CN110632616B - Micro-motion imaging method of airborne inverse synthetic aperture laser radar under sparse sampling - Google Patents

Micro-motion imaging method of airborne inverse synthetic aperture laser radar under sparse sampling Download PDF

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CN110632616B
CN110632616B CN201911089411.1A CN201911089411A CN110632616B CN 110632616 B CN110632616 B CN 110632616B CN 201911089411 A CN201911089411 A CN 201911089411A CN 110632616 B CN110632616 B CN 110632616B
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田鹤
刘铮
毛宏霞
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Beijing Institute of Environmental Features
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Abstract

The invention relates to a micro-motion imaging method of an airborne inverse synthetic aperture laser radar under sparse sampling, which comprises the following steps: establishing a target motion model aiming at the aerial micro-motion target to obtain an inclined distance expression of any point on the target; obtaining a laser radar echo signal model; constructing a compensation function by estimating the radial velocity of a target, and performing radial velocity compensation on the echo signal; discretizing a fast time domain and a slow time domain, and dividing a range direction-azimuth direction imaging space into N multiplied by M grids; aiming at the divided distance direction-azimuth direction imaging space, establishing an airborne inverse synthetic aperture laser radar micro-motion imaging linear measurement model; using compressed sensing theory based on l1/2And establishing an optimized equation by the norm optimization criterion, and solving to obtain an image reconstruction result of the target under sparse sampling. Aiming at laser radar detection, the method can realize high-resolution imaging of the target under a high sparse sampling rate, effectively reduce the requirement on the azimuth data rate and improve the imaging quality of the laser radar.

Description

Micro-motion imaging method of airborne inverse synthetic aperture laser radar under sparse sampling
Technical Field
The invention relates to the technical field of radar imaging processing, in particular to a micro-motion imaging method of an airborne inverse synthetic aperture laser radar under sparse sampling.
Background
With the rapid development of laser technology, the microwave radar imaging technology is applied to Inverse Synthetic Aperture laser radar (ISAL) formed by laser wave bands, so that the data rate of radar imaging can be improved by more than three orders of magnitude. Because of combining coherent laser technology and synthetic aperture technology, the two-dimensional resolution of the inverse synthetic aperture laser radar has better consistency in distance, and is the only optical means which can realize centimeter-level resolution in thousands of kilometers in theory. At present, because the wavelength of a laser radar is short, the required pulse repetition frequency is very high, hardware equipment cannot reach the laser radar at the present stage, and because the motion track of a non-cooperative target is uncertain, the azimuth direction has a sparse sampling problem, so that the detected image has serious side lobe noise and distortion, and the imaging effect is poor.
Disclosure of Invention
The invention aims to solve at least part of problems, and provides a micro-motion imaging method for an airborne inverse synthetic aperture laser radar under sparse sampling, so as to solve the problem of imaging blur of the laser radar in the prior art.
In order to achieve the purpose, the invention provides a micro-motion imaging method of an airborne inverse synthetic aperture laser radar under sparse sampling, which comprises the following steps:
s1, establishing a target motion model aiming at the aerial micro-motion target to obtain an inclined distance expression of any point on the target;
s2, obtaining a laser radar echo signal model by using a slant range expression;
s3, constructing a compensation function by estimating the radial speed of a target based on the laser radar echo signal model, and performing radial speed compensation on the echo signal;
s4, representing a fast time domain and a slow time domain in a laser radar echo signal model in a discretization mode, and dividing a range direction-azimuth direction imaging space into N multiplied by M grids;
s5, aiming at the divided range direction-azimuth direction imaging space, establishing an airborne inverse synthetic aperture laser radar micro-motion imaging linear measurement model based on a laser radar echo signal model and a slant range expression;
s6, utilizing the compressed sensing theory and based on l1/2And establishing an optimized equation according to the norm optimization criterion, and solving the established linear measurement model to obtain an image reconstruction result of the target under sparse sampling.
