A practical methodology to scale velocity uncertainties derived from GNSS campaign time series

GNSS campaigns are still in use today especially for the monitoring of natural hazards such as landslides and local subsidence. Studying the velocity uncertainty of GNSS campaign deformation monitoring is a challenge among scientists cause the velocity error cannot always be characterized as pure white noise.  We test the velocity uncertainty of GNSS campaign measurements referring to the mathematical theory developed to find the velocity uncertainty of GNSS continuous coordinate time series. GPS coordinate time series have been downloaded from the archive of NASA JPL. The time series have been decimated to annual synthetic GNSS campaigns because researchers usually can handle GNSS campaigns once every year in three or more consecutive days. Using the continuous GNSS coordinate campaigns we estimated the spectral indices for the 30 IGS stations spread across the globe. Then using these spectral indices and the formulation given in Zhang et al.1997, Mao et al. 1999, Dixon et al. 2000, and Williams 2003 we have developed a practical methodology to estimate noise amplitudes and velocity errors for the data of synthetically derived annual GNSS campaigns. The methodology avoids large matrix computations and consumes only a little PC memory. The velocity error derived using the above-mentioned approach has been cross validated by the velocity error derived from the sample of annual GPS campaign time series constituted employing the continuous GPS time series. 10-12 synthetically derived independent GPS annual campaign time series were formed from the continuous data of each of the thirty stations we used from the IGS network. Then the velocity error has been computed as the inter-quartile range of the velocities derived from those of the annually sampled time series. The inter-quartile range values are comparable with the velocity errors computed using the methodology described in this study. The significancy of the differences were also tested referring to Wilcoxon's Signed Rank hypothesis testing.  The method has been found to be promising for the velocity error estimation of GNSS campaign measurements.