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Survey of Estimation of Location in Sensor Networks

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Estimate the location of itself from the relationship of distance to beacon nodes ... Broadcast(flags, location(if any)) If 3 nbrs with location or 3 nbrs ... – PowerPoint PPT presentation

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Title: Survey of Estimation of Location in Sensor Networks


1
Survey of Estimation of Location in Sensor
Networks
  • Presented by Wei-Peng Chen

2
Paper
  • Dynamic fine-grained localization in Ad-Hoc
    networks of sensors (Mobicom 2001) by Andreas
    Savvides et. al. UCLA
  • Localized Algorithms In Wireless Ad-Hoc Networks
    Location Discovery and Sensor Exposure by S.
    Meguerdichian et.a al. UCLA (Mobihoc 2001)
  • Convex Optimization Methods for Sensor Node
    Position Estimation by L. Doherty et. Al. (U.C.
    Berkeley) (infocom 2001)

3
Dynamic fine-grained localization in Ad-Hoc
networks of sensors
  • No GPS
  • Given some nodes with known position, estimate
    positions of all other unknown nodes
  • Two phases ranging and estimation

4
Phase I Ranging
  • Ranging estimate distance from the initiator to
    receiver
  • Received Signal Strength Indicator (RSSI)
  • Approximately
  • Radio signal is unreliable
  • RF Ultrasound
  • Time diff btw arrival of two signal ? distance
    (linear)
  • Ultrasound range 3 m
  • Accuracy 2 cm

5
Phase II Estimation
  • Estimation
  • Require some nodes with known position beacon
    node
  • Estimate the location of itself from the
    relationship of distance to beacon nodes
  • Automic multilateration
  • Require at least 3 beacon nodes around itself
  • 3 beacons ML estimate
  • MMSE
  • More than 3 beacons solve ultrasound speed s

6
Phase II Estimation (Cont.)
  • iterative multilateration
  • Start with the unknown node with max number of
    beacons ? atomic multilateration
  • After estimate it location, the unknown node
    becomes a beacon
  • Drawback error accumulation

7
Phase II Estimation (Cont.)
  • Collaborative multilateration
  • Some unknown nodes may not have 3 neighboring
    beacons
  • 5 edges, 5 equations

8
Localized Algorithms Location Discovery and
Sensor Exposure
  • Localized (distributed) algorithm
  • Location Estimation
  • ML Estimation using RSSI info.
  • Whats unique?
  • Determine in which order nodes should accept
    their estimation of location

9
Localized location algorithm I Initialization
  • (1) Initialization
  • Exchange msg including the transmission power
  • Use RSSI to estimate the dist. To the nbr
  • 3 cases
  • Beacon nodes with GPS
  • Nodes with ? 3 Nbr ? orphan flag false
  • Otherwise ? orphan flag true

10
II Information Exchange
  • Broadcast(flags, location(if any))
  • If lt 3 nbrs with location or lt 3 nbrs not
    orphan, then this node can not use trilateration
    to determine its location (skip step 3)

11
III. Trilateration
  • N neighbors with locations
  • Do min((N,3), max attemps) trilateration to
    determine the location
  • Find the center
  • Find the variance
  • Calculate the objective function
  • Variance
  • of nbrs that have already estimated their
    locations

12
IV Objective function comparison
  • Broadcast (value of objective function)
  • If got position or orphan ? OF MAX_INT
  • If lt 3 nbrs with location ? OF MAX_INT-1
  • If your OF value lt the OF values of all nbrs
  • Its your turns to accept the estimated location
  • The algorith is terminated if either you are
    orphan or the location is determined

13
Convex Optimization Methods for Sensor Node
Position Estimation
  • Given positions of solid nodes
  • Find a possible position for each open node
  • Subject to proximity constraints imposed by
    known connections
  • ?Centralized Approach

14
LP v.s. SDP
  • Linear programming
  • Semidefinite program

15
Convex Constraints
  • Radial constraint RF communication
  • Highly anisotropic
  • A circle bounds the maximal range
  • Equivalent linear matrix inequality for maximal
    range R
  • Varying distance a,b R ? rab

16
Problems of Convex Constraints
  • is not a convex constraint
  • No pushing away mechanism

17
Other Constraints
  • Angular constraint optical comminucation
  • Triangular a bound angle distance limitation
  • 3 scalar
  • Quadrant I LMI 2 scalar
  • Trapezoid 4 scalar

18
Bounding the Feasible Set
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