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results of the theoretical investigation are standard errors of 
adjusted tie-point terrain coordinates, which are summarized 
to r.m.s. errors ji, for horizontal coordinates and yu, for ver- 
tical coordinates. Those r.m.s. values represent the accuracy 
of the adjusted blocks. 
It is recalled that the actual magnitudes of the standard er- 
rors do not represent any restrictions, as only the weight 
relations act in least squares adjustment. The results can 
therefore be transferred to other error magnitudes and to 
other photo scales by expressing all standard and r.m.s. er- 
rors in units of og. 
4.2 Some examples 
Let us look first at the accuracy distribution within some 
adjusted GPS blocks in detail. In fig. 2-4 the standard er- 
rors of adjusted tie point coordinates are shown, referring to 
two block sizes with 2096 side overlap and one case with 60% 
side overlap. In all cases 4 ground control points in the cor- 
ners of a block are assumed, and one set of unknown linear 
correction parameters for datum transformation or overall 
drift correction has been applied in the blockadjustment. It 
means that here no unbridged signal discontinuities during 
the flight are considered. The photogrammetric image coor- 
dinate accuracy is set to o9 — 10 Jim, and the ground control 
point coordinates as well as the GPS camera air station co- 
ordinates are given the moderate accuracy of oc p — 30 cm 
and GG ps — 30 cm, respectively, which would be sufficient for 
1 : 10000 scale mapping from 1 : 30 000 scale photographs. 
Those assumed standard errors correspond to Gy, i.e. to the 
precision o9 = 10 um of image coordinates in the photo scale 
1: 30000, projected onto the ground. The tie-point distribu- 
tion is six points per model, giving 3 rows of tie-points along 
each strip, the rows in the common lateral overlap between 
strips coinciding through identical points. The figures 2-4 
show only the upper left quarter of a block, for reasons of 
symmetry. 
The first example (fig. 2) refers to a block of 6 strips with 
21 photographs each. The figures represent theoretical stan- 
dard errors, after combined blockadjustment, of the X, Y, 
Z coordinates of all tie-points, arranged in the regular row 
and column array. Within a strip always 3 x 2 points be- 
long to a stereo-model. It is immediately evident that the 
standard errors are quite evenly distributed over the block. 
Only the border points of the block show generally, as usual, 
the largest errors. If we disregard them, for the moment, all 
other standard errors lie within a narrow band of variation: 
0, between 38 cm and 50 cm, c, between 45 cm and 55 cm, 
a, between 48 cm and 81 cm. In the central parts of the block 
the standard errors are even closer together. The accuracy 
of the perimeter points is generally lower, pushing the max- 
imum standard errors in X, Y, Z to 59 cm, 75 cm, 94 cm 
, respectively. The overall r.m.s. coordinate accuracy of all 
points of the adjusted block amounts to 46 cm, 55 cm, 68 
cm, which corresponds to 1.5 89, 1.8 8$, 2.3 05, respectively. 
Fig. 3 concerns a small block of 4 x 13 photographs. The dis- 
tribution of standard errors in the block displays the same 
overall picture as in the previous case. The magnitudes of 
the standard errors are in general a little larger, by about 
396 in X, Y, and by about 6% in Z. 
695 
  
  
Fig.2 Standard errors [cm] of adjusted 
lie points 
block size 6x21, 1:30000 
Oy —10um £ 30cm 
4 control points for drift correction 
(datum transformation) 
rows/ 
columns 
of points/ 2 3 4 5°6.7 8:9 10 1112 
  
— Strip 
; X 28 40 48 55 58 58 56 55 54 54 54 
i1 Y 29 61 70.74.75 74 73 72 72 72 72 
1 7 29 82 92 92 89 86 84 84 85 86 86 
2 X | 47 38 43 47 50 50 49 48 47 47 47 
46 45 50 54 55 55 55 55 55 55 55 | (1) 
ZZ | 9175 81 81 78 75 74 74 74 75 75 
N 
< 
3. X 55 44 41 42 43 43 43 48 42 42 42 
3. Y 50 47 50 52 53 53 53 52 52 52 52 
3 Z 81 70 67 64 61 59 57 57 57:57 57 
  
4 X | 55 44 43 43 44 44 44 44 43 43 43 
4 Y | 65 53 52 51 52 52 52 52 52 52 52 ® 
4 Z | 94 69 67 66 65 64 63 63 63 63 63 
5 X 59 48 43 42 41 41 41 41 41 41 41 
5 Y 61 52 50 50 50 50 50 50 50 50 50 
5 2 73 61 56 54 53 52 51 51 50 50 50 i 
  
6 X | 57 46 44 43 43 43 43 43 43 43 43 
6 Y | 65 55 52 59 51 51 51 51 51 51 51 G 
6 Z | 90 63 62 62 61 61 60 60 60 60 60 
7 X | 59 48 43 42 41 41 41 41 41 41 41 
7 Y | 62 54 51 51 50 50 50 50 50 50 50 
7 Z | 70 57 52 51 50 49 49 49 49 48 48... | 
  
  
oooo 
0000 
K.m.s. accuracy of block 
[cm] [00] 
Mx | Hy | MHz | Hx | Hy | Hg 
46 55 68 1.5 1.8 2.3 
51 68 1.7 2.3 
  
  
  
  
  
  
  
  
  
  
  
  
The comparable results of a large block of 12 x 41 pho- 
tographs are not displayed here. They would show that the 
distribution of the standard errors within the block is even 
more regular than in smaller blocks. The overall r.m.s. accu- 
racy of the block in X, Y, Z coordinates amounts to 44 cm, 
93 cm, 63 cm, respectively, which is equivalent to 1.5 à, 1.8 
Go, and 2.1 59. Compared with the medium size block (6x21) 
there is an overall improvement of theoretical accuracy of 496 
in X and Y, and of 796 in Z. Those examples confirme the 
expectation that the accuracy of GPS blocks is little depen- 
dent on block size.