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

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Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

Location Discovery – Part IILecture 5 September 16, 2004EENG 460a / CPSC 436 / ENAS 960 Networked Embedded Systems &Sensor Networks

Andreas Savvides

[email protected]

Office: AKW 212

Tel 432-1275

Course Website

http://www.eng.yale.edu/enalab/courses/eeng460a


Today

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

      • GDOP – Angles matter

      • Conditions 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

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

Active Mechanisms

Target

Synchronization channel

Ranging channel

  • 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


Passive mechanisms

Passive Mechanisms

Target

Synchronization channel

Ranging channel

?

  • 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.)


Active vs passive

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

      • TDOA 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

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


Possible implementations computation models

Possible Implementations/ Computation Models

Computing Nodes

  • Centralized

  • Only one node computes

2. Locally Centralized

Some of unknown nodes compute

3. (Fully) Distributed

Every unknown node computes

  • 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

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

      • Both measurement based and connectivity based

    • Vision based algorithms


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

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 objectscoordinates 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(n3)


Applying classical mds

Applying Classical MDS

  • Create a proximity matrix of distances D

  • Convert into a double-centered matrix B

  • Take the Singular Value Decomposition of B

  • Compute the coordinate matrix X (2D coordinates will be in the first 2 columns)

NxN matrix of 1s

NxN identity matrix

NxN matrix of 1s


Example localization using multidimensional scaling mds yi shang et al

Example: Localization Using Multidimensional Scaling (MDS) (Yi Shang et. al)

  • The basic MDS-MAP algorithm:

  • Compute shortest paths between all pairs of nodes.

  • Apply classical MDS and use its result to construct a relative map.

  • Given sufficient anchor nodes, transform the relative map to an absolute map.


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

MDS-MAP ALGORITHM

  • Compute all-pair shortest paths. O(n3)

    • 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

  • Apply classical MDS and use its result to construct a 2-D (or 3-D) relative map. O(n3)

  • Given sufficient anchor nodes, convert the relative map to an absolute map via a linear transformation. O(n+m3)

  • Compute the LSE transformation based on the positions of anchors.

  • O(m3),m is the number of anchors

  • Apply the transformation to the other unknown nodes. O(n)


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

MDS-MAP (P) – The Distributed Version

  • Set-up the range for local maps Rlm (# of hops to consider in a map)

  • Compute maps of individual nodes

    • Compute shortest paths between all pairs of nodes

    • Apply MDS

    • Least-squares refinement

  • 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

  • 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


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

LOCALIZATION USING MDS-MAP

(Shang, et al., Mobihoc’03)

  • The basic MDS-MAP algorithm:

  • Given connectivity or local distance measurement, compute shortest paths between all pairs of nodes.

  • Apply multidimentional scaling (MDS) to construct a relative map containing the positions of nodes in a local coordinate system.

  • 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.


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

MDS-MAP(P) (Shang and Ruml, Infocom’04)

  • 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)

  • For each node, compute a local relative map using MDS

  • Merge/align local maps to form a big relative map

  • Refine the relative map based on the relative positions (optional). (When used, referred to as MDS-MAP(P,R) )

  • Given sufficient anchors, compute absolute positions

  • Refinethe positions of individual nodes based on the absolution positions (optional)


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

SOME IMPLEMENTATION DETAILS OF MDS-MAP(P)

  • For each node, compute a local relative map using MDS

    • Size of local maps: fixed or adaptive

  • Merge/align local maps to form a big relative map

    • Sequential or distributed; scaling or not

  • Refine the relative map based on the relative positions

    • Least squares minimization: what information to use

  • Given sufficient anchors, compute absolute positions

    • Anchor selection; centralized or distributed

  • Refinethe positions of individual nodes based on the absolution positions

    • Minimizing squared errors or absolute errors


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

AN EXAMPLE OF C-SHAPE GRID NETWORKS

Known 1-hop distances with 5% range error

Connectivity information only

MDS-MAP(P) without both optional refinement steps.


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

RANDOM UNIFORMPLACEMENT

Connectivity information only

Known 1-hop distances with 5% range error

200 nodes; 4 random anchors


Andreas savvides andreas savvides yale office akw 212 tel 432 1275 course website

RANDOM C-SHAPEPLACEMENT

Connectivity information only

Known 1-hop distances with 5% range error

160 nodes; 4 random anchors


Understanding fundamental behaviors savvides04b

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

Estimated Location Error Decomposition

Channel

Effects

Setup

Error

Computation

Error

Induced by intrinsic

measurement error

Position

Error


Cramer rao bound analysis

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 Effects

Results from Cramer-Rao Bound Simulations based on White Gaussian Error

Range Tangential Error

m/rad

RMS Location Error

RMS Location Error/sigma

m/m

Range Error Scaling Factor

Density (node/m2)

20mm distance measurement certainty == 0.27 angular certainty


Density effects with different ranging technologies

Density Effects with Different Ranging Technologies

6 neighbors

12 neighbors

RMS Error(m)


Network scalability

Network Scalability

Error propagation on a hexagon scenario (angle measurement)

Rate of error propagation faster with distance measurements but

Much smaller magnitude than angles

RMS Location Error x 10

y-coordinate(m)

x-coordinate(m)


More observations on network scalability

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

Localization Service Middleware

Wishful thinking… some of it running on XYZ Node…


Are we done with localization

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!!!


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