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Ad hoc and Sensor Networks Chapter 9: Localization & positioning

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  1. Ad hoc and Sensor NetworksChapter 9: Localization & positioning Holger Karl

  2. Outline • Introduction • AHLoS • Ad-Hoc Localization Systeme and overview • Atomic Multilateration • Iterative Multilateration • Collaborative Multilateration • Performance evaluation • Conclusion Ad hoc & sensor networs - Ch 9: Localization & positioning

  3. Introduction What is Localization • A mechanism for discovering spatial relationships among objects Ad hoc & sensor networs - Ch 9: Localization & positioning

  4. Known Location Unknown Location Introduction here, It is Location discovery for nodes • Given a network of sensor nodes where a few nodes know their location how do we calculate the location of the nodes? Ad hoc & sensor networs - Ch 9: Localization & positioning

  5. Introduction Why need this kind of localization? Motivation • Support Location Aware Applications • Track Objects • Report event origins • Evaluate network coverage • Assist with routing, GF • Support for upper level protocols. • GPS is not practical • Not work Indoors or if blocked from the GPS satellites • Spends the battery life of the node • Issue of the production cost factor of GPS • Increase the size of sensor nodes Ad hoc & sensor networs - Ch 9: Localization & positioning

  6. Introduction Two phases • Location discovery approaches consist of two phases : Ranging phase, Estimation phase • Ranging phase (distance estimation) • Each node estimate its distance from its neighbors • Estimation phase (distance combining) • Nodes use ranging information and beacon node locations to estimate their positions Ad hoc & sensor networs - Ch 9: Localization & positioning

  7. Introduction phases 1: Ranging phase • Distance measuring methods • Signal Strength • Uses RSSI readings • Time based methods • ToA, TDoA • Used with radio, acoustic, ultrasound • Angle of Arrival (AoA) • Measured with directive antennas or arrays Ad hoc & sensor networs - Ch 9: Localization & positioning

  8. Sines Rule B b A a c C Cosines Rule Introduction phases 2: Estimation phase • Hyperbolic Trilateration • Triangulation • Multi-lateration • Considers all available beacons Ad hoc & sensor networs - Ch 9: Localization & positioning

  9. Introduction Related work • Outdoor • Automatic Vehicle Location (AVL) • Determine the position of police cars • Use ToA, Multi-lateration • Global Positioning System (GPS) & LORAN • GPS:24 NAVSTAR satellites • LORAN: ground based beacons instead of satellites • Time-of-flight, trilateration • Mobile phone position • Cellular base station transmits beacons • Use TDoA, Multi-lateration Ad hoc & sensor networs - Ch 9: Localization & positioning

  10. Introduction Related work • Indoor • RADAR system • Track the location of users within a building • RF strength measurements from three fixed base stations • Build a set of signal strength maps • Mathing the online readings from the maps • Cricket location support system • Use Ultrasound from fixed beacons • Multi-lateration • The Bat system • Node carries an ultrasound transmitter • Multi-lateration Ad hoc & sensor networs - Ch 9: Localization & positioning

  11. Introduction Ranging characterization • Received Signal Strength • RF signal attenuation is a function of distance • Inconsistent Model because of environment fading and shadowing effects and the altitude of the radio antenna • A Model is derived by obtaining a least square fit for each power level Ad hoc & sensor networs - Ch 9: Localization & positioning

  12. Introduction Ranging • ToA using RF and Ultrasound • The time difference between RF and ultrasound • To estimate the speed to sound, perform a best line fit Ad hoc & sensor networs - Ch 9: Localization & positioning

  13. Introduction Discussion • Does ToA suffer from the environment changes? • Obstacles, interference to ToA? • Extra work to identify the pairs of Radio Signal and Ultrasound pulse. • Constraints: Ultrasound range on the Medusa nodes used is about 3 meters (11-12 feet), the ultra-range of second generation of Medusa is about 10-15 meters, far less than the communication radius (30-100m) • Any other comments? Ad hoc & sensor networs - Ch 9: Localization & positioning

  14. Outline • Introduction • AHLoS • Ad-Hoc Localization Systeme and overview • Atomic Multilateration • Iterative Multilateration • Collaborative Multilateration • Performance evaluation • Conclusion Ad hoc & sensor networs - Ch 9: Localization & positioning

