CN111896958B - Ship target forward-looking three-dimensional imaging method based on correlation algorithm - Google Patents

Ship target forward-looking three-dimensional imaging method based on correlation algorithm Download PDF

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CN111896958B
CN111896958B CN202010802160.3A CN202010802160A CN111896958B CN 111896958 B CN111896958 B CN 111896958B CN 202010802160 A CN202010802160 A CN 202010802160A CN 111896958 B CN111896958 B CN 111896958B
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radar
target
echo signal
dimensional
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CN111896958A (en
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李亚超
王晓菲
汤胜杰
郭亮
黄平平
全英汇
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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Abstract

The invention discloses a ship target forward-looking three-dimensional imaging method based on a correlation algorithm, which mainly solves the problems of high complexity and low imaging precision of three-dimensional imaging operation in the prior art. The implementation scheme is as follows: 1) Setting the postures of a radar and a ship, and obtaining an original echo signal of the ship through simulation; 2) Establishing a coordinate system xyz taking a radar Doppler center as an origin and a reconstruction coordinate system uvw taking a ship target Doppler center as the origin; 3) Constructing a Gao Jietai lux model of the original echo signal phase phi (t) of the ship; 5) Estimating ship target scattering point frequency
Figure DDA0002627796970000011
And frequency modulation rate
Figure DDA0002627796970000012
And establish
Figure DDA0002627796970000013
Relation with u, v, w; 6) And calculating ship target dimensional coordinates (u, v, w) according to the u, v and w relation, and drawing the spatial positions of all scattering points of the targets according to the three-dimensional coordinates to obtain a three-dimensional image of the ship. The invention reduces the operation complexity, improves the imaging precision, and can be used for identifying sea surface ship targets.

Description

Ship target forward-looking three-dimensional imaging method based on correlation algorithm
Technical Field
The invention belongs to the technical field of digital signal processing, and particularly relates to a ship target forward-looking three-dimensional imaging method based on a correlation algorithm, which can be used for identifying a sea surface ship target.
Background
Currently, high-resolution imaging of ships is always a key and research hotspot of radar imaging. Different from other space flight targets, the ship targets have the characteristics of large volume, low sailing speed and obvious rotation under the condition of high sea, so that the problems of small imaging accumulation angle and unfixed plane exist in ship target imaging.
The existing radar forward-looking three-dimensional imaging method mainly comprises an array radar forward-looking three-dimensional imaging method, a multichannel deconvolution radar forward-looking imaging method, a microwave-associated radar forward-looking three-dimensional imaging method, a double-base forward-looking three-dimensional imaging method and the like. Wherein:
according to the array radar forward-looking three-dimensional imaging method, a radar forward-looking image is acquired by means of a longer real aperture antenna, and a high-resolution radar forward-looking three-dimensional image is difficult to acquire on a platform with a smaller space, so that the subsequent requirements for identifying a critical part based on the three-dimensional image cannot be met;
the multi-channel deconvolution radar forward-looking imaging method and the microwave correlation forward-looking three-dimensional imaging method both rely on an antenna pattern to invert a radar forward-looking image of a target through matrix inversion solution, and a disease state matrix caused by high-speed movement of a platform and antenna pattern measurement errors has a large influence on imaging, and the two methods have high requirements on signal-to-noise ratio and are difficult to be applied to a high-mobility platform;
the double-base forward-looking three-dimensional imaging method has many problems for inter-bullet communication, space networking control, space time frequency synchronization, compensation of unknown movement errors among bullets and the like by means of the cooperative combat configuration that the mother bullets emit electromagnetic wave signals and the bullets receive echo signals.
The imaging method has the problems of high operation complexity and serious imaging resolution reduction.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a ship target forward-looking three-dimensional imaging method based on a correlation algorithm, so as to effectively reduce the operation complexity and improve the imaging precision.
