空间目标双基地ISAR成像面的三维特性研究
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本文研究的是空间目标双工逆合成孔径雷达(ISAR)成像平面上的变空间特性，发表在《中国物理B》第24卷第4期(2015年)，文章编号为048402。ISAR作为一种高级的雷达成像技术，其核心是利用目标的多普勒频移来获取高分辨率图像，但这种成像过程涉及到空间上的变化，即所谓的“空间变体性”。空间变体性会导致回波散射点在成像平面上的位置迁移，从而影响图像的精度和解析度。
首先，研究者们针对轨道上三维稳定的太空目标，提出了一个基于两体模型的目标运动模型，这为理解目标在复杂运动环境下的行为提供了理论基础。通过对目标运动的精确建模，能够更准确地预测和补偿空间变体效应，保证成像质量。
其次，本文着重探讨了如何实时分析和计算瞬时成像平面，这是实现空间变体性控制的关键步骤。通过计算目标在不同时刻的相对运动参数，研究人员设计了一套方法来跟踪和更新成像平面的动态变化，确保图像的稳定性和一致性。
此外，该研究还可能包括对空间变体性的定量分析，如影响因素、影响程度以及相应的校正策略。这可能涉及到信号处理算法的改进，例如利用自适应滤波或图像处理技术来减少空间变体带来的影响，提高图像的清晰度和定位精度。
最后，考虑到空间目标的特殊性，可能还讨论了与地面目标ISAR成像相比，太空目标的额外挑战，如低信号强度、大距离和复杂的轨道运动。研究者们可能提供了一些创新的方法来克服这些困难，比如利用星座导航系统或利用空间目标的特定特征进行补偿。
这篇研究论文深入探讨了空间目标双工ISAR成像平面上的变空间特性，并提出了解决方案，为改善太空目标成像的精确性和稳定性提供了有价值的技术支持。这在航天、军事侦察和地球观测等领域具有重要意义，有助于提升相关应用的效能。
Chin. Phys. B Vol. 24, No. 4 (2015) 048402
Orbit equation (4) contains three independent parameters:
h, e, and f , and it describes the conic sections in the orbital
plane. In the actual calculation, the angular momentum h and
true anomaly f are frequently replaced by the semi-major axis
a and mean anomaly M, respectively. Describing the orienta-
tion of an orbit in three dimensions requires three additional
parameters, called the Euler angles, which are illustrated in
Fig. 1.
First, we locate the intersection of the orbital plane with
the equatorial (XY ) plane. That line is called the node line.
The point on the node line where the orbit passes above the
equatorial plane from below it, is called the ascending node.
The node line vector 𝑁 extends outward from the origin
through the ascending node. At the other end of the node
line, where the orbit dives below the equatorial plane, is the
descending node. The angle between the positive X axis and
the node line is the first Euler angle Ω, the right ascension of
the ascending node. The right ascension is a positive number
lying between 0
◦
and 360
◦
.
The dihedral angle between the orbital plane and the
equatorial plane is the inclination i, measured according to the
right-hand rule, that is, counterclockwise around the node line
vector from the equator to the orbit. The inclination is also
the angle between the positive Z axis and the normal plane of
the orbit. The inclination is a positive number between 0
◦
and
180
◦
.
The third Euler angle ω, the argument of perigee, is the
angle between the node line vector 𝑁 and the eccentricity vec-
tor 𝑒, measured in the plane of the orbit. The argument of
perigee is a positive value between 0
◦
and 360
◦
.
The orbit of the space target can be determined by the
six orbital elements (
a, M, i, ω, e, Ω
), where the mean
anomaly can be expressed as
M = E − e sin E, (5)
with E being the eccentric anomaly, and the relationship be-
tween the eccentric anomaly and the true anomaly is
tan( f /2) =
p
(1 + e)/(1 − e)tan(E/2). (6)
Considering the two-body motion, the coordinates of the
target’s center of mass in the geocentric observation coordi-
nate system xyz can be expressed as
x
S
, y
S
, z
S
=
r, 0, 0
, (7)
where r is the distance from target center to geocentre, and it
can be obtained from Eq. (4).
Assuming that χ
t
0
= (
a, M
t
0
, i, ω, e, Ω
) is the target’s
orbital element at the initial observation time, ignoring the in-
fluences of precession and nutation on the celestial pole and
equinox, the coordinate system xyz can be rotated into coor-
dinate system XYZ by a sequence of three rotations. The first
step is to rotate an angle f
t
0
+ ω around the z axis clockwise.
The second step is to rotate an angle i around the x axis clock-
wise. Finally, we clockwise-rotate around the z axis through
an angle Ω . Here, f
t
0
is the true anomaly of the initial obser-
vation time; it can be obtained by the initial orbital elements
through Eqs. (5) and (6).
Except the mean anomaly, the remaining orbital elements
are all constants. The mean anomaly can be obtained by
M
t
0
= n(t
0
−t
epoch
) + M
epoch
, (8)
where t
epoch
is the epoch time of initial orbital elements and t
0
is the epoch time of the initial observation time.
At any observation time t, to transfer the coordinate sys-
tem xyz into XY Z, the only difference relative to initial ob-
servation time t
0
is that the rotation angle around the z axis
is f
t
+ ω rather than f
t
0
+ ω, where f
t
is the true anomaly of
observation time t.
Therefore, the transformation matrix xyz into XY Z at the
observation time t can be written as
𝑅
x−X
= 𝑅
z
(−Ω)𝑅
x
(−i)𝑅
z
(− f
t
− ω), (9)
where 𝑅
x
(•) and 𝑅
z
(•) are the rotation matrices around the x
axis and z axis, respectively.
Without considering the polar motion, the difference be-
tween the geocentric equatorial coordinate system XY Z and
the geocentric Earth-fixed coordinate system X
0
Y
0
Z
0
is the
Earth’s rotation angle (i.e., Greenwich hour angle S
G
). Then
the transformation matrix XY Z into X
0
Y
0
Z
0
can be expressed
as
𝑅
X−X
0
= 𝑅
z
(S
G
t
0
+ n
E
t), (10)
where S
G
t
0
is the Greenwich hour angle of the initial observa-
tion time t
0
, n
E
is the Earth’s rotation angular velocity, and its
period is 86164.098903691 s.
The Greenwich hour angle can be calculated from the fol-
lowing equation:
S
G
= 18
h
.6973746 + 879000
h
.0513367t
J
+0
s
.093104t
2
J
− 6
s
.2 × 10
−6
t
3
J
, (11)
where t
J
can be expressed as
t
J
=
JD(t) − JD(J2000.0)
36525.0
, (12)
with JD(t) being the Julian day at the observation time t, and
JD(J2000.0) the Julian day corresponding to epoch J2000.0.
048402-3
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