A weighted average based external clock synchronization protocol for wireless sensor networks

Clock synchronization is an extremely important requirement of wireless sensor networks(WSNs). There are many application scenarios such as weather monitoring and forecasting etc. where external clock synchronization may be required because WSN itself may consists of components which are not connected to each other. A usual approach for external clock synchronization in WSNs is to synchronize the clock of a reference node with an external source such as UTC, and the remaining nodes synchronize with the reference node using an internal clock synchronization protocol. In order to provide highly accurate time, both the offset and the drift rate of each clock with respect to reference node are estimated from time to time, and these are used for getting correct time from local clock reading. A problem with this approach is that it is difficult to estimate the offset of a clock with respect to the reference node when drift rate of clocks varies over a period of time. In this paper, we first propose a novel internal clock synchronization protocol based on weighted averaging technique, which synchronizes all the clocks of a WSN to a reference node periodically. We call this protocol weighted average based internal clock synchronization(WICS) protocol. Based on this protocol, we then propose our weighted average based external clock synchronization(WECS) protocol. We have analyzed the proposed protocols for maximum synchronization error and shown that it is always upper bounded. Extensive simulation studies of the proposed protocols have been carried out using Castalia simulator. Simulation results validate our theoretical claim that the maximum synchronization error is always upper bounded and also show that the proposed protocols perform better in comparison to other protocols in terms of synchronization accuracy. A prototype implementation of the proposed internal clock synchronization protocol using a few TelosB motes also validates our claim.

Predictability and chaotic nature of daily streamflow

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system in many approaches. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbor method. Embedding dimensions of 6-7 obtained indicates the possible presence of low-dimensional chaotic behavior. The predictability of the system is estimated by calculating the system’s Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system.

Phase synchronization in brain networks derived from correlation between probabilities of recurrences in functional MRI data

It is increasingly being recognized that resting state brain connectivity derived from functional magnetic resonance imaging (fMRI) data is an important marker of brain function both in healthy and clinical populations. Though linear correlation has been extensively used to characterize brain connectivity, it is limited to detecting first order dependencies. In this study, we propose a framework where in phase synchronization (PS) between brain regions is characterized using a new metric ``correlation between probabilities of recurrence'' (CPR) and subsequent graph-theoretic analysis of the ensuing networks. We applied this method to resting state fMRI data obtained from human subjects with and without administration of propofol anesthetic. Our results showed decreased PS during anesthesia and a biologically more plausible community structure using CPR rather than linear correlation. We conclude that CPR provides an attractive nonparametric method for modeling interactions in brain networks as compared to standard correlation for obtaining physiologically meaningful insights about brain function.

Predictability and chaotic nature of daily streamflow

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system in many approaches. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbor method. Embedding dimensions of 6-7 obtained indicates the possible presence of low-dimensional chaotic behavior. The predictability of the system is estimated by calculating the system's Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system.

Joint estimation of synchronization impairments in MIMO-OFDM system

A joint Maximum Likelihood (ML) estimation algorithm for the synchronization impairments such as Carrier Frequency Offset (CFO), Sampling Frequency Offset (SFO) and Symbol Timing Error (STE) in single user MIMO-OFDM system is investigated in this work. A received signal model that takes into account the nonlinear effects of CFO, SFO, STE and Channel Impulse Response (CIR) is formulated. Based on the signal model, a joint ML estimation algorithm is proposed. Cramer-Rao Lower Bound (CRLB) for the continuous parameters CFO and SFO is derived for the cases of with and without channel response effects and is used to compare the effect of coupling between different estimated parameters. The performance of the estimation method is studied through numerical simulations.

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO-OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO-OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator. (C) 2013 Elsevier GmbH. All rights reserved.

