ACCURACY IMPROVEMENT OF THREE DIMENSIONAL POSITIONING USING SPOT IMAGERY 
* YEU, BOCK-MO 
* LEE, HYUN-JIK 
** SOHN, DUK-JAE 
* DEPARTMENT OF CIVIL ENGINEERING YONSEI UNIVERSITY, SEOUL, KOREA 
xx DEPARTMENT OF CIVIL ENGINEERING SEONAM UNIVERSITY, NAMWON, KOREA 
COMMISSION IV/2 
ABSTRACT 
This study aims to improve the accuracy of three dimensional positioning of SPOT imagery through 1)analysis of the 
optimum polynomial of exterior orientation for each preprocessing level, 2)through introduction of AP’ s(additional 
parameters) in the geometric adjustment of image distortion and 3)through elimination of gross errors in input data. 
Optimal exterior orientation polynomial for each preprocessing level(1B; 15 parameters, 1AP and 1A; 12 parameters) 
was determined as a result of this study. Also, as a result of studying the accuracy of level 1A it was found that 
in case of accurate GCPs(ground control points), 
self calibration(significance testing) bundle adjustment with 
significant AP's is sufficient, whereas in case of inaccurate GCPs, simultaneous adjustment of bundle adjustment 
with gross error detection is advisable. 
KEYWORD : SPOT imagery, optimal exterior orientation polynomial, 3-D positioning, simultaneous adjustment 
1. INTRODUCTION 
SPOT imagery has stable orbit characteristics, high 
resolution, suitable B/H ratio as well as off nadir viewing 
capabilities which makes stereo imagery possible. These 
characteristics makes SPOT imagery applicable in many fields 
such as agriculture, fishery, oceanography, environment 
studies and geology. Small scale topographic mapping and 
positioning of inaccessible areas are also made possible. 
Factors influencing the accuracy of positioning using the 
SPOT imagery include data format, preprocessing level, 
exterior orientation estimation method, accuracy of GCPs and 
method of adjustment. But it would be difficult to take all 
these factors into account in adjustment. Therefore a phased 
analysis of these factors were made in an effort to improve 
the positioning accuracy. 
The exterior orientation expressed as a function of the 
number of scanned lines and different photogrammetric film 
(level 1B and 1AP) and digital data(1A) of the same area were 
The 
polynomial and the suitable 
determined through analysis of these data. Also, in cases of 
inaccessible areas simultaneous adjustment method with gross 
the self 
used in this study. optimal exterior orientation 
preprocessing level were 
error detection and elimination was applied to 
calibration bundle adjustment method. 
2. THEORY OF SIMULTANEOUS ADJUSTMENT OF SPOT IMAGERY 
The theory of SPOT imagery positioning is applicable by 
used 
mostly in analytical photogrammetry. The geometric stability 
making appropriate changes to the bundle adjustment, 
of SPOT satellite makes it possible to consider the image 
geometry of the HRV sensor and the orbital parameters. 
mi 1 (Xi-Xoi )*mi2(Yi-Yoi )*m13(Zi-Zoi) 
  
  
F(x)=xi-xp-f +Axi=0 
m31 (Xi-Xo i )+m32 (Yi -Yo i )+m33 (Zi -Zo i ) 
m2 1 (Xi -Xo i )+m22 (Yi-Yo i )+m23 (Zi-Zoi ) 
F(y)= O-yp-f + À yi =0 
m3 1 (Xi—Xo i )+m32 (Yi -Yo i )+m33 (Zi-Zo i ) (1) 
The estimation of the exterior orientation, the position 
(Xoi, Yoi, Zoi) and attribute(#i, di, wi) of the satellite, 
was carried out by applying the polynomial of second order of 
scanned lines. This was then changed to apply in the 
determination of optimal polynomial for exterior orientation 
for each preprocessing level. 
Koi = Xo + K1 y + K7 y? 
$oi = bo + K2 y + Kg y? 
Goi = Wo + K3 y + Ko y? (2) 
Xoi 7 Xo * K y * Kio y? 
Yi 7YotKsytkKuy 
Zoi = Zo + K6 y + K12 y? 
The accuracy of input data and the adjustment method used are 
also important factors in the approximation of exterior 
orientation, and the data format changes for different areas. 
It is therefore necessary adjust the random error as well as 
the systematic and gross error in a systematic and a rational 
way. 
2.1 Introduction of AP's 
The AP's have different error characteristics according to 
the selected earth ellipsoid, the preprocessing level and the 
data format. The AP's not only improves the positioning 
accuracy but also contributes to the detection and elimination 
of gross errors. Care should be taken in the selection of the 
AP's because inappropriate selection could result in an 
unstable adjustment and degrading of the accuracy. 
It is effective to use the simultaneous adjustment with AP's 
which makes a simultaneous adjustment of all the observation 
errors, During this process, it is important that only 
effective parameters be selected and the significance testing 
of parameters be logically organized. 
To correct all geometric distortion of imagery, a 3rd order 
polynomial of 18 variables was selected as the AP's. The 
selected parameters are as follows. 
Ax=a1+aax+asy+a7 x2+ag xy+ag y2+a1 3x3+a1 4x2y+a1 5xy? 
Ay=a4+asx+a6y+a10x2+a1 1xy+a1 2Y2+a1 6X3+a1 7x2y+a1 8xy? (3)