Probability and
RFID
Before
discussing Probability and RFID let’s understand what probability
is. Probability is a branch of mathematics that deals with
calculating the likelihood of a given event's occurrence, which is
expressed as a number between 1 and 0. An event with a probability
of 1 can be considered a certainty: for example, the probability of
a coin toss resulting in either "heads" or "tails" is 1, because
there are no other options, assuming the coin lands flat. An event
with a probability of .5 can be considered to have equal odds of
occurring or not occurring: for example, the probability of a coin
toss resulting in "heads" is .5, because the toss is equally as
likely to result in "tails." An event with a probability of 0 can be
considered an impossibility: for example, the probability that the
coin will land (flat) without either side facing up is 0, because
either "heads" or "tails" must be facing up. A little paradoxical,
probability theory applies precise calculations to quantify
uncertain measures of random events.
In its simplest
form, probability can be expressed mathematically as: the number of
occurrences of a targeted event divided by the number of occurrences
plus the number of failures of occurrences (this adds up to the
total of possible outcomes):
p(a) =
p(a)/p(a) + p(b)
Calculating
probabilities in a situation like a coin toss is straightforward,
because the outcomes are mutually exclusive: either one event or the
other must occur. Each coin toss is an independent event; the
outcome of one trial has no effect on subsequent ones. No matter how
many consecutive times one side lands facing up, the probability
that it will do so at the next toss is always .5 (50-50). The
mistaken idea that a number of consecutive results (six "heads" for
example) makes it more likely that the next toss will result in a
"tails" is known as the gambler's fallacy, one that has led to the
downfall of many a bettor.
The function of
the RF-ID system is to provide an exchange of useful information
between readers and tags connected with a population of objects.
Radio-frequency identification systems are highly application
dependent. Performance is defined and evaluated by determining the
extent to which a system meets the needs of the application. ID
tags, readers and coding formats vary in specific embodiments
according to the requirements and constraints of the target
application and environment. Reading range (distance for a reliable
data transaction) and the ability to communicate with tags in motion
with respect to a defined "reading volume" are aspects of RF-ID
system performance. Undoubtedly not all RFID systems are fool proof
and Probability and RFID are always a debatable
topic.
Probability and
RFID of Reading in Dynamic Tag-Reader
Interaction:
Reader Field
Pattern: The electromagnetic field in the reading volume, defined by
the reader coil geometry, the environment near the reader coil(s)
and Maxwell’s equations, will generally not be consistent in
intensity or orientation.. Therefore a deterministic function of tag
activation which ultimately affects Probability and RFID is
associated with the variation of magnetic field strength and
orientation in the reading volume, for any given position and
orientation of a tag stationary in the reading
volume.
Tag
Orientation, Speed and Trajectory: A tag will have the greatest
reading distance at optimum orientation, and lesser reading distance
as a function of sub-optimal orientation. The average reading
distance of a specific stationary tag in the reading volume can be
calculated by [integrating the reading distance for all orientations
by the probability of orientation in the given direction]. The
reading distance for a stationary tag in the reader field is a
function of the field strength and the tag orientation in the field.
Let’s see some
more information about Probability and RFID. As the reading distance
for a stationary tag in the reader field is a function of the field
strength and the tag orientation in the field. The probability of
reading therefore varies proportional to the field strength and is
an inverse function of the distance between the tag and the reader.
The amount of time the tag is activated by the reader field also
affects probability of reading. The theoretical optimum is that the
reader can read the tag if it is active for one message period. A
tag can move through the reading volume at a variety of speeds.
For a given
trajectory through reading volume, there is a maximum speed at which
a tag can move through the volume and remain active for a sufficient
length of time to transmit a complete code message. An "ideal"
reader could receive and decode the message. Above this speed, the
probability for obtaining a reading is zero. For all speeds below
the maximum speed, the probability of reading increases according to
a function dependent on tag orientation, reader signal-to-noise
ratio and other factors. A tag can also move through the reading
volume with varying orientation, thereby varying its relative signal
strength or even going through periods of de-activation on its way.
Another probability function is therefore the probability that a tag
will be readable on account of its
trajectory.
Probability and
RFID using Multiple Tags: If more than one tag is activated within
the reading volume at a given time, the tag signals will interfere
with each other, giving an ambiguous message to the reader.
Depending on the modulation method used in the tags, this mutual
interference has a variable effect on whether a valid reading of any
tag in the field will take place. Even in systems which utilize
"anti-collision" methods, multiple tags in the field will increase
the amount of time necessary for completed data transactions of all
the tags. Therefore another probability function is whether multiple
tags will be in the reading volume simultaneously.
Noise Sources:
Electromagnetic noise sources in the vicinity of the reader sensing
apparatus will decrease the probability of a successful reading
operation and hence poor Probability and RFID equation. If the tag
outputs a perfectly good signal in the presence of noise, the
probability of the reader receiving erroneous information along with
the correct tag signal increases according to a complex function of
the noise intensity and frequency spectrum as related to the signal
processing characteristics of the
reader.
