Research on ultra-short-term prediction of polar motion using least square and spatial attention mechanism model

This study proposes a novel hybrid model integrating least squares (LS) with a spatial attention mechanism (SAM) for 1–10 days polar motion prediction. The LS method primarily predicts principal components, while residual sequences are transformed into image data via Gramian angular field (GAF) representation before being processed by a neural network to forecast future residuals. Three basic sequences with different lengths of 6 a, 10 a, and 14 a are selected as the basic data of this LS + SAM. A total of 400 issues are predicted, with prediction data update at 1-day intervals per issue. The results showed that the mean absolute error (MAE) of PMX and PMY were 0.346–3.319 mas and 0.333–2.113 mas for three different length base sequences, respectively. Notably, predictions based on the 10-year sequence exhibited superior accuracy compared to the other intervals. Meanwhile, comparative analysis with the conventional LS + AR model revealed comparable performance in absolute error (AE), indicating that GAF-based image transformation effectively preserves residual characteristics while demonstrating the feasibility of two-dimensional image approaches for polar motion prediction.