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a building and a grid of ultrasonic sensors placed on the ceiling. The 3D
position of a Bat can be determined by only three distance measurements,
since the sensors placed on the ceiling are always above the receiver.
There are three main approaches for distance measurement:
Direct measurement is the measurement of distances using an action or a
physical movement. For example, a robot may extend a probe until it
touches an object to measure the distance from it. The direct measurement
is simple to understand but difficult to achieve in an automatic way
because of the complexity involved in the coordination of physical
movements of an automaton.
Time-of-flight method estimates the distance between a moving object and
a fixed point by measuring the time a signal takes to travel between the
object and point P at a known speed. In more detail, the mobile device
sends a signal to a reference device, which in turn sends it back to the
mobile device. Then the mobile device measures the round-trip time
(RTT) of the signal. This leads to a circle, whose radius corresponds to
half of RTT and whose centre is on the reference device. Therefore, a
position estimation of the mobile device can be obtained by measuring
three circles at least and by calculating their intersection.
For example, an ultrasound impulse emitted from an object, travelling
at 344 m/s, takes 29 s for the RTT to a fixed reference point P . This
means it takes 14.5 s to arrive to the point P allowing us to conclude that
the object is 5 m away point P .
The use of electromagnetic waves such as RF ones in time-of-flight
measurements is possible but requires very accurate clocks. In fact a light
or RF pulse travelling at a speed of 299,800 m/s, will run 5 m in 16.7 ns.
Another issue related to time-of-flight is the synchronization. When a
single measurement is needed, as in the RTT of sound waves or radar
reflections, synchronization is easy to achieve since the transmitter is the same
as the receiver. In the GPS [5] the receiver is not synchronized with the
satellite transmitters, so it cannot exactly measure the time that signal takes
to reach the Earth from space. Therefore, the GPS satellites are synchronized
with each other and send their local clocks along with the pulses thus allow-
ing receivers to estimate the time-of-flight. As a consequence, GPS receivers
can calculate their position in 3D space (latitude, longitude and altitude)
using four satellites. The satellites are always above the receivers so only three
satellites could be used to provide distance measurements to estimate the
position in a 3D space. The GPS receiver requires a fourth satellite measure-
ment to know the time shift between its local clock and the satellite clocks.
Attenuation method takes into account that the intensity of a signal
decreases as the distance from the source increases. Given a function
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