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 update step of the KF. 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 competitive performance of our method, showcasing its robustness to outliers in filtering scenarios compared to alternative algorithms.

翻译：动态系统状态估计是众多应用中的基本任务，通常采用线性卡尔曼滤波器（KF）来处理。由于KF的凸二次目标函数对离群值具有敏感性，当观测数据中存在离群值时，其性能会显著下降。为缓解此类问题，可应用离群值检测算法。本文提出一种无参数算法，仅需对KF标准更新步骤进行短迭代过程，即可减轻离群值的有害影响。为此，我们将每个潜在离群值建模为具有未知方差的正态过程，并通过期望最大化或交替最大化算法进行在线估计。仿真与现场实验评估表明，与替代算法相比，我们的方法在滤波场景中展现出对离群值的鲁棒性及竞争性性能。