A technique to reduce the edge effect in least squares extrapolation for enhanced Earth orientation prediction

Abstract

A well-known property of the classical least squares (LS) extrapolation is that a fit is best in the middle of the time span of observed data, but worse near the beginning and end of the time span. This phenomenon is called the edge effect in data processing. The goal of this work is to reduce the edge effect to improve predictions of the Earth rotation parameters (ERP), which comprise the Earth’s polar motion and rotation angle (the difference between the smoothed principal form of universal time UT1 and the coordinated universal time UTC) because a best LS fitting near the end of the data used is better for extrapolation. We first use the LS extrapolation for models consisting of one polynomial and two sinusoids in combination with an autoregressive (AR) technique to extend the observed time series forward. We then re-estimate the LS extrapolation model from the extended time series to reduce the edge-effect. ERP predictions are subsequently generated by combining of the edge effect reduced LS extrapolation and AR technique, denoted as ERLS + AR. Through an example, we demonstrate that the edge-effect in the observed data fitting can be reduced by re-estimating the LS extrapolation model with the extended time series. To validate the ERLS + AR method, we calculate the ERP predictions up to 365 days into the future year-by-year for the 4-year period from 2014 to 2017 using the data from the previous 8 years. The results show that the accuracy of the short-term predictions obtained by the ERLS + AR method is comparable with that achieved by the LS + AR approach in terms of the mean absolute error (MAE). However, an accuracy improvement is found mostly for long-term predictions based on the ERLS + AR method. The MAE for the UT1 ? UTC and polar motion predictions can decrease by approximately 15% to 20%, respectively. It is therefore suggested embedding the ERLS extrapolation algorithm into the existing ERP prediction procedure.