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Localization for Mobile Sensor Networks
ACM MobiCom 2004ACM MobiCom 2004Philadelphia, PAPhiladelphia, PA28 September 200428 September 2004
University of VirginiaComputer Science
Lingxuan Hu and David Evans
You are here
www.cs.virginia.edu/mcl 2
Location Matters
• Sensor Net Applications– Mapping– Environment monitoring– Event tracking
• Geographic routing protocols
www.cs.virginia.edu/mcl 3
Determining Location• Direct approaches
– GPS• Expensive (cost, size, energy)• Only works outdoors, on Earth
– Configured manually• Expensive• Not possible for ad hoc, mobile networks
• Indirect approaches– Small number of seed nodes
• Seeds are configured or have GPS
– Other nodes determine location based on messages received
www.cs.virginia.edu/mcl 4
Hop-Count TechniquesDV-HOP [Niculescu & Nath, 2003]Amorphous [Nagpal et. al, 2003]
Works well with a few, well-located seeds and regular, static node distribution. Works poorly if nodes move or are unevenly distributed.
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www.cs.virginia.edu/mcl 5
Local TechniquesCentroid [Bulusu, Heidemann, Estrin, 2000]:Calculate center of all heard seed locations
APIT [He, et. al, Mobicom 2003]:Use triangular regionsDepend on a high density of
seeds (with long transmission ranges)
www.cs.virginia.edu/mcl 6
Our Goal
• (Reasonably) Accurate Localization in Mobile Networks
• Low Density, Arbitrarily Placed Seeds
• Range-free: no special hardware • Low communication (limited
addition to normal neighbor discovery)
www.cs.virginia.edu/mcl 7
Scenarios
NASA Mars TumbleweedImage by Jeff Antol
Nodes moving, seeds stationary
Nodes and seeds moving
Nodes stationary, seeds moving
www.cs.virginia.edu/mcl 8
Our Approach: Monte Carlo Localization
• Adapts an approach from robotics localization
• Take advantage of mobility:– Moving makes things harder…but
provides more information– Properties of time and space limit
possible locations; cooperation from neighbors
Frank Dellaert, Dieter Fox, Wolfram Burgard and Sebastian Thrun. Monte Carlo Localization for Mobile Robots. ICRA 1999.
www.cs.virginia.edu/mcl 9
MCL: Initialization
Initialization: Node has no knowledge of its location.
L0 = { set of N random locations in the deployment area }
Node’s actual position
www.cs.virginia.edu/mcl 10
MCL Step: Predict
Node’s actual position
Predict: Node guesses new possible locations based on previous possible locations and maximum velocity, vmax
www.cs.virginia.edu/mcl 11
Prediction
p(lt | lt-1) = c if d(lt, lt-1) < vmax
0 if d(lt, lt-1) ≥ vmax
Assumes node is equally likely to move in any direction with any speed between 0 and vmax.
Can adjust probability distribution if more is known.
www.cs.virginia.edu/mcl 12
MCL Step: Predict
Node’s actual position
Predict: Node guesses new possible locations based on previous possible locations and maximum velocity, vmax
Filter
Filter: Remove samples that are inconsistent with observations
Seed node: knowsand transmits location
r
www.cs.virginia.edu/mcl 13
Filtering
Indirect SeedIf node doesn’t hear a seed, but one of your neighbors hears it, node must be within distance (r, 2r] of that seed’s location.
Direct SeedIf node hears a seed,the node must (likely) bewith distance r ofthe seed’s location
S S
www.cs.virginia.edu/mcl 14
Resampling
Use prediction distribution to create enough sample points that are consistent with the observations.
www.cs.virginia.edu/mcl 15
Recap: AlgorithmInitialization: Node has no knowledge of its location. L0 = { set of N random locations in the deployment area }
Iteration Step: Compute new possible location set Lt based on Lt-1, thepossible location set from the previous time step, and the new observations. Lt = { } while (size (Lt) < N) do R = { l | l is selected from the prediction distribution } Rfiltered = { l | l where l R and filtering condition is met } Lt = choose (Lt Rfiltered, N)
www.cs.virginia.edu/mcl 16
Results Summary• Effect of network parameters:
– Speed of nodes and seeds– Density of nodes and seeds
• Cost Tradeoffs:– Memory v. Accuracy: Number of samples– Communication v. Accuracy: Indirect seeds
• Radio Irregularity: fairly resilient• Movement: control helps; group motion
hurts
www.cs.virginia.edu/mcl 17
Convergence
Node density nd = 10, seed density sd = 1
The localization error converges in first 10-20 steps
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0 5 10 15 20 25 30 35 40 45 50
Est
imate
Err
or
(r)
Time (steps)
vmax=.2 r, smax=0
vmax=r, smax=0
vmax=r, smax=r
www.cs.virginia.edu/mcl 18
Speed Helps and Hurts
Increasing speed increases location uncertainty ̶R but provides more observations.
