Transcript Minimalism in Sensor Networks.

Minimalism in Sensor Networks
Subhash Suri
UC Santa Barbara
and
ETH Zurich
Moving from Big to Small
Today: Few, big, powerful,
global sensors
Tomorrow: many small, weak,
local sensors
Pervasive computing, sensing, monitoring, actuation.
Challenge: compose global picture from local data
Some Applications
• Structural monitoring (civilian, industrial infrastructure
faults)
• Agriculture (soil moisture, pesticide levels)
• Environmental monitoring (wildfires, hazmat)
• Habitat monitoring (Great Duck Island, UCB Redwoods)
• Surveillance (target tracking, border policing)
How to achieve large scale with mote-caliber devices
Scale Requires Minimalist Design
• Scaling in Space (size)
– Sensors have small coverage area (e.g., bio or chemical)
– Large areas must be covered
– Large deployments must be automated
• Minimalist network protocols
– Location-based naming and addressing
– Geographical routing (e.g. GPSR, GLIDER)
A
B (x,y)
Scaling in Time
• Sensor nodes have limited battery life
– On/off scheduling and power management
– Need minimalist models of energy consumption
– Processing/communication tradeoffs
• transmit/compute cost ratio > 1000
– TinyDB, Cougar style in-network processing
– Lightweight algorithms for lifetime maximization
• Today’s Talk [IPSN 2005]
– Minimalist self-monitoring
– Detect large network failures
– Joint work with Shrivastava and Toth
Scaling in Functionality
• Need minimalist sensing models
– Small, inexpensive, noisy, failure-prone micro-sensors
– Simple broadly applicable architectures
– Fundamental limits of performance
• Today’s Talk [ACM SenSys ‘06]
– Tracking with binary proximity sensors
– Sensors detect presence or absence of target
– How well can a target be tracked?
– Joint work with Shrivastava, Mudumbai, Madhow
Monitoring the Network Health
• Deployment conditions for sensor can be
harsh and adversarial: need to remotely
monitor the overall health of the network.
• Continuously monitoring state of each
sensor too expensive: need lightweight
mechanisms.
• Focus on significant damage to the
network: large network disconnection.
 -cut: partition where  fraction of sensors
are cut off from the rest.
• Sensors embedded in physical space, so
significant failures often spatially
correlated.
Linear Cuts and a Minimalist Model
• Linear -cut: partition by a line.
Base Station
• Base station: a distinguished node.
• Assume linear cut disconnects -fraction of
sensors from the base.
• Designate a small number of nodes as
sentinels, and track only their health.
• Minimalist Model:
– Each sentinel sends to the base
station a bit to indicate it is alive;
absence of bit indicates death.
– Separation of routing from the
monitoring.
• How many sentinels needed to detect
every linear -cut?
A linear cut
Sampling and VC-dimension
• O(1/ log 1/) size random sample is an -net with prob 1-.
• A related problem studied by Kleinberg: detect -cuts in wired network
caused by failure of k edges or nodes.
• Kleinberg shows this set system has VC dimension poly(k), and so
number of sentinels is poly(k, 1/, 1/).
• Improved bounds and variations in A. Gupta and Fakcharoenphol.
• However, these methods give 1-sided guarantees: every -cut is
detected, but not every cut found is necessarily an -cut.
• False positives in (remote) sensor networks can be a major nuisance.
• The -approximation is not scalable: requires (d/ log 1/) nodes.
• Is it possible to do scalable, minimalistic monitoring with the
2-sided guarantee?
Desiderata
• Cuts must be defined as a
fraction of the network size.
• Otherwise, catching all cuts of
size k requires at least n/k
sentinel nodes.
• Sharp threshold impossible as
well: catch all -cuts, but no cuts
of size < n.
• Such a sharp cutoff requires at
least n/2 sentinel nodes.
n-2
n-1
0
1
2
k
Main Result
• Theorem: A sentinel set of size O(1/)
that deterministically detects every cut, and every reported cut has size at
least n/2.
Geometry of Network Cuts
• Think of sensors as points in the plane.
• A linear cut is a line that partitions the point set.
• The point-line duality: point (a,b) <-> line y = ax - b
q
(1,2)
L
p*
q*
p
L*
(1,0)
• It inverts the above/below relationship:
point p above line L <-> point L* above line p*
Geometry of Network Cuts
• L is an -cut if the dual point L* lies above n
dual lines:
Cut
– set of all linear -cuts is the region above
the n level (symmetrically, below the (n
- n) level).
• Imagine a polygonal curve (separator) made
up of dual lines that lies between n/2 and
n levels:
– primal points corresponding to these lines
form a sentinel set.
• Two issues:
– Is there such a separator using just a few
lines?
– We don't know the cut line L. How will we
decide that L* lies above the separator?
L*
Level 0
L
Complexity of a Separator
• A level can have size (nlogn).
• Average complexity of a level is (n).
• We want a separator of size roughly 1/
(independent of n!).
• Fact: Total size of first k levels is O(nk).
• We can choose two levels a and b s.t.
– Each has size O(n), and
– |b - a|  (n).
Complexity of Separator
• Construct a zig-zag path between
levels a and b:
– Start at left, follow the edge until
top level hit.
– Reflect and follow until bottom
level hit, reflect and continue.
• These paths are edge-disjoint.