  15. AHLoSAd-Hoc Localization Systeme • Ranging phase (distance estimation) • ToA • Estimation phase (distance combining) • Multilateration Ad hoc & sensor networs - Ch 9: Localization & positioning

  16. AHLoSOverview • Some percentage of nodes knows their positions • Beacon nodes • Nodes with known positions • Broadcast their locations to their neighbors • Unknown nodes • Nodes with unknown positions • Use ranging information and beacon node locations to estimate their positions • Once knows its location, becomes a beacon node • Atomic, Iterative, and Collaborative Multilateration Ad hoc & sensor networs - Ch 9: Localization & positioning

  17. Outline • Introduction • AHLoS • Ad-Hoc Localization Systeme and overview • Atomic Multilateration • Iterative Multilateration • Collaborative Multilateration • Performance evaluation • Conclusion Ad hoc & sensor networs - Ch 9: Localization & positioning

  18. 1 1 1 1 d1x d1x d1x d1x d1x d1x d3x 3 d3x d3x d1x X X’ X’ X X’ X 3 d2x d2x d2x d2x d2x X 2 2 2 One beacon, location X is not unique Two beacons, location X is not unique Three beacons, location X is unique Three lined beacons, location X is not unique AHLoSAtomic Multilateration • Requirement • Atomic multilateration can take place if the unknown node is within one hop distance from at least three beacon nodes. The node may also estimate the ultrasound propagation speed if four or more beacons are available • Topology for atomic multilateration Ad hoc & sensor networs - Ch 9: Localization & positioning

  19. AHLoSAtomic Multilateration What we know: 1. The location of Three or more beacons N1,N2,N3, …… 2. Ti0, the time from beacon Ni to unknown node 0 for ultrasound propagation What we want to get: The location of the unknown node 0 How to get the location: Make the difference between the measured distance and estimated Euclidean distance to be as small as possible. Method used: The minimum mean square estimate (MMSE), let F to be as small as possible (Equation 3) (Equation 4) Ad hoc & sensor networs - Ch 9: Localization & positioning

  20. AHLoS Incorrectness 1 in Atomic Multilateration The goal is let F(X0,Y0,S) in equation 4to be as small as possible (Equation 4) We should have (Equation 40) Here, equation 5 is generated by setting = 0 So it has (Equation 5) If equations 5 have solutions, they are solutions to equation 4. BUT equations 5 may not have solutions, because Ti0 is a measured value, equations 5 can not be guaranteed to have solutions on the measured values Ti0. Ad hoc & sensor networs - Ch 9: Localization & positioning

  21. AHLoS Incorrectness 2 in Atomic Multilateration Look at the solution of the system of equations (Equation A) (Equation B) How to get it? In the process, one important assumption is If , doesn’t exist. We can not use the method Ad hoc & sensor networs - Ch 9: Localization & positioning

  22. AHLoS Incorrectness 3 in Atomic Multilateration 3 beacons are not enough to get a unique solution with unknown speed s. In the left figure, d1x, d2x, d3x are distance But in the equations, distance is unknown, Another variable is introduced, the ultrasound Propagation speed s. There are only 3 equations with x, y square factors and unknown s. 3 beacons are not enough to get a unique location solution with unknown speed s. 1 d1x d3x X 3 d2x 2 Ad hoc & sensor networs - Ch 9: Localization & positioning

  23. AHLoSAtomic Multilateration Example 1 EXAMPLE Conditions: Three beacons N1(0,1),N2(0,-1),N3(2,0) One unknown node N0 The time of the ultrasound propagation: From N1 to N0, it is sqrt(2) s From N2 to N0, it is sqrt(2) s From N3 to N0, it is 1 s Test: Using the algorithm on the paper to see if we can get the coordinates of N0 or some other interesting results. N1(0,1) 1 N3(2,0) N0(1,0) N2(0,-1) Ad hoc & sensor networs - Ch 9: Localization & positioning

  24. AHLoSAtomic Multilateration Example 1 EXAMPLE From equation above, we have N1(0,1) Equation N1 Equation N2 1 N3(2,0) Equation N3 N0(1,0) N1 – N3 and N2 – N3 , we have N2(0,-1) Ad hoc & sensor networs - Ch 9: Localization & positioning

