Noise Filtering Augmentation of the Helmert Transformation for the Mapping of GNSS-Derived Position Time Series to a Target Frame

Abstract

The generation of position time series in geodetic networks is often based on the successive forward implementation of the Helmert transformation (HT) to daily/weekly solutions using the transformation parameters obtained from a separate least-squares adjustment over a selected set of reference stations. An overlooked problem with this approach is that the noise of the daily/weekly solutions is fully absorbed into the transformed station positions, or even amplified if we consider the additional uncertainty of the estimated Helmert parameters. Its filtering is therefore a desirable task which could enhance the geophysical content of geodetic time series to be analyzed in a global secular frame. To accommodate the need for such filtering, we present in this paper an epoch-wise stacking approach for the HT-based alignment of a series of daily/weekly frames to a common secular frame via an integrated estimation process. The resulting transformation formulae differ from the classic HT solution in terms of Kalman-like corrections, and they lead to an improved solution in the sense of minimizing the error variances of the transformed positions in the target frame.