Physical-model-driven compressive sensing for high-precision off-grid multi-target UAV localization

With the rapid development of advanced wireless networks and the growing reliance on location-based services, the demand for high-precision passive localization of unmanned aerial vehicles (UAVs) in fields such as emergency rescue and the industrial Internet of Things (IoT) has become increasingly urgent. Localization technologies based on received signal strength (RSS) have emerged as a preferred solution due to their low cost and ease of deployment. However, traditional on-grid compressive sensing-based localization in multi-target scenarios suffers from grid mismatch, resulting in limited localization accuracy and poor robustness. To address this issue, this paper proposes a high-precision off-grid multi-target localization method for UAVs based on physical-model-driven block-sparse compressive sensing. First, by employing a Taylor approximation of the RSS path loss model, an off-grid block sparse model with energy coefficients and geometric offset parameters is established, which jointly characterizes the target energy and position information while alleviating discretization errors at the model level. Second, a physical-model-driven fast iterative shrinkage-thresholding algorithm (FISTA) is proposed. The proposed physical-model-driven shrinkage operator replaces the proximal mapping operator, and incorporates physical boundary constraints and a differentiated penalty mechanism into the iterative process, thereby mitigating overfitting arising from higher-order model errors. Extensive Monte Carlo simulation experiments demonstrate that the proposed method achieves significantly superior average localization accuracy under various signal-to-noise ratio (SNR) and target number scenarios, with approximately 35% improvement over traditional on-grid methods and 25% over standard off-grid methods. Furthermore, it exhibits no accuracy saturation at high SNRs, accompanied by remarkably enhanced robustness.