Using Cramer-Rao-Lower-Bound to Reduce Complexity of Localization in Wireless Sensor Networks

1
Using Cramer-Rao-Lower-Bound to Reduce Complexity
of Localization in Wireless Sensor Networks

• Dominik Lieckfeldt, Dirk Timmermann
• Department of Computer Science and Electrical
  Engineering
• Institute of Applied Microelectronics and
  Computer Engineering
• University of Rostock
• dominik.lieckfeldt_at_uni-rostock.de

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Outline

• Introduction
• Goal
• Localization in wireless sensor networks
• Overview
• Cramer-Rao-Lower-Bound
• Complexity and energy consumption
• Characterizing Potential Benefits
• Conclusions / Outlook
• Literature

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Introduction

• Wireless Sensor Network (WSN)
• Random deployment of large number of tiny devices
• Communication via radio frequencies
• Sense parameters of environment
• Applications
• Forest fire
• Volcanic activity
• Precision farming
• Flood protection

• Location of sensed information ? important
  parameter in WSNs

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Introduction Localization Example

• Parameters
• m Number of beacons
• n Number of unknowns
• Nmn Total number of nodes

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Goal of this Work

• Investigate potential impact and applicability of
  adapting and scaling localization accuracy to
• Activity
• Importance
• Energy level
• Other parameters (context)
• Obey fundamental trade-off between
• accuracy lt-gt complexity
• Benefits
• Decreased communication
• Prolonged lifetime of WSN

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Localization in WSN

• Possible approaches
• Lateration (typically used)
• Angulation
• Proximity
• Lateration
• Use received signal strength (RSS) to estimate
  distances
• RSS 1/d²
• Idea
• Estimate distances to beacons
• Solve non-linear system of equations

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Localization in WSN

• Measurements of RSS are disturbed
• Interference
• Noise
• How accurate can estimates of
• position be?
• Cramer-Rao-Lower-Bound (CRLB) poses lower bound
  on variance of any unbiased estimator

Distance
Path loss coefficient standard deviation of
RSS measurements true parameter estimated
parameter
Geometry
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Cramer-Rao-Lower-Bound
Number of beacons
Error model of RSS measurements
Geometry
CRLB
Lower bound on variance of position error
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Cramer-Rao-Lower-Bound

• Example
• 1 dimension
• True position at x0
• Disturbed position estimates
• Probability density of position estimates
• Standard deviation or root mean square error more
  intuitive than variance

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Cramer-Rao-Lower-Bound An Example

• 2 beacons, 1 unknown

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Complexity of Localization

• Complexity depends on
• Dimensionality (2D/3D)
• Number of Beacons
• Number of nodes with unknown position

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Energy Consumption and Localization

• Communication
• Two-way communication beacon lt-gt unknown
• Main contribution to total energy consumption
• Calculation
• Simplest case Energy spend number of beacons

Energy ?
Number of beacons ?
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Reducing Complexity of Localization in WSNs

• How to reduce Complexity?
• Constrain number of beacons used
• Idea
• Select those beacons first that contribute most
  to localization accuracy!

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Related Work
Beacon Placement
Weighting range measurements
Simulate localization error
Variance/Distance LZZ06, CPI06, BRT06
Detect outliers OLT04, PCB00
Choose nearest k beacons CTL05

• Impact of geometry not considered
• No local rule which prevents insignificant
  beacons from broadcasting their position

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Characterizing Potential Benefits

• Simulations using Matlab
• Aim
• Proof of Concept
• Determine how likely it is that constraining the
  number of beacons is possible without increasing
  CRLB significantly

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Characterizing Potential Benefits

• Simulation setup
• Random deployment of m beacons and 1 unknown

• For every deployment calculate
• km consider all beacons
• kltm consider all combinations
• of subsets of beacons
• determine ratio

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Characterizing Potential Benefits

• Potential of approach
• m13 beacons
• Event CRLBok ? (equals 5
  increase)

Potentially highest savings in terms of energy
and communication effort
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Conclusion / Outlook

• Preliminary study based on CRLB
• Considers strong impact of geometry on
  localization accuracy
• Selection of subsets of beacons for localization
  is feasible in terms of
• Prolonging lifetime of sensor network
• Decreasing communication
• Outlook
• Determine/investigate local rules for selecting
  subset of beacons

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Literature

• BHE01 Nirupama Bulusu, John Heidemann, and
  Deborah Estrin. Adaptive beacon placement. In
  ICDCS '01 Proceedings of the The 21st
  International Conference on Distributed Computing
  Systems, pages 489503, Washington, DC, USA,
  2001. IEEE Computer Society.
• BRT06 Jan Blumenthal, Frank Reichenbach, and
  Dirk Timmermann. Minimal transmission power vs.
  signal strength as distance estimation for
  localization in wireless sensor networks. In 3rd
  IEEE International Workshop on Wireless Ad-hoc
  and Sensor Networks, pages 761766, Juni 2006.
  New York, USA.
• CPI06 Jose A. Costa, Neal Patwari, and Alfred
  O. Hero III. Distributed weighted-multidimensional
  scaling for node localization in sensor
  networks. ACM Transactions on Sensor Networks,
  2(1)3964, February 2006.
• CTL05 King-Yip Cheng, Vincent Tam, and
  King-Shan Lui. Improving aps with anchor
  selection in anisotropic sensor networks. Joint
  International Conference on Autonomic and
  Autonomous Systems and International Conference
  on Networking and Services, page 49, 2005.
• LZZ06 Juan Liu, Ying Zhang, and Feng Zhao.
  Robust distributed node localization with error
  management. In MobiHoc '06 Proceedings of the
  seventh ACM international symposium on Mobile ad
  hoc networking and computing, pages 250261, New
  York, NY, USA, 2006. ACM Press.
• OLT04 E. Olson, J. J. Leonard, and S. Teller.
  Robust range-only beacon localization. In
  Proceedings of Autonomous Underwater Vehicles,
  2004.
• PCB00 Nissanka B. Priyantha, Anit Chakraborty,
  and Hari Balakrishnan. The cricket
  location-support system. In 6th ACM
  International Conference on Mobile Computing and
  Networking (ACM MOBICOM), 2000.
• PIP03 N. Patwari, A. III, M. Perkins,
  N. Correal, and R. O'Dea. Relative location
  estimation in wireless sensor networks. In IEEE
  TRANSACTIONS ON SIGNAL PROCESSING, volume 51,
  pages 21372148, August 2003.
• SHS01 Andreas Savvides, Chih-Chieh Han, and
  Mani B. Strivastava. Dynamic fine-grained
  localization in ad-hoc networks of sensors.
  Pages 166179, 2001.

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Questions?

• Thank you for your Attention!

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Introduction Localization Example

• Example Scenario
• N10000 nodes with 10 beacons
• Area (1000x1000)m
• Start-up phase
• Transmission range is chosen to provide
  connection to at least 3 beacons
• Minimum transmission power
• Initial localization of nodes in range of at
  least 3 beacons
• In refinement phase
• Every node has connections to 50 other nodes
• -gt need to select subset of beacons for
  localization