with photogrammetric 
ıtion of the coordinates 
:duction of the number 
imum. The combined 
| GPS observations can 
‘vation equations to the 
and Chapman, 1995). 
howed that, in addition 
rcraft positions, (0 =2 
the ionospheric and 
ors, and uncertainty of 
oned remaining errors, 
tribute the majority of 
sition. 
NGULATION WITH 
OF MAN-MADE 
e common tie points in 
cover all three rotation 
nt. Unfortunately, this 
strip, since the GPS 
o not recover the roll 
, control introduced by 
if not singular system 
ints can be used along 
strip triangulation was 
straints of man-made 
i-rise buildings) located 
n equations for these 
duced to the combined 
tion equation for a high 
of the top of the 
of the bottom of the 
be appropriately chosen 
structure must have the 
r, the absolute ground 
uired since the top and 
) horizontal pass points. 
vers along the flight line 
e aircraft and use these 
round control points. 
na 1996 
4. 1. Precision and Reliability Measures 
The covariance matrix of object points, Cx=05Qxx is 
generally taken as the measure of theoretical precision. The 
average theoretical precision of n object points is given as: 
Bao] 534 Q) 
The average practical precision of object points for simulated or 
check point data is: 
2 2 2 
Io YT (AX? + AY az) 3 
where AX,AY, and AZ are differences between the adjusted 
and known coordinates of an object point. Similarly, my, my, 
m;, and HL, k. H, are the average theoretical and practical 
precision of object points in the X, Y, and Z directions, 
respectively. 
Reliability analysis includes internal and external reliabilities. 
The ability to discover blunders in one particular observation is 
referred by the internal reliability and the effect of an 
undetected blunder in the observation on unknown parameters 
is measured by external reliability. For the reliability analysis, 
the local redundancy numbers, Be(Q up). need to be 
determined, where Q, . is the cofactor matrix of residuals and P 
is the weight matrix of observations. A single blunder is 
generally assumed to exist for the application of this method. 
The internal and external reliability formulas are given as 
(Deren and Jie, 1989): 
Ô 
VoL; 7 0i, ve = OL, 00, (5) 
Doi - 1- ri-àoj (6) 
where 
OL, is RMSE of the ith observation L;, 
50 is the non-centrality parameter, 
00i is the internal reliability factor of observation L;, 
VoL; is the minimum blunder that can be detected 
statistically, 
Soi is the external reliability factor of observation L;, 
with the significant level, & = 0.196, and the power of the test, 
B = 93%, the non-centrality parameter, do, is then equal to 4.0. 
4. 2. Results With Simulated Data 
Many experiments were conducted to evaluate the performance 
of the new model. We considered one single strip of 50 
photographs. The interior and exterior orientation parameters 
were predefined. The image coordinates of all object points 
(pass points and tower points) were computed using the known 
exterior orientation of each photograph. Table 1 lists the 
information concerning this simulated strip. 
Table 1. Simulated Strip 
  
Strip Information 
  
  
  
  
Number of Photos 50 
Photo Scale 1:5000 
Focal Length 152 mm 
Terrain Elevation Difference 150m 
Average Flying Height 900 m 
Forward Overlap 60% 
Photograph Format 23 cm x 23 cm 
Accuracy of Image Coordinates Sum 
Accuracy of Ground Control Points | 0.1 m 
Accuracy of GPS 0.25-1.0 m 
Tower Height 15m 
Number of Towers 50 
Number of Pass points per Photo 15 
  
The behavior of the new model was studied under different 
conditions, such as varying GPS accuracies at the perspective 
centres. The performance of the technique was evaluated using 
the standard deviations of the coordinates of pass points 
obtained from their variance-covariance matrix and comparing 
the adjusted coordinates with simulated coordinates. The 
following methods of the strip adjustment were carried out: 
1- GPS-Photogrammetric strip adjustment with 2 ground 
control points and without tower points 
2- GPS-Photogrammetric strip adjustment with no ground 
control points and with tower points 
3- Full control strip adjustment (no GPS data) 
Figure 1 shows the root mean square error (RMSE) of X, Y, 
and Z coordinates of all pass points without using tower points 
and Figure 2 shows the RMS of X, Y, and Z coordinates of all 
pass points including tower points. The RMS of X, Y, and Z 
coordinates of pass points for the full ground control 
adjustment are 45, 57, and 197 mm, respectively. 
RMS of Adjusted Object 
Coordinates (method 1) 
  
EES 
    
RMS (mm) 
o 
© 
© 
  
0.25 0.5 1 
GPS Accuracy (m) 
  
  
  
Figure 1. RMS of X, Y, and Z Coordinates of All Object Points 
(method 1) 
155 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996