Optimal FIR filtering of the clock time errors

This paper discusses optimal finite impulse response (FIR) filtering of the clock first state known as the time interval error. An exact optimal FIR filter gain is derived assuming arbitrary, zero-mean and jointly independent sources of noise in the clock and in the measurement. The gain is simplified for large averaging horizons associated with clock models that change slowly with time. It is shown that the simplified gain is invariant to the initial state errors, does not depend on noise components in the model and in the measurement and turns out to be equal to the earlier studied unbiased FIR filter gain. A polynomial representation of the gain is also discussed.