A robust navigation system for underwater vehicles using an adaptive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"> <mml:msub> <mml:mi mathvariant="script">H</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> filter based

• A novel adaptive H ∞ –Variational Bayesian filter improves AUV navigation robustness. • The method adaptively estimates time-varying process and measurement noise. • Robustness is achieved under severe DVL outliers, including spikes and dropouts. • Experimental sea trials confirm up to 68% reduction in position error. • The integrated IMU/DVL/depth navigation framework offers practical and reliable performance for real-world missions. This paper presents an adaptive robust navigation framework for autonomous underwater vehicles (AUVs) that synergistically integrates H ∞ minimax optimization with Variational Bayesian inference. The proposed H ∞ -enhanced Variational Bayesian multiplicative error-state Kalman filter ( H ∞ -VBMAESKF) provides deterministic worst-case robustness bounds while enabling automatic adaptive noise estimation—capabilities that neither existing adaptive H ∞ methods (employing heuristic adaptation) nor pure Variational Bayesian approaches (lacking worst-case guarantees) provide simultaneously. The system fuses asynchronous multi-rate IMU, DVL, and depth sensor measurements, autonomously handling diverse DVL anomalies (velocity spikes, biases, dropouts, beam loss) without mission-specific tuning. Extensive sea trial validation compares performance against VB-MAESKF, Student’s t , and H ∞ -ESKF baselines. Under nominal conditions, H ∞ -VBMAESKF achieves 33.87 m position RMSE—representing 49.5%, 21.6%, and 79% improvements over the three baselines. The 79% improvement over H ∞ -ESKF conclusively validates that H ∞ robustness alone fails without adaptive noise estimation. Under systematic 5–15% DVL contamination, the method achieves 73.8–77.4% median error reduction with exceptional stability—only 20.6% error increase across contamination levels versus 83.2% (VB-MAESKF) and 48.5% ( H ∞ -ESKF). Consistency analysis shows 3.1% normalized innovation violation rate versus 6.5% (VB-MAESKF) and 15.2% ( H ∞ -ESKF), confirming superior uncertainty quantification. Operating in real-time (3.71 ms per iteration), the framework provides practical safety-critical navigation combining theoretical worst-case guarantees with automatic environmental adaptation.