eral and flexible self-calibrating bundle adjustment having proved its efficiency 
i in aerial triangulation. For the further analytical treatment reference is made 
| to the model of the existing bundle program MBOP (Munich Bundle Orientation with 
$ | Additional Parameters), originally developed for aerial triangulation problems: 
/ | - eP s a dx « A,dx" + A,dt 4 A dz - 1B i^ p, (ef) 
Ra SAAJOS * ROUX 3 4 B T 
i 23 a Lao Mond, (1) 
| „of. I dx" © ds 
eB rate - Vectors of true errors of image coordinates, additional parameters, 
control point coordinates 
| 
dx,dx’, dt, dz 
Correction vectors of point coordinates, control point coordinates, 
elements of exterior orientation, additional parameters 
A. A AzsAg - Corresponding coefficient matrices 
Z 
1" 2e 
,0 - Vectors of observations of image coordinates, additional parameters, 6? 
control point coordinates 
I - [dentity matrix 
Collecting the matrices and vectors of (1) in the following manner 
Ai A, A3 A, Pp 0 0 
A = 0 0 0 I , P = 0 P7 0 , 
n,u n,n 
00591 2:02:00: ] 0 0 P, 
T T T T 
U A PAR ASR RL LARFRANT LL TALIR AL SLES 
Lau l,n 
T T T T 
e = (eB i e^ e 4 
1;n 
the system (1) formally results in 
5 g5293,40- 5] 093! up (2) v 
and by using the operator of expectation E and the operator D which leads to the 
variances and covariances we get in statistical notation 
AE(x) = E(1) , 
D(e) = ; 2p^l , (c= standard deviation of unit weight 
to be estimated) 
Thereby the correction vectors of the ground point coordinates dx and of the 
elements of exterior orientation dt are always introduced as free unknowns, what 
generally leads to mixed models. 
System (3) is called a Generalized GauB-Markov Model (Koch /12/). For known ex- 
pected values uy, and for P, # 0 it may be interpreted as (mixed) Regression Model, 
for P7 + 0, E(12) = 0 as (mixed) Collocation Model (Ebner /6/). If the geodetic