CN114859349A - Polar coordinate imaging method based on space polar coordinate skew distance model - Google Patents

Polar coordinate imaging method based on space polar coordinate skew distance model Download PDF

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CN114859349A
CN114859349A CN202210460967.2A CN202210460967A CN114859349A CN 114859349 A CN114859349 A CN 114859349A CN 202210460967 A CN202210460967 A CN 202210460967A CN 114859349 A CN114859349 A CN 114859349A
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azimuth
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曹运合
王风飞
刘帅
韩玖胜
王阳
程垣皓
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Abstract

The invention relates to the technical field of radars, in particular to a polar coordinate imaging method based on a space polar coordinate slant distance model. The polar coordinate slant distance model is derived from the most general radar data recording geometry, and no approximation is adopted, so that phase errors cannot be caused; and the orientation filter under the polar coordinate slant range model is obtained by calculation in a distance focusing domain, so that the space-variant phase error does not change along with the distance position coordinate, only the limitation of the orientation focusing range exists, and finally, a better imaging effect is achieved.

Description

Polar coordinate imaging method based on space polar coordinate skew distance model
Technical Field
The invention relates to the technical field of radars, in particular to a polar coordinate imaging method based on a space polar coordinate slant distance model.
Background
With the progress of radar technology, the hypersonic platform becomes an important application direction of the synthetic aperture radar imaging technology. Hypersonic synthetic aperture radars have a larger observation range than airborne synthetic aperture radars and a stronger track flexibility than satellite-borne synthetic aperture radars, which are mainly due to the following two aspects: (1) the platform height of the hypersonic platform is positioned between an airborne platform and a satellite-borne platform; (2) the hypersonic platform has a larger and more complex form of acceleration.
The hypersonic platform has the characteristics of high speed, high maneuverability and flexible track, and the problems of Doppler ambiguity and aliasing caused by high speed and complex acceleration and severe coupling and space-variant phase under the conditions of large strabismus and high frequency band are mainly the problems of the hypersonic platform synthetic aperture imaging. Therefore, the key of the design of the imaging method of the high-frequency-band large-squint hypersonic synthetic aperture radar is to reduce the residual phase error of the imaging algorithm under the conditions of large squint, complex acceleration and high frequency band.
In recent years, much work has been published on high-speed and accelerated platform synthetic aperture radar imaging methods. If the method is easy to generate in 2009, a two-dimensional frequency spectrum of the missile-borne synthetic aperture radar under the diving acceleration motion is approximately deduced by means of a stationary phase point method, series inversion and the like, and a two-dimensional coupling phase and a two-dimensional matched filter are correspondingly compensated, so that the method is a very typical frequency domain algorithm idea; in the 2014 of Down Shiyang, a constant acceleration equivalent distance migration algorithm slant distance model is deduced for a three-dimensional constant acceleration missile-borne synthetic aperture radar, and focusing imaging is performed by combining a distance migration algorithm; the tensity brightness gives a bistatic SAR imaging method with a geosynchronous orbit satellite as a transmitter and a hypersonic platform as a receiver in 2021, and the work focus is on the optimized expression of a bistatic synthetic aperture radar slant range model.
In the imaging methods of the high-speed platform synthetic aperture radar, although the slant range or the frequency spectrum model is reconstructed under the condition of considering the acceleration of the radar, the orientation translation invariance is not applicable under the condition of complex motion of the platform, the beam center approximation is introduced to the binary approximation of the slant range model relative to the imaging coordinate, so that a large residual space-variant phase error is caused, and the effective focusing range of the algorithm is directly influenced.
Disclosure of Invention
In view of the problems in the prior art, the present invention aims to provide a polar coordinate imaging method based on a spatial polar coordinate slant distance model.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
The polar coordinate imaging method based on the space polar coordinate slant distance model comprises the following steps:
step 1, preprocessing a received echo of a hypersonic synthetic aperture radar;
step 2, establishing a space polar coordinate imaging coordinate system to describe a ground point target;
step 3, decoupling echo signals, and then performing inverse distance Fourier transform to a distance focusing domain-azimuth time domain;
step 4, establishing an instantaneous slope distance model under a space polar coordinate;
step 5, solving the corresponding azimuth polar angle wave number;
step 6, homogenizing and resampling the distance focusing domain-azimuth time domain echoes according to the azimuth polar angle wave number of the hypersonic synthetic aperture radar;
and 7, performing azimuth Fourier transform on the echo signal subjected to the azimuth polar angle wave number homogenization resampling to obtain a distance focusing domain-azimuth focusing domain imaging result.
