International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
T from the coordinate system of HISS to a world coordinate 
system is calculated, where the origin of HISS is at the center of 
GPS antenna. On the other hand, a transformation matrix La 
from the coordinate system of LD-A and a transformation 
matrix 7, from the coordinate system of line camera to the 
coordinate system of HISS are calculated based on the exterior 
calibration parameters. A laser point with a range distance of r 
at the angle of a on scanning plan is geo-referenced to the 
world coordinate system as follow, 
(x.v.2]l) = Ty Ty, (=r sin æ,0,-r cos 1)” (1) 
In the case of line image, focus length (/) of the line 
camera as well as a formula defining the relationship between 
the index of an image pixel (/) and its projection angle (o) 
towards the projection axis is obtained from  sensor's 
specification. 
® = 2xarcsin((h — 0)/2/ f) (2) 
where o is the image center, which is obtained by doing 
physical measurement using sample images. Using formula 2, 
projection vector of the image pixel (h) is geo-referenced to the 
world coordinate system as follows, 
(x, p,2,0)" - T, T, (0,-cosæ,sin w,0" (3) 
An example of line images, a view of geo-referenced laser 
points, as well as a projection of laser points onto line images is 
shown in Figure 4. 
EEE 
Tie Vee Zoom (Pm 
  
  
  
Figure 4. An example of the geo-referenced laser points and line 
images 
  
Figure 5. A motivational example of erroneous geo-referencing 
496 
  
P p2 
5 1 Mes 
vo 
= PLT a 
o7 
  
Figure 6. A set of tie points on building corners 
3. RECTIFICATION OF GPS/INS PARAMETERS 
In the followings, we will first introduce the method for 
rectifying GPS/INS parameters at each updates using a number 
of ground truths. The method for obtaining the true value of 
position and orientation parameters at a number of GPS/INS 
updates is addressed subsequently. 
3.1 Rectification using a number of ground truths 
Let (9.50,,0,) denote the xyz coordinates of vehicle position, 
(w,y,x) denote the roll, pitch and yaw angles of vehicle 
orientation, transformation from HISS to the world coordinate 
system can be formulated as follows. 
T. = Shv-R, - R, +R, (4) 
where 
10. 0 o. cosk (= sink 0.0 
0-10 0} sink cosx #00} 
Shv = “| R= 
00 4-9. 0 0 1 0 
0520 0 | = 0 a | 
cosy 0 —siny O0 | 0 0 0 
0 l 0 0p 0 coso -sino 0 
R,=| | R= ; 
siny 0 cosy O0 0 sino cosw 0 
0 0 0 I 0 — 9 0 I 
In this research, four parameters at each GPS/INS update, 
ie. o 20.20 of vehicle position andk of vehicle orientation, 
x2 yt 
are corrected, while pitch and roll angles remain as they are, as 
the errors inside are not so obvious comparing to other 
parameters. Let 
p-Q,yz4) =R,RT,(-rsina,0,~rcosa,l) 6) 
denote the calculations on the parameters that will not be 
adjusted. Geo-referencing of a laser point p = (x, y,z,1)" can 
be re-formularized as follows, 
p=Shv-R_-p (6) 
More specifically, 
P, = p, *cosk— p, *sink+o, 
(7) 
P, = P, *sink + p, *cosk+o, 
p.e pte, 
Figure 5 shows a motivational example of erroneous geo- 
referencing, where the denotation of 7; is simplified to 7, 
g 
representing the transformation matrix that is composed of the 
position and orientation parameters at GPS/INS update #. 7° 
denotes the true value of 7, 2, =T" T, is the vehicle's 
relative motion (relative transformation) from GPS/INS update 
#i to #. Suppose the true transformation matrixes at the 
GPS/INS updates #s and #e are known, where D-T.T' eT. 
Inte 
  
and 
pait 
glol 
con 
iter 
for 
  
  
acci 
gro) 
rep! 
#21 
GP: 
Alg 
nun 
Inp 
Inp 
Out 
GPS 
para 
vert 
Le. 
assi 
the 
grou 
para 
lase 
sam