CN108226926B - Three-dimensional scattering distribution reconstruction method based on networking radar - Google Patents
Three-dimensional scattering distribution reconstruction method based on networking radar Download PDFInfo
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Abstract
The invention provides a three-dimensional scattering distribution reconstruction method based on networking radar, which comprises the following steps: the first step: constructing a three-dimensional scattering distribution reconstruction model of the networking radar by deducing a projection formula of the aerial target projected to an imaging plane; and a second step of: and reconstructing the three-dimensional distribution of the scattering points of the target by using a solution algorithm of the proposed three-dimensional scattering distribution reconstruction model according to the three-dimensional scattering distribution reconstruction model, and realizing three-dimensional imaging of the target in the air. The method can utilize three common imaging radars to realize three-dimensional imaging of the air target, effectively reduces the requirements on the complexity of radar hardware and the process precision, improves the flexibility of three-dimensional imaging of the air target, and provides a powerful method for solving the three-dimensional imaging of the air target under a networking radar system.
Description
Technical Field
The invention relates to a signal and information processing technology, in particular to a three-dimensional imaging technology based on a networking radar.
Background
In recent years, inverse Synthetic Aperture Radar (ISAR) imaging technology has been one of the most important radar tasks in the fields of object recognition and classification by virtue of its own advantages in providing shape and structure information of objects. The ISAR two-dimensional imaging result can be regarded as projection of an aerial target on an ISAR imaging plane, and the imaging plane is determined by the radar sight direction and the target flight direction. The radar observation data is processed by adopting a distance compression and coherent processing method, so that a high-resolution target ISAR image can be obtained. However, for stealth targets and targets flying in the radar line of sight direction, the scattering points of the targets cannot be separated in azimuth, resulting in failure to obtain an ISAR image of such targets. The networking radar is a radar network formed by a plurality of radars distributed at different geographic positions, can observe targets from different directions and obtain observation information of the aerial targets at different visual angles, and is a method for effectively realizing stealth targets and imaging of flying targets along the radar sight line direction. In addition, as the requirement of the aerial target recognition task increases, compared with a target two-dimensional imaging result, the target three-dimensional image can provide more and more accurate target information, and the space target recognition capability is effectively improved.
The existing three-dimensional imaging technology of the aerial target can be mainly divided into three-dimensional interference ISAR imaging and MIMO radar three-dimensional imaging. Wherein Zhao Lizhi in the doctor's thesis (study of space target interference three-dimensional ISAR imaging technology), the system introduces a target interference three-dimensional ISAR imaging method; zhu Yutao A three-dimensional imaging method of MIMO radar is discussed in M-2N-2 receiving MIMO radar planar array and three-dimensional imaging method thereof (China science: information science, 2011,41 (12): 1495-1506). The imaging methods achieve the aim of three-dimensional imaging of an aerial target by increasing the complexity of radar hardware.
As a whole, the existing literature focuses on solving the problem of three-dimensional imaging of an airborne target by using a radar with relatively high functionality, but the following disadvantages are also associated therewith. The radar with stronger functionality generally needs a plurality of antennas to be arranged into a fixed geometric structure, and has higher requirements on the complexity of radar hardware and the working precision. In addition, the radar with stronger functionality has high cost, is difficult to move after deployment, lacks networking working capacity, and has poor flexibility when completing various radar tasks.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a three-dimensional scattering distribution reconstruction method based on a networking radar.
The invention is realized by the following modes:
step one: constructing a three-dimensional scattering distribution reconstruction model of the networking radar;
step two: and reconstructing the three-dimensional distribution of the scattering points of the target by using a solution algorithm of the proposed three-dimensional scattering distribution reconstruction model according to the three-dimensional scattering distribution reconstruction model, and realizing three-dimensional imaging of the target in the air.
