Comparative Analysis of Higher‐Order Ionospheric Delay on PPP Long‐Term Coordinate Time Series and Residual Modeling Using Horizontal Gradients and RINEX Data

Abstract Higher‐order ionospheric corrections, including second‐ and third‐order effects and signal bending, are essential for improving Global Navigation Satellite System (GNSS) time series accuracy. However, their influence on long‐term Precise Point Positioning (PPP) time series, particularly signal bending, remains underexplored. Most studies rely on Global Ionosphere Maps (GIMs) for second‐order delay corrections due to the complexity of RINEX‐based inversions. Analyzing data from 37 International GNSS Service stations (2009–2020), we found that higher‐order ionospheric effects predominantly impact the North component of mid‐ and low‐latitude stations. Second‐ and third‐order delays contribute 50% and 20% to annual and semi‐annual amplitudes, respectively, while signal bending accounts for 5% and 2%. Additionally, signals traveling along the magnetic field direction induce phase delays, with equatorial regions experiencing more frequent and intense ionospheric activity. This leads to maximum horizontal velocity impacts of 0.45 mm/yr at the equator and a distinct southern trend at mid‐ and low‐latitudes. GIM‐based corrections increase seasonal signal amplitudes and root mean square error (RMSE) at some stations due to discrepancies with RINEX‐based corrections, which generate higher‐order ionospheric residuals. These residuals contribute 48.6% of the RMSE in RINEX‐based corrections, surpassing the 39.8% from second‐ and third‐order delays. To address this, we propose a GIM‐based residual model incorporating horizontal gradients, reducing RMSE by 48%, 26%, and 52% for the East, North, and Up components, respectively. Monthly or quarterly gradient updates during quiet ionospheric periods ensure precise corrections, enhancing GNSS time series and coordinate system accuracy.