Novel Clock Phase Offset and Skew Estimation Using Two-Way Timing Message Exchanges for Wireless Sensor Networks
TL;DR: This paper proposes novel clock skew estimators assuming different delay environments to achieve energy-efficient network-wide synchronization for WSNs and derives the Cramer-Rao lower bounds and the maximum likelihood estimators under different delay models and assumptions.
Abstract: Recently, a few efficient timing synchronization protocols for wireless sensor networks (WSNs) have been proposed with the goal of maximizing the accuracy and minimizing the power utilization. This paper proposes novel clock skew estimators assuming different delay environments to achieve energy-efficient network-wide synchronization for WSNs. The proposed clock skew correction mechanism significantly increases the re-synchronization period, which is a critical factor in reducing the overall power consumption. The proposed synchronization scheme can be applied to the conventional protocols without additional overheads. Moreover, this paper derives the Cramer-Rao lower bounds and the maximum likelihood estimators under different delay models and assumptions. These analytical metrics serves as good benchmarks for the thus far reported experimental results
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TL;DR: This article illustrates that many of the proposed clock synchronization protocols can be interpreted and their performance assessed using common statistical signal processing methods, and shows that advanced signal processing techniques enable the derivation of optimal clock synchronization algorithms under challenging scenarios.
Abstract: Clock synchronization is a critical component in the operation of wireless sensor networks (WSNs), as it provides a common time frame to different nodes. It supports functions such as fusing voice and video data from different sensor nodes, time-based channel sharing, and coordinated sleep wake-up node scheduling mechanisms. Early studies on clock synchronization for WSNs mainly focused on protocol design. However, the clock synchronization problem is inherently related to parameter estimation, and, recently, studies on clock synchronization began to emerge by adopting a statistical signal processing framework. In this article, a survey on the latest advances in the field of clock synchronization of WSNs is provided by following a signal processing viewpoint. This article illustrates that many of the proposed clock synchronization protocols can be interpreted and their performance assessed using common statistical signal processing methods. It is also shown that advanced signal processing techniques enable the derivation of optimal clock synchronization algorithms under challenging scenarios.
571 citations
Cites background or methods from "Novel Clock Phase Offset and Skew E..."
...Besides optimal MLEs, suboptimal but lower complexity algorithms were also reported in [21] and [22]....
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...Depending on whether the fixed delay s is known or unknown, themaximum likelihood estimator (MLE) and the corresponding Cramer-Rao bound (CRB) for joint skew and offset estimation under Gaussian variable delays were derived in [21] and [22], respectively....
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...Under the assumption that Xk and Yk are independent and identically distributed zero mean Gaussian RVs, it can be shown that the MLE for h is given by [21]...
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...The above procedure can be mathematically modeled as [21]...
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TL;DR: An energy-efficient clock synchronization scheme for Wireless Sensor Networks (WSNs) based on a novel time synchronization approach which significantly reduces the overall network-wide energy consumption without incurring any loss of synchronization accuracy compared to other well-known schemes.
Abstract: This letter proposes an energy-efficient clock synchronization scheme for Wireless Sensor Networks (WSNs) based on a novel time synchronization approach. Within the proposed synchronization approach, a subset of sensor nodes are synchronized by overhearing the timing message exchanges of a pair of sensor nodes. Therefore, a group of sensor nodes can be synchronized without sending any extra messages. This paper brings two main contributions: 1. Development of a novel synchronization approach which can be partially or fully applied for implementation of new synchronization protocols and for improving the performance of existing time synchronization protocols. 2. Design of a time synchronization scheme which significantly reduces the overall network-wide energy consumption without incurring any loss of synchronization accuracy compared to other well-known schemes.
236 citations
Cites background or methods from "Novel Clock Phase Offset and Skew E..."
...In [13], the joint maximum likelihood estimator of clock offset and skew for normal delays was also derived....
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...In [13], the maximum likelihood estimator (MLE) of clock offset was found to be given by...
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...Although the effects of clock skew have not been considered herein, the clock skew estimators developed in [13] can be directly applied to the proposed PBS protocol with no modifications....
