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The International Archives of the Phoiogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
4.2 Aerial triangulation 
The precision of terrestrial feature extraction is one of the key 
problems that the low altitude remote sensing system faces. It 
directly determines whether the low altitude remote sensing 
system can be used in practice. To fully evaluate the precision 
that the system can achieve, aerial triangulation with ground 
control points is performed in this section. Results of many 
bundle adjustment experiments show that taken lens distortion 
parameters as unknowns are not as effective as additional 
parameters. So only additional parameters are treated as 
unknowns in the following experiments. 
4.2.1 Aerial triangulation with 80% forward and 75% side 
overlap image data 
Image data of all 13 strips are used as sources of information in 
this section. There are totally 68534 ground points in the test 
data, and 28469 of them have at least 3 corresponding image 
points. The maximum image points corresponded to a ground 
points is 27, which is impossible in traditional photogrammetry. 
As shown in figure 4, 33 of the 64 ground points measured by 
total station are used as ground control points (GCPs), and the 
other 31 are used as check points for aerial triangulation. The 
aerial triangulation with 13 strips image data includes two 
experiments, the first with additional parameters as unknowns 
and the second without. All configuration parameters for aerial 
triangulation are exactly the same for the two experiments. 
Unit weight root mean square (RMS) error of the first 
experiment is 0.0023mm, i.e. better than 0.3 pixels. Error 
statistics of GCPs and check points is shown in table 1. As can 
be seen, the RMS error of planar position and height for GCPs 
are both better than 0.02m. The RMS error of planar position 
for check points is also quite small, and the RMS error of height 
is a little bit larger than 0.02m, i.e. about 0.4 GSD. The 
maximum error of GCPs and check points are all smaller than 3 
times of corresponding RMS error, which means that there is no 
gross error in control and check points. Because only 60% 
forward overlap and 30% side overlap is used by traditional 
photogrammetry, the height precision is usually around 1.0 to 
1.5 GSD. So the achieved height precision of check points in 
this experiment is definitely superior to that of the traditional 
photogrammetry. 
Item RMS Mean Maximum 
Control 
Points 
X 
0.015 
0.003 
0.043 
Y 
0.013 
-0.001 
-0.030 
Z 
0.018 
0.002 
-0.052 
Check 
X 
0.011 
-0.002 
0.025 
Y 
0.010 
-0.004 
-0.028 
Points 
Z 
0.021 
-0.004 
-0.061 
Table 1. Precision of aerial triangulation with additional 
parameters by 80% forward and 75% side overlap data (m) 
The results of aerial triangulation without additional parameters 
are shown in table 2. Unit weight RMS error is also 0.0023mm. 
As can be seen, precision of planar position for GCPs and check 
points are similar with the first experiment, while the height 
precision is distinctly decreased. For example the height 
precision of check points is about 1.3 GSD, more than 3 times 
of the precision in the first experiment. The maximum error of 
check points is also 3 times of the first experiment. This result 
shows that additional systematic parameters are essential in 
aerial triangulation of images acquired by non-metric digital 
cameras. 
Item 
RMS 
Mean 
Maximum 
Control 
Points 
X 
0.019 
-0.003 
-0.060 
Y 
0.018 
-0.006 
-0.090 
Z 
0.039 
-0.012 
-0.083 
Check 
Points 
X 
0.008 
-0.002 
-0.018 
Y 
0.014 
-0.006 
-0.051 
Z 
0.065 
0.026 
0.186 
Table 2. Precision of aerial triangulation without additional 
parameters by 80% forward and 75% side overlap data (m) 
4.2.2 Aerial triangulation with 80% forward and 50% side 
overlap image data 
To evaluate the relationship between height precision and side 
overlap, image data of odd strips (7 strips) of the 13 strips are 
used as input data for aerial triangulation. There are totally 
46636 ground points in the test data, and 17596 of them have at 
least 3 corresponding image points. The maximum image points 
corresponded to a ground points is 14. GCPs and check points 
are the same as the experiments in section 4.2.1. The aerial 
triangulation with 7 strips data also includes two experiments, 
the first with additional parameters as unknowns and the second 
without. All configuration parameters for aerial triangulation are 
also exactly the same as that of section 4.2.1. 
Unit weight RMS error of aerial triangulation with additional 
parameters is 0.0024mm. Error statistics of control and check 
points is shown in table 3. As can be seen, RMS errors of planar 
position for GCPs and check points are both better than 0.02m. 
RMS errors of height for GCPs and check points are about 
0.03m, i.e. 0.6 GSD. When compared with the result in section 
4.2.1, the height precision is apparently decreased. 
The results of aerial triangulation without additional parameters 
are shown in table 4. Unit weight RMS error is also 0.0024mm. 
As can be seen, precision of planar position for GCPs and check 
points has decreased a little bit, while height precision is 
distinctly decreased. For example the height precision of check 
points is about 1.6 GSD, about 3 times of the precision with 
additional parameters. This result also verifies that additional 
parameters are essential in aerial triangulation. 
Item 
RMS 
Mean 
Maximum 
Control 
Points 
X 
0.016 
0.003 
0.042 
Y 
0.012 
-0.001 
0.033 
Z 
0.029 
0.004 
-0.087 
Check 
Points 
X 
0.016 
0.004 
0.029 
Y 
0.011 
-0.002 
-0.027 
Z 
0.027 
0.001 
-0.070 
Table 3. Precision of aerial triangulation with additional 
parameters by 80% forward and 50% side overlap data (m) 
Item 
RMS 
Mean 
Maximum 
Control 
Points 
X 
0.017 
-0.001 
0.058 
Y 
0.020 
-0.001 
-0.067 
Z 
0.068 
-0.013 
-0.235 
Check 
Points 
X 
0.027 
-0.006 
-0.081 
Y 
Z 
0.021 
0.080 
-0.011 
-0.014 
-0.076 
-0.277 
Table 4. Precision of aerial triangulation without additional 
parameters by 80% forward and 50% side overlap data (m) 
t