1. Location Discovery – Part II Lecture 5 September 16, 2004 EENG 460a / CPSC 436 / ENAS 960 Networked Embedded Systems & Sensor Networks Andreas Savvides andreas.savvides@yale.edu Office: AKW 212 Tel 432-1275 Course Website http://www.eng.yale.edu/enalab/courses/eeng460a

2. Today  Presentation topics scheduling  Stop by Ed Jackson’s office so that he can swipe your ID for the lab  Internal website access  Project and presentation discussions  Any issues with graduate student registrations?  Today’s discussion topics Quick recap from last time oGDOP – Angles matter oConditions for position uniqueness (another presentation on this later) Improved MDS Localization Material for this lecture from: [Shang04] Y. Shang, W. Ruml, Improved MDS Localization, Proceedings of Infocom 2004 [Savvides04b] A. Savvides, W, Garber, R. L. Moses and M. B. Srivastava, An Analysis of Error Inducing Parameters in Multihop Sensor Node Localization, to appear in the IEEE Transcations on Mobile Computing

3. Taxonomy of Localization Mechanisms  Active Localization System sends signals to localize target  Cooperative Localization The target cooperates with the system  Passive Localization System deduces location from observation of signals that are “already present”  Blind Localization System deduces location of target without a priori knowledge of its characteristics

4. Active Mechanisms  Non-cooperative System emits signal, deduces target location from distortions in signal returns e.g. radar and reflective sonar systems  Cooperative Target Target emits a signal with known characteristics; system deduces location by detecting signal e.g. ORL Active Bat, GALORE Panel, AHLoS, MIT Cricket  Cooperative Infrastructure Elements of infrastructure emit signals; target deduces location from detection of signals e.g. GPS, MIT Cricket Target Synchronization channel Ranging channel

5. Passive Mechanisms  Passive Target Localization Signals normally emitted by the target are detected (e.g. birdcall) Several nodes detect candidate events and cooperate to localize it by cross-correlation  Passive Self-Localization A single node estimates distance to a set of beacons (e.g. 802.11 bases in RADAR [Bahl et al.], Ricochet in Bulusu et al.)  Blind Localization Passive localization without a priori knowledge of target characteristics Acoustic “blind beamforming” (Yao et al.) ? Target Synchronization channel Ranging channel

6. Active vs. Passive  Active techniques tend to work best Signal is well characterized, can be engineered for noise and interference rejection Cooperative systems can synchronize with the target to enable accurate time-of-flight estimation  Passive techniques Detection quality depends on characterization of signal Time difference of arrivals only; must surround target with sensors or sensor clusters oTDOA requires precise knowledge of sensor positions  Blind techniques Cross-correlation only; may increase communication cost Tends to detect “loudest” event.. May not be noise immune

7. Measurement Technologies  Ultrasonic time-of-flight Common frequencies 25 – 40KHz, range few meters (or tens of meters), avg. case accuracy ~ 2-5 cm, lobe-shaped beam angle in most of the cases Wide-band ultrasonic transducers also available, mostly in prototype phases  Acoustic ToF Range – tens of meters, accuracy =10cm  RF Time-of-flight Ubinet UWB claims = ~ 6 inches  Acoustic angle of arrival Average accuracy = ~ 5 degrees (e.g acoustic beamformer, MIT Cricket)  Received Signal Strength Indicator Motes: Accuracy 2-3 m, Range = ~ 10m 802.11: Accuracy = ~30m  Laser Time-of-Flight Range Measurement Range =~ 200, accuracy =~ 2cm very directional  RFIDs and Infrared Sensors – many different technologies Mostly used as a proximity metric

8. Possible Implementations/ Computation Models 1.Centralized Only one node computes 2. Locally Centralized Some of unknown nodes compute 3. (Fully) Distributed Every unknown node computes Computing Nodes Each approach may be appropriate for a different application Centralized approaches require routing and leader election Fully distributed approach does not have this requirement

9. Different Problem Setups & Algorithms  Absolute vs. relative frame of reference Beacons or no beacons Infrastructure vs. ad-hoc Single hop vs. multihop  Many candidate approaches and solution methods (depending on problem setup, measurement technology and computation resources) Least-squares optimization Approaches based on radio connectivity Learning based approaches Semi definite programming approaches oBoth measurement based and connectivity based Vision based algorithms

10. Obtaining a Coordinate System from Distance Measurements: Introduction to MDS MDS maps objects from a high-dimensional space to a low-dimensional space, while preserving distances between objects. similarity between objects coordinates of points Classical metric MDS: The simplest MDS: the proximities are treated as distances in an Euclidean space Optimality: LSE sense. Exact reconstruction if the proximity data are from an Euclidean space Efficiency: singular value decomposition, O(n 3 )

11. Applying Classical MDS 1.Create a proximity matrix of distances D 2.Convert into a double-centered matrix B 3.Take the Singular Value Decomposition of B 4.Compute the coordinate matrix X (2D coordinates will be in the first 2 columns) NxN matrix of 1s NxN identity matrix

12. The basic MDS-MAP algorithm: 1.Compute shortest paths between all pairs of nodes. 2.Apply classical MDS and use its result to construct a relative map. 3.Given sufficient anchor nodes, transform the relative map to an absolute map. Example: Localization Using Multidimensional Scaling (MDS) (Yi Shang et. al)

