Sensors 2016, 16, 169 4 of 18
•
RFS-based multi-target dynamics and sensor observation models: Let
x
k
∈ X
k
denote the state
vector of a target and
X
k
the set of multi-target states at time
k
, where
X
k
is the state space of a
target. The multi-target dynamics is modeled by:
X
k
=
∪
x
k−1
∈X
k−1
Ψ
k|k −1
(
x
k−1
)
∪ Γ
k
(8)
where Ψ
k|k −1
(
x
k−1
)
is the set evolved from the previous state x
k−1
, Ψ
k|k −1
(
x
k−1
)
=
{
x
k
}
with
surviving probability
p
S,k
(
x
k−1
)
and transition density
f
k|k −1
(
x
k
|
x
k−1
)
, otherwise
Ψ
k|k −1
(
x
k−1
)
= ∅ with probability 1 − p
S,k
(
x
k−1
)
; Γ
k
is the set of spontaneous births.
Let
z
k
∈ Z
k
denote a measurement vector and
Z
k
the set of measurements received by a sensor at
time
k
, where
Z
k
is the sensor measurement space. The single-sensor multi-target observation is
modeled by:
Z
k
=
∪
x
k
∈X
k
Θ
k
(
x
k
)
∪ K
k
(9)
where
Θ
k
(
x
k
)
is the measurement set originated from state
x
k
,
Θ
k
(
x
k
)
=
{
z
k
}
with sensor
detection probability
p
D,k
(
x
k
)
and likelihood
g
k
(
z
k
|
x
k
)
, otherwise
Θ
k
(
x
k
)
= ∅
with probability
1 − p
D,k
(
x
k
)
; K
k
is the clutter set, which is modeled as a Poisson RFS with density:
f
c,k
(
K
k
)
= e
−λ
k
∏
z
k
∈K
k
κ
k
(
z
k
)
, with λ
k
=
Z
κ
k
(
z
k
)
dz
k
and κ
k
(
z
k
)
= λ
k
f
c,k
(
z
k
)
(10)
where
κ
k
(
z
k
)
is the clutter intensity,
λ
k
is the average clutter number and
f
c,k
(
z
k
)
is the density of
a clutter.
The transition model in Equation (8) jointly incorporates motion, birth and death for multiple
targets, while the sensor observation model in Equation (9) jointly accounts for detection
uncertainty and clutter. Assume that the RFSs constituting the unions in Equations (8) and
(9) are mutually independent. The multi-target JDE at time
k
is to derive the estimated state set
ˆ
X
k
(
Z
1:k
)
using the collection
Z
1:k
=Z
1
, ...,
Z
k
of all sensor observations up to time
k
. The paper aims
to derive a performance limit to multi-target joint detectors-estimators for the observation of a
single sensor with clutter and missed detection. The performance limit is measured by the bound
of the average error between X
k
and
ˆ
X
k
(
Z
1:k
)
.
3.
Single-Sensor Multi-Target JDE Error Bounds Using Multi-Bernoulli or Poisson Approximation
At time k, the RFS-based mean square error (MSE) between X
k
and
ˆ
X
k
(
Z
1:k
)
is defined as:
σ
2
k
= E
e
2
k
X
k
,
ˆ
X
k
(
Z
1:k
)
=
R R
f
k
(
X
k
, Z
k
|
Z
1:k−1
)
e
2
k
X
k
,
ˆ
X
k
(
Z
1:k
)
δX
k
δZ
k
=
R R
γ
k
(
Z
k
|
X
k
)
f
k|k −1
(
X
k
|
Z
1:k−1
)
e
2
k
X
k
,
ˆ
X
k
(
Z
1:k
)
δX
k
δZ
k
(11)
where
e
k
X
k
,
ˆ
X
k
(
Z
1:k
)
denotes the error metric between
X
k
and
ˆ
X
k
(
Z
1:k
)
, which is defined by the
second-order OSPA distance in (4),
f
k
(
X
k
, Z
k
|
Z
1:k−1
)
denotes the density of
(X
k
,
Z
k
)
given
Z
1:k−1
and
γ
k
(
Z
k
|
X
k
)
= f
k
(
Z
k
|
X
k
)
denotes the likelihood for the total sensor measurement process.
At time
k
, given multi-target state set
X
n
k
and sensor measurement set
Z
m
k
, all association
hypotheses can be represented as a function from target index set
{
1, ...,
n}
to sensor measurement
index set {0, 1, ..., m} [2]. Defining that:
θ
n,m
:
{
1, ..., n
}
→
{
0, 1, ..., m
}
(12)
剩余17页未读，继续阅读
weixin_38717870
- 粉丝: 2
- 资源: 908
我的内容管理
展开
最新资源
- 计算机人脸表情动画技术发展综述
- 关系数据库的关键字搜索技术综述：模型、架构与未来趋势
- 迭代自适应逆滤波在语音情感识别中的应用
- 概念知识树在旅游领域智能分析中的应用
- 构建is-a层次与OWL本体集成：理论与算法
- 基于语义元的相似度计算方法研究：改进与有效性验证
- 网格梯度多密度聚类算法：去噪与高效聚类
- 网格服务工作流动态调度算法PGSWA研究
- 突发事件连锁反应网络模型与应急预警分析
- BA网络上的病毒营销与网站推广仿真研究
- 离散HSMM故障预测模型：有效提升系统状态预测
- 煤矿安全评价：信息融合与可拓理论的应用
- 多维度Petri网工作流模型MD_WFN：统一建模与应用研究
- 面向过程追踪的知识安全描述方法
- 基于收益的软件过程资源调度优化策略
- 多核环境下基于数据流Java的Web服务器优化实现提升性能
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
