基于移动车辆和路边观测的长距离道路几何估计
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这篇文章是IEEE Transactions on Intelligent Transportation Systems期刊上的一篇论文，主要探讨了使用移动车辆和路边观察进行远程道路几何形状估计的方法。作者Lars Hammarstrand、Maryam Fatemi、Ángel F. García-Fernández和Lennart Svensson提出了一个算法，旨在为装有摄像头、雷达以及车载内部传感器的主机车精确估算前方200米的道路几何形状，特别针对高速公路场景。
摘要中提到，该算法基于精确的clothoid（一种数学模型，常用于描述曲线）道路模型，设计了一个贝叶斯融合框架。通过这个框架，算法利用以下几个方面的传感器观测来估算道路几何：车道标线的形状、前方车辆的行驶方向以及路边雷达反射器的位置。实验结果显示，即使在具有挑战性的山区高速公路上，该算法也能有效地捕捉到道路的形状。
这篇论文的关键知识点包括：
1. Clothoid-based Road Model ：Clothoids是一种数学曲线，因其在描述公路曲线时能提供连续变化的曲率而被采用。论文中，作者使用clothoid作为基础模型来精确描述高速公路的几何形状。
2. 贝叶斯融合框架 ：这是一种数据融合技术，允许来自不同传感器的数据（如摄像头图像、雷达数据和车辆内部传感器读数）在估计道路几何时进行有效结合。通过贝叶斯方法，可以更新和融合这些传感器的不确定性信息，提高估计的准确性。
3. Sensor Observations ：传感器观测是算法的核心输入，包括车道线的形状（可能通过摄像头捕获）、领头车辆的方向（可能通过雷达检测）以及路边雷达反射器的位置（提供固定参照点）。这些观测数据共同帮助确定道路的几何特性。
4. 高速公路场景 ：论文专注于高速公路环境，这是因为此类场景通常需要更远距离的预知能力，以便主机车能够安全行驶和做出决策。
5. 挑战性环境 ：作者指出，即使在复杂地形如山区高速公路上，算法也能够有效地工作，这表明其鲁棒性和适应性。
6. 应用于自动驾驶 ：鉴于其在道路几何估计中的准确性和可靠性，该研究对于自动驾驶汽车的安全导航和路径规划至关重要，尤其是在需要预测道路曲线和坡度的场景中。
该论文的贡献在于提出了一种集成多种传感器数据的新型算法，为自动驾驶系统提供更精确的道路信息，从而增强其在各种环境下的性能。这对于自动驾驶技术的发展，特别是对于高精度导航和实时道路条件感知来说，是一个重要的进步。
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
HAMMARSTRAND et al.: ROAD GEOMETRY ESTIMATION USING MOVING VEHICLES AND ROADSIDE OBSERVATIONS 3
1) Lane Marking Observations: If present and detected by
the camera system, the shapes of the left and right lane mark-
ings closest to the host vehicle are described using third degree
polynomials. The polynomials are given in the local vehicle
coordinate frame (x
l
k
,y
l
k
) as,
y
l
k
= l
0
k
+ l
1
k
x
l
k
+ l
2
k
x
l
k
2
+ l
3
k
x
l
k
3
(1)
y
r
k
= r
0
k
+ r
1
k
x
l
k
+ r
2
k
x
l
k
2
+ r
3
k
x
l
k
3
(2)
for the left lane marking and the right lane marking, respec-
tively. Roughly every 100 ms, the camera system delivers the
polynomial coefficients for each side, z
l
k
=[l
0
k
,l
1
k
,l
2
k
,l
3
k
]
T
and
z
r
k
=[r
0
k
,r
1
k
,r
2
k
,r
3
k
]
T
, independently of each other. Addition-
ally, each coefficient vector is coupled with a confidence value
(between 0 and 3) and an indication of the maximum distance
for which the polynomials (1), (2) are valid, denoted x
l
max
and
x
r
max
, respectively.