Connectivity analysis of multichannel EEG signals using recurrence based phase synchronization technique

Real world biological systems such as the human brain are inherently nonlinear and difficult to model. However, most of the previous studies have either employed linear models or parametric nonlinear models for investigating brain function. In this paper, a novel application of a nonlinear measure of phase synchronization based on recurrences, correlation between probabilities of recurrence (CPR), to study connectivity in the brain has been proposed. Being non-parametric, this method makes very few assumptions, making it suitable for investigating brain function in a data-driven way. CPR's utility with application to multichannel electroencephalographic (EEG) signals has been demonstrated. Brain connectivity obtained using thresholded CPR matrix of multichannel EEG signals showed clear differences in the number and pattern of connections in brain connectivity between (a) epileptic seizure and pre-seizure and (b) eyes open and eyes closed states. Corresponding brain headmaps provide meaningful insights about synchronization in the brain in those states. K-means clustering of connectivity parameters of CPR and linear correlation obtained from global epileptic seizure and pre-seizure showed significantly larger cluster centroid distances for CPR as opposed to linear correlation, thereby demonstrating the superior ability of CPR for discriminating seizure from pre-seizure. The headmap in the case of focal epilepsy clearly enables us to identify the focus of the epilepsy which provides certain diagnostic value. (C) 2013 Elsevier Ltd. All rights reserved.

Study of phase synchronization in multichannel seizure EEG using nonlinear recurrence measure

Complex biological systems such as the human brain can be expected to be inherently nonlinear and hence difficult to model. Most of the previous studies on investigations of brain function have either used linear models or parametric nonlinear models. In this paper, we propose a novel application of a nonlinear measure of phase synchronization based on recurrences, correlation between probabilities of recurrence (CPR), to study seizures in the brain. The advantage of this nonparametric method is that it makes very few assumptions thus making it possible to investigate brain functioning in a data-driven way. We have demonstrated the utility of CPR measure for the study of phase synchronization in multichannel seizure EEG recorded from patients with global as well as focal epilepsy. For the case of global epilepsy, brain synchronization using thresholded CPR matrix of multichannel EEG signals showed clear differences in results obtained for epileptic seizure and pre-seizure. Brain headmaps obtained for seizure and preseizure cases provide meaningful insights about synchronization in the brain in those states. The headmap in the case of focal epilepsy clearly enables us to identify the focus of the epilepsy which provides certain diagnostic value. Comparative studies with linear correlation have shown that the nonlinear measure CPR outperforms the linear correlation measure. (C) 2014 Elsevier Ltd. All rights reserved.

A model for the classification and survey of clock synchronization protocols in WSNs

Clock synchronization in wireless sensor networks (WSNs) assures that sensor nodes have the same reference clock time. This is necessary not only for various WSN applications but also for many system level protocols for WSNs such as MAC protocols, and protocols for sleep scheduling of sensor nodes. Clock value of a node at a particular instant of time depends on its initial value and the frequency of the crystal oscillator used in the sensor node. The frequency of the crystal oscillator varies from node to node, and may also change over time depending upon many factors like temperature, humidity, etc. As a result, clock values of different sensor nodes diverge from each other and also from the real time clock, and hence, there is a requirement for clock synchronization in WSNs. Consequently, many clock synchronization protocols for WSNs have been proposed in the recent past. These protocols differ from each other considerably, and so, there is a need to understand them using a common platform. Towards this goal, this survey paper categorizes the features of clock synchronization protocols for WSNs into three types, viz, structural features, technical features, and global objective features. Each of these categories has different options to further segregate the features for better understanding. The features of clock synchronization protocols that have been used in this survey include all the features which have been used in existing surveys as well as new features such as how the clock value is propagated, when the clock value is propagated, and when the physical clock is updated, which are required for better understanding of the clock synchronization protocols in WSNs in a systematic way. This paper also gives a brief description of a few basic clock synchronization protocols for WSNs, and shows how these protocols fit into the above classification criteria. In addition, the recent clock synchronization protocols for WSNs, which are based on the above basic clock synchronization protocols, are also given alongside the corresponding basic clock synchronization protocols. Indeed, the proposed model for characterizing the clock synchronization protocols in WSNs can be used not only for analyzing the existing protocols but also for designing new clock synchronization protocols. (C) 2014 Elsevier B.V. All rights reserved.

