
and S3, solving the objective function by using a Newton-Raphson method.
Further, the specific implementation method of step S1 is as follows: the radar antenna transmits linear frequency modulation signals to realize high resolution of distance direction, the antenna scans to complete the whole forward-looking imaging area to obtain echo signals, and the echo signals are expressed in a two-dimensional form as follows after pulse compression and motion compensation processing:
Figure BDA0002609793720000021
wherein, Ω is a scanning area, and t and τ respectively represent a slow time variable and a fast time variable; sigma (t, tau) is the posterior scattering coefficient of the target, A (t) is the antenna modulation graph function, B and c respectively represent the bandwidth and the light speed of the transmitted linear frequency modulation signal; r (t) is distance history, R0As a history of distance at the initial time, f0Is the carrier frequency; n (tau, t) is additive noise and meets Weibull distribution;
the azimuth echo signals of the same distance unit are represented in a matrix form:
s＝Hx+n (2)
wherein s represents an echo, x is a target scattering coefficient matrix of an imaging scene, and n is noise in the echo; h ═ H1,h2,...,hM]Represents a measurement matrix, and h1,h2,...,hMFor each column of the measurement matrix; the dimension of s is Nx 1, the dimension of x is Mx 1, the dimension of H is Nx M, and the dimension of N is Nx 1; n is the discrete sampling point number of the echo signal azimuth direction, and M is the discrete number of the azimuth imaging area.
Further, the specific implementation method of step S2 is as follows: based on Bayes theory, the sea surface target distribution is recovered through maximum posterior estimation, and the maximum posterior probability criterion is as follows:
Figure BDA0002609793720000022
wherein x isMAPRepresenting the target estimation based on the maximum posterior criterion, and p (x | s) is a maximum posterior probability function; p (s | x)
A representation likelihood function characterizing statistical properties of the noise; p (x) represents prior information;
describing sea clutter characteristics by adopting Weibull distribution, wherein a likelihood function is expressed as:
Figure BDA0002609793720000031
wherein, PweibullFor the Weibull distribution function, i represents the index of the sample unit, niIs the noise of the ith sampling unit, and
Figure BDA0002609793720000032
hijfor the elements of the ith row and the jth column of the measurement matrix, beta and mu respectively represent the proportion parameter and the shape parameter of the Weibull function;
the target prior information is characterized by using Laplace distribution, namely:
Figure BDA0002609793720000033
wherein x isjThe jth element of a target scattering coefficient matrix x of an imaging scene is shown, and gamma is a proportional parameter of a Laplace function;
substituting the formula (5) and the formula (4) into the formula (3) to obtain the target function subjected to the negative natural logarithm operation:
Figure BDA0002609793720000034
wherein λ is 1/γ, which mainly balances the sparsity and imaging quality of the processing results; because of the non-derivable property of the norm of L1, the above objective function is approximately expressed as:
Figure BDA0002609793720000035
where ε is a small non-negative constant.
Further, the specific implementation method of step S3 is as follows: the objective function is derived for x:
Figure BDA0002609793720000036
wherein the content of the first and second substances,
Figure BDA0002609793720000037
t represents a transposition operation; symbol
Figure BDA0002609793720000038
The product of the adam's motor is represented,
Figure BDA0002609793720000039
represents beta-1 (s-Hx) performing the hadamard product;
first let g (x) ═ vx(f (x)), then the Jacobian matrix is
Figure BDA0002609793720000041
The concrete form is as follows:
Figure BDA0002609793720000042
wherein the content of the first and second substances,
Figure BDA0002609793720000043
Jpq(p, q ═ 1 … M) generationThe elements of the table jacobian matrix are in the specific form:
Figure BDA0002609793720000044
further, the iterative solution is derived as:
xz+1＝xz-Jg(x)-1g(xz) (11)
where z is the iteration index, x0Is an initial value; iterative error definition
Figure BDA0002609793720000045
Wherein | · | purple sweet2Represents a two-norm; the threshold for iterative convergence is Δ x-10-3And when the iteration error is less than or equal to the threshold value, the estimated value of the target scattering coefficient is close to the optimal solution, and a super-resolution imaging result is output.
