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2 TO MEASURE AIRCRAFT POSE BASED WITH 
PARAPOINT FEEDBACK ITERATION 
2.1 Imaging model of optical-electric phototheodolite 
It records distances from central of camera to aircraft and 
photography orientation of camera expressed by a vertical 
angle B and a horizontal angle a while optical-electric 
phototheodolite takes photos of aircraft (see Figurel). 
ZA 
   
MA 
   
  
photography 
orientation 
  
  
  
Figure 1 Imaging model of 
optical-electric phototheodolite 
  
P odi i 
Suppose-local G ordina te System n of, ircraft model jkes figure 
"jour 2 Coordináte s Syste airplane Ede 
2 and disiihce between aircralt and camera to be D, then when 
aircraft is in position like figure | during its flight, position [X,, 
Ym Zn] of aircraft in ground coordinate will is: 
X, -Dxcos( B)xsin( a) 
Y, D »sin( //) (1) 
Coordinate ([X'Y'Z'] of any surface point of aircraft in ground 
coordinate can be described in expression (2): 
X X X 
Y |2R Y «| Y, (2) 
zZ zi 
m 
where: R' is a rotation matrix between aiplane coordinate 
system and ground coordinate system; 
[X Y Z] is coordinate of aircraft surface point in aircraft 
coordinate system. 
The relation between coordinate of points on the aircraft in 
ground coordinate system and coordinate of pixels on the 
photos can be expressed by photogrammetry collinear equation: 
a(X —-X,)-b(Y -Y,)e-c(Z -Z,) 
QC X yu poc. 7 
A(X Xr - Yee -Z) 
aX — XV +8, (Y ~- YY +e (Z —Z,) 
  
=f 
  
y — Vo = -f 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 
F, 
  
Vol XXXV, Part B5. Istanbul 2004 
For derivation convenience below, collinear equation 
can be written as expression (3). 
4 y 
XX 7 vf EC YY, = =f E (3) 
Z Z 
X,Y,Z can be described as following form: 
X 
: X An Qt 
yisR"CeRe|y-R'"ely,|-R'«Y. 
7 Z 7. Z5 
where: 
a, a, a,| isrotation matrix of camera, 
R=|5 b b, 
CC 
a. Ga d is rotation matrix of aircraft 
R = b. b, b, itself. 
Cy Cy | 
  
GF. GF 
“da + ud “dk + Ste dX, nF 
og OK X s 
ax, or. ez. 
  
  
GE 
x eos de + 
co 
AF OF or oF AJ oF 
s ar, d : 
=F + do + do + fds + etu. —dy, + a7. 
p Oc J 
vi A 
€ m "m 
  
  
  
  
Its error equations are as following: 
a, Ap +a Amt a Arta AX Ya AY. +a AZ, 1, 
Vm, ND T ODE AK a NY, Cla. Y Td, AZ —1 
5 3 
Formula (1) (3) and (5) constitutes imaging model of 
optical-electric phototheodolite and its error question. 
2.2 Para-point and Parapoint Feedback Iteration Algorithm 
To measure aircraft pose during its flight by using image 
sequences produced by optical-electric phototheodolite, it is 
relatively prefect measurement method to compare real images 
with simulation images, the work steps of the method is as 
following: first of all, high accurate aircraft model is 
established by using close-range photogrammetry method; then 
a simulation imaging system of optical-electric phototheodolite 
is established which can produce simulate aircraft images in 
any flying pose of aircraft; finally taking real image obtained 
by optical-electric  phototheodolite as base image, the 
simulation system is driven to produce images which outline is 
compared with that of base images until the outline is 
consistent with the base image, at this time the aircraft pose in 
last simulation image are deem the final pose of aircraft. 
So as to solve match between simulation image and real image, 
we proposed the Method of Least Squares base on Parapoint 
Feedback Iteration (PFI). PFI adjust dynamically boundaries of 
simulation image by use of least square method according to 
difference between outline edge of image to be approached and