Maximum likelihood estimators of clock offset and skew under exponential delays

Li, Jun; Jeske, Daniel R.

doi:10.1002/asmb.777

Cited by 12 publications

(13 citation statements)

References 17 publications

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“…References [15,16] modeled the random propagation delay following a Gaussian distribution. References [16,17,18,19,20] modeled the random delay as an exponential delay and a bivariate exponential delay, but in molecular communications, the propagation delay is normally assumed to follow an inverse Gaussian distribution [21]. In [22], an approach for clock offset estimation has been proposed which is robust to the distribution of the network delays, however, it has high computational complexity and no closed-form expression of the estimator can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Maximum-Likelihood Estimator of Clock Offset between Nanomachines in Bionanosensor Networks

Lin

Yang

2015

Sensors

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Recent advances in nanotechnology, electronic technology and biology have enabled the development of bio-inspired nanoscale sensors. The cooperation among the bionanosensors in a network is envisioned to perform complex tasks. Clock synchronization is essential to establish diffusion-based distributed cooperation in the bionanosensor networks. This paper proposes a maximum-likelihood estimator of the clock offset for the clock synchronization among molecular bionanosensors. The unique properties of diffusion-based molecular communication are described. Based on the inverse Gaussian distribution of the molecular propagation delay, a two-way message exchange mechanism for clock synchronization is proposed. The maximum-likelihood estimator of the clock offset is derived. The convergence and the bias of the estimator are analyzed. The simulation results show that the proposed estimator is effective for the offset compensation required for clock synchronization. This work paves the way for the cooperation of nanomachines in diffusion-based bionanosensor networks.

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Section: Introductionmentioning

confidence: 99%

Maximum-Likelihood Estimator of Clock Offset between Nanomachines in Bionanosensor Networks

Lin

Yang

2015

Sensors

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“…Assuming symmetric exponential delays with a known mean λ, [33] Li and Jeske [34] proposed a computationally-simpler algorithm to find the MLEs of clock offset and skew. Asymmetric exponential delays with unknown means were assumed in [34], such that the estimation algorithm can be applied to a more general framework.…”

Section: Direct Joint Estimation Of Clock Offset and Skewmentioning

confidence: 99%

“…Asymmetric exponential delays with unknown means were assumed in [34], such that the estimation algorithm can be applied to a more general framework. In this case, the likelihood function resumes as:…”

Section: Direct Joint Estimation Of Clock Offset and Skewmentioning

confidence: 99%

“…To find the MLEs for likelihood function Equation (27), or equivalently Equation (28), the concept of profile likelihood function is employed in [34], such that the MLEs can be alternatively found by maximizing the profile likelihoods. In particular, fixing f, θ 1 and θ 2 , the conditional MLEs of λ 1 and λ 2 are shown to be:…”

Section: Direct Joint Estimation Of Clock Offset and Skewmentioning

confidence: 99%

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An Overview of a Class of Clock Synchronization Algorithms for Wireless Sensor Networks: A Statistical Signal Processing Perspective

Jeske

Serpedin

2015

Algorithms

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Recently, wireless sensor networks (WSNs) have drawn great interest due to their outstanding monitoring and management potential in medical, environmental and industrial applications. Most of the applications that employ WSNs demand all of the sensor nodes to run on a common time scale, a requirement that highlights the importance of clock synchronization. The clock synchronization problem in WSNs is inherently related to parameter estimation. The accuracy of clock synchronization algorithms depends essentially on the statistical properties of the parameter estimation algorithms. Recently, studies dedicated to the estimation of synchronization parameters, such as clock offset and skew, have begun to emerge in the literature. The aim of this article is to provide an overview of the state-of-the-art clock synchronization algorithms for WSNs from a statistical signal processing point of view. This article focuses on describing the key features of the class of clock synchronization algorithms that exploit the traditional two-way message (signal) exchange mechanism. Upon introducing the two-way message exchange mechanism, the main clock offset estimation algorithms for pairwise synchronization of sensor nodes are first reviewed, and their performance is compared. The class of fully-distributed clock offset estimation algorithms for network-wide synchronization is then surveyed. The paper concludes with a list of open research problems pertaining to clock synchronization of WSNs.

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“…On one hand, the PTP is applied for the offset synchronization task only as is done in Pinchas [1], Mizrahi [18,29], Karthik and Blum [14]; Guruswamy et al [4]; Anand Guruswamy et al [30]. On the other hand, we may find other algorithms estimating the clock skew and the offset as is done in Levy and Pinchas [2]; Chin and Chen [31], Puttnies et al [13], Chaudhari et al [32]; Li and Jeske [33], Noh et al [34], Guruswamy et al [4]; Karthik and Blum [12,14,15], Giorgi and Narduzzi [35]. In addition, we may find in the literature algorithms that estimate only the clock skew as is done in Shan et al [5]; Chaloupka et al [36].…”

Section: Introductionmentioning

confidence: 99%

A Novel Clock Skew Estimator and Its Performance for the IEEE 1588v2 (PTP) Case in Fractional Gaussian Noise/Generalized Fractional Gaussian Noise Environment

Avraham

Pinchas

2021

Front. Phys.

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Papers in the literature dealing with the Ethernet network characterize packet delay variation (PDV) as a long-range dependence (LRD) process. Fractional Gaussian noise (fGn) or generalized fraction Gaussian noise (gfGn) belong to the LRD process. This paper proposes a novel clock skew estimator for the IEEE1588v2 applicable for the white-Gaussian, fGn, or gfGn environment. The clock skew estimator does not depend on the unknown asymmetry between the fixed delays in the forward and reverse paths nor on the clock offset between the Master and Slave. In addition, we supply a closed-form-approximated expression for the mean square error (MSE) related to our new proposed clock skew estimator. This expression is a function of the Hurst exponent H, as a function of the parameter a for the gfGn case, as a function of the total sent Sync messages, as a function of the Sync period, and as a function of the PDV variances of the forward and reverse paths. Simulation results confirm that our closed-form-approximated expression for the MSE indeed supplies the performance of our new proposed clock skew estimator efficiently for various values of the Hurst exponent, for the parameter a in gfGn case, for different Sync periods, for various values for the number of Sync periods and for various values for the PDV variances of the forward and reverse paths. Simulation results also show the advantage in the performance of our new proposed clock skew estimator compared to the literature known ML-like estimator (MLLE) that maximizes the likelihood function obtained based on a reduced subset of observations (the first and last timing stamps). This paper also presents designing graphs for the system designer that show the number of the Sync periods needed to get the required clock skew performance (MSE = 10–12). Thus, the system designer can approximately know in advance the total delay or the time the system has to wait until getting the required system’s performance from the MSE point of view.

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Maximum likelihood estimators of clock offset and skew under exponential delays

Cited by 12 publications

References 17 publications

Maximum-Likelihood Estimator of Clock Offset between Nanomachines in Bionanosensor Networks

Maximum-Likelihood Estimator of Clock Offset between Nanomachines in Bionanosensor Networks

An Overview of a Class of Clock Synchronization Algorithms for Wireless Sensor Networks: A Statistical Signal Processing Perspective

A Novel Clock Skew Estimator and Its Performance for the IEEE 1588v2 (PTP) Case in Fractional Gaussian Noise/Generalized Fractional Gaussian Noise Environment

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