GNSS receiver state estimation via Factor Graph Optimization

The data from a GNSS receiver mounted on a slow-moving vehicle can be processed to reconstruct the trajectory and state of the vehicle. With the same receiver and the same set of data, the accuracy of the reconstruction is strongly dependent on the processing technique. The simplest and most immediate technique is Least-Squares Estimation (LSE). Some well-established techniques are Kalman Filtering (KF) and its nonlinear version, Extended Kalman Filtering (EKF), together with smoothing approaches such as the Rauch–Tung–Striebel (RTS) smoother, which constitute the basis of some of the most influential algorithms in navigation. Factor Graph Optimization (FGO) is a probabilistic inference and nonlinear optimization framework that has found successful application in navigation in recent years; one of its main strengths is the flexibility with which different sources of information can be integrated into a single estimation problem. This work shows how an FGO based pipeline, which jointly optimizes the whole trajectory and downweights outlier measurements through a robust loss function, can improve GNSS state estimation with respect to LSE, EKF, and EKF+RTS. The four techniques are applied to real-world data collected by the author with a receiver mounted on a moving cart, processed in MATLAB, with the FGO solution implemented using the GTSAM library. An RTK-based ground truth, obtained through differential processing against the reference station PADO00ITA, is used to directly assess the accuracy of the four techniques. The residuals produced by each technique are also analyzed as a complementary, ground-truth-independent measure of internal consistency. FGO achieves the lowest RMS 3D error (3.45 m, against 4.92 m for EKF+RTS, 6.05 m for the EKF, and 15.46 m for LSE), the best agreement of the residuals with the assumed noise model, and the smallest degradation in the sections affected by multipath, with no error above 7.4 m. All the techniques, however, report an overconfident position covariance, and FGO the most, which highlights the importance of modeling time-correlated errors for a realistic uncertainty estimate.