Chameleonic noise in GPS position series: what is the true color of the GPS error spectra?

Abstract:

Chameleonic: readily changing color or other attributes.

Chameleon: a lizard that changes skin color to match what surrounds it so that it cannot be seen.

The power spectrum of decadal long GPS residual position time series (trend, periodic and offset terms removed) is typically represented by a combination of nearly flicker (pink) noise at long periods and white noise at short periods. Here, using real and synthetic GPS position series, we show how the power spectrum is seriously altered by the estimation of position offsets that populate the GPS series. The estimated position offsets absorb a significant portion of the power spectrum at periods longer than the time separation between their epochs.

The resulting apparent spectrum decays at the longest periods and this implies that:

• the estimated content of colored noise is biased low and can even apparently change its color towards whiter noise, i.e. the true noise color is not observable due to the estimated offsets,
• the red (random walk) noise , most probably present in the series in small quantity, becomes almost undetectable even if long series are used,
• objectively, the pink (flicker) noise is not the best color noise to represent the apparent spectrum in long series containing offsets,
• the colored noise content cannot be compared between series with different sets of offsets.

These findings need to be considered when comparing the noise levels between series from different solutions, networks or monuments. In particular, and contrary to a recently published recommendation, station operators should make every effort to avoid adding new offsets into their station time series if reliable velocity estimates and uncertainties are expected.