Before listing out the details of the algorithm we review the terminology used. A great
circle is de?¬?ned as a circle around the surface of a sphere that has its center at the same
point as the center of the sphere. Great circles which pass through the North and South
poles are called meridians. The great circle that is perpendicular to the axis (the line joining
the two poles) and lies half-way between them is known as the equator, whereas small
circles around the surface that are parallel to the equator with centers lying on the axis are
called parallels. The algorithm may then be described as follows:
Approximation algorithm for creating M uniformly distributed unit vectors on a
unit ball:
Begin
K ?? ?¬??¬??¬??¬??¬??¬??¬??¬? p=4 M pj k;
Divide a meridian into K equal segments with K1 points (p1,p2, . . . , pK1);
FIGURE 10.6
Longitude??“latitude??“grid discretization method.
192 RFID Handbook: Applications, Technology, Security, and Privacy
Draw a parallel Ci at each pi (i??1,2, . . . , K1);
For each Ci
Divide Ci into 2K cos
p
2 ??
i p
K equal segments with 2K cos
p
2 ??
i p
K points;
Add two points, one from each pole;
End;
10.3.3.2 Effects of Discretizing the Tag Space and Orientations
The maximum number of evaluations of Friis??™ equation is CNn
L M in the enumeration
scheme. In most cases, the number of reader antennas n used in a portal tends to be
relatively small, so that the computational complexity is largely determined by the values
of N, L, and M.
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