13. MDS-MAP ALGORITHM 1. Compute all-pair shortest paths. O(n 3 ) Assigning values to the edges in the connectivity graph: Known connectivity only: all edges have value 1 (or R/2) Known neighbor distances: the edges have the distance values 2. Apply classical MDS and use its result to construct a 2-D (or 3-D) relative map. O(n 3 ) 3. Given sufficient anchor nodes, convert the relative map to an absolute map via a linear transformation. O(n+m 3 ) Compute the LSE transformation based on the positions of anchors. O(m 3 ), m is the number of anchors Apply the transformation to the other unknown nodes. O(n)

14. MDS-MAP (P) – The Distributed Version 1. Set-up the range for local maps R lm (# of hops to consider in a map) 2.Compute maps of individual nodes 1.Compute shortest paths between all pairs of nodes 2.Apply MDS 3.Least-squares refinement 3.Patch the maps together Randomly pick a node and build a local map, then merge the neighbors and continue until the whole network is completed 4.If sufficient anchor nodes are present, transform the relative map to an absolute map MDS-MAP(P,R) – Same as MDS-MAP(P) followed by a refinement phase

15. The basic MDS-MAP algorithm: 1.Given connectivity or local distance measurement, compute shortest paths between all pairs of nodes. 2.Apply multidimentional scaling (MDS) to construct a relative map containing the positions of nodes in a local coordinate system. 3.Given sufficient anchors (nodes with known positions), e.g, 3 for 2-D or 4 for 3-D networks, transform the relative map and determine the absolute the positions of the nodes. It works for any n-dimensional networks, e.g., 2-D or 3-D. LOCALIZATION USING MDS-MAP (Shang, et al., Mobihoc’03)

16. The basic MDS-MAP works well on regularly shaped networks, but not on irregularly shaped networks. MDS-MAP(P) (or MDS-MAP based on patches of local maps) 1.For each node, compute a local relative map using MDS 2.Merge/align local maps to form a big relative map 3.Refine the relative map based on the relative positions (optional). (When used, referred to as MDS-MAP(P,R) ) 4.Given sufficient anchors, compute absolute positions 5.Refine the positions of individual nodes based on the absolution positions (optional) MDS-MAP(P) (Shang and Ruml, Infocom’04)

17. 1.For each node, compute a local relative map using MDS Size of local maps: fixed or adaptive 2.Merge/align local maps to form a big relative map Sequential or distributed; scaling or not 3.Refine the relative map based on the relative positions Least squares minimization: what information to use 4.Given sufficient anchors, compute absolute positions Anchor selection; centralized or distributed 5.Refine the positions of individual nodes based on the absolution positions Minimizing squared errors or absolute errors SOME IMPLEMENTATION DETAILS OF MDS-MAP(P)

18. AN EXAMPLE OF C-SHAPE GRID NETWORKS MDS-MAP(P) without both optional refinement steps. Known 1-hop distances with 5% range error Connectivity information only

19. RANDOM UNIFORM PLACEMENT 200 nodes; 4 random anchors Connectivity information onlyKnown 1-hop distances with 5% range error

20. RANDOM C-SHAPE PLACEMENT 160 nodes; 4 random anchors Connectivity information onlyKnown 1-hop distances with 5% range error

21. Understanding Fundamental Behaviors (Savvides04b) What is the fundamental error behavior? Measurement technology perspective Acoustic vs. RF ToF (2cm – 1.5m measurement accuracy) Distances vs. Angules Deployment - what density? Scalability How does error propagate? Beacon density & beacon position uncertainty Intrinsic vs. Extrinsic Error Component

22. Estimated Location Error Decomposition Position Error Channel Effects Computation Error Setup Error Induced by intrinsic measurement error

23. Cramer Rao Bound Analysis  Cramer-Rao Bound Analysis on carefully controlled scenarios Classical result from statistics that gives a lower bound on the error covariance matrix of an unbiased estimate  Assuming White Gaussian Measurement Error  Related work N. Patwari et. al, “Relative Location Estimation in Wireless Sensor Networks”

24. Density Effects Density (node/m 2 ) RMS Location Error 20mm distance measurement certainty == 0.27 angular certainty Range Error Scaling Factor RMS Location Error/sigma Range Tangential Error Results from Cramer-Rao Bound Simulations based on White Gaussian Error m/rad m/m

25. Density Effects with Different Ranging Technologies RMS Error(m) 6 neighbors 12 neighbors

26. Network Scalability x-coordinate(m) y-coordinate(m) RMS Location Error x 10 Error propagation on a hexagon scenario (angle measurement) Rate of error propagation faster with distance measurements but Much smaller magnitude than angles

27. More Observations on Network Scalability…  Performance degrades gracefully as the number of unknown nodes increases.  Increasing the number of beacon nodes does not make a significant improvement  Error in beacons results in an overall translation of the network  Error due to geometry is the major component in propagated error

28. Localization Service Middleware Wishful thinking… some of it running on XYZ Node…

29. Are we done with localization?  Well there is more… Computation using angles Mobility and tracking Probabilistic approaches  More about localization in future lectures  Next time – embedded programming tutorial Read programming assignment 1 before coming to class!!!