Ad hoc and Sensor Networks Chapter 9: Localization & positioning Holger Karl

Ad hoc & sensor networs - Ch 9: Localization & positioning Outline Introduction AHLoS Ad-Hoc Localization Systeme and overview Atomic Multilateration Iterative Multilateration Collaborative Multilateration Performance evaluation Conclusion SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Introduction What is Localization A mechanism for discovering spatial relationships among objects SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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? Known Location Unknown Location SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Introduction phases 2: Estimation phase Hyperbolic Trilateration Triangulation Multi-lateration Considers all available beacons A B C a b c Sines Rule Cosines Rule SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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? SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Outline Introduction AHLoS Ad-Hoc Localization Systeme and overview Atomic Multilateration Iterative Multilateration Collaborative Multilateration Performance evaluation Conclusion SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Ad-Hoc Localization Systeme Ranging phase (distance estimation) ToA Estimation phase (distance combining) Multilateration SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning AHLoS Overview 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Outline Introduction AHLoS Ad-Hoc Localization Systeme and overview Atomic Multilateration Iterative Multilateration Collaborative Multilateration Performance evaluation Conclusion SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic 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 1 d1x X X’ d2x 2 d3x 3 Three lined beacons, location X is not unique 1 d1x X X’ d2x 2 Two beacons, location X is not unique 1 X d1x d2x 2 3 d3x Three beacons, location X is unique 1 d1x X X’ One beacon, location X is not unique SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic 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) SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Incorrectness 1 in Atomic Multilateration The goal is let F(X0,Y0,S) in equation 4 to 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. SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic Multilateration Example 1 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) SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic Multilateration Example 1 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) SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic Multilateration Example 1 We can not directly use the solution provided by the paper. SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic Multilateration Example 1 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic Multilateration Example 1 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic Multilateration Example 2 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) SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Atomic Multilateration Example 2 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Conclusion 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Outline Introduction AHLoS Ad-Hoc Localization Systeme and overview Atomic Multilateration Iterative Multilateration Collaborative Multilateration Performance evaluation Conclusion SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Outline Introduction AHLoS Ad-Hoc Localization Systeme and overview Atomic Multilateration Iterative Multilateration Collaborative Multilateration Performance evaluation Conclusion SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

AHLoS Collaborative 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Outline Introduction AHLoS Ad-Hoc Localization Systeme and overview Atomic Multilateration Iterative Multilateration Collaborative Multilateration Performance evaluation Conclusion SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Performance evaluation What kind of performance evaluation do we need for the localization? What do we care most about the localization? Accuracy Scalability Cost …… SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Performance evaluation Accuracy 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Performance evaluation cost 117 nodes/10,000m2 Uniformly distributed, Range = 10 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Performance evaluation cost SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Outline Introduction AHLoS Ad-Hoc Localization Systeme and overview Atomic Multilateration Iterative Multilateration Collaborative Multilateration Performance evaluation Conclusion SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning References 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 Girod 3.”Survey of Estimation of Location in Sensor Networks” Presented by Wei-Peng Chen 4.”Dynamic Location Discovery in Ad-Hoc Networks” presented byAndreas Savvides, Boulis and Mani B. Srivastava 5.”Distributed localization in wireless ad-hoc sensor network” presented by Vaidyanathan Ramadurai SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Overview Basic approaches Trilateration Multihop schemes SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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, … SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning 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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

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 SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Overview Basic approaches Trilateration Multihop schemes SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Trilateration Assuming distances to three points with known location are exactly given Solve system of equations (Pythagoras!) (xi,yi) : coordinates of anchor point i, ri distance to anchor i (xu, yu) : unknown coordinates of node Subtracting eq. 3 from 1 & 2: Rearranging terms gives a linear equation in (xu, yu)! SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Trilateration as matrix equation Rewriting as a matrix equation: Example: (x1, y1) = (2,1), (x2, y2) = (5,4), (x3, y3) = (8,2), r1 = 100.5 , r2 = 2, r3 = 3 ! (xu,yu) = (5,2) SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Trilateration with distance errors What if only distance estimation ri0 = ri + i available? Use multiple anchors, overdetermined system of equations Use (xu, yu) that minimize mean square error, i.e, SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Minimize mean square error Look at square of the of Euclidean norm expression (note that for all vectors v) Look at derivative with respect to x, set it equal to 0: Normal equation Has unique solution (if A has full rank), which gives desired minimal mean square error Essentially similar for angulation as well SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Overview Basic approaches Trilateration Multihop schemes SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Multihop range estimation How to estimate range to a node to which no direct radio communication exists? No RSSI, TDoA, … But: Multihop communication is possible Idea 1: Count number of hops, assume length of one hop is known (DV-Hop) Start by counting hops between anchors, divide known distance Idea 2: If range estimates between neighbors exist, use them to improve total length of route estimation in previous method (DV-Distance) SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Iterative multilateration Assume some nodes can hear at least three anchors (to perform triangulation), but not all Idea: let more and more nodes compute position estimates, spread position knowledge in the network Problem: Errors accumulate SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Probabilistic position description Similar idea to previous one, but accept problem that position of nodes is only probabilistically known Represent this probability explicitly, use it to compute probabilities for further nodes SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Conclusions Determining location or position is a vitally important function in WSN, but fraught with many errors and shortcomings Range estimates often not sufficiently accurate Many anchors are needed for acceptable results Anchors might need external position sources (GPS) Multilateration problematic (convergence, accuracy) SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning

Ad hoc & sensor networs - Ch 9: Localization & positioning Acknowledgements Notes are partly from slides of : Andreas Savvides, Athanassios Boulis and Mani B. Srivastava Networked and Embedded Systems Lab University of California, Los Angeles Yong Chen Department of Computer Science University of Virginia SS 05 Ad hoc & sensor networs - Ch 9: Localization & positioning