  We study the uniqueness and accuracy of the numerical solution of the problem
of reconstruction of the shape and trajectory of a reflecting obstacle moving
in an inhomogeneous medium from travel times, start and end points, and initial
angles of ultrasonic rays reflecting at the obstacle. The speed of sound in the
domain when there is no obstacle present is known and provided as an input
parameter which together with the other initial data enables the algorithm to
trace ray paths and find their reflection points. The reflection points
determine with high-resolution the shape and trajectory of the obstacle. The
method has predictable computational complexity and performance and is very
efficient when it is parallelized and optimized because only a small portion of
the domain is reconstructed.
