International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
parameters determination using linear features represented
either analytically or in free-form. Finally, in section 5 the status
of an ongoing research project on the subject is presented and
future work is outlined.
2. SAR OVERVIEW
Synthetic Aperture Radar (SAR) is a rapidly emerging
technology with a central role in a wide range of civilian and
military applications. Interferometry (IFSAR), Differential
Interferometry (DIFSAR) and Stereo SAR are the three leading
SAR-based techniques extensively employed in topographic
mapping, targeting, deformation analysis, geological and
metrological exploration and other geospatial fields. Similarly
to optical sensors, a prerequisite for generating accurate
geospatial products from SAR imagery is accurate SAR payload
orientation. For optical imagery this entails determining sensor
position and attitude, here, an accurate knowledge of sensor
position and velocity is required. Traditional methods of
obtaining position and velocity of SAR sensors either entirely
rely on the available on-board navigation telemetry or aim to
improve the accuracy of such telemetry using ground control
points (GCPs) manually identified on SAR images (Curlander,
1982; Mohr et al, 2001; Goncalves, 2002). Unfortunately, quite
in contrast to a relative simplicity of manual identification of
control points in optical imagery, such a task is far from being
simple for SAR images, due to their inherent "speckled" nature.
Moreover, that difficulty is considerably increased when
autonomous extraction and matching procedures are sought. A
promising direction to address the task at hand is to modify the
dimension of the primitives with which the registration is
carried out. Instead of using zero-dimensional GCPs, we may
use one-dimensional linear features, often corresponding to
elongated man-made objects (e.g., roads, rail-roads, hydrologic
features, etc,), that have a distinct appearance in SAR images.
What makes the returned EM signal from such features rather
distinct is the fact that these features are usually
(topographically) smoother than their immediate environment
and their dielectric properties are also quite different. In fact, the
problem of extracting such features both manually and even
automatically has been successfully addressed in the literature
(e.g. Li et al, 1995). However, so far, even when linear features
have been successfully detected and matched with their
counterparts from some GIS network, the subsequent
orientation procedures have remained point-based. Also, as
we'll be motivated in the following feature-based orientation
procedures may be helpful It is therefore this particular gap that
the project reported herein is trying to close.
Before presenting our general framework that deals with
orientation of SAR images with linear features, we briefly
summarize, following (Mikhail et al., 2001) the geometry model
of a generic SAR sensor and make explicit a few central
arguments addressed in the sequel of the paper.
Each pixel in a preprocessed SAR image is associated with two
measurements that are made for a given scatterer, being its
range and its Doppler frequency shift. The range is determined
by the amount of time it takes for the EM pulse to make a
round-trip between the sensor and the scatterer. The Doppler
parameter is established from the well-known physical
phenomenon entitled the "Doppler Effect", according to which
frequency shift occurs when two objects are moving towards
each other. In three-dimensional space, the Doppler parameter
constraints the scatterer to reside on the cone with an apex at the
sensor position, its axis coincident with SAR velocity vector
and with cone angle being equal to the angle between the range
vector (to the scatterer) and the SAR velocity vector as shown
in Figure 1.
Velocity Vector
Aperture Center
Figure 1: Doppler cone condition.
(Adopted from Mikhail et al. (2001))
Formally, the two SAR measurements are:
21 88-5
f= (1)
r=|P-8
where:
f,R are the Doppler shift and range measurements
respectively, PR are the 3-D position and velocity of the
J
sensor, À is the radar wave-length and P corresponds to the
3-D coordinates of the scatterer position on the ground.
The problem of SAR orientation is thus, to accurately determine
the sensor trajectory PR using SAR observables and some
ground control. Traditionally, that is done by applying a simple
correction (in most cases polynomial) model to the trajectory
state vector and using a set of ground control points to estimate
the coefficients of the correction polynomial. However, apart
from the fact that these techniques required a well-defined set of
control points which, as has been stressed earlier, cannot be
easily and reliably detected (even manually) there is another
problem associated with the rather simplistic solution of the
orientation problem. Qualitatively speaking, the traditionally
applied "correction" models only account for systematic errors
in the sensor trajectory. In real scenarios, however, especially,
for highly maneuvering airborne SAR systems, undergoing
rough platform perturbations and instabilities, that simplistic
trajectory modeling may not be adequate. Here, faithfully
modeling both the systematic as well as random effects in the
trajectory may be necessary. One way of doing it is to take
advantage of highly accurate on-board positioning systems (e.g.,
dual frequency GPS receivers with high sampling rates) which
would directly yield an accurate trajectory. Another way, of
course, is to use a large and very densely distributed set of
control: points... ‚But in the, absence, of such
positioning/navigations systems and practical difficulties
associated with collecting sets of ground control points with the
above mentioned characteristics, other indirect methods
employing ground information have to be devised.
It is therefore the purpose of this paper to present a
mathematically and statistically rigorous model for SAR geo-
referencing using general linear-features in objects space. In the
next two sections we will show that the proposed model indeed
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