CN113625276B - Precession feature extraction-based three-dimensional imaging method for spatial cone target ISAR - Google Patents
Precession feature extraction-based three-dimensional imaging method for spatial cone target ISAR Download PDFInfo
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Abstract
The invention discloses a spatial cone target ISAR three-dimensional imaging method based on precession feature extraction, and relates to a spatial cone target ISAR three-dimensional imaging method. The invention aims to solve the problems that the existing method for extracting precession characteristics of a space cone target and three-dimensional ISAR imaging needs multiple radar resources and the calculation process is complex; and the parameter searching calculation amount is large, and the searching result may not be unique. The process is as follows: step one, obtaining target slow time-range profiles of different angles; obtaining a target spin angular velocity and a cone rotational angular velocity; step two, a inching curve generated by a cone top scattering point of the precession space cone target in a target slow time-distance image plane is a sine curve; step three, establishing a nonlinear equation set; step four, obtaining unknown numbers, and further estimating a target spin and cone spin unit vector; and fifthly, obtaining a three-dimensional image of the target, wherein the imaging result reflects the structural size and the spatial posture of the target. The invention is used in the technical field of radars.
Description
Technical Field
The invention belongs to the technical field of radars, and relates to a three-dimensional imaging method of a space cone target ISAR.
Background
The ballistic target mark is one of the key problems of the middle section defense system of the current ballistic missile, and radar imaging can provide visual shape and structural characteristics of targets and can be used as an important means for middle section ballistic target recognition. The shape of the ballistic target is generally cone, and besides the orbital motion, the ballistic target also has micro-motion modes such as spin, cone rotation, precession and the like, and the posture of the precession cone target is complex in radar imaging, so that the traditional imaging method is not applicable any more. To achieve ISAR imaging of a precessional target, it is necessary to obtain precessional features of the target. At present, the method for solving the problems of spatial cone target precession feature extraction and ISAR three-dimensional imaging mainly comprises a distributed radar networking method and a high-dimensional parameter searching method, and can estimate target precession parameters and realize target three-dimensional imaging. However, the distributed radar networking requires multiple radar resources, and the precession feature extraction process needs to consider the situation of different precession postures of targets, so that the calculation process is complex; the high-dimensional parametric search is computationally intensive and the search results may not be unique. Thus, it is necessary to study spatial cone object precession feature extraction and ISAR three-dimensional imaging.
Disclosure of Invention
The invention aims to solve the problems that the existing method for extracting precession characteristics of a space cone target and three-dimensional ISAR imaging needs multiple radar resources and the calculation process is complex; and the calculated amount of parameter search is large, and the search result is probably not unique, and a spatial cone target ISAR three-dimensional imaging method based on precession feature extraction is provided.
The spatial cone target ISAR three-dimensional imaging method based on precession feature extraction is characterized by comprising the following steps of: the method comprises the following specific processes:
firstly, observing a precession space cone target by adopting two radars, namely a radar 1 and a radar 2, obtaining a cone target radar echo, performing pulse compression on the cone target radar echo, and performing motion compensation to obtain target slow time-range images S (f r ,t m )；
Obtaining target spin angular velocity omega by adopting curve separation technology and autocorrelation method s And angular velocity of cone rotation omega c ；
Step two, precession space cone target cone top scattering point is on target slow time-distance image S (f) r ,t m ) The inching curve generated by the plane is a sine curve a i sin(Ω c t m +b i )+d i The slow time-range profile S (f) of the targets of the radar 1 and the radar 2 in the first step is respectively transformed by iRadon r ,t m ) Estimating sinusoidal parameter amplitude a i Phase b i Offset d i ；
i=1, 2 denotes radar 1 and radar 2;
step three, establishing a precession space cone target ISAR imaging model, and deducing a cone top scattering point inching sine curve a i sin(Ω c t m +b i )+d i Parameter amplitude a i Phase b i Offset d i Spin angular velocity unit vector characteristic of precession with targetTarget cone rotation angular velocity unit vector +.>According to the relation of the iRadon transformation in the second step to the parameter estimation result { a } of the sinusoids on the slow time-range image plane of the radar 1 and the radar 2 targets i ,b i ,d i -spin angular velocity unit vector +_>Cone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i A relation of i=1, 2 represents radar 1 and radar 2, and a nonlinear equation set is established;
step four, solving the nonlinear equation set established in the step three by using a quasi Newton method to obtain an unknown number { r } P ′,θ′ P ,z′ P ,α c ,β c And then estimate the target spin and cone spin unit vector
The r is P ' is the polar diameter, theta, in the form of cylindrical coordinates of the cone-top scattering point P ' is the polar angle, z ' in the form of cylindrical coordinates of the cone-top scattering point ' P Is the height alpha in the form of cylindrical coordinates of the cone top scattering point c And beta c The azimuth angle and the elevation angle of the cone-rotation vector in a target coordinate system are respectively;
step five, according to the target spin and cone rotation angular velocity unit vector obtained in the step fourAnd step one estimated target spin, cone angular velocity { Ω } s ,Ω c Determining the slow time-distance image S (f) of scattering points (x, y, z) at different positions of the precessional spatial cone target r ,t m ) Inching curve on plane, using generalized Radon transformation to target slow time-distance image S (f r ,t m ) Integrating the inching curve path on the plane to obtainThree-dimensional image S of object GRT (x, y, z) and imaging results reflect the structural dimensions and spatial pose of the target.
