International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
ANALYSIS OF SATELLITE LASER ALTIMETRY RANGE MEASUREMENTS OVER LAND 
TOPOGRAPHY USING GENERALIZED ATTITUDE PARAMETER EXTRACTION 
J. R. Ridgway, J.B. Minster 
Institute of Geophysics and Planetary Physics 
University of California, San Diego 
U.S.A. 
ridgway@spot.ucsd.edu, jbminster@ucsd.edu 
KEY WORDS: Laser Altimetry, Satellite, Topography, Attitude, Pointing 
ABSTRACT 
Two new laser altimeter satellites are being launched by NASA in the near future: the ICESat (Ice, Clouds, Elevation) satellite and 
the VCL (Vegetation Canopy Lidar) satellite. Although each satellite has a different emphasis (ICESat concentrating on ice sheets 
and VCL on vegetation), both will fly over land for a large portion of their orbit. The alignment of the laser is set prior to launch; 
however, forces on lift-off may cause a mis-alignment. Traditionally these “attitude biases” in aircraft are calculated using dedicated 
roll/pitch maneuvers over a flat surface such as a lake or the ocean. An alternative method to this procedure is the measurement of 
topography along the satellite ground-track and comparison of the measured profile to a well-known “truth grid”. The residual 
topographic signal would then be analyzed and related to spacecraft attitude, range and other mis-alignment sources. We propose an 
attitude extraction approach whereby any given measured profile is related to the truth grid by a laser pointing vector. In addition, 
there may exist orbit and timing errors. The determination of these parameters involves a search for a minimum in a multi-variable 
space. For this study, we simulate roll and pitch errors and use a systematic parameter search to extract them from the topographic 
data. For more extensive parameter spaces, an evolutionary algorithm will be needed. We investigate the tradeoff between orbit and 
pointing errors and determine that use of long profiles in latitude and ascending/descending tracks can separate these sources. We 
examine how the accuracy of the truth grid relates to the parameter estimation. We also examine the question of whether smooth, 
monotonic topography or rougher wide-band topography is more suitable in calibrating the satellite laser. 
simultaneously illuminates the grid with its own laser and takes 
: a picture of the satellites laser spots with a CCD detector. 
1. INTRODUCTION 
The use of sloping land topography to determine laser pointing 
biases is an alternate approach to the methods described above. 
This relies on the surface over which the satellite flies to be 
Two new laser altimeter satellites are being launched by NASA 
in the near future: the ICESat (Ice,Clouds, Elevation) satellite 
and the VCL (Vegetation Canopy Lidar) satellite. Although 
each satellite has a different emphasis (ICESat concentrating on 
ice sheets and VCL concentrating on vegetation canopies), 
both will fly over land for a large portion of their orbit. The 
alignment of the laser is precisely set prior to launch; however, 
mechanical forces on lift-off may cause a mis-alignment, and 
other effects (mainly thermal) may cause a time-dependent 
variation of attitude mis-alignments during the life of the 
mission. Thus in-flight methods to calibrate the attitude errors 
are necessary. 
very well known and used as “ground truth”. The satellite laser 
produces a height profile which is compared to the ground truth 
grid, and a misfit function is calculated using some standard 
technique such as r.m.s. error. The misfit is related to satellite 
pointing/timing/location errors, and an optimal error parameter 
set is found, such that the misfit is minimized. This paper deals 
with some aspects of this “ground truth” calibration method. 
2. LASER POINTING GEOMETRY 
One approach by Rowlands et al. (1999) for the Mars Observer Given a satellite with a nadir-pointing laser, its roll, pitch and 
  
  
Laser Altimeter data utilizes crossovers which are modeled for 
short topographic segments by polynomials. An a priori 
knowledge of the topographic surface is not needed for this 
procedure. Another technique involves a flat surface such as a 
lake or the ocean, over which the vehicle performs dedicated 
roll/pitch maneuvers. Simulations by Luthcke et al. (1999) 
show that, if successful, this may be able to be used to extract 
pointing biased errors in roll, pitch and yaw to about 1 arc- 
second accuracy. A third approach is an experiment using 
corner cube reflectors under the satellite track (Schutz, 1998). 
As the satellite flies over this known grid, an aircraft 
yaw combine to mis-point the laser. This pointing vector can 
be described in the satellite’s along-track (x), cross-track (y), 
and down (z) coordinate system (also called the Satellite Body- 
Fixed system). 
p=ax+by+cz. (1) 
The pointing vector p is a unit vector, so it may be described 
with only 2 parameters: a heading vs. the satellite's along-track