非高斯杂波中新型范围扩展目标检测器的研究
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更新于2024-07-10
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"这篇研究论文探讨了在非高斯杂波环境下的新型测距目标探测技术，特别是针对范围扩展目标的检测。文章提出了一种基于球不变性随机矢量杂波的检测方法，并利用阶数统计理论设计了具有恒定虚警率（CFAR）特性的检测器。"
在现代雷达系统中，尤其是在复杂、非高斯背景的杂波环境中，准确地检测和跟踪范围扩展目标是一项挑战。传统的检测方法在面对非高斯分布的杂波时可能会失效，因为它们通常假设背景是高斯分布的。本文提出的方法则打破了这一限制，为非高斯杂波环境提供了新的解决方案。
首先，文章引入了基于阶数统计量（Order Statistics - OS）的广义似然比检验（Generalized Likelihood Ratio Test - GLRT）。在已知归一化杂波协方差矩阵的前提下，OS-GLRT通过选取最可能的目标散射体所在的距离单元中的最大观测值来进行检测。这种方法在散射体数量估计较为宽松的情况下表现出良好的鲁棒性，但当估计数量过少时，其性能会下降。
为了解决这个问题，作者提出了带有动态阈值的OS-GLRT（DOS-GLRT）。DOS-GLRT能够根据实际情况动态调整检测阈值，以提高检测器在各种环境条件下的性能。此外，为了进一步增强检测器的自适应能力，文章还介绍了自适应OS-GLRT和自适应DOS-GLRT。这两种自适应方法通过使用次要数据来估计归一化杂波协方差矩阵，从而改善了检测性能。
通过蒙特卡洛模拟进行的性能评估显示，这些提出的新型检测器在非高斯杂波环境中表现出了有效的检测效果。这表明，这些方法在实际应用中，如雷达、遥感和无线通信等领域，可能具有广泛的应用前景，特别是在面对非典型环境和复杂干扰时，能提供更可靠的检测结果。
这篇研究论文贡献了一种新的、适应性强的非高斯杂波环境下的目标检测策略，为雷达系统设计者和研究人员提供了新的工具，以应对日益复杂的电磁环境。这些方法有望提高雷达系统的探测性能，增强对范围扩展目标的识别能力，进一步推动雷达技术的发展。
Substituting
ˆ
®
t
in (8), and then exploiting the
derivation for the natural logarithm of f(z
t
j H
0
)and
f(z
t
j H
1
) with respect to ¿
t
, the ML estimate of ¿
t
2 ¿
under each hypothesis is straightforwardly given by
H
0
:
ˆ
¿
t
=
1
N
z
H
t
§
¡1
z
t
(10)
H
1
:
ˆ
¿
t
=
1
N
(z
t
¡
ˆ
®
t
p)
H
§
¡1
(z
t
¡
ˆ
®
t
p): (11)
Substituting (9), (10), and (11) into (8), it can be
shown that the GLRT is denoted as
¡N
X
t2£
h
0
ln
·
1 ¡
jp
H
§
¡1
z
t
j
2
(z
H
t
§
¡1
z
t
)(p
H
§
¡1
p)
¸
H
1
?
H
0
G (12)
where the original threshold constant G has been
reintroduced in (12). When N is a constant in (12)
and any strictly monotonically increasing function
of the detection statistic is available, the detection
statistic for OS-GLRT can be expressed as
¸
OS-GLRT
= ¡2(N ¡1)
X
t2£
h
0
ln
·
1 ¡
jp
H
§
¡1
z
t
j
2
(z
H
t
§
¡1
z
t
)(p
H
§
¡1
p)
¸
:
(13)
It is convenient to introduce the quantity, defined
by
w
t
=
jp
H
§
¡1
z
t
j
2
(z
H
t
§
¡1
z
t
)(p
H
§
¡1
p)
: (14)
The quantity p
H
§
¡1
z
t
in the numerator of (14) can
be considered as the output of the matched filter with
weighing vector §
¡1
p and the input z
t
[2]. However,
in the denominator of (14), z
H
t
§
¡1
z
t
and p
H
§
¡1
p act
as the normalization factors. After normalization, w
t
is
independent of the underlying mixing distribution of
the clutter f
¿
, the normalized clutter covariance matrix
§, and the steering vector of the desired signal p.
