Multiplicative composition of clock-skew components for improving time synchronisation

Time synchronisation is essential to ensure the reliability of distributed computation. Oscillators included in low-cost nodes are highly influenced by temperature variations. Experimental results demonstrate that the clock skew of two nodes (the ratio of the real frequencies of the oscillators) is composed of a multiplicative combination of, at least, two main components: the clock skew due to the variations between the cut of the crystal of each oscillator and the clock skew due to the different temperatures affecting the nodes. By applying a nonlinear filtering, homomorphic filtering, both components are separated in an effective way. Applying a correction factor to the clock skew due to the cut of the crystals, the temperature variations are compensated very accurately. The proposed new approach is called HF2 (homomorphic improved filtering) and can be easily applied to any clock-skew-based time synchronisation protocol. The correction factor has been applied to flooding time synchronisation protocol (FTSP) resulting in HF2-FTSP. An experiment with temperature variation, comparing FTSP, A2T-FTSP and HF2-FTSP is shown. The proposed technique allows the use of cheap and simple oscillators for achieving a quite similar accurate synchronisation level than much more expensive and precise oscillators.