Preferably, when the target motion model is established for the hollow micro-motion target in step S1, there are three coordinate systems, which are: a radar coordinate system (U, V, W), a target specimen coordinate system (X, Y, Z) and a reference coordinate system (X, Y, Z); wherein the origin of the radar coordinate system is Q; the original points of the target specimen body coordinate system and the reference coordinate system are both O; setting the X-axis of the reference coordinate system to coincide with the X-axis initial position of the coordinate system of the target specimen body, positioning the target mass center at the center O point of the bottom surface, and determining the position of the target mass centerThe direction of sight is gamma0；
Obtaining the slope distance expression R of any point P on the target at the time tp(t) is:
Rp(t)＝||R0-rp(t)||≈||R0||+n·rp(t)；
wherein R is0The vector of the slant distance from the target center to the origin of the radar coordinate system; the position of an arbitrary point P on the target at the time t in the target coordinate system is set as (x)p,yp,zp)，rp(t)＝(xp,yp,zp)TIs the initial coordinate vector of the target P point at the time t, n is (0, sin gamma)0,cosγ0) Is the radar line-of-sight vector.
Preferably, the shape of the aerial micro-motion target is conical; in the step S1, an expression R of the slope distance of the arbitrary point P on the target at the time t is obtainedp(t) is:
Rp(t)≈R0+sinγ0(ypcosδ-zpsinδ)+cosγ0(ypsinδ+zpcosδ) +t[vr+sinγ0(xpΩscosδ+Ωcxp)+cosγ0sinδxpΩs]-t2ΩsΩcypsinγ0；
wherein R is0＝||R0| |, the size of the slant range vector from the target center to the origin of the radar coordinate system, ΩsRepresenting the magnitude of a spin vector in the micro-motion form of the micro-motion target in the air, wherein the direction of the spin vector is the Oz direction; omegacThe method comprises the steps of representing the magnitude of a coning vector in an air micro-motion target micro-motion form, wherein the coning vector direction is an ON direction; v. ofrV · n represents the radial velocity of the aerial micro-motion target, and v represents the relative velocity vector of the aerial micro-motion target and the radar airborne platform; δ denotes a unit impulse signal.
Preferably, in step S2, the obtained lidar echo signal model SR(τ, η) is expressed as:
Figure GDA0003116503020000031
where τ and η represent fast and slow times, respectively, T ═ η + τ, TpDenotes the pulse width, fcThe carrier frequency of the laser is gamma, and the frequency is adjusted; rho (beta) is a target reflection coefficient, and beta represents an included angle between a normal vector of a target point and the radar sight line direction.
Preferably, in step S3, the constructed compensation function H (η) is expressed as:
Figure GDA0003116503020000032
wherein the content of the first and second substances,
Figure GDA0003116503020000033
is the target radial velocity estimated by the velocity estimation method.
Preferably, in step S4, the discretization represents that the fast time domain and the slow time domain in the lidar return signal model are:
τ＝[τ1,τ2,...,τr,...τR]1×R；
η＝[η1,η2,...,ηa,...ηA]1×A；
wherein R is more than or equal to 1 and less than or equal to R, and R represents the length of the fast time sequence; a is more than or equal to 1 and less than or equal to A, wherein A represents the length of the slow time sequence;
after the distance direction-azimuth direction imaging space is divided into N multiplied by M grids, the coordinate point corresponding to the (N, M) th grid is (x)nm,ynm,znm)，1≤n≤N，1≤m≤M。
Preferably, in step S5, the established airborne inverse synthetic aperture lidar micro-motion imaging linear measurement model is expressed as:
S＝Φρ；
wherein phi is an observation matrix, rho is a scattering center vector of the target, and S is a radar echo vector.
Preferably, in the established linear measurement model, the observation matrix Φ is represented as:
Figure GDA0003116503020000041
the scattering center vector ρ of the target is expressed as:
ρ＝[ρ(β11),ρ(β12),...,ρ(β1m),…,ρ(β1M),...,ρ(βnm),..., ρ(βNM)]T；
the expression of the radar echo vector S is:
S＝[sR(τ1,η1),sR(τ1,η2),...,sR(τ1,ηA),...,sR(τr,ηa),...sR(τR,ηA)]T。
preferably, in the established linear measurement model, each element in the observation matrix Φ is represented as:
Figure GDA0003116503020000042
wherein the content of the first and second substances,
Figure GDA0003116503020000043
the compensated slope distance for the radial motion speed.