In order to achieve the above purpose, the technical scheme of the invention comprises the following steps:
(1) Acquiring an original echo signal s (t) of a ship:
1a) Setting radar attitude according to the flight track of the high-speed platform installed by the radar;
1b) According to the three-dimensional swing model of the ship, simulating the motion law of the ship along with sea waves, and setting the posture of a ship target;
1c) Assuming that the motion direction and the distance direction of the radar are consistent, the radar transmitting signal is a linear frequency modulation signal, and the set radar and ship target attitude data are imported, so that a ship original echo signal s (t) is obtained through simulation;
(2) According to the obtained ship original echo signal s (t), determining the space three-dimensional position coordinate information of the high-speed platform radar, constructing a space vector of the space three-dimensional position coordinate information, and establishing a Cartesian coordinate system xyz taking a radar Doppler center as an origin and a reconstruction coordinate system uvw taking a ship target Doppler center as the origin;
(3) Constructing a Gao Jietai lux model of the echo signal phase phi (t):
3a) Obtaining unit vectors of slant range process between radar and ship targets
Figure BDA0002627796950000021
And according to the phase phi (t) of the original echo signal of the ship;
3b) According to the result of 3 a), a Gao Jietai lux model of the echo signal phase phi (t) is constructed by using a multi-element taylor expansion method:
Figure BDA0002627796950000022
wherein f c C is the light speed, x is the distance vector between the scattering point and the central point of the ship target, v m For speed vectors of radar，r P Unit vector of unit pitch history
Figure BDA0002627796950000023
Is a modulus of>
Figure BDA0002627796950000024
Reconstructing a u-axis direction unit vector of a coordinate system, wherein t is time,/and the like>
Figure BDA0002627796950000025
When t=0, the second derivative of the radar motion trail r (t), and O (t) is a higher-order term;
(4) According to a Gao Jietai lux model of phi (t), determining a mathematical expression of a ship target reconstruction coordinate axis:
Figure BDA0002627796950000026
wherein, represents the operation of the number product,
Figure BDA0002627796950000027
representing a vector product operation;
(5) Estimating the frequency of the scattering point of the ship target by using a parameter estimation algorithm
Figure BDA0002627796950000028
And frequency modulation rate->
Figure BDA0002627796950000029
(6) Establishment of
Figure BDA00026277969500000210
The correspondence of the estimated values of (a) to the expressions u, v, w:
Figure BDA00026277969500000211
wherein n is the distance sampling position, B is the radar transmitting signal bandwidth, v m Is radarVelocity vector v m Is v m The angle with the x-axis, theta is the angle between the radar motion trail r (t) and the y-axis;
(7) According to
Figure BDA00026277969500000212
And (3) solving the three-dimensional coordinates (u, v, w) of the ship target in the reconstruction coordinate system according to the corresponding relation between the estimated values of the target and the u, v and w expressions, and drawing out the spatial positions of all scattering points 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. three-dimensional imaging has high efficiency
In the moving process, the radar echo of the target scattering point does not have Doppler effect in the azimuth direction due to the fact that the radar looks at the area right in front, and therefore the three-dimensional imaging efficiency of the radar on the target is low. According to the invention, the phase model of the target echo is constructed by adopting a multi-element Taylor unfolding method, so that the information of the ship target reconstruction coordinate system is obtained, and the target three-dimensional imaging efficiency is improved.
2. High calculation accuracy
In the prior art, an interference technology is used for carrying out three-dimensional imaging on a ship target, so that the defect of complex hardware equipment exists, and a high-order phase item caused by ship swing cannot be solved, so that the imaging quality is seriously reduced. The method for reconstructing the coordinates of the ship target is used for three-dimensional imaging of the target, so that the problem of high-order phase items caused by ship swing is effectively solved, and the accuracy of three-dimensional imaging of the target 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 diagram of simulation results of forward looking three-dimensional imaging of a ship target using the present invention.
Detailed Description
Specific embodiments and effects of the present invention are described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the steps of this example are as follows:
step 1, acquiring an original echo signal s (t) of a ship;
1.1 Setting radar attitude according to the flight track of the high-speed platform installed by the radar;
the flight track of the high-speed platform is not horizontal in most cases, a certain diving angle exists, and the high-speed platform can be moved approximately in the horizontal direction due to the short imaging time, so that the radar is arranged to do uniform linear movement with the speed v;
1.2 Simulating the motion law of the ship along with sea waves according to the ship three-dimensional swing model, and setting the posture of a ship target;
1.2.1 If the ship sailing speed is far smaller than the flying speed of the high-speed platform, neglecting the influence of ship sailing on imaging, and calculating the ship rolling instantaneous rotation angle theta according to the geometric relationship between the radar and the ship target roll Instantaneous pitching rotation angle θ pitch Instantaneous rotation angle theta of head swing yaw ：
Figure BDA0002627796950000031
Wherein H is roll To roll swing amplitude, H pitch To pitch swing amplitude, H yaw Amplitude of initial rocking, omega e In order to encounter the angular velocity of the light,
Figure BDA0002627796950000041
for initial phase of roll swing, +.>
Figure BDA0002627796950000042
For initial phase of pitch swing +.>
Figure BDA0002627796950000043
The initial phase is swung for the first time, t time is;
1.2.2 Theta for use of roll 、θ pitch 、θ yaw Construction of ship roll torqueArray R roll Pitching rotation matrix R pitch Yaw rotation matrix R yaw ：
Figure BDA0002627796950000044
1.2.3 With 1b 2) three matrices R roll 、R pitch 、R yaw Calculating the attitude psi (t) of the three-dimensional swing of the ship:
ψ(t)＝R yaw (t)·R pitch (t)·R roll (t)·e，
where e is the ship's position at time zero.
