Gravity-aided inertial navigation system (GAINS) is a significant technique in underwater long-endurance passive navigation. In addition to gravity matching process, comprehensive correction is also a crucial step by implementing the gravity matching results fusing with INS for navigation reset and INS accumulation error correction in GAINS. Due to the uneven distribution of the gravitational field and gravity feature suitability real-time changes, the matching position output frequency is difficult to fix after credibility evaluation and error elimination. The gravity matching results covered continuous or sparse frequency at different filtering periods and ranged from 3 minutes to 10 hours which meant in-coordinate interval characters. In this article, a flexible INS correction method for GAINS covering the improved Kalman filtering and multi-point comprehensive correction is presented to improve filtering navigation stability. After an adaptive navigation state judgment, for continuous gravity matching positions, an Extended Kalman filter was adopted; for sparse matching results, a multi-point comprehensive correction method would be used to estimate INS gyro drifts for navigation reset based INS error accumulation characteristics in long-endurance. The hardware-in-the-loop simulation and marine dynamic experiments in the South China Sea demonstrated that compared with the commonly used filter navigation methods, the FICM could effectively suppress the accumulated INS uncertainty and drift error with a high-precision navigation result, regardless of continuous or sparse gravity matching position.

High-accuracy optical clocks have garnered increasing attention for their potential application in various fields, including geodesy. According to the gravitational red-shift effect, clocks at lower altitudes on the Earth’s surface run slower than those at higher altitudes due to the differential gravitational field. Consequently, the geopotential difference can be determined by simultaneously comparing the frequency of two optical clocks at disparate locations. Here, we report geopotential difference measurements conducted using a pair of transportable ⁴⁰Ca⁺ optical clocks with uncertainties at the ${10}^{-17}$ level. After calibrating the output frequencies of two optical clocks in the horizontal position, frequency comparison is realized by moving Clock 2 to two different positions using a high-precision optical fiber time–frequency transmission link with Clock 1. The elevation difference of the two different positions, as processed by ensemble empirical mode decomposition (EEMD), is measured as −88.4 cm ± 16.7 cm and 104.5 cm ± 20.1 cm, respectively, which is consistent with the geometric measurement results within the error range. This experimental result validates the credibility of the optical clock time–frequency comparison used in determining geopotential differences, thereby providing a novel measurement model for the establishment of a global unified elevation datum.

The significant challenge faced by underwater gravity matching navigation is the precise acquisition of velocity information for real-time Eötvös correction of marine gravimeters without emitting or receiving external signals. To address this issue, we propose a passive velocity compensation method for inertial navigation systems (INSs), which can effectively enhance the velocity measurement and positioning accuracy of the INS in a completely passive state and calculate high-precision Eötvös correction. This method takes into account the impact of horizontal gravity disturbance on the velocity measurement of the INS, utilizes the Earth's gravity field model and satellite altimetry technology to construct a high-precision horizontal gravity disturbance reference map, and uses the information in the map for velocity compensation. Relative to the INS without compensation, it achieves higher precision in velocity and positioning, which can be served in real-time for the Eötvös correction of marine gravimeters. To verify the new method, we equipped a high-precision INS and a marine gravimeter to conduct marine dynamic experiments in the South China Sea. The experimental results show 1) the new velocity compensation method can reduce the average velocity error of the INS by 33.3% in a completely passive state; 2) integrating the velocity results after compensation can obtain higher positioning accuracy than before compensation, with an average reduction of 13.3% in location error; and 3) the passive velocity compensation method, compared with the pure INS, reduces the standard deviation of the Eötvös correction error of the marine gravimeter by 27.0%, which can better serve in many important application fields, including underwater gravity matching navigation.

The high-precision unification of global height datum has long been a hot issue in the field of geodesy. The chronometric leveling method originates from the gravitational redshift effect of general relativity, which may provide a new solution for the unification of global height datum. The height difference between the two locations could be measured via the frequency comparison of high-precision optical clocks. We build the error model for chronometric leveling, mainly including the measurement systematic error of two optical clocks, frequency statistical error of two optical clocks, and transmission path error of optical fiber when using optical fiber as carrier. Then, we put forward the schemes to achieve chronometric leveling. The performance of the height measurement using different schemes is evaluated. Additionally, considering the requirements of geodesy, four typical height measurement accuracy factors for chronometric leveling are proposed. Meanwhile, the corresponding accuracy requirements for optical clocks and frequency transmission techniques are also given. It has important guiding significance for the unification of the global height datum and related geoscience fields using high-accuracy chronometric leveling in the future.