Outlier-Insensitive Kalman Filtering: Theory and Applications

State estimation of dynamical systems from noisy observations is a fundamental task in many applications. It is commonly addressed using the linear Kalman filter (KF), whose performance can significantly degrade in the presence of outliers in the observations, due to the sensitivity of its convex quadratic objective function. To mitigate such behavior, outlier detection algorithms can be applied. In this work, we propose a parameter-free algorithm which mitigates the harmful effect of outliers while requiring only a short iterative process of the standard KF’s update step. To that end, we model each potential outlier as a normal process with unknown variance and apply online estimation through either expectation–maximization or alternating maximization algorithms. Simulations and field experiment evaluations demonstrate our method’s competitive performance, showcasing its robustness to outliers in filtering scenarios compared with alternative algorithms.