Estimation of Clock Offset Using Bootstrap Bias-Correction Techniques

Abstract

A recently proposed estimator of the offset between two clocks in a data communications network is based on an exchange of timing messages between the clocks. It is well known that different distributions of the transmission delays in the two directions associated with the exchanged messages cause the estimator to be biased. We use the bootstrap methodology to obtain a closed-form estimator of the bias and then form a new bias-corrected estimator of the clock offset. We show that for common distribution assumptions for the transmission delays, the bias-corrected estimator has smaller mean squared error (MSE) than the uncorrected estimator. We also derive the order statistic-based best linear unbiased estimator (o-BLUE) of the clock offset under the assumption that transmission delays are exponentially distributed. Several studies on network delay characteristics show that no single distribution adequately characterizes delays. Not only are delays highly dependent on the nature of traffic, they are also time varying. Therefore, any clock offset estimator developed needs to be robust to such variations. We examine the robustness of the o-BLUE and its bias-corrected outgrowth under the alternative assumptions of transmission delay. The bias-corrected o-BLUE outperforms a commonly used estimator and is recommended for applications, based on its robustness and MSE properties.

KEY WORDS :

• Bias correction
• Bootstrap methodology
• O-BLUE
• Order statistics
• Synchronization.