Hardware Reference
In-Depth Information
Determining Position Through Trilateration
Distance ranging tells you how far away an object is from your measuring point in one
dimension, but it doesn't define the whole position. The distance between your position
and the target object determines a circle around your position (or a sphere, if you're
measuring in three dimensions). Your object could be anywhere on that circle.
In order to locate it within a two- or three-dimensional
space, though, you need to know more than distance. The
most common way to do this is by measuring the distance
from at least three points. This method is called
trilatera-
tion
. If you measure the object's distance from two points,
you get two possible places it could be on a plane, as
shown in Figure 8-9. When you add a third circle, you have
one distinct point on the plane where your object could
be. A similar method,
triangulation
, uses two known points
and calculates the position using the distance between
these points; it then uses the angles of the triangle formed
by those points and the position you want to know.
The Global Positioning System uses trilateration to determine
an object's position. GPS uses a network of satellites circling
the globe. The position of each satellite can be determined
from its flight path and the current time. Each one is broad-
casting its clock signal, and GPS receivers pick up that
broadcast. When a receiver has at least three satellites,
it can determine a rough position using the time difference
between transmission and reception. Most receivers use at
least six satellite signals to calculate their position, in order
to correct any errors. Cell phone location systems like
Wireless E911 calculate a phone's approximate position in
a similar fashion, by measuring the distance from multiple
cell towers based on the
time difference of arrival
(TDOA)
of signals from those towers.
Figure 8-9
Trilateration on a two-dimensional plane. Knowing the distance from one point defines a circle of
possible locations. Knowing the distance from two points narrows it to two possible points on the plane.
Knowing the distance from three points determines a single point on the plane.
