The digital elevation model (DEM) is known as one kind of the most significant fundamental geographical data models. The theory, method and application of DEM are hot research issues in geography, especially in geomorphology, hydrology, soil and other related fields. In this paper, we improve the efficient sub-pixel convolutional neural networks (ESPCN) and propose recursive sub-pixel convolutional neural networks (RSPCN) to generate higher-resolution DEMs (HRDEMs) from low-resolution DEMs (LRDEMs). Firstly, the structure of RSPCN is described in detail based on recursion theory. This paper explores the effects of different training datasets, with the self-adaptive learning rate Adam algorithm optimizing the model. Furthermore, the adding-“zero” boundary method is introduced into the RSPCN algorithm as a data preprocessing method, which improves the RSPCN method’s accuracy and convergence. Extensive experiments are conducted to train the method till optimality. Finally, comparisons are made with other traditional interpolation methods, such as bicubic, nearest-neighbor and bilinear methods. The results show that our method has obvious improvements in both accuracy and robustness and further illustrate the feasibility of deep learning methods in the DEM data processing area.

High-accuracy seabed surface modelling provides multi-source high-precision fundamental geographic datasets for marine visual computing, seabed topography detection, marine biology, marine engineering and other fields. Proposed in this paper is a high-precision seabed surface model, which combines B-spline functions and Fourier-series, referred to as the Spline-Fourier-series (S-FS) method. Firstly, the mathematical relationship between the B-spline functions and Fourier-series in the modelling process is explored in depth, deducing the non-recursive basis functions of the $p^{th}$ Spline-Fourier-series model and the specific representation of the two dimensional $p^{th}$ Spline-Fourier-series model. Furthermore, using a publicly available Large-area bathymetric dataset, extensive experiments are conducted for comparisons with traditional methods (nearest-neighbor, bilinear, bicubic) and traditional Fourier-series, which generally shows the S-FS method has higher accuracy, better convergence and stronger robustness. Finally, based on its mathematically theoretical model, three characteristics (dimensionality reduction, multi-resolution expression and multi-scale visualization) of the S-FS method for constructing high-precision seabed surface are analyzed visually and deeply. Compared with B-spline function, the basic functions of the S-FS method inherit its prioritized compactly-supported performance and do not need to be recursively calculated anymore, thereby further showing its feasibility and extensibility in the field of high-precision seabed surface modelling.

Cooperative positioning enhances localization accuracy in intelligent artifact swarms through shared measurements, especially in environments such as urban canyons or disaster zones. Dynamic topologies, heterogeneous measurements, and scalability demands create complex challenges for state estimation. This paper introduces MRCA, the first comprehensive framework unifying heterogeneous measurements, reasoning processes, environment cognition, and scenario-based applications for cooperative positioning. The four-layer architecture comprises: i) the Measurement block converts signals into measurement parameters in a standard format independent of sensor types and measurement methods; ii) the Reasoning block uncovers the underlying principles of state transition using a four reasoning elements; iii) the Cognition block underscores the importance of node-environment interactions by identifying new valid radiation sources and verifying the ongoing validity of existing ones; iv) the Application block offers users task-driven cooperative positioning services, like execute potential navigation actions. Our proposed framework demonstrates performance improvements in various key metrics compared to legacy swarm positioning algorithms. Focusing on the framework itself, we employ the most basic algorithms within each block, and the experimental results are as follows: In scenarios featuring static unknown anchors, sparse perception, and collision interference, MRCA reduces cumulative positioning error by over 51% for dead-reckoning and 39% for traditional distributed cooperative positioning, while reducing average orientation error by over 31% and 27%, respectively. Running on ${\$}5$ consumer-grade IMUs, MRCA achieves a final RMSE of 10.27 m, outperforming even a ${\$}1~500$ industrial-grade IMU in dead-reckoning mode (11.99 m). Through the validation of real - scene datasets, the paper illustrates how this framework integrates into system-level solutions for real-world implementation, further advancing the theoretical understanding of state estimation in cooperative positioning systems.

Cooperative sensor networks relying on Visual-Inertial Odometry (VIO) suffer from monotonically accumulating drift in Global Navigation Satellite System (GNSS)-denied environments, compromising global localization consistency. We model accumulated VIO error as a two-level functional hierarchy: low-frequency collective drift induced by systematic biases, and high-frequency geometric distortion caused by independent measurement noise. To address these coupled error modes, we propose MA-DGNN (Model-Aided Decoupled Graph Neural Network), which combines an Extended Kalman Filter (EKF) prior with a hierarchical dual-head graph neural network under asymmetric supervision. MA-DGNN is evaluated on semi-synthetic quadrotor swarm datasets derived from UZH-FPV under bounded yaw drift (|Δθ_yaw| < 20°). It reduces Absolute Trajectory Error (ATE) by 71.8% over EKF-Only and 25.9% over an input-matched architectural control (p < 10⁻⁵, Cohen’s d_z = 1.58). A five-flight hardware pilot yields 35.1% mean ATE reduction without fine-tuning. Large-scale experiments identify two scalability phenomena—cascaded error coupling and information saturation—with centralized GNN inference under 2.5 ms for 50 agents; communication-aware end-to-end latency is characterized separately.

Cooperative localization for UAV and robotic teams in GPS-denied industrial environments is a system-level measurement problem shaped by inertial drift, UWB NLOS ranging bias, graph-structured communication, and recursive estimator consistency. Graph neural networks (GNNs) can use the cooperative topology to learn residual corrections, but direct injection of unconstrained corrections into an error-state Kalman filter can produce a positive-feedback failure mode: biased corrections contract the covariance, increase the influence of later biased updates, and cause single-step jumps exceeding 10 m. In cooperative settings, a single corrupted agent can further spread this failure through shared inter-agent ranges. To address this problem, we propose Bounded Credibility-Aware Graph Residual Fusion (BCRF), a learning-augmented cooperative localization framework embedding graph residual learning in an explicit estimator-facing interface. This interface bounds correction magnitude and controls correction admission through a robust two-layer UWB front-end, norm-saturated SE(3) residual projection, and a communication-aware filter-domain credibility score (FCS) based on innovation, covariance, dropout, and gate-pass statistics. Across four synthetic test scenarios spanning 18.7%–39.6% NLOS, communication-degradation tests, agent-count variations, and a real three-agent industrial UAV deployment with simultaneous motion, factory-floor NLOS, and real inter-agent ranging and communication constraints, BCRF achieves a 23.6–30.6% P99 ATE reduction over a robust ESKF baseline with zero observed catastrophic failures. Ablation shows that bound projection and credibility scoring are the critical mechanisms, whereas L2-regularised GNN correction without the explicit interface reduces failures but cannot eliminate them. The results show that robust learning-augmented cooperative localization requires an estimator-facing credibility-aware interface, rather than a more accurate learned residual model.