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  1. Localization

  2. Introduction We are here !

  3. Applications • Wildlife Tracking • Weather Monitoring • Location-based Authentication • Routing in ad-hoc networks • Surveillances

  4. Properties of Localization • Physical position versus symbolic location • Absolute versus relative coordinates • Localized versus centralized computation • Percision • Cost • Scale • Limitations

  5. Possible Approaches • Triangulation, Trilateration • Location determined using geometry. • Scene Analysis • Observed features used to infer location. • Proximity • Detection of change near known location.

  6. Scene Analysis • Features of an observed scene from a particular vantage point used to infer location. • Not applicable in WSNs.

  7. Proximity • Can be used for positioning when several overlapping anchors are avialalbe. • Centronoid localization • It can be used to decide whether a node is in the proximity of an anchor. • E.g. Active Badge

  8. Triangulation Vs. Lateration • The proximity helps to determine geometric relationship between nodes. • The distance between them or angle of a singular triangle can be easily estimated.

  9. Lateration vs. Angulation • When distances between entities are used, the approach is called lateration. • when angles between nodes are used, one talks about angulation.

  10. Trilateration • Using distances and anchor positions, the node’s position has to be at the intersection of three circles around the anchors. d d d

  11. Distance measure Approaches • RSSI • ToA • TDoA • Determining Angles

  12. RSSI • Known : • Transmission power Ptx • The path loss model • Path lost coefficient α • Receiver can determine the distance d to the transmitter :

  13. RSSI • Challenges: • Signal propagation issues, especially indoors: • Shadowing, Scattering, Multipath propagation. • It’s usually a random process.

  14. Time of Arrival • Conditions : • The speed of propagation is known. • Sound speed depends on environmental factors. • Receiver and sender are synchronized.(drawback) • The distance can be estimated, using the transmission time.

  15. TDoA • TDoA use two transmissions mediums of different propagation speeds to generate an implicit synchronization. • First signal is used to measure ToA of the second one.

  16. Triangulation • Angulation: using angles to determine distance with directional, or phased-array antennas. • 2D position requires two angle + one distance measurement. • 3D position requires two angle + one length + one azimuth measurement. • d is known d

  17. Mathematics of Lateration • there are three anchors with known positions. • For the unknown position of (xu,yu) and those anchors we have :

  18. Mathematics of Lateration • After subtracting the third equ. and reordering them we have : • That can be expressed using a linear matrix.

  19. Mathematics of Lateration • Which the Matrix on the left side and right side are known constant.

  20. Solving the Distance Errors. • Distance measurements are not perfect but only estimates with an unknown error ε are known. • How to Solve this ? • More than three anchors are needed. • Use Multilateration Problem

  21. Multilateration • When order the so called Euclidian formula , we have : • A solution can be computed that minimizes the mean square error. which is :

  22. Single Hop Localization • This is about systems where a node with unknown position can directly communicate with anchors.

  23. Central Server Badge IR sensor (receiver) Active Badge • Every badge periodically, sends unique identifier, via infrared, to the receivers. receivers, receive this identifiers and store it on a central server.

  24. Active office • The devices which its position is to be determinate act as ultrasound senders • Receivers are placed at well-known position, mounted in array at the ceiling of a room. • controller sends a radio message which contains the address of this specific device. • The device sends out an ultrasound pulse, which is received by the array of receivers.

  25. Active office • This array computes the difference between the arrival of the ultrasound pulse and the time when the radio signal was sent. (TDoA)

  26. Cricket • In both recent cases, infrastructure determines device position. • Here the devices themselves can compute their own positions or locations.

  27. Cricket • Anchors spread in a building send ultrasound pulses that combined with radio pulses, which allow the receiver to employ the TDoA to extract symbolic location information of its position.

  28. Overlapping Connectivity • Try to use only the observation of connectivity to a set of anchors to determine a node’s position.

  29. APIT • Decide whether a node is within or outside of a triangle formed by any three anchors.

  30. APIT • Nodes cannot move always ! • how to decide ?

  31. APIT • Approximate P.I.T Test: If no neighbor of M is further from/closer to all three anchors A, B and C simultaneously, M assumes that it is inside triangle ΔABC. Otherwise, M assumes it resides outside this triangle.

  32. Two possible Errors

  33. Two possible Errors • the percentage of APIT tests exhibiting such an error is relatively small (14% in the worst case).

  34. APIT Aggregation • APIT aggregates the results (inside/outside decisions among which some may be incorrect) through a grid SCAN algorithm.

  35. Using Angle of Arrival • use anchors nodes that use narrow, rotating beams where the rotation speed is constant and known to all nodes.

  36. Positioning in MultiHop • Recent approaches was based on connectivity of nodes to anchors. • This assumption is not always true in a WSN – not every node is in direct contact with at least three anchors.

  37. SDP • Geometric constraints between nodes are represented as linear matrix inequalities (LMIs). • The LMIs can be combined to form a single semidefinite program. • only constraints that form convex regions are amenable to representation as an LMI.

  38. SDP • Angle of arrival data can be represented as a triangle and hop count data can be represented as a circle, but precise range data cannot be conveniently represented.

  39. SDP • Given a set of convex constraints on a node’s position, SDP simply finds the intersection of the constraints.

  40. MDS • MDS-MAP is a centralized algorithm. • Suppose there are n points, suspended in a volume. We don’t know the positions of the points, but we do know the distance between each pair of points. Find the relative positions of the points based on the pairwise distances.

  41. MDS • Estimates shortest path between any pair of nodes , then applies a MDS , and at the end Transform the estimates into global coordinates using some number of fixed anchor nodes using a CSR routine.

  42. MDS • It is fairly stable with respect to anchor placement, achieving good results even if only few anchors are available or placed.

  43. Multihop Range Estimation • Niculescu described three different approach. • DV-Hop • DV-Distance • Euclidean Distance

  44. DV-Hop • Count Shortest hop numbers between all two nodes. • Each anchors estimate hop length and propagates to the network. • Node calculates its position based on average hop length and shortest path to each anchor.

  45. DV Hop • L1 calculates average hope length : • So do L2 and L3 :

  46. DV-Hop • Node A uses trilateration to estimate it’s position by multiplying the average hope length of every received anchor to shortest path length it assumed.

  47. DV-Distance • Distance between neighboring nodes is measured using radio signal strength and is propagated in meters rather than in hops. • Range estimation is more precise. • The algorithm uses the same method to estimate but shortest distance length are assumed.

  48. Euclidean Distance • Assuming that the distances AB, AC, BC, XB, XC are all known, it is possible to compute the unknown distance XA.

  49. Iterative Multilateration • When a node is not located within a range of three anchors, multilateration can not be implemented. • use normal nodes, once they have estimated their positions, just like anchor nodes in a multilateration algorithm.

  50. Iterative Multilateration