ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
Short Base Long Base
Figure 4: Definition of orientation fixes and short and long
base.
Orientation fixes are characterized by:
e An orientation fix is the orientation of the sensor at a
certain time
Geometrically best conditions are obtained when the
distance between two fixes equals the short base
The time interval between two fixes depends on the
gyro (IMU) quality
The six orientation parameters for each fix are updated
by the triangulation process; each fix is identified by
the unique time
One scene (image) has multiple orientation fixes
Forward scene
Nadir scene
Backward scen
Orientation fixes
* Identical orientation for F,N,B
Figure 5: Orientation fixes at predefined fixed intervals.
3. THE MATHEMATICAL MODEL
3.1 Ground to Sensor Transformation
The mathematical model describes the transformation of a point
from the ground system to the orientation fixes.
Figure 6: Point projection between orientation fixes.
The ground to sensor transformation is characterized by:
e Points can be measured at any location
Each projected point falls in between two orientation
fixes
The transformation from ground to sensor is expressed
as a function of the two neighbouring orientation fixes
The image coordinates are expressed as a function of the
ground point (P;) and the orientation parameters of the two
neighbouring orientation fixes (k) and (k+1). The mathematical
model is given in full detail by Miiller (1991).
X; NZ NL OK,
(1)
X ioi Opa Pay K 1)
35 5G ys... Q)
Y To ood o)
The orientation parameters ( X ;K,) are computed from their
neighboring orientation fixes plus a correction term
(OX ,..ÓK,)derived from the GPS/IMU observations. The
interpolation coefficients (c) are a function of the time
differences from the neighboring orientation fixes. The basics
of this mathematical model go back to Otto Hofmann
(Hofmann, 1982)
A- 158
A OX T-cOX -óX,
(3)
K, CK, t -c9)K, OK,
f, -,
C; = /
f, -
ÖX, = e Xe + (1 —c,) Xo - X
OK, CK, ue + (1 cC, )K, > i
J
