Minimum Uncertainty Frequency Estimation using Past Measurements for Various Power-Law Noise Types

We present a method for current frequency estimation with minimum uncertainty using the past measurements. Estimated frequency is calculated as a weighted sum of the frequencies of the previous measurements and the weights are optimized to minimize the uncertainty. Uncertainties and optimum weights are calculated for various power-law noise types. For a case of a next step frequency estimation with N previous consecutive measurements, it is shown that only three previous measurements are enough to reduce the uncertainty to less than 5 % over the achievable minimum uncertainty for flicker FM. For white FM noise, we need to use 10 previous measurements to reach the same result. For a random-walk FM noise type, the uncertainty becomes less than 1 % over the limit value with only two measurements. Simple method to predict the frequency and phase for a drifting timescale is proposed.