1.3 Assuming that the motion direction and the distance direction of the radar are consistent, the radar transmitting signal is a linear frequency modulation signal, importing the set radar and ship target attitude data, and obtaining a ship original echo signal s (t) through simulation;
the simulation results in the ship original echo signal s (t) expressed as follows:
s(t)＝∫D(x)exp[jφ(t)]dx，
where D (x) is the echo signal amplitude, phi (t) is the phase function, and j is the imaginary unit.
Step 2, establishing a Cartesian coordinate system xyz taking a radar Doppler center as an origin and a reconstruction coordinate system uvw taking a ship target Doppler center as the origin, wherein the two coordinate systems are shown in figure 2;
step 3, constructing a Gao Jietai lux model of the echo signal phase phi (t);
3.1 Obtaining unit vector of slant range process between radar and ship target
Figure BDA0002627796950000045
And according to the phase phi (t) of the original echo signal of the ship;
3.1.1 Calculating a high-speed platform radar motion trail r (t) and a ship motion trail P (t):
Figure BDA0002627796950000046
wherein V is m (t) is the speed of the high-speed platform radar, O (0) is the initial position of the radar, V r (t) is the speed of the ship, and P (0) is the initial position of the ship;
3.1.2 Calculating unit vector of the slope distance course according to r (t) and P (t)
Figure BDA0002627796950000047
Figure BDA0002627796950000051
3.1.3 According to the unit vector
Figure BDA0002627796950000052
Calculating the original echo signal phase phi (t) of the ship:
Figure BDA0002627796950000053
wherein f c Carrier frequency, c is speed of light, t is time,
Figure BDA0002627796950000054
is a distance vector between the ship scattering point A and the central point P;
3.2 According to the result of 3.1), adopting a multi-element Taylor expansion method to construct a Gao Jietai-model of the echo signal phase phi (t):
3.2.1 Expanding the phi (t) expression in 3.1) using a multiple taylor formula to:
Figure BDA0002627796950000055
wherein i is 0 Is that
Figure BDA0002627796950000056
Unit vector of (i) 1 Let t=0->
Figure BDA0002627796950000057
I 2 Let t=0->
Figure BDA0002627796950000058
O (t) is a higher-order term;
3.2.2 Calculating a first coefficient i of the phi (t) expression 1 ：
To pitch course
Figure BDA0002627796950000059
Obtaining a first derivative:
Figure BDA00026277969500000510
wherein r (t) is the motion trail of the radar, V r (t) is the speed of the ship, P (0) is the initial position of the ship, and O (0) is the initial position of the radar;
for the above
Figure BDA00026277969500000511
The first derivative expression is further simplified to:
Figure BDA00026277969500000512
wherein w (t) is the relative movement distance of the radar and the ship: w (t) ≡v m (t)，v m (t) is the radar movement speed, r P (t) is
Figure BDA00026277969500000513
Is a modulus of (2);
let t=0
Figure BDA00026277969500000514
The first coefficient i of the expression having a first derivative value phi (t) 1 ：
Figure BDA0002627796950000061
Wherein the method comprises the steps of
Figure BDA0002627796950000062
Is->
Figure BDA00026277969500000613
Unit vector v of (v) m Is radar velocity vector, t is time, r P (0) Let t=0->
Figure BDA0002627796950000063
Is a modulus of (2);
3.2.3 Calculating a second coefficient i of the phi (t) expression 2 ：
For a pair of
Figure BDA0002627796950000064
Obtaining a second derivative:
Figure BDA0002627796950000065
，
let t=0
Figure BDA0002627796950000066
Is phi (t) the second coefficient i of the expression 2 ：
Figure BDA0002627796950000067
Wherein the method comprises the steps of
Figure BDA0002627796950000068
A second derivative of the radar motion trajectory r (t) at t=0;
3.2.4 The two coefficients i) determined in 3.2.2) and 3.2.3) are combined 1 、i 2 Substituting 3.2.1) to obtain a Gao Jietai lux model of the echo signal phase phi (t).