Compared with the prior art, the invention has the beneficial effects that:
(1) the polar coordinate slant distance model is derived from the most general radar data recording geometry, no approximation is adopted, and no phase error is caused, so that the final imaging effect is better; in the existing synthetic aperture radar imaging method under the more common acceleration model, the slant range model is subjected to a large amount of approximations, the method is suitable for the imaging requirement under the low-frequency simplified radar motion parameter, when the radar emission signal carrier frequency is high, the approximation errors can cause a large amount of residual phase errors, especially under the large squint complex motion parameter, the orientation translation invariance depending on the algorithm can completely fail, and most of the synthetic aperture radar imaging algorithm and the motion compensation algorithm established on the basis are not suitable any more.
(2) In the invention, the azimuth filter under the polar coordinate slant range model is obtained by calculation in a distance focusing domain, so that the space-variant phase error does not change with the distance position coordinate, and only the azimuth focusing range is limited, thereby the final imaging effect is better; while the existing high-speed platform synthetic aperture radar imaging algorithm is usually processed in a two-dimensional frequency domain or a two-dimensional wave number domain when the two-dimensional focusing problem is processed, although focusing can be completed under corresponding radar system parameters, the processing in a two-dimensional non-focusing domain inevitably introduces central wave number approximation, namely, a filter is accurate at a reference point, and the residual space-variant phase error of consistent filtering is increased along with the increase of two-dimensional coordinates, so that the two-dimensional effective focusing range of the algorithm is limited.
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The invention is described in further detail below with reference to the figures and specific embodiments.
FIG. 1 is a flow chart of a polar coordinate imaging method based on a spatial polar coordinate slant range model according to the present invention;
FIG. 2 is a schematic diagram of a data recording rectangular coordinate system and a spatial polar coordinate imaging coordinate system of a hypersonic synthetic aperture radar;
FIG. 3 is a schematic diagram of an equivalent model of a spatial polar imaging coordinate system according to the present invention;
FIG. 4 is a schematic diagram of the principle of azimuthal wavenumber homogenization resampling in the present invention;
FIG. 5 is a schematic diagram of coordinates of a point target in a simulation experiment;
FIG. 6(a) shows phase errors caused by the skew model errors of point targets P1-P4 in simulation test 1; FIG. 6(b) is a phase error caused by the skew model errors of the point targets P1-P4 in the simulation test 2;
FIG. 7(a) is a graph showing the imaging results of test 1 on the point target P1 in the simulation test; FIG. 7(b) is a graph showing the imaging results of test 2 on the point target P1 in the simulation test; FIG. 7(c) is a comparison of the orientation impulse response curves of the point target P1 for test 1 and test 2 in a simulation experiment;
FIG. 7(d) is a graph showing the imaging results of test 1 on the point target P2 in the simulation test; FIG. 7(e) is a graph showing the imaging results of test 2 on the point target P2 in the simulation test; FIG. 7(f) is a comparison of the orientation impulse response curves of the point target P2 for test 1 and test 2 in the simulation test;
FIG. 7(g) is a graph showing the imaging results of test 1 on the point target P3 in the simulation test; FIG. 7(h) is a graph showing the imaging results of test 2 on the point target P3 in the simulation test; FIG. 7(i) is a comparison of the orientation impulse response curves of the point target P3 for test 1 and test 2 in the simulation test;
FIG. 7(j) is a graph showing the imaging results of test 1 on the point target P4 in the simulation test; FIG. 7(k) is a graph showing the imaging results of test 2 on the point target P4 in the simulation test; fig. 7(l) is a comparison graph of the orientation impulse response curves of the point target P4 in test 1 and test 2 in the simulation test.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to examples, but it will be understood by those skilled in the art that the following examples are only illustrative of the present invention and should not be construed as limiting the scope of the present invention.
