In this paper, we propose a robust variant of the Ensemble Kalman Filter (EnKF) that remains reliable in the presence of outliers and non-Gaussian noise. The method, called Hybrid Dynamical Adaptive Least Trimmed Squares EnKF (HD-LTS-EnKF), combines adaptive outlier trimming with ensemble covariance weighting to improve filter stability and accuracy. By dynamically identifying and downweighting anomalous ensemble members and ob-servations-based on how uncertainty propagates through the system-our approach preserves the essential covariance structure while reducing the influence of outliers. Although solving the full optimization is infeasible in high-dimensional systems, we show that HD-LTS-EnKF approximates the optimal solution.

The primary objective of this paper is to apply the expectation maximization algorithm for constructing a robust maximum likelihood estimator for the linear state space model in the presence of multisensor observations outliers, particularly if the number of sensors is limited. In this case, we introduce a novel estimator akin to the trimmed least squares method, designed to exhibit high breakdown properties, although it is hard to find the exact solution. However, through a randomized algorithm, we can achieve a solution that converges to the true solution with a probability of one.The effectiveness of these methods is demonstrated through Monte Carlo simulation.

The authors propose a diagnostic technique for the state‐space model fitting of time series by deleting some observations and measuring the change in the parameter estimates. They consider this approach in order to distinguish an observational outlier from an innovational one. Thus, they present a robust subspace identification algorithm that is less sensitive to outliers. A Monte Carlo simulation for a vibrating structure model demonstrates the effectiveness of the proposed algorithm and its ability to detect outliers in the measurements as well as the dynamical state.