ROTI-based statistical regression models for GNSS precise point positioning errors associated with ionospheric plasma irregularities

Haoyang Jia, Zhe Yang, Bofeng Li

Global Navigation Satellite System (GNSS) signals are susceptible to ionospheric plasma irregularities and associated scintillations, causing large deviations in the positioning solutions. This study aims to develop statistical regression models to estimate kinematic three-dimensional (3D) precise point positioning errors associated with ionospheric plasma irregularities based on the Rate Of Total electron content Index (ROTI). By assuming that the positioning errors follow the Laplace distribution, we perform nonlinear regression using the Levenberg–Marquardt algorithm on a collection of experimental data from 700 + Trimble receivers deployed in the NOAA Continuously Operating Reference Stations (CORS) Network. Three ROTI-based regression models are identified by curve fitting with nonlinear functions, i.e., third-degree polynomial (Poly3), two-term exponential (Exp2) and two-term power (Power2) models. A goodness-of-fit test suggests the models fit well into the relationship between ROTI and the 3D positioning errors with the adjusted coefficient of determination above 0.97. The regression models are subsequently employed to predict the 3D positioning errors with a given set of ROTI. Evaluation analysis using the observations from four CORS networks across different geographical regions indicate that the Exp2 model demonstrates encouraging prediction performance, with bias and root mean square error within − 0.14 m and 0.34 m, respectively, and the correct prediction ratio consistently surpasses 60.3%. The ROTI-based regression models have great potential in predictions of the degradation in GNSS positioning due to ionospheric space weather effects.