Evaluation of Temporally Correlated Noise in Global Navigation Satellite System Time Series: Geodetic Monument Performance

Abstract

Estimates of background noise of Global Positioning System-derived time series of positions for 740 sites in the western United States are examined. These data consist of daily epochs of three components of displacements that are at least 9.75 years long within the interval between 2000 and 2018. We find that these time series have significant temporal correlations that could be represented as a combination of white, flicker, random-walk, and band-pass filtered noise. From this noise model, two other metrics are computed: the root-mean-square of seasonal noise, that is, the integrated power spectrum between 0.5 and 2 cycles per year, and the standard error in position rate for a 10-year-long time series. These two metrics are used to evaluate potential correlations with different geographic regions and with different methods of construction of monuments used to attach the Global Positioning System antenna to the Earth's surface. The sites with the lowest noise, both in terms of rate error and seasonal root-mean-square, are located in semiarid regions east of the rain shadow provided by the Cascade and Sierra Nevada mountain ranges. In addition, according to statistical rank tests, monuments known as drilled-braced monuments perform 30% to 50% better than other monument types (buildings, boreholes, piers, etc.) in terms of having smaller rate errors and lower seasonal noise.