Optimal Anchor Placement for Localization in Large-Scale Wireless Sensor Networks

In wireless sensor networks (WSNs), location information of sensor nodes (or simply sensors) plays a vital role in both of the management of WNSs and many other applications. Due to the constraints on costs and energy, only a small portion of nodes in a WSN is deployed as anchor nodes or simply anchors with their locations a priori known or determined through certain hardware (e.g. GPS) to localize normal sensor nodes. However, the placement of such anchors has significant influence on the localization performance of sensor nodes. This paper tackles the problem of optimal anchor placement for localization in large-scale WSNs. But, differently from existing studies assuming independent and identically distributed measurement noises, this paper takes into account more practical distance dependent measurement noises. Then, provided that sensors' locations satisfy a homogeneous Poisson Point process, a theoretical analysis based on the average Cramer-Rao Lower Bound (CRLB) proves that it is optimal to place anchors in a regular fashion. In particular, given that each sensor can measure distances to nearby 3 anchors, the optimal anchor placement pattern is the equilateral triangle pattern, which is consistent with the optimal node deployment for 3-coverage and 6-connectivity. This study not only provides the knowledge for guiding the deployment of large-scale WSNs in practice, but also paves the way for building the theory of sensor localization in WSNs.

[1]  Mounir Ghogho,et al.  Effects of anchor placement on mean-CRB for localization , 2011, 2011 The 10th IFIP Annual Mediterranean Ad Hoc Networking Workshop.

[2]  Baoqi Huang,et al.  Analyzing localization errors in one-dimensional sensor networks , 2012, Signal Process..

[3]  Tao Zhou,et al.  Quantitatively Investigating Multihop Localization Errors in Regular 2-D Sensor Networks , 2018, ICA3PP.

[4]  R. Kershner.  The Number of Circles Covering a Set , 1939 .

[5]  Soura Dasgupta,et al.  Distance estimation from received signal strength under log-normal shadowing: Bias and variance , 2008 .

[6]  Hao Jiang,et al.  A Robust Indoor Positioning System Based on the Procrustes Analysis and Weighted Extreme Learning Machine , 2016, IEEE Transactions on Wireless Communications.

[7]  Tao Zhang,et al.  Recognizing Boundaries in Wireless Sensor Networks Based on Local Connectivity Information , 2014, Int. J. Distributed Sens. Networks.

[8]  Scott Alexander,et al.  On quantification of anchor placement , 2012, 2012 Proceedings IEEE INFOCOM.

[9]  Baoqi Huang,et al.  Shape matching algorithm based on shape contexts , 2015, IET Comput. Vis..

[10]  B. R. Badrinath,et al.  Error characteristics of ad hoc positioning systems (aps) , 2004, MobiHoc '04.

[11]  Brian D. O. Anderson,et al.  Sequential Localization of Sensor Networks , 2009, SIAM J. Control. Optim..

[12]  Baoqi Huang,et al.  Performance limits in sensor localization , 2011, Autom..

[13]  Alfred O. Hero,et al.  Relative location estimation in wireless sensor networks , 2003, IEEE Trans. Signal Process..

[14]  Athanasios V. Vasilakos,et al.  A Framework for the Optimal $k$ -Coverage Deployment Patterns of Wireless Sensors , 2015, IEEE Sensors Journal.

[15]  João Pedro Hespanha,et al.  Optimal sensor placement for time difference of arrival localization , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[16]  Baoqi Huang,et al.  An Online Radio Map Update Scheme for WiFi Fingerprint-Based Localization , 2019, IEEE Internet of Things Journal.

[17]  Baoqi Huang,et al.  On the optimal anchor placement in single-hop sensor localization , 2018, Wirel. Networks.

[18]  Stefano Panzieri,et al.  Sensor Networks Localization: Extending Trilateration via Shadow Edges , 2015, IEEE Transactions on Automatic Control.

[19]  Weijia Jia,et al.  Optimal Patterns for Four-Connectivity and Full Coverage in Wireless Sensor Networks , 2010, IEEE Transactions on Mobile Computing.

[20]  Jiannong Cao,et al.  Iterative Localization of Wireless Sensor Networks: An Accurate and Robust Approach , 2014, IEEE/ACM Transactions on Networking.

[21]  Baoqi Huang,et al.  TDOA-Based Source Localization With Distance-Dependent Noises , 2015, IEEE Transactions on Wireless Communications.

[22]  Hing-Cheung So,et al.  Linear Least Squares Approach for Accurate Received Signal Strength Based Source Localization , 2011, IEEE Trans. Signal Process..

[23]  Baoqi Huang,et al.  Dimension reduction in radio maps based on the supervised kernel principal component analysis , 2018, Soft Computing.

[24]  Kazuya Sakai,et al.  The optimal k-covering tag deployment for RFID-based localization , 2011, J. Netw. Comput. Appl..

[25]  Baoqi Huang,et al.  An Energy-Efficient DV-Hop Localization Algorithm , 2018, ICA3PP.

[26]  Zhiguo Ding,et al.  Joint synchronization and localization using TOAs: A linearization based WLS solution , 2010, IEEE Journal on Selected Areas in Communications.

[27]  Baoqi Huang,et al.  On the Performance Analysis of Wifi Based Localization , 2018, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[28]  Zhi Ding,et al.  Source Localization in Wireless Sensor Networks From Signal Time-of-Arrival Measurements , 2011, IEEE Transactions on Signal Processing.

[29]  B. R. Badrinath,et al.  Ad hoc positioning system (APS) , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[30]  Mani B. Srivastava,et al.  On the Error Characteristics of Multihop Node Localization in Ad-Hoc Sensor Networks , 2003, IPSN.

[31]  Jun Li,et al.  Deployment patterns for k-coverage and l-connectivity in Wireless Sensor Networks , 2010 .

[32]  Baoqi Huang,et al.  Understanding Error Propagation in Multihop Sensor Network Localization , 2013, IEEE Transactions on Industrial Electronics.

[33]  Anant Sahai,et al.  Estimation bounds for localization , 2004, 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, 2004. IEEE SECON 2004..

[34]  Baoqi Huang,et al.  Analysis of TOA localization with heteroscedastic noises , 2014, Proceedings of the 33rd Chinese Control Conference.

[35]  Brian D. O. Anderson,et al.  Optimality analysis of sensor-target localization geometries , 2010, Autom..

[36]  Baoqi Huang,et al.  Selecting Critical WiFi APs for Indoor Localization Based on a Theoretical Error Analysis , 2019, IEEE Access.

[37]  Neil M. White,et al.  A Two-Way Time of Flight Ranging Scheme for Wireless Sensor Networks , 2011, EWSN.

[38]  Lihua Xie,et al.  Decentralized TDOA Sensor Pairing in Multihop Wireless Sensor Networks , 2013, IEEE Signal Processing Letters.

[39]  Weijia Jia,et al.  Optimal Deployment Patterns for Full Coverage and $k$-Connectivity $(k \leq 6)$ Wireless Sensor Networks , 2010, IEEE/ACM Transactions on Networking.