Preferably, in the step S6, based on l1/2Norm optimization criterion the optimization equation is established as:
Figure GDA0003116503020000044
where ξ represents the regularization parameter.
The technical scheme of the invention has the following advantages: the invention provides a frequency spectrum de-aliasing method aiming at the airborne inverse synthetic aperture laser radar detection air micro-motion target and azimuth sparse sampling mode, which can realize high-resolution imaging of a target under a high sparse sampling rate by establishing a linear observation matrix and utilizing a compressed sensing theory to carry out sparse signal solution on radar echo subjected to sparse sampling, thereby effectively reducing the requirement of azimuth data rate and providing technical support for airborne inverse synthetic aperture laser radar imaging engineering application.
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FIG. 1 is a schematic diagram of steps of a method for micro-motion imaging of an airborne inverse synthetic aperture laser radar under sparse sampling according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a model for imaging a micro-motion target by an airborne inverse synthetic aperture laser radar in an embodiment of the present invention;
FIG. 3 is a direct imaging result with radar azimuth data sparse to 12.5% correspondence;
FIG. 4 is an image reconstruction result obtained by using a micro-motion imaging method of an airborne inverse synthetic aperture laser radar under sparse sampling in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
As shown in fig. 1, the micro-imaging method for an airborne inverse synthetic aperture laser radar under sparse sampling provided by the embodiment of the present invention includes the following steps:
s1, establishing a target motion model aiming at the aerial micro-motion target to obtain an inclined distance expression R of any point P on the target at the time tp(t)。
Preferably, in step S1, there are three coordinate systems in the object motion model established for the aerial micro-motion object, which are: a radar coordinate system (U, V, W), a target specimen coordinate system (X, Y, Z) and a reference coordinate system (X, Y, Z). As shown in fig. 2Shown, where the origin of the radar coordinate system is Q; the original points of the target specimen body coordinate system and the reference coordinate system are both O; let the X-axis of the reference coordinate system coincide with the X-axis of the coordinate system of the target specimen body, the center of mass of the target is located at the center O point of the bottom surface, and the sight line direction of the radar is gamma0。
Preferably, the slope distance expression R of any point P on the target at the time tp(t) is:
Rp(t)＝||R0-rp(t)||≈||R0||+n·rp(t)；
wherein R is0The vector of the slant distance from the target center to the origin of the radar coordinate system; the position of any point P on the target at the time t in the target coordinate system is set as (x)p,yp,zp)，rp(t)＝(xp,yp,zp)TIs the initial coordinate vector of the target P point at the time t, n is (0, sin gamma)0,cosγ0) Is the radar line-of-sight vector.
The target has translation and the moving speed of the target is set as v1The flying speed of the radar airborne platform is v2The relative speed between the two is v ═ v1-v2. The object micromotion form comprises spin and coning, wherein the spin vector direction is Oz direction and is expressed as omega in (x, y, z) coordinate systems，Ωs＝||ωsAnd | | represents the magnitude of the spin vector. The direction of the coning vector is ON direction, and the coning vector is represented as omegac，Ωc＝||ωcAnd | | represents the magnitude of the coning vector.
Further, since the rotation angle required for target imaging is small, approximately equation sin Ω is satisfiedst≈Ωst，cosΩst is approximately equal to 0, the shape of the micro-motion target in the air is generally conical, and the slope distance expression R of any point P on the target at the time tp(t) can be approximated as:
Rp(t)≈R0+sinγ0(ypcosδ-zpsinδ)+cosγ0(ypsinδ+zpcosδ) +t[vr+sinγ0(xpΩscosδ+Ωcxp)+cosγ0sinδxpΩs]-t2ΩsΩcypsinγ0；
wherein R is0＝||R0| |, the size of the slant range vector from the target center to the origin of the radar coordinate system, ΩsRepresenting the magnitude of a spin vector in the micro-motion form of the micro-motion target in the air, wherein the direction of the spin vector is the Oz direction; omegacThe method is characterized in that the magnitude of a coning vector in the micro-motion form of the micro-motion target in the air is represented, the coning vector direction is an ON direction, and for convenience of analysis, the coincidence of the coning axis ON and an OZ axis can be assumed; v. ofrV · n represents the radial velocity of the aerial micro-motion target, and v represents the relative velocity vector of the aerial micro-motion target and the radar airborne platform; δ denotes a unit impulse signal.