Specifically, the first step specifically includes:
in order to build a three-dimensional scattering distribution reconstruction model of a target, the complexity and the calculated amount of model solving are reduced, a cube space where the target is positioned is gridded by a small cube (space grid unit), and the side length of the space grid unit is L c Representing that the target length determined by the tracking and target recognition method is L t The defined cube space grid is a space region which can completely contain the air target, therefore, the side length of the space grid is valued as L g ＝2L t The number of grid cells on each side of the space grid is
(R 1 X, Y, Z) represents a spatial coordinate system, the spatial grid is represented by a 0-1 matrix X, F m (. Cndot.) represents the projected image of an aerial object on a projection plane, I m Representing a target ISAR image obtained by an mth radar, M representing the total number of radars in a scene, ω representing the weight of the number of scattering points in an objective function in the reconstructed three-dimensional scattering distribution, G representing all the value sets of the space grid matrix X;
the three-dimensional scattering distribution reconstruction model of the networking radar constructed by taking the minimum error of the ISAR image and the shadowgraph image and the minimum number of scattering points in the reconstructed three-dimensional scattering distribution as an objective function can be expressed as follows:
specifically, the second step specifically includes the following steps:
step 1) defining a three-dimensional grid space matrix c=0, a set of grid cell sequence numbers
Each radar number m= {1,2, & gt, M }, and grid cell number y = {1,2, N c }；
Step 2) each of the three images is used for imaging the target independently, and the ISAR imaging result is I m And calculates a shadowgraph image F for each grid cell m (C (i)) and the second norm D of ISAR image and projection aberration mi ＝||F m (C(i))-I m || 2 ；
Step 3) define a set of potential scattering points
If D mi ＜I m Let alpha m ＝α m ∪i；
Step 4) calculation
And updating the search range of the three-dimensional scattering distribution model solution, wherein the updated search range is G' = { C|C (gamma-beta) =0, C epsilon G };
step 5) introducing a new search range G' into the three-dimensional scattering distribution model, solving the model by adopting a genetic algorithm, and outputting an optimized solution X opt And reconstructing the three-dimensional scattering distribution, thereby realizing three-dimensional imaging of the aerial target.
Further, the networking radar is composed of three self-generating and self-receiving imaging radars distributed at different positions.
Further, the aerial target projection operator F m (. Cndot.) is used for calculating the projection image of the aerial target, and mainly comprises the calculation steps of space grid unit three-dimensional coordinate calculation, projection point two-dimensional coordinate calculation on an imaging plane, projection image generation and the like.
The invention has the beneficial effects that: aiming at the application requirement of a networking radar system formed by common imaging radars in the aspect of three-dimensional imaging of an air target, the three-dimensional scattering distribution reconstruction method based on the networking radars is provided, by comparing the ISAR imaging result of each radar with the projection image of the reconstructed three-dimensional scattering distribution on each radar imaging plane, the three-dimensional imaging of the air target can be realized by adopting a plurality of common imaging radars, the complexity of radar hardware is effectively reduced, the requirement on radar process precision is reduced, and the mature networking radar network can improve the flexibility of three-dimensional imaging of the target.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a geometry of a networked radar;
FIG. 3 is a graph of geometric relationships projected to an aerial object;
FIG. 4 is a graph of geometric relationships of point-to-point target projections;
FIG. 5 is a difference image obtained by subtracting the ISAR image from the shadowgraph image;
FIG. 6 is an ISAR imaging scenario for a plurality of radars;
FIG. 7 is a spatial grid model;
FIG. 8 is a schematic diagram of the ordering of spatial grid cells;
FIG. 9 is a planar grid of imaging planes;
FIG. 10 is a networking radar distribution diagram;
FIG. 11 is a cube object model consisting of 9 scattering points;
FIG. 12 is a schematic diagram showing the contrast of ISAR imaging results and shadowgraphs: fig. 12 (a) shows the imaging result of the first radar, fig. 12 (b) shows the projection image of the first radar, fig. 12 (c) shows the imaging result of the second radar, fig. 12 (d) shows the projection image of the second radar, fig. 12 (e) shows the imaging result of the third radar, and fig. 12 (f) shows the projection image of the third radar;
FIG. 13 is a graph showing three-dimensional scattering distribution results of reconstructed cubic objects, wherein circles are object reconstruction results and circles are object models: FIG. 13 (a) is a schematic view of the reconstructed three-dimensional scattering distribution, FIG. 13 (b) is a schematic view of the reconstructed result in the X-Y plane, FIG. 13 (c) is a schematic view of the reconstructed result in the X-Z plane, and FIG. 13 (d) is a schematic view of the reconstructed result in the Y-Z plane;
FIG. 14 is a model of an aircraft target consisting of 34 scattering points;
FIG. 15 results of reconstructed three-dimensional scattering distribution of aircraft targets: fig. 15 (a) is a schematic view of the reconstructed three-dimensional scattering distribution, fig. 15 (b) is a schematic view of the reconstructed result in the X-Y plane, fig. 15 (c) is a schematic view of the reconstructed result in the X-Z plane, and fig. 15 (d) is a schematic view of the reconstructed result in the Y-Z plane, wherein circles in fig. 15 (b) -15 (d) are target reconstructed results, and dots are target models.
