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

TL;DR

This paper introduces a physics-aware asymmetric filtering method for UAV-based survivor localization in disaster zones, addressing the challenge of non-symmetric NLOS biases that cause estimator stagnation.

Contribution

It proposes the AsymmetricHuberEKF, a novel physically-grounded filter that explicitly models asymmetric NLOS biases, and demonstrates its effectiveness in accelerating convergence in constrained geometries.

Findings

Significantly faster convergence than symmetric filters.

Robustness to scarce data and limited observation geometry.

Theoretical link between symmetric filters and degenerate cases.

Abstract

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.