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TL;DR: This paper reviews the existing clock synchronization protocols for WSNs and the methods of estimating clock offset and clock skew in the most representative clock synchronization Protocol for W SNs.
Abstract: The development of tiny, low-cost, low-power and multifunctional sensor nodes equipped with sensing, data processing, and communicating components, have been made possible by the recent advances in micro-electro-mechanical systems (MEMS) technology. Wireless sensor networks (WSNs) assume a collection of such tiny sensing devices connected wirelessly and which are used to observe and monitor a variety of phenomena in the real physical world. Many applications based on these WSNs assume local clocks at each sensor node that need to be synchronized to a common notion of time. This paper reviews the existing clock synchronization protocols for WSNs and the methods of estimating clock offset and clock skew in the most representative clock synchronization protocols for WSNs.
212 citations
TL;DR: Results show that the proposed joint estimators exhibit performances close to their respective CRLBs and outperform the separate time synchronization and localization approach.
Abstract: Time synchronization and localization are two important issues in wireless sensor networks. Although these two problems share many aspects in common, they are traditionally treated separately. In this paper, we present a unified framework to jointly solve time synchronization and localization problems at the same time. Furthermore, since the accuracy of synchronization and localization is very sensitive to the accuracy of anchor timings and locations, the joint time synchronization and localization problem with inaccurate anchors is also considered in this paper. For the case with accurate anchors, the joint maximum likelihood estimator and a more computationally efficient least squares (LS) estimator are proposed. When the anchor timings and locations are inaccurate, a generalized total least squares (GTLS) scheme is proposed. Crame?r-Rao lower bounds (CRLBs) and the analytical mean square error (MSE) expressions of the LS based estimators are derived for both accurate and inaccurate anchor cases. Results show that the proposed joint estimators exhibit performances close to their respective CRLBs and outperform the separate time synchronization and localization approach. Furthermore, the derived analytical MSE expressions predict the performances of the proposed joint estimators very well.
192 citations
Cites background from "Novel Clock Phase Offset and Skew E..."
...In WSNs, synchronization supports functions such as time-based channel sharing, power scheduling, and time-based localization in WSNs....
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TL;DR: Three clock-synchronization algorithms for wireless sensor networks (WSNs) under unknown delay are derived, including the maximum-likelihood estimator (MLE), a generalization of the estimator of Noh, and a novel low-complexity estimator.
Abstract: In this paper, three clock-synchronization algorithms for wireless sensor networks (WSNs) under unknown delay are derived. They include the maximum-likelihood estimator (MLE), a generalization of the estimator of Noh , and a novel low-complexity estimator. Their corresponding performance bounds are derived and compared, and complexities are also analyzed. It is found that the MLE achieves the best performance with the price of high complexity. For the generalized version of the estimator of Noh , although it has low complexity, its performance is degraded with respect to the MLE. On the other hand, the newly proposed estimator achieves the same performance as the MLE, and the complexity is at the same level as that of the generalized version of the estimator of Noh et al.
137 citations
Cites background or methods from "Novel Clock Phase Offset and Skew E..."
...[15] made such assumption and derived the MLE for the joint estimation of clock offset β0 and clock skew β1....
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...Although another maximum-likelihood-like estimator (MLLE) that does not require knowledge of the fixed delay was also derived in [15], the performance of this estimator is not satisfactory....
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...[15] proposed subtracting Tr,1 from Tr,N to obtain Wr = Tr,N − Tr,1(r = {1, 2, 3, 4}), such that Wr does not depend on β0 and d....
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...However, the CRLB derived in [15] was based on all the time stamps {T1,i, T2,i, T3,i, T4,i}i=1, and CRLB may change according to different realizations of {T2,i, T4,i}i=1....
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...[15], and the other is a newly proposed estimator....
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References
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TL;DR: The Fundamentals of Statistical Signal Processing: Estimation Theory as mentioned in this paper is a seminal work in the field of statistical signal processing, and it has been used extensively in many applications.
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TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory
12,407 citations