Signal Processing Techniques for GNSS Positioning and Tracking

Accurate and robust positioning remains a fundamental challenge in Global Navigation Satellite System (GNSS) navigation, especially in weak-signal, high-dynamics, interference-prone, and model-mismatched environments. Conventional two-step positioning approaches and Kalman Filter (KF)-based methods rely heavily on accurate observation models and state-space dynamics, which often degrade under practical imperfections such as multipath, interference, and structural modeling errors. This dissertation addresses these challenges by advancing the Direct Position Estimation (DPE) framework, developing hybrid learning-based dynamics models, and establishing theoretical performance bounds under Bayesian model misspecification.
First, this thesis systematically extends the DPE framework through a series of advanced techniques and applications. Precise Direct Position Estimation (PDPE) and Single-Difference Direct Position Estimation (SD-DPE) are proposed to incorporate carrier-phase information and mitigate atmospheric errors, enabling high-precision positioning within the DPE paradigm. The inherent robustness of DPE to multipath is analytically and experimentally investigated, revealing its advantage stemming from early-stage multi-satellite information fusion in the signal domain. To enhance robustness against intentional and unintentional interference, a Direct Position Estimation with Robust Interference Mitigation (DPE-RIM) framework is developed. Furthermore, lunar DPE is explored as an extreme application, leveraging the high-sensitivity property of DPE receivers to demonstrate their feasibility for lunar Positioning, Navigation, and Timing (PNT) under ultra-weak signal conditions. To address the computational burden of DPE, a neural-network-based optimization strategy is introduced to predict Cross-Ambiguity Function (CAF) values during the solution search stage, significantly reducing complexity and facilitating practical deployment.
Second, this dissertation investigates dynamics modeling and correction under uncertainty through the Augmented Physics-Based Model (APBM). Multiple learning paradigms are proposed to accommodate varying label availability and system variability within a state-space filtering framework. The APBM is validated across a range of complex systems, including chaotic systems, partially known systems, higher-order Markov systems, and high-dynamics systems. Its effectiveness is further demonstrated in real-world high-dynamics drone navigation scenarios, where it successfully learns time-varying dynamics and improves positioning accuracy, particularly in regions with rapidly changing motion patterns. This framework establishes a principled, state-space–oriented approach for integrating Artificial Intelligence (AI) with Bayesian filtering.
Finally, this thesis provides a comprehensive theoretical investigation of Bayesian performance bounds under model misspecification. Two mismatched Bayesian bounds, namely the Conditional Misspecified Bayesian Cramér–Rao Bound (CMBCRB) and the Misspecified Bayesian Cramér–Rao Bound (MBCRB), are derived based on conditional and unconditional definitions of the pseudotrue parameter. The corresponding classes of mismatched estimators and the tightness properties of these bounds are analyzed and validated in both linear Gaussian and nonlinear non-Gaussian systems. These results establish principled benchmarks for performance evaluation in Bayesian estimation problems subject to model mismatch.
Overall, this dissertation advances the theory and practice of GNSS positioning by jointly addressing signal-domain processing, hybrid model learning, and theoretical performance limits, providing a unified framework for accurate and robust navigation in challenging environments.