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Smart Sleeping Policies for Energy
Efficient Tracking in Sensor Networks
Jason A. Fuemmeler, and Venugopal
V. Veeravalli
Edwin Lei
Problem Description
• Want to track a
randomly moving object
in a network of wireless
sensors
• To conserve energy, we
can put sensors into
sleep mode
• Tradeoff between
energy cost and
tracking errors
Problem Assumptions
• Each sensor has a limited range
• Network is sufficiently dense
• Sensors in sleep mode cannot be awaken
prematurely
• Object described by a Markov chain whose statistics
are assumed to be known a priori
• Once the object leaves the network, it will not return
• Central controller keeps track of the state of the
network and assigns sleep times
Setup
• At each time step
1. If the sensor is awake and the object is within its
range, the sensor detects the object and sends
this information to the central unit
2. The sensor receives a new sleep time (may be 0)
that is decremented by one at each time step
General Idea
• Use information about the state of system to
set sleep time of each sensor
Time Information
• Let rk,l denote the residual sleep time of sensor l at
time k
• Let uk,l denote the sleep time input supplied to
sensor l at time k
• I is an indicator function
• Residual sleep time evolution is
rk 1,l  rk ,l 1 I{rk ,l 0}  uk ,l I{rk ,l 0}
Space Information
• Let bk denote the location of the object at
time k
• Let T denote the terminal state
• Then the actual observable location is
bk if bk  T and rk ,bk  0

sk   if bk  T and rk ,bk  0

T if bk  T
Partially Observable Markov
Decision Process
• The total information available is therefore
I k  s0 , r0 , s1 , r1 ,..., sk , rk , u0 , u1 ,..., uk 1 
• Let pk denote the probability distribution of bk
given Ik, then the state of the system is
vk   pk , rk 
Optimal and Suboptimal Solutions
n


• Cost function I{bk T }  I{rk ,b 0}   cI{rk ,l 0} 
k
l 1


• Optimization problem!
• Optimal solution is intractable even for
relatively small networks
• Make unrealistic assumptions to simplify
problem
– Only made to generate a sleeping policy
Suboptimal Solutions
• First Cost Reduction (FCR)
– Assumes we will have no future observations
• QMDP
– Assumes the location of the object will be known
• Both methods separate problem into a subproblem for each sensor so the global solution
is just the local solutions applied together
Results and Conclusion
• Suboptimal solutions still perform better than
a random duty cycle
• Detecting multiple objects and solving the
problem without assuming the statistics of the
object’s movement are two improvements to
the current algorithm