On the Optimum Design of L-Estimators for Phase Offset Estimation in IEEE 1588

In packet-based time synchronization protocols such as IEEE 1588, clock phase offsets are determined via two-way message exchanges between a master and a slave. Since the end-to-end delays in packet networks are inherently stochastic in nature, the recovery of phase offsets from message exchanges must be treated as a statistical estimation problem. Recently, minimax estimators for this problem were proposed by the authors, which are optimum in terms of minimizing the mean-squared estimation error over all values of the unknown parameters. In this paper, we consider a restricted class of estimators referred to as L-estimators, which are linear functions of order statistics. The problem of designing optimum L-estimators is studied under several hitherto unconsidered criteria of optimality. Our results address the case where the queuing delay distributions are fully known, as well as the case where network model uncertainty exists. Optimum L-estimators that utilize information from past observation windows to improve performance are also described. The derived L-estimators have a much lower computational complexity than minimax estimators, and also require lesser statistical knowledge of the queuing delays. Simulation results indicate that L-estimators exhibit a mean-squared estimation error very close to minimax estimators under many network scenarios.