δ-GLMB多目标跟踪滤波器的实现与优化
需积分: 9 170 浏览量
更新于2024-09-06
收藏 1.09MB PDF 举报
"这篇PDF文件主要探讨了可标签的多目标跟踪技术，涉及分布式系统、集群协同以及信息融合等核心理论。文章详细介绍了基于Labeled Random Finite Sets (LRFS)的Bayes多目标跟踪滤波器，即δ-Generalized Labeled Multi-Bernoulli (δ-GLMB)滤波器的分析解决方案及其高效实现方法。"
在多目标跟踪领域，δ-GLMB滤波器是一种关键的数学工具，它能够处理复杂环境中的多个动态目标，并能为每个目标分配独特的标签，以区分不同的目标。该滤波器在每次迭代中包括更新操作和预测操作，这两个操作都需要处理大量的指数项和权重。然而，由于这些项的数量通常是不可计算的，因此需要采取截断策略。
在更新操作中，论文采用了排名分配算法来确定最具影响力的项，而无需计算所有项。这有助于减少计算复杂性，同时保持滤波器的性能。预测操作则利用了K-th最短路径算法，同样是为了在不完全计算所有项的情况下找到最重要的部分。
此外，通过概率假设密度过滤（Probability Hypothesis Density Filtering, PHD）等方法，文中还提出了相对低成本的前瞻性策略，以降低计算量。PHD滤波是单目标追踪的一个扩展，用于估计场景中目标数量的概率分布，它在此处被用来辅助δ-GLMB滤波器，以更有效地减少计算需求。
这篇文献深入研究了多目标跟踪的基础理论和技术，特别是δ-GLMB滤波器的实施细节，对理解和应用分布式、集群协同的多目标自动跟踪系统具有重要价值。标签"tracking fusion PHD FISST RFS"分别对应着跟踪、融合、概率假设密度滤波、随机有限集理论（Random Finite Set, RFS），这些都是多目标跟踪领域的关键概念和技术。
PREPRINT: IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 62, NO. 24, PP. 6554–6567, 2014 3
where X
0:k
= (X
0
, ..., X
k
), g
k
(·|·) is the multi-target likeli-
hood function at time k, f
k|k−1
(·|·) is th e multi-target tran-
sition density to time k. The multi-target likelihood function
encapsulates the underlying models for d etections and false
alarms while the multi-target transition d ensity encapsulates
the under lying models of target motions, births and deaths.
Multi-target filtering is concerned with the marginal of
the multi-target posterior density, at the current time. Let
π
k
(·|Z
k
) denote the multi-target filtering density at time k,
and π
k+1|k
denote the multi-target prediction density to time
k + 1 (formally π
k
and π
k+1|k
should be written respectively
as π
k
(·|Z
0:k
), and π
k+1|k
(·|Z
0:k
), but for simplicity we omit
the dependence on past measurements). Then , the multi-target
Bayes filter propagates π
k
in time [3], [8] according to the
following update and prediction
π
k
(X
k
|Z
k
) =
g
k
(Z
k
|X
k
)π
k|k−1
(X
k
)
R
g
k
(Z
k
|X)π
k|k−1
(X)δX
, (1)
π
k+1|k
(X
k+1
) =
Z
f
k+1|k
(X
k+1
|X
k
)π
k
(X
k
|Z
k
)δX
k
, (2)
where the integral is a set integral defined for any function
f : F(X×L) → R by
Z
f(X)δX =
∞
X
i=0
1
i!
Z
f({x
1
, ..., x
i
})d(x
1
, ..., x
i
).
The multi-target filtering density captures all information on
the multi-target state, such as the number o f targets and their
states, at the current time.
For convenience, in what follows we omit explicit references
to the time index k, and d enote L , L
0:k
, B , L
k+1
, L
+
, L∪
B, π,π
k
, π
+
,π
k+1|k
, g,g
k
, f ,f
k+1|k
.
C. Measurement likelihood function
For a given multi-target state X, at time k, each state
(x, ℓ) ∈ X is either detected with probability p
D
(x, ℓ)
and gene rates a point z with likelihoo d g(z|x, ℓ), or missed
with probability 1 − p
D
(x, ℓ). The multi-object observation
Z = {z
1
, ..., z
|Z|
} is the superpo sition of the detected points
and Poisson clutter with intensity function κ.
Definition 2 An association map (for the current time) is a
function θ : L → {0, 1, ..., |Z|} such that θ(i) = θ(i
′
) >
0 implies i = i
′
. The set Θ of all such association maps is
called the association map space. The subset of association
maps with domain I is denoted by Θ(I).
An association map describes which tracks gene rated which
measurements, i.e. track ℓ generates measurement z
θ(ℓ)
∈ Z,
with undetected tracks assigned to 0. The condition θ(i) =
θ(i
′
) > 0 implies i = i
′
, means that a track can generate at
most one measurement at any point in time.