Figure BDA0002627796950000069
Wherein O (t) is a higher-order term.
Step 4, determining a mathematical expression of a ship target reconstruction coordinate axis according to a Gao Jietai lux model of phi (t);
4.1 Two coefficients i of the Gao Jietai lux model according to phi (t) in step 3) 0 、i 1 Constructing a mathematical expression of a u-axis and a v-axis of a ship target reconstruction coordinate system:
Figure BDA00026277969500000610
Figure BDA00026277969500000611
4.2 From the mathematical expressions of the u-axis and v-axis, a mathematical expression of the w-axis is constructed:
Figure BDA00026277969500000612
wherein the method comprises the steps of
Figure BDA0002627796950000071
Representing a vector product operation.
Step 5, estimating the frequency of the scattering point of the ship target by using a parameter estimation algorithm
Figure BDA0002627796950000072
And frequency modulation rate->
Figure BDA0002627796950000073
The existing parameter estimation algorithm comprises a maximum likelihood estimation method, a discrete polynomial phase parameter estimation method, a cubic phase function method, a short-time Fourier transform method, a wavelet transform method and a fractional Fourier transform method. The example adopts but is not limited to a cubic phase function method, and the frequency of a ship target scattering point
Figure BDA0002627796950000074
And frequency modulation rate->
Figure BDA0002627796950000075
The estimation is carried out as follows:
5.1 Pair of (a) to (b)
Figure BDA0002627796950000076
Performing second order transformation to calculate the frequency modulation slope of the scattering point of the ship target>
Figure BDA0002627796950000077
Figure BDA0002627796950000078
Wherein m is an autocorrelation time delay variable, n is the number of sampling points, and t is time;
5.2 From 5.1)
Figure BDA0002627796950000079
The estimated value is used for carrying out line demodulation processing on the original echo signal s (t), carrying out FFT (fast Fourier transform) on the signal after line demodulation, and calculating the frequency +.>
Figure BDA00026277969500000710
Figure BDA00026277969500000711
/>
Wherein t is the time of the time,
Figure BDA00026277969500000712
and t=0, and the third derivative of the radar motion trail r (t).
And 6, calculating to obtain three-dimensional coordinates (u, v, w) of the ship target in the reconstruction coordinate system.
6.1 According to ship target scatteringPoint frequency
Figure BDA00026277969500000713
And frequency modulation slope +.>
Figure BDA00026277969500000714
Establishing expressions of v and w:
Figure BDA00026277969500000715
wherein v is m For radar velocity vector v m Is v m The angle with the x-axis, theta is the angle between the radar motion trail r (t) and the y-axis;
6.2 In step 5)
Figure BDA00026277969500000716
Substituting the values of v and w into the expression of 6.1), and calculating to obtain the coordinates v and w of the ship target in the reconstruction coordinate system;
6.3 Calculating to obtain the coordinate u of the ship target in the reconstruction coordinate system:
Figure BDA00026277969500000717
where n is the distance to the sampling position and B is the radar transmit signal bandwidth.
And 7, drawing the spatial positions of all scattering points of the target according to the three-dimensional coordinates (u, v, w) of the ship target in the reconstructed coordinate system obtained in the step 6, and obtaining a three-dimensional image of the ship.
The technical effects of the invention are further described by simulation experiments:
1. simulation conditions
On a computer, a simulation test is performed by using MATLAB R2017a, and system simulation parameters are set as shown in table 1:
table 1 system simulation parameters
Figure BDA0002627796950000081
2. Emulation content
And combining the simulation parameters to generate an original echo signal s (t) of the ship, processing the echo signal phase phi (t) by the method, and calculating the three-dimensional coordinates (u, v, w) of the ship target in a reconstruction coordinate system to obtain a three-dimensional image of the ship, as shown in figure 3.
As can be seen from fig. 3, the method provided by the invention adopts a multi-element taylor expansion method to construct the phase model of the target echo, so that the information of the ship target reconstruction coordinate system is obtained, the problem of high-order phase items caused by ship swing can be effectively solved, and the accuracy of three-dimensional imaging of the target is higher.

