An unbiased FIR filter for TIE model of a local clock in applications to GPS-based timekeeping

An unbiased finite impulse response (FIR) filter is proposed to estimate the time-interval error (TIE) K-degree polynomial model of a local clock in global positioning system (GPS)-based timekeeping in the presence of noise that is not obligatory Gaussian. Generic coefficients for the unbiased FIRs are derived. The low-degree FIRs and noise power gains are given. An estimation algorithm is proposed and examined for the TIE measurements of a crystal clock in the presence of the uniformly distributed sawtooth noise induced by the multichannel GPS timing receiver. Based upon this algorithm, we show that the unbiased FIR estimates are consistent with the reference (rubidium) measurements and fit them better than the standard Kalman filter.