Database Reference
In-Depth Information
sensors in
S
. Data is acquired only as much as it is required to main-
tain such a distribution. Sensor data acquisition queries specify certain
confidence that they require in the acquired data. If the confidence
requirement cannot be satisfied, then more data is acquired from the
sensors, and the Gaussian distribution is updated to satisfy the confi-
dence requirements. The BBQ system models the sensor values using
a multi-variate Gaussian probability density function (pdf) denoted as
p
(
V
i
1
,V
i
2
,...,V
im
), where
V
i
1
,V
i
2
,...,V
im
are the random variables as-
sociated with the sensor values
v
i
1
,v
i
2
,...,v
im
respectively. This pdf
assigns a probability for each possible assignment of the sensor values
v
ij
. Now, let us discuss how the BBQ system processes Query 2.1.
In BBQ, the inferred sensor value of sensor
s
j
,ateachtime
t
i
,is
defined as the mean value of
V
ij
, and is denoted as
v
ij
. For example,
at time
t
1
, the inferred sensor values of the ambient temperature are
v
11
, v
12
,...,v
1
m
. The BBQ system assumes that queries, like Query 2.1,
provide two additional constraints: (i) error bound
, for the values
v
ij
, and (ii) the confidence 1
δ
with which the error bound should be
satisfied. Admittedly, these additional constraints are for controlling the
quality of the query response.
Suppose, we already have a pdf before the first time instance
t
1
,then
the confidence of the sensor value
v
1
j
is defined as the probability of
the random variable
V
1
j
lying in between
v
1
j
−
−
and
v
1
j
+
,andis
denoted as
P
(
V
1
j
∈
[
v
1
j
−
, v
1
j
+
]). If the confidence is greater than
1
δ
, then we can provide a probably approximately correct value for
the temperature, without spending energy in obtaining a sample from
sensor
s
j
. On the other hand, if a sensor's confidence is less than 1
− δ
,
then we should obtain one or more samples from the sensor (or other
correlated sensors), such that the confidence bound is satisfied. In fact,
it is clear that there could be potentially many sensors for which the
confidence bound may not hold.
As a solution to this problem, the BBQ system proposes a procedure
to chose the sensors for obtaining sensor values, such that the confidence
bound specified by the query is satisfied. First, the BBQ system samples
from all the sensors
S
at time
t
1
, then it computes the confidence
−
B
j
(
S
)
thatithasinasensor
s
j
as follows:
B
j
(
S
)=
P
(
V
1
j
∈
[
v
1
j
−
, v
1
j
+
]
|
v
1
)
,
(2.1)
where
v
1
=(
v
11
,v
12
,...,v
1
m
) is the row vector of all the sensor values at
time
t
1
. Second, for choosing sensors to sample, the BBQ system poses
an optimization problem of the following form:
S
o
⊆
S
and
B
(
S
o
)
≥
1
−δ.
C
min
(
S
o
)
,
(2.2)