Claims (9)

1. The ship target forward-looking three-dimensional imaging method based on the correlation algorithm is characterized by comprising the following steps of:
(1) Acquiring an original echo signal s (t) of a ship:
1a) Setting radar attitude according to the flight track of the high-speed platform installed by the radar;
1b) According to the three-dimensional swing model of the ship, simulating the motion law of the ship along with sea waves, and setting the posture of a ship target;
1c) Assuming that the motion direction and the distance direction of the radar are consistent, the radar transmitting signal is a linear frequency modulation signal, and the set radar and ship target attitude data are imported, so that a ship original echo signal s (t) is obtained through simulation;
(2) According to the obtained ship original echo signal s (t), determining the space three-dimensional position coordinate information of the high-speed platform radar, constructing a space vector of the space three-dimensional position coordinate information, and establishing a Cartesian coordinate system xyz taking a radar Doppler center as an origin and a reconstruction coordinate system uvw taking a ship target Doppler center as the origin;
(3) Constructing a Gao Jietai lux model of the echo signal phase phi (t):
3a) Obtaining unit vectors of slant range process between radar and ship targets
Figure FDA0003973935310000011
And according to the phase phi (t) of the original echo signal of the ship;
3b) According to the result of 3 a), a Gao Jietai lux model of the echo signal phase phi (t) is constructed by using a multi-element taylor expansion method:
Figure FDA0003973935310000012
wherein f c C is the light speed, x is the distance vector between the scattering point and the central point of the ship target, v m Is the velocity vector of the radar, r P Unit vector of unit pitch history
Figure FDA0003973935310000013
Is a modulus of>
Figure FDA0003973935310000014
Reconstructing a u-axis direction unit vector of a coordinate system, wherein t is time,
Figure FDA0003973935310000015
when t=0, the second derivative of the radar motion trail r (t), and O (t) is a higher-order term;
(4) According to a Gao Jietai lux model of phi (t), determining a mathematical expression of a ship target reconstruction coordinate axis:
Figure FDA0003973935310000016
wherein, represents the operation of the number product,
Figure FDA0003973935310000017
representing a vector product operation;
(5) Estimating the frequency of the scattering point of the ship target by using a parameter estimation algorithm
Figure FDA0003973935310000018
And frequency modulation rate->
Figure FDA0003973935310000019
(6) Establishment of
Figure FDA00039739353100000110
The correspondence of the estimated values of (a) to the expressions u, v, w:
Figure FDA00039739353100000111
wherein n is the distance sampling position, B is the radar transmitting signal bandwidth, v m For radar velocity vector v m Is v m The angle with the x-axis, theta is the angle between the radar motion trail r (t) and the y-axis;
(7) According to
Figure FDA0003973935310000021
And (3) solving the three-dimensional coordinates (u, v, w) of the ship target in the reconstruction coordinate system according to the corresponding relation between the estimated values of the target and the u, v and w expressions, and drawing out the spatial positions of all scattering points of the target according to the three-dimensional coordinates to obtain a three-dimensional image of the ship.
2. The method of claim 1, wherein the setting of the radar attitude in (1 a) is to take the platform movement direction as a horizontal direction according to the flight trajectory of a high-speed platform on which the radar is mounted, and the setting of the radar makes uniform linear movement at a speed v in the horizontal direction.
3. The method of claim 1, wherein in (1 b), according to the three-dimensional swing model of the ship, the law of the ship moving along with the sea wave is simulated, and the posture of the ship target is set, which is realized as follows:
1b1) The ship sailing speed is far smaller than the flying speed of the high-speed platform, the influence of ship sailing on imaging is ignored, and the ship rolling instantaneous rotation angle theta is calculated according to the geometric relationship between the radar and the ship target roll Instantaneous pitching rotation angle θ pitch Shake firstInstantaneous rotation angle theta yaw ：
Figure FDA0003973935310000022
Wherein H is roll To roll swing amplitude, H pitch To pitch swing amplitude, H yaw Amplitude of initial rocking, omega e In order to encounter the angular velocity of the light,
Figure FDA0003973935310000023
for initial phase of roll swing, +.>
Figure FDA0003973935310000024
For initial phase of pitch swing +.>
Figure FDA0003973935310000025
The initial phase is swung for the first time, t time is;
1b2) By theta roll 、θ pitch 、θ yaw Construction of ship rolling rotation matrix R roll Pitching rotation matrix R pitch Yaw rotation matrix R yaw ：
Figure FDA0003973935310000026
1b3) Three matrices R obtained with 1b 2) roll 、R pitch 、R yaw Calculating the attitude psi (t) of the three-dimensional swing of the ship:
ψ(t)＝R yaw (t)·R pitch (t)·R roll (t)·e，
where e is the ship's position at time zero.
