Three-Corner Hat for the assessment of the uncertainty of non-linear residuals of space-geodetic time series in the context of terrestrial reference frame analysis

We discuss the application of the Three-Corner Hat (TCH) to time series of space-geodetic station position residuals with the purpose of characterizing the uncertainties of GPS, VLBI, SLR, DORIS for the International Terrestrial Reference Frame (ITRF) determination. Adopting simulations, we show that, in the absence of time-correlated errors, TCH is able to fully recover the nominal uncertainties of groups of observations whose intrinsic precisions are remarkably dissimilar to one another, as is the case for the space-geodetic techniques. When time-correlated errors are predominant, as it happens with GPS, TCH is affected by the increased variance of the observations and its estimates are positively biased. TCH applied to 16 ITRF co-located sites confirms that GPS, albeit affected by time-correlated errors, is the most precise of the space-geodetic techniques. GPS median uncertainties are 1.1, 1.2 and 2.8 mm, for the north, east and height component, respectively. VLBI performs particularly well in the horizontal component, the median uncertainties being $${\approx }2$$≈2 mm. The height component is $${\sim }3$$∼3 times larger than the GPS one. SLR and DORIS median uncertainties exceed by far the 7 mm level on all of the three components. Comparing TCH results with station position repeatabilities, we find that the two metrics are in striking agreement for VLBI and DORIS, but not for SLR and GPS. The inconsistencies between TCH and station repeatabilities for co-located GPS and SLR point to the presence of either specific station-dependent biases or low-quality co-locations. Scaling factors derived adopting the ratio between TCH and median formal errors on the positions suggest the station position covariances have to be up-scaled for VLBI, SLR, DORIS and down-scaled for GPS.