A Design for Performance Improvement of Clock Synchronization in WSNs using a TDMA-based MAC Protocol

Clock synchronization in a wireless sensor network (WSN) is quite essential as it provides a consistent and a coherent time frame for all the nodes across the network. Typically, clock synchronization is achieved by message passing using a contention-based scheme for media access, like carrier sense multiple access (CSMA). The nodes try to synchronize with each other, by sending synchronization request messages. If many nodes try to send messages simultaneously, contention-based schemes cannot efficiently avoid collisions. In such a situation, there are chances of collisions, and hence, message losses, which, in turn, affects the convergence of the synchronization algorithms. However, the number of collisions can be reduced with a frame based approach like time division multiple access (TDMA) for message passing. In this paper, we propose a design to utilize TDMA-based media access and control (MAC) protocol for the performance improvement of clock synchronization protocols. The basic idea is to use TDMA-based transmissions when the degree of synchronization improves among the sensor nodes during the execution of the clock synchronization algorithm. The design significantly reduces the collisions among the synchronization protocol messages. We have simulated the proposed protocol in Castalia network simulator. The simulation results show that the proposed protocol significantly reduces the time required for synchronization and also improves the accuracy of the synchronization algorithm.

CheepSync: A Time Synchronization Service for Resource Constrained Bluetooth LE Advertisers

Clock synchronization is highly desirable in distributed systems, including many applications in the Internet of Things and Humans. It improves the efficiency, modularity, and scalability of the system, and optimizes use of event triggers. For IoTH, BLE - a subset of the recent Bluetooth v4.0 stack - provides a low-power and loosely coupled mechanism for sensor data collection with ubiquitous units (e.g., smartphones and tablets) carried by humans. This fundamental design paradigm of BLE is enabled by a range of broadcast advertising modes. While its operational benefits are numerous, the lack of a common time reference in the broadcast mode of BLE has been a fundamental limitation. This article presents and describes CheepSync, a time synchronization service for BLE advertisers, especially tailored for applications requiring high time precision on resource constrained BLE platforms. Designed on top of the existing Bluetooth v4.0 standard, the CheepSync framework utilizes low-level time-stamping and comprehensive error compensation mechanisms for overcoming uncertainties in message transmission, clock drift, and other system-specific constraints. CheepSync was implemented on custom designed nRF24Cheep beacon platforms (as broadcasters) and commercial off-the-shelf Android ported smartphones (as passive listeners). We demonstrate the efficacy of CheepSync by numerous empirical evaluations in a variety of experimental setups, and show that its average (single-hop) time synchronization accuracy is in the 10 mu s range.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

Byzantine-resilient distributed computing systems

This paper is aimed at reviewing the notion of Byzantine-resilient distributed computing systems, the relevant protocols and their possible applications as reported in the literature. The three agreement problems, namely, the consensus problem, the interactive consistency problem, and the generals problem have been discussed. Various agreement protocols for the Byzantine generals problem have been summarized in terms of their performance and level of fault-tolerance. The three classes of Byzantine agreement protocols discussed are the deterministic, randomized, and approximate agreement protocols. Finally, application of the Byzantine agreement protocols to clock synchronization is highlighted.

Design and evaluation of a dual-microcomputer shared memory system with a shared I/O bus

The design, implementation and evaluation are described of a dual-microcomputer system based on the concept of shared memory. Shared memory is useful for passing large blocks of data and it also provides a means to hold and work with shared data. In addition to the shared memory, a separate bus between the I/O ports of the microcomputers is provided. This bus is utilized for interprocessor synchronization. Software routines helpful in applying the dual-microcomputer system to realistic problems are presented. Performance evaluation of the system is carried out using benchmarks.