Probabilistic model for clock synchronization of cascaded network elements

Precision Time Protocol (PTP) synchronizes clocks of networked elements by exchanging messages containing precise time-stamps. A master clock is carefully chosen to provide the reference clock to the rest elements in the network, called slaves. Using the time-stamps, slave element learns the relation between its own clock and the master clock so that it can synchronize its time to the reference time. Uncertainties, e.g., random stamping and quantization errors, affect the synchronization precision. This paper presents a probabilistic state-space model which quantifies the uncertainties and represents the relation between system variables. Estimation of hidden variables, i.e. the system states, is carried out by using Kalman filter. The performance of this approach is verified by numerical results.