The invention has the beneficial effects that: aiming at a forward-looking sea surface target imaging scene, Weibull distribution more suitable for sea surface clutter characteristics is adopted to represent sea clutter characteristics, Laplace distribution is adopted to represent prior information of a sea surface target scattering coefficient, a target function is deduced based on a maximum posterior criterion, the target function is solved by a Newton-Raphson iteration method, a target scattering coefficient iteration solution is obtained, and sea surface target sparse super-resolution imaging is achieved. The method can obviously improve the azimuth resolution of the real-aperture scanning radar for imaging the forward-looking sea surface target, and provides an idea for a super-resolution imaging method of the airborne radar sea surface target.
Drawings
FIG. 1 is a flow chart of a forward looking sea surface target angle super-resolution method based on sparse constraint according to the present invention;
FIG. 2 is a geometric model diagram of sea surface motion of the airborne scanning radar of the present invention;
FIG. 3 is a diagram of simulation results of the present invention.
Detailed Description
The invention provides a forward-looking sea surface target angle super-resolution method based on sparse constraint, aiming at the defects of low azimuth angle resolution of forward-looking sea surface target imaging by a real-aperture scanning radar and the advantage that Weibull distribution is more suitable for describing sea clutter characteristics in the technical background. Firstly, establishing a forward-looking imaging convolution-like signal model, and obtaining an azimuth echo signal with convolution characteristics through motion compensation; secondly, respectively representing the characteristics of the sea clutter and the target prior information by adopting Weibull distribution and Laplace distribution based on the distribution characteristics of the sea clutter and the sea surface targets, and deducing a target function based on a maximum posterior probability estimation method; and finally, solving the target function by adopting a Newton-Raphson iteration method to obtain an iteration solution of the scattering coefficient of the target, thereby realizing sparse super-resolution of the target on the sea surface. The method effectively improves the azimuth angle resolution of the real-aperture scanning radar for imaging the forward-looking sea surface target. As shown in FIG. 1, the present invention provides a forward looking sea surface target angle super-resolution method based on sparse constraint, which comprises the following steps:
s1, establishing a forward-looking imaging azimuth echo signal model; specific system parameters of the airborne platform of the embodiment are shown in table 1, and the system parameters are initialized. The sea surface motion geometric model of airborne scanning radar is shown in figure 2, wherein theta is a target PkCorresponding front viewing angle, θ0Is an initial front viewing angle, P1...PkThe object located at the same range bin, and ω is the scanning speed of the antenna.
The original surface object scene employed by the present invention is shown in fig. 3 (a).
Table 1: radar system simulation parameter table
Simulation parameters Numerical value
Carrier frequency 35GHz
Time width 2us
Bandwidth of 60MHz
Speed of movement 30m/s
Pulse repetition frequency 1000Hz
Scanning speed 60°/s
Scanning range ±6°
The specific implementation method of step S1 is: the radar antenna transmits Linear Frequency Modulation (LFM) signals to realize high resolution of a distance direction:
Figure BDA0002609793720000051
wherein, TrPulse time width, f, of a chirp signal0Is the carrier frequency, KrFor chirp slope, rect (-) is a window function.
The antenna scans to obtain echo signals in the whole forward-looking imaging area, and the echo signals are processed by pulse compression and motion compensation and are expressed in a two-dimensional form as follows:
Figure BDA0002609793720000052
wherein, Ω is a scanning area, and t and τ respectively represent a slow time variable and a fast time variable; sigma (t)Tau) is the posterior scattering coefficient of the target, A (t) is the antenna modulation graph function, and B and c respectively represent the bandwidth and the light speed of the transmitted linear frequency modulation signal; r (t) is distance history, R0As a history of distance at the initial time, f0Is the carrier frequency; n (tau, t) is additive noise and meets Weibull distribution;
in order to further explain the principle that the proposed method achieves high azimuth resolution, the azimuth echo signal of the same distance unit is represented in a matrix form:
s＝Hx+n (14)
wherein s represents an echo, x is a target scattering coefficient matrix of an imaging scene, and n is noise in the echo; h ═ H1,h2,...,hM]Represents a measurement matrix, and h1,h2,...,hMFor each column of the measurement matrix; the dimension of s is Nx 1, the dimension of x is Mx 1, the dimension of H is Nx M, and the dimension of N is Nx 1; n is the number of discrete sampling points in the azimuth direction of the echo signal, and in this embodiment, N is 200; m is the discrete number of the azimuth imaging area, and M is 200.
