CN111896957B - Ship target foresight three-dimensional imaging method based on wavelet transformation and compressed sensing - Google Patents

Ship target foresight three-dimensional imaging method based on wavelet transformation and compressed sensing Download PDF

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CN111896957B
CN111896957B CN202010801380.4A CN202010801380A CN111896957B CN 111896957 B CN111896957 B CN 111896957B CN 202010801380 A CN202010801380 A CN 202010801380A CN 111896957 B CN111896957 B CN 111896957B
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ship
echo signal
original echo
frequency
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CN111896957A (en
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李亚超
王晓菲
汤胜杰
黄平平
全英汇
郭亮
武春风
吕金虎
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Xidian University
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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
    • G01S13/9021—SAR image post-processing techniques
    • 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
    • G01S13/9043—Forward-looking SAR
    • 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
    • G01S7/414—Discriminating targets with respect to background clutter
    • 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
    • G01S7/415—Identification of targets based on measurements of movement associated with the target
    • 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

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  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a ship target foresight three-dimensional imaging method based on wavelet transformation and compressive sensing, and mainly solves the problem of low three-dimensional imaging precision in the prior art. The implementation scheme is as follows: 1) Simulating to obtain a ship echo signal s (t); 2) Establishing a coordinate system xyz taking a radar Doppler center as an origin and a reconstructed coordinate system uvw taking a ship target Doppler center as an origin; 3) Constructing a high-order Taylor model of the phase phi (t) of the echo signal; 4) Constructing a coordinate expression of a reconstructed coordinate system; 5) Performing edge detection on s (t) to obtain sparse representation of s (t); 6) Calculating the starting frequency alpha of s (t) a And a termination frequency alpha b (ii) a 7) Calculating the initial carrier frequency of s (t)
Figure DDA0002627516470000011
And frequency of modulation
Figure DDA0002627516470000012
8) And (5) calculating three-dimensional coordinates (u, v, w) of the ship target to complete the three-dimensional image of the ship. The method effectively reduces the operation complexity, improves the precision of parameter estimation, and can be used for sea surface ship target identification.

Description

Ship target foresight three-dimensional imaging method based on wavelet transformation and compressed sensing
Technical Field
The invention belongs to the technical field of digital signal processing, and particularly relates to a moving target radar three-dimensional imaging method which can be used for sea surface ship target identification.
Background
Currently, imaging conditions are complex for non-cooperative maneuvering targets such as ships. Firstly, as a ship jolts along with the fluctuation of the sea surface, the posture change of the ship simultaneously has three-dimensional motions of yaw, rolling and pitching; secondly, the presence of sea clutter reduces the signal-to-noise ratio of the target echo. These all can present significant difficulties to the motion compensation and imaging process.
The traditional target three-dimensional imaging uses an InISAR technology, and the target height dimension information is obtained by performing interference processing on the target, so that the three-dimensional imaging of the target is realized. However, the requirements of the InISAR technology on radar hardware equipment are high, and limitations exist.
Leather league superman in the "study of hybrid SAR/ISAR based ship target imaging techniques" proposed algorithmic processing of SAR and ISAR while simultaneously performing echo on ship targets. The method has the characteristics of high concealment, strong anti-interference performance and good anti-interception performance, but has high requirement on the target phase synchronism and more limiting factors in practical use.
The multi-antenna interference or amplitude-contrast method proposed by Xu et al realizes three-dimensional imaging of a target by measuring angles of the target in horizontal and elevation directions. However, the radar mainly uses a single antenna at present, and amplitude comparison angle measurement and interference imaging cannot be carried out.
The imaging methods all have the problems of low operation speed and low imaging precision.
