Lifeng Bao

Due to the cumulative error of inertial sensors, the construction of gravity measuring pattern, as a key component in gravity matching integrated navigation algorithms, faces challenges from offset, rotational, and scaling distortions. Most existing algorithms rely on simplified assumptions and compensate for only a single type of distortion, thus proving inadequate in mitigating coupled distortion effects and limiting overall positioning accuracy. In this paper, a novel gravity matching integrated navigation algorithm based on measuring pattern reconstruction (GMPR) is proposed. The parametric distortion compensation model is introduced to establish mapping between the inertial navigation system (INS) indicated pattern and the true gravity measuring pattern. By determining distortion coefficients through topological constraints, it enables precise reconstruction of gravity measuring patterns. To verify the algorithm’s performance, simulation experiments were conducted across multiple sea areas with distinct characteristics, focusing on effects of trajectory deformation, gravity variation characteristics and gravity measurement inconsistency on positioning accuracy. Simulation results demonstrated that when INS accuracy declines to 0.005°/h or gravity consistency drops to 9 mGal, the proposed algorithm maintains an average positioning error within 3.00 nautical miles, outperforming existing methods in both accuracy and stability under rough measurement conditions. Further verification experiments using marine measured data from the South China Sea demonstrated that GMPR algorithm consistently achieves optimal positioning accuracy across all trajectories while maintaining stability. In contrast, other algorithms exhibited performance degradation due to uncompensated distortion coupling effects. Benefitting from the distortion compensation mechanism, the algorithm enables effective reconstruction of the gravity measuring pattern, and is thus more suitable for practical applications under various challenging sea conditions.

The combined exploitation of marine wind and wave energy contributes to addressing pressing energy challenges. Satellite altimetry enables global synergistic assessment of these resources. Here, we utilize the longest altimeter observations available (Jason series, 1993–2024) to assess the spatiotemporal distribution, correlation, variability, and synergy of global wind and wave energy. Altimeter-derived wind speed and significant wave height were validated against buoy data, showing high consistency. Results indicate that wind and wave energy share similar spatiotemporal distributions. The Southern Ocean exhibits the most powerful and persistent resources, with moderate variability and correlation. Other energetic regions, including the Arabian Sea, North Atlantic, and North Pacific, show higher correlation and variability. Maximum covariance analysis (MCA) identified a leading mode of wind–wave co-variability, with a positive correlation between the expansion coefficients (r = 0.72). The result indicates a positive temporal association within the leading mode. The spatial patterns of the leading mode qualitatively resemble features associated with large-scale climate variability, including ENSO-related patterns. However, these similarities do not establish a direct statistical relationship with ENSO or demonstrate a causal climate influence. This study establishes satellite altimetry as a foundational tool for synergistic assessment of global wind and wave energy potential, providing a scientific basis for combined exploitation of marine energy resources.

The geomagnetic reference map is an important component of underwater geomagnetic matching navigation, and it directly affects navigation and positioning accuracy. However, representative global geomagnetic models still cannot fully meet the requirements of high-precision matching navigation. To address this, this study proposes a local marine geomagnetic anomaly model reconstruction method via multi-source data fusion based on a fully connected neural network. The proposed MAG-DFN method uses the EMAG2 model as the background field and learns model residuals from shipborne measurements to reconstruct the geomagnetic model. Two sub-areas in the South China Sea and the western Pacific were selected for this experiment, each containing two withheld 1° × 1° validation blocks, and four baseline methods were introduced for comparison. The results show that MAG-DFN reduces MAE by 14.71%, 23.35%, 22.09%, and 8.96%, and RMSE by 12.41%, 18.87%, 16.73%, and 6.65%, in the four validation blocks, respectively. In addition, MAG-DFN outperforms all baseline methods. These results indicate that the MAG-DFN method, by integrating high-precision shipborne data, can effectively reduce the local deviations of the EMAG2 and better support matching navigation.

Accurate prediction of sea level change in the Mediterranean Sea is essential for coastal risk management; however, the nonstationary behavior of sea level makes this difficult. This study presents a hybrid framework that integrates variational mode decomposition (VMD) and dynamic mode decomposition (DMD) with long short-term memory (LSTM) and extreme gradient boosting (XGBoost) to forecast monthly sea level anomaly (SLA). Thirty years of records from sixteen Mediterranean tide gauge stations (1993–2022) were used. The proposed VMD-DMD algorithm decomposed SLA signals into distinct multi-scale temporal components. It improved reconstructed signal accuracy compared to VMD-only decomposition, reducing average RMSE from 24.22 to 7.38 mm. For prediction, we compared our models against multiple baselines: the mean annual cycle with anomaly persistence (MAC_AP) and three-layer MLP. The proposed VMD-DMD-LSTM achieved the best overall performance (mean R² = 0.92, RMSE = 20.37 mm, and MAE = 15.31 mm) with an 18% error reduction compared to three-layer MLP. VMD-DMD-XGBoost achieved RMSE = 24.90 mm and R² = 0.88. Furthermore, in a direct comparison on identical data, our VMD-DMD-LSTM outperformed the benchmark VMD-EEMD-LSTM model, achieving about 12% lower errors. Thus, the proposed framework effectively isolates multi-scale dynamics and reduces residual noise, providing more reliable sea level forecasts for coastal operational planning.

