152 
distortion parameters) for applications which require high accuracy. In the following, the mathematical link between image co- 
ordinates and object co-ordinates is expressed using the auxiliary system X*, Y*, Z* (ref. figure 1). 
  
  
  
* 
A Zs 
M Pi 
Image Plane O D P ox 
Xy x 
C 
* 
X, 
D 
Object Space 
  
   
Figure 1: Geometry of the central projection 
The calculation of the unknown parameters is usually done in linear models with overdetermined equation systems. One of the 
most difficult tasks there is the identification of gross errors. Several different strategies for detecting them (roubst estimation 
procedures) have been developed in the past, some of which are outlined below. 
3. METHODS IN ROBUST PARAMETER ESTIMATION 
3.1. Robust estimation through iterative reweighting in least sqaures adjustment 
One type of robust estimation procedures has been created through an alteration of the theory of least squares adjustment. Due to 
an iterative reweighting an identification of gross errors in the L»?-norm-method has been tried. 
Iterative reweighting procedures without objective function orientation 
These "trial and error strategies" for the identification of gross errors had been created in general through an investigation of 
certain data series and led to a variaty of empirical methods. Some examples of that category are mentioned below without any 
further comment (t = number of iterations, p = weight). 
1) Danish method: 
1 for &1 
pi(t*D se C070 epi (3) 
e c/o ye fort>3 
2) Stuttgart method: 
Dill) Qz2 
1+ (aj|vi) 
) d ; 
pi(t+1)= pi (je (vi 0«3 Bit * DJ. pu (4) 
Di (1) 
BU co Qu) py 
ajlvy|+10PMIN = pi (8) 
with: 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995