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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
Figure 4: Control points (blue) of the DLR network in comparison with the Duxbury and Callahan control point network (letters).
The density has increased by a factor of two while the uncertainty of the control point coordinates is approx, a 6 times
lower.
To successfully compute a block adjustment with Viking orbiter
data, navigation information needed to be improved prior to the
computation. Therefore, we improved the pointing information
by fitting the predicted limb position in the image to the
observed figure. For images with very high resolution -
showing only parts of the surface but not the limb of Phobos -
an overlay of the Duxbury and Callahan control points was
produced and moved to fit to surface features in the image to
improve the camera orientation. To further optimize results,
accuracy values for orientation data were adjusted according to
the computed normalized residuals. Overall, a bundle block
adjustment with Viking orbiter data was very sensitive to
variations in the stochastic model. Object points were
determined with uncertainties Ox, o y , Oz of 111 m , 90 m, 101
m when a measurement accuracy of 1 pixel was assumed.
For the computation of a global control network both data sets
were combined through conjugate points in overlapping areas.
Since reduction of the Viking orbiter image measurements was
very dependent on the stochastic model chosen Viking image
orientations were introduced as unknown parameters rather than
additional observed values. The computed spacecraft
orientations for MEX and the Viking orbiters were then used to
determine the object point coordinates of the control points in a
second run. Furthermore, a Baarda gross error detection
(Baarda, 1968) was applied to remove misidentified
measurements. Thus, uncertainties of the 3D ground
coordinates could significantly be reduced by a factor of 3 for
points in SRC images and a factor of approx. 6 for points in
Viking images (cf. Tabel 3).
4.4 Global Shape
Control points are irregularly distributed over the surface of
Phobos (see Figure 4). To determine the shape of Phobos a
triangulation between the points was computed. A few gross
errors remain in the coordinates of the control points,
represented by artifacts. Even though the distribution of the 660
control points is quite irregular (Figure 4) the network is a good
basis for a global shape model, which shows many details such
as of medium sized craters. A preliminary version of the shape
model is shown in Figure 5.
4.5 Rotation Parameter
For the reduction of the control point network, nominal values
of unknown parameters of the bundle block adjustment are
computed with respect to the body centered, body fixed,
coordinate frame. Thus, a different orientation of the observed
body may lead to a solution with reduced stresses in the
network as the nominal camera orientations - acting as
unknowns and observed parameters in the adjustment - do
change with the orientation of the body. This situation is
exploited to observe rotational parameters of Phobos.
Even though Phobos is in a synchronous orbit around Mars, a
free libration can be observed due to the varying angular speeds
along an elliptical orbit. Furthermore, Phobos’ pronounced non-
spherical body interacts with the gravitational field of Mars
causing a forced libration, a superimposed sinusoidal oscillation.
We concentrated on the observation of the forced libration
amplitude from the control point network. The least-squares
adjustment of the control point network was computed for a
varying forced libration amplituds. Subsequent studies of the
residuals of the control