Measurement-Interval Dynamically Iterated Kalman Filtering for Tightly Coupled INS/USBL Navigation of AUVs Under Large Initial Errors

Reliable navigation is fundamental to the operation of autonomous underwater vehicles (AUVs) in exploration, environmental monitoring, and so on. Tightly coupled inertial navigation system/ultra-short baseline (INS/USBL) integration provides continuous and drift-constrained navigation for AUVs. However, large initial errors can introduce substantial linearization errors, degrading estimation accuracy and potentially causing filter divergence. The iterated Extended Kalman filter (IEKF) can improve the accuracy of measurement-model linearization through repeated measurement updates, but cannot correct the errors accumulated during nonlinear state propagation between consecutive measurements. To address this limitation, a measurement-interval dynamically iterated Extended Kalman filter (MI-DIEKF) is proposed. After each measurement update, one-step backward smoothing is applied only to the interval-start state. The buffered IMU measurements are then replayed from this updated reference to reconstruct and relinearize the inertial propagation trajectory. A tightly coupled INS/USBL navigation model is developed within this framework. Two-hundred independent Monte Carlo simulations showed that, compared with IEKF, MI-DIEKF reduced the mean overall position and attitude RMSEs by 34.3% and 21.8%, respectively, while achieving earlier convergence. A surface-vessel-based field experiment further verified its feasibility using real inertial and underwater acoustic measurements.