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
剩余16页未读，继续阅读
weixin_38603704
- 粉丝: 7
- 资源: 971
我的内容管理
展开
最新资源
- 彩虹rain bow point鼠标指针压缩包使用指南
- C#开发的C++作业自动批改系统
- Java实战项目：城市公交查询系统及部署教程
- 深入掌握Spring Boot基础技巧与实践
- 基于SSM+Mysql的校园通讯录信息管理系统毕业设计源码
- 精选简历模板分享：简约大气，适用于应届生与在校生
- 个性化Windows桌面：自制图标大全指南
- 51单片机超声波测距项目源码解析
- 掌握SpringBoot实战：深度学习笔记解析
- 掌握Java基础语法的关键知识点
- SSM+mysql邮件管理系统毕业设计源码免费下载
- wkhtmltox下载困难？找到正确的安装包攻略
- Python全栈开发项目资源包 - 功能复刻与开发支持
- 即时消息分发系统架构设计：以tio为基础
- 基于SSM框架和MySQL的在线书城项目源码
- 认知OFDM技术在802.11标准中的项目实践
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
