Transcript sn2007 6751

Smart Sleeping Policies for Wireless
Sensor Networks
Venu Veeravalli
ECE Department & Coordinated Science Lab
University of Illinois at Urbana-Champaign
http://www.ifp.uiuc.edu/~vvv
(with Jason Fuemmeler)
IPAM Workshop on Mathematical Challenges and
Opportunities in Sensor Networks, Jan 10, 2007
Saving Energy in Sensor Networks
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Efficient source coding
Efficient Tx/Rx design
Efficient processor design
Power control
Efficient routing
 Switching nodes between active and
sleep modes
Active
Sleep Transition
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External Activation
 Paging channel to wake up sensors when needed
 But power for paging channel is usually not negligible
compared to power consumed by active sensor
 Passive RF-ID technology?
Active
Z
Sleep Transition
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 Practical Assumption
Sensor that is asleep cannot be communicated
with or woken up prematurely
⇒ sleep duration has to be chosen when sensor
goes to into sleep mode
 Having sleeping sensors could result in
communication/sensing performance degradation
 Design Problem
Find sleeping policies that optimize tradeoff
between energy consumption and performance
Sleeping Policies
active
sleep
active
active
sleep
sleep
Duty Cycle Policy
 Sensor sleeps with deterministic or random (with
predetermined statistics) duty cycle
 Synchronous or asynchronous across sensors
 Duty cycle chosen to provide desired tradeoff
between energy and performance
 Simple to implement, generic
Smart (Adaptive) Policies
 Use all available information about the
state of the sensor system to set sleep
time of sensor
 Application specific
⇒ system-theoretic approach required
 Potential energy savings over duty
cycle policies
Tracking in Dense Sensor Network
 Sensor detects
presence of object
within close vicinity
 Sensors switch
between active
and sleep modes
to save energy
 Sensors need to
come awake in
order to detect
object
Design Problem
 Having sleeping sensors could
result in tracking errors
 Design Problem
Find sleeping policies that optimize
tradeoff between energy consumption
and tracking error
General Problem Description
 Sensors distributed
in two-dimensional
field
 Sensor that is
awake can
generate an
observation
 Object follows
random (Markov)
path whose
statistics are
assumed to be
known
General Problem Description
 Central controller
communicates with
sensors that are awake
 Sensor that wakes up
remains awake for one
time unit, during which it:
Central Controller
 reports its observation to
the central controller
 receives new sleep time
from central controller
 sets its sleep timer to new
sleep time and enters sleep
mode
Markov Decision Process
 Markov model for object
movement with absorbing
terminal state when object
leaves system
 State consists of two parts:
 Position of object
 Residual sleep times of
sensors
 Control inputs:
 New sleep times
 Exogenous input:
Central Controller
 Markov object movement
Partially Observable Markov Decision Process (POMDP)
 The state of the system is
only partially observable
at each time step
(POMDP)
 Object position not known
-- only have distribution
for where the object might
be
 Can reformulate MDP
problem in terms of this
distribution (sufficient
statistic) and residual
sleep times
Central Controller
Sensing Model and Cost Structure
 Sensing Model: Each
sensor that is awake
provides a noisy
observation related to
object location
 Energy Cost: each
sensor that is awake
incurs cost of c
 Tracking Cost: distance
measure d(.,.) between
actual and estimated
object location
Central Controller
Dynamic System Model
Sensor Observations
Nonlinear Filter
Sleeping Policy
Posterior
Optimal location
estimate w.r.t.
distortion metric
^bk
Simple Sensing, Object Movement, Cost Model
 Sensors distributed in
two-dimensional field
 Sensor that is awake
detects object without
error within its sensing
range
 Sensing ranges cover
field of interest without
overlap
 Object follows Markov
path from cell to cell
 Tracking cost of 1 per
unit time that object not
seen
What Can Be Gained
1
Duty Cycle
Always Track
0
n
Number of sensors awake per unit time
Always Track Policy
Unit random walk movement of object
n
1
Central Controller
Always Track Asymptotics
n
1
E[# awake per unit time] » O(log n)
1
n
E[# awake per unit time] » n0.5
Dynamic System Model
Sensor Observations
Nonlinear Filter
Sleeping Policy
Posterior
Optimal location
estimate w.r.t.
distortion metric
^bk
Nonlinear filter (distribution update)
k
k+1
k+1
Optimal Solution via DP
 Can write down dynamic
programming (DP) equations to
solve optimization problem and find
Bellman equation
 However, state space grows
exponentially with number of
sensors
 DP solution is not tractable even for
relatively small networks
Separating the Problem
 Problem separates into set of simpler
problems (one for each sensor) if:
 Cost can be written as sum of costs under
control of each sensor (always true)
 Other sensors’ actions do not affect state
evolution in future (only true if we make
additional unrealistic assumptions)
 We make unrealistic assumptions only to
generate a policy, which can then be
applied to actual system
FCR Solution
 At time sensor is set to sleep
assume we will have no future
observations of object (after sensor
comes awake)
 Policy is to wake up at first time
that expected tracking cost
exceeds expected energy cost
 Thus termed First Cost Reduction
(FCR) solution
QMDP Solution
 At time sensor is set to sleep,
assume we will know location of
object perfectly in future (after
sensor comes awake)
 Can solve for policy with low
complexity
 Assuming more information than is
actually available yields lower
bound on optimal performance!
Line Network Results
Line Network Results
Line Network Results
Two Dimensional Results
Offline Computation
 Can compute policies on-line, but this
requires sufficient processing power and
could introduce delays
 Policies need to be computed for each
sensor location and each possible
distribution for object location
 Storage requirements for off-line computation
may be immense for large networks
 Off-line computation is feasible if we
replace actual distribution with point mass
distribution
 Storage required is n values per sensor
Point Mass Approximations
n
1
 Two options for placing point mass:
 Centroid of distribution
 Nearest point to sensor on support of
distribution
Distributed Implementation
 Off-line computation also allows for
distributed implementation!
Partial Knowledge of Statistics
1
 Support of distribution of object position
can be updated using only support of
conditional pdf of Markov prior!
 Thus “nearest point” point mass
approximation is robust to knowledge of
prior
n
Point Mass Approximation Results
Point Mass Approximation Results
Conclusions
 Tradeoff between energy consumption and
tracking errors can be considerably
improved by using information about the
location of the object
 Optimal solution to tradeoff problem is
intractable, but good suboptimal solutions
can be designed
 Methodology can be applied to designing
smart sleeping for other sensing
applications, e.g., process monitoring,
change detection, etc.
 Methodology can also be applied to other
control problems such as sensor selection
Future Work
 More realistic sensing model
 More realistic object movement models
 Object localization using cooperation among
all awake sensors at each time step
 Joint optimization of sensor sleeping policies
and nonlinear filtering for object tracking
 Partial known or unknown statistics for
object movement
 Decentralized implementation
 Tracking multiple objects simultaneously