PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
June 2016
427
Correction of Atmospheric Refraction
Geolocation Error for High Resolution Optical
Satellite Pushbroom Images
Ming Yan, Chengyi Wang, Jianglin Ma, Zhiyong Wang, and Bingyang Yu
Abstract
When an optical remote sensing satellite is imaging the Earth
in-orbit, the propagation direction of the Line of Sight (
LOS
)
will be changed because of atmospheric refraction. This will
result in a geolocation deviation on the collinear rigorous
geometric model for direct georeferencing, pushbroom images.
To estimate and correct the atmospheric refraction geolocation
error, the
LOS
vector tracking algorithm is introduced and a
weighted mean algorithm is used to simplify the
ISO
standard
atmospheric model into a troposphere and stratosphere, i.e.,
two layers spherical atmosphere. The simulation result shows
the atmospheric refraction will introduce about 2 m and 7.5
m geometric displacement when the spacecraft is off-pointed
view at 30 and 45 degree angle, respectively. For a state-of-the-
art high resolution satellite, the atmospheric refraction dis-
placement shall be corrected. The method has been practiced
in the DMC3/TripleSat Constellation to remove the atmospher-
ic refraction geolocation error without ground control points.
Introduction
Satellite remote sensing image geolocation is about deter-
mining the correspondence between the pixel’s Cartesian
coordinate and geodetic coordinate. The geometric trans-
formation between these two systems can be expressed by a
rigorous geometric model, which is established based on a
collinear equation with interior orientation parameters from
the imaging payload and exterior orientation parameters of
the satellite platform (Crespi
et al
., 2007; Fan
et al
., 2011;
Habib
et al
., 2007; Jeong and Bethel, 2010 and 2014; Jiang
et
al
., 2013 and 2014; Leprince
et al
., 2007; Lussy and Greslou,
2012; Mahapatra
et al
., 2004; Müller
et al
., 2012; Pan
et al
.,
2013; Poli and Toutin, 2012; Radhadevi
et al
., 2011; Tang
et
al
., 2012; Toutin, 2004). The accuracy of a rigorous geometric
model depends on the interior and exterior orientation pa-
rameters, such as the focal length, detector size, lens, detector
line distortion of the imaging payload, and the ephemeris and
attitude systematic error of satellite platform. Also, the atmo-
spheric refraction and light aberration will have an impact on
the rigorous geometric model estimation (Lussy
et al
., 2012;
Oh and Lee, 2011). The distortions of the interior and exterior
orientation parameters are generally corrected during satellite
in-orbit geometric calibration and validation operation (Gruen
and Kocaman, 2008; Leprince
et al
., 2008; Wang
et al
., 2014;
Yastikli and Jacobsen, 2005). Greslou
et al
. (2008) have ana-
lyzed the Line of Sight (
LOS
) in the Earth Centered Earth Fixed
(
ECEF
) coordinate system for the apparent deflection caused
by the relative velocity of the satellite platform and target to
correct light aberration. The atmospheric refraction is rarely
considered and corrected because they are specific to each
acquisition location and information about the atmosphere.
In this paper, we focus on atmospheric refraction and analyze
how it can be better processed to reduce the geolocation error.
The atmospheric refraction changes the
LOS
propagation di-
rection of satellite imaging in-orbit, which results in the points
of detector, projection center of imaging payload, and imaged
object no longer following the rigorous collinear model. Several
pioneering researches have confirmed the effect of atmospheric
refraction on rigorous geometric model estimation. For exam-
ple, Gyer (1996), Wang (2007), and Wei (2006) have found the
atmospheric refraction will have an impact on aerial photo-
grammetry. While the aerial refraction correction formulas are
valid up to the normal aircraft flying height, they are delivering
the wrong results for a spaceborne image (Jacobsen, 2004). For
atmosphere refraction effects on a space image, Jacobsen (2004)
and Dowman (2012) gave the refraction correction formula
for the nadir space image based on the 1959
ARDC
standard
atmospheric. Noerdlinger (1999) targeted on
MODIS
satellite
data and researched the atmospheric refraction by developing
an analytical method to calculate the angle of the refraction
assuming a single layer of spherically symmetrical atmosphere.
Saastamoinen (1972) expressed a simple atmospheric refraction
angle calculation formula for radio ranging of low Earth orbit
satellites. Oh and Lee (2011) simply extended the Saastamoin-
en model to express the constant related to the object’s terrain
and satellite altitude. However, it rarely has the documentation
to study the procedure and method regarding the atmospheric
refraction correction for a high resolution optical satellite.
This study, based on a ray tracking physical model, rigor-
ously describes the
LOS
propagation direction of the satellite
imaging sensor to the Earth surface object through the atmo-
sphere. Meanwhile, the International Organization for Stan-
dardization (
ISO
) (1975) atmospheric model and the Owens
(1967) optical refraction index calculation algorithm are used
to calculate the atmospheric refraction index at any position.
In the following sections, first we will describe the
LOS
ray
tracking geometric algorithm, and then analyze the geoloca-
tion deviation introduced by atmospheric refraction. After
that, we will reveal how we can use the deviation to correct
the atmospheric refraction geolocation error in the
ECEF
coor-
dinate system. Compared to previous research, more reason-
able atmospheric refraction displacement estimation can be
achieved. Because we not only take the latitude and altitude
into account when calculating atmospheric refraction
Ming Yan, Chengyi Wang, and Jianglin Ma are with the Insti-
tute of Remote Sensing and Digital Earth, Chinese Academy of
Sciences, 20 Datun Road, Chaoyang District, Beijing, 100101,
P. R. China
).
Zhiyong Wang and Bingyang Yu are with the Twenty First
Century Aerospace Technology Co., Ltd., 26 Jiancaicheng East
Road, Haidian District, Beijing, 100096, P. R. China.
Photogrammetric Engineering & Remote Sensing
Vol. 82, No. 6, June 2016, pp. 427–435.
0099-1112/16/427–435
© 2016 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.82.6.427