Referring to fig. 1, a polar coordinate imaging method based on a spatial polar coordinate slant range model includes the following steps:
step 1, preprocessing a received echo of a hypersonic synthetic aperture radar;
specifically, as shown in fig. 2, the flight path of the hypersonic platform is complex, and the central position of the synthetic aperture of the hypersonic synthetic aperture radar in the rectangular coordinate system oxyz recorded in the data record is (x) a ,y a ,z a ) The velocity vector at this time is v ═ v (v) x ,v y ,v z ) Target p at any point in the scene is in data recordingThe rectangular coordinate system oxyz has the coordinate (x) p ,y p 0), then the amount of radar position offset due to time varying acceleration is:
Δ＝(Δ x ,Δ y ,Δ z )＝(∫∫a x (t m )dt m dt m ,∫∫a y (t m )dt m dt m ,∫∫a z (t m )dt m dt m )
the slant range vector pointing from the center of the synthetic aperture to the point target is r p ＝(Δx p ,Δy p ,Δz)＝(x p -x a ,y p -y a ,-z a ) Then, the instantaneous slope distance vector that varies with azimuth sampling time is:
r p (t m )＝r p -vt m -Δ
the instantaneous slope distance is:
Figure BDA0003622174770000051
wherein, [ X (t) ] m ),Y(t m ),Z(t m )]＝(v x t m +Δ x ,v y t m +Δ y ,v z t m +Δ z ) Representing the real track position of the hypersonic radar along with the variation of azimuth sampling time;
at azimuth sampling time t m The radar transmits chirp signals as follows:
s(t)＝exp[j2πf c t+jπγt 2 ]
the received echoes of the hypersonic synthetic aperture radar are as follows:
Figure BDA0003622174770000052
removing carrier frequency and distance matching filtering to obtain:
Figure BDA0003622174770000053
the form of the signals after azimuth deskew is as follows:
s 0 (k ra ,t m )＝exp{-jk ra [r p (t m )-r c (t m )]}
wherein the content of the first and second substances,
Figure BDA0003622174770000054
r c (t m ) Is the synthetic aperture center pointing to the scene center point (x) c ,y c 0) instantaneous slope distance.
Step 2, establishing a space polar coordinate imaging coordinate system to describe a ground point target;
specifically, a spatial polar coordinate system related to the velocity is established at the synthetic aperture center (i.e. imaging position) of the hypersonic synthetic aperture radar, as shown in fig. 2, and a velocity vector v at the moment of the synthetic aperture center is located on a vertical plane oy of a ground plane v z v In, the point target p is located at the slant distance vector r p And a diagonal plane omega formed by the velocity vector v p Upper, oblique plane omega p And vertical plane oy v z v Is at an included angle of
Figure BDA0003622174770000061
Then the vertical plane oy of the ground v z v As a reference, use
Figure BDA0003622174770000062
A ground point target is described.
The inclined plane formed by the imaging slant distance vector and the velocity vector of each point target is unique, reflects the radar beam irradiation relation, and leads each inclined plane to rotate according to the plane
Figure BDA0003622174770000063
The rotation can fuse different tilted planes at the central tilted plane (the tilted plane in which the scene center point is located), enabling planar projection of the three-dimensional beam. The coordinate transformation does not use approximations, i.e. the projection is completely accurate.
Step 3, decoupling echo signals, and then performing inverse distance Fourier transform to a distance focusing domain-azimuth time domain;
specifically, the signals after the azimuth deskew are subjected to first-order keystone decoupling and are obtained from a distance focus domain:
Figure BDA0003622174770000064
wherein the distance resolution ρ r ＝c/(2B)，r p (t m )-r c (t m ) Is a pair type middle differential skew distance;
r p (t m )-r c (t m ) Taylor expansion at the center value with respect to the orientation polar coordinate variable is:
r p (t m )≈k 0 (t m )+k 1 (t m )(Θ p -Θ c )
wherein k is 0 (t m ) And k 1 (t m ) Is the coefficient of the taylor expansion;
the echo signal is then expressed as:
Figure BDA0003622174770000065
the one-dimensional azimuth processing is carried out on the decoupled signals by distance units, and the constant phase of the first exponential term is compensated
Figure BDA0003622174770000066
k 1 (t m ) Is the azimuth sampling time t m A function of (a);
let k 1 (t m ) Obtaining new azimuth angle wave number variable after distance homogenization interpolation
Figure BDA0003622174770000067
Simultaneously realizing the linearization of the echo phase relative to the azimuth polar coordinate; fourier transform is carried out on the orientation to realize the orientation (theta) p -Θ c ) To be focused.
