"Drift-Compensated UUV Velocity and Trajectory Estimation Using Hybrid Multi-Sensor Fusion"

"Inertial velocity estimation in underwater environments is fundamentally limited by unbounded drift arising from bias integration and lack of external references. This paper presents a Hybrid Flexible Velocity Sensor\u2013Based Kalman Framework (HyFLEX-Vel-KF) that combines physics-based hydrodynamic sensing with stochastic state estimation. A hybrid flexible sensing architecture, denoted as the HyFLEX-Vel sensor, is developed to reconstruct flow-induced forces using a tri-directional flex rosette and pressure sensing element. 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. The proposed framework bridges physical sensing and optimal estimation, offering a practical and scalable solution for underwater navigation in GPS-denied environments."