A wavelet-based multiscale ensemble time-scale algorithm

The wide-spread availability of ensembles of high-performance clocks has motivated interest in time-scale algorithms. There are many such algorithms in use today in applications ranging from scientific to commercial. Although these algorithms differ in key aspects and are sometimes tailored for specific applications and mixtures of clocks, they all share the goal of combining measured time differences between clocks to form a reference time scale that is more stable than any of the clocks in the ensemble. A new approach to forming time scales is presented here, the multiscale ensemble timescale (METS) algorithm. This approach is based on a multiresolution analysis afforded by the discrete wavelet transform. The algorithm does not assume a specific parametric model for the clocks involved and hence is well-suited for an ensemble of highly disparate clocks. The approach is based on an appealing optimality criterion which yields a reference time scale that is more stable than the constituent clocks over all averaging intervals (scales). The METS algorithm is presented here in detail and is shown in a simulation study to compare favorably with a time-scale algorithm based on Kalman filtering.