Medium- and Long-Term Prediction of Polar Motion Using Weighted Least Squares Extrapolation and Vector Autoregressive Modeling

This article presents the application of weighted least squares (WLS) extrapolation and vector autoregressive (VAR) modeling in polar motion prediction. A piecewise weighting function is developed for the least squares (LS) adjustment in consideration of the effect of intervals between observation and prediction epochs on WLS extrapolation. Furthermore, the VAR technique is used to simultaneously model and predict the residuals of x_p, y_p pole coordinates for WLS misfit. The simultaneous predictions of x_p, y_p pole coordinates are subsequently computed by the combination of WLS extrapolation of harmonic models for the linear trend, Chandler and annual wobbles, and VAR stochastic prediction of the residuals (WLS+VAR). The 365-day-ahead x_p, y_p predictions are compared with those generated by LS extrapolation+univariate AR prediction and LS extrapolation+VAR modeling. It is shown that the x_p, y_p predictions based on WLS+VAR taking into consideration both the interval effect and correlation between x_p and y_p outperform those generated by two others. The accuracies of the x_p predictions are 13.97 mas, 18.47 mas, and 20.52 mas, respectively for the 150-, 270-, and 365-day horizon in terms of the mean absolute error statistics, 36%, 24.8%, and 33.5% higher than LS+AR, respectively. For the y_p predictions, the 150-, 270-, and 365-day accuracies are 15.41 mas, 21.17 mas, and 21.82 mas respectively, 27.4%, 11.9%, and 21.8% higher than LS+AR respectively. Moreover, the absolute differences of the WLS+VAR predictions and observations are smaller than the differences from LS+VAR and LS+AR, which is practically important to practical and scientific users, although the improvement in accuracies is no more than 10% relative to LS+VAR. The further comparison with the predictions submitted to the 1st Earth Orientation Parameters Prediction Comparison Campaign (1st EOP PCC) shows that while the accuracy of the predictions within 30 days is comparable with that by the most accurate prediction techniques including neural networks and LS+AR participating in the campaign for x_p, y_p pole coordinates, the accuracy of the predictions up to 365 days into the future are better than accuracies by the other techniques except best LS+AR used in the EOP PCC. It is therefore concluded that the medium- and long-term prediction accuracy of polar motion can be improved by modeling x_p, y_p pole coordinates together.