BLOCK BUNDLE ADJUSTMENT FOR THEODOLITE STATIONS IN CONTROL 
NETWORKS - THE CASE OF THE GUGGENHEIM MUSUEM IN BILBAO 
G. Fangi 
Dardus — Universita Politecnica delle Marche — Via Brecce Bianche — 60131 Ancona -Italy — g.fangi@univpm.it 
Commission V , WG V/A 
KEY WORDS: Control Network, Surveying, Bundle Adjustment, 3D 
ABSTRACT : 
In surveying missions the volume and the weight of the surveying equipment are often a problem. In a previous work, the A. 
proposed what he called blind traverse for control network assessment in close-range photogrammetry. It is a procedure that forms 
the so-called topographic models, linking together a couple of Theodolite Stations by their observations to the common points, 
similarly to what happens in photogrammetry with the photogrammetric models. The theodolite relative orientation has three +one 
unknown parameters, estimated by means of co-planarity conditions, observing a minimum of three common points. When all the 
possible couples of TS are formed, they are oriented in an absolute reference system with a procedure similar to independent model 
adjustment in aerial triangulation (S-transformations). The advantage consists in the possibility to avoid to link together the TS with 
the reciprocal observations, allowing to reduce the amount of needed equipment by more than 50% in volume and weights (from 
three tripods to one, etc). The term “blind” refers to the null visibility among TS. In the present paper, the analogy between 
photogrammetry and surveying is extended to block bundle adjustment. The angular observations of a theodolite stations are similar 
to an image bundle. Compared to the photogrammetric bundle, the unknown parameters for any single TS, are reduced to four only, 
say the three co-ordinates of the TS and the bearing of zero reading of the horizontal circle. The fundamental equations are the 
horizontal direction and vertical one. Since the approximated values of the co-ordinates for the unknown points are needed, they are 
supplied by the previous stage by the blind traverse. The benefits are again the independence of the theodolite stations and in 
comparison with the blind traverse a more adequate stochastical model and a better accuracy. A computer adjustment programme has 
been written and tested. The A. called it 3Dom, meaning 3d adjustment and freedom in the lay out of the control traverse. As an 
example the control network of the Guggenheim Museum in Bilbao is shown. The adjustment takes place in two steps: computation 
of the approximate co-ordinates by co-planarity (the blind traverse), and final adjustment by 3Dom. 
Therefore it is very advisable to roughly orientate the 
1. THE TOPOGRAPHIC MODEL BY CO-PLANARITY theodolite horizontal circle with the help of a magnetic 
compass. The benefit is the possibility to get rid of the 
In previous papers, the A. introduced the so-called reciprocal observations between adjacent stations, thus 
“topographic models”, (Fangi G, 1999). They consist in the enabling a remarkable reduction of the needed equipment in 
following: taking advantage of the analogy with the terms of weight and volume. 
photogrammetric model, the surveying observations of two 
(or more) theodolite stations, are coupled together by means 
of the co-planarity condition to the common aimed points. 
  
5. 
e 
Figure 2 — Analogy theodolite-photogrammetric bundle: x 
M te and y image coordinates are equivalent to the angular 
= : — Sa measurements / and 9 
Figure 1 — The topographie model by intersection- The three 
coplanar vectors b, r; and r».. Now the analogy between photogrammetry and survcying 
can be further extended to the block adjustment. A theodolite 
Ihe he 1 5 e rm oO sx are sante 5 + T 
When the topographic models are formed, they are oriented station can be compared to a photogrammetric bundle. In the 
in the reference system, with a technique similar to the one of three-dimensional adjustment, the orientation parameters per 
the aerial triangulation, say with the S-transformation. station are four compared to the six of the photogrammetric 
Obviously at icast one distance is needed to correctly bundles. They are the three station co-ordinates Xo, Yo. Zo 
imensi A funk I AY S XI o prp z : - : a ; > 
dimension the network. No approximate value is needed and the zero bearing 0, of the horizontal readings (figures 2, 
except the one for the zero bearing of the horizontal circle. 
   
   
   
  
  
  
  
    
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   
   
  
  
  
   
  
  
  
  
   
  
   
   
   
   
   
    
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