Disclosure of Invention
The invention aims to provide a ship target foresight three-dimensional imaging method based on wavelet transformation and compressive sensing aiming at the defects in the technology, so as to effectively reduce the requirements on hardware equipment and improve the imaging precision.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
(1) Setting the postures of a radar and a ship target, and simulating to obtain an original ship echo signal s (t);
(2) Establishing a Cartesian coordinate system xyz taking a radar Doppler center as an origin and a reconstructed coordinate system uvw taking a ship target Doppler center as an origin;
(3) Constructing a high-order Taylor model of the original echo signal phase phi (t) of the ship:
Figure BDA0002627516450000011
wherein, lambda is wavelength, x is distance vector between scattering point and central point of ship target, v m Is a vector of the velocity of the radar,
Figure BDA0002627516450000021
is a unit vector of the slope course, t is time, r P Is composed of
Figure BDA0002627516450000022
The value of the modulus of the (c) component,
Figure BDA0002627516450000023
for the first derivative value of the ship swaying function p (t) at t =0,
Figure BDA0002627516450000024
for a second derivative value of the ship swaying function p (t) at t =0, O (t) is a high-order term;
(4) According to a high-order Taylor model of the phase phi (t), a three-dimensional coordinate expression of the scattering point of the ship target in a reconstructed coordinate system uvw is constructed:
Figure BDA0002627516450000025
where n is the distance unit, c is the speed of light, B is the bandwidth, λ is the wavelength, α is
Figure BDA0002627516450000026
And v m The included angle between the two is theta which is the included angle between the radar motion track r (t) and the y axis,
Figure BDA0002627516450000027
the frequency of the original echo signal s (t),
Figure BDA0002627516450000028
the frequency modulation rate of the original echo signal s (t);
(5) Performing edge detection on an original echo signal s (t) by using wavelet transform to obtain a sparse representation form of the signal:
Figure BDA0002627516450000029
wherein,
Figure BDA00026275164500000210
as a function of the wavelet scale phi s Inverse Fourier transform of (S) t The method is characterized in that the method is in a discrete mapping form of original echo signals s (t) of ships, q is in a discrete mapping form of wavelet transformation results, F represents a unit discrete Fourier transformation matrix, and diag represents a diagonal matrix;
(6) Calculating the starting frequency alpha of the original echo signal s (t) a And a termination frequency alpha b ：
6a) Calculating two peak values alpha of q by using OMP algorithm 1 、α 2 ；
6b) Two peaks a according to q 1 、α 2 Calculating the initial frequency alpha of the original echo signal a And a termination frequency alpha b ：
Figure BDA00026275164500000211
Wherein N is the number of sampling points, T s Is the sampling interval;
(7) From the starting frequency alpha of the original echo signal s (t) a And a termination frequency alpha b Calculating the initial carrier frequency of the original echo signal s (t)
Figure BDA00026275164500000212
And the frequency of modulation
Figure BDA00026275164500000213
Figure BDA00026275164500000214
Wherein T is the pulse width;
(8) Frequency of the obtained signal
Figure BDA00026275164500000215
And the frequency of modulation
Figure BDA00026275164500000216
And (5) substituting the three-dimensional coordinate expression of the scattering points of the ship target in the reconstructed coordinate system uvw in the step (4), calculating the three-dimensional coordinates (u, v, w) of the ship target, and drawing the spatial position of each scattering point of the target according to the three-dimensional coordinates to obtain a three-dimensional image of the ship.
Compared with the prior art, the invention has the following advantages:
1. the operation speed is high
The invention adopts the method of wavelet transformation and compressed sensing to carry out high-precision parameter estimation, obtains the frequency and frequency modulation information of the ship target reconstruction coordinate system, and greatly improves the operation speed compared with the traditional parameter estimation method.
2. High imaging precision
In the prior art, most of the ship targets are subjected to two-dimensional imaging, useful information in echo of the ship targets is lost, and the method for reconstructing coordinates of the ship targets is used for three-dimensional imaging of the targets, so that the problem is effectively solved, and the accuracy of three-dimensional imaging of the targets is higher.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a Cartesian coordinate system xyz with the radar Doppler center as the origin and a reconstructed coordinate system uvw with the ship target Doppler center as the origin in the present invention;
fig. 3 is a simulation result diagram of forward looking three-dimensional imaging of a ship target using the present invention.
