车辆轨迹预测：经典模型对比与实验评估

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本文主要探讨了"车辆轨迹预测经典模型"在卡尔曼滤波中的应用，特别是针对智能车辆运动估计的重要性和需求。作者Robin Schubert、Christian Adam、Marcus Obst、Norman Mattern、Veit Leonhardt和Gerd Wanielik对现有的典型车辆运动模型进行了系统性审查，并着重评估了它们在不同场景下的适用性。车辆轨迹预测是智能驾驶辅助系统（ADAS）中的关键组成部分，其目标是通过结合各种传感器的数据，如雷达、摄像头和激光雷达等，来精确估算车辆的位置和动态。为了实现这一目标，研究人员依赖于适合的车辆运动模型，这些模型需能够捕捉车辆的加速度、转向角、速度变化等因素，以减小传感器测量误差对决策的影响。卡尔曼滤波是一种常用的技术，它利用概率模型和数据融合方法，通过预测和更新步骤处理观测数据，以获得车辆运动状态的最优估计。论文中提到的经典模型包括：卡尔曼滤波（CA）、扩展卡尔曼滤波（CV）、条件卡尔曼滤波（CCA）、扩展条件卡尔曼滤波（CCV）以及连续轨迹回归（CTRV）和连续轨迹预测（CTRA）。这些模型各有特点，例如，卡尔曼滤波适用于线性系统，而扩展卡尔曼滤波则考虑了非线性因素；条件卡尔曼滤波和扩展条件卡尔曼滤波在处理部分观测数据时更有优势；连续轨迹回归和预测模型则是基于历史轨迹预测未来的运动趋势。作者们通过大量实验，使用精确的参考传感器数据，对这些模型的性能进行了详细的评估。实验结果揭示了每种模型在不同道路条件、交通密度和行驶环境下的优缺点。这些实验结果为选择最优化的车辆轨迹预测模型提供了实用的指导原则，对于智能汽车的设计者和开发者来说，具有重要的实际意义。总结来说，本文的核心内容在于对车辆轨迹预测的经典模型进行比较分析，旨在帮助研究者和工程师理解如何根据具体的应用场景和需求，选择最适合的卡尔曼滤波模型来提高道路安全性和驾驶舒适性。通过深入理解不同模型的工作原理和性能，可以更好地设计和优化智能驾驶系统，推动ADAS技术的发展。

Empirical Evaluation of Vehicular Models for Ego Motion Estimation

Robin Schubert, Christian Adam, Marcus Obst, Norman Mattern, Veit Leonhardt, and Gerd Wanielik

Abstract— Estimating the motion of a vehicle is a crucial

requirement for intelligent vehicles. In order to solve this

problem using a Bayes ﬁlter, an appropriate model of vehicular

motions is required. This paper systematically reviews typical

vehicular motion models and evaluates their suitability in dif-

ferent scenarios. For that, the results of extensive experiments

using accurate reference sensors are presented and discussed in

order to provide guidelines for the choice of an optimal model.

I. INTRODUCTION

One of the most promising technologies for increasing road

safety and driving comfort are advanced driver assistance

systems (ADASs). Such systems are characterized by the

perception of a vehicle’s surrounding using different, often

complementary sensors. In order to bridge the gap between

the inherent uncertainties of the sensor measurements and the

required reliability of the desired information, it is common

to apply statistical signal processing techniques.

One of the most widely used concepts is the Bayes ﬁlter

or, more precisely, one of its practical implementations. Each

Bayes ﬁlter, however, requires an appropriate probabilistic

state space model of the system under consideration which

consists of two parts: While the system or process model de-

scribes the temporal behavior, the sensor model characterizes

the properties of the utilized sensors [1].

For vehicular applications, a system model which accu-

rately represents the motion of a vehicle is often a crucial

requirement. While this is rather obvious for applications

which explicitly address the estimation of a vehicle’s motion

(e.g., systems for localizing the ego vehicle [

] or tracking

vehicles in the surrounding [

]), it is also true for non-

vehicular tracking applications. For instance, pedestrian

detection systems require an accurate ego motion estimation

in order to distinguish the motions of the pedestrians from

those of the ego vehicle [4].

Consequently, ego motion estimation is a part of virtually

any work related to the perception of a vehicle’s surrounding.

Though a number of different models have been proposed,

a systematic empirical evaluation is rarely available. In [

three of the most common models have been compared based

on simulated data. In [

], two models have been evaluated

for a mobile robot. Finally, an evaluation of sophisticated

models for navigation purposes has been presented in [7].

Another related work, which was done by some of the

authors, attempted to evaluate different motion models for

navigation purposes using highly accurate reference sensors

All authors are with the Professorship of Communications Engineer-

ing, Chemnitz University of Technology, Chemnitz, Germany, e-mail:

firstname.lastname@etit.tu-chemnitz.de

[

]. However, there are some factors which limit the signiﬁ-

cance of this evaluation for ADAS applications. In contrast

to usual tracking algorithms, position measurements from a

global navigation satellite system (GNSS) have been used.

Furthermore, in lack of a more appropriate procedure, the

ﬁlter parameters have been tuned manually.

In this paper, the most common vehicular motion models

shall be empirically evaluated, in particular regarding their

suitability for ADAS applications. The basic idea is to

apply identical ﬁlters each of which contains a separate

motion model using automatically optimized parameters. The

experiments are conducted in different environments such as

highways or urban roads using a highly accurate reference

sensor system.

The paper is structured as follows: Section II introduces the

utilized notation and gives a brief overview about probabilistic

ﬁltering and common motion models. In the subsequent

section III, the experimental setup as well as the evaluation

methodology are presented. Section IV contains detailed

quantitative results of the motion model evaluation. The

paper concludes with a discussion and recommendations

about appropriate models in section V.

II. FUNDAMENTALS

A. Probabilistic Filtering

The aim of Bayesian tracking algorithms is to recursively

estimate the probability density function (PDF) of a system’s

-dimensional state vector

∈ R

for each time step

The dynamic behavior of the system is represented by the

discrete-time stochastic model

k+1

= g

, v

, T

), (1)

where

is called state transition equation. The vector

denotes an independent and identically distributed (i.i.d.)

system noise process, which represents the non-deterministic

part of the model.

denotes the time between

and

k + 1

In the general case, the state vector

is not observable;

however, it is assumed that measurements

∈ R

are

available which are connected to

by a known mathematical

relation, called the measurement equation

= g

, w

), (2)

where w

denotes an i.i.d. observation noise time series.

For the ﬁltering problem, the noise processes are assumed

to be white and mutually independent. Furthermore, the

sequence of all measurements which are available at time

denoted by

b= {y

, i = 1, . . . , k}

. If the initial PDF

p(x

)

is assumed to be known, the ﬁltering problem can be deﬁned

as recursively determining the posterior PDF p(x

2011 IEEE Intelligent Vehicles Symposium (IV)

Baden-Baden, Germany, June 5-9, 2011

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