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Ninth International Congress of Photogrammetry, London 1960 
Paper presented to Commission III 
Approximation Method of Block Adjustment in Aerial Triangulation 
with Special Regard to the Bridging of Adjacent Strips 
Procédé approximatif de compensation de blocs dans l'aérotriangulation 
en considérant particulièrement les raccerds des bandes 
Näherungsverfahren für Blockausgleichungen bei Aerotriangulationen 
unter besonderer Berücksichtigung der Streifenanschlüsse 
by Rudolf Förstner, Frankfurt/Main 
Summary: 
In an aerial triangulation the errors of closure pertaining to a flight strip and denoted Ax and Am Ay 
and Ax (or Aa), Az and Ag are interrelated. If the initial stereoscopic model has an absolutely correct 
orientation, then Ax, Ay, Az or Am, Ax (or Aa respectively), Ag usually cause a quadratic increase of 
errors, In case the values of Ax and Am, Ay and Ax, Az and Ag are contradictory, the residual errors 
have to be adjusted by a curve of the third degree. When several of such flight strips shall be connected 
to a block, the bridging of successive models within the flight strips is replaced by the bridging of suc- 
cessive flight strips within a block. From the mathematical point of view the problems are similar. But 
in general we have an overlap between photographs in the same flight strip which amounts to 60 per cent, 
whereas the side lap between photographs in adjacent flight strips is only 20—50 per cent. Thus we 
cannot determine the lateral tilt of the second flight strip by means of identical points, i.e. from a 
connection with the preceding strip. Even if this interrelation is established by special measures, most 
of the so far applied methods of adjustment will only furnish results free of discrepancies in the beginning 
and in the end of the flight strips. But also the bridging in the further course of the strips is very important. 
The discrepancies occurring at the borders of the flight strips are eliminated with the condition that the 
sum of the squares pertaining to the corrections of each strip be minimum. These discrepancies being 
accidental, their sum ought to be zero, theoretically. In this case the method will yield the real corrections, 
though only a part of their differences is known. But unless the sum of discrepancies equals zero, this 
fact will have equal systematical influences on all flight strips. These errors can be determined by help 
of additional control points. The greater the number of strips which are bridged, the easier the sum 
of discrepancies will tend to zero, and the better the result will be. This method is not applicable to 
level adjustment, since in the border zones not only Az but also Aw is effective. In this case we only 
obtain elevations without discrepancies but no true elevations. Even with an increased overlap of flight 
strips the conditions would not be sufficient to solve the equation system unequivocally. This will only 
be possible by measuring either the elevation z or the lateral tilts c. We assume that c rather 
“flutters”, whereas z will have a more continuous course. However, this has still to be proved by 
practical experiments. 
Résumé: 
Dans une bande de vol faisant partie d'une aérotriangulation les écarts de fermeture, à savoir Ax et Am, 
Ay et Ax, respectivement Aa, Az et Ag (m — échelle, y — inclinaison longitudinale, « = inclinaison 
transversale, x — déversement, a — azimut) sont interdépendants. Le stéréogramme de départ étant orienté 
de facon absolument correcte, les Ax, Ay, Az ou Am, Ax, respectivement Aa, ^g entraínent en 
général un accroissement quadratique des erreurs. S'il y a un désaccord parmi les valeurs Ax et Am, 
Ay et Ax, Az et Ag il faut compenser les erreurs résiduelles par une courbe du troisiéme degré. 
Si nous raccordons plusieurs bandes d’un tel caractère pour former un bloc, la mise en place en chemine- 
ment des couples d'images à l'intérieur des bandes est remplacée par une mise en place en cheminement 
des bandes de vol. Du point de vue mathématique les problémes sont similaires. Tandis que normalement 
Nous avons un recouvrement longitudinal de 60% à l'intérieur d'une bande, le recouvrement latéral des 
bandes elles-mémes n'est que de 20 à 30%. Il est impossible de déterminer l'inclinaison transversale 
de la 2e bande à l'aide de points identiques, c'est à dire en nous servant du raccordement avec la premiére 
bande, Méme en établissant ce raccord dans ce but, moyennant des dispositions particulières, la plupart