S2, obtaining a laser radar echo signal model S by using a slant range expressionR(τ,η)。
Preferably, in step S2, the slope distance expression R of an arbitrary point P is usedp(t) laser radar echo signal model sR(τ, η) can be expressed as:
Figure GDA0003116503020000061
wherein, the transmitted signal is a linear frequency modulation signal, the echo signal is received in a deskew mode, tau and eta respectively represent a fast time and a slow time, T ═ eta + tau, TpDenotes the pulse width, fcThe carrier frequency of the laser is gamma, and the frequency is adjusted; rho (beta) is a target reflection coefficient, beta represents an included angle between a normal vector of a target point and the radar sight line direction, and c is the speed of light.
And S3, constructing a compensation function H (eta) by estimating the radial velocity of the target based on the laser radar echo signal model, and performing radial velocity compensation on the echo signal.
Preferably, in step S3, by estimating the target radial velocity, the constructed compensation function H (η) can be expressed as:
Figure GDA0003116503020000071
wherein the content of the first and second substances,
Figure GDA0003116503020000072
is the target radial velocity estimated by the velocity estimation method. The speed estimation method is prior art and will not be repeated here.
The echo signal model includes signal amplitude and phase, where phase is affected by skew. After the echo signal is compensated for radial velocity, the caused change of the slant range is the change of the phase, and further the echo signal model is changed. The echo compensation formula is as follows: sR(τ,η)·H*(η)。
And S4, representing a fast time domain and a slow time domain in the laser radar echo signal model in a discretization mode, dividing a range-direction and azimuth-direction imaging space into N multiplied by M grids, wherein N and M respectively represent the number of division in the range direction and the azimuth direction.
Preferably, in step S4, the fast time domain and the slow time domain are discretized respectively as follows:
τ＝[τ1,τ2,...,τr,...τR]1×R；
η＝[η1,η2,...,ηa,...ηA]1×A；
wherein R is more than or equal to 1 and less than or equal to R, and R represents the length of the fast time sequence; a is more than or equal to 1 and less than or equal to A, and A represents the length of the slow time sequence. After the distance direction-azimuth direction imaging space is divided into N multiplied by M grids, the coordinate point corresponding to the (N, M) th grid is (x)nm,ynm,znm)，1≤n≤N，1≤m≤M。
S5, aiming at the divided range direction-azimuth direction imaging space, establishing an airborne inverse synthetic aperture laser radar micro-motion imaging linear measurement model based on a laser radar echo signal model and a slant range expression.
Preferably, in step S5, the expression of the airborne inverse synthetic aperture lidar micro-motion imaging linear measurement model is established as follows:
S＝Φρ；
wherein phi is an observation matrix, rho is a scattering center vector of the target, and S is a radar echo vector.
Further, for the divided range-azimuth imaging space, the expression of the observation matrix Φ is:
Figure GDA0003116503020000081
the expression for the scattering center vector ρ of the target is:
ρ＝[ρ(β11),ρ(β12),...,ρ(β1m),…,ρ(β1M),...,ρ(βnm),..., ρ(βNM)]T；
the expression of the radar echo vector S is:
S＝[sR(τ1,η1),sR(τ1,η2),...,sR(τ1,ηA),...,sR(τr,ηa),...sR(τR,ηA)]T。
further, the expressions of the elements in the observation matrix Φ are:
Figure GDA0003116503020000082
wherein the content of the first and second substances,
Figure GDA0003116503020000083
the compensated slope distance for the radial motion speed.
