international Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
2. Initialisation with resection, which 
demands the existence of sufficient GCPs 
at the beginning of the survey. 
In the first case, open sky for the GPS is vital. The 
GPS/INS (Grewal et al., 2000) gives us the position 
and attitude of the IMU, which — after applying the 
lever arm and angles transformation — yield the EOP 
of the two cameras. 
As for the second case, at least three GCPs are 
required for the determination of the position and 
attitude of the two cameras by resection. 
After the initialisation, intersection starts to map 
(more) features. The vehicle moves and captures a 
pair of images, and so on and so forth. The flowchart 
of this procedure is laid out in Figure (4). Its 
algorithm will be discussed in the following. 
  
Known initial 
position 
  
  
  
Initialisation 
Capture photos 
  
  
Measure features’ coordinates 
in image (x, y) and compute 
their X, Y, Z by intersection 
  
  
  
  
  
  
Move "s^ seconds 
and capture photos 
  
  
  
  
Measure features’ coordinates in image 
(x, y) of known X, Y, Z. Compute Xo, 
Yo, Zo. ©, @. x of the images by 
resection 
  
  
  
  
  
Measure features’ coordinates 
in image (x, y) and compute 
their X, Y, Z by intersection 
  
  
  
  
Figure 4: Flowchart of the Photogrammetric SLAM 
To simplify the notation, we suppose that at each 
image-acquisition epoch, 5 features are mapped. In 
this way, the vectors and matrices used in the LSA 
are (L/R = Left/Right images): 
Vectors and matrices headed by a prime (e.g., X') 
refer to the resection and those headed by two primes 
(e.g., X' ) refer to the intersection. 
Resection unknowns: 
ôx(L,r) = [8X0 8Y, 8Z, 680 689 6k] (n) 
Intersection unknowns: 
ax <X; 0 AA 3%. ov Ww 
  
Resection measurements: 
; T 
yiLr) = [xi Yeon ZI 
Intersection measurements: 
ii 
Y[ucyxü Xu Yu 759, 9x; 
x 
XRi Yni Xno Yno ZR0 OR On Kn] 
Resection first design matrix: 
A T 
Nw =| 28 x (L.R) 
ox’ ox’ 
Intersection first design matrix: 
Ae fut ev 
Ox" Ox" 
Resection second design matrix: 
T 
; oF(x) oF(y) 
B e e——— A LR 
(RTI y (L.R) 
Intersection second design matrix: 
Starting at epoch k with known coordinates, 
intersection takes over: 
ôx{ - NL UR (2) 
LA „T( n ur s! " 
Ne = Ak By Cy Bi Ar (3) 
" aT "a nT = " 
Uk = Ar (b. cts B; | Wi (4) 
Cia. defined in Equations 12 and 13, is the 
measurements co-variance matrix. wy is the 
misclosure vector in LSA. The elements of xj are 
used as GCPs at epoch k +7 to solve resection: 
  
  
  
ôx; i = NC! Ur 5) 
kd ALK] py (5 
f rt f "f 11. A , 
Nau A OB aC BU] Aya]. (6) 
(LR) 
un = A! (5, CC. BIT , 7 
k+1 = Ares (Burt CynsrBrst) Wand! ) (7) 
(LR) 
C. , defined in Equation 8, is the measurements 
y/k+1 
co-variance matrix. The elements of xk ali r) are 
used in a stereo-model at epoch k + 7 to map n new 
features, xp, - These m new features at epoch 
   
   
   
  
    
   
  
  
   
  
  
   
    
    
   
    
    
  
   
  
  
  
  
  
  
  
   
  
  
  
  
    
  
  
  
  
   
  
  
   
   
  
     
   
  
  
     
Internati 
1 
y/k-