Step 4, establishing an instantaneous slope distance model under a space polar coordinate;
in particular, polar coordinates (r) p ,θ p ) The rectangular coordinates are shown as:
Figure BDA0003622174770000071
is abbreviated as
Figure BDA0003622174770000072
Figure BDA0003622174770000073
Polar coordinate (r) p ,θ p ) The angle of rotation is shown as
Figure BDA0003622174770000074
Is abbreviated as
Figure BDA0003622174770000075
The instantaneous slope distance is then expressed in polar coordinates as:
Figure BDA0003622174770000076
the polar coordinates are expressed as rectangular coordinates of rectangular coordinate system oxyz by data records as:
Figure BDA0003622174770000077
wherein n is p Is the normal vector of the vertical plane of the inclined plane, n p ＝r p ×v；n v Normal vector of the vertical plane of the velocity, n v ＝v×n xy Wherein n is xy ＝(0,0,1)；
Figure BDA0003622174770000078
A dihedral angle or a planar rotation angle; r is p Is the slant pitch; theta p Is an oblique view angle;
by using
Figure BDA0003622174770000079
And the slant distance r p And angle of squint theta p Three variables describe the spatial position of the point target.
To achieve planar imaging, a point target is on the ground plane (i.e. the z coordinate in the data-recorded rectangular coordinate system oxyz is 0), using only the slant distance r p And angle of squint theta p Two coordinates, i.e. the first two of the formula (2)
Figure BDA00036221747700000710
The imaging area corresponds to the intersection of the cylinder and the ground plane in fig. 3. And obtaining rectangular coordinates expressed by a space polar coordinate imaging coordinate system by reverse extrapolation as follows:
Figure BDA00036221747700000711
it can be seen that to obtain a deterministic solution, the derivation of y requires a quadratic equation to be solved, the choice of root is different when the scene parameters are different, and χ is the symbol in the root formula determined from the known scene center point.
The equations (2) and (3) form a complete slant-to-conversion correspondence, and then according to the equation (1), the corresponding spatial polar coordinate instantaneous slant distance model is:
Figure BDA0003622174770000081
it can be seen that the solution of this slope model does not introduce any approximation.
Step 5, solving the corresponding azimuth polar angle wave number;
according to the space polar coordinate instantaneous slope distance model, the differential slope distance r p (t m )-r c (t m ) Taylor coefficients at the center value with respect to the orientation polar coordinate variable are:
Figure BDA0003622174770000082
Figure BDA0003622174770000083
wherein the content of the first and second substances,
Figure BDA0003622174770000084
Figure BDA0003622174770000085
step 6, homogenizing and resampling the distance focusing domain-azimuth time domain echoes according to the azimuth polar angle wave number of the hypersonic synthetic aperture radar; referring to fig. 4, a schematic diagram of the principle of azimuthal wave number homogenization resampling is shown.
And 7, performing azimuth Fourier transform on the echo signal subjected to the azimuth polar angle wave number homogenization resampling to obtain a distance focusing domain-azimuth focusing domain imaging result.
The effect of the invention is further illustrated by the following simulation comparative tests:
1. simulation content:
the simulation parameters are shown in table 1:
TABLE 1
Parameter(s) Numerical value
Carrier frequency 17GHz
Bandwidth of 150MHz
Repetition frequency 3000Hz
Center slope distance 102km
Height 60km
Oblique angle 66.7deg
Synthetic pore size time 0.34s
Speed of rotation (800,1500,-500)m/s
Acceleration of a vehicle (40,100,-40)m/s 2
Referring to FIG. 5, point targets P1-P4 are set.