  25. AHLoSAtomic Multilateration Example 1 EXAMPLE N1(0,1) 1 N3(2,0) N0(1,0) N2(0,-1) We can not directly use the solution provided by the paper. Ad hoc & sensor networs - Ch 9: Localization & positioning

  26. AHLoSAtomic Multilateration Example 1 EXAMPLE From equations above, we have Equation e1 N1(0,1) Equation e2 Equation e3 1 N3(2,0) Eliminating Equation e4 N0(1,0) Equation e5 Equation e6 From Equation e4,e5, we have N2(0,-1) From Equation e5,e6, we have Equation e7 From Equation e3,e5,e6 we have Equation e8 Ad hoc & sensor networs - Ch 9: Localization & positioning

  27. AHLoSAtomic Multilateration Example 1 EXAMPLE Equation e6 N1(0,1) Equation e7 Equation e8 1 N3(2,0) From Equation e6,e7,e8, we have 2 sets of results N0(1,0) N2(0,-1) OR Ad hoc & sensor networs - Ch 9: Localization & positioning

  28. AHLoSAtomic Multilateration Example 1 Taking the algorithm on the paper 3 beacons are not enough to get a unique solution with unknown speed s. N1(0,1) 1 N3(2,0) N0’(7,0) N0(1,0) N2(0,-1) OR Ad hoc & sensor networs - Ch 9: Localization & positioning

  29. AHLoSAtomic Multilateration Example 2 EXAMPLE Conditions: Three beacons N1(0,1),N2(0,-1),N3(2,0) One unknown node N0 The time of the ultrasound propagation: From N1 to N0, it is sqrt(2) ms From N2 to N0, it is sqrt(2) ms From N3 to N0, it is 1 ms Test: Using the standard MMSE method to see if we can get the coordinates of N0 or some other interesting results. N1(0,1) 1 N3(2,0) N0(1,0) N2(0,-1) Ad hoc & sensor networs - Ch 9: Localization & positioning

  30. AHLoSAtomic Multilateration Example 2 EXAMPLE N1(0,1) 1 N3(2,0) N0(1,0) N2(0,-1) Taking the algorithm on MMSE 3 beacons are not enough to get a unique solution with unknown speed s. select Ad hoc & sensor networs - Ch 9: Localization & positioning

  31. AHLoSConclusion in Atomic Multilateration • With the unknown speed of ultrasound pulse or other efficient constraints, generally, it is impossible to get a unique location of one unknown node only depending 3 un-lined beacons • Other constraints, such as a roughly scope of ultrasound speed, angle, etc, must be added to make the solution determined. Or 4 un-lines beacons determine one unknown node’s location • The computation process on the paper is not robust. • In the algorithms later, we assume the speed of ultrasound is known Ad hoc & sensor networs - Ch 9: Localization & positioning

  32. Outline • Introduction • AHLoS • Ad-Hoc Localization Systeme and overview • Atomic Multilateration • Iterative Multilateration • Collaborative Multilateration • Performance evaluation • Conclusion Ad hoc & sensor networs - Ch 9: Localization & positioning

  33. Outline • Introduction • AHLoS • Ad-Hoc Localization Systeme and overview • Atomic Multilateration • Iterative Multilateration • Collaborative Multilateration • Performance evaluation • Conclusion Ad hoc & sensor networs - Ch 9: Localization & positioning

  34. AHLoSCollaborative Multilateration • One node estimates its position by considering use of location information over multiple hops • How it works • For one node, to decide which nodes should be in its participating node set S • For node , i is connected to u, and node u is an unknown node, the goal function is the same as that of the atomic multi-lateration, to minimize the Ad hoc & sensor networs - Ch 9: Localization & positioning

  35. Outline • Introduction • AHLoS • Ad-Hoc Localization Systeme and overview • Atomic Multilateration • Iterative Multilateration • Collaborative Multilateration • Performance evaluation • Conclusion Ad hoc & sensor networs - Ch 9: Localization & positioning

  36. Performance evaluation • What kind of performance evaluation do we need for the localization? What do we care most about the localization? Accuracy Scalability Cost …… Ad hoc & sensor networs - Ch 9: Localization & positioning

