A graduated optimization framework for robust GNSS standard single point positioning in complex environments

Abstract Achieving high-precision positioning in complex environments remains a significant challenge for Global Navigation Satellite Systems (GNSSs). In such scenarios, obstacles including high-rise buildings, overpasses, mountains, and vegetation induce signal reflection and diffraction and can severely obstruct GNSS signals. These effects intensify multipath and non-line-of-sight propagation errors, producing numerous anomalous observations and severely degrading GNSS positioning accuracy. Current robust estimation methods for handling outliers are susceptible to being trapped in local optima, potentially resulting in unreasonable weight assignments when the outlier ratio is high. To address this challenge, this paper introduces a Graduated Optimized Robust Estimation Algorithm for GNSS standard single point positioning (SPP). The method employs a graduated non-convexity Cauchy cost function, which progressively enhances the robustness of the cost function by adjusting its non-convexity. This approach effectively mitigates the impact of outliers, preventing premature convergence of the estimator to local solutions. Static simulation experiments in natural canyon environments and kinematic field tests in complex urban settings were conducted to comprehensively evaluate the performance of the proposed method. Both static simulations and kinematic field tests demonstrate that the employed algorithm achieves robust performance in SPP mode. In the static dataset, compared to non-robust and traditional robust estimation methods, the proposed method improves positioning accuracy by at least 30% in the East ( E ) component, 37% in the North ( N ) component, and 15% in the Up ( U ) component. In the kinematic dataset, the corresponding improvements are at least 40% ( E ), 33% ( N ), and 27% ( U ). These results indicate that the proposed method exhibits substantial robustness and significantly improves both the positioning performance and reliability of GNSS in challenging environments.