GPS position time-series analysis based on asymptotic normality of M-estimation

The efficacy of robust M-estimators is a well-known issue when dealing with observational blunders. When the number of observations is considerably large—long time series for instance—one can take advantage of the asymptotic normality of the M-estimation and compute reasonable estimates for the unknown parameters of interest. A few leading M-estimators have been employed to identify the most likely functional model for GPS coordinate time series. This includes the simultaneous detection of periodic patterns and offsets in the GPS time series. Estimates of white noise, flicker noise, and random walk noise components are also achieved using the robust M-estimators of (co)variance components, developed in the framework of the least-squares variance component estimation (LS-VCE) theory. The method allows one to compute confidence interval for the (co)variance components in asymptotic sense. Simulated time series using white noise plus flicker noise show that the estimates of random walk noise fluctuate more than those of flicker noise for different M-estimators. This is because random walk noise is not an appropriate noise structure for the series. The same phenomenon is observed using the results of real GPS time series, which implies that the combination of white plus flicker noise is well described for GPS time series. Some of the estimated noise components of LS-VCE differ significantly from those of other M- estimators. This reveals that there are a large number of outliers in the series. This conclusion is also affirmed by performing the statistical tests, which detect (large) parts of the outliers but can also leave parts to be undetected.