The gravity navigation reference map is a foundational element of gravity matching-aided navigation systems, as it directly determines positioning accuracy and overall navigation performance. To improve fused gravity anomalies and reduce reliance on manually selected parameters, this study proposes an adaptive multi-scale frequency-domain reconstruction (AMFR) algorithm. Specifically, the target ocean covered by multi-source satellite gravity data is divided into multiple scales, and distinct fusion parameters are assigned according to the characteristics of multi-source gravity data in different sea areas to enhance the accuracy of the fused gravity navigation reference map. Seven fusion schemes with different filtering diameters and weighting strategies are designed for comparative analysis. We evaluate the algorithm’s performance using measured gravity data with varying spatial distributions from the South China Sea and the Western Pacific Ocean, employing both RMS comparison and matching positioning experiments. Experimental results demonstrate that the RMS of the gravity navigation reference map constructed by the proposed AMFR algorithm is reduced by 30.4%, and the matching positioning accuracy is improved by 23.4%. The AMFR algorithm effectively enhances the precision of the gravity navigation reference map and improves the navigation performance of the gravity matching-aided navigation system.

The realization of a geopotential-based height system relies on high-resolution and high-precision regional gravity field modelling. In this study, a two-cumulative spherical radial basis functions (SRBFs) modelling approach is applied to a develop regional gravity field model, with the goal of realizing of a geopotential-based height system in Hong Kong. The traditional one-step SRBF method has difficulty effectively matching the spectral domain and bandwidth of the observations with the target signal. In contrast, this two-cumulative SRBFs approach involves the construction of a high-frequency SRBFs model, which can capture more detailed spectral domain signals. Detailed explanations are given regarding the configuration of the SRBFs modelling parameters: the location of the SRBFs, the SRBFs type, the edge effect, and the degree of expansion. An edge-constrained estimation model is applied to mitigate the edge effects and enhance the stability of SRBFs coefficient estimation. In addition, we use a prior observations comparison method to determine the optimal maximum and minimum degrees of expansion. The remove–compute–restore (RCR) technology is applied to develop a regional quasi-geoid model in Hong Kong by combining the EIGEN_6C4 model, residual terrain model (RTM) and two-cumulative SRBFs model. Numerical comparison results reveal that the two-cumulative SRBFs modelling approach is highly consistent with the GNSS/levelling-based quasi-geoid height, and demonstrates superior accuracy with a standard deviation (STD) of 1.8 cm. The two-cumulative SRBFs modelling approach represents an improvement of 9.1% compared to the one-step SRBFs modelling approach. These results indicate the validity of the two-cumulative SRBFs approach for gravity field modelling. Finally, the geopotential value of the Hong Kong Principal Datum (HKPD) is estimated to be equal to 62,653,859.83 m²s-² ± 0.18 m²s-² based on the two-cumulative SRBFs model. The vertical offset of HKPD with respect to the global reference potential W₀ is derived as -0.657±0.018 m.

In recent decades, sea level has risen markedly along Mediterranean coastlines, highlighting the growing impacts on vulnerable coastal regions. This study analyzed sea-level variability using tide gauge (TG) records from 45 stations, coastal altimetry data (X-TRACK-L2P and X-TRACK/ALES), and virtual altimetry station (VAS) data. Based on TG records from 1993 to 2022, the results reveal positive linear trends, with 11 stations recording rates well above the global mean. The highest rate, 5.281 mm/year, was observed at TARANTO (Station ID: 2095). Strong consistency was also found between TG and X-TRACK-L2P coastal data, with X-TRACK-L2P trends ranging from −3 to 6 mm/year. In addition, sea-level rise in the Adriatic, Aegean, and Levantine sub-basins exceeded the current global mean. The agreement between TG and X-TRACK/ALES data was more limited, observed at only two sites located about 7 km and 20 km apart from the first valid point on the altimetry track, respectively. Furthermore, the findings highlight the diverse impacts of sea-level rise on Egypt's northern coast, where densely populated areas, productive agricultural lands, and cultural heritage sites are particularly at risk. In conclusion, all types of data used indicate positive linear trends in the Mediterranean Sea. In addition, several sites have rates of sea-level trend that exceed the global mean, underscoring the urgent need for proactive adaptation measures.

The gravity matching algorithm plays a crucial role in gravity matching aided underwater navigation. At present, most matching algorithms are constructed based on correlation calculation between numerical gravity measurement sequence with reference maps that the performance of this single spatial domain feature correlation mode may be constrained under rough marine environments in practical tests. In this paper, a novel gravity matching algorithm based on spatial-frequency multidimensional feature fusion (SFM) was proposed. In this algorithm three new frequency features were extracted to present the complete frequency domain characteristics of the gravity measurement sequence: Spatial-frequency Trend Concordance Degree, Spatial-frequency Joint-Correlation Comparison, and Spatial Directional Similarity. Then they are fused with spatial-domain numerical features to construct a multidimensional feature correlation evaluation index for gravity matching navigation. To verify performance of the SFM algorithm, simulation experiments were conducted across eight oceanic regions exhibiting diverse gravity distribution. The results demonstrated that under different conditions, SFM algorithm maintained much better positioning accuracy and stability than other algorithm. Furthermore, marine measured gravity data from the South China Sea was employed for verification experiments. The results indicated that the SFM algorithm consistently achieved a positioning accuracy better than 2.0 nautical miles along each survey line, while other algorithms suffered from emerging mismatches in segments with increased measurement errors. Benefit from the frequency features extraction and spatial-frequency multidimensional feature fusion, the proposed SFM algorithm shows the advantages of robustness and accuracy even under challenging conditions in both simulation and measured data experiments.

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.