Detailed Description
The following describes in detail specific embodiments and effects of the present invention with reference to the drawings.
Referring to fig. 1, the steps of this example are as follows:
step 1, setting the postures of a radar and a ship target, and simulating to obtain an original echo signal s (t) of a ship.
1.1 Setting a radar attitude according to a high-speed platform flight trajectory on which the radar is installed;
the flight track of the high-speed platform is not horizontal under most conditions, a certain dive angle exists, the movement of the high-speed platform can be approximated to the movement along the horizontal direction due to short imaging time, and the radar is set to do uniform linear movement with the speed v;
1.2 According to the three-dimensional swinging model of the ship, simulating the law of the ship moving along with sea waves, and setting the attitude of a ship target;
1.2.1 Let the sailing speed of ship be far less than the flying speed of high-speed platform, neglect the influence of ship sailing on imaging, and calculate the instantaneous corner theta of ship rolling according to the geometric relationship between radar and ship target roll And the pitch instantaneous angle theta pitch Yaw instantaneous angle theta yaw ：
Figure BDA0002627516450000031
Wherein H roll To a rolling amplitude of oscillation, H pitch To the amplitude of pitch oscillation, H yaw Amplitude of yaw, omega e In order to encounter the angular velocity(s),
Figure BDA0002627516450000032
in order to roll the initial phase of the swing,
Figure BDA0002627516450000033
in order to pitch-swing the initial phase,
Figure BDA0002627516450000034
is shaking firstThe initial phase of the wobble is set to be, t is time;
1.2.2 By theta) roll 、θ pitch 、θ yaw Constructing ship rolling rotation matrix R roll Pitching rotation matrix R pitch Yaw rotation matrix R yaw ：
Figure BDA0002627516450000041
1.2.3 Three matrices R) obtained with 1.2.2) roll 、R pitch 、R yaw Calculating the attitude psi (t) of the three-dimensional swinging of the ship:
ψ(t)＝R yaw (t)·R pitch (t)·R roll (t)·e，
wherein e is the position of the ship at zero time;
1.3 Suppose that the motion direction of the radar is consistent with the distance direction, the radar transmitting signal is a linear frequency modulation signal, the set radar and ship target attitude data are imported, and the original ship echo signal s (t) obtained through simulation is expressed as follows: (ii) a
s(t)＝∫D(x)exp[jφ(t)]dx，
Where D (x) is the echo signal amplitude, φ (t) is the phase function, and j is the imaginary unit.
And 2, establishing a Cartesian coordinate system xyz taking the radar Doppler center as an origin and a reconstructed coordinate system uvw taking the ship target Doppler center as an origin, as shown in FIG. 2.
And 3, constructing a high-order Taylor model of the original echo signal phase phi (t) of the ship.
3.1 The phase φ (t) is developed using Taylor's equation as follows:
Figure BDA0002627516450000042
wherein,
Figure BDA0002627516450000043
is the size of the initial slope distance,
Figure BDA0002627516450000044
is composed of
Figure BDA0002627516450000045
First derivative value at t =0,
Figure BDA0002627516450000046
Is composed of
Figure BDA0002627516450000047
A second derivative value at t =0, O (t) being a higher order term;
3.2 ) calculating
Figure BDA0002627516450000048
Figure BDA0002627516450000049
Figure BDA00026275164500000410
3.3 Obtained from 3.2)
Figure BDA00026275164500000411
Substituting into phi (t) expression in 3.1) to obtain a high-order Taylor model of the original echo signal phase phi (t) of the ship:
Figure BDA0002627516450000051
and 4, constructing a three-dimensional coordinate expression of the scattering point of the ship target in a reconstructed coordinate system uvw according to the high-order Taylor model of the phase phi (t).
Figure BDA0002627516450000052
Figure BDA0002627516450000053
Figure BDA0002627516450000054
Where n is the distance unit, c is the speed of light, B is the bandwidth, λ is the wavelength, α is
Figure BDA0002627516450000055
And v m The included angle between the two is theta which is the included angle between the radar motion track r (t) and the y axis,
Figure BDA0002627516450000056
being the frequency of the original echo signal s (t),
Figure BDA0002627516450000057
is the frequency modulation rate of the original echo signal s (t).