Assuming that, conditional on X, detections are indepen-
dent, and that clutter is independent of the detections, the
multi-object likelihood is given by
g(Z|X) = e
−hκ,1i
κ
Z
X
θ∈Θ(L(X))
[ψ
Z
(·; θ)]
X
(3)
where
ψ
Z
(x, ℓ; θ) =
(
p
D
(x,ℓ)g(z
θ(ℓ)
|x,ℓ)
κ(z
θ(ℓ)
)
, if θ(ℓ) > 0
1 − p
D
(x, ℓ), if θ(ℓ) = 0
(4)
Equation (3) is equivalent to the likelihood function given by
(54) in [1], an d is more convenient for implementation.
D. Multi-target transition kernel
Given the current multi-object state X, eac h state (x, ℓ) ∈ X
either continues to exist at the next time step with probability
p
S
(x, ℓ) and evolves to a new state (x
+
, ℓ
+
) with probability
density f(x
+
|x, ℓ)δ
ℓ
(ℓ
+
), or dies with probability 1−p
S
(x, ℓ).
The set of new targets born at the next time step is distributed
accordin g to
f
B
(Y) = ∆(Y)w
B
(L(Y)) [p
B
]
Y
(5)
where w
B
and p
B
are given parame te rs of the multi-target
birth density f
B
, defined on X × B. Note that f
B
(Y) = 0 if Y
contains any element y with L(y) /∈ B. The birth model (5)
covers both labeled Poisson and labeled multi-Bernoulli [1].
The multi-target state at the next time X
+
is the superposi-
tion of surviving targets and new born targets. Assuming that
targets evolve inde pendently of each other and that births ar e
indepen dent of surviving targets, it was shown in [1] that the
multi-target transition kernel is given b y
f (X
+
|X) = f
S
(X
+
∩ (X × L)|X)f
B
(X
+
− (X × L)) (6)
where
f
S
(W|X) = ∆(W)∆(X)1
L(X)
(L(W)) [Φ(W; ·)]
X
(7)
Φ(W; x, ℓ) =
p
S
(x, ℓ)f (x
+
|x, ℓ), if (x
+
, ℓ) ∈ W
1 − p
S
(x, ℓ), if ℓ /∈ L(W)
.(8)
E. Delta-Generalized Labeled Multi-Bernou lli
The δ-generalized labeled multi-Bernoulli filter is a solu-
tion to the Bayes multi-target filter based o n th e family of
generalized labeled multi-Bernoulli (GLMB) distributions
π(X) = ∆(X)
X
ξ∈Ξ
w
(ξ)
(L(X))
h
p
(ξ)
i
X
,
where Ξ is a discrete spac e, each p
(ξ)
(·, ℓ) is a prob-
ability density, and each w
(ξ)
(I) is no n-negative with
P
(I,ξ)∈F(L)×Ξ
w
(ξ)
(I) = 1. A GLM B can b e interpreted as
a mixture of multi-target exponentials [ 1]. While this family
is closed under the Bayes recursion [1], it is no t clear how
numerical implementation can be accomplished. Fortunately,
an alternative for m of the GLMB, known as δ-GLMB
π(X) = ∆(X)
X
(I,ξ)∈F(L)×Ξ
ω
(I,ξ)
δ
I
(L(X))
h
p
(ξ)
i
X
, (9)
where ω
(I,ξ)
= w
(ξ)
(I), provides a representation that facil-
itates numerical implementation. Note that the δ-GLMB can
be obtained fro m the GLMB by u sing the identity w
(ξ)
(J) =
P
I∈F(L)
w
(ξ)
(I)δ
I
(J), since the summand is non-zero if and
only if I = J.
In the δ-GLMB initial multi-target prior
π
0
(X) = ∆(X)
X
I∈F(L
0
)
ω
(I)
0
δ
I
(L(X))p
X
0
, (10)
剩余12页未读，继续阅读
2021-09-06 上传
2022-06-11 上传
2021-09-21 上传
2021-12-26 上传
2021-08-14 上传
2022-11-02 上传
2021-08-13 上传
2021-07-12 上传
2021-09-30 上传
weixin_38918256
- 粉丝: 0
- 资源: 1
我的内容管理
展开
最新资源
- NASM中文手册.......
- PIC8位单片机汇编语言常用指令的识读.doc
- 车牌识别系统算法的研究与实现
- 从MySpace的六次重构经历，来认识分布式系统到底该如何创建
- 软件测试面试题（白盒、黑盒测试）
- 从LiveJournal后台发展看大规模网站性能优化方法
- 2009年上半年网络工程师下午题
- 2009年网络工程师上午题
- 嵌入式c c++集锦
- ajax技术资料 PDF
- ofdm_carrier_sync\A consistent OFDM carrier frequency offset estimator based on distinctively spaced pilot tones.pdf
- jsp+源码+学生成绩管理系统 jsp源代码
- 9F概论（第四版）课后习题的参考答案[1].doc
- linux内核情景分析
- 基于VB的参数化绘图.pdf
- Java设计模式中文版
