154 
  
  
  
original system | A aim system residuals (LMS) residuals (L2) 
Pkt-Nr| y [m] X [m] y [m] x [m] y [m] x [m] y [m] x [m] 
1 755.000 500.000 755.000 500.000 0.0000 0.0000 0.2891 0.0000 
2 811.000 510.000 810.000 510.000 0.0001 0.0000 -0.6737 0.0000 
3 720.000 520.000 720.000 520.000 0.0001 0.0000 0.1006 0.0000 
4 870.000 530.000 870.000 530.000 2.2789 0.0000 0.3102 0.0000 
S 750.000 540.000 750.000 ° | 340.000 0.8844 0.0000 0.0300 0.0000 
6 825.000 555.000 825.000 555.000 2.2620 0.0000 0.0723 0.0000 
7 850.000 570.000 850.000 570.000 2.9392 0.0001 0.0239 0.0000 
8 770.000 575.000 770.000 575.000 1.9898 0.0001 -0.1525 0.0000 
  
  
  
  
  
  
  
  
  
  
  
Table 1: Co-ordinates of the point fields and residuals after parameter estimation 
4. THE APPLICATION OF THE L;-NORM-METHOD WITH BALANCED OBSERVATIONS 
Due to the a. m. difficulties in the parameter estimation when gross data errors occur, a robust estimation technique has been 
introduced apart from the method of least squares. Robust estimation procedures stand out for the fact that the smearing effect of 
peak values in the residuals as known from the method of least squares are largely eliminated. 
In the concept of the norm-estimation procedures to which also the method of least squares belongs, the minimization of the total 
sums of residuals or Li-norm-method stands out for its maximum robustness. In case of a single unknown to be determined, it leads 
to the median which proves to be the maximum robust mean by a maximum break point of 50%. 
When more than one unknown is to be the basis for the balancing process, these ideal conditions of the median are sometimes no 
longer existent. The reason is the differing influence of individual observations on the adjustment result. In particular points which 
are far off in the co-ordinate transformation produce the above mentioned leverage points. 
Leverage points can make the identification of a blunder within the L;-norm even more difficult. They are observations which do 
not receive the same share of the total amount of freedom within the adjustment as other observations. The total degree of freedom 
is the difference between the number n of observations and the number u of unknowns. 
An old geodetic principle (reliability) now tries (e. g. in constructing observation nets) to spread the total amount of freedom as 
even as possible over the participating observations (ref. Grafarend 1979). An “ideal situation” with regard to error detection is 
achieved when every observation receives exactly the share of the total freedom as in theory as it is the case for the arithmetic 
mean where each observation it receives exactly 
n=1-ufn | (10) 
shares of the total amount of freedom (n-u). It follows that 
spur(H*)=(u/n)+(u/n)+ ie +(u/n)=u (11) 
This situation will be referred to as “balanced” observation in the following. If it is possible to balance in the standard case of n 
observations and u unknowns corresponding to (10) the size of the r; with 
* 
-1 
p= rum de) (12) 
ii ; 
A being the (n, u) coefficient matrix and P the matrix of weights, then measured against ri, every observation has the same share of 
the adjustment result, possible leverage points are balanced. Depending on A, P changes its shape which can be determined by 
optimizing the reliability (ref. Müller 1986, Grafarend 1979). P is then as described in (Kampmann, Wolf 1989) also used within 
the L;-norm-method. This combination of minimization of absolute values of the residuals under consideration of the geometry of 
the observations is called balanced L;-norm-method and is signified by the reduced sensibility with regard to leverage points 
within the adjustment. 
8. COMPARISON OF DIFFERENT ESTIMATION METHODS 
For the following calculation, two recordings of triangulation bundles of the St. Johannis church in Ellrich (State of Thüringen, 
FRG) are chosen. Within this project, a point determination by bundle triangulation with subsequent stereo evaluation was carried 
out. The result should be plans for a reconstruction of the church. The 57 photos of the triangulation bundle were taken with a 
Rolleiflex 6006 réseau. To guarantee the possibility of comparing the results in the example calculations, all estimation procedures 
were based on identical starting values. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995