2) Object Observations: The radar-camera fusion system
delivers object estimates every 25 ms. Based on their speed
over-ground and camera classification, these estimates are
divided into two categories, moving/stationary vehicles or
stationary unclassified objects. The latter category typically
includes stationary roadside objects reflecting radar energy,
such as guard-rail posts. We denote the vehicle estimates as z
v
k
and the stationary detections as z
s
k
.
For the ith detected vehicle, the fusion system provides the
following description,
z
v,i
k
=
x
i
k
,y
i
k
,φ
i
k
,v
i
k
T
(3)
where [x
i
k
,y
i
k
] is the position of the vehicle in the local coor-
dinate frame, φ
i
k
is its heading direction and v
i
k
is its speed
over-ground.
For the stationary objects the description is simply given as
the position in the local coordinate frame.
D. Estimation Problem
The aim is to estimate the geometry of the road (including
uncertainty) using the available observations from the onboard
sensors. More specifically, we want to recursively calculate the
posterior density of the road state, p(r
k
|z
1:k
),wherez
1:k
is the
set of all observations up to the current time index k.
III. R
OAD MODEL
We define and motivate our proposed model of the road
in Section III-A, derive approximations to make the model
suitable in a filtering framework in Section III-B and finally
compare our approximation with the commonly used third-
degree polynomial model in Section III-C.
A. Exact Road Model
Roads are typically built in a manner which ensures a smooth
ride for the road users. Among other things, there should be
no abrupt changes in the road curvature. To accommodate this,
it is common to construct roads where straight sections are
connected with constant curvature segments using a transition
curve, i.e., a curve with linearly changing curvature [26]. Our
proposed model is based on this notion.
In the most general form, the 2D geometry of the road can
be described using a 2-dimensional parametric curve c
r
(s)
expressed in arc length s (distance along the road), as
c
r
(s)=
x
r
(s)
y
r
(s)
(4)
where (x
r
(s),y
r
(s)) is the position of the road at arc length s
in the local coordinate system. The parameters used to describe
c
r
(·) are collected in the road state r
k
. That is, if we know r
k
we also know the shape of the road. Below, we will introduce
how we propose to model (4) and consequently how we choose
to parameterize the road state.
We propose to model the road using connected segments
fixed to the road. Fixing the model to the road rather than
to the vehicle, which is a common modeling choice, allows
more efficient use of our observations. As the road model in
large parts is static rather than dynamically changing with the
movement of the host vehicle, there is no need to add process
noise in order to account for changes in the road.
Each segment in our model is described using a paramet-
ric curve (clothoid) of length L that has a linearly changing
curvature as a function of s. The curvature of the ith-segment,
denoted κ
i
r
(s), is thus expressed as
κ
i
r
(s)=κ
i
0
+ κ
i
1
s (5)
where κ
i
0
is the initial curvature of the segment and κ
i
1
is its
curvature change rate. As a consequence of (5), the heading of
the road in each segment, ϕ
i
r
(s), is described as
ϕ
i
r
(s)=ϕ
i
0
+ κ
i
0
s +
κ
i
1
2
s
2
(6)
where ϕ
i
0
is the initial heading of the road at the start of the ith
segment. From (6) we can finally describe the geometry of the
ith segment using the following integral
x
i
r
(s)
y
i
r
(s)
=
x
i
0
y
i
0
+
s
0
cos
ϕ
i
r
(t)
sin (ϕ
i
r
(t))
dt (7)
where (x
i
0
,y
i
0
) are the initial coordinates of the ith segment.
Using (7) we can describe the geometry of each segment in
the road model. In order for the segments to align smoothly, the
segments should be connected such that the complete road has
G
2
-continuity (2nd order geometric), i.e., the position, heading
and curvature of two connected segments should be equal at
the intersection. This is ensured by introducing the following
constraints on the initial conditions,
κ
i
0
= κ
i−1
0
+ κ
i−1
1
L (8)
ϕ
i
0
= ϕ
i−1
0
+ κ
i−1
0
L + κ
i−1
1
L
2
/2(9)
x
i
0
= x
i−1
r
(L) (10)
y
i
0
= y
i−1
r
(L). (11)
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