Linear unbiased prediction of clock errors

Abstract

In this paper, we propose a new formula for linear unbiased prediction of the local clock timescales. To predict future errors over all the measurement data, a new gain is derived for the p-step ramp unbiased finite impulse response (FIR) predictor. We then show that this gain gives the best linear unbiased fit suitable for forming the prediction vector. The predictor proposed is consistent with linear regression and best linear unbiased estimator. Applications are given for a crystal clock and the USNO Master Clock.