• Total number of bends at most the
number of vertices in the top and
bottom levels.
• By the pigeon-hole principle, at least
one of the O(n) paths has O(1/)
segments.
• The dual points of these lines are our
sentinels.
Detecting Cuts from Sentinels
• Base station stores the arrangement formed by the separator lines
• For each dead (live) sensor, we
know that L* must be above
(below) the line.
• Intersection of these halfspaces a
convex cell.
• If this cell is above the separator,
we declare an cut.
• Otherwise, it's a false alarm.
• In this example, w1, w3, w4 are
dead; others alive.
Cut Detection Guarantee
• Separator lies below level
n, so if intersection cell
below it, must be smaller
than a cut.
• Separator lies entirely
above level n
so if
intersection cell above it,
must be at least a
(cut.
Simulation Results
Uniform
Non-uniform
US-census data
N = 5000,  = 0.01
N = 5000,  = 0.01
N = 5000,  = 0.01
No. of sentinels = 14
No. of sentinels = 14
No. of Sentinels = 12
Scalability with Network Size
=0.01
Scalability with 
N = 5000
Sentinels vs. Random Sampling
• Two natural random sampling schemes.
• Choose as many random nodes as our
sentinel schemes.
• Random Sampling
– k nodes chosen uniformly at random.
– Report if more than k sentinels dead.
• Radial Sampling
– k directions chosen at random, and for
each choose the en extreme vertex.
– Report if any of these k dies.
k-random directions
False Positives
• Generated 250 cuts by picking
points randomly between
levels 1 and n/2
• These cuts are all below the
appr threshold, and should not
be reported.
• Random and radial sampling
schemes misreport some of
them as cuts.
No False Positives in Sentinel Set
False Negatives
• 250 cuts by picking points
randomly between level n and
2 n
• These are all above the
approximation threshold, and so
should be reported.
• Random and radial sampling
schemes failed to report some
of them as cuts.
No False Negatives in Sentinel Set
Target Tracking with Binary Sensors
• Minimalist model
– Single bit output: presence/absence of target.
– No information about position, distance, angle etc.
– Idealization: perfect detection, circular range.
– Simple, broadly applicable, robust model
– Appropriate for large-scale deployments
ExScale project at OSU)
• Fundamental limits of network sensing
– Spatial resolution
– Minimal path descriptions
– Efficient geometric algorithms
(e.g.,
The Geometry of Binary Sensing
Sensor Outputs
Target Path
Localization patches
Target Localization
• Sensing output is a binary vector. Ex. F2 = (1,1,0).
• Each vector localizes the target to a localization patch.
• The accuracy (max error) of localization is function of the size
of localization patches.
• What are the minimalist parameters to study this?
Tracking Resolution Theorem
sensor density (#sensors per unit area)
• R: sensing radius
• Theorem: If sensors have sensing radius R and
the field has sensor density then the target can
be tracked with spatial resolution (1/Rand
this is the best possible.
• Cor: In d-space, the resolution is O(1/Rd-1)
Upper Bound on Attainable Resolution
• Consider 2 concentric circles C1
(radius R) and C2 (radius 2R), with
center x.
• Only sensors in C2 can detect a
target in C1.
• Assume C2 has  avg sensor density,
so at most N = (4R2) sensors in it.
• N sensing ranges form  N2-N+2
patches.
• At least one of these patches must
have area >= (R2)/N2 = (1/2R2).
• Worst-case localization accuracy is
the diameter of this patch.
Achieving the Resolution
• Uniform placement of sensors in a grid achieves the
resolution (1/R).
• Geometric and probabilistic analysis shows the same
bound for uniform random distribution.
Localizing a Trajectory
• Target localized to a time-ordered sequence of patches.
• Any path inside this “tube” is within the resolution guarantee.
• What is a good representative path?
OccamTrack: Minimal Representation
• Use Occam’s principle of minimal representation.
• Geometric algorithm computes polygonal path of minimum
number of line segments through the resolution tube.
Spatial Low Pass Filtering
• Sensors act like a low pass filter.
• Local rapid variations invisible.
• Estimating velocity:
only average across patches.
• Target localized to a 1-dim arc at
sensor boundary crossings.
• Interpolate the velocity across
multiple patches.
• Velocity estimation reliable only over
long path segments
• Minimal representation helps again!
Velocity Estimation
Theorem: To achieve relative velocity error , length
of approximating segments must be
L  1
is the spatial resolution (patch size).
For 10% error, L  5; for 5% error, L  6.32
Simulation Results: Path Representation
Weighted Centroid Output
(Kim et al, IPSN 2005)
1000 vertices
OccamTrack Output
50 vertices
Velocity Estimation
Fundamental Resolution Limits
Theoretical resolution attained by both regular and random deployment
Lab-Scale Mote Experiment
Non-ideal sensor
response
OccamTrack
OccamTrack
with ideal sensing
Particle Filter
Particle Filter +
Geometric
Research Problems
• Network monitoring
– More general failure models
– Large but not total failure
• Location based routing
– 3-dimensional networks
• Tracking
– Beyond idealized sensing
– Multiple targets
Sensor Nodes: Motes
Lightweight tiny devices, run on batteries
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QuickTime™ and a
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are needed to see this picture.
Mica motes with light, acoustic, acceleration sensors