*
Corresponding author: [email protected]
Stereo visual-inertial odometry with an online calibration and its
field testing
Jae Hyung Jung1, Sejong Heo2, and Chan Gook Park1*
1Dept. of Mechanical & Aerospace Engineering / Automation and Systems Research Institute, Seoul National University, Republic of Korea
2Hanwha Corporation/Defense, Republic of Korea
Abstract. In this paper, we present a visual-inertial odometry (VIO) with an online calibration using a stereo
camera in planetary rover localization. We augment the state vector with extrinsic (rigid body transformation)
and temporal (time-offset) parameters of a camera-IMU system in a framework of an extended Kalman filter.
This is motivated by the fact that when fusing independent systems, it is practically crucial to obtain precise
extrinsic and temporal parameters. Unlike the conventional calibration procedures, this method estimates both
navigation and calibration states from naturally occurred visual point features during operation. We describe
mathematical formulations of the proposed method, and it is evaluated through the author-collected dataset
which is recorded by the commercially available visual-inertial sensor installed on the testing rover in the
environment lack of vegetation and artificial objects. Our experimental results showed that 3D return position
error as 1.54m of total 173m traveled and 10ms of time-offset with the online calibration, while 6.52m of
return position error without the online calibration.
1 Introduction
Ego-motion estimation is one of the most crucial tasks for
unmanned vehicles such as planetary rovers or
autonomous driving cars to successfully carry out their
missions. However, to deal with the absence or outage of
GNSS signals, alternative navigation algorithms should
be considered. For instance, NASA’s Martian rovers are
equipped with stereo cameras and localize itself by the
vision-based navigation called visual odometry (VO) [1].
While VO suffers from the well-known error
accumulation, visual-inertial odometry (VIO) decreases
its rate by filling a gap between small baselined images
using IMU readings [2]. A fusion of a camera and IMU is
an attractive solution due to their complementary features.
Most of the visual-inertial fusion algorithms assume
that output data from a camera and IMU is timely
synchronized and the sensors are spatially well aligned.
However, this causes significant estimation errors when
time-delay of a camera is not negligible or a camera-IMU
system is not well calibrated since the measurement
model is linearized around the currently available
estimate referenced at the camera frame. Even if a
camera-IMU system is calibrated in advance, this cannot
reflect uncertainties on calibration parameters to an
estimator. In the worst case, calibration parameters could
be changed due to external shocks.
Many efforts to deal with the above issue has been
made. The authors of [3] showed that the cam-IMU
extrinsic parameter, the scale factor, and the global
gravity is observable with the global pose measurements.
Fig. 1. Testing rover mounted the visual-inertial sensor
However, the measurement model which assumes that
images output global poses was somewhat unrealistic.
Guo et al. in [4] proved that cam-IMU extrinsic parameter
is observable using the proposed basis functions under the
known depth (feature point) assumption. The work of [5]
focused on the temporal calibration of a cam-IMU system.
They theoretically showed that time-offset between camIMU system can be recovered, while practically
implemented the online calibration algorithm in the
extended Kalman filter (EKF) framework. Also in [6],
camera intrinsics, as well as IMU intrinsics (misalignment,
g-sensitivity) was modeled in the estimator.
In this paper, we exploit the theoretic results of [4,5]
and formulate EKF-based VIO algorithm using feature
point measurements obtained from the stereo camera.
Specifically, we augment the state vector with the time-
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0
(http://creativecommons.org/licenses/by/4.0/).
E3S Web of Conferences 94, 02005 (2019) https://doi.org/10.1051/e3sconf/20199402005
ISGNSS 2018
offset and extrinsic parameter. Fig. 1 shows the testing
rover equipped with the visual-inertial sensor to record the
dataset which lacks artificial object and vegetation.
2 The filter description
The error state vector of the presented algorithm consists
of the 15th order of IMU state, the calibration parameters:
cam-IMU time-offset, extrinsic parameter and the sliding
window pose/velocity as in Eq. (1).
T
T T T
T
T T T T T 15
T T 7
T T T 9
i i i
I C S
G G
I GB B B a g
C
C C B B d
G G N
S G B B B
t
x x x x
x θ p v b b
x θ p
x θ p v
(1)
In this expression, we denote the global frame as {G}, the
camera frame as {C}, the body (IMU) frame as {B}, and
the number of sliding window as N. Also, we define the
error state as
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