This paper addresses the challenge of probabilistic parameter estimation given measurement uncertainty in real-time. We provide a general formulation and apply this to pose estimation for an autonomous visual landing system. We present three probabilistic parameter estimators: a least-squares sampling approach, a linear approximation method, and a probabilistic programming estimator. To evaluate these estimators, we introduce novel closed-form expressions for measuring calibration and sharpness specifically for multivariate normal distributions. Our experimental study compares the three estimators under various noise conditions. We demonstrate that the linear approximation estimator can produce sharp and well-calibrated pose predictions significantly faster than the other methods but may yield overconfident predictions in certain scenarios. Additionally, we demonstrate that these estimators can be integrated with a Kalman filter for continuous pose estimation during a runway approach where we observe a 50\% improvement in sharpness while maintaining marginal calibration. This work contributes to the integration of data-driven computer vision models into complex safety-critical aircraft systems and provides a foundation for developing rigorous certification guidelines for such systems.

翻译：本文针对实时测量不确定性下的概率参数估计问题提出解决方案。我们建立了通用数学模型框架，并将其应用于自主视觉着陆系统的姿态估计任务。我们提出三种概率参数估计器：最小二乘采样方法、线性近似方法以及概率编程估计器。为评估这些估计器，我们针对多元正态分布特别推导了测量校准度与锐度的新型闭式表达式。实验研究比较了三种估计器在不同噪声条件下的表现。研究表明，线性近似估计器能以显著高于其他方法的速度生成锐利且校准良好的姿态预测，但在特定场景下可能产生过度自信的预测结果。此外，我们验证了这些估计器可与卡尔曼滤波器集成，实现跑道进近过程中的连续姿态估计，在保持边缘校准度的同时将锐度指标提升50%。本研究成果推动了数据驱动计算机视觉模型在复杂安全关键航空系统中的集成应用，并为建立严格的系统认证标准奠定了理论基础。