Figure GDA0003116503020000084
Can be expressed as:
Figure GDA0003116503020000085
s6, utilizing the compressed sensing theory and based on l1/2Establishing an optimized equation according to norm optimization criterion, solving the established linear measurement model, and solving the linear measurementAnd measuring a scattering center vector rho of the target in the model to obtain an image reconstruction result of the target under sparse sampling.
The theory of compressed sensing is prior art and will not be repeated here. Preferably, in step S6, based on l1/2Norm optimization criteria the establishment of an optimization equation can be expressed as:
Figure GDA0003116503020000086
where ξ represents the regularization parameter. And solving rho through the equation to obtain an image reconstruction result of the target under sparse sampling, so as to realize laser radar imaging.
The invention also verifies the proposed micro-motion imaging method of the airborne inverse synthetic aperture laser radar through imaging simulation, as shown in fig. 3 and 4, fig. 3 is a direct imaging result corresponding to the azimuth data being thinned to 12.5%, and the thinning criterion is an M sequence. Aiming at the theory of target echo modeling, two-dimensional ISAL high-resolution imaging simulation is carried out on the cone precession target. The radar transmitting signal is assumed to be a linear frequency modulation signal, the shape of the micro-motion target in the air is a cone, the target on the surface of the cone is composed of 6400 points, the height of the cone is 2m, the half cone angle is 10 degrees, and the micro-motion form is composed of spin and conical rotation. To simplify the analysis, only coning motion is considered for wingless targets. The target moving speed is 7km/s, the modulation bandwidth is 4GHz, the corresponding resolution is 5cm, and the imaging time is 50 mu s. The remaining imaging simulation parameters are detailed in tables 1 and 2. It can be seen from fig. 3 that due to sparse sampling, the image has severe aliasing in the azimuth direction, and cannot reflect the true shape of the target.
TABLE 1 target micromotion parameters
Figure GDA0003116503020000091
TABLE 2 micro-motion target imaging simulation parameters of airborne laser radar
Figure GDA0003116503020000092
Fig. 4 shows the image reconstruction result obtained by using the method for micro-motion imaging of the airborne inverse synthetic aperture laser radar under sparse sampling, which is disclosed by the invention, by similarly thinning the azimuth data to 12.5%. As can be seen from the image reconstruction result, the reconstruction result basically reflects the target shape, and the defocusing phenomenon does not exist. Through rotation compensation and azimuth calibration, target size information can be directly obtained from an imaging result, and the effectiveness of the method is further verified.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (8)

1. A micro-motion imaging method of an airborne inverse synthetic aperture laser radar under sparse sampling is characterized by comprising the following steps:
s1, establishing a target motion model aiming at the aerial micro-motion target to obtain an inclined distance expression of any point on the target;
s2, obtaining a laser radar echo signal model by using a slant range expression;
s3, constructing a compensation function by estimating the radial speed of a target based on the laser radar echo signal model, and performing radial speed compensation on the echo signal;
s4, representing a fast time domain and a slow time domain in a laser radar echo signal model in a discretization mode, and dividing a range direction-azimuth direction imaging space into N multiplied by M grids;
s5, aiming at the divided range direction-azimuth direction imaging space, establishing an airborne inverse synthetic aperture laser radar micro-motion imaging linear measurement model based on a laser radar echo signal model and a slant range expression;
s6, utilizing the compressed sensing theory and based on l1/2Establishing an optimized equation according to the norm optimization criterion, and solving the established linear measurement model to obtain an image reconstruction result of the target under sparse sampling;
