UBI 532 Wireless Sensor Networks Paper Presentation

1. UBI 532 Wireless Sensor NetworksPaper Presentation Esra Rüzgar, 910816920 01.06.2009

2. ROBUST DISTRIBUTED NETWORK LOCALIZATION WITH NOISY RANGE MEASUREMENTS David Moore, John Leonard, Daniela Rus, Seth Teller MIT Computer Science and Artificial Intelligence Laboratory ACM SenSys’04, Baltimore, Maryland, USA

3. OUTLINE • LOCALIZATION CONCEPTS • ABSTRACT • INTRODUCTION • APPROACH • ANALYSIS • EXPERIMENTAL RESULTS • CONCLUSION

4. LOCALIZATION • WHAT IS LOCALIZATION? • A mechanism for discovering spatial relationships among objects • WHY DO WE NEED LOCALIZATION? • It is useful or even necessary for a node in a wireless sensor network to be aware of its location in the physical world in many applications. For example: • TrackingObjects • Reporting event origins • Evaluating network coverage • Assisting with routing • Supporting for upper level protocols

5. PROPERTIES OF LOCALIZATION • Physical position versus symbolic location • Does the system provide data about the physical position of a node (in some numeric coordinate system) or does a node learn about a symbolic location? For example, “living room”, “office 123 in building 4”? • Absolute versus relative coordinates • Does the system provides absolute coordinates of nodes or positions with respect to each other but have no relationship to absolute coordinates? • Localized versus centralized computation • Are any required computations performed locally by nodes or are measurementsreported to a central station that computes positions or locations and distributes them backto the nodes?

6. PROPERTIES OF LOCALIZATION • Accuracy and precision • Positioning accuracy is the largest distance between the estimated and the true position of an entity. • Precision is the ratio with which a given accuracy is reached, averaged over many repeated attempts to determine a position. • Scale • Two important metrics: • Are the area the system can cover per unit of infrastructure? • What is the number of locatable objects per unit of infrastructure per time interval? • Limitations • Measurement noise • Obstacles, for example GPS does not work indoors

7. LOCALIZATION PROBLEM Localization can be formulated as graph realization problem

8. ABSTRACT OF PAPER • Distributed, linear-time algorithm for localizing sensor network nodes is proposed • Robust quadrilaterals is introduced • Trilateration is used for positioning • No absolute position references is needed • Mobility of nodes is supported • Implemented on physical network • Simulated for demonstrating scalability

9. INTRODUCTION • Distributed computation and robustness in the precence of measurement noise are key ingredients for a localization algorithm • In this algorithm: • Nodes have ability to estimate distance to neighbors • Localization problem is formulated as two-dimensional graph realization problem • But localization is not easy!

10. DIFFICULTIES OF LOCALIZATION • Insufficient data to compute a unique position assignment for all nodes • Noisy distance measurements, compounding effects of insufficient data and creating additional uncertainty • Lack of absolute reference points • Unscalable algorithms

11. DIFFICULTIES OF LOCALIZATION • To solve this difficulties robust quadrilaterals are introduced • Robust quads are able to • prevent incorrect realizations of flip ambiguities • cope with arbitrary amounts of measurement noise • But they are not able to localize well under conditions of high measurement noise and low node connectivity

12. RELATED WORK • Algorithms based on local information • Trilateration graphs is constructed and localized in linear time, Eren at al[1] • Local clusters is used for localization, Capkun et al[2] • Lower error bound for localization is derived, Savvides et al[3] • But, none of them consider how measurement noise cause incorrect results!

13. RELATED WORK • Algorithms based on propagation of location information from known reference nodes • Received signal strength(RSS) and time of arrival(ToA) is used, Patwari et al[4] • Distributed localization is proposed for low power devices based on connectivity, Bulusu et al[5] • But, anchor nodes with known positions may not be always available!

14. CHALLENGES OF LOCALIZATION • In graph theory, the problem of finding Euclidean positionsfor the vertices of a graph is known as the graph realization problem. • Saxe showed that finding a realizationis strongly NP-hard for the two-dimensional case or higher. • However, knowing the length of each graph edge does not guarantee a unique realization, because deformationscan exist in the graph structure that preserve edge lengthsbut change vertex positions.

