Hybrid Filtering Technique for Accurate GNSS State Estimation

The Global Navigation Satellite System (GNSS) is extensively utilized in various applications that require triangulation solutions for positioning, navigation, and timing (PNT). These solutions are obtained by solving state estimates, traditionally using methods like weighted least squares (WLS) and Kalman Filters (KF). While these conventional approaches are foundational, they frequently encounter challenges related to robustness, particularly the necessity for precise noise statistics and the reliance on potentially accurate prior assumptions. This paper introduces a hybrid approach to GNSS state estimation, which integrates deep neural networks (DNNs) with the KF framework, employing the maximum likelihood principle for unsupervised training. Our methodology combines the strengths of DNNs with conventional KF techniques, leveraging established model-based priors while enabling flexible, data-driven modifications. We parameterize components of the Extended Kalman Filter (EKF) using neural networks, training them with a probabilistically informed maximum likelihood loss function and backpropagation. We demonstrate that this hybrid method outperforms classical algorithms both in terms of accuracy and flexibility for easier implementation, showing better than 30% improvement in the variance of the horizontal position for the simulated as well as the real-world dynamic receiver dataset. For the real-world dynamic dataset, our method also provides a better fit to the measurements than the classical algorithms.