This paper proposes a novel convex optimization framework for designing robust Kalman filters that guarantee a user-specified steady-state error while maximizing process and sensor noise. The proposed framework simultaneously determines the Kalman gain and the robustness margin in terms of the process and sensor noise. This is the first paper to present such a joint formulation for Kalman filtering. The proposed methodology is validated through two distinct examples: the Clohessy-Wiltshire-Hill equations for a chaser spacecraft in an elliptical orbit and the longitudinal motion model of an F-16 aircraft.

翻译：本文提出一种新颖的凸优化框架，用于设计能保证指定稳态误差的同时最大化过程噪声与传感器噪声的鲁棒卡尔曼滤波器。该框架可同步确定卡尔曼增益以及以过程噪声和传感器噪声表征的鲁棒裕度。这是首篇提出此类卡尔曼滤波联合建模方法的论文。所提方法通过两个不同实例进行验证：椭圆轨道追踪航天器的克洛赫西-威尔特希尔-希尔方程与F-16战斗机纵向运动模型。