4. The method of claim 1, wherein the simulation in (1 c) yields a ship raw echo signal s (t) expressed as follows:
s(t)＝∫D(x)exp[jφ(t)]dx，
where D (x) is the echo signal amplitude, phi (t) is the phase function, and j is the imaginary unit.
5. The method of claim 1, wherein (3 a) a unit vector of the range unit between the radar and the ship target is obtained
Figure FDA0003973935310000031
The realization is as follows:
3a1) Calculating a high-speed platform radar motion trail r (t) and a ship motion trail P (t):
Figure FDA0003973935310000032
wherein V is m (t) is the speed of the high-speed platform radar, O (0) is the initial position of the radar, V r (t) is the speed of the ship, and P (0) is the initial position of the ship;
3a2) Calculating unit vector of the slope distance course according to r (t) and P (t)
Figure FDA0003973935310000033
Figure FDA0003973935310000034
6. The method of claim 1, wherein the ship's original echo signal phase Φ (t) in (3 a) is represented as follows:
Figure FDA0003973935310000035
wherein f c Is the carrier frequency, c is the speed of light,
Figure FDA0003973935310000036
and->
Figure FDA0003973935310000037
Respectively representing vector slant distance between a certain scattering point A and a central point P of radar and ship targets, wherein t is time, < >>
Figure FDA0003973935310000038
Is the unit vector of the range history, +.>
Figure FDA0003973935310000039
Is the distance vector between the scattering point a and the center point P.
7. The method of claim 1, wherein (3 b) uses a multivariate taylor expansion method to construct a Gao Jietai-model of the echo signal phase Φ (t), implemented as follows:
3b1) Expanding the expression of phi (t) in 3 a) using a multi-element taylor formula to:
Figure FDA00039739353100000310
wherein i is 0 When t=0
Figure FDA00039739353100000311
Function value i of (2) 1 Let t=0->
Figure FDA00039739353100000312
I 2 Let t=0->
Figure FDA00039739353100000313
O (t) is a higher-order term;
3b2) Calculating two coefficients i of the expression phi (t) in 3b 1) 1 And i 2 ：
Figure FDA0003973935310000041
Wherein the method comprises the steps of
Figure FDA0003973935310000042
Is->
Figure FDA0003973935310000043
Unit vector of direction, v m Is radar velocity vector, t is time, r P (0) Let t=0->
Figure FDA0003973935310000044
Is used for the control of the (c),
Figure FDA0003973935310000045
reconstructing a u-axis direction unit vector of a coordinate system, < >>
Figure FDA0003973935310000046
A second derivative of the radar motion trajectory r (t) at t=0;
3b3) Combining the two coefficients i determined in 3b 2) 1 、i 2 The polynomial taylor formula substituted into 3b 1) is expanded to obtain a Gao Jietai-model of the echo signal phase phi (t):
Figure FDA0003973935310000047
wherein O (t) is a higher-order term.
8. The method of claim 1, wherein the estimating of the frequency of the scattering points of the ship's target is performed in (5) using a parameter estimation algorithm
Figure FDA0003973935310000048
And frequency modulation rate->
Figure FDA0003973935310000049
Is estimated by adopting a cubic phase function methodThe implementation is as follows:
5a) For a pair of
Figure FDA00039739353100000410
Performing second order transformation to calculate the frequency modulation slope of the scattering point of the ship target>
Figure FDA00039739353100000411
Figure FDA00039739353100000412
Wherein m is an autocorrelation time delay variable, n is the number of sampling points, and t is time;
5b) Obtained from 5 a)
Figure FDA00039739353100000413
The estimated value is used for carrying out line demodulation processing on the original echo signal s (t), carrying out FFT (fast Fourier transform) on the signal after line demodulation, and calculating the frequency +.>
Figure FDA00039739353100000414
Figure FDA00039739353100000415
Wherein t is the time of the time,
Figure FDA00039739353100000416
and t=0, and the third derivative of the radar motion trail r (t).
9. The method according to claim 1, wherein in (7)
Figure FDA00039739353100000417
Corresponding relation between estimated values of (a) and u, v and w expressions, and solving the ship target in a reconstruction coordinate systemIs to add the frequency of scattering points of the ship target to the three-dimensional coordinates (u, v, w)>
Figure FDA00039739353100000418
And frequency modulation rate->
Figure FDA00039739353100000419
Substituting the three-dimensional coordinates into the expressions of u, v and w in the step (6), and calculating to obtain the three-dimensional coordinates (u, v and w) of the ship target in the reconstruction coordinate system. />
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