The beneficial effects of the invention are as follows:
the existing spatial cone target precession feature extraction and ISAR three-dimensional imaging method needs multiple radar resources or is large in calculated amount, and accurate and efficient precession feature extraction and ISAR three-dimensional imaging are difficult to achieve. The invention provides a method for extracting target precession features of a two-part radar observation space cone, which is used for performing ISAR three-dimensional imaging on a target by using a generalized Radon transformation method after the target precession features are obtained, and the imaging result can reflect the structural size and the space posture of the target. According to the invention, two radars are adopted to observe a precession space cone target, so as to obtain target slow time-range images with different angles; the inching curve generated by the cone top scattering point on the slow time-distance image plane is a sine curve, and the parameters of the sine curve are estimated by using the iRadon transformation; according to the precession space cone target ISAR imaging model, deducing the relation between the sinusoidal parameter of the cone top scattering point and the target precession characteristic, and establishing a nonlinear equation set; solving a nonlinear equation set by using a quasi Newton method to obtain a target precession characteristic; according to the target precession characteristics, determining a jogging curve of scattering points at different positions of a precession target on a slow time-distance image plane, integrating the slow time-distance image of the target on a jogging curve path by utilizing generalized Radon transformation, obtaining a three-dimensional image of the target, and enabling an imaging result to reflect the structural size and the spatial attitude of the target.
Compared with the traditional precession feature extraction and ISAR three-dimensional imaging algorithm, the method has the following advantages:
(1) Processing the broadband radar echo without other radar data such as the scattering cross section of the target;
(2) The targets are observed by two radars, so that radar resources are saved relative to the observation of multiple radars;
(3) And solving and extracting precession features through an equation set, so that the problems of large calculation amount of high-dimensional search and possible non-uniqueness of search results are avoided.
Drawings
FIG. 1 is a flow chart of an algorithm of the present invention;
fig. 2 is a view of a precession spatial cone target ISAR imaging model, Q-UVW being the radar coordinate system,for the initial vector of the target centroid in the radar coordinate system, P is the cone top scattering point, +.>For the target spin angular velocity vector,/>The target cone rotation angular velocity vector;
figure 3 is a graph of the positional relationship of the target coordinate system and the intermediate coordinate system,is a radar line-of-sight unit vector in an intermediate coordinate system;
FIG. 4 is a model diagram of a precession space cone target scattering point;
FIG. 5a is a model of a precession spatial cone target scattering point;
FIG. 5b is a three-dimensional imaging result diagram of the target ISAR;
FIG. 5c is a top view of a scattering points model;
FIG. 5d is a top view of the imaging result;
FIG. 5e is a front view of a scattering point model;
FIG. 5f is a front view of an imaging result;
FIG. 5g is a side view of a scattering point model;
FIG. 5h is a side view of the imaging result;
FIG. 6a is a model diagram of a spatial cone target scattering point for different precession poses;
FIG. 6b is a three-dimensional imaging result diagram of the target ISAR;
FIG. 7a is a graph of spatial cone target scattering point models of different precession poses;
FIG. 7b is a three-dimensional imaging result diagram of the target ISAR;
FIG. 8a is a graph of the estimated error of the target slow time-range profile sinusoidal parameters for different signal-to-noise ratio radars 1;
FIG. 8b is a graph of the slow time-range profile sinusoidal parameter estimation error for different signal-to-noise ratio radars 2;
fig. 9 is a graph of estimation errors of different signal-to-noise ratio spatial cone target precession features.
