Anomalous harmonics in the spectra of GPS position estimates

Abstract

Prior studies of the power spectra of GPS position time series have found pervasive seasonal signals against a power-law background of flicker noise plus white noise. Dong et al. (2002) estimated that less than half the observed GPS seasonal power can be explained by redistributions of geophysical fluid mass loads. Much of the residual variation is probably caused by unidentified GPS technique errors and analysis artifacts. Among possible mechanisms, Penna and Stewart (2003) have shown how unmodeled analysis errors at tidal frequencies (near 12-and 24-hour periods) can be aliased to longer periods very efficiently. Signals near fortnightly, semiannual, and annual periods are expected to be most seriously affected. We have examined spectra for the 167 sites of the International GNSS (Global Navigation Satellite Systems) Service (IGS) network having more than 200 weekly measurements during 1996.0-2006.0. The non-linear residuals of the weekly IGS solutions that were included in ITRF2005, the latest version of the International Terrestrial Reference Frame (ITRF), have been used. To improve the detection of common-mode signals, the normalized spectra of all sites have been stacked, then boxcar smoothed for each local north (N), east (E), and height (H) component. The stacked, smoothed spectra are very similar for all three components. Peaks are evident at harmonics of about 1 cycle per year (cpy) up to at least 6 cpy, but the peaks are not all at strictly 1.0 cpy intervals. Based on the 6th harmonic of the N spectrum, which is among the sharpest and largest, and assuming a linear overtone model, then a common fundamental of 1.040 ± 0.008 cpy can explain all peaks well, together with the expected annual and semiannual signals. A flicker noise power-law continuum describes the background spectrum down to periods of a few months, after which the residuals become whiter. Similar sub-seasonal tones are not apparent in the residuals of available satellite laser ranging (SLR) and very long baseline interferometry (VLBI) sites, which are both an order of magnitude less numerous and dominated by white noise. There is weak evidence for a few isolated peaks near 1 cpy harmonics in the spectra of geophysical loadings, but these are much noisier than for GPS positions. Alternative explanations related to the GPS technique are suggested by the close coincidence of the period of the 1.040 cpy frequency, about 351.2 days, to the ''GPS year''; i.e., the interval required for the constellation to repeat its inertial orientation with respect to the sun. This could indicate that the harmonics are a type of systematic error related to the satellite orbits. Mechanisms could involve orbit modeling defects or aliasing of site-dependent positioning biases modulated by the varying satellite geometry.

Realizing a terrestrial reference frame using the Global Positioning System

“…The manner in which measurement model errors (e.g., antenna multipath) manifest as s varies [Ray et al, 2008] may also contribute.…”

Characterization of site‐specific GPS errors using a short‐baseline network of braced monuments at Yucca Mountain, southern Nevada

“…Multipath-induced errors can appear in many forms: The annual repeat in the GPS satellite configuration could cause an approximately annually ($350 day) repeating multipath signal [Ray et al, 2007]; unmodeled subdaily signals, including those from multipath, could propagate to longerperiod signals [Penna et al, 2007;King et al, 2008]; seasonal signals could be caused by changes in the vegetation, snow pack, and surface water of the local area around the antenna [Dong et al, 2002;Larson et al, 2008]; and changes in multipath could appear or disappear at random as the local environment changes [Dong et al, 2002]. Additional to any effects from far-field reflections, near-field signal scattering by the antenna or monument itself can also be a significant source of error [Elósegui et al, 1995].…”

Secular changes in Earth’s shape and surface mass loading derived from combinations of reprocessed global GPS networks

“…strong hydrological signals in tropical river basins (Bevis et al 2005) or annual snowfall at high latitudes (Lidberg et al 2007). Not all apparent signals in the GPS time series are due to geophysical causes; a non-loading signal has been identified in the GPS time series which is believed to be driven by the repetition of the satellite geometry, as it has not been found in SLR and VLBI time series Ray et al 2008). Periodic errors arising from model differences between analysis centres (e.g.…”

“…Ray et al (2008) stacked multiple global station time series power spectra using the IGS operational data, with the aim of eliminating localised geophysical signals and highlighting common (global) higher order draconitic spikes emerging above the background noise. Ray et al (2008) found power at 1 cpy up to the 6th harmonic; however, as mentioned, these periods are not strictly harmonics of the solar period.…”