Estimation of the Dynamics of Frequency Drift in Mature Ultra-stable Oscillators: A Study Based on the In-flight Performance from New Horizons

Detecting atomic clock frequency trends using an optimal stopping method

“…the frequency deviation, is white and this is often the case. Also other cases in which the frequency can be modeled by a Wiener process can be found and the method can be applied as well [7] by interpreting the process X as the frequency deviation. The para meter σ can be easily estimated using the Allan deviation, the parameter /λ 1 indicating the mean occurrence of the anomaly can be guessed as well by the knowledge of the clock, and we have seen that the estimates can also be quite inaccurate and the answers of the method are not that different.…”

“…(ii) Now there are two possible approaches: we can first fix either the parameter c or the parameter A. In the first case, we fix c and compute A as the unique root of the equation (7). In the second case, we fix A and, recalling that…”

“…cf A is a linear function of c, we find c using (7). (iii) We can then apply the detection algorithm, i.e.…”

“…We first need to express the function ψ in closed form. Computing explicitly the integral in (7), we get…”

“…1 and gets closer to zero, the expected delay grows significantly and the result becomes less applicable unless the PFA is enlarged as shown in the application to data from the New Horizons Project [7].…”