And 5, performing edge detection on the original echo signal s (t) by utilizing wavelet transformation to obtain a sparse representation form of the signal.
5.1 Wavelet transform of the original echo signal s (t), the expression is as follows:
Figure BDA0002627516450000058
wherein s (f) is the Fourier transform of the original echo signal s (t) and represents the convolution operation φ s (f) Representing a wavelet scale function phi s (t) a Fourier transform of the (t),
Figure BDA00026275164500000516
in order to perform the fourier transformation, the method,
Figure BDA0002627516450000059
is composed of
Figure BDA00026275164500000510
Inverse Fourier transform of (3);
5.2 ) mixing of 5.1)
Figure BDA00026275164500000511
s(t)、
Figure BDA00026275164500000512
Respectively mapped as discrete forms q, s of length M t And
Figure BDA00026275164500000513
obtaining a sparse representation of the signal:
Figure BDA00026275164500000514
wherein,
Figure BDA00026275164500000515
as a function of the wavelet scale phi s Inverse Fourier transform of (1), s t The method is characterized in that the method is in a discrete mapping form of original echo signals s (t) of ships, q is in a discrete mapping form of wavelet transformation results, F represents a unit discrete Fourier transformation matrix, diag represents a diagonal matrix, and M is a positive integer not equal to zero.
Step 6, calculating the initial frequency alpha of the original echo signal s (t) a And a termination frequency alpha b 。
6.1 Computing the two peaks alpha of q using the OMP algorithm 1 、α 2 ；
6.1.1 Obtaining s from the sparse representation of the signal in (5) t The expression of (c):
Figure BDA0002627516450000061
6.1.2 Vs. s in 6.1.1) t Using an N x K dimensional undersampled matrix S c Sampling to obtain a sampled matrix xt:
Figure BDA0002627516450000062
wherein T is matrix transposition;
6.1.3 X in 6.1.2) t The expression of (2) is used as a constraint condition, and an expression for solving the optimization is constructed:
Figure BDA0002627516450000063
wherein argmin | | | purple sweet 0 Representing solving minimum 0 norm, and st representing constraint conditions;
6.1.4 Solving the optimized expression in 6.1.3) to obtain two peak values of q 1 、α 2 ；
6.2 Two peaks a from q) 1 、α 2 Calculating the initial frequency alpha of the original echo signal a And a termination frequency alpha b ：
Figure BDA0002627516450000064
Wherein N is the number of sampling points, T s Is the sampling interval.
Step 7, calculating the initial carrier frequency of the original echo signal s (t)
Figure BDA0002627516450000065
Frequency-modulated with the original echo signal s (t)
Figure BDA0002627516450000066
7.1 From the starting frequency alpha of the original echo signal s (t) a Calculating the initial carrier frequency of the original echo signal s (t)
Figure BDA0002627516450000067
Figure BDA0002627516450000068
7.2 From the starting frequency alpha of the original echo signal s (t) a And a termination frequency alpha b Calculating the S (t) FM rate of the original echo signal
Figure BDA0002627516450000069
Figure BDA00026275164500000610
Wherein T is the pulse width.
And 8, obtaining a three-dimensional image of the ship.
8.1 Frequency of the signal obtained in step 7)
Figure BDA00026275164500000611
And frequency of modulation
Figure BDA00026275164500000612
Substituting the three-dimensional coordinate expression of the scattering point of the ship target in the reconstructed coordinate system uvw in the step 4, and calculating the three-dimensional coordinates (u, v, w) of the ship target;
8.2 According to the three-dimensional coordinate values in 8.1), drawing the spatial position of each scattering point of the target to obtain a three-dimensional image of the ship.
