used to confirm some findings. In all these studies, the effect of different 
types of error on the image residuals and the adjusted object coordinates has 
been computed for the case where (a) only photogrammetric data were used and 
for the case when (b) the combined adjustment was applied. Before presenting 
the test results some theoretical investigations are presented. 
Error Distribution - Theoretical Study 
Errors in observations (vector L) will affect the adjusted unknowns (vector X) 
and the corrections to the observations,the residuals (vector V). The ratio 
by which the error affects each of these variables depends largely on the 
geometry of the system. This error distribution can be computed by the 
variance covariance matrix of the adjusted observations and of the residuals. 
After the adjustment, the weight-cofactor matrix of the observations can be 
computed by applying the covariance law on the function 
L = F(X) (1) 
T 
a fg roF 
% = lox] % lox or 
as follows: 
Qm AA AT 
where N is the matrix of the normal equations.  Partitioning the the unknowns 
into orientation parameters X, and object coordinates X5, equation C33 
becomes: 
x 
Gyms cod eo 5, A; 
T 
No M] Aq 
from which: DT 21 T 2, A iT 
Qo 70. M5, CAL t. A38,545 t Ao8558215 7815853435 
- A9N55N5915 Aq 7 A46 "Ni5N55A5 (4) 
where = 
£7 ON TN N55N5 (5) 
Nyy = ALP A, ti mi, + ÿ = 1,2) 
and P is the weight matrix of the observations. 
Each diagonal element of Q7, represents the geometrical strength at the 
corresponding observation point. Equation (4) can be rewritten in a diagonal 
form as: 
3.0 2 ey eat en (6) 
where e, is the diagonal of A5 AT, ej is the diagonal of A. 85555, and ej» 
is the diagonal of the remaining right hand side of equation (4)... Factor ei 
represents the part of image error affecting the orientation parameters, and 
e, represents the part affecting the adjusted object coordinates (indication 
of external reliability), while ei») represents 
the interaction between the two effects. 
The part of image error affecting the residuals can be computed from: 
Qu = 0-0, (7) 
where Qp is the a priori (or given) weight-cofactor matrix of the 
observations. The diagonal elements of Quy are called the redundancy numbers 
ry for observation i and represent the part of the error affecting the 
residuals. Factors r and e, are those of importance to us and will be 
referred to in the following tests. They are related by the function: 
Thay ka, bay =], (8) 
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