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. ©2009 IEEE.published_or_final_versionThe IEEE International Conference on Communications (ICC 2009), Dresden, Germany, 14-18 June 2009. In Proceedings of IEEE ICC, 2009, p. 1-

Signal processing techniques for synchronization of wireless sensor networks

Plenary PaperClock synchronization is a critical component in wireless sensor networks, 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 sleep wake-up scheduling, etc. Early studies on clock synchronization for wireless sensor networks mainly focus on protocol design. However, clock synchronization problem is inherently related to parameter estimation, and recently, studies of clock synchronization from the signal processing viewpoint started to emerge. In this article, a survey of latest advances on clock synchronization is provided by adopting a signal processing viewpoint. We demonstrate that many existing and intuitive clock synchronization protocols can be interpreted by common statistical signal processing methods. Furthermore, the use of advanced signal processing techniques for deriving optimal clock synchronization algorithms under challenging scenarios will be illustrated. © 2010 SPIE.published_or_final_versio

Adaptive Time Synchronization for Homogeneous WSNs

Wireless sensor networks (WSNs) are being used for observing real‐world phenomenon. It is important that sensor nodes (SNs) must be synchronized to a common time in order to precisely map the data collected by SNs. Clock synchronization is very challenging in WSNs as the sensor networks are resource constrained networks. It is essential that clock synchronization protocols designed for WSNs must be light weight i.e. SNs must be synchronized with fewer synchronization message exchanges. In this paper, we propose a clock synchronization protocol for WSNs where first of all cluster heads (CHs) are synchronized with the sink and then the cluster nodes (CNs) are synchronized with their respective CHs. CNs are synchronized with the help of time synchronization node (TSN) chosen by the respective CHs. Simulation results show that proposed protocol requires considerably fewer synchronization messages as compared with the reference broadcast synchronization (RBS) protocol and minimum variance unbiased estimation (MUVE) method. Clock skew correction mechanism applied in proposed protocol guarantees long term stability and hence decreases re‐ synchronization frequency thereby conserving more energ

Estimation of clock parameters and performance benchmarks for synchronization in wireless sensor networks

Recent years have seen a tremendous growth in the development of small sensing devices capable of data processing and wireless communication through their embed- ded processors and radios. Wireless Sensor Networks (WSNs) are ad hoc networks consisting of such devices gaining importance due to their emerging applications. For a meaningful processing of the information sensed by WSN nodes, the clocks of these individual nodes need to be matched through some well de¯ned procedures. This dissertation focuses on deriving e±cient estimators for the clock parameters of the network nodes for synchronization with the reference node and the estimators variance thresholds are obtained to lower bound the maximum achievable performance. For any general time synchronization protocol involving a two way message ex- change mechanism, the BLUE-OS and the MVUE of the clock o®set between them is derived assuming both symmetric and asymmetric exponential network delays. Next, with the inclusion of clock skew in the model, the joint MLE of clock o®set and skew under both the Gaussian and the exponential delay model and the corresponding al- gorithms for ¯nding these estimates are presented. Also, for applications where even clock skew correction cannot maintain long-term clock synchronization, a closed-form expression for the joint MLE for a quadratic model is obtained. Although the derived MLEs are not computationally very complex, two compu- tationally e±cient algorithms have been proposed to estimate the clock o®set and skew regardless of the distribution of the delays. Afterwards, extending the idea of having inactive nodes in a WSN overhear the two-way timing message communication between two active (master and slave) nodes, the MLE, the BLUE-OS, the MVUE and the MMSE estimators for the clock o®sets of the inactive nodes located within the communication range of the active nodes are derived, hence synchronizing with the reference node at a reduced cost. Finally, focusing on the the one-way timing exchange mechanism, the joint MLE for clock phase o®set and skew under exponential noise model and the Gibbs Sampler for a receiver-receiver protocol is formulated and found via a direct algorithm. Lower and upper bounds for the MSE of JMLE and Gibbs Sampler are introduced in terms of the MSEs of the MVUE and the conventional BLUE, respectively

Timing Synchronization and Node Localization in Wireless Sensor Networks: Efficient Estimation Approaches and Performance Bounds

