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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
2.1.2 Image observations. A common practice is to extend
the collinearity equation with various parameters to acquire a
model, which more accurately corresponds the imaging conditi-
ons (Brown (1976), Ebner (1976), Kilpelà (1981), Jacobsen
(1982), Fraser (1997), Cramer er al. (2002), Jacobsen (2003)).
Mathematical parameters used in this study were the well-
known Ebner’s parameters (Ebner 1976). The physical defor-
mation model applied in this investigation was the following:
Ax =dxy — RE + xr? + kyr d kar?)
c (1)
2 2
* p(r^ *2x^!)r2poxy t Bx * Bay
y 2 4
Ay = dyy ——de + y(kr^ * kyr T: kar®)
e
2 2
*2pyuxy* po(r^ t 2y^)
2 2 2 . . .
where r^ - x^ y^, kl, K2 and k3 model radial distortions,
pl and p2 model tangential distortions and Bl and B2 model
affinity and shearing.
2.1.3 | GPS/IMU- position observations. In the ideal situati-
on, the model for the GPS/IMU position observations consists
at most of the corrections for the datum and the lever arm. Li-
near zero- or first-order time dependent lever arm or shift cor-
rections are sometimes necessary; especially they were indis-
pensable with the traditional GPS-supported case. A general
model for the GPS/IMU-position observations is the following:
„m u$ jn m
XGps r1MU. = 4Raatum X0 + dX datum
na PT
Datum
m p ef S
FRÜDAXPS e$ ee Xu
V ——^
Leverarm Re mainingerrors
2.14 GPS/IMU-attitude observations. The model for the
GPS/IMU-attitude observations is the following:
zn PRA : s
l'epsrimu 7 T (0° ) +0 + Ont (4)
T transforms the photogrammetric angles to the navigation
angles. The transformation includes the — boresight
- . . b . -
misalignment correction (R = R,R,, with rotation
; B i : Des
matrixes R s from camera frame to IMU body frame, R, from
object frame to IMU body frame and R from camera frame
to object frame). Additional corrections can be used to correct
remaining zero or first order time dependent errors.
2.1.5 Selection of appropriate parameters. With typical
block configurations a feasible parameter combination is 1, 2a
or 2b, 3 and 4 (dX, dY). Due to correlations of the parameters,
the appropriate parameters must be selected based on analysis
of their correlations and quality (Jacobsen 2003).
The height correction is probably the most problematic
unknown. Several causes result in need for the height
correction; these include changes in the principal distance,
lever arm inaccuracies, datum errors and inaccuracy of the GPS
height determination. The camera dependent height corrections
can be separated from the other mentioned sources, if two
blocks with different flying heights are adjusted simultaneously
(Jacobsen 2003, Tempelmann er al. 2003). In this article
blocks with single flying height are used, and the height
correction is modeled as the principal distance correction; this
is an accurate approach, if height error components are the
same in the calibration and the mapping sites (see also
Jacobsen 2003).
2.2 Calibration block structures
An important factor affecting the cost of calibration is the
-alibration block structure. The important parameters are the
flight lines and the ground control points (GCPs). Honkavaara
(2003) evaluated theoretically the determinability of the
boresight and interior orientation parameters with various
block structures and GCP configurations.
Flight line configurations can be grouped, for instance, into
three classes (see also Figure 1):
|l. Comprehensive: several flight lines and crossing flight
lines.
2. Cross: two perpendicular bi-directional flight lines.
3. I-block: single bi-directional flight line
The cross-shaped block appears to be a sufficient choice for the
determination of the most important parameters (e.g.
Honkavaara 2003, Tempelmann er al. 2003). The
comprehensive block is the most accurate alternative, but its
- cost probably does not cover the benefits. Even the I-shaped
167
block allows the determination of the boresight misalignments,
interior orientations and many of the image deformation
parameters.
Basically, in the GPS/IMU-supported case the GCPs are nee-
ded for determination of the datum parameters and the height
corrections, and for the quality control. In addition, some of the
image deformation parameters may require GCPs (Jacobsen
2003). In order to determine the datum and height correction
accurately, several GCPs are needed, e.g. 10. However, even 1
reliable GCP improves reliability (Honkavaara 2003).
If the calibration is performed on a daily basis, the calibration
block should be as cost effective as possible. For this purpose
the most attractive block structure is the I-shaped block with
minimal or no GCPs. The extra expense of this approach is an
additional flying of a short part (e.g. 9 images) of one flight
line in the opposite direction. If the flight mission is long, this
procedure may be necessary both in the beginning and in the
end of it (Scroth 2003).
3. MATERIALS AND METHODS
3.1 Calibration blocks
Empirical investigation was made using 10 calibration blocks
photographed by the National Land Survey of Finland (NLS)
over the FGI's Sjókulla calibration fields in summer 2002; the
details of the blocks are shown in Table 1 and in Figure 2. The
image scales were 1:8000 and 1:16000; calibrations were made
using single flying height. The data have been thoroughly
described by Honkavaara (2003). From the complete blocks
reduced blocks were extracted, resulting in three different
block structures:
