Fast and precise GNSS RTK positioning with ionosphere-constrained weighted least squares quadratic programming
Abstract
Achieving fast and precise real-time kinematic (RTK) positioning depends on effective carrier phase integer ambiguity resolution (IAR), yet ionospheric delays pose significant challenges. Traditional approaches often employ the ionosphere-weighted model, which requires complex variance component estimation and iterative optimization procedures that are sensitive to modeling assumptions and local ionospheric dynamics. To address these limitations, we propose a novel ionosphere-constrained model that transforms ionospheric correction into a bounded optimization problem by applying empirically derived inequality constraints to double-differenced (DD) ionospheric delays within a weighted least squares quadratic programming (QP) framework. This convex formulation guarantees global optimality, provides automatic anomaly detection through boundary convergence, and derives transparent, physically interpretable bounds from historical DD delay statistics as a function of baseline length. The QP framework conditionally activates when the unconstrained ionosphere-float solution violates empirical bounds, either guiding estimation toward reasonable interior solutions or preventing large outlier delays while remaining non-intrusive under benign conditions, thereby improving the precision of float solution and accelerating IAR. Experiments on an ultra-short baseline demonstrate that refining the DD ionospheric constraint significantly enhances the formal ambiguity success rates in case of full IAR, highlighting the critical role of precise constraint intervals. Validation using data from the Hong Kong Satellite Positioning Reference Station Network with baseline lengths ranging from a few meters to 50 km shows that our method improves the formal IAR success rate by 12% to 24% compared to the ionosphere-float model and by 5% to 15% compared to the ionosphere-weighted model, achieving near 100% for baselines up to 15 km. Additionally, the ionosphere-constrained model enhances the accuracy of the float solution through DD ionosphere inequality constraints, accelerates the convergence time of the float solution, and achieves fast IAR. Furthermore, our model improves positioning accuracy by over 20% compared to the ionosphere-weighted model, owing to its effective management of DD ionospheric constraints.
Xingyu Chen
Postdoctoral Fellow
Research interests include GNSS atmospheric delay modeling, precise positioning, and time and frequency transfer.
