
Adaptive Calibration for Fusion-based Cyber-Physical Systems A:5
Table I. Summary of Notation
Symbol Definition
H
0
/ H
1
the ground truth that the target i s absent / present
e
H
0
/
e
H
1
cluster head’s decision that the target is absent / present
µ
i
, σ
2
i
noise mean and variance of sensor i, respectively
s
i
the s i gnal energy received by sensor i
n
i
noise energy of sensor i, n
i
∼ N (µ
i
, σ
2
i
)
y
i
signal energy measurement of sensor i
N the number of sensors in the cluster concerned
Y fused measurement, Y =
P
N
i=1
y
i
µ / σ
2
/ S µ =
P
N
i=1
µ
i
, σ
2
=
P
N
i=1
σ
2
i
, S =
P
N
i=1
s
i
C
ij
the cost of deciding
e
H
i
when the ground truth is H
j
m the number of detections in a calibration cycle
P
F L
/ P
ML
false alarm rate / missing probability of l ow-end sensors
P
F H
/ P
MH
false alarm rate / missing probability of high-quality sensor
P
a
target appearance probability, P
a
= P(H
1
)
D the lower bound of target appearance ti me
The sensor measurements are contaminated by additive random noises from sen-
sor hardware o r environment. For instance, the electronic noise is a common noise
source for sensor circuits. Depending on the hypothesis that the targ et is absent (H
0
)
or present (H
1
), the me asurement of sensor i, deno ted by y
i
, is given by
H
0
: y
i
= n
i
,
H
1
: y
i
= s
i
+ n
i
,
where n
i
is the energy of no ise experienced by sensor i. We assume that the noise n
i
at each sensor i follows the normal distribution, i.e., n
i
∼ N(µ
i
, σ
2
i
), where µ
i
and σ
2
i
are the mean and varianc e of n
i
, respective ly. We assume that the noises, {n
i
|∀i}, are
spatially independent acro ss sensors.
The above stochastic sensor measurement mod el has been widely adopted in the
literature of multi-sensor signal detection [Clouqueur e t al. 2004; Li and Hu 2003;
Sheng and Hu 2005; Varshn ey 1996; Xing e t al. 2009; Tan et al. 2009] and also em-
pirically verified [Hata 1980; Li an d Hu 2003; Tan et al. 2009]. Many previous works
[Clouqueur et al. 2004; Li an d Hu 2003; Sheng and Hu 2005; Xing et al. 2009; Tan et al.
2009] based on the above sensor m easurement m odel assume that the signal energies
{s
i
|∀i} and n oise profiles {µ
i
, σ
2
i
|∀i} are known a priori. However, these parameters are
often difficult to estimate and also subject to change due to the dynamics of target and
environm ent. In this paper, we assume that they are unknown to the system.
Table I summarizes the notation used in this paper.
3.2. Data Fusion and Bayesian Detection Models
Data fusion [Varshney 1996] is an effective signal processing technique to improve the
perform ance of CPS and sensor systems. A CPS system that employs d ata fusion is
often organized into clusters. The cluster head is responsible for making a decision
regarding the presence of an event by fusing the information gathered by member sen-
sors. There exist two basic d ata fusion schemes, namely, decision fusion and value fu-
sion. In decision fusion, each sensor makes a local decision based on its measurements
and send s its decision to the cluster head, which makes a system decision according to
the local decisions. I n value fusion, each sensor sends its measurements to the cluster
head, which makes the detection decision based on the received measurements. In this
ACM Transactions on Embedded Computing Systems, Vol. V, No. N, Article A, Publication date: January YY YY.