Outlier-insensitive Kalman smoothing and marginal message passing

We propose a new approach to outlier-insensitive Kalman smoothing based on normal priors with unknown variance (NUV). In contrast to prior work, the actual computations amount essentially to iterations of a standard Kalman smoother (with few extra computations). The proposed approach is easily extended to nonlinear estimation problems by combining the outlier detection with an extended Kalman smoother. For the Kalman smoothing, we consider both a Modified Bryson-Frasier smoother and the recently proposed Backward Information Filter Forward Marginal smoother, neither of which requires matrix inversions.