Test 1: the method of the invention is used for imaging the point targets P1-P4;
test 2: using a Radius/Angle Algorithm (RAA) of the Tangshi positive to perform imaging processing on point targets P1-P4; RAA is an interpolation type imaging algorithm for a hypersonic platform, but the two-dimensional Taylor expansion based on the polar diameter and the polar angle enables the inclined projection relation to be limited by the beam center hypothesis, more approximations are used in the process of projecting the slant distance and the acceleration of different point targets to a central plane, and the algorithm is sensitive to motion errors under a radar complex motion track.
Referring to fig. 6, for the phase error corresponding to the slant range error of the imaging point target under the two methods, it can be seen that the focusing effect of the corresponding RAA corresponds to the slant range error, and the imaging quality except the scene center point is poor; the method has good imaging quality on the point target, which can be seen from the azimuth impulse response of the point target, and the focusing effect of the point target also laterally proves that the effective focusing range of the method is larger.
The imaging results of the two methods are shown in fig. 7, and it can be seen that the method of the present invention has better imaging effect.
The imaging quality of the point targets P1-P4 under the two methods is quantitatively compared through a peak sidelobe ratio and an integral sidelobe ratio, and the comparison result is shown in a table 2;
TABLE 2
Figure BDA0003622174770000101
As can be seen from table 2, the method of the present invention has better imaging effect.
Although the present invention has been described in detail in this specification with reference to specific embodiments and illustrative embodiments, it will be apparent to those skilled in the art that modifications and improvements can be made thereto based on the present invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.

Claims (5)

1. The polar coordinate imaging method based on the space polar coordinate slant distance model is characterized by comprising the following steps of:
step 1, preprocessing a received echo of a hypersonic synthetic aperture radar;
step 2, establishing a space polar coordinate imaging coordinate system to describe a ground point target;
step 3, decoupling echo signals, and then performing inverse distance Fourier transform to a distance focusing domain-azimuth time domain;
step 4, establishing an instantaneous slope distance model under a space polar coordinate;
step 5, solving the corresponding azimuth polar angle wave number;
step 6, homogenizing and resampling the distance focusing domain-azimuth time domain echoes according to the azimuth polar angle wave number of the hypersonic synthetic aperture radar;
and 7, performing azimuth Fourier transform on the echo signal subjected to the azimuth polar angle wave number homogenization resampling to obtain a distance focusing domain-azimuth focusing domain imaging result.
2. The polar imaging method based on the spatial polar coordinate slant distance model according to claim 1, wherein step 1, specifically, the hypersonic synthetic aperture radar has a synthetic aperture center position of (x) within the rectangular coordinate system oxyz recorded in the data record a ,y a ,z a ) The velocity vector at this time is v ═ v (v) x ,v y ,v z ) The coordinate of the target p at any point in the scene in the data record rectangular coordinate system oxyz is (x) p ,y p 0), then the amount of radar position offset due to time varying acceleration is:
Δ＝(Δ x ,Δ y ,Δ z )＝(∫∫a x (t m )dt m dt m ,∫∫a y (t m )dt m dt m ,∫∫a z (t m )dt m dt m )
the slant range vector pointing from the center of the synthetic aperture to the point target is r p ＝(Δx p ,Δy p ,Δz)＝(x p -x a ,y p -y a ,-z a ) Then, the instantaneous slope distance vector that varies with azimuth sampling time is:
r p (t m )＝r p -vt m -Δ
the instantaneous slope distance is:
Figure FDA0003622174760000021
wherein, [ X (t) ] m ),Y(t m ),Z(t m )]＝(v x t m +Δ x ,v y t m +Δ y ,v z t m +Δ z ) Representing the real track position of the hypersonic radar along with the variation of azimuth sampling time;
at azimuth sampling time t m The radar transmits chirp signals as follows:
s(t)＝exp[j2πf c t+jπγt 2 ]
the received echoes of the hypersonic synthetic aperture radar are as follows:
Figure FDA0003622174760000022
removing carrier frequency and distance matching filtering to obtain:
Figure FDA0003622174760000023
the form of the signals after azimuth deskew is as follows:
s 0 (k ra ,t m )＝exp{-jk ra [r p (t m )-r c (t m )]}
wherein the content of the first and second substances,
Figure FDA0003622174760000024
r c (t m ) Is the synthetic aperture center pointing to the scene center point (x) c ,y c 0) instantaneous slope distance.
