The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part R4. Beijing 2008
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one sequence are dedicated to long exposures to observe faint
background stars with visual magnitudes of m = 4 to 9, which
are used to control the camera pointing.
3.2 Camera Pointing
Camera pointing uncertainties have a major influence on the
accuracy of astrometric measurements. Long-time exposure
images containing background stars were taken during almost
all Phobos flybys since mid 2005. Stars are usually observed
just before and after a Phobos encounter, giving us the
opportunity to control/correct predicted pointing information
and check for possible pointing drifts during the flyby. In cases
in which just one star was observed, we assumed that a twist
angle with respect to the nominal orientation information is
negligible. This was later confirmed by the reduction of the
observations (cf. Section 3.4 ). To control the camera pointing
we compute image coordinates of stars from star catalogs (ESA,
1997, Roser and Bastian, 1992) applying nominal pointing
information and compare these with the observed line/sample
coordinates of the stars. Differences between the star positions
are interpreted as pointing displacement. Hence, all further
observations of the flyby are corrected accordingly. In general
the nominal pointing information for the SRC is in good
agreement with the observed positions of the stars and within
the accuracy constraints set by the initial specifications for
spacecraft orientation. Nevertheless, four outliers were found in
orbits 682, 2706, 2739 and 4568 where discrepancies between
predicted and observed star positions of up to 450 SRC pixels
were observed. During one image sequence the pointing
remains very stable. The average difference between the first
and the last image of a flyby sequence is 8 pixels which relates
to 0.004 degree.
Figure 1: Examples of recent flyby images obtained by the SRC with different flyby distances
3.3 Astrometric Measurements
While our previous analysis (Oberst et al., 2006) was based on
fitting an ellipsoidal model to the observed limb of Phobos, we
further improved our method by making use of a control point
network (Duxbury and Callahan, 1989a, Duxbury, 1991). The
3-D Cartesian coordinates of 315 control points, all of them
craters, some very large, are given with respect to the center of
mass of Phobos. The control points are identified in the SRC
images and line/sample coordinate pairs are measured. These
points are defined as the center of a crater on the mean local
surface (Duxbury and Callahan, 1989b). As craters are typically
observed from quite different viewing angles, much effort was
made to consistently measure their image coordinates. Points on
the crater rim were collected and an ellipse fit method was
applied to reconstruct the center of the crater on the level of the
crater rim. On average 9, but a minimum of 3, surface features
were identified and measured in each image. Using the Phobos
orbit model, the corrected camera pointing and the Phobos-fixed
coordinates of the craters, we computed the predicted image
coordinates of the control points. To fit the observed image
coordinates, the predicted line/sample pairs of the control points
were transformed. An iterative least-squares adjustment was
used to solve for the unknown transformation parameters,
rotation, scale and 2 translations. To derive information on the
position of the COM (center of mass) of Phobos, we then
computed the predicted line/sample coordinates of the the COM
for the specific image and applied the previously determined
transformation parameter.
3.4 Results
By April 2008, over 280 SRC images were obtained during 92
successful flyby maneuvers. As some images suffer from smear,
lack of identifiable control points, insufficient surface coverage,
or lack of background star observations, we considered 120
images from 51 orbits for the analysis. For these images the
iterative least-squares analysis to determine the transformation
parameters converged rapidly. Results indicated that both, the
scale factor and rotation parameter, are negligible for the
transformation leaving translations in line and sample direction
between the predicted and observed image coordinate sets. We
studied the translation vectors in the object space, especially in
along-track and across-track direction (radial to the central body
or out of the orbit plane) for the two recently released orbit
models (Jacobson and Rush, 2006, Lainey et al., 2007). While
no significant across-track offsets were found, small along-track
offsets between orbit prediction models and our observations
remain, ranging from 1.5 km to 2.6 km, depending on the orbit
model used (Willner et al., submitted). Phobos’ positions were
observed with an estimated accuracy of ±0.1km to ±0.5km
depending on the flyby distance. Comparing observed Phobos’
position with orbit predictions, both models show the same
discrepancy pattern, whereas differences to the orbit prediction
by Jacobson and Rush, (2006) are larger by approx 35%