S2, establishing a target function based on the maximum posterior probability of the sea surface target; the specific implementation method comprises the following steps: based on Bayes theory, the sea surface target distribution is recovered through maximum posterior estimation, and the maximum posterior probability criterion is as follows:
Figure BDA0002609793720000061
wherein x isMAPRepresenting the target estimation based on the maximum posterior criterion, and p (x | s) is a maximum posterior probability function; p (s | x) represents a likelihood function that characterizes the statistical properties of the noise; p (x) represents prior information;
describing sea clutter characteristics by adopting Weibull distribution, wherein a likelihood function is expressed as:
Figure BDA0002609793720000062
wherein, PweibullFor the Weibull distribution function, i represents the index of the sampling unit, and i is 200; n isiIs the noise of the ith sampling unit, and
Figure BDA0002609793720000063
hijfor the elements of the ith row and the jth column of the measurement matrix, beta and mu respectively represent the proportion parameter and the shape parameter of the Weibull function;
the target prior information is characterized by using Laplace distribution, namely:
Figure BDA0002609793720000064
wherein x isjThe jth element of a target scattering coefficient matrix x of an imaging scene is shown, and gamma is a proportional parameter of a Laplace function;
substituting the formula (17) and the formula (16) into the formula (15) to obtain an objective function subjected to negative natural logarithm operation:
Figure BDA0002609793720000071
wherein λ is 1/γ, which mainly balances the sparsity and imaging quality of the processing results; because of the non-derivable property of the norm of L1, the above objective function is approximately expressed as:
Figure BDA0002609793720000072
where ε is a small non-negative constant, and ε is 0.001.
And S3, solving the objective function by using a Newton-Raphson method. The specific implementation method comprises the following steps: the objective function is derived for x:
Figure BDA0002609793720000073
wherein the content of the first and second substances,
Figure BDA0002609793720000074
t represents a transposition operation; symbol
Figure BDA00026097937200000712
The product of the adam's motor is represented,
Figure BDA00026097937200000711
represents beta-1 (s-Hx) performing the hadamard product;
first order
Figure BDA0002609793720000075
The jacobian matrix is then
Figure BDA0002609793720000076
The concrete form is as follows:
Figure BDA0002609793720000077
wherein the content of the first and second substances,
Figure BDA0002609793720000078
Jpq(p, q ═ 1 … M) represents the elements of the jacobian matrix, in particular of the form:
Figure BDA0002609793720000079
further, the iterative solution is derived as:
xz+1＝xz-Jg(x)-1g(xz) (23)
where z is the iteration index, x0Is an initial value; iterative error definition
Figure BDA00026097937200000710
Wherein | · | purple sweet2Represents a two-norm; the threshold for iterative convergence is Δ x-10-3When iteratingAnd when the error is less than or equal to the threshold value, the estimated value of the target scattering coefficient is close to the optimal solution, and a super-resolution imaging result is output.
In order to further verify the imaging performance of the proposed method, 15dB Weibull noise is added to the target simulation of this time, and the simulated software and hardware environments are shown in table 2.
Table 2: simulated software and hardware environment
Figure BDA0002609793720000081
The simulation result is shown in fig. 3, where fig. 3(a) is an original target scene graph; FIG. 3(b) is a real aperture radar echo signal, whose transverse echoes are severely aliased, resulting in indistinguishable targets; FIG. 3(c) is the processing result of the TSVD method, which has some smoothing effect but cannot distinguish azimuthally adjacent objects; fig. 3(d) is a processing result of the maximum likelihood method based on Weibull distribution, which can basically distinguish azimuthally adjacent targets, but the sharpening capability is limited. Fig. 3(e) is a processing result of the proposed maximum a posteriori probability based method, and after adding prior information, the method of the present invention can significantly improve the azimuth resolution of the real aperture scanning radar for imaging the forward-looking sea surface target, and realize sparse super resolution of the sea surface target.
