Studies of optimal FIR estimator of clock state employing measurement of time errors

In this paper we investigate a p-shift full horizon optimal finite impulse response (FIR) estimator of clock state employing all the measurement data available of the time interval error (TIE). A solution proposed is general for filtering (p = 0), prediction (p > 0), and smoothing (p <; 0) of discrete time clock models in state space. The optimal estimator self-determines the clock initial mean square state by solving the discrete algebraic Riccati equation on a measurement interval of N points. Noise is allowed to be zero-mean with arbitrary distribution and covariance functions. The unbiased FIR estimator is proposed in the batch form producing near optimal estimates when N ≫ 1 or the clock initial mean square state dominates noise in the order of magnitudes. An application is given to a master clock.