Qasim M. Chaudhari

Clock Synchronization of Wireless Sensor Networks

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.

Novel Clock Phase Offset and Skew Estimation Using Two-Way Timing Message Exchanges for Wireless Sensor Networks

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

On the Joint Synchronization of Clock Offset and Skew in RBS-Protocol

Motivated by the necessity of having a good clock synchronization amongst the nodes of wireless ad-hoc sensor networks, the joint maximum likelihood (JML) estimator for clock phase offset and skew under exponential noise model for reference broadcast synchronization (RBS) protocol is formulated and found via a direct algorithm. The Gibbs sampler is also proposed for joint clock phase offset and skew estimation and shown to provide superior performance relative to JML- estimator. Lower and upper bounds for the mean-square errors (MSE) of JML-estimator and Gibbs Sampler are introduced in terms of the MSE of the uniform minimum variance unbiased (UMVU) estimator and the conventional best linear unbiased estimator (BLUE), respectively.

Energy-Efficient Estimation of Clock Offset for Inactive Nodes in Wireless Sensor Networks

For a meaningful processing of the information sensed by a wireless sensor network (WSN), the clocks of the individual nodes need to be matched through some well-defined procedures. Extending the idea of having silent nodes in a WSN overhear the two-way timing message communication between two active (master and slave) nodes, this paper derives the maximum-likelihood estimator (MLE) for the clock offsets of the listening nodes located within the communication range of the active nodes by assuming an exponential link delay modeling, hence synchronizing with the reference node at a very low cost. A vital advantage for adopting such an approach is that the performance of sender-receiver protocols can be compared with receiver-receiver protocols on equal footings, because their main critical aspect was associated with the high-communication overhead induced by the point-to-point nature of communication links relative to broadcast communications. The MLE is also shown to be the minimum variance unbiased estimator (MVUE) of the clock offset when the mean of exponential link delays is known. Since it is attractive to know in advance the extent to which an estimator can perform through its lower bound, the Chapman-Robbins bound and the Barankin bound for the clock offset estimator are also derived. It is shown that for an exponential link delay model, the mean square error of the clock offset estimator is inversely proportional to the square of the number of observations, and hence its performance is on a similar scale, albeit slightly lesser, as compared to the usual sender-receiver clock offset estimator. In addition, a novel method referred to as the Gaussian mixture Kalman particle filter (GMKPF) is proposed herein to estimate the clock offsets of the listening nodes in a WSN. GMKPF represents a better and flexible alternative to the MLE for the clock offset estimation problem due to its improved performance and applicability in arbitrary and generalized non-Gaussian random delay models.

On Minimum Variance Unbiased Estimation of Clock Offset in a Two-Way Message Exchange Mechanism

For many applications, distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time. Most of the widely used clock synchronization algorithms in such systems employ the sender-receiver protocol based on a two-way timing message exchange paradigm. Maximum likelihood estimator (MLE) of the clock offset based on the timing message exchanges between two clocks was derived in D. R. Jeske, On maximum likelihood estimation of clock offset[IEEE Trans. Commun., vol. 53, pp. 53-54, Jan. 2005], when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean. Herein, the best linear unbiased estimate using order statistics (BLUE-OS) of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays, respectively. The Rao-Blackwell-Lehmann-Scheffe¿ theorem is then exploited to obtain the minimum variance unbiased estimate (MVUE) for the clock offset which it is shown to coincide with the BLUE-OS. In addition, it is found that the MVUE of the clock offset in the presence of symmetric network delays also coincides with the MLE. Finally, in the presence of asymmetric network delays, although the MLE is biased, it is shown to achieve lesser mean-square error (MSE) than the MVUE in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified.

Some improved and generalized estimation schemes for clock synchronization of listening nodes in wireless sensor networks

A sender-receiver paradigm, in which a master and slave node exchange timing packets to estimate the clock offsets of the slave node and other nodes located in the common broadcast region of master and slave nodes, is adopted herein for synchronizing the clocks of individual nodes in a wireless sensor network (WSN). The maximum likelihood estimate of the clock offset of the listening node hearing the broadcasts from both the master and slave nodes was derived, assuming symmetric exponential link delays. This paper advances those results in two directions. First, some improved estimators, each being optimal in its own class, are derived for the clock offset of the listening node and mean link delays. Second, the results are generalized by addressing the more realistic problem of clock offset estimation under asymmetric exponential delays. The results presented in this paper are important for time synchronization of WSNs, where these techniques can be utilized to achieve accurate clock estimates with reduced power consumption.

A Simple and Robust Clock Synchronization Scheme

Previous studies on clock synchronization problem have resulted in diverse techniques ranging from computationally expensive to simple statistical methods. The common conclusion from this investigation has been the classic complexity-performance tradeoff. This research presents a synchronization scheme that is computationally simpler and robust to the underlying network delay density function.

CTH15-2: Analysis of Clock Offset and Skew Estimation in Timing-sync Protocol for Sensor Networks

Recently, a few protocols for synchronizing the nodes of wireless sensor networks (WSNs) to a common time frame have been proposed with the goal of maximizing the accuracy and minimizing the power utilization. Thus far, the performance of the existing protocols for time synchronization is assessed only through computer simulations and experiments without using any rigorous analytical metrics. The goal of this paper is to fill up this gap by deriving the Cramer-Rao lower bound (CRLB) for the clock offset in one of the most popular synchronization algorithms, namely timing-sync protocol for sensor networks (TPSN), assuming commonly used exponential and Gaussian delay models, respectively. Furthermore, this paper proposes novel and practical clock skew estimators requiring no prior information of the fixed portion of delays, which makes the TPSN algorithm very suitable to synchronization in light of its power efficiency constraint.

Clock estimation for long-term synchronization in wireless sensor networks with exponential delays

Although the existing time synchronization protocols in wireless sensor networks (WSNs) are efficient for short periods, many applications require long-term synchronization among the nodes, for example, coordinated sleep and wakeup modes, and synchronized sampling. In such applications, experiments have shown that even clock skew correction cannot maintain long-term clock synchronization and a quadratic model of clock variations can better capture the dynamics of the actual clock model involved, hence increasing the resynchronization period and conserving significant energy. This paper derives the maximum likelihood (ML) estimator for all the clock parameters in a two-way timing exchange model with exponential delays. The same estimation procedure can be applied to one-way timing exchange models with little modification.

Improved Estimation of Clock Offset in Sensor Networks

Clock synchronization is an important issue for the design of a network composed of small sensor nodes. Based on the two-way timing message exchange mechanism and assuming an exponential network delay distribution, many analytical results have been presented in the literature by applying the techniques from statistical signal processing. This paper derives the minimum variance unbiased estimator for the clock offset for both symmetric and asymmetric exponential delay cases. For the asymmetric delays, it is shown to be a function of both the minimum and the mean link delays. This result is a very significant contribution since only the minimum link delay observations have been used to estimate the clock offset in the past. For the symmetric case, it is shown to coincide with the maximum likelihood estimator. In addition, the result is also applicable to clock synchronization problem in general computer networks.