niversity, 
ıtomated 
xtraction 
s Proc. 
les with 
Orlando, 
|. 2486, 
mmercial 
|gulation. 
of Digital 
, Suisse, 
lung von 
digitale 
immetrie, 
surement 
T. Dans 
Stuttgart, 
>. 1995. 
Images. 
25-134. 
)perative 
Ice, 195 
is in 3D 
the Role 
Stockolm, 
A., et 
station of 
Pattern 
) p.570- 
semantic 
ym aerial 
tzerland, 
> relative 
ammetric 
9.47-55. 
tion d'un 
Bulletin 
National, 
Towards 
esolution 
urnal of 
50 (4), 
AIRBORNE GPS 
K. Jeyapalan 
Professor of Civil Engineering 
Iowa State University 
Ames, Iowa 50011 
United States of America 
KEY WORDS: GPS, Photogrammetry, Calibration 
ABSTRACT: 
The paper gives the theory of airborne GPS related to Photogrammetry and the results of a self calibration used to validate the theory. 
Accordingly, no ground control points are required for mapping using a strip or block of photographs provided the site is within 10 Km of 
the calibration site. 
INTRODUCTION 
Global Positioning System (GPS) technology has been developed in 
recent years such that the position of moving objects can be 
determined to about +0.2mm relative accuracy and about + 2cm 
absolute accuracy. The airborne GPS research was conducted at 
Iowa State University from April 1993 to May 1995. A series of 
four tests were carried out in St. Louis, Missouri and in Ames, Iowa. 
All tests, except one, were done in cooperation with Ashtech and 
Surdex Inc., using Cessna aircraft, LMK 2000 camera and Ashtech 
receivers. The objective of this research was to use airborne GPS to 
take aerial photographs at predetermined locations, to determine the 
best aerial camera location and orientation for mapping. 
The research showed that Airborne GPS is feasible. In block 
triangulation no ground controls are required. In a strip, no ground 
controls are required provided either the omega angle (rotation about 
the y axis) of the camera is known or the height difference between 
2 or more points in the y direction are known. The research showed 
that the omega angle of the camera can be determined to an 
accuracy of 0.0001 radians by a self calibration from the omega 
angle of the aircraft determined by airborne GPS, provided the 
calibration site is within 10km of the photographic site. 
The objectives of this paper are to describe briefly photogrammetry 
and kinematic GPS as they relate to airborne GPS, give the 
summary of the self calibration used to test airborne GPS, and the 
conclusions and recommendation. 
PHOTOGRAMMETRY 
In photogrammetry the photo coordinates (x, y) are related to the 
ground coordinates (X5,yg,z5) by the following equation: 
X- X, = f(all(x; - x) * a12 (yo-y,)*a13(25-2,)) (a3 1 (xg - 
X,) + 332 (yo-y,)*a33(25-7,)) * radial distortion ** decentering 
distortion + refraction 
y-y, = f(a21(Xg - X,) + 822 (Yo-Yo) +a23(26-2,))/(a31(X; - X,) 
* a32 (yo-y,)*a33(z5-27,)) * radial distortion + 
decentering distortion + refraction (1) 
where x,, y,, f are interior orientation elements, (x , y , z ) are the 
nodal point coordinates in the ground coordinates system. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
and A =R,RORG = all al2 al3 
a21 a22 a23 
a3l a32 a33 
Where R£R®,Rd are the rotation matrix required to make the photo 
coordinates axes (x,y,z) parallel to the ground coordinate axes by 
rotating first about x axis by à , then about y axis by ¢ and finally 
about z axis by K. The K,$,Ó are known as the orientation angles. 
The x,, y, z,, K,$,Ó are known as the exterior orientation elements. 
The objective of photogrammetry is to determine (Xs, yo, za) of a 
point from the photo coordinates of two or more photographs. This 
is done by three methods: Analog, analytical and self calibration. 
In the analog method, the interior orientation, radial and decentering 
distortions are assumed small. The projectors are used to project the 
images and produce the stereo models. When producing the stereo 
model, five of the twelve exterior orientation elements are 
determined by relative orientation. The stereo model is scaled and 
leveled using external ground control points, thus determining the 
other seven exterior orientation elements. Special instruments such 
as Zeiss Z8 are designed to produce the stereo model and then plot 
the map. 
In the analytical method, the photo coordinates are corrected for 
interior orientation, radial and decentering distortions given by the 
calibration of the camera. The photo coordinates of two or more 
photos, together with three or more known ground control are 
simultaneously adjusted to give the ground coordinates. Software 
such as "Albany" is capable of such adjustment. Some stereo 
plotters which are connected to computers for doing these 
computations in real time and which assist in driving the plotters are 
known as analytical plotters. 
In self calibration, the interior orientation elements, the radial and 
decentering lens distortion elements, and the exterior orientation 
elements are simultaneously determined with unknown ground 
control points using the photo coordinates of two or more photos 
and a number of ground control points. The method used is 
normally the least squares constraint method in which any of the 
parameters are constrained to its known accuracy. The program 
such as *Calib" is capable of this adjustment. 
377