Global Positioning System Reference
In-Depth Information
There is a really difficult problem in this time of flight measurements: the synchronisation
between transmitters and receivers. There are indeed two different synchronisation
problems: the first concerns the synchronisation between transmitters (since multiple
measurements are carried out from different transmitters) and the second concerns the
receiver with the various transmitters. The two problems are not equivalent since if it is
possible (not necessarily simple) to imagine “wiring” the various transmitters, it is often not
possible to have a link from the transmitters to the receiver, other than the radio link Radio
synchronisation is possible but requires a bandwidth proportional to the accuracy needed.
In practice, synchronisation to the nanosecond
6
is not achieved through radio links. In the
case of GNSS, this synchronisation is achieved by adding an additional measurement, from
an additional satellite, in order to solve this new unknown variable. In previous systems,
such as Decca
7
, the synchronisation between transmitters and the receiver was not carried
out: instead, differences of time measurements from two transmitters were carried out. In
such a case, the synchronisation unknown disappears (because of the difference) and the
positions of the receiver, characterised by a given difference of flight times, are located on a
hyperboloid whose foci are the transmitters. Once again, multiple difference measurements
are needed for positioning.
Note that the complexity of synchronisation of radio systems comes from the speed of light.
Ultrasound based approaches do not have the same problem since the speed of the signal is
reduced by a factor of nearly one million. In such a case, synchronisation to the millisecond
is comparable to the nanosecond requirement of the radio system.
For the inter-transmitter synchronisation, two generic approaches have been implemented.
The first one uses cables in order to create a real physical link between transmitters: then, a
simple calibration phase, once only, is carried out in order to know the exact
synchronisation. The second one, implemented in GPS for instance, is to use very slow drift
clocks
8
and to carry out a multitude of measurements from known locations in order to
inverse the positioning problem and to determine the non-synchronisation variables (one for
each transmitter). Of course, this approach is expensive and cannot be followed when
designing low cost indoor positioning solutions.
The
Cell-id
approach is the simplest one and does not need any modelling (see figure 4). As a
matter of fact, a coverage area is associated with the transmitter, whose shape is usually
considered to be a hexagon (of course the actual shape depends highly on the radio
environment). When the receiver is “simply” able to connect to the transmitter, one
considers that it is within the coverage area. This is a simple way to provide a location. This
is not very accurate for high power transmitters that have a wide radio range, but can be
very good for very low range devices. Of course, in this latter case, the number of
transmitters should be high if one wants a wide coverage. As usual, compromises have to be
made.
6
One nanosecond at the speed of light is equivalent to 30cm. When a typical positioning accuracy of one
meter is wanted, such a synchronization precision is needed.
7
Decca was a terrestrial positioning system. Propagation models were developed and it appeared that a
better performance was obtained over sea rather than over land.
8
Please note that using atomic clocks is not enough for synchronization purposes. These clocks are used
for the low rate of their drift, hence the larger time interval required between synchronization updates.
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