«1 2004 
   
, 
Cyt = 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, 
4 
k+1, xy44, are used at epoch k+2 to compute 
Xp2 - The procedure continues until the end of the 
survey. 
It is important to note that not only x’ and x” are 
used from one epoch to its successive, but also the 
variances and co-variances via the matrices C, , 
It pis " 
C, Cy. and Cj. 
Considering firstly the. Cy4,.9, it is given together 
with the initial camera's position at epoch k «0. As 
stated before, this is then used to find the object 
coordinates of n new features by intersection in 
order to compute the EOP of the two cameras at 
epoch k+/=/. 
Secondly, considering the C1,,,, (measurements co- 
variance for the resection), it is computed as: 
  
  
  
  
  
[ photo 
Y 0 ineoi) 0 
object ; 
rat + «+ jobject 
0 e 0 ZiZal 
k+l 
: : : photo 
0 0 cr 0 
; bject 5 [object 
à Pu su. 0 = 
i RA key "list 
(8) 
5|photo . t : 
where Xf is the 2x2 co-variance matrix of the 
  
: ,2 ‚object vu Iobjeet 
photo-coordinates. X; | and ZX; , on the 
kl "Hed 
other hand, are the 3x3 co-variance matrix of 
feature i-th and j-th object coordinates. These 
will be taken from the output of the intersection of 
epoch k , specifically from matrix Cy, that is equal 
to: 
-l 
[d n—1 nT " " oT rl " 
Cyr =Nk [Ai b, cts Bj | A! | 
  
  
  
  
7 
bject San 
»2{°° Kan Object 
Y Y), k (9) 
biect » | object 
Yl, eus Du pme 
k 
where 
2 
; Ox OX, 9X Sx; 07; 
,9 [object „object : 2 
abr qu SON, TN nn fa 
2 
67; 9X, 97i Yi 97. 
(10) 
  
     
   
  
   
     
   
    
   
  
   
  
  
  
  
   
  
  
  
  
   
    
   
    
   
    
  
  
   
   
   
   
  
and 
Ox.Ox, Ox.Ov, Ox.0O7. 
sry object ,|object he "M Mr ifi 
vila nrc, TI Ovx, 0207, 9587, 
07,9%, 67/8 Y 92,97 
(11) 
As for Ci, (measurements co-variance used in 
the intersection), it is computed in a similar way as 
follows: 
  
  
hoto 
2|P 
"n i 0 
CıLyk+1 = 5 (12) 
0 ST i 
i L_EOP iH 
hoto 
2|? 
: 0 
€ a 1 ] 3 
Ry/k+1 = À (13) 
n 
0 ER cor] 
L = k+ 
where igor | and, Ir For are the 
k+I = k+l 
measurement co-variance matrices of the Left and 
Right EOP that are needed to compute new 7 
features at epoch k+/. These are found from the 
output of the resection epoch k+/ as follows 
{i=LR¥ 
v2 pti i re 
X bor, = Cher = Nir 
x (14) 
: "T , 1 ‚FT = f 
= [Aja BC Bi | As | 
In short, the co-variance transportability can be 
described as: 
  
  
C44 7 Given accuracies of the GCPs = C, 
Ck+1 = Computed accuracies of the EOP 
Ci 8 Given accuracies of the EOP 2 Cz, 
y/k+1 x/k-+1 
Ciy41* Computed accuracies of epoch's (k+2) GCPs 
  
The combination of Equations 1 to 14 into a one step 
approach is called “Bundle Adjustment”. The one 
step approach is pursued when there is no other 
technique to determine the EOP, which is not the case 
here. In addition to the two cameras, an IMU will 
also provide the EOP. After incorporating the IMU 
data, the analysis above changes as follows. The 
output of the resection at the epoch X becomes 
external measurements for the INS Kalman Filter 
(KF) (Kalman, 1960). After obtaining the corrections 
of the navigation parameters from the KF, 
Part BS. Istanbul 2004