Underwater real-time inertial measurement unit drift compensation using a multi-sensor velocity estimation sensor system with hybrid velocity sensor fusion

Abstract

Accurate underwater velocity estimation remains a fundamental challenge in marine robotics due to the inherent limitations of conventional navigation technologies in GPS-denied environments. Doppler Velocity Logs (DVLs), while precise, are expensive, bulky, and consume power exceeding5 W, making them unsuitable for compact or energy-constrained micro unmanned underwater vehicles (UUVs). Inertial Measurement Units (IMUs), on the other hand, are bulky and/or expensive which accumulate drift errors over time, severely degrading trajectory accuracy during long-duration missions. Bridging this gap requires the development of a novel sensor system that is compact, low-power, and capable of directly measuring three-dimensional velocity while simultaneously complementing the IMU for drift mitigation. This thesis addresses this need by presenting the design, modeling, fabrication, calibration, validation, and integration of a 3Dvelocity sensor with hybrid sensor fusion for real-time drift compensation. The first part of the thesis introduces a Hybrid Flexible Velocity Sensor (HyFLEX-Vel Sensor)that emulates aquatic lateral-line systems using a Rosetta-shaped arrangement of flex sensors combined with differential pressure sensing. The sensor converts hydrodynamic loading into measurable resistance variations, which are subsequently processed through quarter-bridge circuits and mapped into forces and velocities using Euler–Bernoulli beam theory and quadratic drag relationships. Mathematical modeling provides the complete chain from resistance voltage force velocity, ensuring that the physical principles underlying the sensor are transparent and reproducible. Data-driven regression techniques, including Ridge regression, and robust RANSAC fitting, are incorporated to improve the mapping accuracy and reduce sensitivity to outliers. To capture vertical flow components, dual Melexis MLX90809 pressure sensors are integrated in a diametrically opposed configuration, thereby enabling simultaneous differential pressure measurement for improved resolution of the z-axis velocity component. Fabrication of the sensor leverages CAD-driven design and additive manufacturing, using a3D-printed resin housing with waterproofing features optimized for hydrodynamic stability. A systematic calibration protocol was developed that includes offset detection, directional sensitivity mapping, and controlled velocity profiling in a laboratory water-tank facility. Experimental results demonstrate strong linearity (R2 > 0.95), low mean absolute error, and repeatable performance across multiple trials. The final prototype operates below 0.5 W, significantly outperforming expensive DVLs in terms of energy efficiency while maintaining multi-directional robustness. These findings establish the proposed sensor as a low-cost and scalable alternative for micro-UUVs. The second part of the thesis focuses on real-time Kalman fusion of the sensor with an IMU to overcome drift accumulation and achieve trajectory-level accuracy. A Hybrid Flexible Velocity Sensor–Based Kalman Framework (HyFLEX-Vel-KF) that combines physics-based hydrodynamics ensing with stochastic state estimation is developed. The resulting force measurements are mapped to velocity through a calibrated quadratic drag model and incorporated as pseudo-measurements within a Kalman filtering framework. A complete stochastic state-space formulation is derived, including process and measurement noise characterization, covariance propagation, and observability analysis. The proposed approach enforces physically meaningful constraints on velocity evolution, thereby bounding drift accumulation inherent in inertial-only systems. Experimental validation demonstrates that the proposed HyFLEX-Vel-KF framework reduces velocity RMSE from 1.8072 m/s (IMU-only) to 0.1138 m/s, corresponding to an improvement of approximately 93.7%, while reducing drift rate by 1.0967 m/s/min to 0.0402 m/s/min magnitude which is 96.3%. Finally, the total path error was reduced from 182.872 m to 8.361 m, a 95.4%improvement. Covariance analysis confirms bounded error propagation, and normalized estimation error squared (NEES) evaluation remains within theoretical confidence bounds, indicating statistical consistency. Monte Carlo validation further confirms robustness under parameter variations and measurement noise. These tests show that the fused system maintains bounded error growth over extended missions, positioning it as a promising technology for autonomous navigation in cluttered, shallow, or GPS-denied underwater environments. The contributions of this thesis are fourfold: (i) the design and fabrication of a novel bioinspired 3D velocity sensor (HyFLEX-Vel) based on a Rosetta-shaped flex array with pressure sensing, (ii) the derivation of a rigorous mathematical framework linking sensor outputs to velocity components through drag-based modeling and regression analysis, (iii) the development and validation of a comprehensive calibration and testing protocol demonstrating robust multidirectional velocity measurement in laboratory environments, and (iv) the implementation of a hybrid fusion framework (HyFLEX-Vel-KF) with IMU data for drift compensation and trajectory optimization. Collectively, these efforts establish both theoretical rigor and experimental feasibility, underscoring the novelty of this research. In conclusion, the thesis advances the state of the art in underwater navigation by providing a compact, low-power, and mathematically grounded sensor solution that addresses the dual limitations of existing DVL and IMU technologies. The fusion-enabled system offers improved reliability for autonomous guidance, navigation, and control (GNC) of micro-UUVs and opens new pathways for future exploration, including long-duration missions, open-water deployments, and intelligent adaptive navigation. Beyond marine robotics, the sensing and fusion principles developed here may be extended to other fluidic environments, thereby broadening the impact of this research on environmental monitoring, marine systems, and autonomous robotic platforms. The results presented in this work lay the foundation for a new class of underwater velocity sensing technologies capable of supporting the next generation of resilient and intelligent micro-UUVs.