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 (2)

1. A forward-looking sea surface target angle super-resolution method based on sparse constraint is characterized by comprising the following steps:
s1, establishing a forward-looking imaging azimuth echo signal model;
s2, establishing a target function based on the maximum posterior probability of the sea surface target; the specific implementation method comprises the following steps: based on Bayes theory, the sea surface target distribution is recovered through maximum posterior estimation, and the maximum posterior probability criterion is as follows:
Figure FDA0003339465690000011
wherein x isMAPRepresenting the target estimation based on the maximum posterior criterion, and p (x | s) is a maximum posterior probability function; p (s | x) represents a likelihood function that characterizes the statistical properties of the noise; p (x) represents prior information;
describing sea clutter characteristics by adopting Weibull distribution, wherein a likelihood function is expressed as:
Figure FDA0003339465690000012
wherein, PweibullFor the Weibull distribution function, i represents the index of the sample unit, niIs the noise of the ith sampling unit, and
Figure FDA0003339465690000013
hijfor the elements of the ith row and the jth column of the measurement matrix, beta and mu respectively represent the proportion parameter and the shape parameter of the Weibull function;
the target prior information is characterized by using Laplace distribution, namely:
Figure FDA0003339465690000014
wherein x isjThe jth element of a target scattering coefficient matrix x of an imaging scene is shown, and gamma is a proportional parameter of a Laplace function;
substituting the formula (5) and the formula (4) into the formula (3) to obtain the target function subjected to the negative natural logarithm operation:
Figure FDA0003339465690000015
wherein λ is 1/γ, which mainly balances the sparsity and imaging quality of the processing results; because of the non-derivable property of the norm of L1, the above objective function is approximately expressed as:
Figure FDA0003339465690000021
where ε is a small non-negative constant;
s3, solving an objective function by using a Newton-Raphson method; the specific implementation method comprises the following steps: the objective function is derived for x:
Figure FDA0003339465690000022
wherein the content of the first and second substances,
Figure FDA0003339465690000023
t represents a transposition operation; symbol
Figure FDA00033394656900000210
The product of the adam's motor is represented,
Figure FDA00033394656900000211
represents beta-1 (s-Hx) performing the hadamard product;
first order
Figure FDA0003339465690000024
The jacobian matrix is then
Figure FDA0003339465690000025
The concrete form is as follows:
Figure FDA0003339465690000026
wherein the content of the first and second substances,
Figure FDA0003339465690000027
Jpq(p, q ═ 1 … M) represents the elements of the jacobian matrix, in particular of the form:
Figure FDA0003339465690000028
further, the iterative solution is derived as:
xz+1＝xz-Jg(x)-1g(xz) (11)
where z is the iteration index, x0Is an initial value; iterative error definition
Figure FDA0003339465690000029
Wherein | · | purple sweet2Represents a two-norm; the threshold for iterative convergence is Δ x-10-3And when the iteration error is less than or equal to the threshold value, the estimated value of the target scattering coefficient is close to the optimal solution, and a super-resolution imaging result is output.
2. The sparse constraint-based forward-looking sea surface target angle super-resolution method according to claim 1, wherein the step S1 is implemented by: the radar antenna transmits linear frequency modulation signals to realize high resolution of distance direction, the antenna scans to complete the whole forward-looking imaging area to obtain echo signals, and the echo signals are expressed in a two-dimensional form as follows after pulse compression and motion compensation processing:
Figure FDA0003339465690000031
wherein, Ω is a scanning area, and t and τ respectively represent a slow time variable and a fast time variable; σ (t, τ) is the posterior scattering coefficient of the target, A(t) is an antenna modulation graph function, B and c represent the bandwidth and the speed of light of the transmitted chirp signal respectively; r (t) is distance history, R0As a history of distance at the initial time, f0Is the carrier frequency; n (tau, t) is additive noise and meets Weibull distribution;
the azimuth echo signals of the same distance unit are represented in a matrix form:
s＝Hx+n (2)
wherein s represents an echo, x is a target scattering coefficient matrix of an imaging scene, and n is noise in the echo; h ═ H1,h2,...,hM]Represents a measurement matrix, and h1,h2,...,hMFor each column of the measurement matrix; the dimension of s is Nx 1, the dimension of x is Mx 1, the dimension of H is Nx M, and the dimension of N is Nx 1; n is the discrete sampling point number of the echo signal azimuth direction, and M is the discrete number of the azimuth imaging area.
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