Database Reference
In-Depth Information
SELECT AVG
(
v
i
1
)
FROM pf sensor values WHERE
t>t
start
AND
t<t
end
Query 2.7: Compute the average temperature between time
t
start
and
t
end
.
4.4.2 Static Probabilistic Models.
Cheng
et al.
[9-11]
model the sensor value as obtained from an user-defined uncertainty
range. For example, if the value of a temperature sensor is 15
◦
C, then
the actual value could vary between 13
◦
Cand17
◦
C. Furthermore, the
assumption is that the sensor value is drawn from a static probability
distribution that has support over the uncertainty range.
Thus, for each sensor
s
j
we associate an uncertainty range between
l
ij
and
u
ij
, in which the actual sensor values can be found. In addition,
the pdf of the sensor values of sensor
s
j
is denoted as
p
ij
(
v
). Note that
the pdf has non-zero support only between
l
ij
and
u
ij
.Consideraquery
that requests the average temperature of the sensors
s
1
and
s
2
at time
t
i
. Since the values of the sensors
s
1
and
s
2
are uncertain in nature, the
response to this query is a pdf, denoted as
p
avg
(
v
). This pdf gives us the
probability of the sensor value
v
being the average.
p
avg
(
v
) is computed
using the following formula:
p
avg
(
v
)=
min
(
u
i
1
,v−l
i
2
)
max
(
l
i
1
,v−u
i
2
p
i
1
(
y
)
p
i
2
(
v − x
)
dx.
(2.12)
)
Naturally, Eq. (2.12) becomes more complicated when there are many
(and not only two) sensors involved in the query. Additional details
about handling such scenarios can be found in [9].
4.5 Query Processing over Semantic States
The MIST framework [5] proposes to use Hidden Markov Models
(HMMs) for deriving semantic meaning from the sensor values. HMMs
allow us to capture the hidden states, which are sometimes of more in-
terest than the actual sensor values. Consider, as an example, a scenario
where the sensors
S
are used to monitor the temperature in all the rooms
of a building. Generally, we are only interested to know which rooms
are hot or cold, rather than the actual temperature in those rooms. We,
then, can use a two-state HMM with states
Hot
(denoted as
H
)and
Cold
(denoted as
C
) to continuously infer the semantic states of the
temperature in all the rooms.
Furthermore, MIST proposes an in-network index structure for in-
dexing the HMMs. This index can be used for improving the perfor-
mance of query processing. For instance, if we are interested in finding