15. CHALLENGES OF LOCALIZATION • Rigidity theory is used to overcome this problem. • Rigidity theory distinguishesbetween non-rigid and rigid graphs. • Non-rigid graphs canbe continuously deformed to produce an infinite number ofdifferent realizations, while rigid graphs cannot. • However,in rigid graphs, there are two types of discontinuous deformationsthat can prevent a realization from being unique.

16. CHALLENGES OF LOCALIZATION • Flip Ambiguitiesoccur for a graph in a d-dimensional space when the positions of allneighborsof some vertex span a (d-1)dimensional subspace. Neighbors create a mirror through whichthe vertex can be reflected. Vertex A can be reflected across the line connecting B and C with nochange in the distance constraints.

17. CHALLENGES OF LOCALIZATION • Discontinuous flex ambiguities occur whenthe removal of one edge will allow part of the graph tobe flexed to a different configuration and the removededge reinserted with the same length. If edge AD is removed, thenreinserted, the graph can flex in the direction of thearrow, taking on a different configuration but exactly preserving all distance constraints

18. APPROACH • Algorithm can be broken three main phases • Phase 1. Cluster Localization: localizes clusters into local coordinate systems. Each node becomes the center of a cluster and estimates the relative location of its neighbors which can be unambiguously localized. • Phase 2. Cluster Optimization: refines the localization of the clusters using numerical optimization such as spring relaxation. This phase is optional. • Phase 3. Cluster Transformation:computes coordinate transformationsbetween these local coordinate systems by finding common nodes between clusters.

19. CLUSTER LOCALIZATION • Quadrilaterals are relevant to localization because theyare the smallest possible subgraph that can be unambiguouslylocalized in isolation. • Quadrilaterals are assumed to be globally rigid. • Any two globally rigid quadrilaterals sharing three verticesform a 5-vertex subgraph that is also globallyrigid. By induction, any number of quadrilaterals chainedin this manner form a globally rigid graph. • Global rigidity is not sufficient to guarantee a unique graphrealization when distance measurements are noisy. • Using robust quadrilaterals solves this problem.

20. CLUSTER LOCALIZATION • Algorithm identifies only those triangles with a sufficiently large minimum angle as robust. Those triangles that satisfy following equation are called robust triangles. • b is the length of the shortest side, Θ is the smallest angle • dmin is a threshold based on the measurement noise • This equation bounds the worst-case probability of a flip error for each triangle.

21. CLUSTER LOCALIZATION • With noisy measurements, trilateration canhave flip ambiguity. An example of a flip ambiguity realized due to measurement noise. Node D is trilateratedfrom the known positions of nodes A, B, and C.

22. CLUSTER LOCALIZATION • Algorithm uses the robustquadrilateral as a starting point, and localize additionalnodes by chaining together connected robust quads. • Whenevertwo quads have three nodes in common and the firstquad is fully localized, the second quad can be localized bytrilaterating from the three known positions. • A natural representationof the relationship between robust quads is theoverlap graph.

23. CLUSTER LOCALIZATION • The entire algorithm for Phase Iisas follows: 1. Distance measurements from each one-hop neighborare broadcast to the origin node so that it has knowledgeof the between-neighbor distances. 2. The complete set of robust quadrilaterals in the clusteris computed (Algorithm 1) and the overlap graph isgenerated. 3. Position estimates are computed for as many nodes as possible via a breadth-first search in the overlap graph(Algorithm 2).

24. CLUSTER LOCALIZATION

25. CLUSTER LOCALIZATION

26. COMPUTING INTER-CLUSTER TRANSFORMATIONS • In Phase III, the transformations between coordinate systemsof connected clusters are computed from the finishedcluster localizations. • As long as there are at least threenon-collinear nodes in common between the two localizations,the transformation can be computed. • By testing ifthese three nodes form a robust triangle, non-collinearity and the same resistance to flipambiguities are guaranteed as Phase I of the algorithm.

27. ANALYSIS • Proof of Robustness: Flex ambiguities • The use of robust quadrilaterals rulesout the possibility of flex ambiguities. Discontinuousflex ambiguity occurs only when a rigid graphbecomes non-rigid by the removal of a single edge.

