ISPRS Commission III, Vol.34, Part 3A ,Photogrammetric Computer Vision“, Graz, 2002
“online” orthoimage production for areas with known DTM
without any additional effort in aerial triangulation.
Nonetheless, especially the experiences and results from the
OEEPE test (Heipke et al, 2002) have shown, that the
performance of direct georeferencing is limited by the quality
of the overall system calibration, which is due to the
extrapolation nature of this approach. Therefore, a correct and
highly accurate overall system calibration, sufficiently
describing all physical effects like translations and rotations
between the different sensor components as well as systematic
influences from camera and imagery, is inevitable to obtain
optimal performance in object space. Besides the need for a
correct calibration the stability and validity of these calibration
parameters is still an open task. Within all present test flights
the calibration was done only once, directly before flying the
test project. Furthermore, due to the lack of physically
separated calibration and project sites, the calibration was
performed in the final test area itself resulting in high time and
spatial correlations. Since no experiences on the variations of
system calibration parameters over time are available from
former tests this paper is focused on this specific task.
Within the next sections the functional mathematical model
used for system calibration and the test data material is
presented, where Section 4 is focused on the analysis of results
from the different real calibration flights. Since the flight data
was captured over a 8 week time interval using the same
GPS/inertial-camera system installation, recommendations on
long term stability of system calibration parameters are
possible.
2. SYSTEM CALIBRATION
System calibration is one major task in direct georeferencing.
One possible approach for system calibration is performed in a
two-step procedure, where the directly measured GPS/inertial
positions and attitudes are compared to the estimated exterior
orientations from conventional aerial triangulation. From
analysing positioning and attitude differences at each distinct
camera station the most common six calibration parameters
(translation offsets and misalignments between camera and
GPS/inertial component) are obtained. Although this procedure
has advantages since the output, ie. camera positions and
attitudes, of any bundle adjustment software provides
comparison values for system calibration, this approach almost
neglects the existing correlations between estimated orientation
elements and interior orientation of the imaging sensor. A quite
obvious example for these correlations is obtained from the
experiences of former test flights, where systematic vertical
offsets were proven which might be due to several reasons, e.g.
shifts in GPS/inertial positions, inconsistency in assumed focal
length or uncorrected systematic effects from image space. To
model these dependencies correctly an integrated or combined
bundle adjustment is favoured to determine the calibration
terms within one step. Besides consideration of the correlations
the integrated approach allows for handling the associated
accuracy of directly measured exterior orientation elements
properly. The basic mathematical model is presented in the
following.
2.1 Functional model
The functional model of integrated sensor orientation is based
on the well-known collinearity equations in Equation (1). The
tilde symbol indicates that the corresponding values are
introduced as directly observed unknowns from GPS/inertial
systems.
AUX Xo) *fi(Y - 19) *Tis(Z- Zo) | A.
x-z.2 Sot oM. 593571 A
"n3 (X - Xo) * 3(Y - Yo) * 3(Z - Zo)
(1)
FX ng) + PCT) taZ-Z
Fe Lott Pal? Yo) EM ZA
73 (X — Xo) * 53(Y - Yo) * 53(Z - Zo)
where — X,y,z- reduced image coordinates related to
perspective centre
X9, Yo, Z9 coordinates of perspective centre
rjj ^ elements of rotation matrix R
Ax, Ay = influence of additional parameters.
The elements of rotation Matrix R are obtained from the matrix
product
R=R} =R5(3,.8)- ARG (Aw, Ap,Ak) — Q)
where the indices indicate the P (photo or camera), B (body,
defined by inertial sensor axes) and L (local level) coordinate
frame. More details on the different coordinate frames and
appropriate rotations are given in Cramer, 20015. The attitudes
Q,Q,K are directly obtained from the GPS/inertial navigation
angles after transformation to the photogrammetric, e.g. local-
level reference coordinate system. Aw,A@,AK represent the
physical misalignment — so-called boresight alignment —
between body and camera or photo frame. This unknown
attitude offset has to be determined during calibration. The
translation offsets are not modelled so far, since they are
measured with standard survey methods before the flight
missions and already considered during GPS/inertial data
integration, normally.
Besides the already mentioned calibration parameters for
boresight calibration the functional model is extended by
additional parameters to model systematic offsets or linear
drifts of directly measured positions and attitudes. Therefore,
Equation (1) is modified with following Equation (3):
Ay= X tag tat
Vo=Y, +0, +0, ¢
Zo = 20 + Cp Tor
Q — 0 ug +4 d
Q-9Tvgv-t (3)
K=K+wy+w -t
This approach is quite similar to standard GPS-supported aerial
triangulation, where additional offset and drift correction terms
take care of remaining systematic errors in the GPS determined
perspective centre coordinates. Since the attitude offsets in
Equation (3) are highly correlated with the boresight alignment
as given in Equation (2) the wu, vy, wy parameters are also
modelling the physical misalignment, which replaces the three
attitude offsets in the ARS matrix. Since all unknown
parameters are re-introduced as pseudo-observations to model
the appropriate stochastic properties, the final linearised
observation equations are given in Equation (4).
Yen A mt old
Fp
wp fo epee] Py, "
v, 0 72 0/1. 1 LY
X
Ya 0 0 I g Ls