  37. Performance evaluationAccuracy Only Iterative Multilateration is included as we talked earlier. What is the behind: 1.How many steps are there for accumulated error? 2.How beacons are deployed? 3.Small scale Ad hoc & sensor networs - Ch 9: Localization & positioning

  38. Performance evaluationcost • 117 nodes/10,000m2 Uniformly distributed, Range = 10 Ad hoc & sensor networs - Ch 9: Localization & positioning

  39. Performance evaluationcost Ad hoc & sensor networs - Ch 9: Localization & positioning

  40. Outline • Introduction • AHLoS • Ad-Hoc Localization Systeme and overview • Atomic Multilateration • Iterative Multilateration • Collaborative Multilateration • Performance evaluation • Conclusion Ad hoc & sensor networs - Ch 9: Localization & positioning

  41. Papers:1.”Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors”2.”Distributed Fine-Grained Localization in Ad-Hoc networks”3.”Localization in Ad-Hoc Sensor Networks”Slides:1.”Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors” presented by Kisuk Kweon 2.”LOCALIZATION” presented by Lewis Girod3.”Survey of Estimation of Location in Sensor Networks” Presented by Wei-Peng Chen4.”Dynamic Location Discovery in Ad-Hoc Networks” presented byAndreas Savvides, Boulis and Mani B. Srivastava5.”Distributed localization in wireless ad-hoc sensor network” presented by Vaidyanathan Ramadurai References Ad hoc & sensor networs - Ch 9: Localization & positioning

  42. Goals of this chapter • Means for a node to determine its physical position (with respect to some coordinate system) or symbolic location • Using the help of • Anchor nodes that know their position • Directly adjacent • Over multiple hops • Using different means to determine distances/angles locally Ad hoc & sensor networs - Ch 9: Localization & positioning

  43. Overview • Basic approaches • Trilateration • Multihop schemes Ad hoc & sensor networs - Ch 9: Localization & positioning

  44. Localization & positioning • Determine physical position or logical location • Coordinate system or symbolic reference • Absolute or relative coordinates • Options • Centralized or distributed computation • Scale (indoors, outdoors, global, …) • Sources of information • Metrics • Accuracy (how close is an estimated position to the real position?) • Precision (for repeated position determinations, how often is a given accuracy achieved?) • Costs, energy consumption, … Ad hoc & sensor networs - Ch 9: Localization & positioning

  45. Main approaches (information sources) • Proximity • Exploit finite range of wireless communication • E.g.: easy to determine location in a room with infrared room number announcements • (Tri-/Multi-)lateration and angulation • Use distance or angle estimates, simple geometry to compute position estimates • Scene analysis • Radio environment has characteristic “signatures” • Can be measured beforehand, stored, compared with current situation Ad hoc & sensor networs - Ch 9: Localization & positioning

  46. Estimating distances – RSSI • Received Signal Strength Indicator • Send out signal of known strength, use received signal strength and path loss coefficient to estimate distance • Problem: Highly error-prone process – Shown: PDF for a fixed RSSI PDF PDF Distance Signal strength Distance Ad hoc & sensor networs - Ch 9: Localization & positioning

  47. Estimating distances – other means • Time of arrival (ToA) • Use time of transmission, propagation speed, time of arrival to compute distance • Problem: Exact time synchronization • Time Difference of Arrival (TDoA) • Use two different signals with different propagation speeds • Example: ultrasound and radio signal • Propagation time of radio negligible compared to ultrasound • Compute difference between arrival times to compute distance • Problem: Calibration, expensive/energy-intensive hardware Ad hoc & sensor networs - Ch 9: Localization & positioning

  48. Determining angles • Directional antennas • On the node • Mechanically rotating or electrically “steerable” • On several access points • Rotating at different offsets • Time between beacons allows to compute angles Ad hoc & sensor networs - Ch 9: Localization & positioning

  49. Some range-free, single-hop localization techniques • Overlapping connectivity: Position is estimated in the center of area where circles from which signal is heard/not heard overlap • Approximate point in triangle • Determine triangles of anchor nodes where node is inside, overlap them • Check whether inside a given triangle – move node or simulate movement by asking neighbors • Only approximately correct Ad hoc & sensor networs - Ch 9: Localization & positioning

  50. Overview • Basic approaches • Trilateration • Multihop schemes Ad hoc & sensor networs - Ch 9: Localization & positioning