when the target motion model is established for the hollow micro-motion target in step S1, there are three coordinate systems, which are: a radar coordinate system (U, V, W), a target specimen coordinate system (X, Y, Z) and a reference coordinate system (X, Y, Z); wherein the origin of the radar coordinate system is Q; the original points of the target specimen body coordinate system and the reference coordinate system are both O; let the X-axis of the reference coordinate system coincide with the X-axis of the coordinate system of the target specimen body, the center of mass of the target is located at the center O point of the bottom surface, and the sight line direction of the radar is gamma0；
Obtaining the slope distance expression R of any point P on the target at the time tp(t) is:
Rp(t)＝||R0-rp(t)||≈||R0||+n·rp(t)；
wherein R is0The vector of the slant distance from the target center to the origin of the radar coordinate system; the position of an arbitrary point P on the target at the time t in the target coordinate system is set as (x)p,yp,zp)，rp(t)＝(xp,yp,zp)TIs the initial coordinate vector of the target P point at the time t, n is (0, sin gamma)0,cosγ0) Is a radar sight line direction vector;
the shape of the aerial micro-motion target is conical; in the step S1, an expression R of the slope distance of the arbitrary point P on the target at the time t is obtainedp(t) is:
Rp(t)≈R0+sinγ0(ypcosδ-zpsinδ)+cosγ0(ypsinδ+zpcosδ)+t[vr+sinγ0(xpΩscosδ+Ωcxp)+cosγ0sinδxpΩs]-t2ΩsΩcypsinγ0；
wherein R is0＝||R0| |, the vector of the slant distance from the center of the target to the origin of the radar coordinate systemSize, omegasRepresenting the magnitude of a spin vector in the micro-motion form of the micro-motion target in the air, wherein the direction of the spin vector is the Oz direction; omegacThe method comprises the steps of representing the magnitude of a coning vector in an air micro-motion target micro-motion form, wherein the coning vector direction is an ON direction; v. ofrV · n represents the radial velocity of the aerial micro-motion target, and v represents the relative velocity vector of the aerial micro-motion target and the radar airborne platform; δ denotes a unit impulse signal.
2. The method of claim 1, wherein:
in the step S2, the obtained laser radar echo signal model SR(τ, η) is expressed as:
Figure FDA0003116503010000021
where τ and η represent fast and slow times, respectively, T ═ η + τ, TpDenotes the pulse width, fcThe carrier frequency of the laser is gamma, and the frequency is adjusted; rho (beta) is a target reflection coefficient, and beta represents an included angle between a normal vector of a target point and the radar sight line direction.
3. The method of claim 2, wherein:
in step S3, the compensation function H (η) is constructed by:
Figure FDA0003116503010000022
wherein the content of the first and second substances,
Figure FDA0003116503010000023
is the target radial velocity estimated by the velocity estimation method.
4. The method of claim 3, wherein:
in step S4, the discretization indicates that the fast time domain and the slow time domain in the laser radar echo signal model are:
τ＝[τ1,τ2,...,τr,...τR]1×R；
η＝[η1,η2,...,ηa,...ηA]1×A；
wherein R is more than or equal to 1 and less than or equal to R, and R represents the length of the fast time sequence; a is more than or equal to 1 and less than or equal to A, wherein A represents the length of the slow time sequence;
after the distance direction-azimuth direction imaging space is divided into N multiplied by M grids, the coordinate point corresponding to the (N, M) th grid is (x)nm,ynm,znm)，1≤n≤N，1≤m≤M。
5. The method of claim 4, wherein:
in step S5, the established airborne inverse synthetic aperture laser radar micro-motion imaging linear measurement model is represented as:
S＝Φρ；
wherein phi is an observation matrix, rho is a scattering center vector of the target, and S is a radar echo vector.
6. The method of claim 5, wherein:
in the established linear measurement model, the observation matrix Φ is expressed as:
Figure FDA0003116503010000031
the scattering center vector ρ of the target is expressed as:
ρ＝[ρ(β11),ρ(β12),...,ρ(β1m),...,ρ(β1M),...,ρ(βnm),...,ρ(βNM)]T；
the expression of the radar echo vector S is:
S＝[sR(τ1,η1),sR(τ1,η2),...,sR(τ1,ηA),...,sR(τr,ηa),...sR(τR,ηA)]T。
7. the method of claim 6, wherein:
in the established linear measurement model, each element in the observation matrix Φ is represented as:
Figure FDA0003116503010000032
wherein the content of the first and second substances,
Figure FDA0003116503010000033
the compensated slope distance for the radial motion speed.
8. The method of claim 7, wherein:
in the step S6, based on l1/2Norm optimization criterion the optimization equation is established as:
Figure FDA0003116503010000041
where ξ represents the regularization parameter.
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