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

Outline 1. Introduction 2. Goal 3. Localization in wireless sensor networks  Overview  Cramer-Rao-Lower-Bound  Complexity and energy consumption 4. Characterizing Potential Benefits 5. Conclusions / Outlook 6. Literature Using CRLB to Reduce Complexity of Localization in WSNs 2

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 Using CRLB to Reduce Complexity of Localization in WSNs 3 Location of sensed information  important parameter in WSNs

Introduction – Localization Example 4 Using CRLB to Reduce Complexity of Localization in WSNs Parameters:  m … Number of beacons  n … Number of unknowns  N=m+n … Total number of nodes Beacon Unknown Error ellipse

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 5

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 Using CRLB to Reduce Complexity of Localization in WSNs Beacon Unknown

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 Using CRLB to Reduce Complexity of Localization in WSNs 7 …Path loss coefficient … standard deviation of RSS measurements …true parameter …estimated parameter Distance Geometry

Cramer-Rao-Lower-Bound Using CRLB to Reduce Complexity of Localization in WSNs 8 CRLB Error model of RSS measurements Number of beacons Geometry Lower bound on variance of position error

Cramer-Rao-Lower-Bound Example  1 dimension  True position at x=0  Disturbed position estimates  Probability density of position estimates  Standard deviation or root mean square error more intuitive than variance Using CRLB to Reduce Complexity of Localization in WSNs 9

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

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 11

Energy Consumption and Localization Communication  Two-way communication beacon unknown  Main contribution to total energy consumption Calculation  Simplest case: Energy spend ~ number of beacons Using CRLB to Reduce Complexity of Localization in WSNs 12 Energy  Number of beacons 

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 13

Related Work Impact of geometry not considered No local rule which prevents insignificant beacons from broadcasting their position Using CRLB to Reduce Complexity of Localization in WSNs 14 Beacon Placement Weighting range measurements Simulate localization error Variance/Distance [LZZ06, CPI06, BRT06] Variance/Distance [LZZ06, CPI06, BRT06] Detect outliers [OLT04, PCB00] Detect outliers [OLT04, PCB00] Choose nearest k beacons [CTL05] Choose nearest k beacons [CTL05]

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 15

Characterizing Potential Benefits Simulation setup:  Random deployment of m beacons and 1 unknown Using CRLB to Reduce Complexity of Localization in WSNs 16  For every deployment calculate: – – k=m: consider all beacons – k<m: consider all combinations of subsets of beacons  determine ratio

Characterizing Potential Benefits Using CRLB to Reduce Complexity of Localization in WSNs 17 Potential of approach  m=13 beacons  Event: “CRLB ok “  (equals 5% increase) Potentially highest savings in terms of energy and communication effort

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 18

Literature [BHE01]Nirupama Bulusu, John Heidemann, and Deborah Estrin. Adaptive beacon placement. In ICDCS '01: Proceedings of the The 21 st International Conference on Distributed Computing Systems, pages 489–503, Washington, DC, USA, 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 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 [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, [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 250–261, New York, NY, USA, ACM Press. [OLT04]E. Olson, J. J. Leonard, and S. Teller. Robust range-only beacon localization. In Proceedings of Autonomous Underwater Vehicles, [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), [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 [SHS01]Andreas Savvides, Chih-Chieh Han, and Mani B. Strivastava. Dynamic fine-grained localization in ad-hoc networks of sensors. Pages 166–179, Using CRLB to Reduce Complexity of Localization in WSNs 19

Questions? Thank you for your Attention!

Introduction – Localization Example Using CRLB to Reduce Complexity of Localization in WSNs 21 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