Combined smoothing method and its use in combining Earth orientation parameters measured by space techniques

Abstract

The new combined method of smoothing observational data, being a generalization of the Whittaker-Robinson-Vondrak method based on probability, is designed. Its objective is to remove the high-frequency noise present in the observations of an (analytically unknown) time function and its first derivatives. The method consists in finding a weighted compromise among three different conditions: smoothness of the searched curve, its fidelity to the observed function values and its fidelity to the observed first time derivatives. The method assumes that the observations are distributed non-uniformly, with different uncertainties, and that the epochs of both input series containing the observed function values and first derivatives are not identical. Its possibilities are demonstrated on combining both simulated data and the Earth orientation parameters observed by different space techniques: Very Long Baseline Interferometry and Global Positioning System, namely the Universal Time/length of day changes and polar motion/polar motion rate.