Detailed Description
The first embodiment is as follows: the specific process of the embodiment is as follows:
firstly, observing a precession space cone target by adopting two radars, namely a radar 1 and a radar 2, obtaining a cone target radar echo, performing pulse compression on the cone target radar echo, and performing motion compensation to obtain target slow time-range images S (f r ,t m )；
Obtaining target spin angular velocity omega by adopting curve separation technology and autocorrelation method s And angular velocity of cone rotation omega c ；
Step two, precession space cone target cone top scattering point is on target slow time-distance image S (f) r ,t m ) The inching curve generated by the plane is a sine curve a i sin(Ω c t m +b i )+d i The slow time-range profile S (f) of the targets of the radar 1 and the radar 2 in the first step is respectively transformed by iRadon r ,t m ) Estimating sinusoidal parameter amplitude a i Phase b i Offset d i ；
i=1, 2 denotes radar 1 and radar 2;
step three, establishing a precession space cone target ISAR imaging model (parameter amplitude a i Phase b i Offset d i Spin angular velocity unit vector characteristic of precession with targetTarget cone rotation angular velocity unit vector +.>The relation of (a) of the cone top scattering point inching sine curve a) is deduced i sin(Ω c t m +b i )+d i Parameter amplitude a i Phase b i Offset d i Spin angular velocity unit vector corresponding to target precession feature>Target cone rotation angular velocity unit vector +.>According to the relation of the iRadon transformation in the second step to the parameter estimation result { a } of the sinusoids on the slow time-range image plane of the radar 1 and the radar 2 targets i ,b i ,d i Unit vector of spin angular velocityCone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i A relation of i=1, 2 represents radar 1 and radar 2, and a nonlinear equation set is established;
step four, solving the nonlinear equation set established in the step three by using a quasi Newton method to obtain an unknown number { r' P ,θ′ P ,z′ P ,α c ,β c And then estimate the target spin and cone spin unit vector
The r is P ' is the polar diameter, theta, in the form of cylindrical coordinates of the cone-top scattering point P ' is the polar angle, z ' in the form of cylindrical coordinates of the cone-top scattering point ' P Is the height alpha in the form of cylindrical coordinates of the cone top scattering point c And beta c The azimuth angle and the elevation angle of the cone-rotation vector in a target coordinate system are respectively;
step five, according to the target spin and cone rotation angular velocity unit vector obtained in the step fourSum stepStep one estimated target spin, cone angular velocity { Ω } s ,Ω c Determining the slow time-distance image S (f) of scattering points (x, y, z) at different positions of the precessional spatial cone target r ,t m ) Inching curve on plane, using generalized Radon transformation to target slow time-distance image S (f r ,t m ) Integrating the inching curve path on the plane to obtain a three-dimensional image S of the target GRT (x, y, z) the imaging results may reflect the structural dimensions and spatial pose of the target.
The second embodiment is as follows: in the second step, the slow time-range images S (f) of the targets of the radar 1 and the radar 2 in the first step are respectively obtained by using the iRadon transform, which is different from the first embodiment r ,t m ) Estimating sinusoidal parameter amplitude a i Phase b i Offset d i The method comprises the steps of carrying out a first treatment on the surface of the The specific process is that
The iRadon transformation can map the sinusoids on the plane to a parameter space, realizing the parameter estimation of the sinusoids, typically by a filtered back projection algorithm.
Wherein S is RL (f r ,t m ) Slow time-distance image S (f) representing object r ,t m ) F after filtering by a Ram-Lak filter in a distance domain r Represent distance, t m Indicating slow time, S IRT (a, b, d) a slow time-distance image S (f) r ,t m ) On-plane amplitude search variable a, phase search variable b, offset search variable d sinusoidal iRadon transform values, Ω c The cone rotation angular velocity is the target;
target slow time-range profile S (f r ,t m ) The parameters of the sinusoidal curve on the plane can be determined by S IRT Maximum position estimation of (a, b, d)
Other steps and parameters are the same as in the first embodiment.
And a third specific embodiment: the present embodiment differs from the first or second embodiments in that in the third step, a precessional spatial pyramid target ISAR imaging model (parameter amplitude a i Phase b i Offset d i Spin angular velocity unit vector characteristic of precession with targetTarget cone rotation angular velocity unit vector +.>The relation of (a) of the cone top scattering point inching sine curve a) is deduced i sin(Ω c t m +b i )+d i Parameter amplitude a i Phase b i Offset d i Spin angular velocity unit vector corresponding to target precession feature>Target cone rotation angular velocity unit vector +.>According to the relation of the iRadon transformation in the second step to the parameter estimation result { a } of the sinusoids on the slow time-range image plane of the radar 1 and the radar 2 targets i ,b i ,d i -spin angular velocity unit vector +_>Cone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i A relation of i=1, 2 represents radar 1 and radar 2, and a nonlinear equation set is established; the specific process is as follows:
establishing a nonlinear equation set according to a precession model
The cone top scattering point of the precession space cone target is positioned on the spin axis of the target, spin movement of the cone top scattering point does not affect radar echo, and only cone spin movement of the cone top scattering point can be observed on the target slow time-range profile.
