Simultaneous Localization and Time

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Simultaneous Localization and Time Synchronization in Wireless Sensor Networks via Semidefinite Programming Victoria Ying Zhang, and Albert Kai-sun Wong Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology Clear Water Bay, Hong Kong victoria@ust.hk, eealbert@ust.hk Abstract — For Wireless Sensor Networks (WSNs), utilizing the same set of measurement data for simultaneous localization and time synchronization is potentially useful for achieving higher estimation accuracy, lower communication overhead and power consumption. However, localization and time synchronization are traditionally treated as two separate problems. In this paper, we propose to use Semidefinite Programming (SDP) to jointly solve the two problems at the same time. Two scenarios, Sensor Nodes (SNs) with sufficient and insufficient number of neighboring beacons, are considered. The Cramer-Rao Lower Bound (CRLB) is then derived. Simulation results are presented to contrast the performance of the proposed Simultaneous Localization and Time Synchronization-SDP (SLTS-SDP) and Generalized SLTS-SDP (GSLTS-SDP) algorithms with the conventional SDP method and the corresponding CRLBs. Keywords —cramer-rao lower bound (CRLB); localization; semidefinite programming (SDP); time synchronization; wireless sensor network (WSN) I. INTRODUCTION Wireless Sensor Networks (WSNs) can be applied for cooperative signal detection, monitoring, tracking, and are especially useful for applications in remote and hazardous environments. Localization and time synchronization are usually required among the Sensor Nodes (SNs), and are two of the major issues in WSNs. By itself, time synchronization aims to provide a common timescale for local clocks of SNs in the system based on a reference SN (or so called beacon) or in the Coordinated Universal Time (UTC). It is important for transmission scheduling, data fusion, time-based ranging, power saving, etc. Two well-known solutions for time synchronization are the Network Time Protocol (NTP) [1] and the Global Positioning System (GPS); however, these are not suitable for WSNs because of cost, size, complexity and energy issues. Many time synchronization algorithms in WSNs have been developed, such as Reference-Broadcast Synchronization (RBS) [2], Delay Measurement Time Synchronization (DMTS) [3], etc. These approaches address only the synchronization problem, ignoring the need of localizing the SNs. Localization is to find the position of the SNs, and has also received considerable attention over the past decade. Existing positioning algorithms are based on Time of Arrival (TOA) [4], Time Difference of Arrival (TDOA) [5], [6], Angle of Arrival (AOA) [7], Received Signal Strength (RSS) [8], and in various combinations [9]. Time-based schemes (i.e., TOA and TDOA) are based on the assumption that needed synchronization has already been achieved.
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