Detailed Description
The invention is further described below with reference to the accompanying drawings and examples of the invention.
As shown in fig. 1, the present invention is implemented by the following steps: constructing a three-dimensional scattering distribution reconstruction model of the networking radar by deducing a projection formula of the aerial target projected to an imaging plane; and calculating the three-dimensional scattering distribution of the air target by using the proposed solving algorithm of the three-dimensional scattering distribution reconstruction model, and realizing three-dimensional imaging of the air target. The concrete explanation is as follows:
step one: constructing a three-dimensional scattering distribution reconstruction model of networking radar
As shown in fig. 2, the networking radar system built by the invention is composed of three self-receiving imaging radars, each radar works independently, the obtained information and imaging result are shared, and the central processor realizes data integration; the central processor may be integrated in a radar or may be a separate device. Each radar works independently, the targets are observed from different view angles, echo signals of the targets at different view angles are obtained, and three-dimensional imaging of the networking radar on the aerial targets is achieved by fully utilizing the echo signals at the different view angles. The invention provides a method for realizing three-dimensional imaging of an aerial target by a networking radar by comparing a projection image of a reconstructed three-dimensional scattering distribution on an imaging plane with radar ISAR imaging results, and taking the minimum two norms of the projection image and the ISAR image and the minimum total number of scattering points of the reconstructed three-dimensional scattering distribution as targets to finally obtain the three-dimensional scattering distribution of the aerial target. The projection geometrical relationship between the aerial plane target and the point target on the imaging plane is shown in fig. 3 and 4; by comparing the projection image of the space object on the imaging plane with the ISAR imaging result, we define the image obtained by subtracting the ISAR image from the projection image as a difference image, as shown in FIG. 5; fig. 6 shows an ISAR imaging scenario for multiple radars, where we can initially screen out the potential locations of scattering points of a target, called potential scattering points, from a large number of spatial locations by observing the target from different perspectives using multiple radars.
When constructing a three-dimensional scattering distribution reconstruction model of a networking radar, the most important step is to deduce a projection formula of the projection of an aerial target to an imaging plane according to prior information of the target and the radar, and determine an aerial target projection operator F m (. Cndot.) the use of a catalyst. Aerial target projection operator F m The method comprises the steps of calculating three-dimensional coordinates of a space grid unit, three-dimensional coordinates of a projection point, two-dimensional coordinates of the projection point on an imaging plane, projection image generation and the like.
First, the spatial three-dimensional coordinates of the spatial grid cells are calculated. The cube space where the target is located is gridded with small cubes (space grid cells), as shown in fig. 7. To meet the accuracy requirement of target identification, the side length of the space grid unit is L c Represents, typically, 0.25m; the target length determined by the tracking and target recognition method is L t The method comprises the steps of carrying out a first treatment on the surface of the The defined cube space grid is a space region which can completely contain the air target, and therefore, the side length of the space grid takes the value of L g ＝2L t The method comprises the steps of carrying out a first treatment on the surface of the The number of grid cells on each side of the space grid is
(R 1 X, Y, Z) represents a spatial coordinate system; to facilitate searching each grid cell in model solution, spatial grids are numbered in a manner shown in FIG. 8, and a spatial grid coordinate system (o) is established according to spatial grid numbering rules g ,x g ,y g ,z g ) The method comprises the steps of carrying out a first treatment on the surface of the Defining a reference point P as an air target reference position (x) determined by a radar tracking method g0 ,y g0 ,z g0 ) Representing the position of the reference point P in the space grid coordinate system, (x) 0 ,y 0 ,z 0 ) Representing the position of the reference point P in the spatial coordinate system. Thus, the ith space grid cell sits on the space gridThe coordinates in the label system are:
the position difference between the i-th space grid unit and the reference point P in the space grid coordinate system is as follows:
thus, the coordinates of the ith spatial grid cell in the spatial coordinate system are:
after the coordinates of the space grid unit in the space coordinate system are calculated, the three-dimensional coordinates of the projection points of the space grid unit on the imaging plane are calculated. The imaging plane is determined by the target flight direction and the radar illumination direction, where v= (V) x ,v y ,v z ) A velocity vector representing the flight of the target, (x) r ,y r ,z r ) Representing the coordinates of the radar in a spatial coordinate system. The imaging plane expression of ISAR imaging of the target by the radar is as follows:
n x ·(x s -x 0 )+n y ·(y s -y 0 )+n z ·(z s -z 0 )＝0 (4)
wherein, (x) s ,y s ,z s ) Representing the coordinates of points on the imaging plane. Vector n= (n) x ,n y ,n z ) A normal vector representing an imaging plane; vector RP represents the radar illumination direction vector when the radar images a target. The normal vector calculation formula of the imaging plane is as follows:
where i, j, and k are unit vectors of the space coordinate system. The calculation formula of each element of the normal vector n of the imaging plane is as follows:
the linear expression passing through the center of the ith grid cell and perpendicular to the imaging plane is:
wherein t is a straight line parameter. The straight line parameters t corresponding to different points on the straight line are different. The intersection point of the straight line passing through the center of the ith grid cell and perpendicular to the imaging plane and the imaging plane is the projection point of the ith grid cell on the imaging plane. Bringing equation (7) into equation (4) yields:
n x ·(n x t i +x gi -x 0 )+n y ·(n y t i +y gi -y 0 )+n z ·(n z t i +z gi -z 0 )＝0 (8)
equation (8) can be rewritten as:
therefore, the straight line parameters corresponding to the projection points of the ith grid cell on the imaging plane are as follows:
bringing the formula (10) into the formula (7) can obtain coordinates of the projection point of the ith grid cell in a space coordinate system as follows:
after the three-dimensional coordinates of the projected points of the space grid unit are calculated, the three-dimensional coordinates of the projected points need to be converted into two-dimensional coordinates on an imaging plane. Before converting the three-dimensional coordinates into two-dimensional coordinates, a two-dimensional coordinate system (P, U, W) of an imaging plane needs to be established first, wherein a reference point P is a coordinate system origin, and the direction of the coordinate axis U is consistent with the direction from the radar to the reference point P. The direction vector of the coordinate axis U is:
U＝(l u ,m u ,n u )＝(x 0 -x r ,y 0 -y r ,z 0 -z r ) (12)
the coordinate axis W is perpendicular to the coordinate axis U and the normal vector n of the imaging plane, and according to the right-hand rule, the direction vector of the coordinate axis W is as follows:
further, a linear expression collinear with the coordinate axis U can be obtained as:
the linear expression collinear with the coordinate axis W is:
the distance from the projection point to the two coordinate axes can be calculated by the three-dimensional coordinates of the projection point and the linear expressions of the coordinate axis U and the coordinate axis W, and the distance is as follows:
and
wherein the vector q i P is the vector from the projection point of the ith grid cell to the reference point P;vector q i R is the vector of the projection point of the ith grid cell to the reference point R. Therefore, the coordinates of the projection points of the ith grid cell in the two-dimensional coordinate system of the imaging plane are as follows:
thus, the three-dimensional coordinates of the i-th grid cell projection point are converted into two-dimensional coordinates on the imaging plane.
After the two-dimensional coordinates of the projection points on the imaging plane are calculated, the projection image of the aerial target on the imaging plane is generated according to the plane grid of the ISAR image/the projection image. First, a planar grid of ISAR images/shadowgraphs needs to be determined, as shown in FIG. 9. The size of the planar mesh and the size of the planar mesh cells are related to the sampling rate and imaging resolution of the imaging radar. N (N) r The number of grid units of the planar grid in the distance direction is N when the distance direction sampling point number in ISAR imaging is represented r ；N a The number of grid units representing the azimuth sampling points in ISAR imaging is N a . Distance resolution ρ r Length of the planar grid unit in the distance direction; azimuth resolution ρ a Is the length of the azimuth direction of the planar grid cell.