The cone-rotation motion of the target can be described by using a target coordinate system, wherein the target coordinate system is parallel to a preset radar coordinate system, and the mass center of the target is positioned at the origin of the target coordinate system;
the XYZ axis of the target coordinate system is parallel to the coordinate axis of the radar coordinate system, the radar coordinate system is a right-hand coordinate system which is preset, and uses north as a Y axis and vertical ground as a Z axis;
in the target coordinate system O-XYZ, the inching curve generated by the cone top scattering point on the slow time-distance image is
Wherein R is c In the form of a matrix of target cones,is the coordinates of the cone top scattering point in the target coordinate system,/->Is a radar line-of-sight unit vector; />I 3 Is a 3 x 3 unit array, +.>For the unit vector of the target cone rotational speed>Is an antisymmetric matrix of alpha c And beta c Azimuth and elevation of the cone-rotation vector in the target coordinate system, respectively, (·) T Representing the transpose of the matrix> Alpha and beta are the azimuth angle and elevation angle of the radar sight in the radar coordinate system Q-UVW respectively;
angular velocity of taper at target Ω c And radar line of sight unit vectorIn the known case, the inching curve generated by the cone apex scattering point on the slow time-distance image is defined by the coordinates of the cone apex scattering point in the target coordinate system +.>And the target cone rotational angular velocity unit vector +.>Determining that the target cone top scattering point is positioned on the spin axis of the target, wherein the position of the target cone top scattering point can represent spin angular velocity unit vector +.>The terms represent the modulus of the vector;
establishing an intermediate coordinate system O-X ' Y ' Z ' and determining the precession characteristics (including spin angular velocity unit vectorAnd the unit vector of the cone rotation angular velocity>) Spin angular velocity unit vector +>Cone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i Relationship of };
estimating the parameter estimation results { a } of the sinusoids on the slow-time-range image planes of the radar 1 and radar 2 targets according to the iRadon transform in the second step i ,b i ,d i Unit vector of spin angular velocityCone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i Relation of i=1, 2 denotes radar 1 and radar 2, a nonlinear equation set is established
Wherein alpha is i And beta i Azimuth and elevation of the ith radar line of sight, respectively.
Other steps and parameters are the same as in the first or second embodiment.
The specific embodiment IV is as follows: this embodiment differs from one to three embodiments in that the establishing the intermediate coordinate system O-X ' Y ' Z ' determines the target precession characteristics (including spin angular velocity unit vectorsAnd the unit vector of the cone rotation angular velocity>) Spin angular velocity unit vector +>Cone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i Relationship of }The method comprises the steps of carrying out a first treatment on the surface of the The specific process is as follows:
the coordinate axis unit vector of the intermediate coordinate system coincides with the origin of the target coordinate systemThe method meets the following conditions:
wherein,the coordinate of the target cone top scattering point in the middle coordinate system is the Z-axis unit vector of the target coordinate system>Can be by->Through transformation to obtain
Wherein R is T Is a transformation matrix; (x, y, z) are scattering points at different positions of the precession space cone target;
in the intermediate coordinate system, the jogging curve generated by the cone-top scattering point on the slow time-distance image can be expressed as
Wherein R 'is' c For a cone-rotation matrix of the object in the intermediate coordinate system,is the coordinates of the cone-top scattering point in the intermediate coordinate system, (-) T Denote the transpose, r P ' is the polar diameter, theta, in the form of cylindrical coordinates of the cone-top scattering point P ' is the polar angle, z ' in the form of cylindrical coordinates of the cone-top scattering point ' P Is the height in the cylindrical coordinate form of the cone top scattering point, A r Is a sinusoidal amplitude component +.>Is a sinusoidal phase component, A z A sinusoidal bias component;
from the analysis in the third step, we can obtain the parameters of the inching sinusoid and the unknowns { r 'generated by the cone-top scattering point on the slow time-distance image plane' P ,θ′ P ,z′ P ,α c ,β c Relationships of }.
Other steps and parameters are the same as in one to three embodiments.
