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In-Depth Information
evaluates the query by interpolating values only in the feasible regions,
followed by a straightforward evaluation of the query.
Moreover, FunctionDB treats the temperature of the sensor
s
j
as a
continuous function of time
f
j
(
t
), instead of treating it as discrete values
sampled at time stamps
t
i
. An example of a query in the FunctionDB
framework is given in Query 2.6. This query returns the time values
t
between
t
start
and
t
end
where the temperature of the sensor
s
1
is greater
than 10
◦
C. Note that the time values
t
are not necessarily the time
stamps
t
i
where a particular sensor value was recorded.
SELECT
t
WHERE
f
1
(
t
)
>
10
◦
C
AND
t>t
start
AND
t<t
end
GRID t 1s
Query 2.6: Continuous threshold query.
For defining the values of the time axis
t
(or any continuous variable),
FunctionDB proposes the
GRID
operator. The
GRID
operator specifies
the interval at which the function
f
1
(
t
) should be interpolated between
time
t
start
and
t
end
. For instance,
GRID t 1s
indicates that the time
axis should be interpolated at one second intervals between time
t
start
and
t
end
. To process Query 2.6, FunctionDB first symbolically executes
the
WHERE
clause and obtains the feasible regions of the time axis (in-
dependent variable). Then, using the
GRID
operator, it generates time
stamps
T
I
in the feasible regions. The sensor value is interpolated at
the time stamps
T
I
using regression functions. Lastly, the query is pro-
cessed on these interpolated values, and time stamps
T
I
⊆
T
I
where the
temperature is greater than 10
◦
C are returned.
4.4 Processing Queries over Uncertain Data
In this form of query processing the assumption is that sensor data is
inherently uncertain. This uncertainty can arise due to various factors:
loss of calibration over time, faulty sensors, unsuitable environmental
conditions, low sensor accuracy, etc. Thus, the approaches that treat
sensor data as uncertain, assume that each sensor value is associated with
a random variable, and is drawn from a distribution. In this subsection,
we discuss two such methods that model uncertain data by either a
dynamic probabilistic model or a static probability distribution.
4.4.1 Dynamic Probabilistic Models.
Dynamic probabilis-
tic models (DPMs) are proposed for query processing in [33, 29]. These
models continuously estimate a probability distribution. The estimated
probability distribution is used for query processing. Mainly, there are
two types of models that are frequently used for estimating dynamic
probability distributions: particle filters and Kalman filters. Particle
