a, CA, 9-11 Nov. 1999 
because phase ambiguities were 
of the flight. 
the GPSurvey processing, one 
'TAR (GPS Inferred Trajectories 
tesy of John Sonntag, EG & G). 
1aving a maximum difference of 
in the vertical. 
  
(a) 
     
outlier 
  
  
  
-282.352 -282.348 
X (km) 
sue (b) 
15 
  
  
4 8 
distance (m) 
horizontal position of the Down-B 
ccording to the day of the year that 
a and b, were conducted on days 14 
vest fit through the data calculated 
The X and Y coordinates are polar 
ch Down-B position plotted versus 
is the mean, elevation calculated 
. Error bars are based on a 1-sigma 
liode pumped Nd:YAG pulsed 
the near infrared domain (1064 
travel time of a laser pulse from 
ice and back to the receiver. To 
' transmitted and the received 
rangefinder uses 50% constant 
imer starts at some consistent 
. Each timing event ends when 
aches half of its maximum 
X "range walk" correction is 
  
   
International Archíves of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
eliminated. The manufacturer reports a single pulse accuracy 
of 0.1m for distances up to 1.7 km. The ranger records at 500 
Hz and 64 pulses are averaged to yield one range. The beam 
divergence was set for 4.5 mrad, producing a footprint with 1.5 
meter diameter from the 300 m nominal flight height. This 
results in one average elevation for every 1.5 by 8 m area when 
the aircraft flies at 300-m terrain clearance. 
3.4 Aircraft attitude 
The attitude of the aircraft, that is the heading, pitch, and roll 
angles determine the pointing direction of the laser. These 
angles are measured with a laser gyroscope that is part of the 
Litton Aero Products LTN-92 INS unit. The INS has a quoted 
accuracy of 0.05° in all three angles (Vaughn et al., 1996), 
which translates to less than a 0.06 m error in calculated surface 
elevations when the aircraft is flying at less than 300 meters 
terrain clearance and the off-nadir pointing angles are less than 
15°. These angles are not exceeded during survey missions, so 
the measured attitude contributes very little to the overall error 
budget. 
3.5 System timing 
Each data collecting system operates independently and not in 
synchrony with the others. Universal Coordinated Time (UTC) 
is used as the standard to which all other times are corrected. 
The laser and INS measurements are tagged by a counter time 
that is corrected to UTC using information provided by the 
GPS time code generator. An additional correction is required 
for the: individual attitude parameters, because the INS only 
records one angle at a time. The manufacturer specifies that 
these time lags are as follows: 110 ms in true heading, 60 ms in 
pitch and 50 ms in roll for the LTN-92 (Vaughn et al., 1996). 
lt is possible to check whether these values are correct using 
pitch and roll maneuvers over a flat test field because timing 
offsets cause deformation of the measured surface when off- 
nadir angles are large. When performed, this test yielded 
slightly different time lags of 60 ms in roll and 85 ms in pitch. 
The measured time lags are preferred over the reported ones. 
The final step in correlating the data streams is to interpolate 
the INS and GPS data for the times when laser ranges have 
been recorded. Interpolation is necessary because the GPS data 
are recorded at 2 Hz, while laser measurements are recorded 
every at 500/64 Hz, and INS measurements at 8 Hz. 
4. COMPUTATION OF LASER FOOTPRINT 
The laser range recorded during the flight is a slant range to the 
surface. To compute the position of the laser footprint in a 
global, geographic coordinate system, the laser range, aircraft 
position, and aircraft attitude are combined according to the 
Scheme described in Lindenberger (1993), Vaughan et al., 
(1996), and Ridgway et al., (1997). Equation 1 sums up the 
procedure, which includes a series of coordinate 
transformations starting at a local reference system centered at 
the laser firing point (indicated subscript L) and ending in the 
WGS-84 Cartesian reference frame (indicated subscript W). 
Rotations are indicated by R (x, y, or z subscripts indicate a 
rotation about a specific axis). 
LPF GPS. aps aa GPS. GPS Fer 
Py (X,Y,Z)= Py + db +R_( lon ) wa + ; R(r, p,h) 
GPSLFP 
A 0 
R(Ar, Ap, Ah) | GP SLPP 4 Rp, qp). 0 
GPS.LFP LFP,S i 
ZA 7 + Arum t Arias 
(Eqn. 1) 
4.1. Range measurement corrections 
The laser ranger is mounted inside the aircraft pointing towards 
nadir. The ranger measures the distance (rn ? 8j between the 
Laser Firing Point (LFP) and the snow surface (S) from points 
along the flight trajectory. The measured laser range is 
corrected for atmospheric delay and a range bias: 
e The atmospheric correction (ar, ) accounts for the 
reduced speed of light and refraction in the atmosphere. It 
reduces the measured range by approximately 2 cm for 
every 100 m of altitude. The computation of this 
correction is taken from Vaughn et al. (1996), Ridgway et 
al. (1997), and Marini and Murray (1973). Pressure, 
temperature and water vapor are extrapolated at the 
aircraft location from data collected by automatic weather 
stations at Siple Dome and on Ice Stream C. The 
meteorological data are collected and distributed courtesy 
of John Stearns of the Automatic Weather Station Project 
(Stearns, via internet) 
* A range bias (Ar, )of 0.35 m is added to each range 
measurement. This bias is determined by comparing 
surface elevations derived using laser altimetry to 
elevations derived using precise surveying methods on the 
ground (see details in Sect. 5.1). The bias is most likely 
due to a constant lag in the timing of the laser pulse, 
although this has yet to be proven and is currently being 
investigated. 
4.2. Transformation from local laser reference system to 
local Earth tangent reference system 
The corrected laser range vector [0,0, d dulce 1! 
atm bias 
is transformed into a local aircraft reference system (indicated 
subscript A) centered at the GPS antenna. The aircraft 
reference system is defined using several symmetrical *hard' 
points on the aircraft (joists, flap indicators, and seats) whose 
positions are measured using a theodolite. One axis runs the 
length of the aircraft between symmetric points. A second axis 
is perpendicular to the first axis and is aligned with the aircraft 
wings. The third axis is vertical and perpendicular to the other 
two. This transformation is carried out by rotating the laser 
range vector by the laser mounting bias (dp,dr,0)(see Section 
5.2). The offset vector between the laser firing point and the 
GPS antenna (brum vim nin is then added. The 
’