Modified Sidereal Filtering – Tool for the Analysis of High-Rate GPS Coordinate Time Series

Abstract

In the error budget of high-rate GPS coordinate time series the geometry satellite – antenna plays a significant role, by means of which the repeat time interval of the identical configuration of GPS satellites must be determined. Instead of the sidereal time interval a more detailed investigation yields a smaller value, namely the so-called “modified sidereal time interval”. The exact value depends on an average of the orbit repeat period of satellites under consideration.

The recurrence period can be determined also empirically by the cross covariance function of time series of consecutive days. For the example noted above the diminution w.r.t. the sidereal time interval amounts to 10-14 seconds, and within this range being equal for position and height.

The difference reduces the root mean square error in the time series to up to half of the original value. With respect to the sidereal time interval the modified one reduces the rms again by a few percent. In the spectral domain the improvement can be seen within the range of 50 to 500 sec.

The spectrum of displacements due to waves caused by the Sumatra earthquake of Dec 26, 2004 could be determined, using 1 Hz GPS data covering Central Europe. With respect to the ground truth given by the STS-2 seismometer the agreement in sharp lines is very satisfying, particularly for the horizontal components.