Linear unbiased prediction of clock errors.

Area of Science:

• Metrology and Timekeeping
• Signal Processing
• Statistical Modeling

Background:

• Accurate prediction of local clock timescales is crucial for various scientific and technological applications.
• Existing methods for time scale prediction may have limitations in accuracy and efficiency.
• The finite impulse response (FIR) predictor is a common tool in signal processing, but its application to time scale prediction requires specific adaptations.

Discussion:

• The paper introduces a novel formula for linear unbiased prediction of local clock timescales.
• A new gain is derived for the p-step ramp unbiased finite impulse response (FIR) predictor to forecast future errors.
• The proposed predictor is shown to provide the best linear unbiased fit for constructing the prediction vector.

Key Insights:

• The derived gain ensures optimal linear unbiased prediction of time scale errors.
• The predictor aligns with established principles of linear regression and best linear unbiased estimation.
• The method is validated through applications on a crystal clock and the USNO Master Clock.

Outlook:

• This work offers a more accurate and reliable method for predicting local clock timescales.
• Potential applications include improving the performance of atomic clocks and navigation systems.
• Further research could explore nonlinear prediction models or adaptive FIR predictors for enhanced accuracy.