scholarly journals Maximum Likelihood Estimation of Clock Skew in IEEE 1588 with Fractional Gaussian Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-24 ◽  
Author(s):  
Chagai Levy ◽  
Monika Pinchas
Keyword(s):  
Maximum Likelihood ◽  
Gaussian Noise ◽  
Likelihood Estimation ◽  
Packet Delay ◽  
Fractional Gaussian Noise ◽  
Clock Skew ◽  
Ieee 1588 ◽  
Accuracy And Precision ◽  
Ethernet Network ◽  
Synchronization Accuracy

To support system-wide synchronization accuracy and precision in the sub-microsecond range without using GPS technique, the precise time protocol (PTP) standard IEEE-1588 v2 is chosen. Recently, a new clock skew estimation technique was proposed for the slave based on a dual slave clock method that assumes that the packet delay variation (PDV) in the Ethernet network is a constant delay. However, papers dealing with the Ethernet network have shown that this PDV is a long range dependency (LRD) process which may be modeled as a fractional Gaussian noise (fGn) with Hurst exponent (H) in the range of0.5<H<1. In this paper, we propose a new clock skew estimator based on the maximum likelihood (ML) technique and derive an approximated expression for the Cramer-Rao lower bound (CRLB) both valid for the case where the PDV is modeled as fGn (0.5<H<1). Simulation results indicate that our new clock skew method outperforms the dual slave clock approach and that the simulated mean square error (MSE) obtained by our new proposed clock skew estimator approaches asymptotically the developed CRLB.

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

2021 ◽  
Vol 9 ◽  
Author(s):  
Yehonatan Avraham ◽  
Monika Pinchas
Keyword(s):  
Closed Form ◽  
Gaussian Noise ◽  
Hurst Exponent ◽  
Likelihood Function ◽  
Packet Delay ◽  
Fractional Gaussian Noise ◽  
Clock Skew ◽  
Total Delay ◽  
System Designer ◽  
Simulation Results

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.

Novel Maximum Likelihood Estimation of Clock Skew in One-Way Broadcast Time Synchronization

2020 ◽  
Vol 67 (11) ◽  
pp. 9948-9957
Author(s):  
Fanrong Shi ◽  
Huailiang Li ◽  
Simon X. Yang ◽  
Xianguo Tuo ◽  
Maosong Lin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Time Synchronization ◽  
Likelihood Estimation ◽  
Clock Skew ◽  
Broadcast Time

A maximum likelihood approach for identifying dive bouts improves accuracy, precision and objectivity

Behaviour ◽  
2007 ◽  
Vol 144 (11) ◽  
pp. 1315-1332 ◽  
Author(s):  
Sebastián Luque ◽  
Christophe Guinet
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Systematic Effect ◽  
Fur Seals ◽  
Accuracy And Precision

AbstractForaging behaviour frequently occurs in bouts, and considerable efforts to properly define those bouts have been made because they partly reflect different scales of environmental variation. Methods traditionally used to identify such bouts are diverse, include some level of subjectivity, and their accuracy and precision is rarely compared. Therefore, the applicability of a maximum likelihood estimation method (MLM) for identifying dive bouts was investigated and compared with a recently proposed sequential differences analysis (SDA). Using real data on interdive durations from Antarctic fur seals (Arctocephalus gazella Peters, 1875), the MLM-based model produced briefer bout ending criterion (BEC) and more precise parameter estimates than the SDA approach. The MLM-based model was also in better agreement with real data, as it predicted the cumulative frequency of differences in interdive duration more accurately. Using both methods on simulated data showed that the MLM-based approach produced less biased estimates of the given model parameters than the SDA approach. Different choices of histogram bin widths involved in SDA had a systematic effect on the estimated BEC, such that larger bin widths resulted in longer BECs. These results suggest that using the MLM-based procedure with the sequential differences in interdive durations, and possibly other dive characteristics, may be an accurate, precise, and objective tool for identifying dive bouts.

scholarly journals One-step estimation for the fractional Gaussian noise at high-frequency

2020 ◽  
Vol 24 ◽  
pp. 827-841
Author(s):  
Alexandre Brouste ◽  
Marius Soltane ◽  
Irene Votsi
Keyword(s):  
Maximum Likelihood ◽  
Gaussian Noise ◽  
High Frequency ◽  
Finite Size ◽  
Maximum Likelihood Estimators ◽  
Parametric Estimation ◽  
Fractional Gaussian Noise ◽  
One Step ◽  
Asymptotically Efficient ◽  
Frequency Observation

The present paper concerns the parametric estimation for the fractional Gaussian noise in a high-frequency observation scheme. The sequence of Le Cam’s one-step maximum likelihood estimators (OSMLE) is studied. This sequence is defined by an initial sequence of quadratic generalized variations-based estimators (QGV) and a single Fisher scoring step. The sequence of OSMLE is proved to be asymptotically efficient as the sequence of maximum likelihood estimators but is much less computationally demanding. It is also advantageous with respect to the QGV which is not variance efficient. Performances of the estimators on finite size observation samples are illustrated by means of Monte-Carlo simulations.

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