AI 中文总结
本文提出结构化协方差建模与校准方法，应对恶劣天气导致的到达方向估计失真，通过单源闭式算法和多源LASSO/核范数方法提升精度与可分辨性。
AI 中文摘要
在恶劣天气下，到达方向（DoA）估计会因传播引起的相位和幅度失真而退化，这些失真违反了经典子空间方法所假设的协方差结构。受基于物理的降雨传播模型启发，我们针对单源和多源场景开发了一种用于降雨失真阵列的结构化协方差公式。一个关键要素是放宽物理参数化的失真模型，转而将失真协方差建模为未知的实值厄米特托普利茨矩阵。对于单源情况，我们推导了一种闭式协方差匹配校准算法，并提供了结构化协方差和基于物理的克拉美-罗下界（CRLBs）。对于多源情况，我们证明了原始的每源失真模型是不可辨识的，并引入了跨角度的共线近似。在此近似下，我们提出了三种多源校准方法：交替LASSO、联合LASSO和联合核范数公式。在暴雨下的仿真表明，与传统基线相比，所提方法提高了DoA精度和源可分辨性，凸显了结构化协方差建模和校准对安全关键感知的益处。
英文摘要
Direction-of-arrival (DoA) estimation in adverse weather is degraded by propagation-induced phase and amplitude distortions that violate the covariance structure assumed by classical subspace methods. Motivated by a physics-based model of rain propagation, we develop a structured covariance formulation for rain-distorted arrays in both single- and multi-source scenarios. A key ingredient is to relax the physically parameterized distortion model and instead model the distortion covariance as an unknown real-valued Hermitian Toeplitz matrix. For the single-source case, we derive a closed-form covariance-matching calibration algorithm and provide structured-covariance and physics-informed Cramer-Rao lower bounds (CRLBs). For the multi-source case, we prove that the original per-source distortion model is non-identifiable and introduce a collinear approximation across angles. Under this approximation, we propose three multi-source calibration methods: alternating LASSO, joint LASSO, and a joint nuclear-norm formulation. Simulations under heavy rain demonstrate improved DoA accuracy and source resolvability compared with conventional baselines, highlighting the benefit of structured covariance modeling and calibration for safety-critical sensing.
