Shape and Trajectory Tracking of Moving Obstacles

TL;DR

This paper introduces innovative algorithms for tracking the shape and movement of obstacles using ultrasonic reflections, applicable in variable sound speed environments and with unknown receiver locations, enhancing efficiency and security.

Contribution

It presents new methods for shape and trajectory tracking of moving obstacles with reflected ultrasonic rays, including algorithms for unknown receiver positions and absorbing obstacles, applicable in variable sound speed conditions.

Findings

Efficient shape and trajectory reconstruction without full domain traversal.

Algorithms work with unknown receiver locations, improving flexibility.

Application demonstrated in one-hop Internet routing.

Abstract

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.