Location Discovery – Part II Lecture 5 September 16, 2004 EENG 460a / CPSC 436 / ENAS 960 Networked Embedded Systems & Sensor Networks Andreas Savvides Office: AKW 212 Tel Course Website

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

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

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

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 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

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

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 : 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

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

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

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 )

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

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)

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)

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

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)

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)

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)

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

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

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

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

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

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”

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

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

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

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

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

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!!!