A numerical comparison of the unbiased FIR and Kalman filters in applications to GPS-based timekeeping

The 3-state unbiased finite impulse response (FIR) filter and the 3-state Kalman filters are investigated for the time interval error (TIE) K-degree polynomial model of a local crystal clock in GPS-based timekeeping in presence of the sawtooth noise induced by the receiver. We show that both algorithms produce consistent estimates for the reference (rubidium) measurements. We also demonstrate that the unbiased FIR algorithm produces a lower error than the standard Kalman filter in presence of the sawtooth noise