Localization for Mobile Sensor Networks

1. Lingxuan Hu and David Evans Localization for Mobile Sensor Networks You are here ACM MobiCom 2004 Philadelphia, PA 28 September 2004 University of Virginia Computer Science

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 Techniques r 4 DV-HOP [Niculescu & Nath, 2003] Amorphous [Nagpal et. al, 2003] 1 2 7 3 1 4 3 5 2 4 8 3 3 6 4 4 5 Works well with a few, well-located seeds and regular, static node distribution. Works poorly if nodes move or are unevenly distributed. www.cs.virginia.edu/mcl

5. Local Techniques Centroid [Bulusu, Heidemann, Estrin, 2000]: Calculate center of all heard seed locations APIT [He, et. al, Mobicom 2003]: Use triangular regions Depend 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 Nodes stationary, seeds moving NASA Mars Tumbleweed Image by Jeff Antol Nodes moving, seeds stationary Nodes and 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 Node’s actual position Initialization: Node has no knowledge of its location. L0 = { set of N random locations in the deployment area } 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. Filter MCL Step: Predict Node’s actual position r Seed node: knows and transmits location Predict: Node guesses new possible locations based on previous possible locations and maximum velocity, vmax Filter: Remove samples that are inconsistent with observations www.cs.virginia.edu/mcl

13. Filtering S S Indirect Seed If 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 Seed If node hears a seed, the node must (likely) be with distance r of the seed’s location 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: Algorithm Initialization: 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, the possible 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 | lwhere l Rand 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 2 Node density nd = 10, seed density sd = 1 1.8 1.6 1.4 1.2 v =.2 r s =0 max max 1 , Estimate Error (r) 0.8 v = r , s =0 max max 0.6 0.4 v = r , s = r max max 0.2 0 0 5 10 15 20 25 30 35 40 45 50 Time (steps) The localization error converges in first 10-20 steps www.cs.virginia.edu/mcl

18. Speed Helps and Hurts 1 Node density nd = 10 0.9 0.8 0.7 0.6 s =1, s =0, s = v d min max max 0.5 Estimate Error (r) s =1, s = s = r d max min 0.4 0.3 s =2, s = v d max max 0.2 s =2, s = s = r 0.1 d max min 0 0.1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 vmax(r distances per time unit) Increasing speed increases location uncertainty ̶ but provides more observations. www.cs.virginia.edu/mcl

19. Seed Density 3 nd = 10, vmax = smax=.2r 2.8 2.6 Centroid: Bulusu, Heidemann and Estrin. IEEEPersonal Communications Magazine. Oct2000. Amorphous: Nagpal, Shrobe and Bachrach. IPSN 2003. 2.4 Centroid 2.2 2 1.8 1.6 Estimate Error (r) 1.4 1.2 Amorphous 1 0.8 0.6 0.4 MCL 0.2 0 0.1 0.5 1 1.5 2 2.5 3 3.5 4 Seed Density Better accuracy than other localization algorithms over range of seed densities www.cs.virginia.edu/mcl

20. Cost Tradeoff: Samples Maintained 1.2 nd = 10 1.1 s =1, v = s =.2 r d max max 1.0 0.9 0.8 0.7 Estimate Error (r) 0.6 0.5 s =1, v = s = r 0.4 d max max 0.3 s =2, v = s = r d max max s =2, v = s =.2 r 0.2 d max max 0.1 0 1 2 5 10 20 50 100 200 500 1000 Sample Size (N) Good accuracy is achieved with only 20 samples (~100 bytes) www.cs.virginia.edu/mcl

21. Cost Tradeoff: Impact of Indirect Seeds 3 nd = 10, vmax = smax=.2r 2.8 2.6 2.4 2.2 2 1.8 Estimate Error (r) 1.6 1.4 1.2 1 0.8 Direct seeds only 0.6 Direct and Indirect seeds 0.4 0.2 0 0.1 0.5 1 1.5 2 2.5 3 3.5 4 Seed Density Indirect seeds help, and cost is low if neighbor discovery is required. www.cs.virginia.edu/mcl

22. Radio Irregularity 2 nd= 10, sd = 1, vmax = smax=.2r 1.8 1.6 Centroid 1.4 1.2 1 Amorphous Estimate Error (r) 0.8 0.6 MCL 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 Degree of Irregularity (r varies ±dr) Insensitive to irregular radio pattern www.cs.virginia.edu/mcl

23. Motion Stream and Currents Random Waypoint vs. Area Scan 6 6 4 nd=10, vmax=smax=r 5.5 5.5 5 5 Random, vmax=0, smax=.2r 4.5 4.5 3 4 4 sd =.3 3.5 3.5 3 3 Estimate Error (r) 2 Estimate Error (r) Random, vmax=smax=.2r 2.5 2.5 2 2 sd =1 1.5 1.5 Area Scan 1 1 1 sd =2 0.5 0.5 Scan 0 0 0 0 0.5 0.5 1 1 2 2 4 4 6 6 0 0 20 40 60 80 100 120 140 160 180 200 Maximum Group Motion Speed (r units per time step) Time Adversely affected by consistent group motion 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 www.cs.virginia.edu/mcl