Statistical-Geometric Degeneracy in UAV Search: A Physics-Aware Asymmetric Filtering Approach

Post-disaster survivor localization using Unmanned Aerial Vehicles (UAVs) faces a fundamental physical challenge: the prevalence of Non-Line-of-Sight (NLOS) propagation in collapsed structures. Unlike standard Gaussian noise, signal reflection from debris introduces strictly non-negative ranging biases. Existing robust estimators, typically designed with symmetric loss functions (e.g., Huber or Tukey), implicitly rely on the assumption of error symmetry. Consequently, they experience a theoretical mismatch in this regime, leading to a phenomenon we formally identify as Statistical-Geometric Degeneracy (SGD)-a state where the estimator stagnates due to the coupling of persistent asymmetric bias and limited observation geometry. While emerging data-driven approaches offer alternatives, they often struggle with the scarcity of training data and the sim-to-real gap inherent in unstructured disaster zones. In this work, we propose a physically-grounded solution, the AsymmetricHuberEKF, which explicitly incorporates the non-negative physical prior of NLOS biases via a derived asymmetric loss function. Theoretically, we show that standard symmetric filters correspond to a degenerate case of our framework where the physical constraint is relaxed. Furthermore, we demonstrate that resolving SGD requires not just a robust filter, but specific bilateral information, which we achieve through a co-designed active sensing strategy. Validated in a 2D nadir-view scanning scenario, our approach significantly accelerates convergence compared to symmetric baselines, offering a resilient building block for search operations where data is scarce and geometry is constrained.