  Assume that a source emits a signal in $3$-dimensional space at an unknown
time, which is received by at least~$5$ sensors. In almost all cases the
emission time and source position can be worked out uniquely from the knowledge
of the times when the sensors receive the signal. The task to do so is the
multilateration problem. But when there are several emission events originating
from several sources, the received signals must first be matched in order to
find the emission times and source positions. In this paper, we propose to use
algebraic relations between reception times to achieve this matching. A special
case occurs when the signals are actually echoes from a single emission event.
In this case, solving the signal matching problem allows one to reconstruct the
positions of the reflecting walls. We show that, no matter where the walls are
situated, our matching algorithm works correctly for almost all positions of
the sensors.
  In the first section of this paper we consider the multilateration problem,
which is equivalent to the GPS-problem, and give a simple algebraic solution
that applies in all dimensions.