Note that the quantity w
t
is equal to the normalization
form of the squared modulus of z
t
after matched
filtering with the weighing vector §
¡1
p;inother
words, w
t
can be interpreted as the normalized energy
of z
t
after matched filtering. As mentioned before, the
range-spread target is completely contained within
a range window equal to K resolution cells. The set
£
h
0
could be estimated according to the values of
normalized energy w
t
,i.e.,theh
0
largest values of w
t
s,
t =1,:::K. The rationale for this procedure, of course,
is that the echo amplitudes of range cells occupied by
target scatterers are significantly greater than those of
range cells with clutter only.
In sort ascending, the order statistics of w
t
s,
t =1,:::, K are denoted as [27]
0 · w
(1)
·¢¢¢·w
(k)
·¢¢¢·w
(K)
· 1: (15)
According to (13), by exploiting the h
0
largest
values of w
(t)
s, t =1,:::, K, the detection statistic for
OS-GLRT can also be given by
¸
OS-GLRT
= ¡2(N ¡1)
K
X
k=K¡h
0
+1
ln(1 ¡w
(k)
): (16)
For comparati ve convenience, the detection statistic
for NSDD-GLRT is presented as [24]
¸
NSDD-GLRT
= ¡2(N ¡1)
K
X
t=1
ln(1 ¡w
t
): (17)
The detection statistics of (16) and (17) deserve
some comments. By comparing (16) with (17),
OS-GLRT has a similar form to NSDD-GLRT, but
the range cells integrated in the detection statistics
are different. More precisely, OS-GLRT corresponds
to the set £
h
0
while NSDD-GLRT corresponds to
the set £
K
. In the sparse scattering scenario, unlike
NSDD-GLRT, OS-GLRT can lessen the collapsing
loss due to the presence of cells that contain mostly
clutter, which is confirmed in later performance
assessment. It is also worth noting that, if h
0
= K,
namely, for target scatterers occupying all K range
cells, OS-GLRT coincides with NSDD-GLRT;
however, if h
0
= 1, namely, for a point-like target,
OS-GLRT coincides with the 1=M detector.
B. False Alarm Probability of OS-GLRT
The formula relating the false alarm probability to
the detection threshold for OS-GLRT is deduced in
this subsection.
Let
u
t
= ¡2(N ¡1) ln(1 ¡w
t
), t =1,:::,K: (18)
Equation g(x)=¡2(N ¡1)ln(1 ¡x) is strictly
monotonically increasing function for x 2 (0,1)
according to (16) and (18); the set £
h
0
can also
be estimated based on the h
0
largest values of u
t
s,
t =1,:::,K.
In like manner , the order statistics of u
t
s, t =
1,:::,K are described as
0 · u
(1)
·¢¢¢·u
(k)
·¢¢¢·u
(K)
: (19)
The test statistic for OS-GLRT can now be
simplified to the following form
¸
OS-GLRT
=
K
X
k=K¡h
0
+1
u
(k)
: (20)
Likewise, the test statistic for NSDD-GLRT can
also be represented as
¸
NSDD-GLRT
=
K
X
t=1
u
t
=
K
X
t=1
u
(k)
: (21)
Under the H
0
hypothesis, u
t
has an exponential
distribution with the pdf as [24]
f
u
(u)=e
¡u=2
=2, u ¸ 0 (22)
HE ET AL.: NOVEL RANGE-SPREAD TARGET DETECTORS IN NON-GAUSSIAN CLUTTER 1315
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