FPGA实现的粒子PHD滤波器：一种硬件友好的观测选择设计
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"基于硬件的友好的基于粒子的观测选择PHD滤波器的设计"
这篇研究论文探讨了"姿势：基于硬件的友好的基于粒子的观测选择PHD滤波器的设计"，该主题属于多目标跟踪领域的概率假设密度(PHD)过滤技术。PHD滤波是一种在复杂环境中对多个目标进行追踪的高效算法，特别是在自动驾驶、无人机系统和雷达信号处理等应用中具有广泛前景。
传统粒子PHD滤波器虽然在理论上表现出色，但其高计算复杂性成为实时工业应用中的主要瓶颈。这主要源于滤波过程中需要处理的时间变化观测数量，而硬件电路（如现场可编程门阵列FPGA）中的并行处理单元数量通常是固定的。因此，如何在FPGA平台上实现适应性、高效且硬件友好的PHD滤波器是当前面临的一大挑战。
论文作者，包括Zhiguo Shi、Yongkang Liu、Shaohua Hong、Jiming Chen以及Xuemin (Sherman) Shen，都是电气电子工程师学会(IEEE)的成员或资深会员，他们提出了一种创新方法来解决这个问题。他们设计的新型粒子PHD滤波器着重于优化观测选择策略，旨在降低计算复杂度，同时保持良好的跟踪性能。
文章可能详细介绍了以下几点：
1. 观测选择策略：为了适应不断变化的观测数量，他们可能提出了一个智能的观测选择机制，只处理最有价值的数据，从而减少不必要的计算负担。
2. 硬件优化：在FPGA平台上，可能采用了定制化硬件结构，以动态调整处理单元的数量，以适应不同时间步的观测负载。
3. 并行处理：可能利用FPGA的并行计算能力，设计了可扩展的并行架构，使得滤波过程能高效地在硬件上执行。
4. 实时性能：论文可能评估了新设计的实时性能，对比了传统方法，展示了其在处理速度和资源利用率方面的优势。
5. 实验验证：通过实际案例或仿真测试，论文可能证明了所提方法的有效性和可行性，展示了在各种条件下跟踪精度的提升。
这篇研究论文为解决粒子PHD滤波器在硬件实施上的难题提供了一个有前途的解决方案，有望推动多目标跟踪技术在实时应用中的广泛应用。然而，由于提供的摘要内容有限，具体的实现细节和技术细节尚未完全展开，这些内容通常会在论文的完整版本中详细阐述。
Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
3
any arbitrary directions and no road information is available
for the observer. The state of a target at the moment k,
x
k
= [x
k
, ˙x
k
, y
k
, ˙y
k
]
T
, contains the position information of
the target, (x
k
, y
k
), and its velocities, ( ˙x
k
, ˙y
k
), in the x and y
directions respectively. The state equation of the target in the
x-y plan is described by
x
k
=
1 δT 0 0
0 1 0 0
0 0 1 δT
0 0 0 1
x
k
−
1
+
δT
2
2
0
δT 0
0
δT
2
2
0 δT
κ
1,k
κ
2,k
(1)
where δT is the sensing period, and κ
1,k
and κ
2,k
are
independent zero-mean white Gaussian noises with standard
deviations σ
κ
1
and σ
κ
2
, respectively [11]. As many symbols
are used in this paper, Table I summarizes the important ones.
For the observer, the number of targets in the region varies
with time. Thus, the tracked targets at each scan can be cate-
gorized into two types: survival targets and new-born targets,
accordingly. The survival targets are those which appear in
previous scans while the new-born targets are those newly
detected in the region. We consider that at most one new-born
target can appear in a short δT . For the new-born targets, they
can appear spontaneously according to a Poisson point process
with intensity function γ
k
= 0.2N (·|¯x
0
, Q), which denotes a
normal distribution with mean ¯x
0
and covariance Q. For the
survival targets, the probability of target survival from time
k −1 to time k is e
k|k−1
. No target spawning is considered in
this paper [10]. The maximum number of the targets at each
sensing moment is denoted as P . The probability of detection
is denoted as p
D
.