The technical effects of the invention can be further explained by the following simulation experiments:
1. simulation conditions
On a computer, a simulation test is carried out by using MATLAB R2017a, and system simulation parameters are set, as shown in Table 1:
TABLE 1 System simulation parameters
Figure BDA0002627516450000071
2. Emulated content
Combining the simulation parameters to generate an original echo signal s (t) of the ship, processing the phase phi (t) of the echo signal by using the method of the invention, and calculating the three-dimensional coordinates (u, v, w) of the ship target in a reconstructed coordinate system to obtain a three-dimensional image of the ship, as shown in fig. 3.
As can be seen from FIG. 3, the method effectively solves the problem of image defocusing existing in the traditional radar imaging algorithm by establishing the functional relationship between the echo signal high-order phase term parameter and the three-dimensional coordinate information of the scattering point of the ship target, and extracts the echo signal high-order phase term information, so that the target three-dimensional imaging accuracy is higher.

Claims (6)

1. A ship target foresight three-dimensional imaging method based on wavelet transformation and compressed sensing is characterized by comprising the following steps:
(1) Setting the postures of a radar and a ship target, and simulating to obtain an original ship echo signal s (t);
(2) Establishing a Cartesian coordinate system xyz taking a radar Doppler center as an origin and a reconstructed coordinate system uvw taking a ship target Doppler center as an origin;
(3) Constructing a high-order Taylor model of the original echo signal phase phi (t) of the ship:
Figure FDA0003973420710000011
wherein, lambda is wavelength, x is distance vector between scattering point and central point of ship target, v m Is a vector of the velocity of the radar,
Figure FDA0003973420710000012
is a unit vector of slope distance process, t is time, r P Is composed of
Figure FDA0003973420710000013
The value of the modulus of the (c) signal,
Figure FDA0003973420710000014
for the first derivative value of the ship swaying function p (t) at t =0,
Figure FDA0003973420710000015
for a second derivative value of the ship swaying function p (t) at t =0, O (t) is a high-order term;
(4) According to a high-order Taylor model of the phase phi (t), a three-dimensional coordinate expression of the scattering point of the ship target in a reconstructed coordinate system uvw is constructed:
Figure FDA0003973420710000016
where n is the distance unit, c is the speed of light, B is the bandwidth, λ is the wavelength, α is
Figure FDA0003973420710000017
And v m The included angle between the two is theta which is the included angle between the radar motion track r (t) and the y axis,
Figure FDA0003973420710000018
the initial carrier frequency of the original echo signal s (t),
Figure FDA0003973420710000019
the frequency modulation rate of the original echo signal s (t);
(5) Performing edge detection on an original echo signal s (t) by using wavelet transformation to obtain a sparse representation of the signal:
Figure FDA00039734207100000110
wherein,
Figure FDA00039734207100000111
as a function of the wavelet scale phi s Inverse Fourier transform of (S) t The method is characterized in that the method is in a discrete mapping form of original echo signals s (t) of ships, q is in a discrete mapping form of wavelet transformation results, F represents a unit discrete Fourier transformation matrix, and diag represents a diagonal matrix;
(6) Calculating the initial frequency alpha of the original echo signal s (t) a And a termination frequency alpha b ：
6a) Calculating two peak values alpha of q by utilizing OMP algorithm 1 、α 2 ；
6b) Two peaks a according to q 1 、α 2 Calculating the initial frequency alpha of the original echo signal a And a termination frequency alpha b ：
Figure FDA0003973420710000021
Wherein N is the number of sampling points, T s Is the sampling interval;
(7) From the starting frequency alpha of the original echo signal s (t) a And a termination frequency alpha b Calculating the initial carrier frequency of the original echo signal s (t)
Figure FDA0003973420710000022
And the frequency of modulation
Figure FDA0003973420710000023
Figure FDA0003973420710000024
Wherein T is the pulse width;
(8) Frequency of the obtained signal
Figure FDA0003973420710000025
And the frequency of modulation
Figure FDA0003973420710000026
And (5) substituting the three-dimensional coordinate expression of the scattering points of the ship target in the reconstructed coordinate system uvw in the step (4), calculating the three-dimensional coordinates (u, v, w) of the ship target, and drawing the spatial position of each scattering point of the target according to the three-dimensional coordinates to obtain a three-dimensional image of the ship.
