Fourier transform for non-uniformly sampled data in the study of systematic errors in common-view time transfer

A new mathematical formulation for the Fourier transform applicable to non-uniformly sampled data has been derived. The importance of this to the Global Positioning System (GPS) is identification of harmonics of the orbital period in the frequency of both the space vehicle and the ground reference clocks relative to the DoD Master Clock. The presence of such a periodicity was discovered in doing the exhaustive computation of frequency stability, i.e., in estimating the stability at sample times equal to every multiple of the basic sample period of the data as opposed to the common method of under-sampling the stability at a canonic set of sample times equally spaced along a logarithmic axis. Analysis of the frequency stability of the time reference at the Air Force GPS ground tracking station at Colorado Springs showed a pronounced periodic component at 2.99 hours-the fourth harmonic of the operational GPS space vehicle orbital period of 11.97 hours.