  The Kalman filter (KF) is a widely-used algorithm for tracking the latent
state of a dynamical system from noisy observations. For systems that are
well-described by linear Gaussian state space models, the KF minimizes the
mean-squared error (MSE). However, in practice, observations are corrupted by
outliers, severely impairing the KFs performance. In this work, an
outlier-insensitive KF is proposed, where robustness is achieved by modeling
each potential outlier as a normally distributed random variable with unknown
variance (NUV). The NUVs variances are estimated online, using both
expectation-maximization (EM) and alternating maximization (AM). The former was
previously proposed for the task of smoothing with outliers and was adapted
here to filtering, while both EM and AM obtained the same performance and
outperformed the other algorithms, the AM approach is less complex and thus
requires 40 percentage less run-time. Our empirical study demonstrates that the
MSE of our proposed outlier-insensitive KF outperforms previously proposed
algorithms, and that for data clean of outliers, it reverts to the classic KF,
i.e., MSE optimality is preserved
