4-5-4 
G),, (fi, 5 
Ci) 0 . (ft, K, 6 CO , 6 <j) , 6 K 
Strapdown 
INS 
Mechanization 
X,7, R(o) ,(p)^ 
Aerotrianguiation 
estimation of 
- INS errors 
- System calibration 
I A A I 
GPS 
Remote phase , > GPS data 
doppler, 
Master P seudoran 9 e > processing 
==LJ 
R(w . <p) , k 
^GPS’ V GPS 
Y* v 
GPS ,V GPS 
matcSina 
Image data 9 > Coplanarity 
> Offset correction < 
A 
Spatial offset 
Exterior 
> orientation 
X, R(co , <p) , k 
Ground control > 
measurement 
Collinearity 
Figure 1 : Workflow of georeferencing. 
To take the different error terms into account, the standard 
collinearity equation 
X 171 = Xg 1 + A R™ • x 9 
(2) 
where 
coordinates of perspective centre 
denoted in the mapping frame m 
coordinates of object points given in 
the mapping frame m 
rotation matrix from image p to map 
ping frame m 
coordinates of image point given in 
image frame p 
scaling factor 
has to be modified as follows: 
X m = it™ + Rr • [A R™ • & + AX b am - a4 ps ] (3) 
where 
K= ( 
'5) 
coordinates of the phase centre of 
V ^0 ) 
the GPS antenna denoted in map 
X m = [ 
< X\ 
ping frame m 
Y 
coordinates of object points given in 
\ 
\ z ) 
the mapping frame m 
( AXcam \ 
AYcam offset between INS and perspective 
AZcam ) centre of imaging sensor given in 
body frame 6 
/ AXgps \ 
AXq PS = AV G ps offset between GPS antenna and 
\ AZqps / perspective centre of imaging sen 
sor given in body frame b 
R™ = R™(u, <p,fi) rotation matrix from INS body 6 to 
mapping frame m 
r£ = R b (5u,6tp, 5k) rotation matrix from camera frame p 
to INS body frame 6 
coordinates of image point given in 
image frame p 
A 
scaling factor 
Equation 3 gives the complete mathematical model for the di 
rect georeferencing of the image data. The different error states 
mentioned in section 3.1 are integrated in the extended collinear 
ity equation. Setting up this equation for each ground control 
point or tie point allows the estimation of the unknown INS errors 
(^0)y^o,^Oi^iji K i an< -l misalignment 6uj,6ip,6k between 
the INS body b and image coordinate frame p. After estimating 
the unknowns in the combined aerial triangulation, the results are 
fed back to the mechanization to improve the starting values sig 
nificantly. Using these corrected parameters the mechanization of 
the INS data is repeated, and the improved exterior orientations 
are used as input for a second adjustment process. Therefore, the 
combined evaluation of GPS, INS and image data consists of two 
major parts: The strap-down INS mechanization and the subse 
quent aerotrianguiation for error estimation. The whole process is 
performed iteratively until the final solution is reached.