Wireless sensor networks (WSNs) consist of a large number of sensor nodes, capable of on-board sensing and data processing, that are employed to observe some phenomenon of interest. With their desirable properties of flexible deployment, resistance to harsh environment and lower implementation cost, WSNs envisage a plethora of applications in diverse areas such as industrial process control, battle- field surveillance, health monitoring, and target localization and tracking. Much of the sensing and communication paradigm in WSNs involves ensuring power efficient transmission and finding scalable algorithms that can deliver the desired performance objectives while minimizing overall energy utilization. Since power is primarily consumed in radio transmissions delivering timing information, clock synchronization represents an indispensable requirement to boost network lifetime. This dissertation focuses on deriving efficient estimators and performance bounds for the clock parameters in a classical frequentist inference approach as well as in a Bayesian estimation framework. A unified approach to the maximum likelihood (ML) estimation of clock offset is presented for different network delay distributions. This constitutes an analytical alternative to prior works which rely on a graphical maximization of the likelihood function. In order to capture the imperfections in node oscillators, which may render a time-varying nature to the clock offset, a novel Bayesian approach to the clock offset estimation is proposed by using factor graphs. Message passing using the max-product algorithm yields an exact expression for the Bayesian inference problem. This extends the current literature to cases where the clock offset is not deterministic, but is in fact a random process. A natural extension of pairwise synchronization is to develop algorithms for the more challenging case of network-wide synchronization. Assuming exponentially distributed random delays, a network-wide clock synchronization algorithm is proposed using a factor graph representation of the network. Message passing using the max- product algorithm is adopted to derive the update rules for the proposed iterative procedure. A closed form solution is obtained for each node's belief about its clock offset at each iteration. Identifying the close connections between the problems of node localization and clock synchronization, we also address in this dissertation the problem of joint estimation of an unknown node's location and clock parameters by incorporating the effect of imperfections in node oscillators. In order to alleviate the computational complexity associated with the optimal maximum a-posteriori estimator, two iterative approaches are proposed as simpler alternatives. The first approach utilizes an Expectation-Maximization (EM) based algorithm which iteratively estimates the clock parameters and the location of the unknown node. The EM algorithm is further simplified by a non-linear processing of the data to obtain a closed form solution of the location estimation problem using the least squares (LS) approach. The performance of the estimation algorithms is benchmarked by deriving the Hybrid Cramer-Rao lower bound (HCRB) on the mean square error (MSE) of the estimators. We also derive theoretical lower bounds on the MSE of an estimator in a classical frequentist inference approach as well as in a Bayesian estimation framework when the likelihood function is an arbitrary member of the exponential family. The lower bounds not only serve to compare various estimators in our work, but can also be useful in their own right in parameter estimation theory

Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation.We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally we turn to the issue of gathering relevant information, that sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE

An Exploratory Analysis Of A Time Synchronization Protocol For UAS

This dissertation provides a numerical analysis of a Receiver Only Synchronization (ROS) protocol which is proposed for use by Unmanned Aircraft Systems (UAS) in Beyond Visual Line of Sight (BVLOS) operations. The use of ROS protocols could reinforce current technologies that enable transmission over 5G cell networks, decreasing latency issues and enabling the incorporation of an increased number of UAS to the network, without loss of accuracy. A minimum squared error (MSE)-based accuracy of clock offset and clock skew estimations was obtained using the number of iterations and number of observations as independent parameters. Although the model converged after only four iterations, the number of observations needed was considerably large, of no less than about 250. The noise, introduced in the system through the first residual, the correlation parameter and the disturbance terms, was assumed to be autocorrelated. Previous studies suggested that correlated noise might be typical in multipath scenarios, or in case of damaged antennas. Four noise distributions: gaussian, exponential, gamma and Weibull were considered. Each of them is adapted to different noise sources in the OSI model. Dispersion of results in the first case, the only case with zero mean, was checked against the Cramér-Rao Bound (CRB) limit. Results confirmed that the scheme proposed was fully efficient. Moreover, results with the other three cases were less promising, thus demonstrating that only zero mean distributions could deliver good results. This fact would limit the proposed scheme application in multipath scenarios, where echoes of previous signals may reach the receiver at delayed times. In the second part, a wake/sleep scheme was imposed on the model, concluding that for wake/sleep ratios below 92/08 results were not accurate at p=.05 level. The study also evaluated the impact of noise levels in the time domain and showed that above -2dB in time a substantial contribution of error terms disturbed the initial estimations significantly. The tests were performed in Matlab®. Based on the results, three venues confirming the assumptions made were proposed for future work. Some final reflections on the use of 5G in aviation brought the present dissertation to a close