Aluir Dal Poz 
  
Ih .Tix + DL» ly + I54.nz 
as FA AZ 
(8) 
F2; x + y .Ny + 2 MZ 
2s 
bref 2 
where, all elements were already explained. 
The unknowns of photogrammetric model are the exterior orientation parameters (KE, W, Xo Yos Zo). These 
elements are the components of the vector of parameters or the state vector (xx), which is estimated by an iterative 
process using equation 9 (Jazwinski, 1970): 
where, 
e x, is the vector of parameters estimated using a previous correspondence; 
e handh,,, are variables for controlling the iterative process and are estimates for x, in the iterations i and i+1, 
respectively; in the first iteration h, 2X; 
® kk n = Pp1. Mk; hi T( Mk; hi Pi. Mk; hi T RY’ is the Kalman gain matrix; 
e  PB,,isthe covariance matrix of xy; and 
Ih(x:) 
e Mr: hi = q 
Xe x= hi 
  
is the partial derivative matrix computed in the point h;. 
The convergence of the iterative process is reached when Ih, , - hl is smaller than a predefined threshold. At this point, the 
state vector is updated with the last value of the iterative variable h, , and the state covariance matrix (Py) is estimated by 
equation (Jazwinski, 1970): 
PieT- kk; x . Mk x Pa (I- Kk. Mix ) e Kk Rye. Kom | (10) 
where, Mx; x. is computed at the linearization point x,= h, , and kk; x is computed by using Mk; x . 
The predicted residual (vy) and its covariance matrix (c,) are computed using equations 11 and 12: 
Vy Zy - Mk; x Xk-1 (1 1) 
a= Mk: x Pur. Mix T+ Ry (12) 
Remembering that the correspondence being analyzed is (fi, F,) and that the observations in the filtering are the angular (a or 
a*) and linear (b or b*) parameters of fj, the data snooping statistical test uses the following values: 
Na/a* pp 
  
  
and Wo/b*= 
ala* S p/b* 
Waja*— 
(13) 
where, 
e. n4. isthe predicted residual of a or a* and is the first element of vi; 
  
210 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.