The gravity navigation performance is challenged by gravity measurement accuracy and heading precision which is determined by navigation equipment and measurement environment. In this letter, a new gravity matching algorithm based on comprehensive features matching (CFM) is proposed to evaluate the similarity correlation between gravity measurement sequences and reference map. Different from classical matching algorithms based on the single gravity statistical values characteristics, this method could combine gravity roughness comparison correlation, gravity contrast comparison correlation, and regression fitting degree of two gravity sequences, respectively, which helps to incorporate the gravity numerical error sensitivity and structural similarity of gravity sequences in matching navigation process. Simulation and measured data experiments in the South China Sea were carried out, and a better than 1.5 n miles matching navigation accuracy was maintained by CFM method regardless of an increase in gravity measurement error and heading error. Experimental results demonstrated that the proposed method had less dependence on gravity measurement accuracy or vehicle heading precision for higher gravity matching navigation performance, which could provide a new option for future underwater passive autonomous navigation.

Unification of the global vertical datum has been a key problem to be solved for geodesy over a long period, and the main challenge for a unified vertical datum system is to determine the vertical offset between the local vertical datum and the global vertical datum. For this purpose, the geodetic boundary value problem (GBVP) approach based on the remove-compute-restore (RCR) technique is used to determine the vertical datum parameters in this paper. In the RCR technique, a global geopotential model (GGM) is required to remove and restore the long wavelengths of the gravity field. The satellite missions of the GRACE (Gravity Recovery and Climate Experiment) and GOCE (Gravity field and steady-state Ocean Circulation Exploration) offer high accuracy medium–long gravity filed information, but GRACE/GOCE-based GGMs are restricted to medium–long wavelengths because the maximum degree of their spherical harmonic representation is limited, which is known as an omission error. To compensate for the omission error of GRACE/GOCE-based GGM, a weighting method is used to determine the combined GGM by combining the high-resolution EGM2008 model (Earth Gravitational Model 2008) and GRACE/GOCE-based GGM to effectively bridge the spectral gap between satellite and terrestrial data. An additional consideration for the high-frequency gravity signals is induced by the topography, and the residual terrain model (RTM) is used to recover the omission errors effect of the combined GGM. In addition, to facilitate practical implementation of the GBVP approach, the effects of the indirect bias term, the spectral accuracy of the GGM, and the systematic levelling errors and distortions in estimations of the vertical datum parameters are investigated in this study. Finally, as a result of the GBVP solution based on the combined DIR_R6/EGM2008 model, RTM, and residual gravity, the geopotential values of the North American Vertical Datum of 1988 (NAVD88), the Australian Height Datum (AHD), and the Hong Kong Principal Datum (HKPD) are estimated to be equal to 62636861.31 ± 0.96, 62653852.60 ± 0.95 and 62636860.55 ± 0.29 m²s⁻², respectively. The vertical offsets of NAVD88, AHD, and HKPD with respect to the global geoid are estimated as −0.809 ± 0.090, 0.082 ± 0.093, and −0.731 ± 0.030 m, respectively.

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.

Remote sensing object detection remains challenging because objects often appear with large scale variation, dense spatial layouts, and strong interference from complex geographical backgrounds. To address these coupled difficulties, we propose EDM-Net, an end-to-end multi-scale detector that organizes feature processing into three coordinated stages: adaptive extraction, intra-scale interaction, and cross-scale fusion. First, an efficient sparse mixture-of-experts (ES-MoE) module is embedded in the backbone to allocate scale-specific convolutional experts according to scene-level feature responses, providing a more adaptive feature basis than a single static extraction path. Second, a dynamic mixing intra-scale feature interaction (DMIFI) module is introduced into the Transformer encoder. This module combines global self-attention with dynamic spatial mixing, thereby preserving long-range context while reintroducing local two-dimensional inductive bias for dense and small objects. Third, a multi-scale synergistic attention fusion (MSAF) module aligns adjacent feature levels through parallel local and global attention branches and structural re-parameterization, reducing semantic dilution during feature aggregation. Comprehensive experiments on three large-scale remote sensing benchmark datasets, DIOR, NWPU VHR-10, and RSOD, demonstrate that EDM-Net consistently improves over the re-trained RT-DETR-R18 baseline under the same experimental protocol, attaining mAP50 scores of 83.7%, 95.6%, and 95.8% respectively. Additional ablation and scale-specific analyses indicate that the three modules contribute complementary gains, especially for small and densely distributed objects. These results suggest that coordinated extraction, interaction, and fusion can improve remote sensing object detection under complex scale and background conditions.

Identifying and localizing small objects in UAV imagery is a highly challenging task. Existing detection models are prone to missed detections, false detections, and inaccurate localization, while improvements in detection accuracy and real-time performance are often accompanied by an increase in the number of model parameters. To address these issues, this paper proposes an efficient end-to-end network for real-time small-object detection in UAV imagery, termed FBR-DETR. Through coordinated design across three stages, namely feature extraction, efficient encoding, and cross-scale fusion, the proposed network achieves higher detection accuracy and real-time performance for small objects with fewer parameters. FBR-DETR incorporates three core innovations. First, to address the tendency of small objects to be overwhelmed by background textures in deep features, we design a frequency-domain inverse-convolution-enhanced feature extraction network (FICE-Net), which introduces frequency-domain inverse convolution into the backbone feature extraction process to enhance the joint perception of global spectral structures and fine-grained spatial features at the source. Second, to reduce the inference overhead introduced by full-precision attention computation in AIFI, we construct a binary attention-based intra-scale feature interaction module (Binary-AIFI), which binarizes the query and key matrices while preserving global contextual representation with controlled additional computational cost. Third, to alleviate the dilution of small-object information during cross-scale fusion, we propose a re-parameterized cross-scale feature fusion module (RCFF), which enhances feature representation during training through a multi-branch re-parameterized structure and is equivalently merged into a single convolution during inference, thereby balancing fusion capability and real-time inference efficiency. On the VisDrone2019-DET and HIT-UAV datasets, the proposed method achieves mAP_0.5 values of 51.2% and 83.4%, respectively. Compared with the baseline model, our method improves mAP_0.5 by 5.3% and 5.9%, reduces the number of parameters by 30.8%, and improves the average precision for small objects (APs) by 2.4% and 4.9%, respectively.