If the projection point of the ith space grid cell falls in a plane grid cell, the matrix element corresponding to the plane grid cell is set to be 1. The number of the plane grid cells is shown in FIG. 9, and the number of the plane grid cells on which the reference point P falls is u 'according to the ISAR imaging principle' o ＝(N r 2+1) and w' 0 ＝(N a /2+1). Therefore, the number of planar grid cells into which the projection points of the ith spatial grid cell fall is:
u i ′＝u′ 0 +<u i /ρ r > (20)
w i ′＝w′ 0 -<w i /ρ a > (21)
wherein,,<·>to round the operator. And (3) obtaining a projection image of the aerial target on the imaging plane by finding a plane grid cell corresponding to the space grid cell. Thus, equations (1) through (21) constitute the aerial target projection operator F m (·)。
Based on the above formula deduction about the aerial target projection process, with the minimum error between the ISAR image and the projection image and the minimum number of scattering points in the reconstructed three-dimensional scattering distribution as an objective function, the constructed three-dimensional scattering distribution reconstruction model of the networking radar can be expressed as:
wherein the space grid is represented by 0-1 matrix X, I m The target ISAR image obtained by the mth radar is shown. M represents the total number of radars in the scene. ω represents the weight of the number of scattering points in the objective function in the reconstructed three-dimensional scattering distribution. G represents all the value sets of the space grid matrix X.
Thus, the establishment of the three-dimensional scattering distribution reconstruction model of the networking radar is completed.
Step two: according to the three-dimensional scattering distribution reconstruction model, reconstructing the three-dimensional distribution of the target scattering points by using a solution algorithm of the proposed three-dimensional scattering distribution reconstruction model, and realizing three-dimensional imaging of the aerial target
The three-dimensional scattering distribution of the air target is reconstructed, and three-dimensional imaging of the target is realized.
The specific three-dimensional scattering distribution reconstruction model solving algorithm is as follows:
input: results of radar ISAR imaging at each site I m Aerial target projection operator F m (·)；
And (3) outputting: a reconstructed three-dimensional scattering distribution X of the target;
step 1) defining a three-dimensional grid space matrix c=0, a set of grid cell sequence numbers
Each radar number m= {1,2, & gt, M }, and grid cell number y = {1,2, N c }；
Step 2) each of the three images is used for imaging the target independently, and the ISAR imaging result is I m And calculates a shadowgraph image F for each grid cell m (C (i)) and the second norm D of ISAR image and projection aberration mi ＝||F m (C(i))-I m || 2 ；
Step 3) define a set of potential scattering points
If D mi ＜I m Let alpha m ＝α m ∪i；
Step 4) calculation
And updating the search range of the three-dimensional scattering distribution model solution, wherein the updated search range is G' = { C|C (gamma-beta) =0, C epsilon G };
step 5) introducing a new search range G' into the three-dimensional scattering distribution model, solving the model by adopting a genetic algorithm, and outputting an optimized solution X opt And reconstructing the three-dimensional scattering distribution, thereby realizing three-dimensional imaging of the aerial target.
Thereby completing three-dimensional imaging of the hollow target.
Examples: networking radar-based target three-dimensional scattering distribution reconstruction simulation experiment
Simulation experiment: to verify the effectiveness of the proposed method, we performed the following computer simulation. The three spontaneous self-radar deployment modes are shown in fig. 10, and the three-dimensional imaging of the cube target and the airplane target is performed respectively.
Simulation 1: to verify the validity of the algorithm, the aerial cube target is three-dimensionally imaged. The cube target model is shown in fig. 11. The target parameters of the cube targets are shown in table 1.
Table 1 cube target parameters
TABLE 1Parameters of the Cube Target
And performing ISAR imaging and projection operation on the scattering point model. The ISAR imaging results of the radars 1,2, and 3 on the target are shown in fig. 12 (a), 12 (c), and 12 (e), respectively. The projection results of the targets on the imaging planes of the radars 1,2, and 3 are shown in fig. 12 (b), 12 (d), and 12 (f). By comparing the imaging result and the projection result of each radar, it can be seen that the ISAR image and the projection image of each radar are consistent, and the effectiveness of the projection operator is verified. Fig. 13 shows the three-dimensional scattering distribution reconstruction result of a cubic target, circles are the target reconstruction result, and dots are the target model. By comparison, the error between the reconstructed three-dimensional scattering distribution and the scattering point position of the target model is smaller, so that the reconstruction of the three-dimensional scattering distribution of the air target is realized, and the effectiveness of the method is verified.
