Multi-Hop Timestamp-Free Synchronization With Arbitrary Distributed Delays in Wireless Networks

Timestamp-free synchronization protocol is tailored to provide a global time understanding for resource-limited wireless networks as it eliminates timestamp interaction, thereby minimizing additional resource overheads. However, the existing two-hop based timestamp-free protocols are not suitable for synchronizing all nodes in multi-hop networks, as they necessitate multiple response times to establish the timestamp relationship between each pair of neighboring nodes. To this end, we introduce a novel multi-hop timestamp-free synchronization protocol. The proposed protocol allows any two nodes to be synchronized using only local timestamps and the skew estimates embedded within packets traversing the reverse path. Furthermore, considering that synchronization accuracy suffers from delay variation resulting from packet loss or retransmission in wireless networks, we derive a Pitman estimator to estimate the clock skew under arbitrary delay models, given known information. To further target unknown arbitrary delay distributions, we approximate the probability density function (pdf) of stochastic delays using a Gaussian mixture model, and then learn the pdf using the rival penalized expectation maximization algorithm. With the aid of the learned pdf, the robustness-enhanced Pitman estimator is derived, which is robust against arbitrary distributed delays without known knowledge. The effectiveness and performance enhancement of estimators are validated by simulations.