Open-Source Factor Graph Optimization Package for GNSS: Examples and Applications

State estimation methods using factor graph optimization (FGO) have garnered significant attention in global navigation satellite system (GNSS) research. FGO exhibits superior estimation accuracy compared with traditional state estimation methods that rely on least-squares or Kalman filters. However, only a few FGO libraries are specialized for GNSS observations. This paper introduces an open-source GNSS FGO package named gtsam\_gnss, which has a simple structure and can be easily applied to GNSS research and development. This package separates the preprocessing of GNSS observations from factor optimization. Moreover, it describes the error function of the GNSS factor in a straightforward manner, allowing for general-purpose inputs. This design facilitates the transition from ordinary least-squares-based positioning to FGO and supports user-specific GNSS research. In addition, gtsam\_gnss includes analytical examples involving various factors using GNSS data in real urban environments. This paper presents three application examples: the use of a robust error model, estimation of integer ambiguity in the carrier phase, and combination of GNSS and inertial measurements from smartphones. The proposed framework demonstrates excellent state estimation performance across all use cases.