Simulation 2: to verify the effectiveness of the algorithm, the air-to-air aircraft target is three-dimensionally imaged. The aircraft target model is shown in fig. 14. The target parameters of the aircraft targets are shown in table 2.
TABLE 2 aircraft target parameters
TABLE 1Parameters of the Aircraft Target
And carrying out three-dimensional scattering distribution reconstruction on the scattering point model. Fig. 15 (a) shows the three-dimensional scattering distribution reconstruction result of the cubic object, and in fig. 15 (b) -15 (d), circles are the object reconstruction result, and dots are the object model. By comparison, the error between the reconstructed three-dimensional scattering distribution and the scattering point position of the target model is smaller, the reconstruction of the three-dimensional scattering distribution of the air target is realized, the three-dimensional imaging of the air target is completed, and the effectiveness of the method is verified.
Claims (3)
1. A three-dimensional scattering distribution reconstruction method based on networking radar comprises the following steps:
step one: constructing a three-dimensional scattering distribution reconstruction model of the networking radar;
the first step specifically comprises the following steps:
in order to build a three-dimensional scattering distribution reconstruction model of a target, the complexity and the calculated amount of model solving are reduced, a cube space where the target is positioned is gridded by a small cube (space grid unit), and the side length of the space grid unit is L c Representing that the target length determined by the tracking and target recognition method is L t The defined cube space grid is a space region which can completely contain the air target, therefore, the side length of the space grid takes the value of lg=2l t The total number of space grid cells included in the space grid is
(R 1 X, Y, Z) represents a spatial coordinate system, the spatial grid is represented by a matrix X, F m (. Cndot.) represents the projected image of an aerial object on a projection plane, I m Representing a target ISAR image obtained by an mth radar, M representing the total number of radars in a scene, ω representing the weight of the number of scattering points in an objective function in the reconstructed three-dimensional scattering distribution, G representing all the value sets of the space grid matrix X;
the three-dimensional scattering distribution reconstruction model of the networking radar constructed by taking the minimum error of the ISAR image and the shadowgraph image and the minimum number of scattering points in the reconstructed three-dimensional scattering distribution as an objective function can be expressed as follows:
step two: according to the three-dimensional scattering distribution reconstruction model in the first step, reconstructing the three-dimensional distribution of the target scattering points by utilizing a solving algorithm of the three-dimensional scattering distribution reconstruction model, and realizing three-dimensional imaging of the aerial target;
the second step specifically comprises the following steps:
step 1) defining a three-dimensional grid space matrix c=0, a set of grid cell sequence numbers
Each radar number m= {1,2, & gt, M }, and grid cell number y = {1,2, N c }；
Step 2) each of the three images is used for imaging the target independently, and the ISAR imaging result is I m And calculates a shadowgraph image F for each grid cell m (C (i)) and the second norm D of ISAR image and projection aberration mi ＝||F m (C(i))-I m || 2 ；
Step 3) define a set of potential scattering points
If D mi ＜I m Let alpha m ＝α m ∪i；
Step 4) calculation
And updating the search range of the three-dimensional scattering distribution model solution, wherein the updated search range is G' = { C|C (gamma-beta) =0, C epsilon G };
step 5) introducing a new search range G' into the three-dimensional scattering distribution model, solving the model by adopting a genetic algorithm, and outputting an optimized solution X opt And reconstructing the three-dimensional scattering distribution, thereby realizing three-dimensional imaging of the aerial target.
2. The three-dimensional scattering distribution reconstruction method based on networking radar according to claim 1, wherein the method comprises the following steps: the networking radar is composed of three self-generating and self-receiving imaging radars distributed at different positions.
3. The three-dimensional scattering distribution reconstruction method based on networking radar according to claim 1, wherein the method comprises the following steps: in the airObject projection operator F m (. Cndot.) is used for calculating the projection image of the aerial target, and mainly comprises the calculation steps of space grid unit three-dimensional coordinate calculation, projection point two-dimensional coordinate calculation on an imaging plane, projection image generation and the like.
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| CN103217674A (en) * | 2013-04-22 | 2013-07-24 | 西北工业大学 | Method for reconstructing target three-dimensional scattering center of inverse synthetic aperture radar |
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