Direct Position Determination of Distributed Signal Sources in Low-Altitude Environments

To address the degradation of the localization accuracy of unmanned aerial vehicle （UAV） in urban low-altitude environments， caused by multipath propagation， local scattering， and angular spread， a gridless sparse Bayesian learning （SBL） direct localization method was proposed in this study for distributed sources. Conventional direct localization approaches are typically developed under the ideal point-source assumption， which is inadequate for complex urban propagation environments that are characterized by significant multipath and angular spread effects. This mismatch often leads to model errors and performance degradation. To overcome this limitation， the target was modeled as a coherently distributed source， and a direct localization framework was established under a multi-base-station cooperative observation scheme. From a methodological perspective， the distributed source localization problem was reformulated as a sparse reconstruction problem. A hierarchical probabilistic model was constructed within the SBL framework， where prior distributions were imposed on both signal and noise precisions. The hyperparameters were then adaptively estimated via the expectation-maximization algorithm. To mitigate the grid mismatch issue， a gridless optimization strategy was introduced. Specifically， a first-order Taylor expansion of the steering vector was employed to compensate for position deviations， and a dictionary matrix was dynamically updated during the iterative process， thus enabling continuous refinement toward the true source locations. Furthermore， to address the resolution degradation caused by closely spaced multiple targets， the statistical resolution limit was derived based on the Cramér-Rao lower bound， which served as a quantitative measure of system resolvability. Simulation results demonstrated that the proposed method achieved stable localization performance under various signal-to-noise ratio （SNR） and snapshot conditions. Its performance approached the theoretical lower bound in moderate-to-high SNR regimes while maintaining strong robustness in low-SNR scenarios. In addition， it exhibited superior capability in resolving closely spaced targets. These results indicate that the proposed method effectively alleviates model as well as grid mismatch issues， thus making it well suited for UAV localization in complex urban low-altitude environments.