Robust Estimation Methods Using Factor Graphs in GNSS Applications

Achieving high-accuracy and robust navigation solutions is crucial in various domains, such as autonomous vehicles, aviation, and mobile devices. In this context, Global Navigation Satellite Systems (GNSS) play a pivotal role in modern navigation and positioning applications due to their capability of providing absolute position fixes. However, many target applications have strict safety and precision requirements, which standalone GNSS is unable to achieve in harsh environments such as urban scenarios, thus requiring improvements in terms of accuracy and robustness. Factor graphs have proven to be a powerful mathematical framework for modelling and solving complex estimation and optimization problems such as Simultaneous Localization and Mapping (SLAM). At its core, factor graphs represent relationships between variables using nodes and factors, where nodes correspond to variables of interest, while factors encode constraints or dependencies between these variables. By leveraging the graphical structure of the problem, factor graphs exploit sparsity and modularity to break down large-scale problems into smaller, more manageable components. Furthermore, these features allow for the seamless integration of additional constraint and measurement models to implement more advanced estimation techniques. Due to their increased flexibility, factor graphs have recently emerged as an alternative method for GNSS positioning with respect to traditional methods such as Extended Kalman Filter (EKF). Several algorithms can be found in literature that are proven to further increase the accuracy and reliability in harsh environments, implemented on top of the GNSS solution since due to the flexible structure of the factor graphs, it is possible to integrate other methods. In this thesis, two robust estimation methods called Switch Constraints (SC), and Gaussian Max-Mixtures (GMM) were implemented to mitigate the effects caused by the errors in urban environments. SC utilize switch functions that act like weighting constants that handle the erroneous data and forces their weight to be closer to zero if the data deviates from the optimal. GMM introduces bi-modal or multi-modal Gaussian distribution to help defining the characteristics of the erroneous data so that they can fit into the model better and provide better accuracy. Those two methods were implemented on MATLAB on top the already existing receiver structure, and experimental datasets were collected in an urban scenario, in Torino, near Politecnico di Torino to test the algorithms. The results have shown that the errors have been reduced thanks to the robust estimation methods of SC and GMM in urban environment, and they have been compared with the standalone factor graph framework.