Performance of the modified clock skew estimator and its upper bound for the IEEE 1588v2 (PTP) case under packet loss and fractional Gaussian noise environment

Precision Time Protocol (PTP) is a time protocol based on the Master and Slave exchanging messages with time stamps. In practical PTP systems, we have packet loss, a phenomenon where some of the PTP messages get lost in the Network. Packet loss may reduce the performance of the clock skew estimator from the mean square error (MSE) perspective. Recently, the same authors presented simulation results that show the clock skew performance of the three clock skew estimators (the two-way delay (TWD) clock skew estimator and the one-way delay (OWD) clock skew estimator for the Forward and Reverse paths) under the packet loss case in the fractional Gaussian noise (fGn) environment with Hurst exponent parameter (H) in the range of 0.5 ≤ H < 1, where indeed the clock skew performance was degraded compared to the non-packet loss case. Please note that for 0.5 < H < 1, the corresponding fGn is of long-range dependency (LRD). This paper proposes an algorithm that estimates the missing timestamps in the packet loss and fGn (0.5 ≤ H < 1) case. We use those estimates to generate three modified clock skew estimators (the two-way delay (TWD) modified clock skew estimator and the one-way delay (OWD) modified clock skew estimator for the Forward and Reverse paths) applicable to the packet loss, non-packet loss, and fGn (0.5 ≤ H < 1) case based on the same authors’ previously developed clock skew estimators. Those modified clock skew estimators led, based on simulation results, to an improved clock skew performance in the packet loss and fGn (0.5 ≤ H < 1) case compared with the authors’ previously developed clock skew estimators and those known from the literature (the ML-like (MLLE) and Kalman clock skew estimators). With the MSE expression, the system designer can know how many Sync periods are needed for the clock skew synchronization task to reach the system’s requirements from the MSE perspective. But no MSE expression exists in the literature for the packet loss case. In this paper, we derive closed-form approximated expressions for the MSE upper bounds related to the modified TWD and OWD clock skew estimators valid for the packet loss and fGn (0.5 ≤ H < 1) cases.