Fifth embodiment: this embodiment differs from the embodiments by one to four in that the target has a cone-rotation matrix R 'in the intermediate coordinate system' c Sinusoidal amplitude component A r Sinusoidal phase componentSinusoidal bias component A z The expression is:
wherein epsilon represents the included angle between the unit vector of the cone rotation angular velocity and the radar sight line.
Other steps and parameters are the same as in one to four embodiments.
Specific embodiment six: the difference between the present embodiment and one to fifth embodiments is that in the fourth step, the nonlinear equation set established in the third step is solved by using a quasi-Newton method to obtain an unknown { r' P ,θ′ P ,z′ P ,α c ,β c And then estimate the target spin and cone spin unit vectorThe specific process is as follows:
for a nonlinear equation set F (x) =0, the quasi-Newton method can be used to solve for
Where i=0, 1,2,.. 0 Representing an initial approximate solution, A 0 Represents F (x) 0 ) Jacobi matrix of (-) -1 Representing the inverse of the matrix, y i ＝F(x i+1 )-F(x i )，r i ＝x i+1 -x i . When applying a quasi Newton method to solve an approximate solution of a nonlinear equation set, an initial approximate solution x is selected 0 And an initial matrix A 0 A better approximation solution can be obtained in general, the iteration sequence { x } i Has a super linear convergence speed.
Solving the unknowns { r } of a system of nonlinear equations by quasi Newton method P ′,θ′ P ,z′ P ,α c ,β c }；
Target spin, cone rotation angular velocity unit vectorObtained by
Other steps and parameters are the same as in one of the first to fifth embodiments.
Seventh embodiment: the present embodiment differs from the first to sixth embodiments in that the target spin and cone angular velocity unit vector obtained in the fifth step according to the fourth stepAnd step one estimated target spin, cone angular velocity { Ω } s ,Ω c Determining the slow time-distance image S (f) of scattering points (x, y, z) at different positions of the precessional spatial cone target r ,t m ) Inching curve on plane, using generalized Radon transformation to target slow time-distance image S (f r ,t m ) Integrating the inching curve path on the plane to obtain a three-dimensional image S of the target GRT (x, y, z) the imaging results may reflect the structural dimensions and spatial pose of the target; the specific process is as follows:
the unit vector of the target spin and the cone rotational speed obtained according to the step fourAnd step one estimated target spin, cone angular velocity { Ω } s ,Ω c Determining the slow time-distance image S (f) of scattering points (x, y, z) at different positions of the precessional spatial cone target r ,t m ) The micro curve generated on the plane has the expression:
wherein R is c In the form of a matrix of target cones,for the spin matrix of the object to be achieved,for the target spin angular velocity unit vector +.>Is an antisymmetric matrix of alpha s And beta s Azimuth and elevation of spin vector in target coordinate system, respectively, +.>For the coordinates of a certain scattering point in the target coordinate system,/->Is radar sight line unit vector, A 0 、A 1 、A 2 、A 3 、A 4 、φ 1 、φ 2 、φ 3 、φ 4 Is an intermediate variable;
establishing an imaging grid in a three-dimensional space, taking a inching curve of imaging grid coordinates (x, y, z) as an integral path, and obtaining a target slow time-distance image S (f r ,t m ) And carrying out generalized Radon transformation to realize three-dimensional imaging of the target.
Other steps and parameters are the same as in one of the first to sixth embodiments.
Eighth embodiment: this embodiment differs from one of the embodiments one to seven in that the intermediate variable A 0 、A 1 、A 2 、A 3 、A 4 Specifically defined as:
other steps and parameters are the same as those of one of the first to seventh embodiments.
Detailed description of the preferred embodimentsFormula nine: this embodiment differs from one to eight of the embodiments in that the intermediate variable φ 1 、φ 2 、φ 3 、φ 4 Specifically defined as:
other steps and parameters are the same as in one to eight of the embodiments.
Detailed description ten: the difference between the present embodiment and one of the first to ninth embodiments is that the imaging grid is built in three-dimensional space, and the inching curve of the imaging grid coordinates (x, y, z) is taken as an integral path, and the target slow time-distance image S (f r ,t m ) Performing generalized Radon transformation to realize three-dimensional imaging of the target; the expression is:
wherein S is GRT (x, y, z) is a three-dimensional image of the object.
Other steps and parameters are the same as in one of the first to ninth embodiments.
The following examples are used to verify the benefits of the present invention:
embodiment one:
because of the lack of real measurement data of the space cone target ISAR imaging, the invention is mainly verified by using simulation data, and the effectiveness of the invention on the extraction of precession characteristics of the space cone target and the three-dimensional imaging of the ISAR can be proved.
