PhD Studentship: Constraint-Aware Data-Driven GNSS Pseudorange Correction Using Multi-Objective Optimisation

Project details:

Global Navigation Satellite Systems (GNSS) support a wide range of applications, from smartphone navigation to autonomous vehicles. The global GNSS market is substantial, with billions of consumer devices relying on accurate positioning daily. Improving GNSS accuracy, especially for low-cost, mass-market receivers, therefore has significant economic and societal impact. However, GNSS positioning is highly susceptible to errors from atmospheric distortions, multipath effects, and receiver noise. Recent advances in deep learning have shown that data-driven pseudorange correction can significantly enhance GNSS positioning. For example, PrNet learns to correct pseudoranges using features such as raw pseudoranges, signal-to-noise ratio, elevation and azimuth angles, and preliminary receiver positions. Despite these advances, current literature provides little guidance on how to systematically incorporate domain-specific constraints into the training and inference of pseudorange correction models. Enforcing such constraints offers substantial potential benefits, including faster convergence, improved generalisation, and reduced overfitting. At the same time, these benefits come with trade-offs, such as a potential reduction in model flexibility and a risk of model misspecification if constraints are invalid.

This project will focus on investigating constraint-aware pseudorange correction through multiobjective optimisation. The research will explore multiple classes of constraints that will be embedded as objectives: 

1. Internal pseudorange consistency: ensuring that corrected pseudoranges correspond to physically consistent receiver positions across all satellites.
2. Temporal smoothness: enforcing corrections that are consistent with expected receiver dynamics, such as velocity continuity or GNSS-derived velocity estimates.
3. Sensor fusion consistency: aligning pseudorange corrections with complementary sensors, such as inertial navigation systems.
4. Map-based constraints: enforcing that corrected positions comply with known map constraints, e.g., restricting ground vehicles to the Earth’s surface.
5. Satellite homogeneity: for example, assuming uniform satellite behavior, or applying consistent correction models across inter- and intra-satellite interactions. 

The use of multi-objective optimisation will enable systematic exploration of trade-offs between different classes of constraints, which would not be possible with conventional constrained optimisation. This approach will provide insight into how constraints interact, how they affect positioning accuracy and robustness, and how best to balance competing objectives. We will also investigate architectural design strategies that implicitly encourage constraint adherence, such as averaging features across satellites. In addition, data augmentation methods to improve generalisation will be explored, for example through structured transformations such as permuting satellite IDs to enforce homogeneity. The project may also investigate how corrections can be integrated into GNSS-IMU fusion frameworks, allowing the use of low-cost sensor outputs as proxy labels for large-scale, low-cost training. This approach has the potential to reduce reliance on expensive ground truth data while improving the performance of tightly coupled navigation systems. 

The project will benefit from an essential industrial collaboration with Spirent Communications plc, who will offer access to simulation tools, as well as technical and scientific support, thereby ensuring alignment with practical GNSS testing requirements.

Please direct project specific enquiries to: Johan Wahlstrom (j.wahlstrom@exeter.ac.uk) Please ensure you read the entry requirements for the potential programme you are applying for. To Apply for this project please click on the following link - https://www.exeter.ac.uk/study/funding/award/?id=5733

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