As a core technology for autonomous navigation technology, inertial navigation offers high disturbance robustness as well as low observability. It plays a crucial role in various domains, including underwater vehicle operations. The accuracy of the inertial navigation calculation determines the precision of underwater navigation and positioning. However, owing to the non-uniformity of the gravitational field distribution of the Earth and the influence of component errors, the performance of inertial navigation degrades over long-term operation as it is influenced by the gravitational field of the Earth. Conventional inertial navigation replaces the actual gravitational field with an idealized normal gravitational field for computational simplicity. However, in complex underwater environments, such gravity-modeling approximations compromise overall solution accuracy. This study investigates the application of underwater gravity compensation in inertial navigation and examines its comprehensive influence on navigation performance, including compensation algorithms based on the spherical harmonic function model of the gravity field and gravity compensation methods for long-duration inertial navigation based on attitude damping. Simulation and experimental results demonstrated that the use of the gravity compensation method with attitude damping significantly improved the navigation solution accuracy of low-speed and long-endurance carriers. The final on-board measurement experiment results show that by adopting attitude damping for gravity compensation, the latitude accuracy of inertial navigation will increase by more than 10%, and the longitude accuracy will increase by over 60%. These findings provide theoretical support for the optimal design of inertial navigation systems and offer practical guidance for implementing gravity compensation techniques in engineering applications.

The conventional average acceleration approach relies on K-band range observation, containing an unknown bias, which leads to possible degradation of the precision of Earth’s gravity field modelling. It also suffers from correlated errors caused by three-point numerical differentiation. In this study, an improved approach is proposed that makes use of K-band range-rate observations instead and overcoming the influence of correlated errors by introducing a whitening filter. GRACE-Follow On data spanning the period from January 2019 to December 2022 were processed by the proposed approach and a series of time-varying gravity field models was derived, referred to as SSM-AAA-GFO in this paper. This model series is compared comprehensively with three official model series. Results demonstrate that all model series are highly coincident below degree 30 and reflect similar time-varying gravity field signals in both large and small basins. After filtering, SSM-AAA-GFO shows uncertainty, in the form of equivalent water height below 2.5 cm, which is comparable with three official model series. The comparison results confirm the effectiveness of the proposed approach for precisely modelling a time-varying gravity field based on K-band range-rate observations.

High-resolution and high-precision marine gravity reference maps are core prerequisites for the practical application of gravity-assisted inertial navigation algorithms, and their accuracy directly determines the performance of the navigation system. In view of the problems existing in the current geographic rectangular grid gravity reference map, such as severe polar deformation, poor adjacent consistency, and low positioning accuracy in high latitudes, this study introduces a hexagonal grid system to construct a gravity reference map. It systematically analyzes its compatibility and accuracy in navigation applications. A multi-resolution hexagonal grid scheme with a 7-aperture structure is further proposed to meet the characterization requirements of gravitational fields with different complexities. Experimental verification shows that the accuracy of the gravity-assisted inertial navigation algorithm improved by 0.4%, while that of gravity sequence matching improved by 50%. The proposed hybrid resolution grid can achieve a maximum gravity data compression rate of 68% while ensuring navigation accuracy, especially with regard to the computational efficiency and accuracy requirements of gravity-assisted inertial navigation.