Enhancing Precise Navigation with Factor Graphs for Robust State Estimation

Kurzfassung

This work presents a utilization of the factor graph optimization approach on Precise Point Positioning (PPP) navigation in challenging, fault-prone environments. While PPP solutions already achieve high precision (~20 cm), their performance can degrade under multiple simultaneous faults, sensor degradation and non-line-of-sight (NLOS) signal disruptions. Such conditions can lead to solution instability, large biases, or complete outages. Here, we focus on enhancing overall precision, integrity, and availability by leveraging a resilient factor graph formulation that supports both sliding-window (real-time) and full-batch operation, integrating SSR/HAS corrections and 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, all within a unified factor-graph representation. In this study, we perform an extensive performance evaluation via Monte Carlo simulation. The metrics considered include positioning performance, solution availability, and integrity. The factor-graph-based solution demonstrates substantially lower RMSE than EKF, and RTS baselines, with reductions on the order of 40–60% in both horizontal and vertical components, indicating clear benefits in this stage. We further discuss the implications of these findings for a broader inertial and multi-sensor stack, as part of an ongoing effort to develop resilient navigation solutions for autonomous systems. In particular, we emphasize factor graph based PPP both as a state of the art ground truth estimator (via large batch windows) and as a powerful real-time processor (via fixed-lag, sliding-window inference), against which low-latency navigation solutions can be benchmarked. 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 initial results from factor graph optimization on PPP systems, with plans to validate the proposed methods using representative real-world datasets in a subsequent journal publication. By unifying PPP estimation within a factor graph, we aim to advance fault-tolerant, near–ground truth precision and high-availability performance in next-generation navigation systems.