Full horizon optimal FIR estimator of clock state employing measurement of time errors
This paper addresses 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) ( p > 0 ) , and smoothing (p<0) ( 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 N ? 1 or the clock initial mean square state dominates noise in the order of magnitudes. An application is given to a master clock.
optimal fir estimator clock state time error unbiased fir estimator