Installation guide

10
Wi-Fi Location-Based Services—Design and Deployment Considerations
OL-11612-01
Location Tracking Approaches
The Global Positioning System (GPS) is a example of a well-known ToA system where precision timing
is provided by atomic clocks.
Time Difference of Arrival (TDoA)
Time Difference of Arrival (TDoA) techniques use relative time measurements at each receiving sensor
in place of absolute time measurements. Because of this, TDoA does not require coordination of received
timestamps with a precision time source at the point of transmission to locate the mobile device. With
TDoA, a transmission with an unknown starting time is received at various receiving sensors, with only
the receivers requiring time synchronization.
TDoA is commonly implemented via a mathematical process known as hyperbolic lateration. In this
approach, at least three time-synchronized receiving sensors A, B, and C are required. In Figure 4,
assume that when station X transmits a message, this message arrives at receiving sensor A with time T
A
and at receiving station B with time T
B
. Calculate the time difference of arrival for this message between
the locations of sensors B and A as the positive constant k:
TDoA
B-A
= | T
B
– T
A
| = k
You can use the value of TDoA
B-A
to construct a hyperbola with foci at the locations of both receiving
sensors A and B. This hyperbola represents the locus of all the points in the x-y plane, the difference of
whose distances from the two foci is equal to k(c) meters. Mathematically, this represents all possible
locations of mobile device X such that:
| D
XB
– D
XA
| = k(c)
The probable location of mobile station X can then be represented by a point along this hyperbola. To
further resolve the location of station X, a third receiving sensor at location C is used to calculate the
message time difference of arrival between sensors C and A, or:
TDoA
C-A
= | T
C
– T
A
| = k
1
Knowledge of constant k
1
allows you to construct a second hyperbola representing the locus of all the
points in the x-y plane, the difference of whose distances from the two foci (that is, the two receiving
sensors A and C) is equal to k
1
(c) meters. Mathematically, this can be seen as representing all possible
locations of mobile device X such that:
| D
XC
– D
XA
| = k
1
(c)
Figure 4 illustrates how the intersection of the two hyperbolas TDoA
C-A
and TDoA
B-A
is used to resolve
the position of station X.