Analysis of the frequency stability history of GPS Navstar clocks

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The two-sample Allan variance has been the standard metric for assessing the frequency stability of atomic clocks which may be characterized by nonstationary noise processes. The convergence of the Allan variance for the noise types typical of atomic clocks might appear to suggest that the variance could be estimated to an arbitrary degree of accuracy by processing more data, over longer and longer periods of time, which would lead to progressively smaller confidence intervals. This tacit assumption, however, was called into question because of the behavior of one of the Global Positioning System (GPS) on-orbit Navstar atomic clocks whose frequency stability profile exhibited significant change with the processing of additional data. Because of the peculiar nonstationary behavior of this clock, a model for the frequency stability history was developed and is now incorporated as a routine part of the analysis of Navstar clocks conducted by the Naval Research Laboratory (NRL). The frequency stability history corresponds to the output of an N-sample moving average filter operating on the sequence of squared first differences of the M-day frequency offset measurements. This procedure assumes that the stochastic process has increments whose second order properties are slowly evolving over time such that, to a reasonable approximation, it has stationary increments over the N sample-interval. Frequency stability histories are presented using from one to 120-sample averages-the number of samples averaged representing a compromise between the time resolution and the stability of the estimate. Included are frequency stability histories for both cesium and rubidium on-orbit Navstar clocks. The results indicate that the frequency stability of most of the Navstar clocks is invariant over the useful life of the clock, that the frequency stability of some of the clocks degrades over the life of the clock, and that the frequency stability of still others improves after an initial transient. The frequency stability history is now used to detect and measure degradation in the frequency stability. Significant changes in the frequency stability are reported to the GPS Master Control Station (MCS).