2. The method according to claim 1, wherein the setting of the attitude of the radar and the ship target in (1) is setting of the radar to move linearly in a horizontal direction at a velocity v, and setting the attitude ψ (t) of the ship three-dimensional swinging to:
ψ(t)＝R yaw (t)·R pitch (t)·R roll (t)·e
wherein R is yaw (t) is ship rolling rotation matrix, R pitch (t) is ship pitching rotation matrix, R roll And (t) is a yaw rotation matrix, and e is the position of the ship at zero time.
3. The method of claim 1, wherein the ship original echo signal s (t) is obtained by simulation in (1) and is expressed as follows:
s(t)＝∫D(x)exp[jφ(t)]dx ，
where D (x) is the echo signal amplitude, φ (t) is the phase function, and j is the imaginary unit.
4. The method of claim 1 wherein a higher order taylor model of the ship's original echo signal phase, phi (t), is constructed in (3) by:
3a) The phase function φ (t) is developed using Taylor's equation as:
Figure FDA0003973420710000031
wherein,
Figure FDA0003973420710000032
is the size of the initial slope distance,
Figure FDA0003973420710000033
is composed of
Figure FDA0003973420710000034
First derivative value at t =0,
Figure FDA0003973420710000035
Is composed of
Figure FDA0003973420710000036
A second derivative value at t =0, O (t) being a higher order term;
3b) Calculating out
Figure FDA0003973420710000037
Figure FDA0003973420710000038
3c) Subjecting the product obtained in 3 b)
Figure FDA0003973420710000039
Substituting the expression phi (t) in the step 3 a) to obtain a high-order Taylor model of the original echo signal phase phi (t) of the ship:
Figure FDA00039734207100000310
5. the method of claim 1, wherein the edge detection is performed on the original echo signal s (t) using wavelet transform in (5), and a sparse representation of the signal is obtained, which is implemented as follows:
5a) Performing wavelet transformation on the original echo signal s (t), wherein the expression is as follows:
Figure FDA00039734207100000311
wherein s (f) is the Fourier transform of the original echo signal s (t) and represents the convolution operation φ s (f) Representing a wavelet scale function phi s (t) a Fourier transform of the (t),
Figure FDA00039734207100000312
in order to perform the fourier transformation, the method,
Figure FDA00039734207100000313
is composed of
Figure FDA00039734207100000314
Inverse fourier transform of (d);
5b) Mixing the solution of 5 a)
Figure FDA00039734207100000315
s(t)、
Figure FDA00039734207100000316
Respectively mapped as discrete forms q, s of length M t And
Figure FDA00039734207100000317
obtaining a sparse representation of the signal:
Figure FDA00039734207100000318
wherein,
Figure FDA00039734207100000319
as a function of the wavelet scale phi s Inverse Fourier transform of (S) t The method is characterized in that the method is in a discrete mapping form of original echo signals s (t) of ships, q is in a discrete mapping form of wavelet transformation results, F represents a unit discrete Fourier transformation matrix, diag represents a diagonal matrix, and M is a positive integer not equal to zero.
6. The method of claim 1, wherein the two peaks α of q are calculated in (6 a) using an OMP algorithm 1 、α 2 It is implemented as follows:
6a1) Obtaining s according to the sparse representation form of the signal in (5) t Expression (c):
Figure FDA0003973420710000041
6a2) For s in 6a 1) t Using an N x K dimensional undersampled matrix S c Sampling is carried out to obtain a sampled matrix xt:
Figure FDA0003973420710000042
wherein T is matrix transposition;
6a3) X in 6a 2) t The expression of (2) is used as a constraint condition, and an expression for solving the optimization is constructed:
Figure FDA0003973420710000043
wherein argmin | | | Y calculation 0 Representing solving minimum 0 norm, and st representing constraint conditions;
6a4) Solving the optimized expression in 6a 3) to obtain two peak values of q 1 、α 2 。
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