Today I read a paper titled “Shape and Trajectory Tracking of Moving Obstacles”
The abstract is:
This work presents new methods and algorithms for tracking the shape and trajectory of moving reflecting obstacles with broken rays, or rays reflecting at an obstacle
While in tomography the focus of the reconstruction method is to recover the velocity structure of the domain, the shape and trajectory reconstruction procedure directly finds the shape and trajectory of the obstacle
The physical signal carrier for this innovative method are ultrasonic beams
When the speed of sound is constant, the rays are straight line segments and the shape and trajectory of moving objects will be reconstructed with methods based on the travel time equation and ellipsoid geometry
For variable speed of sound, we start with the eikonal equation and a system of differential equations that has its origins in acoustics and seismology
In this case, the rays are curves that are not necessarily straight line segments and we develop algorithms for shape and trajectory tracking based on the numerical solution of these equations
We present methods and algorithms for shape and trajectory tracking of moving obstacles with reflected rays when the location of the receiver of the reflected ray is not known in advance
The shape and trajectory tracking method is very efficient because it is not necessary for the reflected signal to traverse the whole domain or the same path back to the transmitter
It could be received close to the point of reflection or far away from the transmitter
This optimizes the energy spent by transmitters for tracking the object, reduces signal attenuation and improves image resolution
It is a safe and secure method
We also present algorithms for tracking the shape and trajectory of absorbing obstacles
The new methods and algorithms for shape and trajectory tracking enable new applications and an application to one-hop Internet routing is presented