At each sensing moment, the observer obtains observations,
˜
Z
k
, from the targets and clutters in the circular region with a
radius R. The target-oriented observation equation is given by
z
k
= H(x
k
) =
r
k
θ
k
(2)
where
r
k
=
1 0 0 0
0 0 1 0
x
k
+ ζ
r,k
(3)
θ
k
= arctan
0 0 1 0
x
k
1 0 0 0
x
k
+ ζ
θ,k
. (4)
The observations consist of both the target range r
k
and
bearing θ
k
. ζ
r,k
and ζ
θ,k
are independent zero-mean white
Gaussian noises with standard deviations σ
r
and σ
θ
.
Clutters are uniformly distributed in the observation region
and the number of clutter points per scan obeys a Poisson
distribution with an average rate of λ [9].
III. ALGORITHMIC DESIGN AND HARDWARE
IMPLEMENTATION
In this section, we first propose the POSE PHD filter
design which is suitable for hardware implementation in FPGA
platforms. We then analyze the observation selection process
and show that the observation selection error probability is
negligible in the POSE PHD filter. Furthermore, we address
the hardware implementation issues of the POSE PHD filter.
Finally, we propose a heuristic method to select the proper
particle number based on the “lost tracking ratio” parameter
and discuss the computational complexity problem.
A. POSE PHD Filter Overview
The processing flow of the POSE PHD filter contains six
steps, namely Initialization, Prediction, Observation Selection,
Update, Resampling, Target Estimation, as shown in Fig. 2.
In comparison with the traditional particle PHD filter, we
introduce a novel Observation Selection module to pre-process
the observations to meet the hardware design requirements. In
the processing flow, Initialization is executed at the beginning
to initiate the processing parameters, while the other five steps
are executed recursively each time new observations arrive at
time k = 1, 2, 3....
1) Initialization: At time k = 0, the posterior PHD of targets
is represented by a set of particles (samples) {x
(i)
0
, w
(i)
0
}
L
i=1
where x
(i)
0
denotes the i-th particle at time k = 0, and w
(i)
0
denotes the associated weight of the particle x
(i)
0
.
2) Prediction: The algorithm generates L particles
{
˜
x
(i)
k|k−1
}
L
i=1
from the proposal density q
k
(·|x
(i)
k−1
, Z
k
) for the
surviving targets, and generates J particles {
˜
x
(i)
k|k−1
}
L+J
i=L+1
from the proposal density p
k
(·|Z
k
) for the new-born targets.
The prediction weight of the i-th particle at time k is given
by
ˆw
(i)
k|k−1
=
ϕ
k|k−1
(
˜
x
(i)
k|k−1
,x
(i)
k−1
)
q
k
(
˜
x
(i)
k|k−1
|x
(i)
k−1
,z
k
)
w
(i)
k−1
i = 1, . . . , L
1
J
γ
k
(
˜
x
(i)
k|k−1
)
p
k
(
˜
x
(i)
k|k−1
|z
k
)
i = L + 1, . . . L + J
(5)
where ϕ
k|k−1
(x, ξ) = e
k|k−1
(ξ)f
k|k−1
(x|ξ). e
k|k−1
(ξ) is the
target survival probability given the previous state was ξ, and
f
k|k−1
(x|ξ) is the transition probability of the survival target
from previous state ξ to the sampled particle x.
3) Observation Selection: For the survival targets, it gener-
ates the Euclidean distance D
sur
and selects M
1
targets from
the observation set
˜
Z
k
with elements
˜
z
k
. For the new-born
targets, it generates the Euclidean distance D
new
and then
selects M
2
targets from
˜
Z
k
. The selected observation set is
denoted as Z
k
. We will address the details of this step later.
4) Update: Using the selected observations Z
k
at time k, it
updates the weights of particles
˜w
(i)
k
=
1 − p
D
+
z∈Z
k
ψ
k,z
(
˜
x
(i)
k|k−1
)
κ
k
(z) + C
k
(z)
ˆw
(i)
k|k−1
(6)
where
C
k
(z) =
L+J
i=1
ψ
k,z
(
˜
x
(i)
k|k−1
) ˆw
(i)
k|k−1
. (7)
with ψ
k,z
(x) = p
D
g
k
(z|x) and κ
k
(z) = λc
k
(z). g
k
(z|x)
denotes the likelihood of individual targets, and c
k
(z) is the
probability density of clutters.
5) Resampling: By computing the sum of all weights, i.e.,
˜
N
k|k
=
L+J
i=1
˜w
(i)
k
, it first estimates the number of targets
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