Optimum synthesis for time scale generation

A time scale can be regarded as a synthesis of readings from precise clocks. Usually such synthesis is based on the principle of weighted averaging, which balances the contribution of each clock according to its noise level. It is well known that there are five different noise processes in precise clocks. Therefore, a good synthesis should balance each of those noise levels. Most existing algorithms control only one or two noise types. If an algorithm can control all five noise types simultaneously, we consider it to be optimum. The key point of constructing an optimum algorithm is the separation of all five noise types. In this paper, an optimum algorithm is presented using the half-integrating/half-differentiating model by which the five noise types are separated correctly. Performances of the new algorithm are demonstrated with simulated and real data.