The Effect of Terrestrial Surface Slope and
Roughness on Laser Footprint Geolocation Error
for Spaceborne Laser Altimeter
Zhou Hui, Chen Yuwei, Ma Yue, Li Song, Hyyppä Juha, and Pei Ling
Abstract
The quality of spaceborne laser altimeter observation mainly
depends on the geolocation accuracy of laser footprint. To
thoroughly analyze the footprint geolocation errors, math-
ematical models of Root-Mean-Square Error (
RMSE
) of laser
footprint geolocation are established based on footprint geo-
location procedure and principle of error propagation. Taking
Geoscience Laser Altimeter System (
GLAS
) as an example,
the influences of surface slope and roughness on the
RMSE
of
laser footprint geolocation (
LFG
) are simulated. The simula-
tion results for nine representative terrains indicate that the
horizontal errors are constant of 5.86 meters that mainly
caused by instrument mounting errors, laser pointing errors,
and platform attitude errors; while the vertical error increases
from 0.07 m to 2.49 m, which is primarily contributed by the
laser pointing error. To validate the proposed mathematical
model, 20 reference
LFG
differences are computed by the dif-
ferences of original geolocation of
GLAS
and refined footprint
geolocation based on a waveform matching method with
coincident airborne Light Detection and Ranging (lidar) data.
The validated results prove that the
RMSE
models of laser foot-
print geolocation are applicable in evaluating performance
and sensor error allocations of spaceborne laser altimeter.
Introduction
As a kind of remote sensing instrument, spaceborne laser
altimeter is an active sensing modality in the application of
measuring the topography of Earth, Moon, and planets [1].
The laser altimeter determines the range from the instru-
ment to the ground surface by measuring the time of flight of
transmitted laser pulses [2]. Combined with position derived
from a positioning system and attitude stemmed from a star
camera and gyroscopes, the geolocation of laser footprint on
the ground illuminated by a laser pulse can be determined
[3]. The series of such footprint geolocations with the move-
ment of the spacecraft generates a digital elevation model
(
DEM
) in global scale. A variety of spaceborne laser altimeters
implemented the measurements for several planets and as-
teroids include Clementine Light Detection and Radar (lidar)
[4], Mars orbiter laser altimeter [5], Mercury Laser Altimeter
[6], CE-series laser altimeter [7], SELENE Laser altimeter [8],
Lunar orbiter laser altimeter [9], Bepicolombo laser altimeter
[10]. Obtaining high-accuracy planetary
DEM
is one of signifi-
cant tasks for spaceborne laser altimeter.
The Geoscience Laser Altimeter System (
GLAS
) onboard
the Ice, Cloud, and land Elevation Satellite (
ICESat
) is the
first spaceborne earth observing system using laser pulse
to measure the ice-sheet topography, sea ice freeboard, and
global vegetation, eventually, to evaluate their influence on
the Earth environment [11]. Different from other spaceborne
laser altimeters, the
GLAS
records all raw waveforms reflected
from the Earth’s surface with time resolution of 1 ns (changed
to 4 ns since phase L3A) [12]. The time-of-flight is deter-
mined by using Gaussian fitting of recorded waveforms in
the post-processing way, and the timing accuracy is several
times more precise than using threshold crossing times. The
National Snow and Ice Data Center (
NSIDC
) has distributed 15
Level-1 and Level-2 data products from the
GLAS
that have
been applied in the researches of oceanography, geodynamics,
geomorphology, ecology, and glaciology [13;14; 15].
One of significant objectives of spaceborne laser altimeter
is to generate global-scale
DEMs
, and its accuracy is deter-
mined by the precision of laser footprint geolocation (
LFG
).
Hence,
LFG
errors become one of key indicators to evaluate the
measurements of the spaceborne laser altimeters. Normally,
the
LFG
errors consist of random errors and systematic errors,
which are influenced by many factors such as range error,
laser pointing error, and spaceborne platform errors. There are
two primary evaluation approaches on
LFG
errors: (1) calculat-
ing the difference between theoretical footprint and collected
footprint based on a geolocation equation; and (2) establishing
a mathematical model of
LFG
error.
Many researchers utilize the first method to estimate and
mitigate the systematic errors of
LFG
based on the natural
surface [16], the attitude maneuvering [17] and the direct foot-
print detection [18-19]. Filin provided a calibration algorithm
over general natural topography to recover the systematic
errors [16]. Luthcke presented a range-residual calibration
method depended on the commanded spacecraft attitude
Zhou Hui, Ma Yue, and Li Song are with the Electronic
Information School, Wuhan University, Geospatial
Information Collaborative Innovation Center, Luojia Hill,
Wuchang District, Wuhan, Hubei Province, China, 430072
(
).
Chen Yuwei is with the Department of Remote Sensing and
Photogrammetry, Finnish Geospatial Research Institute,
Geodeetinrinne 2, Kirkkonummi, Uusimaa Province, Finland,
02431; and with the Key Laboratory of Quantitative Remote
Sensing Information Technology, Chinese Academy of
Sciences (CAS), Haidian District,Beijing, China,100094.
Hyyppä Juha is with the Department of Remote Sensing
and Photogrammetry, Finnish Geospatial Research Institute,
Geodeetinrinne 2, Kirkkonummi, Uusimaa Province, Finland,
02431.
Pei Ling is with Shanghai Key Laboratory of Navigation and
Location-based Services, School of Electronic Information
and Electrical Engineering, Shanghai Jiao Tong University,
Shanghai, China, 200240.
Photogrammetric Engineering & Remote Sensing
Vol. 84, No. 10, October 2018, pp. 647–656.
0099-1112/18/647–656
© 2018 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.84.10.647
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
October 2018
647
