Optimum Time Step and Memory for GPS-based Unbiased FIR Estimates of the Local Clock TIE Model

In this paper, we address a theoretical analysis of errors of the l-degree unbiased finite impulse response (FIR) filter applied to the if-degree time interval error (TIE) model of a local clock. Emphasizing the fact that the TIE model originates from the slowly changing Brownian phase and thus cannot obligatorily be distinct on a horizon of N points, we investigate estimates for l ne K and derive optimal horizons N_opt(T_opt) as functions of the optimal time step T_opt. Practical justification is provided based upon GPS-based sawtooth measurements of the TIE of a crystal clock imbedded to the Stanford Frequency Counter SR620 and using the SynPaQ III GPS Sensor and Symmetricom cesium standard of frequency as a reference source.