Bridging the Sampling Distribution Shift in Radio Map Estimation: A Trajectory-Aware Paradigm

Radio map (RM) estimation aims to reconstruct the spatial distribution of wireless signal characteristics, such as received signal strength (RSS), from sparse measurements, a task that is critical for spectrum management, interference mitigation, and localization in modern wireless networks. Traditional approaches, including interpolation and deep learning, either struggle to capture complex propagation effects or require large-scale retraining for each new sampling pattern, which limits their generalization. More recently, prior-based methods have combined pre-trained generative models with measurements to reduce the need for deployment-time model fine-tuning, but they typically treat the prior as a simple regularizer and lack explicit transmitter-aware integration. In this paper, we propose RadioTrace, a novel RM estimation framework without deployment-time fine-tuning that tightly integrates sparse RSS measurements with a frozen pre-trained diffusion prior. RadioTrace incorporates transmitter (Tx) location estimation directly into the denoising loop, iteratively refining Tx coordinates based on reconstruction quality to guide the generative process. To further enhance robustness, we introduce a propagation-guided K-means initialization that mitigates poor local minima in the Tx update and provides a geometry-consistent starting point. Moreover, we provide a stochastic stability analysis for the Tx-coordinate refinement component, showing that the Tx update remains stable under perturbations induced by diffusion sampling and Tx-map relaxation. Extensive experiments demonstrate that RadioTrace achieves competitive performance with state-of-the-art learning-based methods under random sampling, and maintains strong reconstruction quality under restricted-area sampling, highlighting its adaptability, robustness, and practical relevance.

Large-scale point cloud maps are essential for robotics and spatial intelligence tasks. UAVs provide an efficient means for large-scale map acquisition; however, due to limited flight endurance and onboard storage, mapping a large-scale scene within a single flight remains difficult. Existing multi-session map merging methods can extend the mapping range, yet in UAV scenarios they still struggle to simultaneously suppress long-range drift and preserve local geometric accuracy. To address this issue, an uncertainty-aware multi-session point cloud map merging and coarse-to-fine optimization system is proposed. The proposed method first performs initial multi-session map merging based on a scene graph, and then incorporates RTK observations through an RTK spatiotemporal alignment module, where temporal offsets are estimated using Dynamic Time Warping (DTW), and continuous RTK constraints are recovered using Multi-Output Gaussian Processes (MOGP) under incomplete sampling and frame dropouts. On this basis, a unified uncertainty-aware factor graph is constructed, and local geometric accuracy is further improved through iterative plane-factor refinement. Experiments on real-world datasets validate the effectiveness and robustness of the proposed method. To facilitate further research and development in the community, our code and dataset will be publicly released.

Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile monitoring. For flying agents in particular, this challenge is acute: trajectories must balance coverage fidelity against tight energy budgets, no-fly zones, and acceleration limits. Existing methods either re-optimize each trajectory online (with cost growing in the horizon and re-running for every target, agent, and realization) or rely on bespoke analytical constructions that must be re-derived for each new constraint. We propose a \emph{epushforward} framework that decouples ergodicity from density matching: an analytic latent trajectory provides exact uniform ergodicity on a simple annular domain, and a single map, learned offline by optimal-transport conditional flow matching, transports this latent occupancy onto the prescribed target density. The composed trajectory is then asymptotically ergodic with respect to the learned pushforward distribution, with deviation from the target controlled by the flow-matching training loss. Once trained for a given target density and constraint set, the map serves an unbounded number of trajectories and a multi-agent fleet without per-agent retraining, and many differentiable operational constraints (no-fly zones, acceleration ceilings, or fairness penalties) enter as additive soft penalties in the training loss without re-deriving the design. We prove three results (an acceleration-energy bound, an $O(1/\sqrt{K})$ ergodic convergence rate in the number of trajectory cycles $K$, and an approximation-error bound) that combine into an end-to-end coverage bound estimable from CFM training diagnostics (certified given an architectural Lipschitz bound on $v_θ$).