28. ANALYSIS • If thegraph is such that no single edge removal will make it nonrigid,the graph is redundantly rigid, and no flex ambiguitiesare possible. The robust quad has six edges. By removingany edge, we are left with a 5-edged graph, which must berigid according to Laman’s theorem. • Robust quad with its missing edge has 4 vertices and 5edges, satisfying the condition in Laman's Theorem. Sinceevery 3-vertex subgraph has 3 or fewer edges and every 2-vertex subgraph has 1 or fewer edges, the 5-edged quad isrigid. Thus, the 6-edged robust quad is redundantly rigid.Therefore, ex ambiguities are impossible for a graph constructedof robust quads.

29. ANALYSIS • Proof of robustness : Flip Ambiguities

30. ANALYSIS • If measured distanceis a random variable X, then the worst-case probability oferror is P(X > d + derr) • If measurement noise is zeromeanGaussian with standard deviationσthe worst-caseprobability of error is

31. ANALYSIS • Computational Complexity • Finding set of robust quadrilaterals has worst-case runtime is , m is maximum node degree. • Solving position estimates for one cluster is , q is number of robust quadrilaterals. • Finding inter-cluster transformations for one cluster has runtime , m is number of transformations. • Communication overhead for measuring distances between neighbors is .

32. EXPERIMENTAL RESULTS • The algorithm has been tested on a networkconstructed of Crickets,a hardware platform developed by MIT. Crickets are hardware-compatible with the Mica2 Motes. This hardware enablesthe sensor nodes to measure inter-node ranges using the timedifference of arrival (TDoA) between Ultrasonic and RF signals. • Algorithm has been simulated with 183 nodes in order to show scalability. In simulations, node degree was varied by changing maximum ranging distance. Three different degrees of measurement noise was also considered.

33. EVALUATION CRITERIA • The error that computed localization differs fromknown ground truth: • The mean-square error of the distance measurements: • The cluster success rate:

34. ACCURACY STUDY In this experiment 16 nodes placed randomly. Phase 1 of the algoritm is tested. Results are given below.

35. ACCURACY STUDY In this experiment 40 nodes placed randomly. Both Phase 1 and Phase 3 are tested. Results are given below.

36. SCALABILITY STUDY Simulation is done with 183 nodes for testing scalability of algorithm.

37. SCALABILITY STUDY

38. SCALABILITY STUDY

39. ERROR PROPAGATION

40. LOCATION OF MOBILE NODES

41. CONCLUSION • Algorithm successfully localizesnodes in a sensor network with noisy distance measurements, using no beacons or anchors. • Simulations andexperiments showed the relationship between measurementnoise and ability of a network to localize itself. • Even with no noise, each node in the network must have approximatelydegree 10 or more before 100% node localization canbe attained. • As noise increases, so will the connectivity requirements. • Algorithmadapts to node mobility by filtering the underlyingmeasurements.

42. REFERENCES • [1] Eren, T., Goldenberg, D., Whiteley, W., Yang,Y. R., Morse, A. S., Anderson, B. D. O., andBelhumeur, P. N. Rigidity, computation, andrandomization in network localization. In Proc. IEEEINFOCOM (March 2004) • [2] Capkun, S., Hamdi, M., and Hubaux, J.-P.GPS-free positioning in mobile ad-hoc networks. InProceedings of the 34th Hawaii InternationalConference on System Sciences (2001) • [3] Savvides, A., Garber, W., Adlakha, S., Moses,R., and Srivastava, M. B. On the errorcharacteristics of multihop node localization in ad-hocsensor networks. In Proc. IPSN (Palo Alto, CA, April2003) • [4] Patwari, N., III, A. O. H., Perkins, M., Correal,N. S., and O'Dea, R. J. Relative location estimationin wireless sensor networks. IEEE Trans. SignalProcess. 51, 8 (August 2003) • [5] Bulusu, N., Heidemann, J., and Estrin, D.GPS-less low cost outdoor localization for very smalldevices. IEEE Personal Communications Magazine 7,5 (October 2000) • Karl,H., Willig, A. Protocols and Architectures for Wireless Sensor Networks, John Wiley & Sons, Ltd. ISBN: 0-470-09510-5, 2005