FIG. 2 is a precession space cone target ISAR imaging model, FIG. 3 is a positional relationship of a target coordinate system and an intermediate coordinate system, FIG. 4 is a precession space cone target scattering point model, a cone target precesses in space, including spin and cone spin;
table 1 is a target slow time-range profile sinusoidal parameter estimation result of radar 1 and radar 2, iRadon transformation is carried out on a target slow time-range profile plane, the parameter estimation result of sinusoidal amplitude, phase and offset is not greatly different from a true value, and the method can be used for extracting the follow-up target precession feature, table 2 is a space cone target precession feature estimation result, a nonlinear equation set is solved by using a quasi-Newton method, the target precession feature is obtained, and the precession feature estimation result is not greatly different from the true value, so that the method can realize the precession feature extraction of the target;
fig. 5a is a precession space target cone target scattering point model, fig. 5b is a three-dimensional imaging result of a target ISAR, fig. 5c, fig. 5e, fig. 5g are a top view, a front view, and a side view of the scattering point model, and fig. 5d, fig. 5f, and fig. 5h are a top view, a front view, and a side view of the imaging result, respectively;
the estimation result of the target precession characteristic can determine the inching curve of scattering points at different positions, the slow time-distance image of the target is integrated in the path of the inching curve by utilizing generalized Radon transformation, and the obtained imaging result can truly reflect the structural size and the spatial attitude of the target, so that the invention can realize the three-dimensional imaging of the precession space cone target ISAR.
TABLE 1
TABLE 2
Tables 3 and 4 are respectively the estimation results of the precession characteristics of the spatial cone target under different precession postures, and the estimation results have little difference from the true values;
fig. 6a and fig. 7a are different precession attitude space cone target scattering point models, and fig. 6b and fig. 7b are target ISAR three-dimensional imaging result diagrams, so that precession feature extraction and ISAR three-dimensional imaging of a target can be effectively realized under different precession attitudes.
TABLE 3 Table 3
TABLE 4 Table 4
Fig. 8a and 8b show the estimation errors of the sine parameters of the slow time-range profile of the radar 1 and radar 2 targets under different signal-to-noise ratios, and fig. 9 shows the estimation errors of the precession characteristics of the spatial cone targets under different signal-to-noise ratios, wherein the estimation errors are converged rapidly when the signal-to-noise ratio is higher than-30 dB, so that better parameter estimation and precession characteristic extraction effects can be realized.
From the processing result of the simulation data, the invention can realize the precession feature extraction and ISAR three-dimensional imaging of the space cone target, and can obtain good precession feature extraction effect and three-dimensional images of the target.
The present invention is capable of other and further embodiments and its several details are capable of modification and variation in light of the present invention, as will be apparent to those skilled in the art, without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (6)
1. The spatial cone target ISAR three-dimensional imaging method based on precession feature extraction is characterized by comprising the following steps of: the method comprises the following specific processes:
firstly, observing a precession space cone target by adopting two radars, namely a radar 1 and a radar 2, obtaining a cone target radar echo, performing pulse compression on the cone target radar echo, and performing motion compensation to obtain target slow time-range images S (f r ,t m )；
Obtaining target spin angular velocity omega by adopting curve separation technology and autocorrelation method s And angular velocity of cone rotation omega c ；
Step two, precession space cone target cone top scattering point is on target slow time-distance image S (f) r ,t m ) The inching curve generated by the plane is a sine curve a i sin(Ω c t m +b i )+d i The slow time-range profile S (f) of the targets of the radar 1 and the radar 2 in the first step is respectively transformed by iRadon r ,t m ) Estimating sinusoidal parameter amplitude a i Phase b i Offset d i ；
i=1, 2 denotes radar 1 and radar 2;
step three, establishing a precession space cone target ISAR imaging model, and deducing a cone top scattering point inching sine curve a i sin(Ω c t m +b i )+d i Parameter amplitude a i Phase b i Offset d i Spin angular velocity unit vector characteristic of precession with targetTarget cone rotation angular velocity unit vector +.>According to the relation of the iRadon transformation in the second step to the parameter estimation result { a } of the sinusoids on the slow time-range image plane of the radar 1 and the radar 2 targets i ,b i ,d i -spin angular velocity unit vector +_>Cone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i A relation of i=1, 2 represents radar 1 and radar 2, and a nonlinear equation set is established;
step four, solving the nonlinear equation set established in the step three by using a quasi Newton method to obtain an unknown number { r' P ,θ′ P ,z′ P ,α c ,β c And then estimate the target spin and cone spin unit vector
Said, r' P Is the polar diameter, theta 'in the cylindrical coordinate form of the conical top scattering point' P Is polar angle, z 'in the form of cylindrical coordinates of the cone-top scattering point' P Is the height alpha in the form of cylindrical coordinates of the cone top scattering point c And beta c The azimuth angle and the elevation angle of the cone-rotation vector in a target coordinate system are respectively;
