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@uni-rostock.de

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Cramer-Rao-Lower-Bound – An Example • 2 beacons, 1 unknown Beacon Unknown Using CRLB to Reduce Complexity of Localization in WSNs

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. Questions? Thank you for your Attention!

21. 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