of unknowns. In the conventional approach, the exterior
orientation parameters are estimated only for so-called ori-
entation points Ix, which are introduced at certain time
intervals, e.g. once for every 1000'^ readout cycle. In
between, the parameters of each 3-line image I; are ex-
pressed as polynomial functions of the parameters at the
neighbouring orientation points (Ebner et al. 1994). While
this approach reduces the number of unknown exterior ori-
entation parameters to a reasonable amount, its inherent
disadvantage is that the estimated position parameters are
not associated with a physical model of the spacecraft tra-
jectory.
3.2 Combined Approach
To overcome this drawback, the bundle adjustment algo-
rithm is supplemented by a rigorous dynamical modeling
of the spacecraft motion to take orbital constraints into ac-
count. The camera position parameters æ“(t) which have
been estimated so far at certain time intervals, are now
expressed by the 6 parameters of the epoch state vector
yo and additional force model parameters p:
e^ (t) — e(t, yo, p) (2)
The force model parameters p may comprise e.g. the drag
coefficient. Figure 2 demonstrates the combined approach,
which exploits the fact that the spacecraft proceeds along
an orbit trajectory and all camera positions lie on this
trajectory, when estimating the spacecraft’s epoch state
vector.
Epoch State Vector y, and A Priori
Covariance Cov(y,)
x
Predicted Trajectory
Cov(y,)
Estimation of y, by Combined
Adjustment wv. Improved
Trajectory
Figure 2: Combined approach for the reconstruction of
the exterior orientation of 3-line images (Montenbruck et
al. 1994)
Compared to the conventional approach the combined ap-
proach has essential advantages, which can be summarized
as follows:
e Full utilization of the information content of the
tracking data in a statistically consistent way
e À reduced number of unknown parameters
e Accuracy improvements for the photogrammetric re-
sults as well as the epoch state vector
160
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Statistically, the resulting estimation procedure is equiva-
lent to a combined orbit determination and bundle adjust-
ment from tracking data and 3-line image data.
Due to the lack of a dynamical model describing the cam-
era's attitude behaviour during an imaging sequence, it is
not possible to introduce attitude constraints into the bun-
dle adjustment in a similar way as the orbital constraints.
To this end, the concept of orientation points is maintained
for the camera's attitude. The attitude
0(t) 2 0(t,0) (3)
of the camera can be represented by the attitude vector ©
at selected orientation points. Based on (1), (2) and (3),
the image coordinates may finally be written as
u = uU) = u(t2,99,5,0) . (4)
The mathematical model of the combined approach is de-
scribed in detail in Montenbruck et al. (1994) and Ohlhof
(1996).
4 PRACTICAL RESULTS ON MOMS-02/D2
IMAGE ORIENTATION
4.1 Preprocessing
The first step in the photogrammetric processing chain
is the determination of conjugate points in the images.
Digital image matching is an appropriate technique to au-
tomatically determine these points. Before starting the
matching procedure, the image strip of the nadir looking
CCD array was resampled by factor 3 to obtain the same
pixel size in all 3 strips. Using the least squares region-
growing matching algorithm (Heipke et al. 1996) about
14000 conjugate points were found. The standard devi-
ations of the image coordinates were assumed to be 0.3
pixel.
In the area covered by the 3 image strips 79 DGPS-derived
natural ground control points (GCP) were available with
a standard deviation of 0.1m in X, Y and Z. 75 points
were identified and measured in the images by Baltsavias
(1995). Due to difficulties with the localization of the
points, the standard deviations of the measured image co-
ordinates were chosen to 0.5 pixel.
During the D2 mission tracking was routinely performed
using the Tracking and Data Relay Satellite System
(TDRSS). The orbit determination for orbit #75B is based
on 900 S-Band Doppler measurements with a sampling
rate of 10s covering about 180 minutes. The force mod-
eling comprises the drag coefficient and 5 parameters de-
scribing perturbations caused by the attitude thruster sys-
tem. The pure statistical standard deviations of the epoch
state vector components were 30 m in X,Y, Z, whereas un-
modeled effects resulting from the attitude thruster system
contribute an additional error of up to 50m in X,Y and
Z (Braun, Reigber 1994).
A major problem arose from the fact that the image
recording times could only approximately be related to
the time scale UTC of the orbit and attitude information.
Since no parameter for the time offset exists in the bundle
adjustment algorithm, a realistic weighting matrix for the
epoch state vector components has been derived relaxing
the orbital
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