step five, according to the target spin and cone rotation angular velocity unit vector obtained in the step fourAnd step one estimated target spin, cone angular velocity { Ω } s ,Ω c Determining the slow time-distance image S (f) of scattering points (x, y, z) at different positions of the precessional spatial cone target r ,t m ) Inching curve on plane, using generalized Radon transformation to target slow time-distance image S (f r ,t m ) Integrating the inching curve path on the plane to obtain a three-dimensional image S of the target GRT (x, y, z) the imaging results reflect the structural dimensions and spatial pose of the target;
in the second step, the iRadon transformation is used to respectively obtain target slow time-range images S (f) of the radar 1 and the radar 2 in the first step r ,t m ) Estimating sinusoidal parameter amplitude a i Phase b i Offset d i The method comprises the steps of carrying out a first treatment on the surface of the The specific process is as follows:
wherein S is RL (f r ,t m ) Slow time-distance image S (f) representing object r ,t m ) F after filtering by a Ram-Lak filter in a distance domain r Represent distance, t m Indicating slow time, S IRT (a, b, d) a slow time-distance image S (f) r ,t m ) On-plane amplitude search variable a, phase search variable b, offset search variable d sinusoidal iRadon transform values, Ω c The cone rotation angular velocity is the target;
radar 1 andtarget slow time-range profile S (f) of radar 2 r ,t m ) The parameters of the sinusoidal curve on the plane can be determined by S IRT Maximum position estimation of (a, b, d)
In the third step, a precession space cone target ISAR imaging model is built, and a cone top scattering point inching sine curve a is deduced i sin(Ω c t m +b i )+d i Parameter amplitude a i Phase b i Offset d i Spin angular velocity unit vector characteristic of precession with targetTarget cone rotation angular velocity unit vector +.>According to the relation of the iRadon transformation in the second step to the parameter estimation result { a } of the sinusoids on the slow time-range image plane of the radar 1 and the radar 2 targets i ,b i ,d i -spin angular velocity unit vector +_>Cone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i A relation of i=1, 2 represents radar 1 and radar 2, and a nonlinear equation set is established; the specific process is as follows:
in the target coordinate system O-XYZ, the inching curve generated by the cone top scattering point on the slow time-distance image is
Wherein R is c In the form of a matrix of target cones,is the coordinates of the cone top scattering point in the target coordinate system,/->Is a radar line-of-sight unit vector; />I 3 Is a 3 x 3 unit array, +.>For the unit vector of the target cone rotational speed>Is an antisymmetric matrix of alpha c And beta c Azimuth and elevation of the cone-rotation vector in the target coordinate system, respectively, (·) T Representing the transpose of the matrix> Alpha and beta are the azimuth angle and elevation angle of the radar sight in the radar coordinate system Q-UVW respectively;
angular velocity of taper at target Ω c And radar line of sight unit vectorIn the known case, the inching curve generated by the cone apex scattering point on the slow time-distance image is defined by the coordinates of the cone apex scattering point in the target coordinate system +.>And target cone rotationAngular velocity unit vector>Determining that the target cone top scattering point is positioned on the spin axis of the target, wherein the target cone top scattering point represents the spin angular velocity unit vector +.>The terms represent the modulus of the vector;
establishing an intermediate coordinate system O-X ' Y ' Z ', and determining a spin angular velocity unit vector of the target precession characteristicCone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i Relationship of };
estimating the parameter estimation results { a } of the sinusoids on the slow-time-range image planes of the radar 1 and radar 2 targets according to the iRadon transform in the second step i ,b i ,d i Unit vector of spin angular velocityCone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i Relation of i=1, 2 denotes radar 1 and radar 2, a nonlinear equation set is established
Wherein alpha is i And beta i Azimuth and elevation of the ith radar sight;
establishing an intermediate coordinate system O-X ' Y ' Z ' and determining a spin angular velocity unit vector of the target precession characteristicCone angular velocity unit vector->And the inching sinusoidal parameter { a } i ,b i ,d i Relationship of }; the specific process is as follows:
the coordinate axis unit vector of the intermediate coordinate system coincides with the origin of the target coordinate systemThe method meets the following conditions:
wherein,the coordinate of the target cone top scattering point in the middle coordinate system is the Z-axis unit vector of the target coordinate system>Can be by->Through transformation to obtain
Wherein R is T Is a transformation matrix; (x, y, z) are scattering points at different positions of the precession space cone target;
in the intermediate coordinate system, the jogging curve generated by the cone-top scattering point on the slow time-distance image can be expressed as
Wherein R 'is' c For a cone-rotation matrix of the object in the intermediate coordinate system,is the coordinates of the cone-top scattering point in the intermediate coordinate system, (-) T Representing the transpose, r' P Is the polar diameter, theta 'in the cylindrical coordinate form of the conical top scattering point' P Is polar angle, z 'in the form of cylindrical coordinates of the cone-top scattering point' P Is the height in the cylindrical coordinate form of the cone top scattering point, A r Is a sinusoidal amplitude component +.>Is a sinusoidal phase component, A z A sinusoidal bias component;
obtaining parameters of inching sine curve and unknown number { r 'generated by cone top scattering point on slow time-distance image plane' P ,θ′ P ,z′ P ,α c ,β c Relationship of };
cone-rotation matrix R 'of the target in the intermediate coordinate system' c Sinusoidal amplitude component A r Sinusoidal phase componentSinusoidal bias component A z The expression is:
wherein epsilon represents the included angle between the unit vector of the cone rotation angular velocity and the radar sight line.
2. The spatial cone target ISAR three-dimensional imaging method based on precession feature extraction according to claim 1, wherein: in the fourth step, the nonlinear equation set established in the third step is solved by using a quasi Newton method to obtain an unknown number { r' P ,θ′ P ,z′ P ,α c ,β c And then estimate the target spin and cone spin unit vectorThe specific process is as follows:
solving the unknowns { r 'of a system of nonlinear equations by quasi Newton method' P ,θ′ P ,z′ P ,α c ,β c }；
Target spin, cone rotation angular velocity unit vectorObtained by
3. The spatial cone target ISAR three-dimensional imaging method based on precession feature extraction according to claim 2, wherein: the fifth step is to obtain the unit vector of the target spin and the cone rotational angular velocity according to the fourth stepAnd step one estimated target spin, cone angular velocity { Ω } s ,Ω c Determining the slow time-distance image S (f) of scattering points (x, y, z) at different positions of the precessional spatial cone target r ,t m ) Inching curve on plane, using generalized Radon transformation to target slow time-distance image S (f r ,t m ) Integrating the inching curve path on the plane to obtain a three-dimensional image S of the target GRT (x, y, z) the imaging results may reflect the structural dimensions and spatial pose of the target; the specific process is as follows:
the unit vector of the target spin and the cone rotational speed obtained according to the step fourAnd step one estimated target spin, cone angular velocity { Ω } s ,Ω c Determining the slow time-distance image S (f) of scattering points (x, y, z) at different positions of the precessional spatial cone target r ,t m ) The micro curve generated on the plane has the expression:
wherein R is c In the form of a matrix of target cones,for the target spin matrix +.>For the target spin angular velocity unit vector +.>Is an antisymmetric matrix of alpha s And beta s Azimuth and elevation of spin vector in target coordinate system, respectively, +.>For the coordinates of a certain scattering point in the target coordinate system,/->Is radar sight line unit vector, A 0 、A 1 、A 2 、A 3 、A 4 、φ 1 、φ 2 、φ 3 、φ 4 Is an intermediate variable;
establishing an imaging grid in a three-dimensional space, taking a inching curve of imaging grid coordinates (x, y, z) as an integral path, and obtaining a target slow time-distance image S (f r ,t m ) And carrying out generalized Radon transformation to realize three-dimensional imaging of the target.
4. The spatial cone target ISAR three-dimensional imaging method based on precession feature extraction according to claim 3, wherein: said intermediate variable A 0 、A 1 、A 2 、A 3 、A 4 Specifically defined as:
5. the spatial cone target ISAR three-dimensional imaging method based on precession feature extraction according to claim 4, wherein: the intermediate variable phi 1 、φ 2 、φ 3 、φ 4 Specifically defined as:
6. the precession feature extraction-based spatial pyramid target ISAR three-dimensional imaging method in accordance with claim 5, wherein: the imaging grid is established in the three-dimensional space, and the inching curve of the coordinates (x, y, z) of the imaging grid is taken as an integral path to obtain a target slow time-distance image S (f r ,t m ) Performing generalized Radon transformation to realize three-dimensional imaging of the target; the expression is:
wherein S is GRT (x, y, z) is a three-dimensional image of the object.
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