Using Invariant Theory to Obtain Estimates of Unknown Shape and Motion, and Imaging Moving Objects in 3D from Single Aperture<br/><br/>Synthetic Aperture Radar

Tuesday, October 18, 2005 - 10:20am - 11:10am
EE/CS 3-180
Mark Stuff (General Dynamics Advanced Information Systems)
When a moving object is imaged with conventional synthetic aperture radar (SAR) the result is a displaced smear. This is due to
the extra information the objectmotion is imparting to the radar return. When a sensor collects data from a moving extended object,
estimation of the direction vectors from the object to the sensor is often essential to the extraction of useful information from
the sensor data. If the object or the sensor moves as result of uncontrolled or unknown forces, simple parametric models for the
angular motions often rapidly loose fidelity. So, even if the object can be modeled parametrically, nonparametric motion estimates
are desirable.

In one example of such a problem, a direct approach to estimating all the unknowns leads to difficult nonlinear optimization
problems. But a characterization of the shape of the object, using the right choice of geometric invariants, can decouple the
problem, temporarily isolating the object shape estimation from the motion estimation. This facilitates the extraction of
nonparametric motion estimates both by subdividing the parameter space, and by enabling parts of the problem to be solved using
linear methods.

If the motion is rich enough there should be a possibility of forming a 3D image of the object. This involves understanding the
way the radar data is arranged in phase space. The data lies on a convoluted surface that occupies three dimensions rather than the
two dimensional plane used in conventional SAR. To achieve three dimensional images the data must be extrapolated from the surface
into a volume. In this complex space, there is a great deal of structure and therefore the possibility of extrapolating to a volume
of data.
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