measured offset of [-1.378, 0.411, 1.566] is found using a 
theodolite and tape measure. 
The next rotation uses the INS mounting biases (Ar, Ap, AA) to 
transform the laser vector from the local aircraft reference 
system into the local INS reference frame with axes defined by 
the roll, pitch, and heading axes of the INS. The INS mounting 
biases account for the angular differences between the aircraft 
body system and the roll, pitch and yaw axes. This step also 
accounts for the difference between local vertical and the 
direction perpendicular to the geodetic ellipsoid (WGS-84). 
SOAR reports a -0.30 degree bias in both pitch and roll. 
Because these angles are small, the SOAR values are simply 
added to the attitude angles reported by the INS. 
The last rotation of this series transforms the laser vector from 
the INS reference from to the local-level reference frame using 
the attitude of the aircraft (-,p,h). The local-level reference 
frame is an Earth-tangential reference system centered at the 
GPS antenna. The z-axis is perpendicular to the WGS-84 
ellipsoid and points downward. The x-axis lies along the 
intersection of the local GPS meridian and a plane parallel with 
the tangent plane to the ellipsoid (i.e., points north). The y-axis 
completes the right hand system. 
4.3. Transformation from local-level reference system to 
WGS-84 Cartesian system 
The laser vector from the GPS antenna to the laser spot on the 
snow surface is transformed into the WGS-84 global Cartesian 
system. Rotations for the latitude, R , (lat GPS 2), and 
longitude, R_(—lon € 5 ) , of the aircraft are performed to align 
the local-level reference frame axes with the WGS-84 axes. 
The final position of the laser footprint is computed by adding 
the laser vector to the vector recorded by the GPS on board the 
aircraft. Because the GPS position has uncertainties, some 
authors (e.g., Lindenberger) use an adjustable parameter 
(ap$PS) to remove any GPS bias.  Lindenberger, (1993), 
calculated this parameter by surveying a rough but stable 
surface before and after each flight. Ice sheet surfaces are too 
flat and not stable enough for this kind of calibration. Other 
researchers use an adjustment scheme based on the analysis of 
large set of cross-overs to remove any GPS bias. Our data set 
does not have enough flights and cross-overs to take advantage 
of this method either. For these reasons, 52^ — is assumed to 
be zero for this study. After applying simplifications Equation 
] becomes: 
Py (X.Y.Z) - py - R, Clon? 5). R, [uen RE J 
GPS. 
2 LFP 0 
R(r+Ar, p+Ap,h+Ah)}| y3PSLFP | R(dp, dr,0)-| 0 
gree a + Arm + Miss 
(Eqn.2) 
  
  
  
  
     
   
  
  
  
  
  
  
  
   
     
   
   
    
  
   
      
     
    
    
      
    
     
   
    
    
   
   
    
    
    
     
       
    
   
  
    
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
5. CALIBRATION AND VALIDATION 
5.1. Laser range calibration 
Two skiways next to the Siple Dome base camp were surveyed 
using both snowmobile-mounted GPS and laser altimetry in 
mid-December, 1997 (Figs. 3, 4, and 5). 
  
(Kr) : 
      
   
   
0 Aircrage S 
"Aa 
S 
-2 
-4 
-6 
Skidoo SPS surveys = 
  
Laser altimetry survèys 
-8 ; Apt isl E s | 
-4 2 0 2 4 6 (km) 
  
Fig. 3. 
Antarctica. 
Laser altimetry calibration surveys at Siple Dome, West 
The snowmobile (also referred to as skidoo) surveys are used to 
produce a reliable surface profile for comparison with laser 
derived elevations. A 40.35 m bias was found for the laser 
elevations. This bias is due to a systematic timing error in laser 
ranging and is added to every laser range during processing. 
To determine this bias the data are converted into a local, 
Earth-tangential reference system where the x-axis points to 
true North, z-axis points toward the center of the Earth, and the 
y-axis completes a right-hand system. The position of the GPS 
base station antenna mounted on the SOAR tent was selected as 
the origin (pg X Y,2)). Equation 3 describes the 
transformation and figures 3, 4 and 5 show how the reference 
system is used. 
BL? oc ; Vice : Ze) = R, (lat SO JT / 2) : R, (og 623 i 
(Ix Y zy pre y zy (Eqn.3) 
5.2. Laser mounting biases 
Due to mounting errors, the laser is not perfectly aligned with 
the aircraft’s roll and pitch axes, as defined by the INS. The 
laser mounting bias is defined as the angular difference 
between the aircraft body and the laser axes. The estimated 
laser mounting bias is -1.2 degrees in pitch and -0.3 degrees in 
roll during the 1997/98 field season (SOAR field notes). Pitch 
and roll maneuvers over a relatively flat test field are used to 
check these values. The deformed surface shown in Figure 5 is 
the result of a laser survey where no mounting bias corrections 
were used. By changing dr and dp to minimize the surface 
   
International 
deformation the mount 
the initial estimate of - 
roll was confirmed by u 
rpg ge 
um 
  
  
-40L 
Fig. 4. Surface derived : 
snowmobile-mounted GPS 
5.3. System Accura 
After correction of rang 
performed well over : 
Skiwayl show a 2.8 cn 
The bias is attributed to 
lines were approximate 
measurement of surface 
decimeter accuracy w 
elevations were compa 
snowmobile surveys. 
B UU TUAE 
  
  
Fig. 5. Comparison of me 
with snowmobile-mounted 
profiles are derived from tk 
of the laser mounting bias. 
about 8 degrees off nadir.