Using cramer rao lower bound to reduce complexity of localization in wireless sensor networks
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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

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Using cramer rao lower bound to reduce complexity of localization in wireless sensor networks

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

[email protected]


Outline
Outline

  • Introduction

  • Goal

  • Localization in wireless sensor networks

    • Overview

    • Cramer-Rao-Lower-Bound

    • Complexity and energy consumption

  • Characterizing Potential Benefits

  • Conclusions / Outlook

  • Literature

Using CRLB to Reduce Complexity of Localization in WSNs


Introduction
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

Using CRLB to Reduce Complexity of Localization in WSNs


Introduction localization example
Introduction – Localization Example

Parameters:

  • m … Number of beacons

  • n … Number of unknowns

  • N=m+n … Total number of nodes

Beacon

Unknown

Error ellipse

Using CRLB to Reduce Complexity of Localization in WSNs


Goal of this work
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 <-> complexity

  • Benefits:

    • Decreased communication

    • Prolonged lifetime of WSN

Using CRLB to Reduce Complexity of Localization in WSNs


Localization in wsn
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

2

3

Beacon

Unknown

1

4

Using CRLB to Reduce Complexity of Localization in WSNs


Localization in wsn1
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

Using CRLB to Reduce Complexity of Localization in WSNs


Cramer rao lower bound
Cramer-Rao-Lower-Bound

Number of beacons

Error model of RSS measurements

Geometry

CRLB

Lower bound on variance of position error

Using CRLB to Reduce Complexity of Localization in WSNs


Cramer rao lower bound1
Cramer-Rao-Lower-Bound

  • Example

    • 1 dimension

    • True positionat x=0

    • Disturbedpositionestimates

    • Probabilitydensityofpositionestimates

    • Standard deviationorrootmeansquareerrormore intuitive thanvariance

Using CRLB to Reduce Complexity of Localization in WSNs


Cramer rao lower bound an example
Cramer-Rao-Lower-Bound – An Example

  • 2 beacons, 1 unknown

Beacon

Unknown

Using CRLB to Reduce Complexity of Localization in WSNs


Complexity of localization
Complexity of Localization

  • Complexity depends on:

    • Dimensionality (2D/3D)

    • Number of Beacons

    • Number of nodes with unknown position

Using CRLB to Reduce Complexity of Localization in WSNs


Energy consumption and localization
Energy Consumption and Localization

  • Communication

    • Two-way communication beacon <-> unknown

    • Main contribution to total energy consumption

  • Calculation

    • Simplest case: Energy spend ~ number of beacons

Energy 

Number of beacons 

Using CRLB to Reduce Complexity of Localization in WSNs


Reducing complexity of localization in wsns
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!

Using CRLB to Reduce Complexity of Localization in WSNs


Related work
Related Work

Beacon Placement

Weighting range measurements

  • Impact of geometry not considered

  • No local rule which prevents insignificant beacons from broadcasting their position

Simulate localization error

Choose nearest k beacons

[CTL05]

Variance/Distance

[LZZ06, CPI06, BRT06]

Detect outliers

[OLT04, PCB00]

Using CRLB to Reduce Complexity of Localization in WSNs


Characterizing potential benefits
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

Using CRLB to Reduce Complexity of Localization in WSNs


Characterizing potential benefits1
Characterizing Potential Benefits

  • Simulation setup:

    • Random deployment of m beacons and 1 unknown

  • For every deployment calculate:

    • k=m: consider all beacons

    • k<m: consider all combinations

    • of subsets of beacons

    • determine ratio

Using CRLB to Reduce Complexity of Localization in WSNs


Characterizing potential benefits2
Characterizing Potential Benefits

  • Potential of approach

    • m=13 beacons

    • Event: “CRLBok“  (equals 5% increase)

Potentially highest savings

in terms of energy and

communication effort

Using CRLB to Reduce Complexity of Localization in WSNs


Conclusion outlook
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

Using CRLB to Reduce Complexity of Localization in WSNs


Literature
Literature

[BHE01] NirupamaBulusu, John Heidemann, and Deborah Estrin. Adaptive beacon placement. In ICDCS '01: Proceedings of the The 21st International Conference on Distributed Computing Systems, pages 489–503, 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 761–766, 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):39–64, 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. InMobiHoc '06: Proceedings of the seventh ACM international symposium on Mobile ad hoc networking and computing, pages 250–261, 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, AnitChakraborty, and HariBalakrishnan. The cricket location-support system. In 6th ACM International Conference on Mobile Computing and Networking (ACM MOBICOM), 2000.

[PIP+03] 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 2137–2148, August 2003.

[SHS01] Andreas Savvides, Chih-Chieh Han, and Mani B. Strivastava. Dynamic fine-grained localization in ad-hoc networks of sensors. Pages 166–179, 2001.

Using CRLB to Reduce Complexity of Localization in WSNs


Questions

Questions?

Thank you for your Attention!


Introduction localization example1
Introduction – Localization Example

  • Example Scenario:

    • N=10000 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

    • -> need to select subset of beacons for localization

Using CRLB to Reduce Complexity of Localization in WSNs


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