(1) 
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(4) 
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Ogra- 
00h50 Dd yn v: 
The structure of the D matrix reflects the photo-variation 
of the additional parameters. In case we use photo-variant 
additional parameters then D = D; and y = y;. Therefore 
the switching from photo-variant (non-metric photos) to 
photo-invariant (metric photos) is an algorithmically trivial 
matter. 
The least squares criterion is 
m 
= vi P; v; = min. (6) 
i=l 
where P;= Q;! is the weight matrix pertaining to observa- 
tions on the i th photograph 
The system of normals is then 
  
  
  
  
  
  
  
  
  
  
  
  
  
N NN, |[, à 
2T .9 .. ie = i. 
N NN; Xx |=] u (7) 
. .. u 
NI NI N, y 
or in detail 
N |N, N, RIN NS, N {{* u 
NT N, 0 0 Ny, 0 0 X ü, 
NO. RK 0 Ny, 0 X, ü, 
Reo 0 .. {0 0.2% IIz, [*]1&, (8) 
e. oe. u 
Ny, Ny, 6 … 9IN 0. 0 Yi y 
° ve u 
Ny, 0 Ny, ... 0 0 N,, ... 0 Y? y? 
Ny 0 «9 RS [0 0 Ny. | | 7n un 
where 
m m 
. . HM S . 
N-YN-XATBÀ 
i=1 i=1 
m m T 
a=) =) A} Pb; (9) 
i=1 i=1 
Ni = AT Pi ‘À; N; = AT Pi ‘A; (10) 
N,= DTP,D; N,=ATP,D; N,=A;MD; CD 
and 
=A} Pb uy, = Di P;b; . (12) 
2.2 Definition of the reference frame 
Since additional parameters are not related to the refe- 
rence frame, they can be eliminated and thus the final sys- 
tem is 
z^ a3 
R-N-N,Ny;NI  r-ü-N,Nyu, 
R-N-N,NyNI  rf-uü-Ny,N;'u, (14) 
In order to define the reference frame the minimum requi- 
red constraints can be introduced with the help of relation- 
ships, of the general form 
Hx+Hx=z (15) 
where H = [H, H, oh Hal. Besides this general form, the 
constraints may refer only to e.o. parameters Hx-z (H 
= 0), or refer only to ground control points H x - z (H 
0). 
In the most common case, in order to define a reference 
frame we can simply constraint same coordinates of con- 
trol points or some e.o. parameters. In this simple case the 
system of normal equations is easily solved by elimination 
of the corresponding rows and columns of matrices R,R 
and R and the corresponding vectors r and ®. This techni- 
que is valid both for minimal and redundant number of 
known parameters (i.e. coordinates of control points, e.o. 
parameters). 
2.3 The sequential photo-wise adjustment 
The following matrices can be computed for each photo- 
graph using the general form (15) of the minimum con- 
straints relationship 
. MUR . -Ix;T e d TK —l 
Ri=N;— Ny, Ny, Ny, ri =u; — Ny, Ny; uy, 
~ — e IST eo Tee 
Ri=N;- Ny, NI NJ + HT H; (16) 
m 
R-R-RR-{ART-Y (R,- R,RHRT) 
j=l 
— 99 in — oe 
r=u-R Ri =), (i;-R; R71; ) 
i=1