FIR smoothing of discrete-time state-space models with applications to clocks

We address a smoothing finite impulse response (FIR) filter for discrete time-invariant state-space polynomial models commonly used to model signals over finite data. A general gain is derived for the relevant p-lag unbiased smoothing FIR filter. An application is given for the time interval errors of local slave clocks of digital communications networks. An excellent performance of the best unbiased fit is demonstrated along with its ability to extrapolate linearly the clock behaviors for holdover required by the IEEE Standards.