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P : ; 
VOX x =v, Z +7) (6) 
Suppose rotation matrix of optical-electric phototheodolite 
camera is R and rotation matrix of aircraft is R , the beam 
is transform to coordinate system of aircraft model, so 
: -1 -l 
VRR (7) 
Normally aircraft model is expressed by triangular irregular net 
(TIN). First of all, the data collection of parallel projection 
between beam vector and triangle net on aircraft model surface 
in three plane space are produced, then triangles intersecting 
with projection beam are calculated so as to remove a lot of 
triangle that don't intersect beam. Large amount of intersection 
calculation can be avoided; then, intersection point of spatial 
triangle net extracted and projection beam are calculated by 
using rapid intersection algorithm proposed by Tomas Moller 
etc. [10]. 
Suppose O(X,Y,Z) is one point in beam and D is direction 
vector of beam, beam equation is: 
V ( H=0+1D (8) 
Suppose three vertex coordinates of triangle is Vi(X,,Y Zi)! 
V)(X5,Y5,Z5) V 4(X5, Y ,Z3)L coordinate of each point in triangle 
can be expressed follow as by parameter variable u and v: 
Tu v)yz(u-u-vV s Hl, (9) 
where: (u,v) is central coordinate of triangle that meet: 
u 2 0,v Z 0,(u *- v) €1 because beam intersect triangle, 
there are V(f) = T(u,v) ncombination between(8)and 
BIBIT 
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y 
Defining: £, =) m scis =V, -FTzO0-F, 
There are] 
t (Tx Ee E, 
=——| (Dx E,)oT 
iE (DxE,) (11) 
y F (ZxE )e D 
If coordinates of three points in every triangle are input into 
formula (11), parameter coordinate of intersection point 
between beam and triangle lt u v] can be calculated, 
then [1 u v| is input into formula (9), intersection point 
coordinate between beam and triangle is obtained. 
3 EXPERIMENT 
At the beginning of the experiment, consecutive image 
sequences of aircraft flying are captured by optical-electric 
phototheodolite camera. Images and corresponding TIN model 
are shown in Figure 4. 
If aircraft pose in the first frame of image sequence is taken as 
known values, due to shooting at the speed of 1000 frames per 
second by high speed camera, it is possible that aircraft pose of 
former frame are taken as initial value of next frame to 
calculate final aircraft pose by using PFI method. Table 1 is the 
result of simulation image pose and the result of aircraft pose 
produced by using PFI method. 
  
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
Figure 4 Textured Model and Wireframe Model of 
Airplane in frame 1 and frame 16 
  
  
  
   
    
   
  
   
    
  
   
   
   
    
  
  
  
0. 50 
0. 40 
  
0. 30 
0. 20 
0. 10 
0. 00 
- 0. 10 
  
  
   
   
   
    
   
   
   
  
  
  
  
- 0. 20 
Figure 5 Absolute error curve of pose measurement 
Figure 5 shows the curve of difference between known real 
pose angle and pose angle calculated by PFI method. It can be 
seen from the curve that the accuracy of angle Kapa is highest 
and that of angle wis lowest. The reason is that at current pose, 
the range of aircraft objective on image is wider in its X 
direction and Y direction and rotation angle around Z axis 
greatly affects change of outline while change of angle w 
affects outline little. Generally it can be said that the result is 
correlated closely with the pose of simulation image sequence. 
4 CONCLUSION 
The paper proposed a new measurement method of aircraft 
pose based on image sequence. Based on the analysis of all 
existing measurement methods of aircraft pose, we proposed 
the measurement method using Parapoint Feedback Iteration. 
Experiments have been conducted and the results show the 
validity of PFI method. PFI method is extension of traditional 
least square method, it is dynamic approximation process. The 
method can be applied to other rigid moving body. 
ACKNOWLEDGE 
We would like to thank the support of The Research Fund for 
the Doctoral Program of Higher Education (20010486011).