Hybrid Tree Based Models for GNSS Position Error Estimation

This paper tackles GNSS position error estimation in challenging environments where reliable error bounds are required for real-time applications. While regression trees and random forests can model nonlinear relations between GNSS observables and position error, their accuracy is limited by coarse input partitioning. We introduce two hybrid models, RT-LLR and RF-LLR, which combine tree-based partitioning with local linear regression on lagged GNSS observables to perform piecewise linear modeling of spatial-temporal error dependencies. The methods are evaluated over 20 runs using RMSE of the x, y, and z position error components. The hybrids tie or outperform the baseline trees in about 75% of x-axis cases, 95% of y-axis cases, and 85% of z-axis cases, achieving relative RMSE reductions up to roughly 22% horizontally and 17% vertically, with comparable runtime. These results show that hybrid tree-linear models provide more accurate and stable GNSS error estimates, making them suitable for deployment in low-cost receivers and cooperative positioning systems.