A centralized normal barrier approach for min‐sup robust Kalman filtering with unknown covariance bounds

Abstract The min‐sup robust Kalman filter (RKF) provides robust state estimation for uncertain linear dynamic systems, relying on centered distribution classes with bounded covariances. Identifying the upper‐bound matrices that define these covariances is crucial for RKF implementation. Existing approaches, such as the penalized uncoverage function introduced in 2022, may produce overly conservative bounds. This paper introduces a new centralized normal barrier identification (CNBI) function and a pruned variant (PCNBI) to improve upper‐bound covariance matrix identification. The PCNBI methodology is applied to robust state estimation in a two‐dimensional linear system. Simulation results show that PCNBI significantly outperforms recent robust approaches, including those based on the Huber loss function, Student's distribution, Kullback–Leibler divergence, and the robust autocovariance least‐squares (RALS, 2022) method, in the presence of outliers and Laplace‐distributed noise, while achieving competitive performance with RALS under ‐contamination distributions.