International Archives of the Photogrammetry, Remote Sensing 
x,=r -cosp, 
r,'sing, 
Il 
Y, =r-sinÿ-sinp+xXx,  SMP- Ve" cos 
Zi =r-cos@ 
Equation 2: Final transformation from the laser spherical 
coordinate frame to a laser cartesian coordinate 
frame 
If the laser remains static while collecting a scene it would be 
easy to determine the transformation to a mapping reference 
frame by measuring some control points. Once a global 
translation (X4, YoZi) and a rotation matrix Mf," are 
determined every laser point (X, YyZi) on the scene can be 
transformed by applying the same function (see equation 3). 
X Ar X, 
= m 
Y. us Y, * M, ! 
Em La Lin. Z, 
Equation 3: Transformation between the laser cartesian 
coordinate frame to a mapping cartesian 
coordinate frame (static case) 
This transformation can also be determined directly by the 
GPS/IMU subsystem using the formulas described in 
equation 4. 
According to the explanations in the previous paragraphs, the 
laser was rigidly mounted on the integration platform (figure 
5). Assuming that the GPS/IMU systems are capable to 
determine the orientation of the integration platform at any 
moment, the transfer of the reference frame from the 
GPS/IMU to the laser can be done as long as the laser data is 
synchronized with the GPS/IMU observations and the spatial 
transformation between the GPS/IMU frame and the laser 
frame is known, i.c. determined in a calibration procedure. 
   
    
Figure 5: Terrestrial Laser integrated in the Geomobil 
The laser labels the beginning of cach line with a precise 
internal clock. The synchronization is performed by relating 
the laser time system to the GPS time system. The laser 
and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
992 
internal clock can be reset by an external TTL signal. By 
using this possibility a modified PPS signal is 
pseudorandomly sent to the laser. After the survey, at the 
office, a software synchronizes the laser internal time system 
to a global GPS time system by comparing the 
pseudorandomly resets of the laser internal clock to the 
previously stored time at which the TTL signals were 
generated. Knowing the GPS time at the start of each line, 
the GPS time of every laser point is computed by adding the 
laser repetition period to the time of the previous laser point. 
The orientation subsystem of the Geomóbil allows a 
continuous determination of the transformation between the 
IMU reference frame to the mapping reference frame. Once 
every laser point is time labeled in GPS time the 
transformation between the laser reference frame to the 
mapping reference frame (e.g. WGS84) can be done 
according to equation 4 in two steps: a) transformation from 
the laser to the IMU reference frame and b) transformation 
from the IMU to the mapping reference frame. The first step 
comprises the offset determination between the laser and the 
IMU reference frame (p^ in equation 4) and the 
misalignment matrix between laser and the IMU reference 
* m equation 4). The offset and the misalignment 
matrix (y^and A^) remain constant as long as both systems 
M! g 
frame ( M 
(IMU and laser) are rigidly mounted on the integration 
platform and the platform does not have any distortion due to 
the stress. As explained in the next section these constant 
/alues are determined in a calibration survey. [n a second 
step the rotation matrix (M in equation 4) and the 
translation vector (Xgpsamus Y GPSAMU. Zapsamu in equation 4) 
are determined using the integration of the GPS/IMU 
observations. Notice that the rotation and translation matrix 
applied in the second step are not constant and keep varying 
during the survey. Therefore, for each laser point a different 
translation and rotation matrix will be derived from the 
computed trajectory. 
, : 
X. X GPS! IMU X, Y 
i y m h 7 zb 
Y: = Yops / IMU + M, M, Y, V V, 
Z. Z, 
Z aps / IMU 
Equation 4: Transformation between the laser cartesian 
coordinate frame to a mapping cartesian 
coordinate frame (kinematic case) 
The use of integrated GPS/IMU data to directly orient laser 
data has the advantage that the transformation between the 
e 
local laser reference frame and the mapping reference frame 
is known at any moment (as far as the laser is synchronized), 
independently if the laser is collecting data in a static mode 
or in kinematic mode. Therefore, the laser can be used as à 
pushbroom sensor while fixing the scan angle and sweeping 
the scene with profiles while the vehicle is in movement. 
3.1 Calibration 
The offset and the misalignment matrix are determined by 
applying equation 4 to a set of static laser scenes where 
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