This PhD project, hosted within the EPSRC Centre for Doctoral Training in Quantum Technology Engineering at the University of Southampton, aims to advance levitated optomechanical technology for autonomous underwater vehicle (AUV) navigation in GPS-denied environments. The research focuses on developing a levitated gradiometer, a quantum sensor system comprising two or four levitated optomechanical sensors stabilized by optical interferometry for common-mode noise rejection. Levitated optomechanical systems are emerging as powerful quantum technologies for ultra-sensitive force measurements, with successful demonstrations in space but limited exploration in oceanic and underwater contexts. The project addresses the need for highly stable and precise sensing in environments where GNSS signals are unavailable, enabling reliable navigation for long-duration AUV missions. Beyond navigation, the sensor concept may be extended to geophysical applications, such as detecting small-scale density anomalies in the ocean and sub-seafloor, opening new avenues for environmental and resource exploration. The student will contribute to the design, modelling, and experimental realization of the prototype gradiometer, and investigate quantum-enhanced sensing for resilient Positioning, Navigation, and Timing (PNT) underwater. Key research challenges include sensor calibration, noise and disturbance rejection, and gravity-based map-matching techniques. The project is a collaboration between the School of Physics & Astronomy, the Southampton Marine & Maritime Institute, the National Oceanographic Centre, and Sonardyne. Substantial training in scientific, technical, and commercial skills is provided. Funding is competitive, with UK students eligible for a 4-year UKRI TechExpert stipend of approximately £31k per year; EU, Horizon Europe, and international students may receive studentships at the UKRI base rate, and overseas students with external funding are encouraged to apply. Applicants must hold at least a UK 2:1 honours degree or international equivalent. The university supports equality, diversity, and inclusivity, and welcomes part-time study applications. The application deadline is 31 July 2026 (international applicants: 31 March 2026).