Factor Graph Based Precise Point Positioning (PPP) Framework

Kurzfassung

This work presents a utilization of the factor graph optimization approach on Precise Point Positioning (PPP) navigation. While PPP solutions already achieves high precision (~ 20 cm), their performance can degrade under multiple simultaneous faults or sensor degradation. Here, we focus on enhancing overall precision and availability by leveraging a resilient factor graph formulation, integrating SSRZ/HAS corrections, and possibly combining data from multiple sensors. Our approach systematically compares three methods for state estimation: (A) recursive filtering, (B) smoothing, and (C) batch least squares. These methods differ primarily in how past and current information are incorporated to estimate the integer and real-valued parameters critical to PPP. By applying these estimation strategies within a simple, controlled simulation, we highlight their relative strengths and weaknesses in terms of accuracy, computational load, and robustness to sensor or measurement faults. In this study, we evaluate an extensive performance evaluation via Monte Carlo simulation. The metrics considered include positioning performance, solution availability and integrity. We further discuss the implications of these findings for a broader inertial stack, as part of an ongoing effort to develop resilient navigation solutions for autonomous vessel systems. Preliminary conclusions suggest that hybrid solutions—where real-time filtering is complemented by periodic smoothing or batch processing—may offer the most advantageous balance of robustness and availability. This work represents the initial results from factor graph optimization on PPP systems, with plans to validate the proposed methods using real-world datasets in a subsequent journal publication. By unifying PPP estimation within a factor graph, we aim to advance fault-tolerant precision and availability in next-generation navigation systems.