Heteroskedasticity between GNSS time-series repeatabilities and noise magnitudes

In the analysis of GNSS time series, when the sampling frequency and time-series lengths are almost identical, it is possible to highlight a linear relationship between the series repeatabilities (i.e. WRMS) and noise magnitudes. In the literature, linear equations as a function of WRMSs allowed many researchers to estimate the noise magnitudes. However, this was built upon homoskedasticity. We experienced the higher WRMSs, the more erroneous analysis results using the noise magnitudes from the linear equations stated. We hence studied whether or not homoscedasticity clearly describes the modeling errors. To test that, we used the published results of GPS baseline components from the previous work in the literature and realized here that each component forms part of the totality. We introduced all baseline component results as a whole into statistical analysis to check heteroskedasticity. We established null and alternative hypotheses on the residuals which are homoscedastic (H0) or heteroskedastic (HA). We adopted both the Breusch-Pagan test and the Goldfeld-Quandt test to prove heteroskedasticity and obtained p-values for both methods. The p-value, which is the probability measure, equals to almost zero for both test methods, that is, we fail to accept the null hypothesis. Consequently, we can confidently state that the relationship between the WRMSs and the noise magnitudes is heteroskedastic.

Keywords: Noise magnitudes, repeatabilities, heteroskedasticity, time-series analysis