RROR DETECTION IN THE 
REALIZATION OF AUTOMATIC ER 
PAT-M43 USING ROBUST ESTIMATORS 
BLOCK ADJUSTMENT PRCGRAM 
Hermann Klein and Wolfgang Fürstner 
Photogrammetric Institute, Stuttgart University 
Germany, Federal Republic 
Commission III 
Abstract: The detection of outliers can be automated using robust estimators. The principle is to 
interpret the residuals vj of the observations after each iteration as errors in order to calcu- 
late new weights based on a weight function p(vi). The new weights p4 » p(vi) are then used in the 
following iteration step. 
The paper reports on the realization of this error detection strategy in PAT-M43. Main topic is 
the extension of the method, especially the choice of a proper weight function, the iteration 
sequence and the stopping rule. The significant facilitation in handling the program is explained. 
l. The original program: 
The computer program PAT-M43 performs a blockadjustment by independent photogrammetric models. 
This approach implies a spatial similarity transformation for each model. The adjustment is based 
on a least squares solution. The nonlinear observational equations are linearized with respect to 
the orientation parameters. Because of computational economy the program iterates sequential hori- 
zontal and vertical adjustments, applying 4-parameter and 3-parameter transformations, respective- 
ly. For each iteration the partiallv reduced normal equations that contain only the unknown orien- 
tation parameters are formed directly from the model and control coordinates and are solved by a 
modified Cholesky method (Ackermann et. al. , 1970). An extension allows the combined adjustment 
of photogrammetric models with APR and/or statoscope data, including photogrammetric height measure- 
ments of sharelines of lakes (Ackermann et. al. 1972). 
2. Manual data cleaning: 
One of the main problems handling blockadjustment programs is the detection and location of out- 
Tiers. Dependent on the number and distribution of the observations, errors are shown up only 
partly by the residuals of the corresponding observations, the other parts falsify the absolute 
orientation of the photogrammetric models (Fürstner, 1978). The mutual interference of outliers, 
especially of different size, is a further handicap. For that reason several adjustments for a 
step by step location and elimination of outliers in accordance with the size of the errors and 
some further adjustments in order to avoid wrong decisions are necessary. Nevertheless the quality 
of manual data cleaning is sufficiently good and comparable with most of the more sophisticated 
procedures (Fórstner, 1982), but in general it requires a great deal of time by fully qualified 
persons. Thus the main argument for the development of an automatic procedure has been: to shorten 
the processing time needed by persons in charge with blockadjustment. 
3. From least squares to robust adjustment: 
The above mentioned problems arising by adjustment of data with gross errors are not a specific 
attribute of the manual data cleaning procedure, but a bad point of the method of st squares. 
a 
" allis az us 
| first derivative 
Applying a constant weight p s const for each observation the inf 
of the minimum function by the residual) shows, that the influence 
uence function 
9 
onto the result of the adjustment is directly proportional to the si 
2 
matter of fact the method of es is applicable for errorfree data only and unsuitable