3. The polar imaging method based on the spatial polar slant range model of claim 1, wherein step 2, specifically, a spatial polar coordinate system related to the velocity is established at the synthetic aperture center of the hypersonic synthetic aperture radar, and the velocity vector v at the time of the synthetic aperture center is located on a vertical plane oy of the ground plane v z v In, the point target p is located at the slant distance vector r p And a diagonal plane omega formed by the velocity vector v p Upper, oblique plane omega p And vertical plane oy v z v Is at an included angle of
Figure FDA0003622174760000025
Then the vertical plane oy of the ground v z v As a reference, use
Figure FDA0003622174760000026
A ground point target is described.
4. The polar coordinate imaging method based on the spatial polar coordinate slant range model according to claim 1, wherein in step 3, specifically, the first-order keystone decoupling and focusing to the range domain are performed on the signals after the azimuth declivity to obtain:
Figure FDA0003622174760000031
wherein the distance resolution ρ r ＝c/(2B)，r p (t m )-r c (t m ) Is a pair type middle differential skew distance;
rp (tm) -rc (tm) taylor's expansion at the center value with respect to the orientation polar coordinate variable is:
r p (t m )≈k 0 (t m )+k 1 (t m )(Θ p -Θ c )
wherein k is 0 (t m ) And k 1 (t m ) Is the coefficient of the taylor expansion;
the echo signal is then expressed as:
Figure FDA0003622174760000032
the one-dimensional azimuth processing is carried out on the decoupled signals by distance units, and the constant phase of the first exponential term is compensated
Figure FDA0003622174760000033
k 1 (t m ) Is the azimuth sampling time t m A function of (a);
let k 1 (t m ) Obtaining new azimuth angle wave number variable after distance homogenization interpolation
Figure FDA0003622174760000034
Simultaneously realizing the linearization of the echo phase relative to the azimuth polar coordinate; fourier transform is carried out on the orientation to realize the orientation (theta) p -Θ c ) To be focused.
5. The polar imaging method based on the spatial polar-slant range model of claim 1, wherein step 4, specifically, the polar coordinates (r) p ,θ p ) The rectangular coordinates are shown as:
Figure FDA0003622174760000035
Figure FDA0003622174760000036
is abbreviated as
Figure FDA0003622174760000037
Polar coordinate (r) p ,θ p ) The angle of rotation is shown as
Figure FDA0003622174760000038
Is abbreviated as
Figure FDA0003622174760000039
The instantaneous slope distance is then expressed in polar coordinates as:
Figure FDA00036221747600000310
the polar coordinates are expressed as rectangular coordinates of rectangular coordinate system oxyz by data records as:
Figure FDA0003622174760000041
Figure FDA0003622174760000042
wherein n is p Is the normal vector of the vertical plane of the inclined plane, n p ＝r p ×v；n v Normal vector of the vertical plane of the velocity, n v ＝v×n xy Wherein n is xy ＝(0,0,1)；
Figure FDA0003622174760000043
Is a dihedral angle; r is p Is the slant pitch; theta p Is an oblique view angle;
with point targets on the ground plane, using only the slant distance r p And angle of squint theta p Two coordinates; and obtaining rectangular coordinates expressed by a space polar coordinate imaging coordinate system by reverse extrapolation as follows:
Figure FDA0003622174760000044
the spatial polar instantaneous slope distance model is:
Figure FDA0003622174760000045
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CN116528172A (en) * 2023-06-25 2023-08-01 成都工业学院 Civil aviation very high frequency ground-air communication anti-interference method integrating secondary radar information

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116528172A (en) * 2023-06-25 2023-08-01 成都工业学院 Civil aviation very high frequency ground-air communication anti-interference method integrating secondary radar information
CN116528172B (en) * 2023-06-25 2023-09-05 成都工业学院 Civil aviation very high frequency ground-air communication anti-interference method integrating secondary radar information

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