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Est
imat
e E
rror
(r)
vmax (r distances per time unit)
sd=1, smin=0, smax=vmax
sd=1, smax=smin=r
sd=2, smax=vmax
sd=2, smax=smin=r
Node density nd = 10
www.cs.virginia.edu/mcl 19
00.20.40.60.81
1.21.41.61.82
2.22.42.62.83
0.1 0.5 1 1.5 2 2.5 3 3.5 4
Est
imate
Err
or
(r)
Seed Density
MCL
Centroid
Amorphous
Seed Density
nd = 10, vmax = smax=.2r
Better accuracy than other localization algorithms over range of seed densities
Centroid: Bulusu, Heidemann and Estrin. IEEE Personal Communications Magazine. Oct 2000.
Amorphous: Nagpal, Shrobe and Bachrach. IPSN 2003.
www.cs.virginia.edu/mcl 20
Cost Tradeoff: Samples Maintained
00.10.20.30.40.50.60.70.80.91.0
1.2
1 2 5 10 20 50 100 200 5001000
Est
imate
Err
or
(r)
Sample Size (N)
sd=1, vmax=smax=.2r
sd=1, vmax=smax=r
sd=2, vmax=smax=.2rsd=2, vmax=smax=r
1.1 nd = 10
Good accuracy is achieved with only 20 samples (~100 bytes)
www.cs.virginia.edu/mcl 21
Cost Tradeoff: Impact of Indirect Seeds
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0.1 0.5 1 1.5 2 2.5 3 3.5 4
Est
imate
Err
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(r)
Seed Density
Direct seeds onlyDirect and Indirect seeds
Indirect seeds help, and cost is low if neighbor discovery is required.
nd = 10, vmax = smax=.2r
www.cs.virginia.edu/mcl 22
Radio Irregularity
nd = 10, sd = 1, vmax = smax=.2r
Insensitive to irregular radio pattern
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Est
imate
Err
or
(r)
Degree of Irregularity (r varies ±dr)
MCL
Centroid
Amorphous
www.cs.virginia.edu/mcl 23
Motion
nd=10, vmax=smax=r
Adversely affected by consistent group motion
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0 0.5 1 2 4 60
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Est
imate
Err
or
(r)
Maximum Group Motion Speed (r units per time step)
sd =.3
sd =1
sd =2
0
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0 20 40 60 80 100 120 140 160 180 200Est
imate
Err
or
(r)
Time
Random, vmax=smax=.2r
Area Scan
Random, vmax=0, smax=.2r
Scan
Stream and Currents Random Waypoint vs. Area Scan
Controlled motion of seeds improves accuracy
www.cs.virginia.edu/mcl 24
Future Work: Security• Attacks on localization:
– Bogus seed announcements• Require authentication between seeds and
nodes
– Bogus indirect announcements• Retransmit tokens received from seeds
– Replay, wormhole attacks• Filtering has advantages as long as you get
one legitimate announcement
• Proving node location to others
www.cs.virginia.edu/mcl 25
Summary• Mobility can improve localization:
– Increases uncertainty, but more observations
• Monte Carlo Localization– Maintain set of samples representing
possible locations– Filter out impossible locations based on
observations from direct and indirect seeds– Achieves accurate localization cheaply with
low seed density
www.cs.virginia.edu/mcl 26
Thanks!
http://www.cs.virginia.edu/mcl
People: Tarek Abdelzaher, Tian He, Anita Jones, Brad Karp, Kenneth Lodding, Nathaneal Paul, Yinlin Yang, Joel Winstead, Chalermpong Worawannotai
Funding: NSF ITR, NSF CAREER, DARPA SRS