On the capabilities of the inaction method for extracting the periodic components from GPS clock data

Almost all GPS signal clocks show a periodic fluctuation. Harmonics in GPS satellites are a well-known feature, such as 3-, 4-, 6- and 12-h terms, accurate extraction of these harmonics are helpful to improve the clock modeling. The inaction method (IM) originating from the concept of normal time–frequency transform (NTFT) can precisely extract the periodic signals which significantly present the NTFT spectrum. This method is essentially line-pass filtering, so it can avoid being polluted by noises to the maximum extent and then have the ability to extract the time-varying periodic signals with robustness. The simulation test demonstrates that IM is the best method for extracting the harmonics and time-varying harmonics from a time signal, compared to singular spectrum analysis and zero-phase digital filter. We focus on GPS satellite clock data, after removing 6- and 12-h terms extracted by IM, the oscillation phenomenon in Hadamard deviation virtually disappears; this demonstrates that these periodic signals have been extracted effectively by the IM.