Traditional fusion methods for integrating multi-source gravity data rely on predefined mathematical models that inadequately capture complex nonlinear relationships, particularly at wavelengths shorter than 10 km. We developed a convolutional neural network incorporating differential marine geodetic data (DMGD-CNN) to enhance marine gravity anomaly recovery from HY-2A satellite altimetry. The DMGD-CNN framework encodes spatial gradient information by computing differences between target points and their surrounding neighborhoods, enabling the model to explicitly capture local gravity field variations. This approach transforms absolute parameter values into spatial gradient representations, functioning as a spatial high-pass filter that enhances local gradient information critical for short-wavelength gravity signal recovery while reducing the influence of long-wavelength components. Through systematic ablation studies with eight parameter configurations, we demonstrate that incorporating first- and second-order seabed topography derivatives significantly enhances model performance, reducing the root mean square error (RMSE) from 2.26 mGal to 0.93 mGal, with further reduction to 0.85 mGal achieved by the differential learning strategy. Comprehensive benchmarking against international gravity models (SIO V32.1, DTU17, and SDUST2022) demonstrates that DMGD-CNN achieves 2–10% accuracy improvement over direct CNN predictions in complex topographic regions. Power spectral density analysis reveals enhanced predictive capabilities at wavelengths below 10 km for the direct CNN approach, with DMGD-CNN achieving further precision enhancement at wavelengths below 5 km. Cross-validation with independent shipborne surveys confirms the method’s robustness, showing 47–63% RMSE reduction in shallow water regions (<2000 m depth) compared to HY-2A altimeter-derived results. These findings demonstrate that deep learning with differential marine geodetic features substantially improves marine gravity field modeling accuracy, particularly for capturing fine-scale gravitational features in challenging environments.

To address the challenge of monitoring BeiDou RDSS signals under low signal-to-noise ratio (SNR) and high-dynamic conditions, this paper introduces a hierarchical joint processing algorithm combining PMF-FFT and PMF-FRFT. The method counters the energy dispersion issue in conventional FFT-based techniques by employing a two-stage “coarse–fine” strategy. A computationally efficient PMF-FFT performs a rapid coarse search, followed by an intelligent trigger, based on a correlation peak morphology, that initiates a localized PMF-FRFT fine search for high-dynamic signals, to precisely estimate the code phase, center frequency, and Doppler rate. Experimental results demonstrated that the algorithm’s acquisition performance was comparable to a global PMF-FRFT search and superior to the conventional PMF-FFT, achieving a 4.91% correlation peak improvement at −10 dB SNR and a gain of nearly 30% in extreme conditions (−20 dB SNR, 1000 Hz offset). Crucially, its average processing time (∼0.088 s) was on the same order of magnitude as PMF-FFT (∼0.0568 s) and significantly faster than global PMF-FRFT (∼0.3317 s). The proposed algorithm effectively balances detection performance with computational efficiency, offering a viable solution for the real-time monitoring of high-dynamic DSSS signals.

In long-endurance and high-precision navigation scenarios, gravity disturbances have become the core bottleneck limiting the performance improvement of high-precision Inertial Navigation Systems (INSs). This paper aims to investigate the compensation efficacy of gravity field spherical harmonic models of different degrees for high-precision INS. The influence mechanisms of gravity disturbances on INS error propagation are derived, and corresponding simulation analyses are performed. The gravity compensation mechanism based on gravity field spherical harmonic models is elaborated, and the performance differences in gravity disturbance compensation among spherical harmonic models of different orders are comparatively analyzed. Based on long-endurance ship trial experiments using high-precision inertial navigation equipment, the compensation efficacy of the 360-order and 2159-order compensation schemes on multiple navigation performance indicators is quantitatively evaluated across sea areas with different gravity characteristics. The experimental results demonstrate that the widely held consensus within the field—that a higher model degree yields better compensation efficacy when improving high-precision INS accuracy based on gravity field spherical harmonic model compensation—does not hold universal applicability. The research findings can provide theoretical support for the engineering implementation of gravity compensation schemes and the selection of model degrees for high-precision INS.